  3-minute oscillations in the chromosphere are attributed to both slow
magnetoacoustic waves propagating from the photosphere, and to oscillations
generated within the chromosphere itself at its natural frequency as a response
to a disturbance. Here we present an investigation of the spatial and temporal
behavior of the chromospheric 3-minute oscillations before, during, and after
the SOL2011-02-15T01:56 X2.2 flare. Observations in ultraviolet emission
centered on 1600 and 1700 Angstroms obtained at 24- second cadence from the
Atmospheric Imaging Assembly on board the Solar Dynamics Observatory are used
to create power maps as functions of both space and time. We observe higher
3-minute power during the flare, spatially concentrated in small areas 10
pixels (4 arcseconds) across. This implies that the chromospheric plasma is not
oscillating globally as a single body. The locations of increased 3-minute
power are consistent with observations of HXR flare emission from previous
studies, suggesting that these small areas are manifestations of the
chromosphere responding to injection of energy by nonthermal particles. This
supports the theory that the chromosphere oscillates at the acoustic cutoff
frequency in response to a disturbance.


  In this article we study a new kind of unbounded solutions to the Novikov
equation, found via a Lie symmetry analysis. These solutions exhibit peakon
creation, i.e., these solutions are smooth up until a certain finite time, at
which a peak is created. We show that the functions are still weak solutions
for those times where the peak lives. We also find similar unbounded solutions
with peakon creation in the related Camassa-Holm equation, by making an ansatz
inspired by the Novikov solutions. Finally, we see that the same ansatz for the
Degasperis-Procesi equation yields unbounded solutions where a peakon is
present for all times.


  The effect of two- and three-body interactions on the modulation instability
(MI) domain formation of a spin-orbit (SO) and Rabi-coupled Bose-Einstein
condensate is studied within a quasi-one-dimensional model. To this aim, we
perform numerical and analytical investigations of the associated dispersion
relations derived from the corresponding coupled Gross-Pitaevskii equation. The
interplay between the linear (SO and Rabi) couplings with the nonlinear
cubic-quintic interactions are explored in the mixture, considering miscible
and immiscible configurations, with a focus on the impact in the analysis of
experimental realizations with general binary coupled systems, in which
nonlinear interactions can be widely varied together with linear couplings.


  In recent years methods from optimal linear experimental design have been
leveraged to obtain state of the art results for linear bandits. A design
returned from an objective such as $G$-optimal design is actually a probability
distribution over a pool of potential measurement vectors. Consequently, one
nuisance of the approach is the task of converting this continuous probability
distribution into a discrete assignment of $N$ measurements. While
sophisticated rounding techniques have been proposed, in $d$ dimensions they
require $N$ to be at least $d$, $d \log(\log(d))$, or $d^2$ based on the
sub-optimality of the solution. In this paper we are interested in settings
where $N$ may be much less than $d$, such as in experimental design in an RKHS
where $d$ may be effectively infinite. In this work, we propose a rounding
procedure that frees $N$ of any dependence on the dimension $d$, while
achieving nearly the same performance guarantees of existing rounding
procedures. We evaluate the procedure against a baseline that projects the
problem to a lower dimensional space and performs rounding which requires $N$
to just be at least a notion of the effective dimension. We also leverage our
new approach in a new algorithm for kernelized bandits to obtain state of the
art results for regret minimization and pure exploration. An advantage of our
approach over existing UCB-like approaches is that our kernel bandit algorithms
are also robust to model misspecification.


  We show that the tropicalization of a connected variety over a higher rank
valued field is a path connected topological space. This establishes an
affirmative answer to a question posed by Banerjee. Higher rank tropical
varieties are studied as the images of "Hahn analytifications", introduced in
this paper. A Hahn analytification is a space of valuations on a scheme over a
higher rank valued field. We prove that the Hahn analytification is related to
higher rank tropicalization by means of an inverse limit theorem, extending
well-known results in the non-Archimedean case. We also establish comparison
results between the Hahn analytification and the Huber and Berkovich
analytifications, as well as the Hrushovski-Loeser stable completion.


  We provide a general and tractable framework under which all multiple yield
curve modeling approaches based on affine processes, be it short rate, Libor
market, or HJM modeling, can be consolidated. We model a numeraire process and
multiplicative spreads between Libor rates and simply compounded OIS rates as
functions of an underlying affine process. Besides allowing for ordered spreads
and an exact fit to the initially observed term structures, this general
framework leads to tractable valuation formulas for caplets and swaptions and
embeds all existing multi-curve affine models. The proposed approach also gives
rise to new developments, such as a short rate type model driven by a Wishart
process, for which we derive a closed-form pricing formula for caplets. The
empirical performance of two specifications of our framework is illustrated by
calibration to market data.


  In this paper we study the qualitative features induces by corrections to GR
coming from String Theory, on the shadows of rotating black holes. We deal with
the slowly rotating black hole solutions up to order $\mathcal{O}(a^3)$, to
first order in $\alpha'$, including also the dilaton. We provide a detailed
characterization of the geometry, as well as the innermost stable circular
orbit (ISCO) and photon ring, and then we proceed to obtain the black hole
images within the relativistic thin-disk model. We characterize the images by
computing the diameter, displacement and asymmetry. A comparison with the Kerr
case, indicates that all these quantities grow due to the $\alpha'$ correction,
and that the departure from GR for different observable is enhanced depending
on the angle of view, namely for the diameter the maximum departure is obtained
when the system is face-on, while for the displacement and asymmetry the
departure from GR is maximized for edge-on point of view.


  Relational particle mechanics is useful for modelling whole-universe issues
such as quantum cosmology or the problem of time in quantum gravity, including
some aspects outside the reach of comparably complex minisuperspace models. In
this article, we consider the mechanics of pure shape and not scale of 4
particles on a line, so that the only physically significant quantities are
ratios of relative separations between the constituents' physical objects. Many
of our ideas and workings extend to the N-particle case. As such models'
configurations resemble depictions of metro lines in public transport maps, we
term them `N-stop metrolands'. This 4-stop model's configuration space is a
2-sphere, from which our metroland mechanics interpretation is via the `cubic'
tessellation. This model yields conserved quantities which are mathematically
SO(3) objects like angular momenta but are physically relative dilational
momenta (i.e. coordinates dotted with momenta). We provide and interpret
various exact and approximate classical and quantum solutions for 4-stop
metroland; from these results one can construct expectations and spreads of
shape operators that admit interpretations as relative sizes and the
`homogeneity of the model universe's contents', and also objects of
significance for the problem of time in quantum gravity (e.g. in the naive
Schrodinger and records theory timeless approaches).


  We propose a generalized multiscale finite element method (GMsFEM) based on
clustering algorithm to study the elliptic PDEs with random coefficients in the
multi-query setting. Our method consists of offline and online stages. In the
offline stage, we construct a small number of reduced basis functions within
each coarse grid block, which can then be used to approximate the multiscale
finite element basis functions. In addition, we coarsen the corresponding
random space through a clustering algorithm. In the online stage, we can obtain
the multiscale finite element basis very efficiently on a coarse grid by using
the pre-computed multiscale basis. The new GMsFEM can be applied to multiscale
SPDE starting with a relatively coarse grid, without requiring the coarsest
grid to resolve the smallest-scale of the solution. The new method offers
considerable savings in solving multiscale SPDEs. Numerical results are
presented to demonstrate the accuracy and efficiency of the proposed method for
several multiscale stochastic problems without scale separation.


  Background: In this paper we present the approaches and methods employed in
order to deal with a large scale multi-label semantic indexing task of
biomedical papers. This work was mainly implemented within the context of the
BioASQ challenge of 2014. Methods: The main contribution of this work is a
multi-label ensemble method that incorporates a McNemar statistical
significance test in order to validate the combination of the constituent
machine learning algorithms. Some secondary contributions include a study on
the temporal aspects of the BioASQ corpus (observations apply also to the
BioASQ's super-set, the PubMed articles collection) and the proper adaptation
of the algorithms used to deal with this challenging classification task.
Results: The ensemble method we developed is compared to other approaches in
experimental scenarios with subsets of the BioASQ corpus giving positive
results. During the BioASQ 2014 challenge we obtained the first place during
the first batch and the third in the two following batches. Our success in the
BioASQ challenge proved that a fully automated machine-learning approach, which
does not implement any heuristics and rule-based approaches, can be highly
competitive and outperform other approaches in similar challenging contexts.


  We discuss a time-harmonic inverse scattering problem for the Helmholtz
equation with compactly supported penetrable and possibly inhomogeneous
scattering objects in an unbounded homogeneous background medium, and we
develop a monotonicity relation for the far field operator that maps
superpositions of incident plane waves to the far field patterns of the
corresponding scattered waves. We utilize this monotonicity relation to
establish novel characterizations of the support of the scattering objects in
terms of the far field operator. These are related to and extend corresponding
results known from factorization and linear sampling methods to determine the
support of unknown scattering objects from far field observations of scattered
fields. An attraction of the new characterizations is that they only require
the refractive index of the scattering objects to be above or below the
refractive index of the background medium locally and near the boundary of the
scatterers. An important tool to prove these results are so-called localized
wave functions that have arbitrarily large norm in some prescribed region while
at the same time having arbitrarily small norm in some other prescribed region.
We present numerical examples to illustrate our theoretical findings.


  The extinction profiles in Gamma-Ray Burst (GRB) afterglow spectral energy
distributions (SEDs) are usually described by the Small Magellanic Cloud
(SMC)-type extinction curve. In different empirical extinction laws, the
total-to-selective extinction, RV, is an important quantity because of its
relation to dust grain sizes and compositions. We here analyse a sample of 17
GRBs (0.34<z<7.84) where the ultraviolet to near-infrared spectroscopic
observations are available through the VLT/X-shooter instrument, giving us an
opportunity to fit individual extinction curves of GRBs for the first time. Our
sample is compiled on the basis that multi-band photometry is available around
the X-shooter observations. The X-shooter data are combined with the Swift
X-ray data and a single or broken power-law together with a parametric
extinction law is used to model the individual SEDs. We find 10 cases with
significant dust, where the derived extinction, AV, ranges from 0.1-1.0mag. In
four of those, the inferred extinction curves are consistent with the SMC
curve. The GRB individual extinction curves have a flat RV distribution with an
optimal weighted combined value of RV = 2.61+/-0.08 (for seven broad coverage
cases). The 'average GRB extinction curve' is similar to, but slightly steeper
than the typical SMC, and consistent with the SMC Bar extinction curve at ~95%
confidence level. The resultant steeper extinction curves imply populations of
small grains, where large dust grains may be destroyed due to GRB activity.
Another possibility could be that young age and/or lower metallicities of GRBs
environments are responsible for the steeper curves.


  The celebrated area-entropy formula for black holes has provided the most
important clue in the search for the elusive theory of quantum gravity. We
explore the possibility that the (linear) area-entropy relation acquires some
smaller corrections. Using the Boltzmann-Einstein formula, we rule out the
possibility for a power-law correction, and provide severe constraints on the
coefficient of a possible log-area correction. We argue that a non-zero
logarithmic correction to the area-entropy relation, would also imply a
modification of the area-mass relation for quantum black holes.


  In this paper, we use what we call the shift operator so that general delay
dynamic equations of the form \[
x^{\Delta}(t)=a(t)x(t)+b(t)x(\delta_{-}(h,t))\delta_{-}^{\Delta}% (h,t),\ \ \
t\in\lbrack t_{0},\infty)_{\mathbb{T}}% \] can be analyzed with respect to
stability and existence of solutions. By means of the shift operators we define
a general delay function opening an avenue for the construction of Lyapunov
functional on time scales. Thus, we use the Lyapunov's direct method to obtain
inequalities that lead to stability and instability. Therefore, we extend and
unify stability analysis of delay differential, delay difference, delay
$h-$difference, and delay $q-$difference equations which are the most important
particular cases of our delay dynamic equation. \textbf{Keywords}: Delay
dynamic equation, instability, shift operators, stability, time scales.


  This paper develops a new mathematical framework that enables nonparametric
joint semantic and geometric representation of continuous functions using data.
The joint embedding is modeled by representing the processes in a reproducing
kernel Hilbert space. The functions can be defined on arbitrary smooth
manifolds where the action of a Lie group aligns them. The continuous functions
allow the registration to be independent of a specific signal resolution. The
framework is fully analytical with a closed-form derivation of the Riemannian
gradient and Hessian. We study a more specialized but widely used case where
the Lie group acts on functions isometrically. We solve the problem by
maximizing the inner product between two functions defined over data, while the
continuous action of the rigid body motion Lie group is captured through the
integration of the flow in the corresponding Lie algebra. Low-dimensional cases
are derived with numerical examples to show the generality of the proposed
framework. The high-dimensional derivation for the special Euclidean group
acting on the Euclidean space showcases the point cloud registration and
bird's-eye view map registration abilities. An implementation of this framework
for RGB-D cameras outperforms the state-of-the-art robust visual odometry and
performs well in texture and structure-scarce environments.


  Based on generalized holographic formalism, we establish a holographic
realization of constant roll inflation during the early universe, where the
corresponding cut-off depends on the Hubble parameter and its derivatives (up
to the second order). The viability of this holographic constant roll inflation
with respect to the Planck data in turn puts a certain bound on the infrared
cut-off at the time of horizon crossing. Such holographic correspondence of
constant roll inflation is extended to the scenario where the infrared cut-off
is corrected by the ultraviolet one, which may originate due to quantum
effects. Besides the mere inflation, we further propose the holographic
realization of an $unified$ cosmic scenario from constant roll inflation (at
the early time) to the dark energy era (at the late time) with an intermediate
radiation dominated era followed by a Kamionkowski like reheating stage. In
such a unified holographic scenario, the inflationary quantities (like the
scalar spectral index and the tensor-to-scalar ratio) and the dark energy
quantities (like the dark energy EoS parameter and the present Hubble rate)
prove to be simultaneously compatible with observable constraints for suitable
ranges of the infrared cut-off and the other model parameters. Moreover the
curvature perturbations at super-Hubble scale prove to be a constant (with
time) during the entire cosmic era, which in turn ensures the stability of the
model under consideration.


  We derive the star formation history for several regions of the LMC, using
deep near-infrared data from the VISTA near-infrared YJKs survey of the
Magellanic system (VMC). The regions include three almost-complete 1.4 sqdeg
tiles located 3.5 deg away from the LMC centre in distinct directions. To this
dataset, we add two 0.036 sqdeg subregions inside the 30 Doradus tile. The SFH
is derived from the simultaneous reconstruction of two different CMDs, using
the minimization code StarFISH. The distance modulus (m-M)_0 and extinction Av
is varied within intervals 0.2 and 0.5 mag wide, respectively, within which we
identify the best-fitting star formation rate SFR(t), age-metallicity relation
(AMR), (m-M)_0 and Av. Our results demonstrate that VMC data, due to the
combination of depth and little sensitivity to differential reddening, allow
the derivation of the space-resolved SFH of the LMC with unprecedented quality
compared to previous wide-area surveys. In particular, the data clearly reveal
the presence of peaks in the SFR(t) at ages log(t/yr)=9.3 and 9.7, which appear
in most of the subregions. The most recent SFR is found to vary greatly from
subregion to subregion, with the general trend of being more intense in the
innermost LMC, except for the tile next to the N11 complex. In the bar region,
the SFR seems remarkably constant over the time interval from 8.4 to 9.7. The
AMRs, instead, turn out to be remarkably similar across the LMC. The fields
studied so far are fit extremely well by a single disk of inclination 26.2+-2.0
deg, position angle of the line of nodes 129.1+-13.0 deg, and distance modulus
of 18.470+-0.006 mag (random errors only) up to the LMC centre.


  In this paper we study (non-commutative) rings $R$ over which every finitely
generated left module is a direct sum of cyclic modules (called left
FGC-rings). The commutative case was a well-known problem studied and solved in
1970s by various authors. It is shown that a Noetherian local left FGC-ring is
either an Artinian principal left ideal ring, or an Artinian principal right
ideal ring, or a prime ring over which every two-sided ideal is principal as a
left and a right ideal. In particular, it is shown that a Noetherian local
duo-ring $R$ is a left FGC-ring if and only if $R$ is a right FGC-ring, if and
only if, $R$ is a principal ideal ring. Moreover, we obtain that if
$R=\Pi_{i=1}^n R_i$ is a finite product of Noetherian duo-rings $R_i$ where
each $R_i$ is prime or local, then $R$ is a left FGC-ring if and only if $R$ is
a principal ideal ring.each $R_i$ is prime or local, then $R$ is a left
FGC-ring if and only if $R$ is a principal ideal ring.


  Phonon spectrum of cubic barium zirconate is calculated from first principles
using the density functional theory. Unstable phonon mode with the $R_{25}$
symmetry in the phonon spectrum indicates an instability of the cubic structure
with respect to rotations of the oxygen octahedra. It is shown that the
ground-state structure of the crystal is $I4/mcm$. In order to find the
manifestations of the predicted instability, EXAFS measurements at the Ba
$L_{\rm III}$-edge are used to study the local structure of BaZrO$_3$ at 300 K.
An enhanced value of the Debye-Waller factor for the Ba-O atomic pair
($\sigma^2_1 \sim 0.015$ {\AA}$^2$) revealed in the experiment is associated
with the predicted structural instability. The average amplitude of the thermal
octahedra rotation estimated from the measured $\sigma^2_1$ value is $\sim$4
degrees at 300 K. The closeness of the calculated energies of different
distorted phases resulting from the condensation of the $R_{25}$ mode suggests
a possible structural glass formation in BaZrO$_3$ when lowering temperature,
which explains the cause of the discrepancy between the calculations and
experiment.


  Since 1950 when Oort published his paper on the structure of the cloud of
comets it is believed that stars passing near this hypothetical cometary
reservoir play an important role in the dynamical evolution of long period
comets and injecting them into the observability region of the Solar System.
The aim of this paper is to discuss two cases in which the data obtained from
observations were used and stellar perturbations (of different intensity,
strong case of C/2002 A3 LINEAR and weaker case of C/2013 F3 PANSTARRS) on
cometary motion were detected. Using the best available data from the Gaia DR2
catalogue and some other sources we searched for close stellar passages near
the Sun. Our study took into account that some of the stars are parts of
multiple systems. Over 600 stars or systems that approached or will approach
the Sun closer than 4.0 pc were found. Having the list of perturbers completed
we studied their influence on a sample of 277 Oort spike comets that were
observed since 1901 and discovered that two comets might have their orbits
fundamentally changed due to a close stellar encounter. Our results show how
much different the dynamical evolution of comets would have looked when their
motion was considered only in the Galactic potential. Uncertainties both in
stellar and cometary data were carefully taken into account. Our analysis
indicates that the occurrence of stellar perturbations on cometary motions is
very rare and the uncertainties of these effects are hard to estimate.


  WLAN is one of the most successful applications of wireless communications in
daily life because of low cost and ease of deployment. The enabling technique
for this success is the use of random access schemes for the wireless channel.
Random access requires minimal coordination between the nodes, which
considerably reduces the cost of the infrastructure. Recently, cooperative
communication in wireless networks has been of increasing interest because it
promises higher rates and reliability. An additional MAC overhead is necessary
to coordinate the nodes to allow cooperation and this overhead can possibly
cancel out the cooperative benefits. In this work, a completely distributed
protocol is proposed that allows nodes in the network to cooperate via Two-Hop
and Decode-and-Forward for transmitting their data to a common gateway node. It
is shown that high throughput gains are obtained in terms of the individual
throughput that can be guaranteed to any node in the network. These results are
validated by Monte Carlo simulations.


  The nonlinear character of general relativity leaves its imprint in the
coalescence of two black holes, from the inspiral to the final ringdown stage.
To quantify the impact of nonlinearities, we work at second order in black hole
perturbation theory and we study the excitation of second-order modes relative
to the first-order modes that drive them as we vary the black hole spin and the
initial data for the perturbations. The relative amplitude of second-order
modes is only mildly dependent on the initial data that we consider, but it
strongly decreases for large black hole spins. This implies that the
extrapolation of calculations based on the Kerr-CFT correspondence to
subextremal Kerr black holes should be viewed with caution.


  The integration of heavy scalar fields is discussed in a class of BSM models,
containing more that one representation for scalars and with mixing. The
interplay between integrating out heavy scalars and the Standard Model
decoupling limit is examined. In general, the latter cannot be obtained in
terms of only one large scale and can only be achieved by imposing further
assumptions on the couplings. Systematic low-energy expansions are derived in
the more general, non-decoupling scenario, including mixed tree-loop and mixed
heavy-light generated operators. The number of local operators is larger than
the one usually reported in the literature.


  Current measurements of the spectral energy distribution in radio,
X-and-gamma-ray provide a sufficiently wide basis for determining basic
properties of energetic electrons and protons in the extended lobes of the
radio galaxy Fornax A. Of particular interest is establishing observationally,
for the first time, the level of contribution of energetic protons to the
extended emission observed by the Fermi satellite. Two recent studies concluded
that the observed gamma-ray emission is unlikely to result from Compton
scattering of energetic electrons off the optical radiation field in the lobes,
and therefore that the emission originates from decays of neutral pions
produced in interactions of energetic protons with protons in the lobe plasma,
implying an uncomfortably high proton energy density. However, our exact
calculation of the emission by energetic electrons in the magnetized lobe
plasma leads to the conclusion that all the observed emission can, in fact, be
accounted for by energetic electrons scattering off the ambient optical
radiation field, whose energy density (which, based on recent observations, is
dominated by emission from the central galaxy NGC 1316) we calculate to be
higher than previously estimated.


  Factors, such as rapid relative motion, clutter background, etc., make robust
small aerial target detection for airborne infrared detection systems a
challenge. Existing methods are facing difficulties when dealing with such
cases. We consider that a continuous and smooth trajectory is critical in
boosting small infrared aerial target detection performance. A simple and
effective small aerial target detection method for airborne infrared detection
system using light gradient boosting model (LightGBM) and trajectory
constraints is proposed in this article. First, we simply formulate target
candidate detection as a binary classification problem. Target candidates in
every individual frame are detected via interesting pixel detection and a
trained LightGBM model. Then, the local smoothness and global continuous
characteristic of the target trajectory are modeled as short-strict and
long-loose constraints. The trajectory constraints are used efficiently for
detecting the true small infrared aerial targets from numerous target
candidates. Experiments on public datasets demonstrate that the proposed method
performs better than other existing methods. Furthermore, a public dataset for
small aerial target detection in airborne infrared detection systems is
constructed. To the best of our knowledge, this dataset has the largest data
scale and richest scene types within this field.


  We introduce an unfitted finite element method with Lagrange-multipliers to
study an Eulerian time stepping scheme for moving domain problems applied to a
model problem where the domain motion is implicit to the problem. We consider a
parabolic partial differential equation (PDE) in the bulk domain, and the
domain motion is described by an ordinary differential equation (ODE), coupled
to the bulk partial differential equation through the transfer of forces at the
moving interface. The discretisation is based on an unfitted finite element
discretisation on a time-independent mesh. The method-of-lines time
discretisation is enabled by an implicit extension of the bulk solution through
additional stabilisation, as introduced by Lehrenfeld & Olshanskii (ESAIM:
M2AN, 53:585-614, 2019). The analysis of the coupled problem relies on the
Lagrange-multiplier formulation, the fact that the Lagrange-multiplier solution
is equal to the normal stress at the interface and that the motion of the
interface is given through rigid body motion. This paper covers the complete
stability analysis of the method and an error estimate in the energy norm,
under an assumption on the discrete interface velocity. This includes the
dynamic error in the domain motion resulting from the discretised ODE and the
forces from the discretised PDE. To the best of our knowledge this is the first
error analysis of this type of coupled moving domain problem in a fully
Eulerian framework. Numerical examples illustrate the theoretical results.


  The goal of this paper is to study how the symmetry of the spherical domain
influences solutions of elliptic equations on such domain. The method pursued
is a variant of the moving plane method, discovered by Alexandrov (1962) and
used for differential equations by Gidas, Ni and Nirenberg (1979). We obtain a
reflectional symmetry result with respect to maxima and minima of solutions.


  We consider a model of preheating where the coupling of the inflaton to the
preheat field is modulated by an additional scalar field which is light during
inflation. We establish that such a model produces the observed curvature
perturbation analogously to the modulated reheating scenario. The contribution
of modulated preheating to the power spectrum and to non-Gaussianity can
however be significantly larger compared to modulated perturbative reheating.
We also consider the implications of the current constraints on isocurvature
perturbations in case where the modulating field is responsible for cold dark
matter. We find that existing bounds on CDM isocurvature perturbations imply
that modulated preheating is unlikely to give a dominant contribution to the
curvature perturbation and that the same bounds suggest important constraints
on non-Gaussianity and the amount of primordial gravitational waves.


  The Kahn--Saks inequality is a classical result on the number of linear
extensions of finite posets. We give a new proof of this inequality for posets
of width two using explicit injections of lattice paths. As a consequence we
obtain a $q$-analogue, a multivariate generalization and an equality condition
in this case. We also discuss the equality conditions of the Kahn--Saks
inequality for general posets and prove several implications between conditions
conjectured to be equivalent.


  A query algorithm based on homomorphism counts is a procedure for determining
whether a given instance satisfies a property by counting homomorphisms between
the given instance and finitely many predetermined instances. In a left query
algorithm, we count homomorphisms from the predetermined instances to the given
instance, while in a right query algorithm we count homomorphisms from the
given instance to the predetermined instances. Homomorphisms are usually
counted over the semiring N of non-negative integers; it is also meaningful,
however, to count homomorphisms over the Boolean semiring B, in which case the
homomorphism count indicates whether or not a homomorphism exists. We first
characterize the properties that admit a left query algorithm over B by showing
that these are precisely the properties that are both first-order definable and
closed under homomorphic equivalence. After this, we turn attention to a
comparison between left query algorithms over B and left query algorithms over
N. In general, there are properties that admit a left query algorithm over N
but not over B. The main result of this paper asserts that if a property is
closed under homomorphic equivalence, then that property admits a left query
algorithm over B if and only if it admits a left query algorithm over N. In
other words and rather surprisingly, homomorphism counts over N do not help as
regards properties that are closed under homomorphic equivalence. Finally, we
characterize the properties that admit both a left query algorithm over B and a
right query algorithm over B.


  We construct a model of gravity in 1+1 spacetime dimensions in which the
solutions approach the Schwarzschild metric at large $r$ and de Sitter space
far inside the horizon. Our model may be viewed as a two dimensional
application of the `Limiting Curvature Construction' recently proposed by two
of the authors.


  Animals exhibit an innate ability to learn regularities of the world through
interaction. By performing experiments in their environment, they are able to
discern the causal factors of variation and infer how they affect the world's
dynamics. Inspired by this, we attempt to equip reinforcement learning agents
with the ability to perform experiments that facilitate a categorization of the
rolled-out trajectories, and to subsequently infer the causal factors of the
environment in a hierarchical manner. We introduce {\em causal curiosity}, a
novel intrinsic reward, and show that it allows our agents to learn optimal
sequences of actions and discover causal factors in the dynamics of the
environment. The learned behavior allows the agents to infer a binary quantized
representation for the ground-truth causal factors in every environment.
Additionally, we find that these experimental behaviors are semantically
meaningful (e.g., our agents learn to lift blocks to categorize them by
weight), and are learnt in a self-supervised manner with approximately 2.5
times less data than conventional supervised planners. We show that these
behaviors can be re-purposed and fine-tuned (e.g., from lifting to pushing or
other downstream tasks). Finally, we show that the knowledge of causal factor
representations aids zero-shot learning for more complex tasks. Visit
https://sites.google.com/usc.edu/causal-curiosity/home for website.


  As photosynthesis on Earth produces the primary signatures of life that can
be detected astronomically at the global scale, a strong focus of the search
for extrasolar life will be photosynthesis, particularly photosynthesis that
has evolved with a different parent star. We take planetary atmospheric
compositions simulated by Segura, et al. (2003, 2005) for Earth-like planets
around observed F2V and K2V stars, modeled M1V and M5V stars, and around the
active M4.5V star AD Leo; our scenarios use Earth's atmospheric composition as
well as very low O2 content in case anoxygenic photosynthesis dominates. We
calculate the incident spectral photon flux densities at the surface of the
planet and under water. We identify bands of available photosynthetically
relevant radiation and find that photosynthetic pigments on planets around F2V
stars may peak in absorbance in the blue, K2V in the red-orange, and M stars in
the NIR, in bands at 0.93-1.1 microns, 1.1-1.4 microns, 1.5-1.8 microns, and
1.8-2.5 microns. In addition, we calculate wavelength restrictions for
underwater organisms and depths of water at which they would be protected from
UV flares in the early life of M stars. We estimate the potential productivity
for both surface and underwater photosynthesis, for both oxygenic and
anoxygenic photosynthesis, and for hypothetical photosynthesis in which longer
wavelength, multi-photosystem series are used.


  We determine the image of the Artin groups of types B and D inside the
Iwahori-Hecke algebras, when defined over finite fields, in the semisimple
case. This generalizes earlier work on type A by Brunat, Magaard and Marin. In
this multi-parameter case, this image depends heavily on the parameters.


  We develop a semiclassical second microlocal calculus of pseudodifferential
operators associated to linear coisotropic submanifolds $\mathcal{C}\subset T^*
\mathbb{T}^n$, where $\mathbb{T}^n = \mathbb{R}^n / \mathbb{Z}^n$. First
microlocalization is localization in phase space $T^* \mathbb{T}^n$; second
microlocalization is finer localization near a submanifold of $T^*
\mathbb{T}^n$. Our second microlocal operators test distributions on
$\mathbb{T}^n$ (e.g., Laplace eigenfunctions) for a coisotropic wavefront set,
a second microlocal measure of absence of \emph{coisotropic regularity}. This
wavefront set tells us where, in the coisotropic, and in what directions,
approaching the coisotropic, a distribution lacks coisotropic regularity.
  We prove propagation theorems for coisotropic wavefront that are analogous to
H\"{o}rmander's theorem for pseudodifferential operators of real principal
type. Furthermore, we study the propagation of coisotropic regularity for
quasimodes of semiclassical pseudodifferential operators. We Taylor expand the
relevant Hamiltonian vector field, partially in the characteristic variables,
at the spherical normal bundle of the coisotropic. Provided the principal
symbol is real valued and depends only on the fiber variables in the cotangent
bundle, and the subprincipal symbol vanishes, we show that coisotropic
wavefront is invariant under the first two terms of this expansion.


  Numerical simulations of plasma flows are crucial for advancing our
understanding of microscopic processes that drive the global plasma dynamics in
fusion devices, space, and astrophysical systems. Identifying and classifying
particle trajectories allows us to determine specific on-going acceleration
mechanisms, shedding light on essential plasma processes.
  Our overall goal is to provide a general workflow for exploring particle
trajectory space and automatically classifying particle trajectories from
plasma simulations in an unsupervised manner. We combine pre-processing
techniques, such as Fast Fourier Transform (FFT), with Machine Learning
methods, such as Principal Component Analysis (PCA), k-means clustering
algorithms, and silhouette analysis. We demonstrate our workflow by classifying
electron trajectories during magnetic reconnection problem. Our method
successfully recovers existing results from previous literature without a
priori knowledge of the underlying system.
  Our workflow can be applied to analyzing particle trajectories in different
phenomena, from magnetic reconnection, shocks to magnetospheric flows. The
workflow has no dependence on any physics model and can identify particle
trajectories and acceleration mechanisms that were not detected before.


  3D human pose and shape estimation from monocular images has been an active
research area in computer vision. Existing deep learning methods for this task
rely on high-resolution input, which however, is not always available in many
scenarios such as video surveillance and sports broadcasting. Two common
approaches to deal with low-resolution images are applying super-resolution
techniques to the input, which may result in unpleasant artifacts, or simply
training one model for each resolution, which is impractical in many realistic
applications.
  To address the above issues, this paper proposes a novel algorithm called
RSC-Net, which consists of a Resolution-aware network, a Self-supervision loss,
and a Contrastive learning scheme. The proposed method is able to learn 3D body
pose and shape across different resolutions with one single model. The
self-supervision loss enforces scale-consistency of the output, and the
contrastive learning scheme enforces scale-consistency of the deep features. We
show that both these new losses provide robustness when learning in a
weakly-supervised manner. Moreover, we extend the RSC-Net to handle
low-resolution videos and apply it to reconstruct textured 3D pedestrians from
low-resolution input. Extensive experiments demonstrate that the RSC-Net can
achieve consistently better results than the state-of-the-art methods for
challenging low-resolution images.


  We numerically investigate local defectiveness control of self-assembled
diblock copolymer patterns through appropriate substrate design. We use a
nonlocal Cahn-Hilliard (CH) equation for the phase separation dynamics of
diblock copolymers. We discretize the nonlocal CH equation by an
unconditionally stable finite difference scheme on a tapered trench design and,
in particular, we use Dirichlet, Neumann, and periodic boundary conditions. The
value at the Dirichlet boundary comes from an energy-minimizing equilibrium
lamellar profile. We solve the resulting discrete equations using a
Gauss-Seidel iterative method. We perform various numerical experiments such as
effects of channel width, channel length, and angle on the phase separation
dynamics. The simulation results are consistent with the previous experimental
observations.


  Using first-principles calculations, we analyze the evolution of the
electronic structure and magnetic properties of infinite-layer nickelates
RNiO$_2$ (R= rare-earth) as R changes across the lanthanide series from La to
Lu. By correlating these changes with in-plane and out-of-plane lattice
parameter reductions, we conclude that the in-plane Ni-O distance is the
relevant control parameter in infinite-layer nickelates. An antiferromagnetic
ground state is obtained for all RNiO$_2$ (R=La-Lu). This antiferromagnetic
state remains metallic across the lanthanide series and is defined by a
multiorbital picture with low-energy relevance of a flat Ni-d$_{z^2}$ band
pinned at the Fermi level, in contrast to cuprates. Other non-cuprate-like
properties such as the involvement of R-$d$ bands at the Fermi level, a large
charge transfer energy, and a suppressed superexchange are robust for all
RNiO$_2$ materials.


  We introduce a polariton-waveguide structure, comprised of a nanowire-based
photonic crystal waveguide with a quantum dot embedded in each unit cell. Using
realistic designs and parameters, we derive and calculate the fundamental
electromagnetic properties of these polariton waveguides, with an emphasis on
the photon Green function and local optical density of states (LDOS). Both
infinite and finite-size waveguides are considered, where the latter's
properties are calculated using a Dyson equation approach without any
approximations. We demonstrate dramatic increases, and rich fundamental
control, of the LDOS due to strong light-matter interactions in each unit cell
through periodic quantum dot interactions. Consequently, these structures allow
the exploration of new regimes of waveguide quantum electrodynamics. As an
example application, we consider the coupling of an external target quantum dot
with a finite-sized polariton waveguide, and show that the single quantum dot
strong coupling regime is easily accessible, even for modest dipole strengths.


  We present NLO QCD predictions for the prompt photon photoproduction at the
THERA, and compare them with results for the HERA collider.


  New results reported at the Moriond-QCD 2003 conference from the experiments
ALEPH, DELPHI, L3, and OPAL on the structure of the photon as well as heavy
quark production in gammagamma collisions are presented. The hadronic structure
of the photon is studied in single-tagged events; the interaction of two
virtual photons is investigated in double-tagged events. Di-jet events allow,
besides constraining the photon structure, investigations on the structure of
jets, measurement of the di-jet as well as inclusive and differential cross
sections. Inclusive charm and bottom production are investigated at LEP~2
energies. The total and differential cross sections for charm quarks are now
measured by all four LEP collaborations, the total bottom by two. Charmonia are
detected inclusively via the muonic decay of the J/psi and separated for the
resolved and diffractive processes. Updated results are available for exclusive
production of the eta_c meson. The search for exclusive eta_b production is
presented.


  We propose a convex variational principle to find sparse representation of
low-lying eigenspace of symmetric matrices. In the context of electronic
structure calculation, this corresponds to a sparse density matrix minimization
algorithm with $\ell_1$ regularization. The minimization problem can be
efficiently solved by a split Bergman iteration type algorithm. We further
prove that from any initial condition, the algorithm converges to a minimizer
of the variational principle.


  This paper contains several results about the Chabauty space of a general
locally compact abelian group. Notably, we determine its topological dimension,
we characterize when it is totally disconnected or connected; we characterize
isolated points.


  The goal of this paper is to establish the classification of all homogeneous
surfaces of 3-sphere by using the moving frame method. We will show that such
surfaces are 2-spheres and flat torus.


  We prove a connected sum formula for involutive Heegaard Floer homology, and
use it to study the involutive correction terms of connected sums. In
particular, we give an example of a three-manifold with $\underline{d}(Y) \neq
d(Y) \neq \overline{d}(Y)$. We also construct a homomorphism from the
three-dimensional homology cobordism group to an algebraically defined Abelian
group, consisting of certain complexes (equipped with a homotopy involution)
modulo a notion of local equivalence.


  It is well known that to accelerate stencil codes on CPUs or GPUs and to
exploit hardware caches and their lines optimizers must find spatial and
temporal locality of array accesses to harvest data-reuse opportunities. On
FPGAs there is the burden that there are no built-in caches (or only pre-built
hardware descriptions for cache blocks that are inefficient for stencil codes).
But this paper demonstrates that this lack is also a chance as polyhedral
methods can be used to generate stencil-specific cache-structures of the right
sizes on the FPGA and to fill and flush them efficiently with wide bursts
during stencil execution. The paper shows how to derive the appropriate
directives and code restructurings from stencil codes so that the FPGA compiler
generates fast stencil hardware. Switching on our optimization improves the
runtime of a set of 10 stencils by between 43x and 156x.


  Diffusion Monte Carlo results for the phonon-roton excitation branch in bulk
liquid $^4$He at zero temperature are presented. The sign problem associated to
the excited wave function has been dealt both with the fixed-node approximation
and the released-node technique. The upper bounds provided by the fixed-node
approximation are shown to become exact when using the released-node method. An
excellent agreement with experimental data is achieved both at the equilibrium
and near the freezing densities.


  We have demonstrated that ferroelectric polarization in a spin-driven
multiferroic CuFe1-xGaxO2 with x = 0.035 can be controlled by the application
of uniaxial pressure. Our neutron diffraction and in-situ ferroelectric
polarization measurements have revealed that the pressure dependence of the
ferroelectric polarization is explained by repopulation of three types of
magnetic domains originating from the trigonal symmetry of the crystal. We
conclude that the spin-driven anisotropic lattice distortion and the fixed
relationship between the directions of the magnetic modulation wave vector and
the ferroelectric polarization are the keys to this spin-mediated piezoelectric
effect.


  Since the 5D canonical metric embeds all 4D vacuum solutions of Einstein's
equations, I review its application to the cosmological 'constant', quantized
particles, deBroglie waves, scalar fields and wave-particle duality. There are
several ways to ra-tionalize these things using an extra dimension. A possible
explanation of wave-particle duality is that an observed particle manifests two
isometries of flat 5D space in different 4D ways, one with waves and one
without.


  High-resolution ghost image and ghost diffraction experiments are performed
by using a single source of thermal-like speckle light divided by a beam
splitter. Passing from the image to the diffraction result solely relies on
changing the optical setup in the reference arm, while leaving untouched the
object arm. The product of spatial resolutions of the ghost image and ghost
diffraction experiments is shown to overcome a limit which was formerly thought
to be achievable only with entangled photons.


  The spread of ideas across a social network can be studied using complex
contagion models, in which agents are activated by contact with multiple
activated neighbors. The investigation of complex contagions can provide
crucial insights into social influence and behavior-adoption cascades on
networks. In this paper, we introduce a model of a multi-stage complex
contagion on networks. Agents at different stages --- which could, for example,
represent differing levels of support for a social movement or differing levels
of commitment to a certain product or idea --- exert different amounts of
influence on their neighbors. We demonstrate that the presence of even one
additional stage introduces novel dynamical behavior, including interplay
between multiple cascades, that cannot occur in single-stage contagion models.
We find that cascades --- and hence collective action --- can be driven not
only by high-stage influencers but also by low-stage influencers.


  In this paper a detailed simulation of irradiated pixel sensors was used to
investigate the effects of radiation damage on the position determination and
optimize the hit reconstruction algorithms. The simulation implements a model
of radiation damage by including two defect levels with opposite charge states
and trapping of charge carriers. The simulation shows that a position
resolution below 15 $\mu$m along the CMS $r-\phi$ plane can be achieved after
an irradiation fluence of $5.9\times10^{14}$ n$_{\rm{eq}}/$cm$^2$. In addition,
we show that systematic errors in the position determination can be largely
reduced by applying $\eta$ corrections.


  The effects of inbreeding on human health depend critically on the number and
severity of recessive, deleterious mutations carried by individuals. In humans,
existing estimates of these quantities are based on comparisons between
consanguineous and non-consanguineous couples, an approach that confounds
socioeconomic and genetic effects of inbreeding. To circumvent this limitation,
we focused on a founder population with almost complete Mendelian disease
ascertainment and a known pedigree. By considering all recessive lethal
diseases reported in the pedigree and simulating allele transmissions, we
estimated that each haploid set of human autosomes carries on average 0.29 (95%
credible interval [0.10, 0.83]) autosomal, recessive alleles that lead to
complete sterility or severe disorders at birth or before reproductive age when
homozygous. Comparison to existing estimates of the deleterious effects of all
recessive alleles suggests that a substantial fraction of the burden of
autosomal, recessive variants is due to single mutations that lead to death
between birth and reproductive age. In turn, the comparison to estimates from
other eukaryotes points to a surprising constancy of the average number of
recessive lethal mutations across organisms with markedly different genome
sizes.


  This paper addresses the problem of reducing the delivery time of data
messages to cellular users using instantly decodable network coding (IDNC) with
physical-layer rate awareness. While most of the existing literature on IDNC
does not consider any physical layer complications and abstract the model as
equally slotted time for all users, this paper proposes a cross-layer scheme
that incorporates the different channel rates of the various users in the
decision process of both the transmitted message combinations and the rates
with which they are transmitted. The consideration of asymmetric rates for
receivers reflects more practical application scenarios and introduces a new
trade-off between the choice of coding combinations for various receivers and
the broadcasting rate for achieving shorter completion time. The completion
time minimization problem in such scenario is first shown to be intractable.
The problem is, thus, approximated by reducing, at each transmission, the
increase of an anticipated version of the completion time. The paper solves the
problem by formulating it as a maximum weight clique problem over a newly
designed rate aware IDNC (RA-IDNC) graph. The highest weight clique in the
created graph being potentially not unique, the paper further suggests a
multi-layer version of the proposed solution to improve the obtained results
from the employed completion time approximation. Simulation results indicate
that the cross-layer design largely outperforms the uncoded transmissions
strategies and the classical IDNC scheme.


  The SEDs of some nearby stars show mid-infrared excesses from warm habitable
zone dust, known as exozodiacal dust. This dust may originate in collisions in
a planetesimal belt before being dragged inwards. This paper presents an
analytical model for the size distribution of particles at different radial
locations in such a scenario, considering evolution due to destructive
collisions and Poynting-Robertson (P-R) drag. Results from more accurate but
computationally expensive numerical simulations of this process are used to
validate the model and fit its free parameters. The model predicts 11 $\mu$m
excesses ($R_{11}$) for discs with a range of dust masses and planetesimal belt
radii using realistic grain properties. We show that P-R drag should produce
exozodiacal dust levels detectable with the Large Binocular Telescope
Interferometer (LBTI) ($R_{11} > 0.1\%$) in systems with known outer belts;
non-detection may indicate dust depletion, e.g. by an intervening planet. We
also find that LBTI could detect exozodiacal dust dragged in from a belt too
faint to detect at far-infrared wavelengths, with fractional luminosity $f\sim
10^{-7}$ and radius $\sim 10-80$ au. Application to systems observed with LBTI
shows that P-R drag can likely explain most (5/9) of the exozodiacal dust
detections in systems with known outer belts; two systems ($\beta$ Uma and
$\eta$ Corvi) with bright exozodi may be due to exocomets. We suggest that the
three systems with exozodiacal dust detections but no known belt may have cold
planetesimal belts too faint to be detectable in the far-infrared. Even systems
without outer belt detections could have exozodiacal dust levels $R_{11} >
0.04\%$ which are problematic for exo-Earth imaging.


  We report on the infrared absorption spectra of three oxides where charged
superlattices have been recently observed in diffraction experiments. In
La$_{1.67}$Sr$_{0.33}$NiO$_4$, polaron localization is found to suppress the
low-energy conductivity through the opening of a gap and to split the
$E_{2u}$-$A_{2u}$ vibrational manifold of the oxygen octahedra. Similar effects
are detected in Sr$_{1.5}$La$_{0.5}$MnO$_4$ and in La$_2$NiO$_{4+y}$, with
peculiar differences related to the type of charge ordering.


  Free-standing exfoliated monolayer graphene is an ultra-thin flexible
membrane, which exhibits out of plane deformation or corrugation. In this
paper, a technique is described to measure the band structure of such
free-standing graphene by angle-resolved photoemission. Our results show that
photoelectron coherence is limited by the crystal corrugation. However, by
combining surface morphology measurements of the graphene roughness with
angle-resolved photoemission, energy dependent quasiparticle lifetime and
bandstructure measurements can be extracted. Our measurements rely on our
development of an analytical formulation for relating the crystal corrugation
to the photoemission linewidth. Our ARPES measurements show that, despite
significant deviation from planarity of the crystal, the electronic structure
of exfoliated suspended graphene is nearly that of ideal, undoped graphene; we
measure the Dirac point to be within 25 meV of $E_F$ . Further, we show that
suspended graphene behaves as a marginal Fermi-liquid, with a quasiparticle
lifetime which scales as $(E - E_F)^{-1}$; comparison with other graphene and
graphite data is discussed.


  Interlayer valley excitons in bilayer MoS2 feature concurrently large
oscillator strength and long lifetime, and hence represent an advantageous
scenario for valleytronic applications. However, control of valley pseudospin
of interlayer excitons in pristine bilayer MoS2, which lies at the heart of
valleytronics, has remained elusive. Here we report the observation of highly
circularly polarized photoluminescence from interlayer excitons of bilayer MoS2
with both optical and magnetic addressability. Under excitation of circularly
polarized light near exciton resonance, interlayer excitons of bilayer MoS2
show a near-unity, but negative circular polarization. Significantly, by
breaking time-reversal symmetry with an out-of-plane magnetic field, a record
level of spontaneous valley polarization (7.7%/Tesla) is identified for
interlayer excitons in bilayer MoS2. The giant valley polarization of the
interlayer excitons in bilayer MoS2, together with the feasibility of
electrical/optical/magnetic control and strong oscillator strength, provides a
firm basis for the development of next-generation electronic and optoelectronic
applications.


  In the mini-superspace approximation to cosmology, the canonical measure can
be used to compute probabilities when a cutoff is introduced in the phase space
to regularize the divergent measure. However, the region initially constrained
by a simple cutoff evolves non-trivially under the Hamiltonian flow. We
determine the deformation of the regularized phase space along the orbits when
a cutoff is introduced for the scale factor of the universe or for the Hubble
parameter. In the former case, we find that the cutoff for the scale factor
varies in the phase space and effectively decreases as one evolves backwards in
time. In the later case, we calculate the probability of slow-roll inflation in
a chaotic model with a massive scalar, which turns out to be cutoff dependent
but not exponentially suppressed. We also investigate the measure problem for
non-abelian gauge fields giving rise to inflation.


  This paper presents simple variants of the BlockQuicksort algorithm described
by Edelkamp and Weiss (ESA 2016). The simplification is achieved by using
Lomuto's partitioning scheme instead of Hoare's crossing pointer technique to
partition the input. To achieve a robust sorting algorithm that works well on
many different input types, the paper introduces a novel two-pivot variant of
Lomuto's partitioning scheme. A surprisingly simple twist to the generic
two-pivot quicksort approach makes the algorithm robust. The paper provides an
analysis of the theoretical properties of the proposed algorithms and compares
them to their competitors. The analysis shows that Lomuto-based approaches
incur a higher average sorting cost than the Hoare-based approach of
BlockQuicksort. Moreover, the analysis is particularly useful to reason about
pivot choices that suit the two-pivot approach. An extensive experimental study
shows that, despite their worse theoretical behavior, the simpler variants
perform as well as the original version of BlockQuicksort.


  I review the status of neutrino physics post-Neutrino~98, including the
implications of solar and atmospheric neutrino data, which strongly indicate
nonzero neutrino masses. LSND and the possible role of neutrinos as hot dark
matter (HDM) are also mentioned. The simplest schemes proposed to reconcile
these requirements invoke a light sterile neutrino in addition to the three
active ones, two of them at the MSW scale and the other two maximally-mixed
neutrinos at the HDM/LSND scale. In the simplest theory the latter scale arises
at one-loop, while the solar and atmospheric parameters $\Delta {m^2}_\odot$ &
$\Delta {m^2}_{atm}$ appear at the two-loop level. The lightness of the sterile
neutrino, the nearly maximal atmospheric neutrino mixing, and the generation of
$\Delta {m^2}_\odot$ & $\Delta {m^2}_{atm}$ follow naturally from the assumed
lepton-number symmetry and its breaking. These two basic schemes can be
distinguished at future solar & atmospheric neutrino experiments and have
different cosmological implications.


  Sound educational policy recommendations require valid estimates of causal
effects, but observational studies in physics education research sometimes have
loosely specified causal hypotheses. The connections between the observational
data and the explicit or implicit causal conclusions are sometimes misstated.
The link between the causal conclusions reached and the policy recommendations
made is also sometimes loose. Causal graphs are used to illustrate these issues
in several papers from Physical Review Physics Education Research. For example,
the core causal conclusion of one paper rests entirely on the choice of a
causal direction although an unstated plausible alternative gives an exactly
equal fit to the data.


  The advent of the "pre-train, prompt" paradigm has recently extended its
generalization ability and data efficiency to graph representation learning,
following its achievements in Natural Language Processing (NLP). Initial graph
prompt tuning approaches tailored specialized prompting functions for Graph
Neural Network (GNN) models pre-trained with specific strategies, such as edge
prediction, thus limiting their applicability. In contrast, another pioneering
line of research has explored universal prompting via adding prompts to the
input graph's feature space, thereby removing the reliance on specific
pre-training strategies. However, the necessity to add feature prompts to all
nodes remains an open question. Motivated by findings from prompt tuning
research in the NLP domain, which suggest that highly capable pre-trained
models need less conditioning signal to achieve desired behaviors, we advocate
for strategically incorporating necessary and lightweight feature prompts to
certain graph nodes to enhance downstream task performance. This introduces a
combinatorial optimization problem, requiring a policy to decide 1) which nodes
to prompt and 2) what specific feature prompts to attach. We then address the
problem by framing the prompt incorporation process as a sequential
decision-making problem and propose our method, RELIEF, which employs
Reinforcement Learning (RL) to optimize it. At each step, the RL agent selects
a node (discrete action) and determines the prompt content (continuous action),
aiming to maximize cumulative performance gain. Extensive experiments on graph
and node-level tasks with various pre-training strategies in few-shot scenarios
demonstrate that our RELIEF outperforms fine-tuning and other prompt-based
approaches in classification performance and data efficiency.


  Sparse-to-dense interpolation for optical flow is a fundamental phase in the
pipeline of most of the leading optical flow estimation algorithms. The current
state-of-the-art method for interpolation, EpicFlow, is a local average method
based on an edge aware geodesic distance. We propose a new data-driven
sparse-to-dense interpolation algorithm based on a fully convolutional network.
We draw inspiration from the filling-in process in the visual cortex and
introduce lateral dependencies between neurons and multi-layer supervision into
our learning process. We also show the importance of the image contour to the
learning process. Our method is robust and outperforms EpicFlow on competitive
optical flow benchmarks with several underlying matching algorithms. This leads
to state-of-the-art performance on the Sintel and KITTI 2012 benchmarks.


  Multi-task neural networks learn tasks simultaneously to improve individual
task performance. There are three mechanisms of multi-task learning (MTL) which
are explored here for the context of structural health monitoring (SHM): (i)
the natural occurrence of multiple tasks; (ii) using outputs as inputs (both
linked to the recent research in population-based SHM (PBSHM)); and, (iii)
additional loss functions to provide different insights. Each of these problem
settings for MTL is detailed and an example is given.


  We investigate the phase diagram of quantum gravity with a vertex expansion
about constantly-curved backgrounds. The graviton two- and three-point function
are evaluated with a spectral sum on a sphere. We obtain, for the first time,
curvature-dependent UV fixed point functions of the dynamical fluctuation
couplings $g^*(R)$, $\mu^*(R)$, and $\lambda_3^*(R)$, and the background
$f(R)$-potential. Based on these fixed point functions we compute solutions to
the quantum and the background equation of motion with and without Standard
Model matter. We have checked that the solutions are robust against changes of
the truncation.


  An overview of advanced dynamical algorithms capable of spanning the widely
disparate time scales that govern the decay of metastable phases in discrete
spin models is presented. The algorithms discussed include constrained
transfer-matrix, Monte Carlo with Absorbing Markov Chains (MCAMC), and
projective dynamics (PD) methods. The strengths and weaknesses of each of these
algorithms are discussed, with particular emphasis on identifying the parameter
regimes (system size, temperature, and field) in which each algorithm works
best.


  Gravitational waves carry away both energy and angular momentum as binary
black holes inspiral and merge. The relative efficiency with which they are
radiated determines whether the final black hole of mass $M_f$ and spin $S_f$
saturates the Kerr limit ($\chi_f \equiv S_f/M_f^2 \leq 1$). Extrapolating from
the test-particle limit, we propose expressions for $S_f$ and $M_f$ for mergers
with initial spins aligned or anti-aligned with the orbital angular momentum.
We predict the the final spin at plunge for equal-mass non-spinning binaries to
better than 1%, and that equal-mass maximally spinning aligned mergers lead to
nearly maximally spinning final black holes ($\chi_f \simeq 0.9988$). We also
find black holes can always be spun up by aligned mergers provided the mass
ratio is small enough.


  In the past decades, researches on parity-time (PT) and anti-parity-time(APT)
systems have garnered unprecedented attention, showcasing their various
intriguing characteristics and promising potentiality in extending canonical
Hermitian quantum mechanics. However, despite significant endeavors devoted to
this new field of physics, non-Hermitian dynamics of contextuality still
remains an uncharted region, either in PT-symmetry or APT-symmetry systems.
Since contextuality has also been proven to be the core resource for quantum
state discrimination (QSD) tasks, here we systematically investigate the novel
performance of contextuality through QSD in both systems, taking
mirror-symmetric three-state minimum error discrimination (MED) and maximum
confidence discrimination (MCD) scenarios as two examples. The time evolution
of contextuality in two scenarios and eight regimes (four regimes for each
scenario) are comprehensively compared and analyzed, with the difference of
initial states also considered. In the symmetry-unbroken regimes, our
simulation shows periodic oscillations of contextuality for both MED and MCD
scenarios, the period of which is state-independent but related to
non-Hermiticity of the system. Both MED and MCD shows non-trivial recovery of
contextuality exceeding its initial value in PT system, which is only existent
for MCD in APT system. In the symmetry-broken regimes, the success
probabilities of both scenarios start from a prompt decay at first, ending up
with a stable value which is constantly 1/3. Non-triviality is found only for
MCD scenario in PT system, where the recovered contextuality exceeds its
initial value.


  The Sunyaev Zel'dovich (SZ) signal is highly non-Gaussian, so the SZ power
spectrum (along with the mean $y$ parameter) does not provide a complete
description of the SZ effect. Therefore, SZ-based constraints on cosmological
parameters and on cluster gastrophysics which assume Gaussianity will be
biased.
  We derive an analytic expression for the $n$-point joint PDF of the SZ power
spectrum. Our derivation, which is based on the halo model, has several
advantages: it is expressed in an integral form which allows quick computation;
it is applicable to any given survey and any given angular scale; it is
straightforward to incorporate many of the complexities which arise when
modeling the SZ signal. To illustrate, we use our expression to estimate
$p(C_\ell)$, the one-point PDF of the SZ power spectrum. For small sky coverage
(applicable to BIMA/CBI and the Sunyaev Zel'dovich Array experiments), our
analysis shows that $p(C_\ell)$ on the several arc-minute scale is expected to
be strongly skewed, peaking at a value well below the mean and with a long tail
which extends to tail high $C_\ell$ values. In the limit of large sky coverage
(applicable to the South Pole Telescope and Planck), $p(C_\ell)$ approaches a
Gaussian form. However, even in this limit, the variance of the power spectrum
is very different from the naive Gaussian-based estimate. This is because
different $\ell$ models are strongly correlated, making the cosmic variance of
the SZ band-power much larger than the naive estimate. Our analysis should also
be useful for modeling the PDF of the power spectrum induced by gravitational
lensing at large $\ell$.


  To induce the Sense of Embodiment~(SoE) on the virtual 3D avatar during a
Virtual Reality~(VR) walking scenario, VR interfaces have employed the
visuotactile or visuomotor approaches. However, people with reduced lower-body
mobility and sensation~(PRLMS) who are incapable of feeling or moving their
legs would find this task extremely challenging. Here, we propose an upper-body
motion tracking-based partial-visuomotor technique to induce SoE and positive
feedback for PRLMS patients. We design partial-visuomotor stimulation
consisting of two distinctive inputs~(\textit{Button Control} \& \textit{Upper
Motion tracking}) and outputs~(\textit{wheelchair motion} \& \textit{Gait
Motion}). The preliminary user study was conducted to explore subjective
preference with qualitative feedback. From the qualitative study result, we
observed the positive response on the partial-visuomotor regarding SoE in the
asynchronous VR experience for PRLMS.


  We study a robust optimal stopping problem with respect to a set $\cP$ of
mutually singular probabilities. This can be interpreted as a zero-sum
controller-stopper game in which the stopper is trying to maximize its pay-off
while an adverse player wants to minimize this payoff by choosing an evaluation
criteria from $\cP$. We show that the \emph{upper Snell envelope $\ol{Z}$} of
the reward process $Y$ is a supermartingale with respect to an appropriately
defined nonlinear expectation $\ul{\sE}$, and $\ol{Z}$ is further an
$\ul{\sE}-$martingale up to the first time $\t^*$ when $\ol{Z}$ meets $Y$.
Consequently, $\t^*$ is the optimal stopping time for the robust optimal
stopping problem and the corresponding zero-sum game has a value. Although the
result seems similar to the one obtained in the classical optimal stopping
theory, the mutual singularity of probabilities and the game aspect of the
problem give rise to major technical hurdles, which we circumvent using some
new methods.


  This pseudo-paper consists of excerpts drawn from two of my quantum-email
samizdats. Section 1 draws a picture of a physical world whose essence is
``Darwinism all the way down.'' Section 2 outlines how quantum theory should be
viewed in light of this, i.e., as being an expression of probabilism (in Bruno
de Finetti or Richard Jeffrey's sense) all the way back up. Section 3 describes
how the idea of ``identical'' quantum measurement outcomes, though sounding
atomistic in character, nonetheless meshes well with a Jamesian style ``radical
pluralism.'' Sections 4 and 5 further detail how quantum theory should not be
viewed so much as a ``theory of the world,'' but rather as a theory of
decision-making for agents immersed within a world of a particular
character--the quantum world. Finally, Sections 6 and 7 attempt to sketch the
very positive sense in which quantum theory is incomplete, but still just as
complete is it can be. In total, I hope these heady speculations convey some of
the excitement and potential I see for the malleable world quantum mechanics
hints of.


  Given a large social or information network, how can we partition the
vertices into sets (i.e., colors) such that no two vertices linked by an edge
are in the same set while minimizing the number of sets used. Despite the
obvious practical importance of graph coloring, existing works have not
systematically investigated or designed methods for large complex networks. In
this work, we develop a unified framework for coloring large complex networks
that consists of two main coloring variants that effectively balances the
tradeoff between accuracy and efficiency. Using this framework as a fundamental
basis, we propose coloring methods designed for the scale and structure of
complex networks. In particular, the methods leverage triangles,
triangle-cores, and other egonet properties and their combinations. We
systematically compare the proposed methods across a wide range of networks
(e.g., social, web, biological networks) and find a significant improvement
over previous approaches in nearly all cases. Additionally, the solutions
obtained are nearly optimal and sometimes provably optimal for certain classes
of graphs (e.g., collaboration networks). We also propose a parallel algorithm
for the problem of coloring neighborhood subgraphs and make several key
observations. Overall, the coloring methods are shown to be (i) accurate with
solutions close to optimal, (ii) fast and scalable for large networks, and
(iii) flexible for use in a variety of applications.


  We report a study of the intensity and time dependence of scintillation
produced by weak alpha particle sources in superfluid helium in the presence of
an electric field (0 - 45 kV/cm) in the temperature range of 0.2 K to 1.1 K at
the saturated vapor pressure. Both the prompt and the delayed components of the
scintillation exhibit a reduction in intensity with the application of an
electric field. The reduction in the intensity of the prompt component is well
approximated by a linear dependence on the electric field strength with a
reduction of 15% at 45 kV/cm. When analyzed using the Kramers theory of
columnar recombination, this electric field dependence leads to the conclusion
that roughly 40% of the scintillation results from species formed from atoms
originally promoted to excited states and 60% from excimers created by
ionization and subsequent recombination with the charges initially having a
cylindrical Gaussian distribution about the alpha track of 60 nm radius. The
intensity of the delayed component of the scintillation has a stronger
dependence on the electric field strength and on temperature. The implications
of these data on the mechanisms affecting scintillation in liquid helium are
discussed.


  We point out that the non-gaussianity arising from cubic self interactions of
the inflaton field is proportional to \xi N_e where \xi ~ V"' and N_e is the
number of e-foldings from horizon exit till the end of inflation. For scales of
interest N_e = 60, and for models of inflation such as new inflation, natural
inflation and running mass inflation \xi is large compared to the slow roll
parameter \epsilon ~ V'^{2}. Therefore the contribution from self interactions
should not be outrightly ignored while retaining other terms in the
non-gaussianity parameter f_{NL}. But the N_e dependent term seems to imply the
growth of non-gaussianities outside the horizon. Therefore we briefly discuss
the issue of the constancy of correlations of the curvature perturbation \zeta
outside the horizon. We then calculate the 3-point function of the inflaton
fluctuations using the canonical formalism and further obtain the 3-point
function of \zeta_k. We find that the N_e dependent contribution to f_{NL} from
self interactions of the inflaton field is cancelled by contributions from
other terms associated with non-linearities in cosmological perturbation
theory.


  We present an analytical diffusion-expansion Forbush decrease (FD) model
ForbMod which is based on the widely used approach of the initially empty,
closed magnetic structure (i.e. flux rope) which fills up slowly with particles
by perpendicular diffusion. The model is restricted to explain only the
depression caused by the magnetic structure of the interplanetary coronal mass
ejection (ICME). We use remote CME observations and a 3D reconstruction method
(the Graduated Cylindrical Shell method) to constrain initial boundary
conditions of the FD model and take into account CME evolutionary properties by
incorporating flux rope expansion. Several flux rope expansion modes are
considered, which can lead to different FD characteristics. In general, the
model is qualitatively in agreement with observations, whereas quantitative
agreement depends on the diffusion coefficient and the expansion properties
(interplay of the diffusion and the expansion). A case study was performed to
explain the FD observed 2014 May 30. The observed FD was fitted quite well by
ForbMod for all expansion modes using only the diffusion coefficient as a free
parameter, where the diffusion parameter was found to correspond to expected
range of values. Our study shows that in general the model is able to explain
the global properties of FD caused by FR and can thus be used to help
understand the underlying physics in case studies.


  Let $A$ be a random $m\times n$ matrix over the finite field $F_q$ with
precisely $k$ non-zero entries per row and let $y\in F_q^m$ be a random vector
chosen independently of $A$. We identify the threshold $m/n$ up to which the
linear system $A x=y$ has a solution with high probability and analyse the
geometry of the set of solutions. In the special case $q=2$, known as the
random $k$-XORSAT problem, the threshold was determined by [Dubois and Mandler
2002, Dietzfelbinger et al. 2010, Pittel and Sorkin 2016], and the proof
technique was subsequently extended to the cases $q=3,4$ [Falke and Goerdt
2012]. But the argument depends on technically demanding second moment
calculations that do not generalise to $q>3$. Here we approach the problem from
the viewpoint of a decoding task, which leads to a transparent combinatorial
proof.


  Imbalance (on-line energy gap between contracted supply and actual demand,
and associated cost) reduction is going to be a crucial service for a Power
Producer and Supplier (PPS) in the deregulated energy market. PPS requires
forward market interactions to procure energy as precisely as possible in order
to reduce imbalance energy. This paper presents, 1) (off-line) an effective
demand aggregation based strategy for creating a number of balancing groups
that leads to higher predictability of group-wise aggregated demand, 2)
(on-line) a robust energy storage scheduling that minimizes the imbalance for a
particular balancing group considering the demand prediction uncertainty. The
group formation is performed by a Probabilistic Programming approach using
Bayesian Markov Chain Monte Carlo (MCMC) method after applied on the historical
demand statistics. Apart from the group formation, the aggregation strategy
(with the help of Bayesian Inference) also clears out the upper-limit of the
required storage capacity for a formed group, fraction of which is to be
utilized in on-line operation. For on-line operation, a robust energy storage
scheduling method is proposed that minimizes expected imbalance energy and cost
(a non-linear function of imbalance energy) while incorporating the demand
uncertainty of a particular group. The proposed methods are applied on the real
apartment buildings' demand data in Tokyo, Japan. Simulation results are
presented to verify the effectiveness of the proposed methods.


  Ground level Ozone is one of the six common air-pollutants on which the EPA
has set national air quality standards. In order to capture the spatio-temporal
trend of 1-hour and 8-hour average ozone concentration in the US, we develop a
method for spatio-temporal simultaneous quantile regression. Unlike existing
procedures, in the proposed method, smoothing across the sites is incorporated
within modeling assumptions thus allowing borrowing of information across
locations, an essential step when the number of samples in each location is
low. The quantile function has been assumed to be linear in time and smooth
over space and at any given site is given by a convex combination of two
monotone increasing functions $\xi_1$ and $\xi_2$ not depending on time. A
B-spline basis expansion with increasing coefficients varying smoothly over the
space is used to put a prior and a Bayesian analysis is performed. We analyze
the average daily 1-hour maximum and 8-hour maximum ozone concentration level
data of US and California during 2006-2015 using the proposed method. It is
noted that in the last ten years, there is an overall decreasing trend in both
1-hour maximum and 8-hour maximum ozone concentration level over the most parts
of the US. In California, an overall a decreasing trend of 1-hour maximum ozone
level is observed while no particular overall trend has been observed in the
case of 8-hour maximum ozone level.


  This paper presents LibMTL, an open-source Python library built on PyTorch,
which provides a unified, comprehensive, reproducible, and extensible
implementation framework for Multi-Task Learning (MTL). LibMTL considers
different settings and approaches in MTL, and it supports a large number of
state-of-the-art MTL methods, including 12 loss weighting strategies, 7
architectures, and 84 combinations of different architectures and loss
weighting methods. Moreover, the modular design in LibMTL makes it easy-to-use
and well extensible, thus users can easily and fast develop new MTL methods,
compare with existing MTL methods fairly, or apply MTL algorithms to real-world
applications with the support of LibMTL. The source code and detailed
documentations of LibMTL are available at
https://github.com/median-research-group/LibMTL and
https://libmtl.readthedocs.io, respectively.


  The task of typhoon center location plays an important role in typhoon
intensity analysis and typhoon path prediction. Conventional typhoon center
location algorithms mostly rely on digital image processing and mathematical
morphology operation, which achieve limited performance. In this paper, we
proposed an efficient fully convolutional end-to-end deep neural network named
TCLNet to automatically locate the typhoon center position. We design the
network structure carefully so that our TCLNet can achieve remarkable
performance base on its lightweight architecture. In addition, we also present
a brand new large-scale typhoon center location dataset (TCLD) so that the
TCLNet can be trained in a supervised manner. Furthermore, we propose to use a
novel TCL+ piecewise loss function to further improve the performance of
TCLNet. Extensive experimental results and comparison demonstrate the
performance of our model, and our TCLNet achieve a 14.4% increase in accuracy
on the basis of a 92.7% reduction in parameters compared with SOTA deep
learning based typhoon center location methods.


  We provide a simple method to obtain an upper bound on the secret key rate
that is particularly suited to analyze practical realizations of quantum key
distribution protocols with imperfect devices. We consider the so-called
trusted device scenario where Eve cannot modify the actual detection devices
employed by Alice and Bob. The upper bound obtained is based on the available
measurements results, but it includes the effect of the noise and losses
present in the detectors of the legitimate users.


  With widespread applications of artificial intelligence (AI), the
capabilities of the perception, understanding, decision-making and control for
autonomous systems have improved significantly in the past years. When
autonomous systems consider the performance of accuracy and transferability,
several AI methods, like adversarial learning, reinforcement learning (RL) and
meta-learning, show their powerful performance. Here, we review the
learning-based approaches in autonomous systems from the perspectives of
accuracy and transferability. Accuracy means that a well-trained model shows
good results during the testing phase, in which the testing set shares a same
task or a data distribution with the training set. Transferability means that
when a well-trained model is transferred to other testing domains, the accuracy
is still good. Firstly, we introduce some basic concepts of transfer learning
and then present some preliminaries of adversarial learning, RL and
meta-learning. Secondly, we focus on reviewing the accuracy or transferability
or both of them to show the advantages of adversarial learning, like generative
adversarial networks (GANs), in typical computer vision tasks in autonomous
systems, including image style transfer, image superresolution, image
deblurring/dehazing/rain removal, semantic segmentation, depth estimation,
pedestrian detection and person re-identification (re-ID). Then, we further
review the performance of RL and meta-learning from the aspects of accuracy or
transferability or both of them in autonomous systems, involving pedestrian
tracking, robot navigation and robotic manipulation. Finally, we discuss
several challenges and future topics for using adversarial learning, RL and
meta-learning in autonomous systems.


  To explain \eta-distributions at RHIC energies we consider the
Ornstein-Uhlenbeck process. To account for hadrons produced in the central
region, we assume existence of third source located there (y \approx 0) in
addition to two sources located at the beam and target rapidities (\pm y_{max}
= \pm \ln[\sqrt{s_{NN}}/m_{N}]). This results in better \chi^2/n.d.f. than
those for only two sources when analysing data.


  This document describes the Netherlands' decadal strategic planning process
for the current decade. We give the scientific rationale for our prioritization
of research areas and the facility choices that follow from our scientific
priorities. We also describe actions needed for the sustainability of our
community and our work, and the budgets needed to fulfil our stated ambitions.
The names listed as authors are in fact the editors of this paper, which
results from the work of the entire Netherlands astronomy community.


  Asymptotic approximations of the first three cumulants of the
quasi-stationary distribution of the stochastic power law logistic model are
derived. The results are based on a system of ODEs for the first three
cumulants. We deviate from the classical moment closure approach by determining
approximations without closing the system of equations. The approximations are
explicit in the model's parameters, conditions for validity of the
approximations are given, magnitudes of approximation errors are known, and
spurious solutions are easily detected and eliminated. In these ways, we
provide improvements on previous results for this model.


  Let $(M^n,g,e^{-\phi}dV_g,e^{-\phi}dA_g,m)$ be a compact smooth metric
measure space with boundary with $n\geqslant 3$. In this article, we consider
several Yamabe-type problems on a compact smooth metric measure space with or
without boundary: uniqueness problem on the weighted Yamabe problem with
boundary, characterization of the weighted Yamabe solitons with boundary and
the existence of positive minimizers in the weighted Escobar quotient.


  It is shown that, for stationary isotropic turbulence, Taylor's well known
surrogate for the dissipation can be derived directly from the Karman-Howarth
equation and is in fact a surrogate for inertial transfer, which becomes equal
to the dissipation rate as the Reynolds number tends to infinity.


  This brief article sums up results obtained in arXiv:0911.2653, which
develops a constrained SU(2) lattice gauge theory in the "dipole"
approximation. This is a further step toward the issue of a (inhomogeneous)
loop quantum cosmology and its merging into loop quantum gravity.


  This paper presents a non-parametric approach for segmenting trees from
airborne LiDAR data in deciduous forests. Based on the LiDAR point cloud, the
approach collects crown information such as steepness and height on-the-fly to
delineate crown boundaries, and most importantly, does not require a priori
assumptions of crown shape and size. The approach segments trees iteratively
starting from the tallest within a given area to the smallest until all trees
have been segmented. To evaluate its performance, the approach was applied to
the University of Kentucky Robinson Forest, a deciduous closed-canopy forest
with complex terrain and vegetation conditions. The approach identified 94% of
dominant and co-dominant trees with a false detection rate of 13%. About 62% of
intermediate, overtopped, and dead trees were also detected with a false
detection rate of 15%. The overall segmentation accuracy was 77%. Correlations
of the segmentation scores of the proposed approach with local terrain and
stand metrics was not significant, which is likely an indication of the
robustness of the approach as results are not sensitive to the differences in
terrain and stand structures.


  Reinforcement learning (RL) has achieved remarkable success in complex
robotic systems (eg. quadruped locomotion). In previous works, the RL-based
controller was typically implemented as a single neural network with
concatenated observation input. However, the corresponding learned policy is
highly task-specific. Since all motors are controlled in a centralized way,
out-of-distribution local observations can impact global motors through the
single coupled neural network policy. In contrast, animals and humans can
control their limbs separately. Inspired by this biological phenomenon, we
propose a Decentralized motor skill (DEMOS) learning algorithm to automatically
discover motor groups that can be decoupled from each other while preserving
essential connections and then learn a decentralized motor control policy. Our
method improves the robustness and generalization of the policy without
sacrificing performance. Experiments on quadruped and humanoid robots
demonstrate that the learned policy is robust against local motor malfunctions
and can be transferred to new tasks.


  Motivated by Hirano-Tominaga's work \cite{HT} on rings for which every
element is a sum of two idempotents and by de Seguins Pazzis's results
\cite{de} on decomposing every matrix over a field of positive characteristic
as a sum of idempotent matrices, we address decomposing every matrix over a
commutative ring as a sum of three idempotent matrices and, respectively, as a
sum of three involutive matrices.


  We study the transport of atoms across a localized Bose-Einstein condensate
in a one-dimensional optical lattice. For atoms scattering off the condensate
we predict total reflection as well as full transmission for certain parameter
values on the basis of an exactly solvable model. The findings of analytical
and numerical calculations are interpreted by a tunable Fano-like resonance and
may lead to interesting applications for blocking and filtering atom beams.


  We provide a version of the transference principle. It says that certain
optimization problems for functions on the circle, the interval, and the line
have the same answers. In particular, we show that the sharp constants in the
John--Nirenberg inequalities for naturally defined $\mathrm{BMO}$-spaces on the
circle, the interval, and the line coincide. The same principle holds true for
the Reverse H\"older inequality for Muckenhoupt weights.


  After 28 years from the conception of the pyramid WFS several new kind of
devices able to convert wavefront shape into some sort of different
illumination on a detector have been conceived. While, suspending momentarily
any kind of modesty, I claim credit for being among the few that contributed to
show at the time that there could be much more than just a lenslet array I
continued -- with alternating successes -- to conceive other types of such
devices.


  Magnetic skyrmions, topologically nontrivial whirling spin textures at
nanometer scales, have emerged as potential information carriers for spintronic
devices. The ability to efficiently create and erase magnetic skyrmions is
vital yet challenging for such applications. Based on first-principles studies,
we find that switching between intrinsic magnetic skyrmion and high-temperature
ferromagnetic states can be achieved in two-dimensional van der Waals (vdW)
multiferroic heterostructure CrSeI/In2Te3 by reversing the ferroelectric
polarization of In2Te3. The core mechanism of this switching is traced to the
controllable magnetic anisotropy of CrSeI influenced by the ferroelectric
polarization of In2Te3. We propose a useful descriptor linking the presence of
magnetic skyrmions to magnetic parameters, and validate this connection through
studies of a variety of similar vdW multiferroic heterostructures. Our work
demonstrates that manipulating magnetic skyrmions via tunable magnetic
anisotropies in vdW multiferroic heterostructures represents a highly promising
and energy-efficient strategy for future development of spintronics.


  A linear algebraic group $G$ is represented by the linear space of its
algebraic functions $F(G)$ endowed with multiplication and comultiplication
which turn it into a Hopf algebra. Supplying $G$ with a Poisson structure, we
get a quantized version $F_q(G)$ which has the same linear structure and
comultiplication, but deformed multiplication. This paper develops a similar
theory for abelian varieties. A description of abelian varieties $A$ in terms
of linear algebra data was given by Mumford: $F(G)$ is replaced by the graded
ring of theta functions with symmetric automorphy factors, and comultiplication
is replaced by the Mumford morphism $M^*$ acting on pairs of points as
$M(x,y)=M(x+y,x-y).$ After supplementing this by a Poisson structure and
replacing the classical theta functions by the quantized ones, introduced by
the author earlier, we obtain a structure which essentially coincides with the
classical one so far as comultiplication is concerned, but has a deformed
multiplication which moreover becomes only partial. The classical graded ring
is thus replaced by a linear category. Another important difference from the
linear case is that abelian varieties with different period groups (for
multiplication) and different quantization parameters (for comultiplication)
become interconnected after quantization.


  We experimentally generate a non-classical correlated two-color photon pair
at 780 and 1529.4 nm in a ladder-type configuration using a hot 85Rb atomic
vapor with the production rate of ~107/s. The non-classical correlation between
these two photons is demonstrated by strong violation of Cauchy-Schwarz
inequality by the factor R=48+-12. Besides, we experimentally investigate the
relations between the correlation and some important experimental parameters
such as the single-photon detuning, the powers of pumps. We also make a
theoretical analysis in detail and the theoretical predictions are in
reasonable agreement with our experimental results.


  The shortest-remaining-processing-time (SRPT) scheduling policy has been
extensively studied, for more than 50 years, in single-server queues with
infinitely patient jobs. Yet, much less is known about its performance in
multiserver queues. In this paper, we present the first theoretical analysis of
SRPT in multiserver queues with abandonment. In particular, we consider the
M/GI/s+GI queue and demonstrate that, in the many-sever overloaded regime,
performance in the SRPT queue is equivalent, asymptotically in steady state, to
a preemptive two-class priority queue where customers with short service times
(below a threshold) are served without wait, and customers with long service
times (above a threshold) eventually abandon without service. We prove that the
SRPT discipline maximizes, asymptotically, the system throughput, among all
scheduling disciplines. We also compare the performance of the SRPT policy to
blind policies and study the effects of the patience-time and service-time
distributions.


  Self-supervised learning is a central component in recent approaches to deep
multi-view clustering (MVC). However, we find large variations in the
development of self-supervision-based methods for deep MVC, potentially slowing
the progress of the field. To address this, we present DeepMVC, a unified
framework for deep MVC that includes many recent methods as instances. We
leverage our framework to make key observations about the effect of
self-supervision, and in particular, drawbacks of aligning representations with
contrastive learning. Further, we prove that contrastive alignment can
negatively influence cluster separability, and that this effect becomes worse
when the number of views increases. Motivated by our findings, we develop
several new DeepMVC instances with new forms of self-supervision. We conduct
extensive experiments and find that (i) in line with our theoretical findings,
contrastive alignments decreases performance on datasets with many views; (ii)
all methods benefit from some form of self-supervision; and (iii) our new
instances outperform previous methods on several datasets. Based on our
results, we suggest several promising directions for future research. To
enhance the openness of the field, we provide an open-source implementation of
DeepMVC, including recent models and our new instances. Our implementation
includes a consistent evaluation protocol, facilitating fair and accurate
evaluation of methods and components.


  We perform numerical simulations of cosmic necklaces (systems of monopoles
connected to two strings each) and investigate the conditions under which
monopoles annihilate. When the total monopole energy is large compared to the
string energy, we find that the string motion is no longer periodic, and thus
the strings will be chopped up by self intersection. When the total monopole
energy is much smaller than the string energy, the string motion is periodic,
but that of the monopoles is not, and thus the monopoles travel along the
string and annihilate with each other.