  Nonparametric kernel density estimation is a very natural procedure which
simply makes use of the smoothing power of the convolution operation. Yet, it
performs poorly when the density of a positive variable is to be estimated
(boundary issues, spurious bumps in the tail). So various extensions of the
basic kernel estimator allegedly suitable for $\mathbb{R}^+$-supported
densities, such as those using Gamma or other asymmetric kernels, abound in the
literature. Those, however, are not based on any valid smoothing operation
analogous to the convolution, which typically leads to inconsistencies. By
contrast, in this paper a kernel estimator for $\mathbb{R}^+$-supported
densities is defined by making use of the Mellin convolution, the natural
analogue of the usual convolution on $\mathbb{R}^+$. From there, a very
transparent theory flows and leads to new type of asymmetric kernels strongly
related to Meijer's $G$-functions. The numerous pleasant properties of this
`Mellin-Meijer-kernel density estimator' are demonstrated in the paper. Its
pointwise and $L_2$-consistency (with optimal rate of convergence) is
established for a large class of densities, including densities unbounded at 0
and showing power-law decay in their right tail. Its practical behaviour is
investigated further through simulations and some real data analyses.


  Searches for electromagnetic counterparts of gravitational-wave signals have
redoubled since the first detection in 2017 of a binary neutron star merger
with a gamma-ray burst, optical/infrared kilonova, and panchromatic afterglow.
Yet, one LIGO/Virgo observing run later, there has not yet been a second,
secure identification of an electromagnetic counterpart. This is not surprising
given that the localization uncertainties of events in LIGO and Virgo's third
observing run, O3, were much larger than predicted. We explain this by showing
that improvements in data analysis that now allow LIGO/Virgo to detect weaker
and hence more poorly localized events have increased the overall number of
detections, of which well-localized, gold-plated events make up a smaller
proportion overall. We present simulations of the next two LIGO/Virgo/KAGRA
observing runs, O4 and O5, that are grounded in the statistics of O3 public
alerts. To illustrate the significant impact that the updated predictions can
have, we study the follow-up strategy for the Zwicky Transient Facility.
Realistic and timely forecasting of gravitational-wave localization accuracy is
paramount given the large commitments of telescope time and the need to
prioritize which events are followed up. We include a data release of our
simulated localizations as a public proposal planning resource for astronomers.


  Ten years ago, Beresnevich-Dickinson-Velani initiated a project that develops
the general Hausdorff measure theory of dual approximation on non-degenerate
manifolds. In particular, they established the divergence part of the theory
based on their general ubiquity framework. However, the convergence counterpart
of the project remains wide open and represents a major challenging question in
the subject. Until recently, it was not even known for any single
non-degenerate manifold. In this paper, we settle this problem for all curves
in $\mathbb{R}^2$, which represents the first complete theory of its kind for a
general class of manifolds.


  The LENA (Low Energy Neutrino Astronomy) detector is proposed to be a
large-volume liquid-scintillator device which will be highly suitable for the
investigation of a variety of topics in astrophysics, geophysics and particle
physics. In this paper, the potential of such a detector concerning the search
for proton decay in the SUSY favored decay channel p->K+antineutrino is
investigated. Based on Geant4, Monte Carlo simulations of the proton decay in
the LENA detector as well as of the background radiation in the detection
energy windows have been developed. From these simulations an efficiency of 65%
for the detection of a possible proton decay has been determined. Within ten
years of measuring time a lower limit for the proton lifetime, concerning the
decay channel investigated, of tau>4.10^{34} y could be reached.


  Collective properties of complex systems composed of many interacting
components such as neurons in our brain can be modeled by artificial networks
based on disordered systems. We show that a disordered neural network of
superconducting loops with Josephson junctions can exhibit computational
properties like categorization and associative memory in the time evolution of
its state in response to information from external excitations. Superconducting
loops can trap multiples of fluxons in many discrete memory configurations
defined by the local free energy minima in the configuration space of all
possible states. A memory state can be updated by exciting the Josephson
junctions to allow the movement of fluxons through the network as the current
through them surpasses their critical current thresholds. Simulations performed
with a lumped element circuit model of a 4-loop network show that information
written through excitations is translated into stable states of trapped flux
and their time evolution. Experimental implementation on a high-Tc
superconductor YBCO-based 4-loop network shows dynamically stable flux flow in
each pathway characterized by the correlations between junction firing
statistics. Neural network behavior is observed as energy barriers separating
state categories in simulations in response to multiple excitations, and
experimentally as junction responses characterizing different flux flow
patterns in the network. The state categories that produce these patterns have
different temporal stabilities relative to each other and the excitations. This
provides strong evidence for time-dependent (short-to-long-term) memories, that
are dependent on the geometrical and junction parameters of the loops, as
described with a network model.


  The non-equilibrium boron nitride (BN) phase of zinc oxide (ZnO) has been
reported for thin films and nanostructures, however, its properties are not
well understood due to a persistent controversy that prevents reconciling
experimental and first-principles results for its atomic coordinates. We use
first-principles theoretical spectroscopy to accurately compute electronic and
optical properties, including single-quasiparticle and excitonic effects: Band
structures and densities of states are computed using density functional
theory, hybrid functionals, and the $GW$ approximation. Accurate optical
absorption spectra and exciton binding energies are computed by solving the
Bethe-Salpeter equation for the optical polarization function. Using this data
we show that the band-gap difference between BN-ZnO and wurtzite (WZ) ZnO
agrees very well with experiment when the theoretical lattice geometry is used,
but significantly disagrees for the experimental atomic coordinates. We also
show that the optical anisotropy of BN-ZnO differs significantly from that of
WZ-ZnO, allowing to optically distinguish both polymorphs. By using the
transfer-matrix method to solve Maxwell's equations for thin films composed of
both polymorphs, we illustrate that this opens up a promising route for tuning
optical properties.


  Let $X$ be a stationary process with values in some $\sigma$-finite measured
state space $(E,\mathcal{E},\pi)$, indexed by ${\mathbb Z}$. Call ${\mathcal
F}^X$ its natural filtration. In \cite{ceillierstationary}, sufficient
conditions were given for ${\mathcal F}^X$ to be standard when $E$ is finite.
The proof of this result used a coupling of all probabilities on the finite set
$E$.
  In this paper, we construct a coupling of all laws having a density with
regard to $\pi$, which is much more involved. Then, we provide sufficient
conditions for ${\mathcal F}^X$ to be standard, generalizing those in
\cite{ceillierstationary}.


  We give a short proof that every contracting self-similar group embeds into a
finitely presented simple group. In particular, any contracting self-similar
group embeds into the corresponding R\"over--Nekrashevych group, and this in
turn embeds into one of the twisted Brin--Thompson groups introduced by the
first author and Matthew Zaremsky. The proof here is a simplification of a more
general argument given by the authors, Collin Bleak, and Matthew Zaremsky for
contracting rational similarity groups.


  Broadband dual-comb spectroscopy has attracted increasing interests due to
its unique advantages in high spectral resolution, fast detection, and so on.
Although the dual-comb technique is relatively mature in the infrared
wavelengths, it is, currently, not commercially capable of practical
applications in the terahertz regime due to the lack of high performance
broadband terahertz dual-comb sources. In the terahertz frequency range, the
electrically pumped quantum cascade laser (QCL) is a suitable candidate for the
dual-comb operation. However, free running terahertz QCL dual-comb sources
normally show limited optical bandwidths ($\sim$100-200 GHz). Although the
resonant microwave injection locking has been widely used to broaden the
emission spectra of terahertz QCLs by modulating the laser drive current at the
cavity round-trip frequency, it is hard to be employed to broaden the dual-comb
bandwidths due to the large phase noise induced by the resonant injection and
non-ideal microwave circuits. Therefore, it is challenging to obtain broadband
terahertz dual-comb sources that can fully exploits the laser gain bandwidth.
Here, we employ an off-resonant microwave injection to significantly broaden
the dual-comb bandwidth of a terahertz QCL dual-comb source emitting around 4.2
THz. The measured optical dual-comb bandwidth is broadened from 147 GHz in free
running to $>$450 GHz under the off-resonant injection. The broadened dual-comb
bandwidth is experimentally proved by the transmission measurements of a filter
and a GaAs etalon. By performing a simple numerical analysis based on a rate
equation model, we explain that the broadband dual-comb operation under the
off-resonant microwave injection could be resulted from a wider lasing
bandwidth and a higher degree of phase matching.


  We study the finite generation of the intersection algebra of two principal
ideals I and J in a unique factorization domain R. We provide an algorithm that
produces a list of generators of this algebra over R. In the special case that
R is a polynomial ring, this algorithm has been implemented in the commutative
algebra software system Macaulay2. A new class of algebras, called fan
algebras, is introduced.


  Conformal prediction is a distribution-free method that wraps a given machine
learning model and returns a set of plausible labels that contain the true
label with a prescribed coverage rate. In practice, the empirical coverage
achieved highly relies on fully observed label information from data both in
the training phase for model fitting and the calibration phase for quantile
estimation. This dependency poses a challenge in the context of online learning
with bandit feedback, where a learner only has access to the correctness of
actions (i.e., pulled an arm) but not the full information of the true label.
In particular, when the pulled arm is incorrect, the learner only knows that
the pulled one is not the true class label, but does not know which label is
true. Additionally, bandit feedback further results in a smaller labeled
dataset for calibration, limited to instances with correct actions, thereby
affecting the accuracy of quantile estimation. To address these limitations, we
propose Bandit Class-specific Conformal Prediction (BCCP), offering coverage
guarantees on a class-specific granularity. Using an unbiased estimation of an
estimand involving the true label, BCCP trains the model and makes set-valued
inferences through stochastic gradient descent. Our approach overcomes the
challenges of sparsely labeled data in each iteration and generalizes the
reliability and applicability of conformal prediction to online decision-making
environments.


  We investigate the properties of persistent charge current driven by magnetic
flux in a quasi-periodic mesoscopic Fibonacci ring with Rashba and Dresselhaus
spin-orbit interactions. Within a tight-binding framework we work out
individual state currents together with net current based on second-quantized
approach. A significant enhancement of current is observed in presence of
spin-orbit coupling and sometimes it becomes orders of magnitude higher
compared to the spin-orbit interaction free Fibonacci ring. We also establish a
scaling relation of persistent current with ring size, associated with the
Fibonacci generation, from which one can directly estimate current for any
arbitrary flux, even in presence of spin-orbit interaction, without doing
numerical simulation. The present analysis indeed gives a unique opportunity of
determining persistent current and has not been discussed so far.


  The statistical coalescence model for the production of open and hidden charm
is considered within the canonical ensemble formulation. The data for the J/psi
multiplicity in Pb+Pb collisions at 158 A GeV are used for the model prediction
of the open charm yield which has not yet been measured in these reactions.


  Turing's theory of pattern formation has been used to describe the formation
of self-organised periodic patterns in many biological, chemical and physical
systems. However, the use of such models is hindered by our inability to
predict, in general, which pattern is obtained from a given set of model
parameters. While much is known near the onset of the spatial instability, the
mechanisms underlying pattern selection and dynamics away from onset are much
less understood. Here, we provide new physical insight into the dynamics of
these systems. We find that peaks in a Turing pattern behave as point sinks,
the dynamics of which are determined by the diffusive fluxes into them. As a
result, peaks move towards a periodic steady-state configuration that minimizes
the mass of the diffusive species. We also show that the preferred number of
peaks at the final steady-state is such that this mass is minimised. Our work
presents mass minimization as a simple, generalisable, physical principle for
understanding pattern formation in reaction diffusion systems far from onset.


  We consider the problem of screening of an electrically charged impurity in a
clean graphene sheet. When electron-electron interactions are neglected, the
screening charge has a sign opposite to that of the impurity, and is localized
near the impurity. Interactions between electrons smear out the induced charge
density to give a large-distance tail that follows approximately, but not
exactly, an r^{-2} behavior and with a sign which is the same as that of the
impurity.


  Radiologists use time series of medical images to monitor the progression of
a patient condition. They compare information gleaned from sequences of images
to gain insight on progression or remission of the lesions, thus evaluating the
progress of a patient condition or response to therapy. Visual methods of
determining differences between one series of images to another can be
subjective or fail to detect very small differences. We propose the use of
quantization errors obtained from Self Organizing Maps for image content
analysis. We tested this technique with MRI images to which we progressively
added synthetic lesions. We have used a global approach that considers changes
on the entire image as opposed to changes in segmented lesion regions only. We
claim that this approach does not suffer from the limitations imposed by
segmentation, which may compromise the results. Results show quantization
errors increased with the increase in lesions on the images. The results are
also consistent with previous studies using alternative approaches. We then
compared the detectability ability of our method to that of human novice
observers having to detect very small local differences in random-dot images.
The quantization errors of the SOM outputs compared with correct positive
rates, after subtraction of false positive rates (guess rates), increased
noticeably and consistently with small increases in local dot size that were
not detectable by humans. We conclude that our method detects very small
changes in complex images and suggest that it could be implemented to assist
human operators in image based decision making.


  An emerging internet based super computing model is represented by cloud
computing. Cloud computing is the convergence and evolution of several concepts
from virtualization, distributed storage, grid, and automation management to
enable a more flexible approach for deploying and scaling applications.
However, cloud computing moves the application software and databases to the
large data centers, where the management of the data and services may not be
fully trustworthy. The concept of cloud computing on the basis of the various
definitions available in the industry and the characteristics of cloud
computing are being analyzed in this paper. The paper also describes the main
cloud service providers and their products followed by primary cloud computing
operating systems.


  We provide a new characterization of homogeneous Besov and Sobolev spaces in
Carnot groups using the fractional heat kernel and Poisson kernel. We apply our
results to study commutators involving fractional powers of the sub-Laplacian.


  Any subset of the plane can be approximated by a set of square pixels. This
transition from a shape to its pixelation is rather brutal since it destroys
geometric and topological information about the shape. Using a technique
inspired by Morse Theory, we algorithmically produce a PL approximation of the
original shape using only information from its pixelation. This approximation
converges to the original shape in a very strong sense: as the size of the
pixels goes to zero we can recover important geometric and topological
invariants of the original shape such as Betti numbers, area, perimeter and
curvature measures.


  A generalization of the Euler-Plateau problem to account for the energy
contribution due to twisting of the bounding loop is proposed. Euler-Lagrange
equations are derived in a parameterized setting and a bifurcation analysis is
performed. A pair of dimensionless parameters govern bifurcations from a flat,
circular ground state. While one of these is familiar from the Euler-Plateau
problem, the other encompasses information about the ratio of the twisting to
bending rigidities, twist, and size of the loop. For sufficiently small values
of the latter parameter, two separate groups of bifurcation modes are
identified. On the other hand, for values greater than the critical twist
arising in Michell's problem of the bifurcation of a twisted annular ring, only
one bifurcation mode exists. Bifurcation diagrams indicate that a loop with
greater twisting rigidity shows more resistance to transverse buckling.
However, a twisted and closed filament spanned by a surface endowed with
uniform surface tension buckles at a twist less than the critical value for an
elastic ring.


  Recently it was shown that essentially all regular black hole models
constructed so far can be obtained as solutions of vacuum gravity equations,
upon considering an infinite series of quasi-topological higher curvature
corrections. Here we show that such a construction can be upgraded to yield
regular black holes with vanishing inner horizon surface gravity. In four
dimensions, such a condition is necessary for the absence of classical
instabilities associated with mass inflation on the inner horizon.


  We develop a proper nonempirical spin-density formalism for the van der Waals
density functional (vdW-DF) method. We show that this generalization, termed
svdW-DF, is firmly rooted in the single-particle nature of exchange and we test
it on a range of spin systems. We investigate in detail the role of spin in the
nonlocal-correlation driven adsorption of H$_2$ and CO$_2$ in the linear
magnets Mn-MOF74, Fe-MOF74, Co-MOF74, and Ni-MOF74. In all cases, we find that
spin plays a significant role during the adsorption process despite the general
weakness of the molecular-magnetic responses. The case of CO$_2$ adsorption in
Ni-MOF74 is particularly interesting, as the inclusion of spin effects results
in an increased attraction, opposite to what the diamagnetic nature of CO$_2$
would suggest. We explain this counter-intuitive result, tracking the behavior
to a coincidental hybridization of the O $p$ states with the Ni $d$ states in
the down-spin channel. More generally, by providing insight on nonlocal
correlation in concert with spin effects, our nonempirical svdW-DF method opens
the door for a deeper understanding of weak nonlocal magnetic interactions.


  We study the local structure of the representation variety of a knot group
into SL(n,C) at certain diagonal representations. In particular we determine
the tangent cone of the representation variety at these diagonal
representations, and show that the latter can be deformed into irreducible
representations. Furthermore, we use Luna's slice theorem to analyze the local
structure of the character variety.


  Let $F$ be a nilpotent group acted on by a group $H$ via automorphisms and
let the group $G$ admit the semidirect product $FH$ as a group of automorphisms
so that $C_G(F) = 1$. We prove that the order of $\gamma_\infty(G)$, the rank
of $\gamma_\infty(G)$ are bounded in terms of the orders of
$\gamma_{\infty}(C_G(H))$ and $H$, the rank of $\gamma_{\infty}(C_G(H))$ and
the order of $H$, respectively in cases where either $FH$ is a Frobenius group;
$FH$ is a Frobenius-like group satisfying some certain conditions; or
$FH=\langle \alpha,\beta\rangle$ is a dihedral group generated by the
involutions $\alpha$ and $\beta$ with $F =\langle \alpha\beta\rangle$ and $H
=\langle\alpha \rangle$.


  When children learn new words, they employ constraints such as the mutual
exclusivity (ME) bias: a novel word is mapped to a novel object rather than a
familiar one. This bias has been studied computationally, but only in models
that use discrete word representations as input, ignoring the high variability
of spoken words. We investigate the ME bias in the context of visually grounded
speech models that learn from natural images and continuous speech audio.
Concretely, we train a model on familiar words and test its ME bias by asking
it to select between a novel and a familiar object when queried with a novel
word. To simulate prior acoustic and visual knowledge, we experiment with
several initialisation strategies using pretrained speech and vision networks.
Our findings reveal the ME bias across the different initialisation approaches,
with a stronger bias in models with more prior (in particular, visual)
knowledge. Additional tests confirm the robustness of our results, even when
different loss functions are considered.


  We argue that the theory of a massive higher spin field coupled to
electromagnetism in flat space possesses an intrinsic, model independent,
finite upper bound on its UV cutoff. By employing the Stueckelberg formalism we
do a systematic study to quantify the degree of singularity of the massless
limit in the cases of spin 2, 3, 3/2, and 5/2. We then generalize the results
for arbitrary spin to find an expression for the maximum cutoff of the theory
as a function of the particle's mass, spin, and electric charge. We also
briefly explain the physical implications of the result and discuss how it
could be sharpened by use of causality constraints.


  Kim and Fedele discovered experimental evidence for the breakdown of the
Millikan's Law for the fall rate of oil droplets in Nitrogen gas and the
discrepancy is most pronounced for the smallest, sub-micron size particles.
Here we explain these results by showing that the particle's motion is
determined in part by the bare shear viscosity which is defined by the
averaging length lambda. This is in contrast to the usual theory which involves
the renormalized shear viscosity. An increase in gas pressure produces a
decrease in the bare shear viscosity and as a result the fall rate increases.
This behavior is opposite the Millikan Law prediction that an increase in
pressure produces a decrease in fall rate. As a result, the bare shear
viscosity is experimentally measurable by the fallrate. The theory here uses a
convective diffusion equation and a Langevin approach will be presented
elsewhere.


  Three major planets, Venus, Earth, and Mercury formed out of the solar
nebula. A fourth planetesimal, Theia, also formed near Earth where it collided
in a giant impact, rebounding as the planet Mars. During this impact Earth lost
${\approx}4$\% of its crust and mantle that is now is found on Mars and the
Moon. At the antipode of the giant impact, $\approx$60\% of Earth's crust,
atmosphere, and a large amount of mantle were ejected into space forming the
Moon. The lost crust never reformed and became the Earth's ocean basins. The
Theia impact site corresponds to Indian Ocean gravitational anomaly on Earth
and the Hellas basin on Mars. The dynamics of the giant impact are consistent
with the rotational rates and axial tilts of both Earth and Mars. The giant
impact removed sufficient CO$_2$ from Earth's atmosphere to avoid a runaway
greenhouse effect, initiated plate tectonics, and gave life time to form near
geothermal vents at the continental margins. Mercury formed near Venus where on
a close approach it was slingshot into the Sun's convective zone losing 94\% of
its mass, much of which remains there today. Black carbon, from CO$_2$
decomposed by the intense heat, is still found on the surface of Mercury.
Arriving at 616 km/s, Mercury dramatically altered the Sun's rotational energy,
explaining both its anomalously slow rotation rate and axial tilt. These
results are quantitatively supported by mass balances, the current locations of
the terrestrial planets, and the orientations of their major orbital axes.


  We present an analysis designed to search for Lorentz and CPT violations as
predicted by the SME framework using the charged current neutrino events in the
MINOS near detector. In particular we develop methods to identify periodic
variations in the normalized number of charged current neutrino events as a
function of sidereal phase. To test these methods, we simulated a set of 1,000
experiments without Lorentz and CPT violation signals using the standard MINOS
Monte Carlo. We performed an FFT on each of the simulated experiments to find
the distribution of powers in the sidereal phase diagram without a signal. We
then injected a signal of increasing strength into the sidereal neutrino
oscillation probability until we found a 5$\sigma$ deviation from the mean in
the FFT power spectrum. By this method, we can establish upper limits for the
Lorentz and CPT violating terms in the SME.


  Manifold calculus of functors, due to M. Weiss, studies contravariant
functors from the poset of open subsets of a smooth manifold to topological
spaces. We introduce "multivariable" manifold calculus of functors which is a
generalization of this theory to functors whose domain is a product of
categories of open sets. We construct multivariable Taylor approximations to
such functors, classify multivariable homogeneous functors, apply this
classification to compute the derivatives of a functor, and show what this
gives for the space of link maps. We also relate Taylor approximations in
single variable calculus to our multivariable ones.


  The aftermath of supernova (SN) 1987A continues to provide spectacular
insights into the interaction between a SN blastwave and its circumstellar en-
vironment. We here present 36 GHz observations from the Australia Telescope
Compact Array of the radio remnant of SN 1987A. These new images, taken in 2008
Apr and 2008 Oct, substantially extend the frequency range of an ongo- ing
monitoring and imaging program conducted between 1.4 and 20 GHz. Our 36.2 GHz
images have a diffraction-limited angular resolution of 0.3-0.4 arcseconds,
which covers the gap between high resolution, low dynamic range VLBI images of
the remnant and low resolution, high dynamic range images at frequencies
between 1 and 20 GHz. The radio morphology of the remnant at 36 GHz is an
elliptical ring with enhanced emission on the eastern and western sides,
similar to that seen previously at lower frequencies. Model fits to the data in
the Fourier domain show that the emitting region is consistent with a thick
inclined torus of mean radius 0.85 arcsec, and a 2008 Oct flux density of 27
+/- 6 mJy at 36.2 GHz. The spectral index for the remnant at this epoch,
determined between 1.4 GHz and 36.2 GHz, is -0.83. There is tentative evidence
for an unresolved central source with flatter spectral index.


  Thanks to the execution of extensive spectroscopic surveys that have covered
large fractions of the sky down to magnitudes as faint as $i \approx 19$, it
has been possible to identify several narrow-line Seyfert 1 galaxies (NLS1s)
and to investigate their properties over a large range of the electro-magnetic
spectrum. The interpretation of their nature, however, is still hampered by the
statistical uncertainties related to the way in which NLS1 candidates are
selected. In this contribution, we present a study to detect and to model
emission lines in optical spectra extracted from the Sloan Digital Sky Survey
(SDSS), adopting the most proper strategy to identify the source of line
excitation and to produce a detailed model with measurements of several
emission-line parameters. We demonstrate the application of this technique to
explore fundamental questions, such as the presence of gas and dust around the
core of AGNs and the spectral energy distribution of their ionizing radiation.
We compare the spectral properties of NLS1s with those of other type 1 active
galaxies and we summarize the potential of this approach to identify NLS1s in
present day and future spectroscopic surveys. We finally consider the
implications of multi-frequency data analysis in the debate concerning the
intrinsic nature of NLS1s.


  We combine generative adversarial network (GAN) with light microscopy to
achieve deep learning super-resolution under a large field of view (FOV). By
appropriately adopting prior microscopy data in an adversarial training, the
neural network can recover a high-resolution, accurate image of new specimen
from its single low-resolution measurement. Its capacity has been broadly
demonstrated via imaging various types of samples, such as USAF resolution
target, human pathological slides, fluorescence-labelled fibroblast cells, and
deep tissues in transgenic mouse brain, by both wide-field and light-sheet
microscopes. The gigapixel, multi-color reconstruction of these samples
verifies a successful GAN-based single image super-resolution procedure. We
also propose an image degrading model to generate low resolution images for
training, making our approach free from the complex image registration during
training dataset preparation. After a welltrained network being created, this
deep learning-based imaging approach is capable of recovering a large FOV (~95
mm2), high-resolution (~1.7 {\mu}m) image at high speed (within 1 second),
while not necessarily introducing any changes to the setup of existing
microscopes.


  Estimating the relative alignment between the frontier molecular orbitals
that dominates the charge transport through single-molecule junctions
represents a challenge for theory. This requires approaches beyond the widely
employed framework provided by the density functional theory, wherein the
Kohn-Sham "orbitals" are treated as if they were real molecular orbitals, which
is not the case. In this paper, we report results obtained by means of quantum
chemical calculations, including the EOM-CCSD (equation-of-motion
coupled-cluster singles and doubles), which is the state-of-the-art of quantum
chemistry for medium-size molecules like those considered here. These
theoretical results are validated against data on the molecular orbital energy
offset relative to the electrodes' Fermi energy extracted from experiments for
junctions based on 4,4'-bipyridine and 1,4-dicyanobenzene.


  Paper withdrawn.
  There is a gap in the proof of Proposition 4.3 (its conclusion ``d'o\`{u} la
proposition.'' is incorrect). Therefore theorems 1.1 and 3.1, which were the
main results of the paper, are not proved.


  We investigate experimentally and model the mechanical response of a soft
Hookean ribbon submitted to large twist $\eta$ and longitudinal tension $T$,
under clamped boundary conditions. We derive a formula for the torque $M$ using
the \FvK equations up to third order in twist, incorporating a twist-tension
coupling. In the stable helicoid regime, quantitative agreement with
experimental data is obtained. When twisted above a critical twist $\eta_L(T)$,
ribbons develop wrinkles and folds which modify qualitatively the mechanical
behavior. We show a surprisingly large longitudinal contraction upon twist,
reminiscent of a Poynting effect, and a much lower torsional stiffness. Far
from threshold, we identify two regimes depending on the applied $T$. In a
high-$T$ regime, we find that the torque scales as $\eta\cdot T$ and the
contraction as $\eta^2$, in agreement with a far from threshold analysis where
compression and bending stresses are neglected. In a low-$T$ regime, the
contraction still scales as $\eta^2$ but the torque appears $T$-independent and
linear with $\eta$. We argue that the large curvature of the folds now
contribute significantly to the torque. This regime is discussed in the context
of asymptotic isometry for very thin plates submitted to vanishing tension but
large change of shape, as in crumpling.


  We used Herschel Hi-GAL survey data to determine whether massive young
stellar objects (MYSOs) are resolved at 70$\mu$m and to study their envelope
density distribution. Our analysis of three relatively isolated sources in the
l=30{\deg} and l=59{\deg} Galactic fields show that the objects are partially
resolved at 70$\mu$m. The Herschel Hi-GAL survey data have a high scan velocity
which makes unresolved and partially resolved sources appear elongated in the
70$\mu$m images. We analysed the two scan directions separately and examine the
intensity profile perpendicular to the scan direction. Spherically symmetric
radiative transfer models with a power law density distribution were used to
study the circumstellar matter distribution. Single dish sub-mm data were also
included to study how different spatial information affects the fitted density
distribution. The density distribution which best fits both the 70$\mu$m
intensity profile and SED has an average index of ~0.5. This index is shallower
than expected and is probably due to the dust emission from bipolar outflow
cavity walls not accounted for in the spherical models. We conclude that 2D
axisymmetric models and Herschel images at low scan speeds are needed to better
constrain the matter distribution around MYSOs.


  Quantum key distribution (QKD) is a cryptographic system that generates an
information-theoretically secure key shared by two legitimate parties. QKD
consists of two parts: quantum and classical. The latter is referred to as
classical post-processing (CPP). Information reconciliation is a part of CPP in
which parties are given correlated variables and attempt to eliminate the
discrepancies between them while disclosing a minimum amount of information.
The elegant reconciliation protocol known as \emph{Cascade} was developed
specifically for QKD in 1992 and has become the de-facto standard for all QKD
implementations. However, the protocol is highly interactive. Thus, other
protocols based on linear block codes such as Hamming codes, low-density
parity-check (LDPC) codes, and polar codes have been researched. In particular,
reconciliation using LDPC codes has been mainly studied because of its
outstanding performance. Nevertheless, with small block size, the bit error
rate performance of polar codes under successive-cancellation list (SCL)
decoding with a cyclic redundancy check (CRC) is comparable to state-of-the-art
turbo and LDPC codes. In this study, we demonstrate the use of polar codes to
improve the performance of information reconciliation in a QKD system with
small block size. The best decoder for polar codes, a CRC-aided SCL decoder,
requires CRC-precoded messages. However, messages that are sifted keys in QKD
are obtained arbitrarily as a result of a characteristic of the QKD protocol
and cannot be CRC-precoded. We propose a method that allows arbitrarily
obtained sifted keys to be CRC precoded by introducing a virtual string. Thus
the best decoder can be used for reconciliation using polar codes and improves
the efficiency of the protocol.


  In many cyber-physical systems, imaging can be an important but expensive or
'difficult to deploy' sensing modality. One such example is detecting
combustion instability using flame images, where deep learning frameworks have
demonstrated state-of-the-art performance. The proposed frameworks are also
shown to be quite trustworthy such that domain experts can have sufficient
confidence to use these models in real systems to prevent unwanted incidents.
However, flame imaging is not a common sensing modality in engine combustors
today. Therefore, the current roadblock exists on the hardware side regarding
the acquisition and processing of high-volume flame images. On the other hand,
the acoustic pressure time series is a more feasible modality for data
collection in real combustors. To utilize acoustic time series as a sensing
modality, we propose a novel cross-modal encoder-decoder architecture that can
reconstruct cross-modal visual features from acoustic pressure time series in
combustion systems. With the "distillation" of cross-modal features, the
results demonstrate that the detection accuracy can be enhanced using the
virtual visual sensing modality. By providing the benefit of cross-modal
reconstruction, our framework can prove to be useful in different domains well
beyond the power generation and transportation industries.


  In this paper, we propose generating synthetic multiple sclerosis (MS)
lesions on MRI images with the final aim to improve the performance of
supervised machine learning algorithms, therefore avoiding the problem of the
lack of available ground truth. We propose a two-input two-output fully
convolutional neural network model for MS lesion synthesis in MRI images. The
lesion information is encoded as discrete binary intensity level masks passed
to the model and stacked with the input images. The model is trained end-to-end
without the need for manually annotating the lesions in the training set. We
then perform the generation of synthetic lesions on healthy images via
registration of patient images, which are subsequently used for data
augmentation to increase the performance for supervised MS lesion detection
algorithms. Our pipeline is evaluated on MS patient data from an in-house
clinical dataset and the public ISBI2015 challenge dataset. The evaluation is
based on measuring the similarities between the real and the synthetic images
as well as in terms of lesion detection performance by segmenting both the
original and synthetic images individually using a state-of-the-art
segmentation framework. We also demonstrate the usage of synthetic MS lesions
generated on healthy images as data augmentation. We analyze a scenario of
limited training data (one-image training) to demonstrate the effect of the
data augmentation on both datasets. Our results significantly show the
effectiveness of the usage of synthetic MS lesion images. For the ISBI2015
challenge, our one-image model trained using only a single image plus the
synthetic data augmentation strategy showed a performance similar to that of
other CNN methods that were fully trained using the entire training set,
yielding a comparable human expert rater performance


  Strong correlations lead to emergent excitations at low energies. When
combined with symmetry constraints, they may produce topological electronic
states near the Fermi energy. Within this general framework, here we address
the topological features in iron-based superconductors. We examine the effects
of orbital-selective correlations on the band inversion in the iron
chalcogenide FeSe$_{x}$Te$_{1-x}$ near its doping of optimal superconductivity,
within a multiorbital model and using a $U(1)$ slave spin theory. The orbital
selectivity of the quasiparticle spectral weight, along with its counterpart of
the energy level renormalization, leads to a band inversion and Dirac node
formation pinned to the immediate vicinity of the Fermi energy. Our work
demonstrates both the naturalness and robustness of the topological properties
in FeSe$_{x}$Te$_{1-x}$, and uncovers a new setting in which strong
correlations and space-group symmetry cooperate in generating strongly
correlated electronic topology.


  We explore a novel application of zero-dimensional persistent homology from
Topological Data Analysis (TDA) for bracketing zero-crossings of both
one-dimensional continuous functions, and uniformly sampled time series. We
present an algorithm and show its robustness in the presence of noise for a
range of sampling frequencies. In comparison to state-of-the-art software-based
methods for finding zeros of a time series, our method generally converges
faster, provides higher accuracy, and is capable of finding all the roots in a
given interval instead of converging only to one of them. We also present and
compare options for automatically setting the persistence threshold parameter
that influences the accurate bracketing of the roots.


  Let $f:\Z/q\Z\rightarrow\Z$ be such that $f(a)=\pm 1$ for $1\le a<q$, and
$f(q)=0$. Then Erd\"os conjectured that $\sum_{n\ge1}\frac{f(n)}{n} \ne 0$. For
$q$ even, this is trivially true. If $q\equiv 3$ ( mod $4$), Murty and Saradha
proved the conjecture. We show that this conjecture is true for $82\%$ of the
remaining integers $q\equiv 1$ ( mod $4$).


  Theoretical and phenomenological aspects of high energy heavy ion collisions
are reviewed. Main emphasis is on ideas related to Color Glass Condensate (CGC)
physics.


  The evolution of quantum networking requires architectures capable of
dynamically reconfigurable entanglement distribution to meet diverse user needs
and ensure tolerance against transmission disruptions. We introduce multihop
quantum networks to improve network reach and resilience by enabling quantum
communications across intermediate nodes, thus broadening network connectivity
and increasing scalability. We present multihop two-qubit
polarization-entanglement distribution within a quantum network at the Oak
Ridge National Laboratory campus. Our system uses wavelength-selective switches
for adaptive bandwidth management on a software-defined quantum network that
integrates a quantum data plane with classical data and control planes,
creating a flexible, reconfigurable mesh. Our network distributes entanglement
across six nodes within three subnetworks, each located in a separate building,
optimizing quantum state fidelity and transmission rate through adaptive
resource management. Additionally, we demonstrate the network's resilience by
implementing a link recovery approach that monitors and reroutes quantum
resources to maintain service continuity despite link failures -- paving the
way for scalable and reliable quantum networking infrastructures.


  ChatGPT's proficiency in handling modern standard languages suggests
potential for its use in understanding ancient Chinese. This paper explores
ChatGPT's capabilities on ancient Chinese via two tasks: translating ancient
Chinese to modern Chinese and recognizing ancient Chinese names. A comparison
of ChatGPT's output with human translations serves to evaluate its
comprehension of ancient Chinese. The findings indicate that: (1.)the
proficiency of ancient Chinese by ChatGPT is yet to reach a satisfactory level;
(2.) ChatGPT performs the best on ancient-to-modern translation when feeding
with three context sentences. To help reproduce our work, we display the python
code snippets used in this study.


  Test beam data reconstruction is a task that requires a large amount of
flexibility due to the heterogeneous data acquisition environments found in
these experiments. Often, detectors with different readout schemes such as
triggered, frame-based or data driven approaches are combined in a single
setup. In order to correlate these data and to reconstruct particle tracks, a
versatile event building algorithm and analysis framework is required.
Corryvreckan is a flexible, fast and lightweight test beam data reconstruction
framework based on a modular concept of the reconstruction chain. It is written
in modern C++ , requires a minimum of external dependencies and is designed to
be fully configurable by the user without the need to alter code. This document
presents the user manual of the software as of release version 1.0.


  The topology of a power grid affects its dynamic operation and settlement in
the electricity market. Real-time topology identification can enable faster
control action following an emergency scenario like failure of a line. This
article discusses a graphical model framework for topology estimation in bulk
power grids (both loopy transmission and radial distribution) using
measurements of voltage collected from the grid nodes. The graphical model for
the probability distribution of nodal voltages in linear power flow models is
shown to include additional edges along with the operational edges in the true
grid. Our proposed estimation algorithms first learn the graphical model and
subsequently extract the operational edges using either thresholding or a
neighborhood counting scheme. For grid topologies containing no three-node
cycles (two buses do not share a common neighbor), we prove that an exact
extraction of the operational topology is theoretically guaranteed. This
includes a majority of distribution grids that have radial topologies. For
grids that include cycles of length three, we provide sufficient conditions
that ensure existence of algorithms for exact reconstruction. In particular,
for grids with constant impedance per unit length and uniform injection
covariances, this observation leads to conditions on geographical placement of
the buses. The performance of algorithms is demonstrated in test case
simulations.


  Despite the improved accuracy of deep neural networks, the discovery of
adversarial examples has raised serious safety concerns. In this paper, we
study two variants of pointwise robustness, the maximum safe radius problem,
which for a given input sample computes the minimum distance to an adversarial
example, and the feature robustness problem, which aims to quantify the
robustness of individual features to adversarial perturbations. We demonstrate
that, under the assumption of Lipschitz continuity, both problems can be
approximated using finite optimisation by discretising the input space, and the
approximation has provable guarantees, i.e., the error is bounded. We then show
that the resulting optimisation problems can be reduced to the solution of
two-player turn-based games, where the first player selects features and the
second perturbs the image within the feature. While the second player aims to
minimise the distance to an adversarial example, depending on the optimisation
objective the first player can be cooperative or competitive. We employ an
anytime approach to solve the games, in the sense of approximating the value of
a game by monotonically improving its upper and lower bounds. The Monte Carlo
tree search algorithm is applied to compute upper bounds for both games, and
the Admissible A* and the Alpha-Beta Pruning algorithms are, respectively, used
to compute lower bounds for the maximum safety radius and feature robustness
games. When working on the upper bound of the maximum safe radius problem, our
tool demonstrates competitive performance against existing adversarial example
crafting algorithms. Furthermore, we show how our framework can be deployed to
evaluate pointwise robustness of neural networks in safety-critical
applications such as traffic sign recognition in self-driving cars.


  In the present paper we survey the most recent classification results for
proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some
new results concerning geometric properties of proper biharmonic constant mean
curvature submanifolds in spheres.


  We present a method for intrusion detection which is based on the
Mach-Zehnder interference effect. This device provides monitored surveillance
by continuously measuring the intensity of light collected by a pair of
photodetectors. We find that our protocol allows for the detection of intrusion
attempts which employ path- redirection and/or intercept-resend techniques.
Expectation values for the registered output flux are provided for normal and
interrupted operation.


  Sentence representations can capture a wide range of information that cannot
be captured by local features based on character or word N-grams. This paper
examines the usefulness of universal sentence representations for evaluating
the quality of machine translation. Although it is difficult to train sentence
representations using small-scale translation datasets with manual evaluation,
sentence representations trained from large-scale data in other tasks can
improve the automatic evaluation of machine translation. Experimental results
of the WMT-2016 dataset show that the proposed method achieves state-of-the-art
performance with sentence representation features only.


  The physical properties of molecular gas can be deduced from the analysis of
line intensity ratios, most commonly of the CO isotopomers 12CO and 13CO.
Barred galaxies, especially those with central starbursts, provide an excellent
laboratory to study the changing properties of the gas as it approaches the
center. Four galaxies (UGC2855, UGC2866, NGC7479 and NGC4123) are presented as
examples of the results that can be obtained. Special attention is given to the
case of (abnormally) high 12CO/13CO R_12/13 line ratios (exceeding 20), which
may indicate unusual gas properties. Qualitative scenarios for the structure of
the ISM explaining a range of values of R_12/13 are discussed.


  We present the properties of 8 star-forming regions, or 'clumps,' in 3
galaxies at z~1.3 from the WiggleZ Dark Energy Survey, which are resolved with
the OSIRIS integral field spectrograph. Within turbulent discs, \sigma~90 km/s,
clumps are measured with average sizes of 1.5 kpc and average Jeans masses of
4.2 x 10^9 \Msolar, in total accounting for 20-30 per cent of the stellar mass
of the discs. These findings lend observational support to models that predict
larger clumps will form as a result of higher disc velocity dispersions
driven-up by cosmological gas accretion. As a consequence of the changes in
global environment, it may be predicted that star-forming regions at high
redshift should not resemble star-forming regions locally. Yet despite the
increased sizes and dispersions, clumps and HII regions are found to follow
tight scaling relations over the range z=0-2 for size, velocity dispersion,
luminosity, and mass when comparing >2000 HII regions locally and 30 clumps at
z>1 (\sigma \propto r^{0.42+/-0.03}, L(H\alpha) \propto r^{2.72+/-0.04},
L(H\alpha) \propto \sigma^{4.18+/-0.21}, and L(H\alpha) \propto
M_{Jeans}^{1.24+/-0.05}). We discuss these results in the context of the
existing simulations of clump formation and evolution, with an emphasis on the
processes that drive-up the turbulent motions in the interstellar medium. Our
results indicate that while the turbulence of discs may have important
implications for the size and luminosity of regions which form within them, the
same processes govern their formation from high redshift to the current epoch.


  Understanding the atomistic mechanism in graphene growth is crucial for
controlling the number of layers or domain sizes to meet practical needs. In
this work, focusing on the growth of graphene by chemical vapor deposition on
copper substrates, the surface kinetics in the growth are systematically
investigated by first-principles calculations. The phase diagram, predicting
whether the growth mode is monolayer graphene or bilayer graphene under various
experimental conditions, is constructed based on classical nucleation theory.
Our phase diagram well illustrates the effect of high hydrogen pressure on
bilayer graphene growth and clarifies the mechanism of the most widely used
experimental growth approaches. The phase diagram can provide guidance and
predictions for experiments and inspires the study of other two-dimensional
materials with graphene-like growth mechanisms.


  Automatic abusive language detection is a difficult but important task for
online social media. Our research explores a two-step approach of performing
classification on abusive language and then classifying into specific types and
compares it with one-step approach of doing one multi-class classification for
detecting sexist and racist languages. With a public English Twitter corpus of
20 thousand tweets in the type of sexism and racism, our approach shows a
promising performance of 0.827 F-measure by using HybridCNN in one-step and
0.824 F-measure by using logistic regression in two-steps.


  We analyze a recently proposed temporal centrality measure applied to an
empirical network based on person-to-person contacts in an emergency department
of a busy urban hospital. We show that temporal centrality identifies a
distinct set of top-spreaders than centrality based on the time-aggregated
binarized contact matrix, so that taken together, the accuracy of capturing
top-spreaders improves significantly. However, with respect to predicting
epidemic outcome, the temporal measure does not necessarily outperform less
complex measures. Our results also show that other temporal markers such as
duration observed and the time of first appearance in the the network can be
used in a simple predictive model to generate predictions that capture the
trend of the observed data remarkably well.


  In this article we determine feasible parameter sets for (what could
potentially be) commutative association schemes with noncyclotomic eigenvalues
that are of smallest possible rank and order. A feasible parameter set for a
commutative association scheme corresponds to a standard integral table algebra
with integral multiplicities that satisfies all of the parameter restrictions
known to hold for association schemes. For each rank and involution type, we
generate an algebraic variety for which any suitable integral solution
corresponds to a standard integral table algebra with integral multiplicities,
and then try to find the smallest suitable solution. Our main results show the
eigenvalues of commutative association schemes of rank 4 and nonsymmetric
commutative association schemes of rank 5 will always be cyclotomic. In the
rank 5 cases these our conclusions rely on calculations done by computer for
Gr\"obner bases or for bases of rational vector spaces spanned by polynomials.
We give several examples of feasible parameter sets for small symmetric
association schemes of rank 5 that have noncyclotomic eigenvalues.


  We obtain an asymptotic formula for the number of integer $2\times 2$
matrices that have determinant $\Delta$ and whose absolute values of the
entries are at most $H$. The result holds uniformly for a large range of
$\Delta$ with respect to $H$.


  We completely classify the rational solutions of the Sasano system of type
$D5^{(1)}.$ The rational solutions are classified to four classes by the
B\"acklund transformation group.


  A new notion of controllability for quantum systems that takes advantage of
the linear superposition of quantum states is introduced. We call such notion
von Neumann controllabilty and it is shown that it is strictly weaker than the
usual notion of pure state and operator controlability. We provide a simple and
effective characterization of it by using tools from the theory of unitary
representations of Lie groups. In this sense we are able to approach the
problem of control of quantum states from a new perspective, that of the theory
of unitary representations of Lie groups. A few examples of physical interest
and the particular instances of compact and nilpotent dynamical Lie groups are
discussed.


  The discovery of therapeutic molecules is fundamentally a multi-objective
optimization problem. One formulation of the problem is to identify molecules
that simultaneously exhibit strong binding affinity for a target protein,
minimal off-target interactions, and suitable pharmacokinetic properties.
Inspired by prior work that uses active learning to accelerate the
identification of strong binders, we implement multi-objective Bayesian
optimization to reduce the computational cost of multi-property virtual
screening and apply it to the identification of ligands predicted to be
selective based on docking scores to on- and off-targets. We demonstrate the
superiority of Pareto optimization over scalarization across three case
studies. Further, we use the developed optimization tool to search a virtual
library of over 4M molecules for those predicted to be selective dual
inhibitors of EGFR and IGF1R, acquiring 100% of the molecules that form the
library's Pareto front after exploring only 8% of the library. This workflow
and associated open source software can reduce the screening burden of
molecular design projects and is complementary to research aiming to improve
the accuracy of binding predictions and other molecular properties.


  The first-order interaction correction to the irreducible polarization
function of pristine graphene is studied at arbitrary relation between momentum
and frequency. The results are used to calculate the dielectric function and
the dynamical conductivity of graphene beyond the standard random-phase
approximation. The computed static dielectric constant compares favorably with
recent experiments.


  We introduce a new arithmetic function $a(n)$ defined to be the number of
random multiplications by residues modulo $n$ before the running product is
congruent to 0 modulo $n$. We give several formulas for computing the values of
this function and analyze its asymptotic behavior. We find that it is closely
related to $P_1(n)$, the largest prime divisor of $n$. In particular, $a(n)$
and $P_1(n)$ have the same average order asymptotically. Furthermore, the
difference between the functions $a(n)$ and $P_1(n)$ is $o(1)$ as $n$ tends to
infinity on a set with density approximately $0.623$. On the other hand
however, we see that (except on a set of density zero) the difference between
$a(n)$ and $P_1(n)$ tends to infinity on the integers outside this set. Finally
we consider the asymptotic behaviour of the difference between these two
functions and find that $\sum_{n\leq x}\big( a(n)-P_1(n)\big) \sim
\left(1-\frac{\pi}{4}\right)\sum_{n\leq x} P_2(n)$, where $P_2(n)$ is the
second largest divisor of $n$.


  An optical imager that exploits off-center image rotation to encode both the
lateral and depth coordinates of point sources in a single snapshot can perform
3D localization and tracking of space debris. When actively illuminated,
unresolved space debris, which can be regarded as a swarm of point sources, can
scatter a fraction of laser irradiance back into the imaging sensor.
Determining the source locations and fluxes is a large-scale sparse 3D inverse
problem, for which we have developed efficient and effective algorithms based
on sparse recovery using non-convex optimization. Numerical simulations
illustrate the efficiency and stability of the algorithms.


  Tvarak efficiently implements system-level redundancy for direct-access (DAX)
NVM storage. Production storage systems complement device-level ECC (which
covers media errors) with system-checksums and cross-device parity. This
system-level redundancy enables detection of and recovery from data corruption
due to device firmware bugs (e.g., reading data from the wrong physical
location). Direct access to NVM penalizes software-only implementations of
system-level redundancy, forcing a choice between lack of data protection or
significant performance penalties. Offloading the update and verification of
system-level redundancy to Tvarak, a hardware controller co-located with the
last-level cache, enables efficient protection of data from such bugs in memory
controller and NVM DIMM firmware. Simulation-based evaluation with seven
data-intensive applications shows Tvarak's performance and energy efficiency.
For example, Tvarak reduces Redis set-only performance by only 3%, compared to
50% reduction for a state-of-the-art software-only approach.


  We investigate the effect of white-noise perturbations on chaotic
trajectories in open billiards. We focus on the temporal decay of the survival
probability for generic mixed-phase-space billiards. The survival probability
has a total of five different decay regimes that prevail for different
intermediate times. We combine new calculations and recent results on noise
perturbed Hamiltonian systems to characterize the origin of these regimes, and
to compute how the parameters scale with noise intensity and billiard openness.
Numerical simulations in the annular billiard support and illustrate our
results.


  Inflation Gravity Waves B-Modes polarization detection is the ultimate goal
of modern large angular scale cosmic microwave background (CMB) experiments
around the world. A big effort is undergoing with the deployment of many
ground-based, balloon-borne and satellite experiments using different methods
to separate this faint polarized component from the incoming radiation. One of
the largely used technique is the Stokes Polarimetry that uses a rotating
half-wave plate (HWP) and a linear polarizer to separate and modulate the
polarization components with low residual cross-polarization. This paper
describes the QUBIC Stokes Polarimeter highlighting its design features and its
performances. A common systematic with these devices is the generation of large
spurious signals synchronous with the rotation and proportional to the
emissivity of the optical elements. A key feature of the QUBIC Stokes
Polarimeter is to operate at cryogenic temperature in order to minimize this
unwanted component. Moving efficiently this large optical element at low
temperature constitutes a big engineering challenge in order to reduce friction
power dissipation. Big attention has been given during the designing phase to
minimize the differential thermal contractions between parts. The rotation is
driven by a stepper motor placed outside the cryostat to avoid thermal load
dissipation at cryogenic temperature. The tests and the results presented in
this work show that the QUBIC polarimeter can easily achieve a precision below
0.1{\deg} in positioning simply using the stepper motor precision and the
optical absolute encoder. The rotation induces only few mK of extra power load
on the second cryogenic stage (~ 8 K).


  We study spectra for a 2D electron in the lowest Landau level with randomly
distributed, repulsively correlated electric impurities. The lowest energy band
reflects an effective magnetic field downshifted by an integer multiple of the
impurity density. The downshift is precisely half that for the corresponding
electron density in the composite-fermion picture of the fractional quantum
Hall regime.


  It is known that in phase covariant quantum cloning the equatorial states on
the Bloch sphere can be cloned with a fidelity higher than the optimal bound
established for universal quantum cloning. We generalize this concept to
include other states on the Bloch sphere with a definite $z$ component of spin.
It is shown that once we know the $z$ component, we can always clone a state
with a fidelity higher than the universal value and that of equatorial states.
We also make a detailed study of the entanglement properties of the output
copies and show that the equatorial states are the only states which give rise
to separable density matrix for the outputs.


  We report the changes in dispersion relations of hypersonic acoustic phonons
in free-standing silicon membranes as thin as \sim 8 nm. We observe a reduction
of the phase and group velocities of the fundamental flexural mode by more than
one order of magnitude compared to bulk values. The modification of the
dispersion relation in nanostructures has important consequences for noise
control in nano and micro-electromechanical systems (MEMS/NEMS) as well as
opto-mechanical devices.


  Among the existing works on enhancing system performance via prescribed
performance functions (PPFs), the decay rates of PPFs need to be predetermined
by the designer, directly affecting the convergence time of the closed-loop
system. However, if only considering accelerating the system convergence by
selecting a big decay rate of the performance function, it may lead to the
severe consequence of closed-loop system failure when considering the prevalent
actuator saturation in practical scenarios. To address this issue, this work
proposes a control scheme that can flexibly self-adjust the convergence rates
of the performance functions (PFs), aiming to achieve faster steady-state
convergence while avoiding the risk of error violation beyond the PFs'
envelopes, which may arise from input saturation and improper decay rate
selection in traditional prescribed performance control (PPC) methods.
Specifically, a performance index function (PIF) is introduced as a reference
criterion, based on which the self-adjusting rates of the PFs are designed for
different cases, exhibiting the following appealing features: 1) It can
eliminate the need to prespecify the initial values of the PFs. In addition, it
can also accommodate arbitrary magnitudes of initial errors while avoiding
excessive initial control efforts. 2) Considering actuator saturation, this
method can not only reduce the decay rates of the PFs when necessary to avoid
violation of the PFs, but also increase the decay rates to accelerate system
convergence when there is remaining control capacity. Finally, several
numerical simulations are conducted to confirm the effectiveness and
superiority of the proposed method.


  We investigate a class of actions for lattice QCD with staggered quarks aimed
at reducing the flavour symmetry violations associated with using staggered
fermions. These actions replace the gauge field link fields in the quark action
with covariantly smeared fields. As such they are an extension of actions
considered by the MILC collaboration. We show that such actions systematically
reduce flavour symmetry violations in the weak coupling limit. Using the mass
splitting between Goldstone and non-Goldstone pions as a measure of flavour
symmetry violations we find that these actions have considerably less flavour
symmetry violations than the standard staggered action, and represent an
improvement on what can be achieved with the MILC action, on quenched
configurations with $\beta=5.7$.


  Our goal is to use formal methods to analyse normative documents written in
English, such as privacy policies and service-level agreements. This requires
the combination of a number of different elements, including information
extraction from natural language, formal languages for model representation,
and an interface for property specification and verification. We have worked on
a collection of components for this task: a natural language extraction tool, a
suitable formalism for representing such documents, an interface for building
models in this formalism, and methods for answering queries asked of a given
model. In this work, each of these concerns is brought together in a web-based
tool, providing a single interface for analysing normative texts in English.
Through the use of a running example, we describe each component and
demonstrate the workflow established by our tool.


  This paper deals with the existence of $N$ vortex patches located at the
vertex of a regular polygon with $N$ sides that rotate around the center of the
polygon at a constant angular velocity. That is done for Euler and
(SQG)$_\beta$ equations, with $\beta\in(0,1)$, but may be also extended to more
general models. The idea is the desingularization of the Thomsom polygon for
the $N$ point vortex system, that is, $N$ point vortices located at the vertex
of a regular polygon with $N$ sides. The proof is based on the study of the
contour dynamics equation combined with the application of the infinite
dimensional Implicit Function theorem and the well--chosen of the function
spaces.


  We present the average rest-frame spectrum of the final catalog of dusty
star-forming galaxies (DSFGs) selected from the South Pole Telescope SZ survey
(SPT-SZ) and measured with Band 3 of the Atacama Large Millimeter/submillimeter
Array (ALMA). This work builds on the previous average rest-frame spectrum,
given in Spilker et al. (2014) for the first 22 sources, and is comprised of a
total of 78 sources, normalized by their respective apparent dust masses. The
spectrum spans $1.9$$<$z$<$$6.9$ and covers rest-frame frequencies of 240$-$800
GHz. Combining this data with low-J CO observations from the Australia
Telescope Compact Array (ATCA), we detect multiple bright line features from
$^{12}$CO, $[$CI$]$, and H$_2$O, as well as fainter molecular transitions from
$^{13}$CO, HCN, HCO$^+$, HNC, CN, H$_2$O$^+$, and CH. We use these detections,
along with limits from other molecules, to characterize the typical properties
of the interstellar medium (ISM) for these high redshift DSFGs. We are able to
divide the large sample into subsets in order to explore how the average
spectrum changes with various galaxy properties, such as effective dust
temperature. We find that systems with hotter dust temperatures exhibit
differences in the bright $^{12}$CO emission lines, and contain either warmer
and more excited dense gas tracers, or larger dense gas reservoirs. These
observations will serve as a reference point to studies of the ISM in distant
luminous DSFGs (L$_{\mathrm{IR}}$$>$$10^{12}$L$_\odot$), and will inform
studies of chemical evolution before the peak epoch of star formation at
$z=2-3$.


  We prove that the finite condensation rank (FC-rank) of the lexicographic
ordering of a context-free language is strictly less than $\omega^\omega$.


  In this paper we present an influence of discontinuous coupling on the
dynamics of multistable systems. Our model consists of two periodically forced
oscillators that can interact via soft impacts. The controlling parameters are
the distance between the oscillators and the difference in the phase of the
harmonic excitation. When the distance is large two systems do not collide and
a number of different possible solutions can be observed in both of them. When
decreasing of the distance, one can observe some transient impacts and then the
systems settle down on non-impacting attractor. It is shown that with the
properly chosen distance and difference in the phase of the harmonic
excitation, the number of possible solutions of the coupled systems can be
reduced. The proposed method is robust and applicable in many different
systems.


  Different kinematical regimes of semi-inclusive deeply inelastic scattering
(SIDIS) processes correspond to different underlying partonic pictures, and it
is important to understand the transition between them. This is particularly
the case when there is sensitivity to intrinsic transverse momentum, in which
case kinematical details can become especially important. We address the
question of how to identify the current fragmentation region --- the
kinematical regime where a factorization picture with fragmentation functions
is appropriate. We distinguish this from soft and target fragmentation regimes.
Our criteria are based on the kinematic regions used in derivations of
factorization theorems. We argue that, when hard scales are of order a few
GeVs, there is likely significant overlap between different rapidity regions
that are normally understood to be distinct. We thus comment on the need to
take this into account with more unified descriptions of SIDIS, which should
span all rapidities for the produced hadron. Finally, we propose general
criteria for estimating the proximity to the current region at large Q.


  The effect of a q-deformation of flavor symmetry on octet baryon magnetic
moments is investigated by taking the quantum group Uq(su(3)) as a flavor
symmetry and calculating expressions for the magnetic moments of the octet
baryons. Using the experimental values for the magnetic moments of the proton,
neutron, and Lambda baryons as input, the magnetic moments of the up, down, and
strange quarks, and by extension those of the remaining octet baryons, depend
on the value of the deformation parameter q. Plotting the least square error as
a function of q we find the undeformed value q=1 is a local maximum. Nearby are
a relative minimum (at q=0.610) and an absolute minimum (at q=1.774). The value
q=1.774 gives an approximately 10% decrease in the least square error compared
to the undeformed case. For this value of q the quark masses of the up and down
quarks are calculated to be 331 MeV and 305 MeV respectively.


  In astrophysical situations, e.g. in the interstellar medium (ISM), neutrals
can provide viscous damping on scales much larger than the magnetic diffusion
scale. Through numerical simulations, we have found that the magnetic field can
have a rich structure below the dissipation cutoff scale. This implies that
magnetic fields in the ISM can have structures on scales much smaller than
parsec scales. Our results show that the magnetic energy contained in a
wavenumber band is independent of the wavenumber and magnetic structures are
intermittent and extremely anisotropic. We discuss the relation between our
results and the formation of the tiny-scale atomic structure (TSAS).


  There is a common belief in the condensed matter community that bulk
quantities become insensitive to the boundary condition in the infinite-volume
limit. Here we reconsider this statement in terms of recent arguments of
non-Hermitian skin effects, -strong dependence of spectra on boundary
conditions for the non-Hermitian Hamiltonians-, in the traditional Green's
function formalism. We find the criterion for quantities to be
sensitive/insensitive against the boundary condition in Hermitian
correlated/disordered systems, which is characterized by the residue theorem.
We also discuss the uncertainty of the quasiparticle energy under the skin
effects in terms of nonnormal pseudospectra, which can be tested via the sharp
optical absorption from the bulk-surface coupling. Our result indicates that
"pseudo quantum number" emerges as a consequence of large nonnormality.


  Fingerprint recognition and matching is a common form of user authentication.
While a fingerprint is unique to each individual, authentication is vulnerable
when an attacker can forge a copy of the fingerprint (spoof). To combat these
spoofed fingerprints, spoof detection and liveness detection algorithms are
currently being researched as countermeasures to this security vulnerability.
This paper introduces a fingerprint anti-spoofing mechanism using machine
learning.


  "Generalized Gibbs' approach" of Schmelzer et al [J. Chem. Phys. 119, 6166
(2003); 124, 194503 (2006)] results in wrong conditions of equilibrium of a
critical embryo with the ambient phase. The presented analysis shows the
shortcomings of this approach and proves the thermodynamic conditions of
equilibrium. Also, a generalized adsorption equation is obtained in different
forms.


  We discuss the brane world model of Dvali, Gabadadze and Porrati in which
branes evolve in an infinite bulk and the brane curvature term is added to the
action. If Z_2 symmetry between the two sides of the brane is not imposed, we
show that the model admits the existence of "stealth branes" which follow the
standard 4D internal evolution and have no gravitational effect on the bulk
space. Stealth branes can nucleate spontaneosly in a Minkowski bulk. This
process is described by the standard 4D quantum cosmology formalism with
tunneling boundary conditions for the brane world wave function. The notorious
ambiguity in the choice of boundary conditions is fixed in this case due to the
presence of the embedding spacetime. We also point to some problematic aspects
of models admitting stealth brane solutions.


  In this article we give combinatorial criteria to decide whether a transitive
cyclic combinatorial d-manifold can be generalized to an infinite family of
such complexes, together with an explicit construction in the case that such a
family exists. In addition, we substantially extend the classification of
combinatorial 3-manifolds with transitive cyclic symmetry up to 22 vertices.
Finally, a combination of these results is used to describe new infinite
families of transitive cyclic combinatorial manifolds and in particular a
family of neighborly combinatorial lens spaces of infinitely many distinct
topological types.


  The large set of accurate data on differential cross section and analyzing
power from the CERN LEAR experiment on $\bar pp \to \pi^+\pi^-$ in the range
from 360 to 1550 MeV/c is well reproduced within a distorted wave approximation
approach. The initial $\bar pp$ scattering wave functions originate from a
recent $\bar N N$ model. The transition operator is obtained from a combination
of the $^3P_0$ and $^3S_1$ quark-antiquark annihilation mechanisms. A good fit
to the data, in particular the reproduction of the double dip structure
observed in the analyzing powers, requires quark wave functions for proton,
antiproton, and pions with radii slightly larger than the respective measured
charge radii. This corresponds to an increase in range of the annihilation
mechanisms and consequently the amplitudes for total angular momentum J=2 and
higher are much larger than in previous approaches. The final state $\pi\pi$
wave functions, parameterized in terms of $\pi\pi$ phase shifts and
inelasticities, are also a very important ingredient for the fine tuning of the
fit to the observables.


  We present the $U$-Statistic Permutation (USP) test of independence in the
context of discrete data displayed in a contingency table. Either Pearson's
chi-squared test of independence, or the $G$-test, are typically used for this
task, but we argue that these tests have serious deficiencies, both in terms of
their inability to control the size of the test, and their power properties. By
contrast, the USP test is guaranteed to control the size of the test at the
nominal level for all sample sizes, has no issues with small (or zero) cell
counts, and is able to detect distributions that violate independence in only a
minimal way. The test statistic is derived from a $U$-statistic estimator of a
natural population measure of dependence, and we prove that this is the unique
minimum variance unbiased estimator of this population quantity. The practical
utility of the USP test is demonstrated on both simulated data, where its power
can be dramatically greater than those of Pearson's test and the $G$-test, and
on real data. The USP test is implemented in the R package USP.


  We compute 1-loop correction E_1 to the energy of folded string in AdS_5 x
S^5 (carrying spin S in AdS_5 and momentum J in S^5) using ``long string''
approximation in which S >> J >> 1. According to AdS/CFT E_1 should represent
the first subleading correction to strong coupling expansion of anomalous
dimension of higher twist SL(2) sector operators of the form Tr D^S Z^J. We
show that E_1 smoothly interpolates between the ln S regime (previously found
in the J=0 case) and the \lambda/J^2 ln^3 (S/J) regime (which is the leading
correction to the thermodynamic limit on the spin chain side). This supports
the universality of the ln S scaling. As in previous work, we also find
``non-analytic'' corrections related to non-trivial 1-loop phase in the
corresponding Bethe ansatz S-matrix.


  The 21-cm line fluctuations and the cosmic microwave background (CMB) are
powerful probes of the epoch of reionisation of the universe. We study the
potential of the cross-correlation between 21-cm line fluctuations and CMB
anisotropy to obtain further constraints on the reionisation history. We
compute analytically the 21-cm cross-correlation with the CMB temperature
anisotropy and polarisation, and we calculate the signal-to-noise (SN) ratio
for its detection with Planck together with LOFAR, MWA and SKA. We find, on the
one hand, that the 21-cm cross-correlation signal with CMB polarisation from
the instant reionisation can be detected with an SN ratio of $\sim 1$ for LOFAR
and $\sim 10$ for SKA. On the other hand, we confirm that the detection of the
21-cm cross-correlation with CMB polarisation is practically infeasible.


  We present near-infrared (NIR) spectroscopic observations in the wavelength
range 0.90-2.40mum of eighteen low-metallicity blue compact dwarf (BCD)
galaxies and six HII regions in spiral and interacting galaxies. Hydrogen and
helium emission lines are detected in all spectra, while H2 and iron emission
lines are detected in most spectra. The NIR data for all objects have been
supplemented by optical spectra. In all objects, except perhaps for the highest
metallicity ones, we find that the extinctions A(V) in the optical and NIR
ranges are similar, implying that the NIR hydrogen emission lines in
low-metallicity BCDs do not reveal more star formation than seen in the
optical. We conclude that emission-line spectra of low-metallicity BCDs in the
0.36-2.40mum wavelength range are emitted by a relatively transparent ionized
gas. The H2 emission line fluxes can be accounted for by fluorescence in most
of the observed galaxies. We find a decrease of the H2 2.122mum emission line
relative to the Brgamma line with increasing ionization parameter. This
indicates an efficient destruction of H2 by the stellar UV radiation. The
intensities of the [FeII] 1.257mum and 1.644mum emission lines in the spectra
of all galaxies, but one, are consistent with the predictions of Cloudy stellar
photoinization models. There is thus no need to invoke shock excitation for
these lines, and they are not necessarily shock indicators in low-metallicity
high-excitation BCDs. The intensity of the HeI 2.058mum emission line is lower
in high-excitation BCDs with lower neutral gas column densities and higher
turbulent motions.


  We provide a comprehensive examination of the predictive accuracy of panel
forecasting methods based on individual, pooling, fixed effects, and Bayesian
estimation, and propose optimal weights for forecast combination schemes. We
consider linear panel data models, allowing for weakly exogenous regressors and
correlated heterogeneity. We quantify the gains from exploiting panel data and
demonstrate how forecasting performance depends on the degree of parameter
heterogeneity, whether such heterogeneity is correlated with the regressors,
the goodness of fit of the model, and the cross-sectional ($N$) and time ($T$)
dimensions. Monte Carlo simulations and empirical applications to house prices
and CPI inflation show that forecast combination and Bayesian forecasting
methods perform best overall and rarely produce the least accurate forecasts
for individual series.


  Subsampling is one of the popular methods to balance statistical efficiency
and computational efficiency in the big data era. Most approaches aim at
selecting informative or representative sample points to achieve good overall
information of the full data. The present work takes the view that sampling
techniques are recommended for the region we focus on and summary measures are
enough to collect the information for the rest according to a well-designed
data partitioning. We propose a multi-resolution subsampling strategy that
combines global information described by summary measures and local information
obtained from selected subsample points. We show that the proposed method will
lead to a more efficient subsample-based estimator for general large-scale
classification problems. Some asymptotic properties of the proposed method are
established and connections to existing subsampling procedures are explored.
Finally, we illustrate the proposed subsampling strategy via simulated and
real-world examples.


  In this paper, we examine regularity and stability issues for two damped
abstract elastic systems. The damping involves the average velocity and a
fractional power $\theta$, with $\theta$ in $[-1,1]$, of the principal
operator. The matrix operator defining the damping mechanism for the coupled
system is degenerate. First, we prove that for $\theta$ in $(1/2,1]$, the
underlying semigroup is not analytic, but is differentiable for $\theta$ in
$(0,1)$; this is in sharp contrast with known results for a single similarly
damped elastic system, where the semigroup is analytic for $\theta$ in
$[1/2,1]$; this shows that the degeneracy dominates the dynamics of the
interacting systems, preventing analyticity in that range. Next, we show that
for $\theta$ in $(0,1/2]$, the semigroup is of certain Gevrey classes. Finally,
we show that the semigroup decays exponentially for $\theta$ in $[0,1]$, and
polynomially for $\theta$ in $[-1,0)$. To prove our results, we use the
frequency domain method, which relies on resolvent estimates. Optimality of our
resolvent estimates is also established. Several examples of application are
provided.


  A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a
nonvanishing parallel spinor field; here the connection is assumed to be
Levi-Civita. We generalise this definition to metric compatible spacetimes with
torsion and describe basic properties of such spacetimes. We use our
generalised pp-waves for constructing new explicit vacuum solutions of
quadratic metric-affine gravity.


  A key component of a quantum machine learning model operating on classical
inputs is the design of an embedding circuit mapping inputs to a quantum state.
This paper studies a transfer learning setting in which classical-to-quantum
embedding is carried out by an arbitrary parametric quantum circuit that is
pre-trained based on data from a source task. At run time, a binary quantum
classifier of the embedding is optimized based on data from the target task of
interest. The average excess risk, i.e., the optimality gap, of the resulting
classifier depends on how (dis)similar the source and target tasks are. We
introduce a new measure of (dis)similarity between the binary quantum
classification tasks via the trace distances. An upper bound on the optimality
gap is derived in terms of the proposed task (dis)similarity measure, two
R$\'e$nyi mutual information terms between classical input and quantum
embedding under source and target tasks, as well as a measure of complexity of
the combined space of quantum embeddings and classifiers under the source task.
The theoretical results are validated on a simple binary classification
example.


  Let $E$ be an elliptic curve and $\pi:E\to\mathbb{P}^{1}$ a standard double
cover identifying $\pm P\in E$. It is known that for some torsion points
$P_{i}\in E$, $1\leq i\leq4$, the cross ratio of $\{\pi(P_{i})\}_{i=1}^{4}$ is
independent of $E$. In this article, we will give a complete classification of
such quadruples.


  This paper addresses consensus optimization problems in a multi-agent
network, where all agents collaboratively find a minimizer for the sum of their
private functions. We develop a new decentralized algorithm in which each agent
communicates only with its neighbors.
  State-of-the-art decentralized algorithms use communications between either
all pairs of adjacent agents or a random subset of them at each iteration.
Another class of algorithms uses a random walk incremental strategy, which
sequentially activates a succession of nodes; these incremental algorithms
require diminishing step sizes to converge to the solution, so their
convergence is relatively slow.
  In this work, we propose a random walk algorithm that uses a fixed step size
and converges faster than the existing random walk incremental algorithms. Our
algorithm is also communication efficient. Each iteration uses only one link to
communicate the latest information for an agent to another. Since this
communication rule mimics a man walking around the network, we call our new
algorithm Walkman. We establish convergence for convex and nonconvex
objectives. For decentralized least squares, we derive a linear rate of
convergence and obtain a better communication complexity than those of other
decentralized algorithms. Numerical experiments verify our analysis results.


  We propose a strongly coupled supersymmetric gauge theory that can
accommodate both the inflation (in the form of generalized hybrid inflation)
and dark matter (DM). In this set-up, we identify the DM as the Goldstones
associated with the breaking of a global symmetry ($SU(4)\times SU(4) \to
SU(4)$) after inflation ends. Due to the non-abelian nature of this symmetry,
the scenario provides with multiple DMs. We then construct a low energy theory
which generates a Higgs portal like coupling of the DMs with Standard Model
(SM), thus allowing them to thermally freeze out. While the scales involved in
the inflation either have a dynamical origin or related to UV interpretation in
terms of a heavy quark field in the supersymmetric QCD (SQCD) sector, the DM
masses however are generated from explicit breaking of the chiral symmetry of
the SQCD sector. We discuss DM phenomenology for both degenerate and
non-degenerate cases, poised with DM-DM interactions and find allowed region of
parameter space in terms of relic density and direct search constraints.


  The feeling that those two forcing notions-Cohen and Random-(equivalently the
corresponding Boolean algebras Borel(R)/(meager sets), Borel(R)/(null sets))
are special, was probably old and widespread. A reasonable interpretation is to
show them unique, or ``minimal'' or at least characteristic in a family of
``nice forcing'' like Borel. We shall interpret ``nice'' as Souslin as
suggested by Judah Shelah [JdSh 292]. We divide the family of Souslin forcing
to two, and expect that: among the first part, i.e. those adding some
non-dominated real, Cohen is minimal (=is below every one), while among the
rest random is quite characteristic even unique. Concerning the second class we
have weak results, concerning the first class, our results look satisfactory.
We have two main results: one (1.14) says that Cohen forcing is ``minimal'' in
the first class, the other (1.10) says that all c.c.c. Souslin forcing have a
property shared by Cohen forcing and Random real forcing, so it gives a weak
answer to the problem on how special is random forcing, but says much on all
c.c.c. Souslin forcing.


  Let $D$ be a bounded strongly convex domain with smooth boundary in $\mathbb
C^N$. Let $(\phi_t)$ be a continuous semigroup of holomorphic self-maps of $D$.
We prove that if $p\in \partial D$ is an isolated boundary regular fixed point
for $\phi_{t_0}$ for some $t_0>0$, then $p$ is a boundary regular fixed point
for $\phi_t$ for all $t\geq 0$. Along the way we also study backward iteration
sequences for elliptic holomorphic self-maps of $D$.


  We study self-similar solutions of the binormal curvature flow which governs
the evolution of vortex filaments and is equivalent to the Landau-Lifshitz
equation. The corresponding dynamics is described by the real solutions of
$\sigma$-Painlev\'{e} IV equation with two real parameters. Connection formulae
for Painlev\'{e} IV transcendents allow for a complete characterization of the
asymptotic properties of the curvature and torsion of the filament. We also
provide compact hypergeometric expressions for self-similar solutions
corresponding to corner initial conditions.


  This is a course of lectures given for students of the Regional Mathematical
Center of the Novosibirsk State University from October 20 to November 3, 2017.
  The course is devoted to some geometric problems of ramified coverings of the
Riemann sphere. A special attention is payed to compact surfaces of genus one
(complex tori). In the first section we give a short introduction to the theory
of elliptic functions.
  Section 2 is devoted to one-parametric families of holomorphic and
meromorphic functions. We recall the role of such families on Loewner's
equation in solving some problems of the theory of univalent functions. Further
we deduce a system of ODEs expressing dependence of critical points of a family
of rational functions from their critical values. This gives an approximate
method to find a conformal mapping of the Riemann sphere onto a given
simply-connected compact Riemann surface over the sphere. Thereafter a similar
problem is solved for elliptic functions uniformizing complex tori over the
Riemann sphere. The corresponding system of ODEs also contains a differential
equation for the modules of complex tori.
  In Section 3 we apply complex tori in some problems connected to Pade-Hermit
approximations. We study the partition of a 3-sheeted Riemann surface into
sheets induced by some abelian integrals (so-called Nattall's partition). In
the symmetric case we describe the structure of trajectories of quadratic
differentials connected with the abelian integrals.


  We propose Drinfeld's second realisation of the quantum group relevant to the
Lax-operator approach developed in the work of Bazhanov, Frassek, Lukowski,
Meneghelli and Staudacher.


  We investigate finite-$N$ corrections to the superconformal indices of the
theories realized on M2- and M5-branes. For three-dimensional theories realized
on a stack of $N$ M2-branes we calculate the finite-$N$ corrections as the
contribution of extended M5-branes in the dual geometry $AdS_4\times
\boldsymbol{S}^7$. We take only M5-brane configurations with a single wrapping
into account, and neglect multiple-wrapping configurations. We compare the
results with the indices calculated from the ABJM theory, and find agreement up
to expected errors due to the multiple wrapping. For six-dimensional theories
on $N$ M5-branes we calculate the indices by analyzing extended M2-branes in
$AdS_7\times \boldsymbol{S}^4$. Again, we include only configurations with
single wrapping. We first compare the result for $N=1$ with the index of the
free tensor multiplet to estimate the order of the error due to multiple
wrapping. We calculate first few terms of the index of $A_{N-1}$ theories
explicitly, and confirm that they can be expanded by superconformal
representations. We also discuss multiple-wrapping contributions to the
six-dimensional Schur-like index.


  We start from the observation that, anytime two Markov generators share an
eigenvalue, the function constructed from the product of the two eigenfunctions
associated to this common eigenvalue is a duality function. We push further
this observation and provide a full characterization of duality relations in
terms of spectral decompositions of the generators for finite state space
Markov processes. Moreover, we study and revisit some well-known instances of
duality, such as Siegmund duality, and extract spectral information from it.
Next, we use the same formalism to construct all duality functions for some
solvable examples, i.e., processes for which the eigenfunctions of the
generator are explicitly known.


  We explore the existence of irreducible and reducible arc-sections in an
irreducible hypersurface singularity germ along finite projections.
  In particular we provide examples of irreducible isolated hypersurface
singularities for which no irreducible arc-sections exist, and show that
reducible ones always exist. Moreover, we give an algorithm to check if a given
projection allows irreducible arc-sections, and find them if they exist.


  In highest quality organic single-crystal field-effect transistors, electron
transport occurs in the band-like regime, with the carrier mobility increasing
upon lowering temperature. Neither the microscopic nature of this regime, nor
why it occurs only in a small number of materials is currently understood.
Here, comparative studies of closely related materials, exhibiting high-quality
reproducible transport properties are needed. We performed a study of electron
transport in single-crystals of different TCNQ (tetracyanoquinodimethane)
molecules, combined with band structure calculations. We show that F2-TCNQ
devices exhibit very high electron mobility and an unprecedented increase in
mobility upon cooling, whereas in TCNQ and F4-TCNQ the mobility is
substantially lower and decreases upon cooling. We analyze the crystal and
electronic structures of these materials and find that F2-TCNQ crystals are
indeed ideal to achieve outstanding transport properties. Our analysis also
shows that to understand the difference between the three materials, studying
their band structure is not sufficient, and that the electron-phonon coupling
needs to be investigated as well. Besides the outstanding transport properties
of F2-TCNQ, a key result of our work is the identification of the Fx-TCNQ
family as a paradigm to investigate the most fundamental aspects of electronic
transport in organic crystals.


  Beam management (BM), i.e., the process of finding and maintaining a suitable
transmit and receive beam pair, can be challenging, particularly in highly
dynamic scenarios. Side-information, e.g., orientation, from on-board sensors
can assist the user equipment (UE) BM. In this work, we use the orientation
information coming from the inertial measurement unit (IMU) for effective BM.
We use a data-driven strategy that fuses the reference signal received power
(RSRP) with orientation information using a recurrent neural network (RNN).
Simulation results show that the proposed strategy performs much better than
the conventional BM and an orientation-assisted BM strategy that utilizes
particle filter in another study. Specifically, the proposed data-driven
strategy improves the beam-prediction accuracy up to 34% and increases mean
RSRP by up to 4.2 dB when the UE orientation changes quickly.