  In this paper, we propose a two-timescale delay-optimal base station
Discontinuous Transmission (BS-DTX) control and user scheduling for downlink
coordinated MIMO systems with energy harvesting capability. To reduce the
complexity and signaling overhead in practical systems, the BS-DTX control is
adaptive to both the energy state information (ESI) and the data queue state
information (QSI) over a longer timescale. The user scheduling is adaptive to
the ESI, the QSI and the channel state information (CSI) over a shorter
timescale. We show that the two-timescale delay-optimal control problem can be
modeled as an infinite horizon average cost Partially Observed Markov Decision
Problem (POMDP), which is well-known to be a difficult problem in general. By
using sample-path analysis and exploiting specific problem structure, we first
obtain some structural results on the optimal control policy and derive an
equivalent Bellman equation with reduced state space. To reduce the complexity
and facilitate distributed implementation, we obtain a delay-aware distributed
solution with the BS-DTX control at the BS controller (BSC) and the user
scheduling at each cluster manager (CM) using approximate dynamic programming
and distributed stochastic learning. We show that the proposed distributed
two-timescale algorithm converges almost surely. Furthermore, using queueing
theory, stochastic geometry and optimization techniques, we derive sufficient
conditions for the data queues to be stable in the coordinated MIMO network and
discuss various design insights.


  Let $\alpha$ and $\beta$ be uniformly random permutations of orders $2$ and
$3$, respectively, in $S_{N}$, and consider, say, the permutation
$\alpha\beta\alpha\beta^{-1}$. How many fixed points does this random
permutation have on average? The current paper studies questions of this kind
and relates them to surprising topological and algebraic invariants of elements
in free products of groups.
  Formally, let $\Gamma=G_{1}*\ldots*G_{k}$ be a free product of groups where
each of $G_1,\ldots,G_k$ is either finite, finitely generated free, or an
orientable hyperbolic surface group. For a fixed element $\gamma\in\Gamma$, a
$\gamma$-random permutation in the symmetric group $S_{N}$ is the image of
$\gamma$ through a uniformly random homomorphism $\Gamma\to S_{N}$. In this
paper we study local statistics of $\gamma$-random permutations and their
asymptotics as $N$ grows. We first consider
$\mathbb{E}\left[\mathrm{fix}_{\gamma}\left(N\right)\right]$, the expected
number of fixed points in a $\gamma$-random permutation in $S_{N}$. We show
that unless $\gamma$ has finite order, the limit of
$\mathbb{E}\left[\mathrm{fix}_{\gamma}\left(N\right)\right]$ as $N\to\infty$ is
an integer, and is equal to the number of subgroups $H\le\Gamma$ containing
$\gamma$ such that $H\cong\mathbb{Z}$ or $H\cong C_{2}*C_{2}$. Equivalently,
this is the number of subgroups $H\le\Gamma$ containing $\gamma$ and having
(rational) Euler characteristic zero. We also prove there is an asymptotic
expansion for $\mathbb{E}\left[\mathrm{fix}_{\gamma}\left(N\right)\right]$ and
determine the limit distribution of the number of fixed points as $N\to\infty$.
These results are then generalized to all statistics of cycles of fixed
lengths.


  We use 12 cosmological $N$-body simulations of Local Group systems (the
Apostle models) to inspect the relation between the virial mass of the main
haloes ($M_{\rm vir,1}$ and $M_{\rm vir,2}$), the mass derived from the
relative motion of the halo pair ($M_{\rm tim}$), and that inferred from the
local Hubble flow ($M_{\rm lhf}$). We show that within the Spherical Collapse
Model (SCM), the correspondence between the three mass estimates is exact, i.e.
$M_{\rm lhf}=M_{\rm tim}=M_{\rm vir,1}+M_{\rm vir,2}$. However, comparison with
Apostle simulations reveals that, contrary to what the SCM states, a relatively
large fraction of the mass that perturbs the local Hubble flow and drives the
relative trajectory of the main galaxies is not contained within $R_{\rm vir}$,
and that the amount of "extra-virial" mass tends to increase in galaxies with a
slow accretion rate. In contrast, modelling the peculiar velocities around the
Local Group returns an unbiased constraint on the virial mass ratio of the main
galaxy pair. Adopting the outer halo profile found in $N$-body simulations,
which scales as $\rho\sim R^{-4}$ at $R\gtrsim R_{\rm vir}$, indicates that the
galaxy masses perturbing the local Hubble flow roughly correspond to the
asymptotically-convergent (total) masses of the individual haloes. We show that
estimates of $M_{\rm vir}$ based on the dynamics of tracers at $R\gg R_{\rm
vir}$ require a priori information on the internal matter distribution and the
growth rate of the main galaxies, both of which are typically difficult to
quantify.


  We prove that a polygonal billiard with one-sided mirrors has zero
topological entropy. In certain cases we show sub exponential and for other
polynomial estimates on the complexity.


  In this paper, we define the eta cochain form and prove its regularity when
the kernel of a family of Dirac operators is a vector bundle. We decompose the
eta form as a pairing of the eta cochain form with the Chern character of an
idempotent matrix and we also decompose the Chern character of the index bundle
for a fibration with boundary as a pairing of the family Chern-Connes character
for a manifold with boundary with the Chern character of an idempotent matrix.
We define the family $b$-Chern-Connes character and then we prove that it is
entire and give its variation formula. By this variation formula, we prove
another noncommutative family Atiyah-Patodi-Singer index theorem. Thus, we
extend the results of Gezler and Wu to the family case.


  We have employed spin-polarized scanning tunneling microscopy and Monte-Carlo
simulations to investigate the effect of lateral confinement onto the
nanoskyrmion lattice in Fe/Ir(111). We find a strong coupling of one diagonal
of the square magnetic unit cell to the close-packed edges of Fe
nanostructures. In triangular islands this coupling in combination with the
mismatching symmetries of the islands and of the square nanoskyrmion lattice
leads to frustration and triple-domain states. In direct vicinity to
ferromagnetic NiFe islands, the surrounding skyrmion lattice forms additional
domains. In this case a side of the square magnetic unit cell prefers a
parallel orientation to the ferromagnetic edge. These experimental findings can
be reproduced and explained by Monte-Carlo simulations. Here, the single-domain
state of a triangular island is lower in energy, but nevertheless multi-domain
states occur due to the combined effect of entropy and an intrinsic domain wall
pinning arising from the skyrmionic character of the spin texture.


  The properties of hydrogen at high pressure have wide implications in
astrophysics and high-pressure physics. Its phase change in the liquid is
variously described as a metallization, H2-dissociation, density discontinuity
or plasma phase transition. It has been tacitly assumed that these phenomena
coincide at a first-order liquid-liquid transition (LLT). In this work, the
relevant pressure-temperature conditions are thoroughly explored with
first-principles molecular dynamics. We show there is a large dependency on
exchange-correlation functional and significant finite size effects. We use
hysteresis in a number of measurable quantities to demonstrate a first-order
transition up to a critical point, above which molecular and atomic liquids are
indistinguishable. At higher temperature beyond the critical point,
H2-dissociation becomes a smooth cross-over in the supercritical region that
can be modelled by a pseudo-transition, where the H2-2H transformation is
localized and does not cause a density discontinuity at metallization.
Thermodynamic anomalies and counter-intuitive transport behavior of protons are
also discovered even far beyond the critical point, making this dissociative
transition highly relevant to the interior dynamics of Jovian planets. Below
the critical point, simulation also reveals a dynamic H2-2H chemical
equilibrium with rapid interconversion, showing that H2 and H are miscible. The
predicted critical temperature lies well below the ionization temperature. Our
calculations unequivocally demonstrate that there are three distinct regimes in
the liquid-liquid transition of warm dense hydrogen.


  In image super-resolution, both pixel-wise accuracy and perceptual fidelity
are desirable. However, most deep learning methods only achieve high
performance in one aspect due to the perception-distortion trade-off, and works
that successfully balance the trade-off rely on fusing results from separately
trained models with ad-hoc post-processing. In this paper, we propose a novel
super-resolution model with a low-frequency constraint (LFc-SR), which balances
the objective and perceptual quality through a single model and yields
super-resolved images with high PSNR and perceptual scores. We further
introduce an ADMM-based alternating optimization method for the non-trivial
learning of the constrained model. Experiments showed that our method, without
cumbersome post-processing procedures, achieved the state-of-the-art
performance. The code is available at https://github.com/Yuehan717/PDASR.


  Imaging of structural defects in a material can be realized with a
radio-frequency atomic magnetometer by monitoring the material's response to a
radio-frequency excitation field. We demonstrate two measurement configurations
that enable the increase of the amplitude and phase contrast in images that
represent a structural defect in highly electrically conductive and high
magnetic permeability samples. Both concepts involve the elimination of the
excitation field component, orthogonal to the sample surface, from the atomic
magnetometer signal. The first method relies on the implementation of a set of
coils that directly compensates the excitation field component in the
magnetometer signal. The second takes advantage of the fact that the
radio-frequency magnetometer is not sensitive to the magnetic field oscillating
along one of its axes. Results from simple modelling confirm the experimental
observation and are discussed in detail.


  We find the minimal dimension for a truncated polynomial algebra over an
arbitrary field for which there exists a "non-thin" subalgebra. Moreover, we
discuss examples of subalgebras, and count them in low dimensions.


  We have realized a scheme for continuous loading of a magnetic trap (MT).
^{52}Cr atoms are continuously captured and cooled in a magneto-optical trap
(MOT). Optical pumping to a metastable state decouples atoms from the cooling
light. Due to their high magnetic moment (6 Bohr magnetons), low-field seeking
metastable atoms are trapped in the magnetic quadrupole field provided by the
MOT. Limited by inelastic collisions between atoms in the MOT and in the MT, we
load 10^8 metastable atoms at a rate of 10^8 atoms/s below 100 microkelvin into
the MT. After loading we can perform optical repumping to realize a MT of
ground state chromium atoms.


  Supervised learning methods with missing data have been extensively studied
not just due to the techniques related to low-rank matrix completion. Also in
unsupervised learning one often relies on imputation methods. As a matter of
fact, missing values induce a bias in various estimators such as the sample
covariance matrix. In the present paper, a convex method for sparse subspace
estimation is extended to the case of missing and corrupted measurements. This
is done by correcting the bias instead of imputing the missing values. The
estimator is then used as an initial value for a nonconvex procedure to improve
the overall statistical performance. The methodological as well as theoretical
frameworks are applied to a wide range of statistical problems. These include
sparse Principal Component Analysis with different types of randomly missing
data and the estimation of eigenvectors of low-rank matrices with missing
values. Finally, the statistical performance is demonstrated on synthetic data.


  We report a measurement of the CP-violation parameter sin2beta with B^0 ->
J/psi K^0_S decays in which the J/psi decays to hadrons or to muons that do not
satisfy our standard identification criteria. With a sample of 88 million BBbar
events collected by the BaBar detector at the PEP-II asymmetric-energy $B$
factory at SLAC, we reconstruct 100 +/- 17 such events, with J/psi -> pi^+ pi^-
pi^0 being the most prevalent, and measure sin2beta = 1.56 +/- 0.42 (stat.) +/-
0.21 (syst.).


  An intense laser pulse propagating in a medium of inhomogeneously broadened
quantum dots massively creates entangled exciton states. After passage of the
pulse all single-exciton states remain unpopulated (self-induced transparency)
whereas biexciton coherence (exciton entanglement) is generated through
two-photon transitions. We propose several experimental techniques for the
observation of such unexpected behavior.


  One of the key challenges to the IoT's success is how to secure and anonymize
billions of IoT transactions and devices per day, an issue that still lingers
despite significant research efforts over the last few years. On the other
hand, technologies based on blockchain algorithms are disrupting today's
cryptocurrency markets and showing tremendous potential, since they provide a
distributed transaction ledger that cannot be tampered with or controlled by a
single entity. Although the blockchain may present itself as a cure-all for the
IoT's security and privacy challenges, significant research efforts still need
to be put forth to adapt the computation-intensive blockchain algorithms to the
stringent energy and processing constraints of today's IoT devices. In this
paper, we provide an overview of existing literature on the topic of blockchain
for IoT, and present a roadmap of research challenges that will need to be
addressed to enable the usage of blockchain technologies in the IoT.


  The recent completion of Advanced LIGO suggests that gravitational waves
(GWs) may soon be directly observed. Past searches for gravitational-wave
transients have been impacted by transient noise artifacts, known as glitches,
introduced into LIGO data due to instrumental and environmental effects. In
this work, we explore how waveform complexity, instead of signal-to-noise
ratio, can be used to rank event candidates and distinguish short duration
astrophysical signals from glitches. We test this framework using a new
hierarchical pipeline that directly compares the Bayesian evidence of explicit
signal and glitch models. The hierarchical pipeline is shown to have strong
performance, and in particular, allows high-confidence detections of a range of
waveforms at realistic signal-to-noise ratio with a two detector network.


  Unipolar switching phenomena have attracted a great deal of recent attention,
but the wide distributions of switching voltages still pose major obstacles for
scientific advancement and practical applications. Using NiO capacitors, we
investigated the distributions of the RESET voltage and current. We found that
they scaled with the resistance value Ro in the low resistance state, and that
the scaling exponents varied at Ro = 30 Ohm. We explain these intriguing
scaling behaviors and their crossovers by analogy with percolation theory. We
show that the connectivity of conducting filaments plays a crucial role in the
RESET process.


  The coax based MO distribution system in the ALS is going to be replaced by a
modernized, lower phase noise and more interference tolerant version, ready to
support ALS-U operation. System aspects are shown and several commercial analog
and digital optical transceiver modules are compared for their suitability in
this application. Furthermore, recent phase noise optimizing efforts in the ALS
RF system are discussed and several prototypes for a custom built, low phase
noise, frequency adjustable master oscillator around 500 MHz are shown.


  We report exact predictions for universal scaling exponents and scaling
functions associated with the distribution of the maximum collective avalanche
propagation velocities $v_m$ in the mean field theory of the interface
depinning transition. We derive the extreme value distribution $P(v_m|T)$ for
the maximum velocities in avalanches of fixed duration $T$, and verify the
results by numerical simulation near the critical point. We find that the tail
of the distribution of maximum velocity for an arbitrary avalanche duration,
$v_m$, scales as $P(v_m)\sim v_m^{-2}$ for large $v_m$. These results account
for the observed power-law distribution of the maximum amplitudes in acoustic
emission experiments of crystal plasticity, and are also broadly applicable to
other systems in the mean-field interface depinning universality class, ranging
from magnets to earthquakes.


  This paper presents COREALMLIB, an ALM library of commonsense knowledge about
dynamic domains. The library was obtained by translating part of the COMPONENT
LIBRARY (CLIB) into the modular action language ALM. CLIB consists of general
reusable and composable commonsense concepts, selected based on a thorough
study of ontological and lexical resources. Our translation targets CLIB states
(i.e., fluents) and actions. The resulting ALM library contains the
descriptions of 123 action classes grouped into 43 reusable modules that are
organized into a hierarchy. It is made available online and of interest to
researchers in the action language, answer-set programming, and natural
language understanding communities. We believe that our translation has two
main advantages over its CLIB counterpart: (i) it specifies axioms about
actions in a more elaboration tolerant and readable way, and (ii) it can be
seamlessly integrated with ASP reasoning algorithms (e.g., for planning and
postdiction). In contrast, axioms are described in CLIB using STRIPS-like
operators, and CLIB's inference engine cannot handle planning nor postdiction.
Under consideration for publication in TPLP.


  In 5G Ultra-Dense Networks, a distributed wireless backhaul is an attractive
solution for forwarding traffic to the core. The macro-cell coverage area is
divided into many small cells. A few of these cells are designated as gateways
and are linked to the core by high-capacity fiber optic links. Each small cell
is associated with one gateway and all small cells forward their traffic to
their respective gateway through multi-hop mesh networks. We investigate the
gateway location problem and show that finding near-optimal gateway locations
improves the backhaul network capacity. An exact p-median integer linear
program is formulated for comparison with our novel K-GA heuristic that
combines a Genetic Algorithm (GA) with K-means clustering to find near-optimal
gateway locations. We compare the performance of KGA with six other approaches
in terms of average number of hops and backhaul network capacity at different
node densities through extensive Monte Carlo simulations. All approaches are
tested in various user distribution scenarios, including uniform distribution,
bivariate Gaussian distribution, and cluster distribution. In all cases K-GA
provides near-optimal results, achieving average number of hops and backhaul
network capacity within 2% of optimal while saving an average of 95% of the
execution time.


  Vibrations of the Jeffcott rotor are modelled by a three degree of freedom
system including coupling between lateral and torsional modes. The crack in a
rotating shaft of the rotor is introduced via time dependent stiffness with off
diagonal couplings. Applying the external torque to the system allows to
observe the effect of crack "breathing" and gain insight into the system. It is
manifested in the complex dynamic behaviour of the rotor in the region of
internal resonance, showing a quasi--periodic motion or even non-periodic
behaviour. In the present paper report, we show the system response to the
external torque excitation using nonlinear analysis tools such as bifurcation
diagram, phase portraits, Poincare maps and wavelet power spectrum. In the
region of resonance we study intermittent motions based on laminar phases
interrupted by a series nonlinear beats.


  We study the finite-temperature behaviour of two-dimensional S=1/2 Heisenberg
antiferromagnets with very weak easy-axis and easy-plane exchange anisotropies.
By means of quantum Monte Carlo simulations, based on the continuous-time loop
and worm algorithm, we obtain a rich set of data that allows us to draw
conclusions about both the existence and the type of finite-temperature
transition expected in the considered models. We observe that the essential
features of the Ising universality class, as well as those of the
Berezinskii-Kosterlitz-Thouless (BKT) one, are preserved even for anisotropies
as small as 10^{-3} times the exchange integral; such outcome, being referred
to the most quantum case S=1/2, rules out the possibility for quantum
fluctuations to destroy the long or quasi-long range order, whose onset is
responsible for the Ising or BKT transition, no matter how small the
anisotropy. Besides this general issue, we use our results to extract, out of
the isotropic component, the features which are peculiar to weakly anisotropic
models, with particular attention for the temperature region immediately above
the transition. By this analysis we aim to give a handy tool for understanding
the experimental data relative to those real compounds whose anisotropies are
too weak for a qualitative description to accomplish the goal of singling out
the genuinely two-dimensional critical behaviour.


  Keplerian-Stacker is an algorithm able to combine multiple observations
acquired at different epochs taking into account the orbital motion of a
potential planet present in the images to boost the ultimate detection limit.
In 2019, a total of 100 hours of observation were allocated to VLT VISIR-NEAR,
a collaboration between ESO and Breakthrough Initiatives, to search for low
mass planets in the habitable zone of the Alpha Cen AB binary system. A weak
signal (S/N = 3) was reported around Alpha Cen A, at a separation of 1.1 a.u.
which corresponds to the habitable zone. We have re-analysed the NEAR data
using K-Stacker. This algorithm is a brute-force method able to find planets in
time series of observations and to constrain their orbital parameters, even if
they remain undetected in a single epoch. We scanned a total of about 3.5e+5
independent orbits, among which about 15 % correspond to fast moving orbits on
which planets cannot be detected without taking into account the orbital
motion. We find only a single planet candidate, which matches the C1 detection
reported in Wagner et al. 2021. Despite the significant amount of time spent on
this target, the orbit of this candidate remains poorly constrained due to
these observations being closely distributed in 34 days. We argue that future
single-target deep surveys would benefit from a K-Stacker based strategy, where
the observations would be split over a significant part of the expected orbital
period to better constrain the orbital parameters. This application of
K-Stacker on high contrast imaging data in the mid-infrared demonstrates the
capability of this algorithm to aid in the search for Earth-like planets in the
habitable zone of the nearest stars with future instruments of the E-ELT such
as METIS.


  Can stress affect not only your life but also how you read and interpret a
text? Healthcare has shown evidence of such dynamics and in this short paper we
discuss customising texts based on user stress level, as it could represent a
critical factor when it comes to user engagement and behavioural change. We
first show a real-world example in which user behaviour is influenced by
stress, then, after discussing which tools can be employed to assess and
measure it, we propose an initial method for tailoring the document by
exploiting complexity reduction and affect enforcement. The result is a short
and encouraging text which requires less commitment to be read and understood.
We believe this work in progress can raise some interesting questions on a
topic that is often overlooked in NLG.


  The main aim of this paper is to study the growth of solutions of higher
order linear differential equations using the concepts of $(\alpha ,\beta
,\gamma )$-order and $(\alpha ,\beta ,\gamma )$-type. We obtain some results
which improve and generalize some previous results of Kinnunen \cite{13}, Long
et al. \cite{L} as well as Bela\"{\i}di \cite{b3}, \cite{b5}.


  This work studies minimization problems with zero-order noisy oracle
information under the assumption that the objective function is highly smooth
and possibly satisfies additional properties. We consider two kinds of
zero-order projected gradient descent algorithms, which differ in the form of
the gradient estimator. The first algorithm uses a gradient estimator based on
randomization over the $\ell_2$ sphere due to Bach and Perchet (2016). We
present an improved analysis of this algorithm on the class of highly smooth
and strongly convex functions studied in the prior work, and we derive rates of
convergence for two more general classes of non-convex functions. Namely, we
consider highly smooth functions satisfying the Polyak-{\L}ojasiewicz condition
and the class of highly smooth functions with no additional property. The
second algorithm is based on randomization over the $\ell_1$ sphere, and it
extends to the highly smooth setting the algorithm that was recently proposed
for Lipschitz convex functions in Akhavan et al. (2022). We show that, in the
case of noiseless oracle, this novel algorithm enjoys better bounds on bias and
variance than the $\ell_2$ randomization and the commonly used Gaussian
randomization algorithms, while in the noisy case both $\ell_1$ and $\ell_2$
algorithms benefit from similar improved theoretical guarantees. The
improvements are achieved thanks to a new proof techniques based on Poincar\'e
type inequalities for uniform distributions on the $\ell_1$ or $\ell_2$
spheres. The results are established under weak (almost adversarial)
assumptions on the noise. Moreover, we provide minimax lower bounds proving
optimality or near optimality of the obtained upper bounds in several cases.


  Rigorous computer simulations of propagating electromagnetic fields have
become an important tool for optical metrology and design of nanostructured
optical components. A vectorial finite element method (FEM) is a good choice
for an accurate modeling of complicated geometrical features. However, from a
numerical point of view solving the arising system of linear equations is very
demanding even for medium sized 3D domains. In numerics, a domain decomposition
method is a commonly used strategy to overcome this problem. Within this
approach the overall computational domain is split up into smaller domains and
interface conditions are used to assure continuity of the electromagnetic
field. Unfortunately, standard implementations of the domain decomposition
method as developed for electrostatic problems are not appropriate for wave
propagation problems. In an earlier paper we therefore proposed a domain
decomposition method adapted to electromagnetic field wave propagation
problems. In this paper we apply this method to 3D mask simulation.


  A model for two-dimensional colloids confined laterally by "structured
boundaries" (i.e., ones that impose a periodicity along the slit) is studied by
Monte Carlo simulations. When the distance D between the confining walls is
reduced at constant particle number from an initial value D_0, for which a
crystalline structure commensurate with the imposed periodicity fits, to
smaller values, a succession of phase transitions to imperfectly ordered
structures occur. These structures have a reduced number of rows parallel to
the boundaries (from n to n-1 to n-2 etc.) and are accompanied by an almost
periodic strain pattern, due to "soliton staircases" along the boundaries.
Since standard simulation studies of such transitions are hampered by huge
hysteresis effects, we apply the phase switch Monte Carlo method to estimate
the free energy difference between the structures as a function of the misfit
between D and D_0, thereby locating where the transitions occurs in
equilibrium. For comparison, we also obtain this free energy difference from a
thermodynamic integration method: the results agree, but the effort required to
obtain the same accuracy as provided by phase switch Monte Carlo would be at
least three orders of magnitude larger. We also show for a situation where
several "candidate structures" exist for a phase, that phase switch Monte Carlo
can clearly distinguish the metastable structures from the stable one. Finally,
applying the method in the conjugate statistical ensemble (where the normal
pressure conjugate to D is taken as an independent control variable) we show
that the standard equivalence between the conjugate ensembles of statistical
mechanics is violated.


  Satellite remote sensing has been widely used in the last decades for
agricultural applications, {both for assessing vegetation condition and for
subsequent yield prediction.} Existing remote sensing-based methods to estimate
gross primary productivity (GPP), which is an important variable to indicate
crop photosynthetic function and stress, typically rely on empirical or
semi-empirical approaches, which tend to over-simplify photosynthetic
mechanisms. In this work, we take advantage of all parallel developments in
mechanistic photosynthesis modeling and satellite data availability for
advanced monitoring of crop productivity. In particular, we combine
process-based modeling with the soil-canopy energy balance radiative transfer
model (SCOPE) with Sentinel-2 {and Landsat 8} optical remote sensing data and
machine learning methods in order to estimate crop GPP. Our model successfully
estimates GPP across a variety of C3 crop types and environmental conditions
even though it does not use any local information from the corresponding sites.
This highlights its potential to map crop productivity from new satellite
sensors at a global scale with the help of current Earth observation cloud
computing platforms.


  A recent article [W.C.W. Huang and H. Batelaan, arXiv:1708.0057v1] analysed
the dualism between optical and difference parametric amplification, performing
a classical analysis of a system where two electromagnetic fields are produced
by another of a frequency which is the difference of the frequency of the other
two. The authors claimed that this process would not violate energy
conservation at the classical level, but that a quantum description would
necessarily require a non-Hermitian Hamiltonian and therefore would not exist.
In this work we show that the process can proceed quantum mechanically if
described by the correct Hamiltonian, that energy conservation is not violated,
and that fields are produced with interesting quantum statistics. Furthermore,
we show that the process can be thought of as different types of already known
three-wave mixing processes, with the actual type depending on either initial
conditions or personal preference.


  This paper presents the design of deep learning architectures which allow to
classify the social relationship existing between two people who are walking in
a side-by-side formation into four possible categories --colleagues, couple,
family or friendship. The models are developed using Neural Networks or
Recurrent Neural Networks to achieve the classification and are trained and
evaluated using a database of readings obtained from humans performing an
accompaniment process in an urban environment. The best achieved model
accomplishes a relatively good accuracy in the classification problem and its
results enhance partially the outcomes from a previous study [1]. Furthermore,
the model proposed shows its future potential to improve its efficiency and to
be implemented in a real robot.


  We develop the version of the $J$-invariant for hermitian forms over
quadratic extensions in a similar way Alexander Vishik did it for quadratic
forms. This discrete invariant contains informations about rationality of
algebraic cycles on the maximal unitary grassmannian associated with a hermitan
form over a quadratic extension. The computation of the canonical $2$-dimension
of this grassmannian in terms of the $J$-invariant is provided, as well as a
complete motivic decomposition.


  Particular class of skew orthogonal polynomials are introduced and
investigated, which possess Laurent symmetry. They are also shown to appear as
eigenfunctions of symplectic generalized eigenvalue problems. The modification
of these polynomials gives some symplectic eigenvalue problem and the
corresponding matrix is shown to be equivalent to butterfly matrix, which is a
canonical form of symplectic matrices.


  In this paper, we further expand on the work in [1] that focused on the
localization of targets in a 2D space using 1-bit dithered measurements coming
from a 2 receiving antennae radar. Our aim is to further reduce the hardware
requirements and bit-rate, by dropping one of the baseband IQ channel from each
receiving antenna. To that end, the structure of the received signals is
exploited to recover the positions of multiple targets. Simulations are
performed to highlight the accuracy and limitations of the proposed scheme
under severe bit-rate reduction.


  We have computed the light quark masses using the O(a^2) improved Alpha
action, in the quenched approximation. The renormalized masses have been
obtained non-perturbatively. By eliminating the systematic error coming from
the truncation of the perturbative series, our procedure removes the
discrepancies, observed in previous calculations, between the results obtained
using the vector and the axial-vector Ward identities. It also gives values of
the quark masses larger than those obtained by computing the renormalization
constants using (boosted) perturbation theory. Our main results, in the RI
(MOM) scheme and at a renormalization scale \mu=2 GeV, are m^{RI}_s= 138(15)
MeV and m^{RI}_l= 5.6(5) MeV, where m^{RI}_s is the mass of the strange quark
and m^{RI}_l=(m^{RI}_u+m^{RI}_d)/2 the average mass of the up-down quarks. From
these results, which have been obtained non-perturbatively, by using continuum
perturbation theory we derive the \bar{MS} masses, at the same scale, and the
renormalization group invariant (m^{RGI}) masses. We find m^{NLO \bar{MS}}_s=
121(13)$ MeV and m^{NLO\bar{MS}}_l= 4.9(4) MeV at the next-to-leading order;
m^{N^2LO \bar{MS}}_s= 111(12) MeV, m^{N^2LO \bar{MS}}_l= 4.5(4) MeV, m_s^{RGI}=
177(19) MeV and m^{RGI}_l= 7.2(6) MeV at the next-to-next-to-leading order.


  We find a gravitational instanton that connects an initial state
corresponding to a single-centered extremal Reissner-Nordstrom (ERN) black hole
configuration, to a final state corresponding to a multi-centered
configuration. This instanton is interpreted as describing quantum tunneling
between the two different black hole solutions. We evaluate the Euclidean
action for this instanton and find that the amplitude for the tunneling process
is equal to half the difference in entropy between the initial and final
configurations.


  A current concern in the field of Artificial Intelligence (AI) is to ensure
the trustworthiness of AI systems. The development of explainability methods is
one prominent way to address this, which has often resulted in the assumption
that the use of explainability will lead to an increase in the trust of users
and wider society. However, the dynamics between explainability and trust are
not well established and empirical investigations of their relation remain
mixed or inconclusive. In this paper we provide a detailed description of the
concepts of user trust and distrust in AI and their relation to appropriate
reliance. For that we draw from the fields of machine learning, human-computer
interaction, and the social sciences. Furthermore, we have created a survey of
existing empirical studies that investigate the effects of AI systems and XAI
methods on user (dis)trust. With clarifying the concepts and summarizing the
empirical investigations, we aim to provide researchers, who examine user trust
in AI, with an improved starting point for developing user studies to measure
and evaluate the user's attitude towards and reliance on AI systems.


  We find broad classes of solutions to the field equations for d-dimensional
gravity coupled to an antisymmetric tensor of arbitrary rank and a scalar field
with non-vanishing potential. Our construction generates these configurations
from the solution of a single nonlinear ordinary differential equation, whose
form depends on the scalar potential. For an exponential potential we find
solutions corresponding to brane geometries, generalizing the black p-branes
and S-branes known for the case of vanishing potential. These geometries are
singular at the origin with up to two (regular) horizons. Their asymptotic
behaviour depends on the parameters of the model. When the singularity has
negative tension or the cosmological constant is positive we find
time-dependent configurations describing accelerating universes. Special cases
give explicit brane geometries for (compact and non-compact) gauged
supergravities in various dimensions, as well as for massive 10D supergravity,
and we discuss their interrelation. Some examples lift to give new solutions to
10D supergravity. Limiting cases with a domain wall structure preserve part of
the supersymmetries of the vacuum. We also consider more general potentials,
including sums of exponentials. Exact solutions are found for these with up to
three horizons, having potentially interesting cosmological interpretation. We
give several additional examples which illustrate the power of our techniques.


  Let M be a compact, connected and simply-connected Riemannian manifold, and
suppose that G is a compact, connected Lie group acting on M by isometries. The
dimension of the space of orbits is called the cohomogeneity of the action. If
the direct sum of the higher homotopy groups of M, tensored with the field of
rational numbers, is a finite-dimensional vector space over the rationals, then
M is said to be rationally elliptic. It is known that M is rationally elliptic
if it supports an action of cohomogeneity zero or one. When the cohomogeneity
is two, this general result is no longer true. However, we prove that M is
rationally elliptic in the two-dimensional case under the added assumption that
M has nonnegative sectional curvature.


  The measurement of the Casimir force between a large gold coated sphere and
single crystal silicon plate is performed with an atomic force microscope. A
rigorous statistical comparison of data with theory is done, without use of the
concept of root-mean-square deviation, and excellent agreement is obtained. The
Casimir force between metal and semiconductor is demonstrated to be
significantly different than between two similar or dissimilar metals.


  We introduce the so-called Clifford-Gegenbauer polynomials in the framework
of Dunkl operators, as well on the unit ball B(1), as on the Euclidean space
$R^m$. In both cases we obtain several properties of these polynomials, such as
a Rodrigues formula, a differential equation and an explicit relation
connecting them with the Jacobi polynomials on the real line. As in the
classical Clifford case, the orthogonality of the polynomials on $R^m$ must be
treated in a completely different way than the orthogonality of their
counterparts on B(1). In case of $R^m$, it must be expressed in terms of a
bilinear form instead of an integral. Furthermore, in this paper the theory of
Dunkl monogenics is further developed.


  We construct the chiral low-energy effective theory for 2+1+1 flavor lattice
QCD with twisted mass Wilson fermions. In contrast to existing results we
assume a heavy charm quark mass such that the D mesons are too heavy to appear
as degrees of freedom in the effective theory. As an application we compute the
kaon mass to 1-loop order in the LCE regime. The result contains a chiral
logarithm involving the neutral pion mass which has no analogue in continuum
ChPT.


  Recent development of lensless imagers has enabled three-dimensional (3D)
imaging through a thin piece of optics in close proximity to a camera sensor. A
general challenge of wide-field lensless imaging is the high computational
complexity and slow speed to reconstruct 3D objects through iterative
optimization process. Here, we demonstrated GEOMScope, a lensless 3D microscope
that forms image through a single layer of microlens array and reconstructs
objects through a geometrical-optics-based pixel back projection algorithm and
background suppressions. Compared to others, our method allows local
reconstruction, which significantly reduces the required computation resource
and increases the reconstruction speed by orders of magnitude. This enables
near real-time object reconstructions across a large volume of 23x23x5 mm^3,
with a lateral resolution of 40 um and axial resolution of 300 um. Our system
opens new avenues for broad biomedical applications such as endoscopy, which
requires both miniaturized device footprint and real-time high resolution
visualization.


  This paper presents a motion planning algorithm for quadruped locomotion
based on density functions. We decompose the locomotion problem into a
high-level density planner and a model predictive controller (MPC). Due to
density functions having a physical interpretation through the notion of
occupancy, it is intuitive to represent the environment with safety
constraints. Hence, there is an ease of use to constructing the planning
problem with density. The proposed method uses a simplified model of the robot
into an integrator system, where the high-level plan is in a feedback form
formulated through an analytically constructed density function. We then use
the MPC to optimize the reference trajectory, in which a low-level PID
controller is used to obtain the torque level control. The overall framework is
implemented in simulation, demonstrating our feedback density planner for
legged locomotion. The implementation of work is available at
\url{https://github.com/AndrewZheng-1011/legged_planner}


  An unusually deep (V,I) imaging dataset for the Virgo supergiant M87 with the
Hubble Space Telescope ACS successfully resolves its brightest red-giant stars,
reaching M_I(lim) = -2.5. After assessing the photometric completeness and
biasses, we use this material to estimate the metallicity distribution for the
inner halo of M87, finding that the distribution is very broad and likely to
peak near [m/H] ~ -0.4 and perhaps higher. The shape of the MDF strongly
resembles that of the inner halo for the nearby giant E galaxy NGC 5128. As a
byproduct of our study, we also obtain a preliminary measurement of the
distance to M87 with the TRGB (red-giant branch tip) method; the result is
(m-M)_0 = 31.12 +- 0.14 (d = 16.7 +- 0.9 Mpc). Averaging this result with three
other recent techniques give a weighted mean d(M87) = (16.4 +- 0.5) Mpc.


  Aiming at analyzing performance in cloud computing, some unpredictable
perturbations which may lead to performance downgrade are essential factors
that should not be neglected. To avoid performance downgrade in cloud computing
system, it is reasonable to measure the impact of the perturbations, and
further propose a robust scheduling strategy to maintain the performance of the
system at an acceptable level. In this paper, we first describe the
supply-demand relationship of service between cloud service providers and
customers, in which the profit and waiting time are objectives they most
concerned. Then, on the basis of introducing the lowest acceptable profit and
longest acceptable waiting time for cloud service providers and customers
respectively, we define a robustness metric method to declare that the number
and speed of servers should be adequately configured in a feasible region, such
that the performance of cloud computing system can stay at an acceptable level
when it is subject to the perturbations. Subsequently, we discuss the
robustness metric method in several cases, and propose heuristic optimization
algorithm to enhance the robustness of the system as much as possible. At last,
the performances of the proposed algorithm are validated by comparing with DE
and PSO algorithm, the results show the superiority of the proposed algorithm.


  The availability of scaling solutions in renormalisation group improved
versions of cosmology are investigated in the high-energy limit. We adopt
$f(R)$-type models of quantum gravity which display an interacting ultraviolet
fixed point at shortest distances. Expanding the gravitational fixed point
action to very high order in the curvature scalar, we detect a
convergence-limiting singularity in the complex field plane. Resummation
techniques including Pad\'e approximants as well as infinite order
approximations of the effective action are used to maximise the domain of
validity. We find that the theory displays near de Sitter solutions as well as
an anti-de Sitter solution in the UV whereas real de Sitter solutions, for
small curvature, appear to be absent. The significance of our results for
inflation, and implications for more general models of quantum gravity are
discussed.


  We say a family of sets is intersecting if any two of its sets intersect, and
we say it is trivially intersecting if there is an element which appears in
every set of the family. In this paper we study the maximum size of a
non-trivially intersecting family in a natural "multi-part" setting. Here the
ground set is divided into parts, and one considers families of sets whose
intersection with each part is of a prescribed size. Our work is motivated by
classical results in the single-part setting due to Erd\H{o}s, Ko and Rado, and
Hilton and Milner, and by a theorem of Frankl concerning intersecting families
in this multi-part setting. In the case where the part sizes are sufficiently
large we determine the maximum size of a non-trivially intersecting multi-part
family, disproving a conjecture of Alon and Katona.


  We deduce Diophantine arithmetic inequalities for big linear systems and with
respect to finite extensions of number fields. Our starting point is the
Parametric Subspace Theorem, for linear forms, as formulated by Evertse and
Ferretti \cite{Evertse:Ferretti:2013}. Among other features, this viewpoint
allows for a partitioning of the linear scattering, for the Diophantine
Exceptional set, that arises in the Subspace Theorem. Our perspective builds on
our work \cite{Grieve:points:bounded:degree}, combined with earlier work of
Evertse and Ferretti, \cite{Evertse:Ferretti:2013},
  Evertse and Schlickewei, \cite{Evertse:Schlickewei:2002}, and others. As an
application, we establish a novel linear scattering type result for the
Diophantine exceptional set that arises in the main Diophantine arithmetic
inequalities of Ru and Vojta \cite{Ru:Vojta:2016}. This result expands, refines
and complements our earlier works (including \cite{Grieve:2018:autissier} and
\cite{Grieve:points:bounded:degree}). A key tool to our approach is the concept
of \emph{linear section} with respect to a linear system. This was defined in
\cite{Grieve:points:bounded:degree}. Another point, which we develop in this
article, is a notion of logarithmic \emph{twisted height functions} for local
Weil functions and linear systems. As an additional observation, which is also
of an independent interest, we use the theory of Iitaka fibrations to determine
the asymptotic nature of such linear sections.


  As a newly emerging advance in deep generative models, diffusion models have
achieved state-of-the-art results in many fields, including computer vision,
natural language processing, and molecule design. The remote sensing community
has also noticed the powerful ability of diffusion models and quickly applied
them to a variety of tasks for image processing. Given the rapid increase in
research on diffusion models in the field of remote sensing, it is necessary to
conduct a comprehensive review of existing diffusion model-based remote sensing
papers, to help researchers recognize the potential of diffusion models and
provide some directions for further exploration. Specifically, this paper first
introduces the theoretical background of diffusion models, and then
systematically reviews the applications of diffusion models in remote sensing,
including image generation, enhancement, and interpretation. Finally, the
limitations of existing remote sensing diffusion models and worthy research
directions for further exploration are discussed and summarized.


  This paper is devoted to solve the galactic rotation problem for ESO138-G014
galaxy based on two theories: dark matter and Modified Newtonian Dynamics. Here
we did the rotation curve analysis with two possible choices for the dark
matter density profile, namely Burkert and Navarro, Frenk and White profiles.
The analysis shows the dark matter distribution favored to Burkert profile
(cored dark matter). The standard hypothesis for most spiral galaxies are known
to be embedded in dark matter haloes has now been overshadowed by Modified
Newtonian Dynamics, known as MOND, the leading alternative of dark matter. MOND
addresses the problem of a new fundamental constant $a_0$, called the
acceleration constant, at which acceleration scale of Newton second law fails
to hold. In this respect, we investigate this issue by testing the rotation
curve within the MOND framework with the observations to obtain the reliable
disk mass, $M_D$. We investigate whether ESO138-G014 is compatible with MOND or
dark matter is still favorable for the galactic rotation problem.


  We study the large-time and small-time asymptotic behaviors of the spectral
heat content for time-changed stable processes, where the time change belongs
to a large class of inverse subordinators. For the large-time behavior, the
spectral heat content decays polynomially with the decay rate determined by the
Laplace exponent of the underlying subordinator, which is in sharp contrast to
the exponential decay observed in the case when the time change is a
subordinator. On the other hand, the small-time behavior exhibits three
different decay regimes, where the decay rate is determined by both the Laplace
exponent and the index of the stable process.


  We analyse Join-the-Shortest-Queue in a contemporary scaling regime known as
the Non-Degenerate Slowdown regime. Join-the-Shortest-Queue (JSQ) is a
classical load balancing policy for queueing systems with multiple parallel
servers. Parallel server queueing systems are regularly analysed and
dimensioned by diffusion approximations achieved in the Halfin-Whitt scaling
regime. However, when jobs must be dispatched to a server upon arrival, we
advocate the Non-Degenerate Slowdown regime (NDS) to compare different
load-balancing rules.
  In this paper we identify novel diffusion approximation and timescale
separation that provides insights into the performance of JSQ. We calculate the
price of irrevocably dispatching jobs to servers and prove this to within 15%
(in the NDS regime) of the rules that may manoeuvre jobs between servers. We
also compare ours results for the JSQ policy with the NDS approximations of
many modern load balancing policies such as Idle-Queue-First and
Power-of-$d$-choices policies which act as low information proxies for the JSQ
policy. Our analysis leads us to construct new rules that have identical
performance to JSQ but require less communication overhead than
power-of-2-choices.


  Radioactivity was recently discovered as a source of decoherence and
correlated errors for the real-world implementation of superconducting quantum
processors. In this work, we measure levels of radioactivity present in a
typical laboratory environment (from muons, neutrons, and gamma's emitted by
naturally occurring radioactive isotopes) and in the most commonly used
materials for the assembly and operation of state-of-the-art superconducting
qubits. We develop a GEANT-4 based simulation to predict the rate of impacts
and the amount of energy released in a qubit chip from each of the mentioned
sources. We finally propose mitigation strategies for the operation of
next-generation qubits in a radio-pure environment.


  We introduce an embedding of the Torelli group of a compact connected
oriented surface with non-empty connected boundary into the completed Kauffman
bracket skein algebra of the surface, which gives a new construction of the
first Johnson homomorphism.


  We study random walks on the three-strand braid group $B_3$, and in
particular compute the drift, or average topological complexity of a random
braid, as well as the probability of trivial entanglement. These results
involve the study of magnetic random walks on hyperbolic graphs (hyperbolic
Harper-Hofstadter problem), what enables to build a faithful representation of
$B_3$ as generalized magnetic translation operators for the problem of a
quantum particle on the hyperbolic plane.


  Based on the results of F. Wilf on the need to take into account the
quantum-mechanical correspondence rules in the Dirac equation for an electron,
it was shown that the equation obtained by giving physical meaning to
$\alpha$-Dirac operators should be considered as a phenomenological equation
for a particle of non-zero size - the EM polaron, previously introduced by the
author. This allows a solution to be found to the inherent paradox of the Dirac
equation, which consists of the equality of the velocity of the moving
particles to the speed of light $c$ in a vacuum, which is a priori
unobtainable, and to understand the physical essence of spin as the intrinsic
mechanical moment of an EM polaron. It is also shown that the Dirac-Wilf
equation for a single spatial dimension can be considered a generalization of
the Schrodinger equation for relativistic energies.


  Lascoux, Leclerc and Thibon\cite{LLT} introduced a family of symmetric
polynomials, called LLT polynomials. We prove a $q$-multinomial expansion of
the coefficients of LLT polynomials in the case where $ \boldsymbol{\mu} =
\underbrace{(\mu,...,\mu)}_{n}$ and define a $q$-analog of a sum of the
plethysm multiplicities.


  Human bias is capable of changing the analysis of measured data sufficiently
to alter the results of an experiment. It is incumbent upon modern experiments,
especially those investigating quantities considered contentious in the broader
community, to blind their analysis in an effort to minimize bias. The choice of
a blinding model is experiment specific, but should also aim to prevent
accidental release of results before an analysis is finalized. In this paper,
we discuss common threats to an unbiased analysis, as well as common quantities
that can be blinded in different types of nuclear physics experiments. We use
the Muon Scattering Experiment as an example, and detail the blinding scheme
used therein.


  The cubic regularization method (CR) and its adaptive version (ARC) are
popular Newton-type methods in solving unconstrained non-convex optimization
problems, due to its global convergence to local minima under mild conditions.
The main aim of this paper is to develop a momentum-accelerated adaptive cubic
regularization method (ARCm) to improve the convergent performance. With the
proper choice of momentum step size, we show the global convergence of ARCm and
the local convergence can also be guaranteed under the \KL property. Such
global and local convergence can also be established when inexact solvers with
low computational costs are employed in the iteration procedure. Numerical
results for non-convex logistic regression and robust linear regression models
are reported to demonstrate that the proposed ARCm significantly outperforms
state-of-the-art cubic regularization methods (e.g., CR, momentum-based CR,
ARC) and the trust region method. In particular, the number of iterations
required by ARCm is less than 10\% to 50\% required by the most competitive
method (ARC) in the experiments.


  This paper illustrates the power of the entropy method in addressing problems
from large deviation theory. We provide and review entropy proofs for most
fundamental results in large deviation theory, including Cramer's theorem, the
G\"artner--Ellis theorem, and Sanov's theorem. Moreover, by the entropy method,
we also strengthen Sanov's theorem to the strong version.


  In molecular photofragmentation processes by soft X-rays, a number of ionic
fragments can be produced, each having a different abundance and correlation
with the emitted electron kinetic energy. For investigating these fragmentation
processes, electron-ion and electron-ion-ion coincidence experiments, in which
the kinetic energy of electrons are analyzed using an electrostatic analyzer
while the mass of the ions is analyzed using a pulsed electric field, are very
powerful. For such measurements, however, the contribution of random
coincidences is substantial and affects the data in a non-trivial way. Simple
intuitive subtraction methods cannot be applied. In the present paper, we
describe these electron-ion and electron-ion-ion coincidence experiments
together with a subtraction method for the contribution from random
coincidences. We provide a comprehensive set of equations for the data
treatment, including equations for the calculation of error-bars. We
demonstrate the method by applying it to the fragmentation of free CF$_3$SF$_5$
molecules.


  We study the crossover from self--similar scaling behavior to asymptotically
self--affine (anisotropic) structures. As an example, we consider bond
percolation with one preferred direction. Our theory is based on a
field--theoretical representation, and takes advantage of a renormalization
group approach designed for crossover phenomena. We calculate effective
exponents for the connectivity describing the entire crossover region from
isotropic to directed percolation, and predict at which scale of the anisotropy
the crossover should occur. We emphasize the broad range of applicability of
our method.


  We have recently proposed a mechanism of photon-axion oscillations as a way
of rendering supernovae dimmer without cosmic acceleration. Subsequently, it
has been argued that the intergalactic plasma may interfere adversely with this
mechanism by rendering the oscillations energy dependent. Here we show that
this energy dependence is extremely sensitive to the precise value of the free
electron density in the Universe. Decreasing the electron density by only a
factor of 4 is already sufficient to bring the energy dependence within the
experimental bounds. Models of the intergalactic medium show that for redshifts
z<1 about 97% of the total volume of space is filled with regions of density
significantly lower than the average density. From these models we estimate
that the average electron density in most of space is lower by at least a
factor of 15 compared to the estimate based on one half of all baryons being
uniformly distributed and ionized. Therefore the energy dependence of the
photon-axion oscillations is consistent with experiment, and the oscillation
model remains a viable alternative to the accelerating Universe for explaining
the supernova observations. Furthermore, the electron density does give rise to
a sufficiently large plasma frequency which cuts off the photon-axion mixing
above microwave frequencies, shielding the cosmic microwave photons from axion
conversions and significantly relaxing the lower bounds on the axion mass
implied by the oscillation model.


  We present new Large Binocular Telescope, Hubble Space Telescope, and Spitzer
Space Telescope data for the failed supernova candidate N6946-BH1. We also
report an unsuccessful attempt to detect the candidate with Chandra. The
~300,000 Lsun red supergiant progenitor underwent an outburst in 2009 and has
since disappeared in the optical. In the LBT data from May 2008 through October
2019, the upper limit on any increase in the R-band luminosity of the source is
2000 Lsun. HST and Spitzer observations show that the source continued to fade
in the near-IR and mid-IR, fading by approximately a factor of 2 between
October 2015 and September 2017 to 2900 Lsun at H band (F160W). Models of the
spectral energy distribution are inconsistent with a surviving star obscured
either by an ongoing wind or dust formed in the transient. The disappearance of
N6946-BH1 remains consistent with a failed supernova.


  We prove several results of the following general form: automorphisms of (or
actions of ${\mathbb{Z}}^d$ on) certain kinds of simple separable unital
C*-algebras $A$ which have a suitable version of the Rokhlin property are
generic among all automorphisms (or actions), or in a suitable class of
automorphisms. That is, the ones with the version of the Rokhlin property
contain a dense $G_{\delta}$-subset of the set of all such automorphisms (or
actions).
  Specifically, we prove the following. If $A$ is stable under tensoring with
the Jiang-Su algebra $Z,$ and has tracial rank zero, then automorphisms with
the tracial Rokhlin property are generic. If $A$ has tracial rank zero, or,
more generally, $A$ is tracially approximately divisible together with a
technical condition, then automorphisms with the tracial Rokhlin property are
generic among the approximately inner automorphisms. If $A$ is stable under
tensoring with the Cuntz algebra ${\mathcal{O}}_{\infty}$ or with a UHF algebra
of infinite type, then actions of ${\mathbb{Z}}^d$ on $A$ with the Rokhlin
property are generic among all actions of ${\mathbb{Z}}^d.$ We further give a
related but more restricted result for actions of finite groups.


  Optimal control of wheel loaders in short loading cycles is studied in this
paper. For modeling the wheel loader, the data from a validated diesel engine
model is used to find a control oriented mean value engine model. The driveline
is modeled as a switched system with three constant gear ratios (modes) of
$-60$ for backwarding, $60$ for forwarding, and zero for stopping. With these
three modes, the sequence of active modes in a short loading cycle is fixed as
backwarding, stopping, forwarding, and stopping. For the control part, it is
assumed that the optimal path is known a priori. Given the mode sequence, the
control objective is finding the optimal switching time instants between the
modes while the wheel loader tracks the optimal path. To solve the optimal
control problem, approximate dynamic programming is used. Simulation results
are provided to show the effectiveness of the solution.


  Two important classes of the quantum statistical model, the locally
quasi-classical model and the quasi-classical model, are introduced from the
estimation theoretical viewpoint, and they are characterized geometrically by
the vanishing conditions of the relative phase factor (RPF), implying the close
tie between Uhlmann parallel transport and the quantum estimation theory.


  The development of Digital Twins (DTs) represents a transformative advance
for simulating and optimizing complex systems in a controlled digital space.
Despite their potential, the challenge of constructing DTs that accurately
replicate and predict the dynamics of real-world systems remains substantial.
This paper introduces an intelligent framework for the construction and
evaluation of DTs, specifically designed to enhance the accuracy and utility of
DTs in testing algorithmic performance. We propose a novel construction
methodology that integrates deep learning-based policy gradient techniques to
dynamically tune the DT parameters, ensuring high fidelity in the digital
replication of physical systems. Moreover, the Mean STate Error (MSTE) is
proposed as a robust metric for evaluating the performance of algorithms within
these digital space. The efficacy of our framework is demonstrated through
extensive simulations that show our DT not only accurately mirrors the physical
reality but also provides a reliable platform for algorithm evaluation. This
work lays a foundation for future research into DT technologies, highlighting
pathways for both theoretical enhancements and practical implementations in
various industries.


  This article studies the global well-posedness for a class of defocusing,
generalized sixth-order Boussinesq equations, extending a previous result
obtained by Wang and Esfahani for the case when the nonlinear term is cubic.


  We say that $(x,y,z)\in Q^3$ is an associative triple in a quasigroup $Q(*)$
if $(x*y)*z=x*(y*z)$. Let $a(Q)$ denote the number of associative triples in
$Q$. It is easy to show that $a(Q)\ge |Q|$, and we call the quasigroup
maximally nonassociative if $a(Q)= |Q|$. It was conjectured that maximally
nonassociative quasigroups do not exist when $|Q|>1$. Dr\'apal and Lison\v{e}k
recently refuted this conjecture by proving the existence of maximally
nonassociative quasigroups for a certain infinite set of orders $|Q|$. In this
paper we prove the existence of maximally nonassociative quasigroups for a much
larger set of orders $|Q|$. Our main tools are finite fields and the Weil bound
on quadratic character sums. Unlike in the previous work, our results are to a
large extent constructive.


  We develop machinery to explicitly determine, in many instances, when the
difference $x^2-y^n$ is divisible only by powers of a given fixed prime. This
combines a wide variety of techniques from Diophantine approximation (bounds
for linear forms in logarithms, both archimedean and non-archimedean, lattice
basis reduction, methods for solving Thue-Mahler and $S$-unit equations, and
the Primitive Divisor Theorem of Bilu, Hanrot and Voutier) and classical
Algebraic Number Theory, with results derived from the modularity of Galois
representations attached to Frey-Hellegoaurch elliptic curves. By way of
example, we completely solve the equation \[ x^2+q^\alpha = y^n, \] where $2
\leq q < 100$ is prime, and $x, y, \alpha$ and $n$ are integers with $n \geq 3$
and $\gcd (x,y)=1$.


  Optical coherence tomography (OCT) is commonly used to analyze retinal layers
for assessment of ocular diseases. In this paper, we propose a method for
retinal layer segmentation and quantification of uncertainty based on Bayesian
deep learning. Our method not only performs end-to-end segmentation of retinal
layers, but also gives the pixel wise uncertainty measure of the segmentation
output. The generated uncertainty map can be used to identify erroneously
segmented image regions which is useful in downstream analysis. We have
validated our method on a dataset of 1487 images obtained from 15 subjects (OCT
volumes) and compared it against the state-of-the-art segmentation algorithms
that does not take uncertainty into account. The proposed uncertainty based
segmentation method results in comparable or improved performance, and most
importantly is more robust against noise.


  Cell detection and counting in the image-based ELISPOT and Fluorospot
immunoassays is considered a bottleneck. The task has remained hard to
automatize, and biomedical researchers often have to rely on results that are
not accurate. Previously proposed solutions are heuristic, and data-based
solutions are subject to a lack of objective ground truth data. In this paper,
we analyze a partial differential equations model for ELISPOT, Fluorospot, and
assays of similar design. This leads us to a mathematical observation model for
the images generated by these assays. We use this model to motivate a
methodology for cell detection. Finally, we provide a real-data example that
suggests that this cell detection methodology and a human expert perform
comparably.


  Spiking neural networks can compensate for quantization error by encoding
information either in the temporal domain, or by processing discretized
quantities in hidden states of higher precision. In theory, a wide dynamic
range state-space enables multiple binarized inputs to be accumulated together,
thus improving the representational capacity of individual neurons. This may be
achieved by increasing the firing threshold, but make it too high and sparse
spike activity turns into no spike emission. In this paper, we propose the use
of `threshold annealing' as a warm-up method for firing thresholds. We show it
enables the propagation of spikes across multiple layers where neurons would
otherwise cease to fire, and in doing so, achieve highly competitive results on
four diverse datasets, despite using binarized weights. Source code is
available at https://github.com/jeshraghian/snn-tha/


  We calculate temperature anisotropies of the cosmic microwave background
(CMB) for several initial power spectra of density perturbations with a
built-in scale suggested by recent optical data on the spatial distribution of
rich clusters of galaxies. Using cosmological models with different values of
spectral index, baryon fraction, Hubble constant and cosmological constant, we
compare the calculated radiation power spectrum with the CMB temperature
anisotropies measured by the Saskatoon experiment. We show that spectra with a
sharp peak at 120 h^{-1} Mpc are in agreement with the Saskatoon data. The
combined evidence from cluster and CMB data favours the presence of a peak and
a subsequent break in the initial matter power spectrum. Such feature is
similar to the prediction of an inflationary model where an inflaton field is
evolving through a kink in the potential.


  A wide variety of phenomena of engineering and scientific interest are of a
continuous-time nature and can be modeled by stochastic differential equations
(SDEs), which represent the evolution of the uncertainty in the states of a
system. For systems of this class, some parameters of the SDE might be unknown
and the measured data often includes noise, so state and parameter estimators
are needed to perform inference and further analysis using the system state
path. The distributions of SDEs which are nonlinear or subject to non-Gaussian
measurement noise do not admit tractable analytic expressions, so state and
parameter estimators for these systems are often approximations based on
heuristics, such as the extended and unscented Kalman smoothers, or the
prediction error method using nonlinear Kalman filters. However, the Onsager
Machlup functional can be used to obtain fictitious densities for the
parameters and state-paths of SDEs with analytic expressions. In this thesis,
we provide a unified theoretical framework for maximum a posteriori (MAP)
estimation of general random variables, possibly infinite-dimensional, and show
how the Onsager--Machlup functional can be used to construct the joint MAP
state-path and parameter estimator for SDEs. We also prove that the minimum
energy estimator, which is often thought to be the MAP state-path estimator,
actually gives the state paths associated to the MAP noise paths. Furthermore,
we prove that the discretized MAP state-path and parameter estimators, which
have emerged recently as powerful alternatives to nonlinear Kalman smoothers,
converge hypographically as the discretization step vanishes. Their
hypographical limit, however, is the MAP estimator for SDEs when the
trapezoidal discretization is used and the minimum energy estimator when the
Euler discretization is used, associating different interpretations to each
discretized estimate.


  In this paper, we provide upper bounds on the d2 distance between a large
class of functionals of a multivariate compound Hawkes process and a given
Gaussian vector. This is proven using Malliavin's calculus defined on an
underlying Poisson embedding. The upper bound is then used to infer the speed
of convergence of Central Limit Theorems for the multivariate compound Hawkes
process with exponential kernels as the observation time T goes to infinity.


  In this paper we deal with the problem of regularity for non hypo-elliptic
partial differential equations with polynomial coefficients. An operator $A$ on
on the space of tempered distributions $\mathcal{S}^\prime$ is regular if $u$
belongs to the Schwartz class $\mathcal S$ whenever $Au\in \mathcal S$. By
using tensor products of topological vector spaces and a kind of Wigner
transform we reduce the study of regularity of a non hypo-elliptic differential
operator, like the twisted laplacian, to a hypo-elliptic one, like the harmonic
oscillator.


  Like the two-photon and two-gluon decays of the $P$-wave $\chi_{c0,2}$ and
$\chi_{b0,2}$ charmonium state for which the Born term produces a very simple
decgays amplitude in terms of an effective Lagrangian with two-quark local
operator, the Born term for the processes $c\bar{d} \to (\pi,K) \ell \nu $ and
$b \bar{d}\to (\pi, K) \ell\nu $, could also produce the $D$ and $B$ meson
semileptonic decays with the light meson $\pi, K$ in the final state. In this
approach to heavy-light meson form factors with the $\pi$, K meson treated as
Goldstone boson, a simple expression is found for the decays form factors,
given as~: $ f_{+}(0)/(1 -q^{2}/(m_{H}^{2}+ m_{\pi}^{2}))$, with $H=D,B$ for
$D,B \to \pi$ form factors, and $f_{+}(0)/(1 -q^{2}/(m_{H}^{2}+ m_{K}^{2}))$
for $B,D\to K$ form factor. The purpose of this paper is to show that this
expression for the form factors could describe rather well the $q^{2}$-
behaviour observed in the BaBar, Belle and BESIII measurements and lattice
simulation. In particular, the $D\to K$ form factors are in good agreement with
the measured values in the whole range of $q^{2}$ showing evidence for $SU(3)$
breaking with the presence of $m_{K}^{2}$ term in the quark propagator, but
some corrections to the Born term are needed at large $q^{2}$ for $D,B \to \pi$
form factors.


  Aluminum Indium Nitride (AlInN) alloys offer great potential for photovoltaic
devices thanks to their wide direct bandgap energy that covers the solar
spectrum from 0.7 eV (InN) to 6.2 eV (AlN), and their superior resistance to
high temperatures and high-energy particles. In this paper, we report the
design of AlInN on silicon heterojunctions, with the aim to explore their
potential for solar cell devices through the analysis and optimization of the
properties of the AlInN on Si heterojunction. In particular, we study the
influence of the AlInN bandgap energy, AlInN thickness and carrier
concentration, silicon surface recombination, interface defects and Si wafer
quality on the photovoltaic properties (conversion efficiency and external
quantum efficiency) of the AlInN on Si heterojunctions. The effect of
introducing an anti-reflective coating is also studied. Optimized AlInN on Si
heterostructure shows a conversion efficiency of 18% under 1-sun AM1.5G
illumination for low-quality Si wafers, which increases to 23.6% for
high-quality Si wafers and incorporating a properly designed anti-reflective
layer. In comparison with standard Si solar cells without AlInN, the external
quantum efficient of the devices increases for wavelengths below 500 nm, making
them appealing for space applications. These results lead to the AlInN on Si
heterojunction a promising future as a novel technology for solar cell devices.


  We show that, given a closed subset $E$ of the unit circle of Lebesgue
measure zero, there exists a positive sequence $u_n\to\infty$ with the
following property: if $T$ is a Hilbert-space contraction such that
$\sigma(T)\subset E$ and $\|T^{-n}\|=O(u_n)$ and rank$(I-T^*T)<\infty$, then
$T$ is a unitary operator. We further show that the condition of measure zero
is sharp.


  Critical gravitational collapse and self similarity are used to probe the
mass distribution of subsolar objects. We demonstrate that at very low mass the
distribution is given by a power law, with an exponent opposite in sign to that
observed at high-mass regime. We further show that the value of this low-mass
exponent is in principle calculable via dynamical systems theory applied to
gravitational collapse. Qualitative agreement between numerical experiments and
observational data is good.


  We computed the power spectrum of weak cosmic shear in models with
non-Gaussian primordial density fluctuations. Cosmological initial conditions
deviating from Gaussianity have recently attracted much attention in the
literature, especially with respect to their effect on the formation of
non-linear structures and because of the bounds that they can put on the
inflationary epoch. The fully non-linear matter power spectrum was evaluated
with the use of the physically motivated, semi-analytic halo model, where the
mass function and linear halo bias were suitably corrected for non-Gaussian
cosmologies. In agreement with previous work, we found that a level of
non-Gaussianity compatible with CMB bounds and with positive skewness produces
an increase in power of the order of a few percent at intermediate scales. We
then used the matter power spectrum, together with observationally motivated
background source redshift distributions in order to compute the cosmological
weak lensing power spectrum. We found that the degree of deviation from the
power spectrum of the reference Gaussian model is small compared to the
statistical error expected from even future weak lensing surveys. However,
summing the signal over a large range of multipoles can beat down the noise,
bringing to a significant detection of non-Gaussianity at the level of
$|f_\mathrm{NL}| \simeq $ few tens, when all other cosmological parameters are
held fixed. Finally, we have shown that the constraints on the level of
non-Gaussianity can be improved by $\sim 20%$ with the use of weak lensing
tomography.


  The dispersion measure (DM) of fast radio bursts (FRBs) provides a unique way
to probe ionised baryons in the intergalactic medium (IGM). Cosmological models
with different parameters lead to different DM-redshift ($\mathrm{DM}-z$)
relations. Additionally, the over/under-dense regions in the IGM and the
circumgalactic medium of intervening galaxies lead to scatter around the mean
$\mathrm{DM}-z$ relations. We have used the Evolution and Assembly of GaLaxies
and their Environments (EAGLE) simulations to measure the mean $\mathrm{DM}-z$
relation and the scatter around it using over one billion lines-of-sight
between redshifts $0<z<3$. We investigated two techniques to estimate
line-of-sight DM: `pixel scrambling' and `box transformations'. We find that
using box transformations (a technique from the literature) causes strong
correlations due to repeated replication of structure. Comparing a linear and
non-linear model, we find that the non-linear model with cosmological
parameters, provides a better fit to the $\mathrm{DM}-z$ relation. The
differences between these models are the most significant at low redshifts
($z<0.5$). The scatter around the $\mathrm{DM}-z$ relation is highly
asymmetric, especially at low redshift $\left(z<0.5\right)$, and becomes more
Gaussian as redshift approaches $z\sim3$, the limit of this study. The increase
in Gaussianity with redshift is indicative of the large scale structures that
is better probed with longer lines-of-sight. The minimum simulation size
suitable for investigations into the scatter around the $\mathrm{DM}-z$
relation is 100~comoving~Mpc. The $\mathrm{DM}-z$ relation measured in EAGLE is
available with an easy-to-use python interface in the open-source FRB redshift
estimation package FRUITBAT.


  We have calculated the cross section of the process e^+e^- \to \gamma\gamma
\to b\bar{b} in the littlest Higgs model with T parity (LHT). We find that, for
the favorable parameters, the total cross section \sigma(e^+e^- \to
\gamma\gamma \to b\bar{b}) is sensitive to the breaking scale f, mixing
parameter x_L, the masses of the mirror quarks m_{Hi}, and the relative
correction of the LHT model is a few percent to dozens of percent. The cross
section is significantly larger than the corresponding results in the standard
model and in the other typical new physics models. Therefore the prediction in
the LHT model is quite different from the predictions in other new physics
models and such a process is really interesting in searching for the signs of
the LHT model.


  We present an open-source accessory for the NAO robot, which enables to test
computationally demanding algorithms in an external platform while preserving
robot's autonomy and mobility. The platform has the form of a backpack, which
can be 3D printed and replicated, and holds an ODROID XU4 board to process
algorithms externally with ROS compatibility. We provide also a software bridge
between the B-Human's framework and ROS to have access to the robot's sensors
close to real-time. We tested the platform in several robotics applications
such as data logging, visual SLAM, and robot vision with deep learning
techniques. The CAD model, hardware specifications and software are available
online for the benefit of the community:
https://github.com/uchile-robotics/nao-backpack


  We show that representations of the group of spacetime diffeomorphism and the
Dirac algebra both arise in a phase-space histories version of canonical
general relativity. This is the general-relativistic analogue of the novel time
structure introduced previously in history theory: namely, the existence in
non-relativistic physics of two types of time translation; and the existence in
relativistic field theory of two distinct Poincare groups.


  Simulated tempering is popular method of allowing MCMC algorithms to move
between modes of a multimodal target density {\pi}. One problem with simulated
tempering for multimodal targets is that the weights of the various modes
change for different inverse-temperature values, sometimes dramatically so. In
this paper, we provide a fix to overcome this problem, by adjusting the mode
weights to be preserved (i.e., constant) over different inverse-temperature
settings. We then apply simulated tempering algorithms to multimodal targets
using our mode weight correction. We present simulations in which our
weight-preserving algorithm mixes between modes much more successfully than
traditional tempering algorithms. We also prove a diffusion limit for an
version of our algorithm, which shows that under appropriate assumptions, our
algorithm mixes in time O(d [log d]^2).


  In fluid-structure interaction problems, some people use a penalty method for
positioning the structure inside the fluid. This is usually performed by
considering that the fluid is very stiff or/and very heavy at the place
occupied by the structure. These methods are very convenient for the
programming point of view but lead to ill conditioned operators. This is a
drawback in the numerical solution methods. In particular the forces applied to
the structure by the surrounding flow are not accurately estimated because the
penalty parameter -- which is a very large number -- appears in their
expressions. We suggest in this paper a mathematical analysis of the
difficulties encountered and we discuss how the penalty-duality method of D.
Bertsekas can be an interesting alternative to overcome them.


  Simulations of condensed matter systems often focus on the dynamics of a few
distinguished components but require integrating the dynamics of the full
system. A prime example is a molecular dynamics simulation of a (macro)molecule
in solution, where both the molecules(s) and the solvent dynamics needs to be
integrated. This renders the simulations computationally costly and often
unfeasible for physically or biologically relevant time scales. Standard coarse
graining approaches are capable of reproducing equilibrium distributions and
structural features but do not properly include the dynamics. In this work, we
develop a stochastic data-driven coarse-graining method inspired by the
Mori-Zwanzig formalism. This formalism shows that macroscopic systems with a
large number of degrees of freedom can in principle be well described by a
small number of relevant variables plus additional noise and memory terms. Our
coarse-graining method consists of numerical integrators for the distinguished
components of the system, where the noise and interaction terms with other
system components are substituted by a random variable sampled from a
data-driven model. Applying our methodology on three different systems -- a
distinguished particle under a harmonic potential and under a bistable
potential; and a dimer with two metastable configurations -- we show that the
resulting coarse-grained models are not only capable of reproducing the correct
equilibrium distributions but also the dynamic behavior due to temporal
correlations and memory effects. Our coarse-graining method requires data from
full-scale simulations to be parametrized, and can in principle be extended to
different types of models beyond Langevin dynamics.


  Emerging autonomous vehicles (AV) can either supplement the public
transportation (PT) system or compete with it. This study examines the
competitive perspective where both AV and PT operators are profit-oriented with
dynamic adjustable supply strategies under five regulatory structures regarding
whether the AV operator is allowed to change the fleet size and whether the PT
operator is allowed to adjust headway. Four out of the five scenarios are
constrained competition while the other one focuses on unconstrained
competition to find the Nash Equilibrium. We evaluate the competition process
as well as the system performance from the standpoints of four stakeholders --
the AV operator, the PT operator, passengers, and the transport authority. We
also examine the impact of PT subsidies on the competition results including
both demand-based and supply-based subsidies. A heuristic algorithm is proposed
to update supply strategies for AV and PT based on the operators' historical
actions and profits. An agent-based simulation model is implemented in the
first-mile scenario in Tampines, Singapore. We find that the competition can
result in higher profits and higher system efficiency for both operators
compared to the status quo. After the supply updates, the PT services are
spatially concentrated to shorter routes feeding directly to the subway station
and temporally concentrated to peak hours. On average, the competition reduces
the travel time of passengers but increases their travel costs. Nonetheless,
the generalized travel cost is reduced when incorporating the value of time.
With respect to the system efficiency, the bus supply adjustment increases the
average vehicle load and reduces the total vehicle kilometer traveled measured
by the passenger car equivalent (PCE), while the AV supply adjustment does the
opposite.


  Image steganography refers to the process of hiding information inside
images. Steganalysis is the process of detecting a steganographic image. We
introduce a steganalysis approach that uses an ensemble color space model to
obtain a weighted concatenated feature activation map. The concatenated map
helps to obtain certain features explicit to each color space. We use a
levy-flight grey wolf optimization strategy to reduce the number of features
selected in the map. We then use these features to classify the image into one
of two classes: whether the given image has secret information stored or not.
Extensive experiments have been done on a large scale dataset extracted from
the Bossbase dataset. Also, we show that the model can be transferred to
different datasets and perform extensive experiments on a mixture of datasets.
Our results show that the proposed approach outperforms the recent state of the
art deep learning steganalytical approaches by 2.32 percent on average for 0.2
bits per channel (bpc) and 1.87 percent on average for 0.4 bpc.


  Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation.


  The global degradation of water resources is a matter of great concern,
especially for the survival of humanity. The effective monitoring and
management of existing water resources is necessary to achieve and maintain
optimal water quality. The prediction of the quality of water resources will
aid in the timely identification of possible problem areas and thus increase
the efficiency of water management. The purpose of this research is to develop
a water quality prediction model based on water quality parameters through the
application of a specialised recurrent neural network (RNN), Long Short-Term
Memory (LSTM) and the use of historical water quality data over several years.
Both multivariate single and multiple step LSTM models were developed, using a
Rectified Linear Unit (ReLU) activation function and a Root Mean Square
Propagation (RMSprop) optimiser was developed. The single step model attained
an error of 0.01 mg/L, whilst the multiple step model achieved a Root Mean
Squared Error (RMSE) of 0.227 mg/L.


  Writing $\mathbb A$ for the 2-primary Steenrod algebra, which is the algebra
of stable natural endomorphisms of the mod 2 cohomology functor on topological
spaces. Working at the prime 2, computing the cohomology of $\mathbb A$ is an
important problem of Algebraic topology, because it is the initial page of the
Adams spectral sequence converging to stable homotopy groups of the spheres. A
relatively efficient tool to describe this cohomology is the Singer algebraic
transfer of rank $n$ in [Math. Z. 202 (1989), 493-523], which passes from a
certain subquotient of a divided power algebra to the cohomology of $\mathbb
A.$ Singer predicted that this transfer is a monomorphism, but this remains
open for $n\geq 4.$ This short note is to verify the conjecture in the ranks 4
and 5 and some generic degrees.


  For an integer $n$, write $X_n(K)$ for the 4-manifold obtained by attaching a
2-handle to the 4-ball along the knot $K\subset S^3$ with framing $n$. It is
known that if $n< \overline{\text{tb}}(K)$, then $X_n(K)$ admits the structure
of a Stein domain, and moreover the adjunction inequality implies there is an
upper bound on the value of $n$ such that $X_n(K)$ is Stein. We provide
examples of knots $K$ and integers $n\geq \overline{\text{tb}}(K)$ for which
$X_n(K)$ is Stein, answering an open question in the field. In fact, our family
of examples shows that the largest framing such that the manifold $X_n(K)$
admits a Stein structure can be arbitrarily larger than
$\overline{\text{tb}}(K)$. We also provide an upper bound on the Stein framings
for $K$ that is typically stronger than that coming from the adjunction
inequality.


  We continue the study of the following Hamiltonian equation on the Hardy
space of the circle, $$i\partial _tu=\Pi(|u|^2u)\ ,$$ where $\Pi $ denotes the
Szeg\"o projector. This equation can be seen as a toy model for totally non
dispersive evolution equations. In a previous work, we proved that this
equation admits a Lax pair, and that it is completely integrable. In this
paper, we construct the action-angle variables, which reduces the explicit
resolution of the equation to a diagonalisation problem. As a consequence, we
solve an inverse spectral problem for Hankel operators. Moreover, we establish
the stability of the corresponding invariant tori. Furthermore, from the
explicit formulae, we deduce the classification of orbitally stable and
unstable traveling waves.


  We argued that the standard field scalar potential couldn't be widely used
for getting the adequate galaxies' curve lines and determining the profiles of
dark matter their halo. For discovering the global properties of scalar fields
that can describe the observable characteristics of dark matter on the
cosmological space and time scales, we propose the simplest form of central
symmetric potential celestial - mechanical type, i.e. U(\phi) = -\mu/\phi. It
was shown that this potential allows get rather satisfactorily dark matter
profiles and rotational curves lines for dwarf galaxies. The good agreement
with some previous results, based on the N-body simulation method, was pointed
out. A new possibility of dwarf galaxies' masses estimation was given, also.


  We consider the advection-diffusion equation on $\mathbb{T}^2$ with a
Lipschitz and time-periodic velocity field that alternates between two
piecewise linear shear flows. We prove enhanced dissipation on the timescale
$|\log \nu|$, where $\nu$ is the diffusivity parameter. This is the optimal
decay rate as $\nu \to 0$ for uniformly-in-time Lipschitz velocity fields. We
also establish exponential mixing for the $\nu = 0$ problem.


  We propose a novel topic discovery algorithm for unlabeled images based on
the bag-of-words (BoW) framework. We first extract a dictionary of visual words
and subsequently for each image compute a visual word occurrence histogram. We
view these histograms as rows of a large matrix from which we extract sparse
principal components (PCs). Each PC identifies a sparse combination of visual
words which co-occur frequently in some images but seldom appear in others.
Each sparse PC corresponds to a topic, and images whose interference with the
PC is high belong to that topic, revealing the common parts possessed by the
images. We propose to solve the associated sparse PCA problems using an
Alternating Maximization (AM) method, which we modify for purpose of
efficiently extracting multiple PCs in a deflation scheme. Our approach attacks
the maximization problem in sparse PCA directly and is scalable to
high-dimensional data. Experiments on automatic topic discovery and category
prediction demonstrate encouraging performance of our approach.


  In this paper, we consider the universality of the local eigenvalue
statistics of random matrices. Our main result shows that these statistics are
determined by the first four moments of the distribution of the entries. As a
consequence, we derive the universality of eigenvalue gap distribution and
$k$-point correlation and many other statistics (under some mild assumptions)
for both Wigner Hermitian matrices and Wigner real symmetric matrices.


  Over the past two decades, numerous studies have demonstrated how less
predictable (i.e., higher surprisal) words take more time to read. In general,
these studies have implicitly assumed the reading process is purely responsive:
Readers observe a new word and allocate time to process it as required. We
argue that prior results are also compatible with a reading process that is at
least partially anticipatory: Readers could make predictions about a future
word and allocate time to process it based on their expectation. In this work,
we operationalize this anticipation as a word's contextual entropy. We assess
the effect of anticipation on reading by comparing how well surprisal and
contextual entropy predict reading times on four naturalistic reading datasets:
two self-paced and two eye-tracking. Experimentally, across datasets and
analyses, we find substantial evidence for effects of contextual entropy over
surprisal on a word's reading time (RT): in fact, entropy is sometimes better
than surprisal in predicting a word's RT. Spillover effects, however, are
generally not captured by entropy, but only by surprisal. Further, we
hypothesize four cognitive mechanisms through which contextual entropy could
impact RTs -- three of which we are able to design experiments to analyze.
Overall, our results support a view of reading that is not just responsive, but
also anticipatory.


  The peer-to-peer (P2P) economy relies on establishing trust in distributed
networked systems, where the reliability of a user is assessed through digital
peer-review processes that aggregate ratings into reputation scores. Here we
present evidence of a network effect which biases digital reputation, revealing
that P2P networks display exceedingly high levels of reciprocity. In fact,
these are much higher than those compatible with a null assumption that
preserves the empirically observed level of agreement between all pairs of
nodes, and rather close to the highest levels structurally compatible with the
networks' reputation landscape. This indicates that the crowdsourcing process
underpinning digital reputation can be significantly distorted by the attempt
of users to mutually boost reputation, or to retaliate, through the exchange of
ratings. We uncover that the least active users are predominantly responsible
for such reciprocity-induced bias, and that this fact can be exploited to
obtain more reliable reputation estimates. Our findings are robust across
different P2P platforms, including both cases where ratings are used to vote on
the content produced by users and to vote on user profiles.


  On the off-the-shelf navigational assistance devices, the localization
precision is limited to the signal error of global navigation satellite system
(GNSS). During travelling outdoors, the inaccurately localization perplexes
visually impaired people, especially at key positions, such as gates, bus
stations or intersections. The visual localization is a feasible approach to
improving the positioning precision of assistive devices. Using multiple image
descriptors, the paper proposes a robust and efficient visual localization
algorithm, which takes advantage of priori GNSS signals and multi-modal images
to achieve the accurate localization of key positions. In the experiments, we
implement the approach on the wearable system and test the performance of
visual localization under practical scenarios.


  The study solves the general solution to 2D steady Navier-Stokes equation for
incompressible flow without vorticity diffusion, which is more general than
Stokes flow. In order to obtain the general solution, two potential functions
are introduced to express the velocity: a vector potential describing the
rotational incompressible flow and a scalar potential describing the
irrotational incompressible flow. The results show that the vorticity equation
expressed with potential functions is a biharmonic function, which means that
the potential functions describing the flow field are polynomials of no more
than fourth degree. For a steady unidirectional shear flow, the velocity and
pressure fields can be described with the vector potential expressed by a
polynomial of third degree. For non unidirectional two-dimensional steady shear
flow, there may be four independent parameters in the two potential functions.