  We study the detectability of neutrino bursts from nearby direct black
hole-forming collapses (failed supernovae) at Megaton detectors. Due to their
high energetics, these bursts could be identified - by the time coincidence of
N >= 2 or N >= 3 events within a ~ 1 s time window - from as far as ~ 4-5 Mpc
away. This distance encloses several supernova-rich galaxies, so that failed
supernova bursts could be detected at a rate of up to one per decade,
comparable to the expected rate of the more common, but less energetic, neutron
star-forming collapses. Thus, the detection of a failed supernova within the
lifetime of a Mt detector is realistic. It might give the first evidence of
direct black hole formation, with important implications on the physics of this
phenomenon.


  Generic interactions e.g. the Coulomb or other long ranged radially symmetric
repulsive interactions between monomers of bead-spring model of a semi-flexible
polymer induce instabilities in a initially straight polymer chain to form long
lived helical structures. This mechanism can explain the spontaneous emergence
of helices in stiff (bio-)polymers as effective charge of the chain increases.
The helix formation is independent of the chemistry and torsional potentials
are not used. So this method can be used to synthesize helical springs at
length scales of nm-10$\mu$.


  We present a Conversational Chain-of-Action (Conv-CoA) framework for
Open-domain Conversational Question Answering (OCQA). Compared with literature,
Conv-CoA addresses three major challenges: (i) unfaithful hallucination that is
inconsistent with real-time or domain facts, (ii) weak reasoning performance in
conversational scenarios, and (iii) unsatisfying performance in conversational
information retrieval. Our key contribution is a dynamic reasoning-retrieval
mechanism that extracts the intent of the question and decomposes it into a
reasoning chain to be solved via systematic prompting, pre-designed actions,
updating the Contextual Knowledge Set (CKS), and a novel Hopfield-based
retriever. Methodologically, we propose a resource-efficiency Hopfield
retriever to enhance the efficiency and accuracy of conversational information
retrieval within our actions. Additionally, we propose a
conversational-multi-reference faith score (Conv-MRFS) to verify and resolve
conflicts between retrieved knowledge and answers in conversations.
Empirically, we conduct comparisons between our framework and 23
state-of-the-art methods across five different research directions and two
public benchmarks. These comparisons demonstrate that our Conv-CoA outperforms
other methods in both the accuracy and efficiency dimensions.


  We study how an evanescence process affects the number of distinct sites
visited by a continuous time random walker in one dimension. We distinguish two
very different cases, namely, when evanescence can only occur concurrently with
a jump, and when evanescence can occur at any time. The first is characteristic
of trapping processes on a lattice, whereas the second is associated with
spontaneous death processes such as radioactive decay. In both of these
situations we consider three different forms of the waiting time distribution
between jumps, namely, exponential, long-tailed, and ultra-slow.


  Radiation is important for the propagation of streamers in dielectric
liquids. Photoionization is a possibility, but the effect is difficult to
differentiate from other contributions. In this work, we model radiation from
the streamer head, causing photoionization when absorbed in the liquid. We find
that photoionization is local in space ({\mu}m-scale). The radiation absorption
cross section is modeled considering that the ionization potential (IP) is
dependent on the electric field. The result is a steep increase in the
ionization rate when the electric field reduces the IP below the energy of the
first electronically excited state, which is interpreted as a possible
mechanism for changing from slow to fast streamers. By combining a simulation
model for slow streamers based on the avalanche mechanism with a change to fast
mode based on a photoionization threshold for the electric field, we
demonstrate how the conductivity of the streamer channel can be important for
switching between slow and fast streamer propagation modes.


  In this paper, we consider a multi-user wireless system with one full duplex
(FD) base station (BS) serving a set of half duplex (HD) mobile users.To cope
with the in-band self-interference (SI) and co-channel interference, we
formulate a quality-of-service (QoS) based linear transceiver design problem.
The problem jointly optimizes the downlink (DL) and uplink (UL) beamforming
vectors of the BS and the transmission powers of UL users so as to provide both
the DL and UL users with guaranteed signal-to-interference-plus-noise ratio
performance, using a minimum UL and DL transmission sum power.The considered
system model not only takes into account noise caused by non-ideal RF circuits,
analog/digital SI cancellation but also constrains the maximum signal power at
the input of the analog-to-digital converter (ADC) for avoiding signal
distortion due to finite ADC precision. The formulated design problem is not
convex and challenging to solve in general. We first show that for a special
case where the SI channel estimation errors are independent and identically
distributed, the QoS-based linear transceiver design problem is globally
solvable by a polynomial-time bisection algorithm.For the general case, we
propose a suboptimal algorithm based on alternating optimization (AO). The AO
algorithm is guaranteed to converge to a Karush-Kuhn-Tucker solution.To reduce
the complexity of the AO algorithm, we further develop a fixed-point method by
extending the classical uplink-downlink duality in HD systems to the FD
system.Simulation results are presented to demonstrate the performance of the
proposed algorithms and the comparison with HD systems.


  Background: The early stage of defect prediction in the software development
life cycle can reduce testing effort and ensure the quality of software. Due to
the lack of historical data within the same project, Cross-Project Defect
Prediction (CPDP) has become a popular research topic among researchers. CPDP
trained classifiers based on labeled data sets of one project to predict fault
in another project. Goals: Software Defect Prediction (SDP) data sets consist
of manually designed static features, which are software metrics. In CPDP,
source and target project data divergence is the major challenge in achieving
high performance. In this paper, we propose a Generative Adversarial Network
(GAN)-based data transformation to reduce data divergence between source and
target projects. Method: We apply the Generative Adversarial Method where label
data sets are choosing as real data, while target data sets are choosing as
fake data. The Discriminator tries to measure the perfection of domain
adaptation through loss function. Through the generator, target data sets try
to adapt the source project domain and, finally, apply machine learning
classifier (i.e., Naive Bayes) to classify faulty modules. Results: Our result
shows that it is possible to predict defects based on the Generative
Adversarial Method. Our model performs quite well in a cross-project
environment when we choose JDT as a target data sets. However, all chosen data
sets are facing a large class imbalance problem which affects the performance
of our model.


  Electrical communication between cardiomyocytes can be perturbed during
arrhythmia, but these perturbations are not captured by conventional
electrocardiographic metrics. We developed a theoretical framework to quantify
electrical communication using information theory metrics in 2-dimensional cell
lattice models of cardiac excitation propagation. The time series generated by
each cell was coarse-grained to 1 when excited or 0 when resting. The Shannon
entropy for each cell was calculated from the time series during four
clinically important heart rhythms: normal heartbeat, anatomical reentry,
spiral reentry, and multiple reentry. We also used mutual information to
perform spatial profiling of communication during these cardiac arrhythmias. We
found that information sharing between cells was spatially heterogeneous. In
addition, cardiac arrhythmia significantly impacted information sharing within
the heart. Entropy localized the path of the drifting core of spiral reentry,
which could be an optimal target of therapeutic ablation. We conclude that
information theory metrics can quantitatively assess electrical communication
among cardiomyocytes. The traditional concept of the heart as a functional
syncytium sharing electrical information cannot predict altered entropy and
information sharing during complex arrhythmia. Information theory metrics may
find clinical application in the identification of rhythm-specific treatments
which are currently unmet by traditional electrocardiographic techniques.


  This paper establishes conditions for optimality of an $(s,S)$ ordering
policy for the minimization of the long-term average cost of one-dimensional
diffusion inventory models. The class of such models under consideration have
general drift and diffusion coefficients and boundary points that are
consistent with the notion that demand should tend to decrease the inventory
level. Characterization of the cost of a general $(s,S)$ policy as a function
$F$ of two variables naturally leads to a nonlinear optimization problem over
the ordering levels $s$ and $S$. Existence of an optimizing pair $(s_*,S_*)$ is
established for these models. Using the minimal value $F_*$ of $F$, along with
$(s_*,S_*)$, a function $G$ is identified which is proven to be a solution of a
quasi-variational inequality provided a simple condition holds. At this level
of generality, optimality of the $(s_*,S_*)$ ordering policy is established
within a large class of ordering policies such that local martingale and
transversality conditions involving $G$ hold. For specific models, optimality
of an $(s,S)$ policy in the general class of admissible policies can be
established using comparison results. This most general optimality result is
shown for the classical drifted Brownian motion inventory model with holding
and fixed plus proportional ordering costs and for a geometric Brownian motion
inventory model with fixed plus level-dependent ordering costs. However, for a
drifted Brownian motion process with reflection at $\{0\}$, a new class of
non-Markovian policies is introduced which have lower costs than the $(s,S)$
policies. In addition, interpreting reflection at $\{0\}$ as "just-in-time"
ordering, a necessary and sufficient condition is given that determines when
just-in-time ordering is better than traditional $(s,S)$ policies.


  Networks of nonlinear resonators offer intriguing perspectives as quantum
simulators for non-equilibrium many-body phases of driven-dissipative systems.
Here, we employ photon correlation measurements to study the radiation fields
emitted from a system of two superconducting resonators, coupled nonlinearly by
a superconducting quantum interference device (SQUID). We apply a
parametrically modulated magnetic flux to control the linear photon hopping
rate between the two resonators and its ratio with the cross-Kerr rate. When
increasing the hopping rate, we observe a crossover from an ordered to a
delocalized state of photons. The presented coupling scheme is intrinsically
robust to frequency disorder and may therefore prove useful for realizing
larger-scale resonator arrays.


  We construct an experimental setup in which changing the scale of
initialization strongly impacts the implicit regularization induced by SGD,
interpolating from good generalization performance to completely memorizing the
training set while making little progress on the test set. Moreover, we find
that the extent and manner in which generalization ability is affected depends
on the activation and loss function used, with $\sin$ activation demonstrating
extreme memorization. In the case of the homogeneous ReLU activation, we show
that this behavior can be attributed to the loss function. Our empirical
investigation reveals that increasing the scale of initialization correlates
with misalignment of representations and gradients across examples in the same
class. This insight allows us to devise an alignment measure over gradients and
representations which can capture this phenomenon. We demonstrate that our
alignment measure correlates with generalization of deep models trained on
image classification tasks.


  Around the time of its perihelion passage the observability of
67P/Churyumov-Gerasimenko from Earth was limited to very short windows each
morning from any given site, due to the low solar elongation of the comet. The
peak in the comet's activity was therefore difficult to observe with
conventionally scheduled telescopes, but was possible where service/queue
scheduled mode was possible, and with robotic telescopes. We describe the
robotic observations that allowed us to measure the total activity of the comet
around perihelion, via photometry (dust) and spectroscopy (gas), and compare
these results with the measurements at this time by Rosetta's instruments. The
peak of activity occurred approximately two weeks after perihelion. The total
brightness (dust) largely followed the predictions from Snodgrass et al. 2013,
with no significant change in total activity levels from previous apparitions.
The CN gas production rate matched previous orbits near perihelion, but
appeared to be relatively low later in the year.


  This work investigates the relationships between quantum state synthesis
complexity classes (a recent concept in computational complexity that focuses
on the complexity of preparing quantum states) and traditional decision
complexity classes. We especially investigate the role of the synthesis error
parameter, which characterizes the quality of the synthesis in quantum state
synthesis complexity classes. We first show that in the high synthesis error
regime, collapse of synthesis classes implies collapse of the equivalent
decision classes. For more reasonable synthesis error, we then show a similar
relationships for BQP and QCMA. Finally, we show that for quantum state
synthesis classes it is in general impossible to improve the quality of the
synthesis: unlike the completeness and soundness parameters (which can be
improved via repetition), the synthesis error cannot be reduced, even with
arbitrary computational power.


  The completely general radiative corrections to lowest order, including the
final and initial state radiations, are studied in proton-antiproton
annihilation to an electron-positron pair. Numerical estimates have been made
in a realistic configuration of the PANDA detector at FAIR for the proton
time-like form factors measurements.


  We report on submillimeter and infrared observations of 28 radio-selected
galaxies in the Spitzer First Look Survey Verification field (FLSV). All of the
radio-selected galaxies that show evidence for emission at 850um with SCUBA
have Spitzer counterparts at 24um, while only half of the radio-selected
galaxies without 850um emission have detectable counterparts at 24um. The data
show a wide range of infrared colors (S70/S24 < 5--30, S8/S3.6 < 0.3--4),
indicative of a mixture of infrared-warm AGN and cooler starburst dominated
sources. The galaxies showing 850um emission have Spitzer flux densities and
flux density ratios consistent with the range of values expected for
high-redshift (z=1--4) ultraluminous infrared galaxies.


  The influence of static disorder on a quantum phase transition (QPT) is a
fundamental issue in condensed matter physics. As a prototypical example of a
disorder-tuned QPT, the superconductor-insulator transition (SIT) has been
investigated intensively over the past three decades, but as yet without a
general consensus on its nature. A key element is good control of disorder.
Here, we present an experimental study of the SIT based on precise in-situ
tuning of disorder in dual-gated bilayer graphene proximity-coupled to two
superconducting electrodes through electrical and reversible control of the
band gap and the charge carrier density. In the presence of a static disorder
potential, Andreev-paired carriers formed close to the Fermi level in bilayer
graphene constitute a randomly distributed network of proximity-induced
superconducting puddles. The landscape of the network was easily tuned by
electrical gating to induce percolative clusters at the onset of
superconductivity. This is evidenced by scaling behavior consistent with the
classical percolation in transport measurements. At lower temperatures, the
solely electrical tuning of the disorder-induced landscape enables us to
observe, for the first time, a crossover from classical to quantum percolation
in a single device, which elucidates how thermal dephasing engages in
separating the two regimes.


  We investigate particle production \`a la Schwinger mechanism in an
expanding, flat de Sitter patch as is relevant for the inflationary epoch of
our universe. Defining states and particle content in curved spacetime is
certainly not a unique process. There being different prescriptions on how that
can be done, we have used the Schr\"odinger formalism to define instantaneous
particle content of the state etc. This allows us to go past the adiabatic
regime to which the effect has been restricted in the previous studies and
bring out its multifaceted nature in different settings. Each of these settings
gives rise to contrasting features and behaviour as per the effect of electric
field and expansion rate on the instantaneous mean particle number. We also
quantify the degree of classicality of the process during its evolution using a
"classicality parameter" constructed out of parameters of the Wigner function
to obtain information about the quantum to classical transition in this case.


  One of the most important and actual issues in relativistic astrophysics is
testing gravity theories and obtaining constraint values for the parameters of
black holes using observational data. In this research, we aimed to explore the
optical features of a Kerr--Newman black hole model in the presence of a
quintessential field, which may be a candidate for a dark-energy model with a
nonzero cosmological constant. First, we obtain the equations of motion for
photons using the Hamilton--Jacobi formalism. We also study the horizons and
shapes of the apparent regions of the photon region around the said black hole.
In various scenarios, we investigate shadows cast by the black hole using
celestial coordinates. Furthermore, we analyze the effects of the
quintessential field and black hole charge on the shadow radius and distortion.
Furthermore, we look into the constraints on the spin and charge of
supermassive black holes M87$^*$ and Sagittarius A$^*$ for different values of
the quintessential field using their shadow size measured by the Event Horizon
Telescope Collaboration. Finally, we study the effects of the quintessential
field, black hole spin and charge on its energy emission rate by Hawking
radiation and compare our results with those of the available literature.


  We show at the example of the matrix element between pion states of a
twist-2, non-singlet operator that Wilson twisted mass fermions allow to
compute this phenomenologically relevant quantitiy at small pseudo scalar
masses of O(270 MeV). In the quenched approximation, we investigate the scaling
behaviour of this observable that is derived from a 3-point function by
applying two definitions of the critical mass and find a scaling compatible
with the expected O(a^2) behaviour in both cases. A combined continuum
extrapolations allows to obtain reliable results at small pion masses, which
previously could not be explored by lattice QCD simulations.


  We present a non-parametric Lagrangian biasing model and fit the ratio of the
halo and mass densities at the field level using the mass-weighted halo field
in the AbacusSummit simulations at $z=0.5$. Unlike the perturbative halo bias
model widely used in interpreting the observed large-scale structure traced by
galaxies, we find a non-negative halo-to-mass ratio that increases
monotonically with the linear overdensity $\delta_1$ in the initial Lagrangian
space. The bias expansion, however, does not guarantee non-negativity of the
halo counts, and may give rising halo number counts at negative overdensities.
The shape of the halo-to-mass ratio is unlikely to be described by a polynomial
of $\delta_1$ and other quantities. Especially for massive halos with
$6\times10^{12}\ h^{-1}\ M_\odot$, the halo-to-mass ratio starts soaring up at
$\delta_1>0$, substantially different from the predictions of the bias
expansion. We show that for the halo masses we consider ($M>3\times10^{11}\
h^{-1}\ M_\odot$) a non-parametric halo-to-mass ratio as a function of
$\delta_1$ and its local derivative $\nabla^2\delta_1$ can recover the halo
power spectra to sub-percent level for wavenumbers $k=0.01-0.1\ h\ {\rm
Mpc}^{-1}$ given a proper smoothing scale to filter the initial density field,
even though we do not fit the power spectrum directly. However, there is mild
dependence of the recovery of the halo power spectrum on the smoothing scale
and other input parameters. At $k<0.01\ h\ {\rm Mpc}^{-1}$ and for massive
halos with $M>6\times10^{12}\ h^{-1}\ M_\odot$, our non-parametric model leads
to a few percent overestimation of the halo power spectrum, indicating the need
for larger or multiple smoothing scales. The halo-to-mass ratios obtained
qualitatively agree with intuitions from extended Press-Schechter theory. We
compare our framework to the bias expansion and discuss possible extensions.


  This paper defines a method for lexicon in the biomedical domain from
comparable corpora. The method is based on compositional translation and
exploits morpheme-level translation equivalences. It can generate translations
for a large variety of morphologically constructed words and can also generate
'fertile' translations. We show that fertile translations increase the overall
quality of the extracted lexicon for English to French translation.


  Worldsheet techniques can be used to argue for the integrability of string
theory on AdS_5xS^5/Z_S, which is dual to the strongly coupled Z_S-orbifold of
N=4 SYM. We analyze the integrability of these field theories in the
perturbative regime and construct the relevant Bethe equations.


  We present a Waveform Relaxation (WR) version of the Neumann-Neumann
algorithm for the wave equation in space-time. The method is based on a
non-overlapping spatial domain decomposition, and the iteration involves
subdomain solves in space-time with corresponding interface condition, followed
by a correction step. Using a Fourier-Laplace transform argument, for a
particular relaxation parameter, we prove convergence of the algorithm in a
finite number of steps for finite time intervals. The number of steps depends
on the size of the subdomains and the time window length on which the algorithm
is employed. We illustrate the performance of the algorithm with numerical
results, followed by a comparison with classical and optimized Schwarz WR
methods.


  Using molecular dynamics simulations and integral equations (Rogers-Young,
Percus-Yevick and hypernetted chain closures) we investigate the thermodynamic
of particles interacting with continuous core-softened intermolecular
potential. Dynamic properties are also analyzed by the simulations. We show
that, for a chosen shape of the potential, the density, at constant pressure,
has a maximum for a certain temperature. The line of temperatures of maximum
density (TMD) was determined in the pressure-temperature phase diagram.
Similarly the diffusion constant at a constant temperature, $D$, has a maximum
at a density $\rho_{max}$ and a minimum at a density $\rho_{min}<\rho_{max}$.
In the pressure-temperature phase-diagram the line of extrema in diffusivity is
outside of TMD line. Although in this interparticle potential lacks
directionality, this is the same behavior observed in SPC/E water.


  A Maxwell solver derived from finite element method with \mathcal{O}(N)
computing cost is developed to improve the numerical dispersion properties in
relativistic particle-in-cell (PIC) simulations. The correction of the
dispersion relation of the electromagnetic wave is achieved using the
neighboring cells via an iteration scheme without decomposing into Fourier
modes. The local nature of the communication is ideally suited to massively
parallel computer architectures. This Maxwell solver constrains the Numerical
Cherenkov instability (NCI) for the ultra-relativistic drifting pair plasma in
x direction to large wave vectors for two dimensional grid. The growth rate of
NCI is suppressed by using the low pass filtering.


  Forum discussion data differ in both structure and properties from generic
form of textual data such as news. Henceforth, summarization techniques should,
in turn, make use of such differences, and craft models that can benefit from
the structural nature of discussion data. In this work, we propose attending to
the beginning of a document, to improve the performance of extractive
summarization models when applied to forum discussion data. Evaluations
demonstrated that with the help of bidirectional attention mechanism, attending
to the beginning of a document (initial comment/post) in a discussion thread,
can introduce a consistent boost in ROUGE scores, as well as introducing a new
State Of The Art (SOTA) ROUGE scores on the forum discussions dataset.
Additionally, we explored whether this hypothesis is extendable to other
generic forms of textual data. We make use of the tendency of introducing
important information early in the text, by attending to the first few
sentences in generic textual data. Evaluations demonstrated that attending to
introductory sentences using bidirectional attention, improves the performance
of extractive summarization models when even applied to more generic form of
textual data.


  Results from the latest searches for pair-produced scalar leptoquarks using
36.1 $\text{fb}^{-1}$ of $pp$-collision data recorded by the ATLAS detector at
$\sqrt{s}$ = 13 TeV were presented. No statistically significant excess of data
over Standard Model prediction is observed. The observed limits on first-
(second-) generation leptoquark masses are excluded up to 1400 (1560) GeV in
the minimal Buchm\"uller-R\"uckl-Wyler model, assuming a leptoquark decay
branching ratio of 100% into a charged lepton and a quark. Third generation
leptoquark masses are excluded up to 1000 GeV at the highest and lowest decay
branching ratios for both up-type and down-type leptoquarks.


  Context: Variations in the mass accretion rate appear to be responsible for
the rapid transitions in spectral type that are observed in increasingly more
active galactic nuclei (AGNs). These objects are now labeled "changing-look"
AGNs and are key objects for understanding the physics of accretion onto
supermassive black holes. Aims: We aim to complement the analysis and
interpretation of changing-look AGNs by modeling the polarization variations
that can be observed, in particular, polarized-light echoes. Methods: We built
a complex and representative model of an AGN and its host galaxy and ran
radiative transfer simulations to obtain realistic time-dependent polarization
signatures of changing-look objects. Based on actual data, we allowed the
system to become several times fainter or brighter within a few years, assuming
a rapid change in accretion rate. Results: We obtain time-dependent
polarization signatures of distant high-luminosity (quasars) and nearby
low-luminosity (Seyferts) changing-look AGNs for a representative set of
inclinations. We predict the evolution of the continuum polarization for future
polarimetric campaigns with the goal to better understand the physics at work
in these objects. We also investigate highly inclined AGNs that experience
strong accretion rate variations without appearing to change state. We apply
our modeling to Mrk 1018, the best-documented case of a changing-look AGN, and
predict a variation in its polarization after the recent dimming of its
continuum.


  We introduce a definition of the volume for a general rectangular matrix,
which for square matrices is equivalent to the absolute value of the
determinant. We generalize results for square maximum-volume submatrices to the
case of rectangular maximal-volume submatrices, show connection of the
rectangular volume with optimal experimental design and provide estimates for
the growth of the coefficients and approximation error in spectral and
Chebyshev norms. Three promising applications of such submatrices are
presented: recommender systems, finding maximal elements in low-rank matrices
and preconditioning of overdetermined linear systems. The code is available
online.


  Evaluating large summarization corpora using humans has proven to be
expensive from both the organizational and the financial perspective.
Therefore, many automatic evaluation metrics have been developed to measure the
summarization quality in a fast and reproducible way. However, most of the
metrics still rely on humans and need gold standard summaries generated by
linguistic experts. Since BLANC does not require golden summaries and
supposedly can use any underlying language model, we consider its application
to the evaluation of summarization in German. This work demonstrates how to
adjust the BLANC metric to a language other than English. We compare BLANC
scores with the crowd and expert ratings, as well as with commonly used
automatic metrics on a German summarization data set. Our results show that
BLANC in German is especially good in evaluating informativeness.


  In this paper an explanation of the Pioneer anomaly is given, using the
hypothesis of the time dependent gravitational potential. The implications of
this hypothesis on the planetary orbits and orbital periods are given in
section 2. In sections 3 and 4 we give a detailed explanation of the Pioneer
anomaly, which corresponds to the observed phenomena.


  Defect-free graphene is impermeable to all atoms and ions at ambient
conditions. Experiments that can resolve gas flows of a few atoms per hour
through micrometre-sized membranes found that monocrystalline graphene is
completely impermeable to helium, the smallest of atoms. Such membranes were
also shown to be impermeable to all ions, including the smallest one, lithium.
On the other hand, graphene was reported to be highly permeable to protons,
nuclei of hydrogen atoms. There is no consensus, however, either on the
mechanism behind the unexpectedly high proton permeability or even on whether
it requires defects in graphene's crystal lattice. Here using high resolution
scanning electrochemical cell microscopy (SECCM), we show that, although proton
permeation through mechanically-exfoliated monolayers of graphene and hexagonal
boron nitride cannot be attributed to any structural defects, nanoscale
non-flatness of 2D membranes greatly facilitates proton transport. The spatial
distribution of proton currents visualized by SECCM reveals marked
inhomogeneities that are strongly correlated with nanoscale wrinkles and other
features where strain is accumulated. Our results highlight nanoscale
morphology as an important parameter enabling proton transport through 2D
crystals, mostly considered and modelled as flat, and suggest that strain and
curvature can be used as additional degrees of freedom to control the proton
permeability of 2D materials.


  In this paper we show that the negative sample distance covariance function
is a quasi-concave set function of samples of random variables that are not
statistically independent. We use these properties to propose greedy algorithms
to combinatorially optimize some diversity (low statistical dependence)
promoting functions of distance covariance. Our greedy algorithm obtains all
the inclusion-minimal maximizers of this diversity promoting objective.
Inclusion-minimal maximizers are multiple solution sets of globally optimal
maximizers that are not a proper subset of any other maximizing set in the
solution set. We present results upon applying this approach to obtain diverse
features (covariates/variables/predictors) in a feature selection setting for
regression (or classification) problems. We also combine our diverse feature
selection algorithm with a distance covariance based relevant feature selection
algorithm of [7] to produce subsets of covariates that are both relevant yet
ordered in non-increasing levels of diversity of these subsets.


  It was shown recently that Birkhoff's theorem for doubly stochastic matrices
can be extended to unitary matrices with equal line sums whenever the dimension
of the matrices is prime. We prove a generalization of the Birkhoff theorem for
unitary matrices with equal line sums for arbitrary dimension.


  Massless neutrino exchange leads to a new long-range force between matter.
Recently, it was claimed both that the potential energy due to this interaction
i) dominates the total energy of neutron stars and ii) that it is zero. We
recalculate the energy of a neutrino propagating in a classical, uniform
background of neutrons and find a negligible, but non-zero contribution to the
total energy of neutron stars. We estimate the neutrino pair creation rate of a
neutron star caused by a density gradient of the background neutrons but found
it too small to be observable.


  The teleportation channel associated with an arbitrary bipartite state
denotes the map that represents the change suffered by a teleported state when
the bipartite state is used instead of the ideal maximally entangled state for
teleportation. This work presents and proves an explicit expression of the
teleportation channel for the teleportation using Weyl's projective unitary
representation of the space of 2n-tuples of numbers from Z/dZ for integers d>1,
n>0, which has been known for n=1. This formula allows any correlation among
the n bipartite mixed states, and an application shows the existence of
reliable schemes for distillation of entanglement from a sequence of mixed
states with correlation.


  In this paper, an electromagnetic sensor which can operate simultaneously in
capacitive and inductive modalities with sensitivities to permittivity,
conductivity, and permeability is developed, and a novel measurement strategy
is proposed accordingly. The sensor is composed of two planar spiral coils with
a track width of 4 mm, which promotes its capacitive mode. The capacitive
coupling is measured in common mode, while the inductive coupling is measured
in differential mode. In capacitive mode, the sensor is sensitive to changes in
permittivity, i.e., the dielectric material distribution; while in inductive
mode, it is sensitive to magnetically permeable material and electrically
conductive material. Furthermore, it is demonstrated that the sensor can
simultaneously measure dielectric and conductive materials. This novel sensing
element has been designed and implemented. Experimental results verified its
effectiveness in dual modality measurement.


  In this paper we give a diameter bound for Sasaki manifolds with positive
transverse Ricci curvature. As an application, we obtain the uniqueness of
Sasaki-Einstein metrics on compact Sasaki manifolds modulo the action of the
identity component of the automorphism group for the transverse holomorphic
structure.


  In this work, we study convergence in probability and almost sure convergence
for weighted partial sums of random variables that are related to the class of
generalized Oppenheim expansions. It is worth noting that the random variables
under study have infinite mean and the results are obtained without any
dependence assumptions.


  We propose a branching process based on a dynamical scaling hypothesis
relating time and mass. In the context of earthquake occurrence, we show that
experimental power laws in size and time distribution naturally originate
solely from this scaling hypothesis. We present a numerical protocol able to
generate a synthetic catalog with an arbitrary large number of events. The
numerical data reproduce the hierarchical organization in time and magnitude of
experimental inter-event time distribution.


  For a pair of spaces $X$ and $Y$ such that $Y \subseteq X$, we define the
relative topological complexity of the pair $(X,Y)$ as a new variant of
relative topological complexity. Intuitively, this corresponds to counting the
smallest number of motion planning rules needed for a continuous motion planner
from $X$ to $Y$. We give basic estimates on the invariant, and we connect it to
both Lusternik-Schnirelmann category and topological complexity. In the
process, we compute this invariant for several example spaces including wedges
of spheres, topological groups, and spatial polygon spaces. In addition, we
connect the invariant to the existence of certain types of axial maps.


  TIC137608661/TYC4544-2658-1/FBS0938+788 is a new sdBV+dM reflection-effect
binary discovered by the TESS space mission with an orbital period of 7.21
hours. In addition to the orbital frequency and its harmonics, the Fourier
transform of TIC137608661 shows many g-mode pulsation frequencies from the sdB
star. The amplitude spectrum is particularly simple to interpret as we
immediately see several rotational triplets of equally spaced frequencies. The
central frequencies of these triplets are equally spaced in period with a mean
period spacing of 270.12 s, corresponding to consecutive l=1 modes. From the
mean frequency spacing of 1.25 {\mu}Hz we derive a rotation period of 4.6 days
in the deep layers of the sdB star, significantly longer than the orbital
period. Among the handful of sdB+dM binaries for which the sdB rotation was
measured through asteroseismology, TIC137608661 is the non-synchronized system
with both the shortest orbital period and the shortest core rotation period.
Only NY Vir has a shorter orbital period but it is synchronized. From a
spectroscopic follow-up of TIC137608661 we measure the radial velocities of the
sdB star, determine its atmospheric parameters, and estimate the rotation rate
at the surface of the star. This measurement allows us to exclude synchronized
rotation also in the outer layers and suggests a differential rotation, with
the surface rotating faster than the core, as found in few other similar
systems. Furthermore, an analysis of the spectral energy distribution of
TIC137608661, together with a comparison between sdB pulsation properties and
asteroseismic models, gives us further elements to constrain the system.


  Given $n\in\mathbb{N}$ and $\tau>\frac1n$, let $\mathcal{S}_n(\tau)$ denote
the classical set of $\tau$-approximable points in $\mathbb{R}^n$, which
consists of ${\bf x}\in \mathbb{R}^n$ that lie within distance $q^{-\tau-1}$
from the lattice $\frac1q\mathbb{Z}^n$ for infinitely many $q\in\mathbb{N}$. In
pioneering work, Kleinbock $\&$ Margulis showed that for any non-degenerate
submanifold $\mathcal{M}$ of $\mathbb{R}^n$ and any $\tau>\frac1n$ almost all
points on $\mathcal{M}$ are not $\tau$-approximable. Numerous subsequent papers
have been geared towards strengthening this result through investigating the
Hausdorff measure and dimension of the associated null set
$\mathcal{M}\cap\mathcal{S}_n(\tau)$. In this paper we suggest a new approach
based on the Mass Transference Principle, which enables us to find a sharp
lower bound for $\dim \mathcal{M}\cap\mathcal{S}_n(\tau)$ for any $C^2$
submanifold $\mathcal{M}$ of $\mathbb{R}^n$ and any $\tau$ satisfying
$\frac1n\le\tau<\frac1m$. Here $m$ is the codimension of $\mathcal{M}$. We also
show that the condition on $\tau$ is best possible and extend the result to
general approximating functions.


  In this paper, we propose a novel approach to learning semantic contextual
relationships in videos for semantic object segmentation. Our algorithm derives
the semantic contexts from video object proposals which encode the key
evolution of objects and the relationship among objects over the
spatio-temporal domain. This semantic contexts are propagated across the video
to estimate the pairwise contexts between all pairs of local superpixels which
are integrated into a conditional random field in the form of pairwise
potentials and infers the per-superpixel semantic labels. The experiments
demonstrate that our contexts learning and propagation model effectively
improves the robustness of resolving visual ambiguities in semantic video
object segmentation compared with the state-of-the-art methods.


  Community Question Answering (CQA) sites have spread and multiplied
significantly in recent years. Sites like Reddit, Quora, and Stack Exchange are
becoming popular amongst people interested in finding answers to diverse
questions. One practical way of finding such answers is automatically
predicting the best candidate given existing answers and comments. Many studies
were conducted on answer prediction in CQA but with limited focus on using the
background information of the questionnaires. We address this limitation using
a novel method for predicting the best answers using the questioner's
background information and other features, such as the textual content or the
relationships with other participants. Our answer classification model was
trained using the Stack Exchange dataset and validated using the Area Under the
Curve (AUC) metric. The experimental results show that the proposed method
complements previous methods by pointing out the importance of the
relationships between users, particularly throughout the level of involvement
in different communities on Stack Exchange. Furthermore, we point out that
there is little overlap between user-relation information and the information
represented by the shallow text features and the meta-features, such as time
differences.


  Nonrigid mathematical structures may no longer form usual Eilenberg - Mac
Lane categories, but more general ones, as illustrated by pseudo-topologies. A
rather general concept of pseudo-topology was used in constructing differential
algebras of generalized functions containing the Schwartz distributions,
[4-6,8-11]. These algebras proved to be convenient in solving large classes of
nonlinear partial differential equations, see [12,13] and the literature cited
there, as well as section 46F30 in the Subject Classification 2000 of the
American Mathematical Society, at www.ams.org/index/msc/46Fxx.html The totality
of such pseudo-topologies no longer constitutes a usual Eilenberg - Mac Lane
category, but an extended one which is presented here. Other nonrigid
mathematical structures are mentioned and treated briefly. This is a revised
and augmented version of the earlier published paper [7].


  gamma Dor-type oscillations have been discovered in the star HD218427 through
simultaneous uvby photometric observations carried out in the year 2003. A few
Hbeta-Crawford measurements were also collected for calibration purposes which
place this star well-located inside the gamma Dor instability region.
Deficiency in metal content, similar to other well-defined gamma Dor stars, is
found in HD218427 and the possibility of a lambda Boo nature is discussed.
Frequency analysis was carried out for different filters, the combined "vby"
filter was also used and five frequencies were found as significant with
periods ranging between 0.3 and 0.8 days. The recently developed Frequency
Ratio Method is used in order to perform an identification of the excited
modes. The results are consistent with an l=2 identification for all the modes
and high radial quantum numbers (n~40) for the three main observed
periodicities. The possibility of multiplet structures is also discussed.
However, no consistency is found when the Time-Dependent Convection treatment
is used for modes discrimination. The disagreement can be due to the large
rotation velocity taking place in HD218427 and, consequently, the significant
coupling between the modes.


  Examples of repeatable procedures and maps are found in the open quantum
dynamics of one qubit that interacts with another qubit. They show that a
mathematical map that is repeatable can be made by a physical procedure that is
not.


  Deep learning has led to tremendous advancements in the field of Artificial
Intelligence. One caveat however is the substantial amount of compute needed to
train these deep learning models. Training a benchmark dataset like ImageNet on
a single machine with a modern GPU can take upto a week, distributing training
on multiple machines has been observed to drastically bring this time down.
Recent work has brought down ImageNet training time to a time as low as 4
minutes by using a cluster of 2048 GPUs. This paper surveys the various
algorithms and techniques used to distribute training and presents the current
state of the art for a modern distributed training framework. More
specifically, we explore the synchronous and asynchronous variants of
distributed Stochastic Gradient Descent, various All Reduce gradient
aggregation strategies and best practices for obtaining higher throughout and
lower latency over a cluster such as mixed precision training, large batch
training and gradient compression.


  Context. Some of of the most prominent sources for energetic particles in our
Solar System are huge eruptions of magnetised plasma from the Sun called
coronal mass ejections (CMEs), which usually drive shocks that accelerate
charged particles up to relativistic energies. In particular, energetic
electron beams can generate radio bursts through the plasma emission mechanism.
The main types of bursts associated with CME shocks are type II and herringbone
bursts. However, it is currently unknown where early accelerated electrons that
produce metric type II bursts and herringbones propagate and when they escape
the solar atmosphere. Aims. Here, we investigate the acceleration location,
escape, and propagation directions of electron beams during the early evolution
of a strongly expanding CME-driven shock wave associated with herrinbgone
bursts. Methods. We used ground-based radio observations from the Nan\c{c}ay
Radioheliograph combined with space-based extreme-ultraviolet and white-light
observations from the Solar Dynamics Observatory and and the Solar Terrestrial
Relations Observatory. We produced a three-dimensional (3D) representation of
the electron acceleration locations which, combined with results from
magneto-hydrodynamic (MHD) models of the solar corona, was used to investigate
the origin of the herringbone bursts observed. Results. Multiple herringbone
bursts are found close to the CME flank in plane-of-sky images. Some of these
herringbone bursts have unusual inverted J shapes and opposite drifting
herringbones also show opposite senses of circular polarisation. By using a 3D
approach combined with the radio properties of the observed bursts, we find
evidence that the first radio emission in the CME eruption most likely
originates from electrons that initially propagate in regions of low Alfv\'en
speeds and along closed magnetic field lines forming a coronal streamer.


  While the daily user of digital, Internet-enabled devices has some explicit
control over what they read and see, the providers fulfilling searches,
offering options, and presenting material are using increasingly sophisticated
real-time algorithms that tune and target content for the particular user. They
redefine the historical relationships between tellers and users, providing a
responsiveness paralleled only by forms of live performance incorporating
elements of improvisation and audience interaction. The general accessibility
of algorithmically driven content delivery techniques suggests significant
untapped potential for new approaches to narrative beyond advertising and
commercially orientated customization.


  The recently developed refractory multi-principle element alloy (MPEA),
AlMo$_{0.5}$NbTa$_{0.5}$TiZr, shows an interesting microstructure with cuboidal
precipitates of a disordered phase (${\beta}$, bcc) coherently embedded in an
ordered phase (${\beta}'$, B2) matrix, unlike the conventional Ni-based
superalloys where the ordered phase (${\gamma}'$, L12) is the precipitate phase
and the disordered phase (${\gamma}$, fcc) is the matrix phase. It becomes
critical to understand the phase transformation pathway (PTP) leading to this
microstructure in order to tailor the microstructure for specific engineering
applications. In this study, we first propose a possible PTP leading to the
microstructure and employ the phase-field method to simulate microstructural
evolution along the PTP. We then explore possible PTPs and materials parameters
that lead to an inverted microstructure with the ordered phase being the
precipitate phase and the disordered phase being the matrix phase, a
microstructure similar to those observed in Ni-based superalloys. We find that
in order to maintain the precipitates as highly discrete particles along these
PTPs, the volume fraction of the precipitate phase needs to be smaller than
that of the matrix phase and the elastic stiffness of the precipitate phase
should be higher than that of the matrix phase.


  The Sun and the undisturbed interstellar magnetic field and plasma velocity
vectors (Bis,Vis) define a mirror symmetry plane of the flow at large
heliospheric distances. We show that for the Bis direction defined by IBEX
Ribbon center, the radial direction of Voyager 2 over the last decade, and the
(thermal proton) plasma velocity measured by the spacecraft since 2010.5, are
almost parallel to the (Bis,Vis)-plane, which coincides in practice with the
Hydrogen Deflection Plane. These facts can be simply explained if approximate
mirror symmetry is also maintained on the inner side of the heliopause. Such
approximate symmetry is possible since the solar wind ram pressure is almost
spherically symmetric and the plasma beta value in the inner heliosheath is
high. In the proposed symmetry, the plasma flow speed measured by Voyager 2 in
the inner heliosheath is expected to rotate more in the transverse than in the
polar direction (explanation alternative to McComas & Schwadron (2014)), in
evident agreement with available spacecraft data (our Fig.1).


  The IEEE 754-2008 standard recommends the correct rounding of some elementary
functions. This requires to solve the Table Maker's Dilemma which implies a
huge amount of CPU computation time. We consider in this paper accelerating
such computations, namely Lefe'vre algorithm on Graphics Processing Units
(GPUs) which are massively parallel architectures with a partial SIMD execution
(Single Instruction Multiple Data). We first propose an analysis of the
Lef\`evre hard-to-round argument search using the concept of continued
fractions. We then propose a new parallel search algorithm much more efficient
on GPU thanks to its more regular control flow. We also present an efficient
hybrid CPU-GPU deployment of the generation of the polynomial approximations
required in Lef\`evre algorithm. In the end, we manage to obtain overall
speedups up to 53.4x on one GPU over a sequential CPU execution, and up to 7.1x
over a multi-core CPU, which enable a much faster solving of the Table Maker's
Dilemma for the double precision format.


  We show how to perform a resummation, to all orders in perturbation theory,
of a certain class of gauge invariant diagrams in Lattice QCD. These diagrams
are often largely responsible for lattice artifacts. Our resummation leads to
an improved perturbative expansion. Applied to a number of cases of interest,
this expansion yields results remarkably close to corresponding nonperturbative
estimates.


  This report presents the usage results of Grid'5000 over year 2008. Usage of
the main operationnal Grid'5000 sites (Bordeaux, Lille, Lyon, Nancy, Orsay,
Rennes, Sophia-Antipolis, Toulouse) is presented and analyzed.


  By performing experiments with thin-film resonators of NbSi, we elucidate a
decoherence mechanism at work in disordered superconductors. This decoherence
is caused by charged Two Level Systems (TLS) which couple to the conduction
electrons in the BCS ground state; it does not involve any out-of-equilibrium
quasiparticles, vortices, etc. Standard theories of mesoscopic disordered
conductors enable making predictions regarding this mechanism, notably that
decoherence should increase as the superconductor cross section decreases.
Given the omnipresence of charged TLS in solid-state systems, this decoherence
mechanism affects, to some degree, all experiments involving disordered
superconductors. In particular, we show it easily explains the poor coherence
observed in quantum phase slip experiments and may contribute to lowering the
quality factors in some disordered superconductor resonators.


  Many real applications of bandits have sparse non-zero rewards, leading to
slow learning rates. A careful distribution modeling that utilizes
problem-specific structures is known as critical to estimation efficiency in
the statistics literature, yet is under-explored in bandits. To fill the gap,
we initiate the study of zero-inflated bandits, where the reward is modeled as
a classic semi-parametric distribution called zero-inflated distribution. We
carefully design Upper Confidence Bound (UCB) and Thompson Sampling (TS)
algorithms for this specific structure. Our algorithms are suitable for a very
general class of reward distributions, operating under tail assumptions that
are considerably less stringent than the typical sub-Gaussian requirements.
Theoretically, we derive the regret bounds for both the UCB and TS algorithms
for multi-armed bandit, showing that they can achieve rate-optimal regret when
the reward distribution is sub-Gaussian. The superior empirical performance of
the proposed methods is shown via extensive numerical studies.


  The key idea is that rewriting procedures can be enhanced so that they not
only rewrite words but record (log) how the rewriting has taken place. We
introduce logged rewrite systems and present a variation on the Knuth-Bendix
algorithm for obtaining (where possible) complete logged rewrite systems. This
procedure is then applied to work of Brown and Razak Salleh, and an algorithm
is developed which provides a set of generators for the module of identities
among relations of a group presentation.


  In galactic disks, galactic rotation sets the bulk motion of gas, and its
energy and momentum can be transferred toward small scales. Additionally, in
the interstellar medium, random and noncircular motions arise from stellar
feedback, cloud-cloud interactions, and instabilities, among other processes.
Our aim is to comprehend to which extent small-scale gas dynamics is decoupled
from galactic rotation. We study the relative contributions of galactic
rotation and local noncircular motions to the circulation of gas, $\Gamma$, a
macroscopic measure of local rotation, defined as the line integral of the
velocity field around a closed path. We measure the circulation distribution as
a function of spatial scale in a set of simulated disk galaxies and we model
the velocity field as the sum of galactic rotation and a Gaussian random field.
The random field is parameterized by a broken power law in Fourier space, with
a break at the scale $\lambda_c$. We define the spatial scale $\lambda_{\rm
eq}$ at which galactic rotation and non-circular motions contribute equally to
$\Gamma$. For our simulated galaxies, the gas dynamics at the scale of
molecular clouds is usually dominated by noncircular motions, but in the center
of galactic disks galactic rotation is still relevant. Our model shows that the
transfer of rotation from large scales breaks at the scale $\lambda_c$ and this
transition is necessary to reproduce the circulation distribution. We find that
$\lambda_{\rm eq}$, and therefore the structure of the gas velocity field, is
set by the local conditions of gravitational stability and stellar feedback.


  It has been suggested that space-time might undergo fluctuations because of
its intrinsic quantum nature. These fluctuations would pose a fundamental limit
to the ability of measuring distances with arbitrary precision, beyond any
limitations due to standard quantum mechanics. Laser interferometers have
recently been proposed as being suited for a search for the existence of
space-time fluctuations. Here we present results of a search for space-time
fluctuations of very low fluctuation frequencies, in the range from 1 microHz
to 0.5 Hz. Rigid optical interferometers made out of sapphire and operated at
cryogenic temperature were used. We find an upper limit of 1.10^-24 Hz^-1 for
the normalized distance noise spectral density at 6 microHz, and of 1.10^-28
Hz^-1 above 5 mHz, and establish an experimental limit for the parameter of a
recently proposed random-walk hypothesis.


  Gene expression is inherently noisy, posing a challenge to understanding how
precise and reproducible patterns of gene expression emerge in mammals. We
investigate this phenomenon using gastruloids, an in vitro model for early
mammalian development. Our study reveals intrinsic reproducibility in the
self-organization of gastruloids, encompassing growth dynamics and gene
expression patterns. We observe a remarkable degree of control over gene
expression along the main body axis, with pattern boundaries positioned at
single-cell precision. Furthermore, as gastruloids grow, both their physical
proportions and gene expression patterns scale proportionally with system size.
Notably, these properties emerge spontaneously in self-organizing cell
aggregates, distinct from many in vivo systems constrained by fixed boundary
conditions. Our findings shed light on the intricacies of developmental
precision, reproducibility, and size scaling within a mammalian system,
suggesting that these phenomena might constitute fundamental features of
multicellularity.


  We demonstrate that electromagnons can be used to directly probe the nature
of a phase transition between magnetically ordered phases in an improper
ferroelectric. The antiferromagnetic/paraelectric to
antiferromagnetic/ferroelectric phase transition in Cu$_{1-x}$Zn$_{x}$O ($x=0,
0.05$) alloys was tracked via the electromagnon response using terahertz
time-domain spectroscopy, on heating and cooling through the phase transition.
The transition was found to exhibit thermal hysteresis, confirming its
first-order nature, and to broaden under the influence of spin-disorder upon Zn
substitution. The energy of the electromagnon increases upon alloying, as a
result of the non-magnetic ions modifying the magnetic interactions that give
rise to the multiferroic phase and electromagnons. We describe our findings in
the context of recent theoretical work that examined improper ferroelectricity
and electromagnons in CuO from phenomenological and first-principles
approaches.


  In the paper we introduce the notions of a singular fibration and a singular
Seifert fibration. These notions are natural generalizations of the notion of a
locally trivial fibration to the category of stratified pseudomanifolds. For
singular foliations defined by such fibrations we prove a de Rham type theorem
for the basic intersection cohomology introduced the authors in a recent paper.
One of important examples of such a structure is the natural projection onto
the leaf space for the singular Riemannian foliation defined by an action of a
compact Lie group on a compact smooth manifold.


We review many topics and results about numeric gauge fixing in lattice QCD.


  The pumping intensity (I) dependence of the photoluminescence (PL) spectra of
perfectly laterally two-dimensionally ordered SiGe quantum dots on Si(001)
substrates was studied. The PL results from recombinations of holes localized
in the SiGe quantum dots and electrons localized due to the strain field in the
surrounding Si matrix. The analysis of the spectra revealed several distinct
bands, attributed to phonon-assisted recombination and no-phonon recombination
of the excitonic ground state and of the excited excitonic states, which all
exhibit a linear I dependence of the PL intensity. At approximately I>3W/cm^2,
additional bands with a nearly quadratic I dependence appear in the PL spectra,
resulting from biexcitonic transitions. These emerging PL contributions shift
the composite no-phonon PL band of the SiGe quantum dots to higher energies.
The experimentally obtained energies of the no-phonon transitions are in good
agreement with the exciton and biexciton energies calculated using the envelope
function approximation and the configuration interaction method.


  We discovered secular trend bias in a drug effectiveness study for a recently
approved drug. We compared treatment outcomes between patients who received the
newly approved drug and patients exposed to the standard treatment. All
patients diagnosed after the new drug's approval date were considered. We built
a machine learning causal inference model to determine patient subpopulations
likely to respond better to the newly approved drug. After identifying the
presence of secular trend bias in our data, we attempted to adjust for the bias
in two different ways. First, we matched patients on the number of days from
the new drug's approval date that the patient's treatment (new or standard)
began. Second, we included a covariate in the model for the number of days
between the date of approval of the new drug and the treatment (new or
standard) start date. Neither approach completely mitigated the bias. Residual
bias we attribute to differences in patient disease severity or other
unmeasured patient characteristics. Had we not identified the secular trend
bias in our data, the causal inference model would have been interpreted
without consideration for this underlying bias. Being aware of, testing for,
and handling potential bias in the data is essential to diminish the
uncertainty in AI modeling.


  We describe a simple scheme by which "optical flux lattices" can be
implemented in ultracold atomic gases using two-photon dressed states. This
scheme can be applied, for example, to the ground state hyperfine levels of
commonly used atomic species. The resulting flux lattices simulate a magnetic
field with high mean flux density, and have low energy bands analogous to the
lowest Landau level. We show that in practical cases the atomic motion
significantly deviates from the adiabatic following of one dressed state, and
that this can lead to significant interactions even for fermions occupying a
single band. Our scheme allows experiments on cold atomic gases to explore
strong correlation phenomena related to the fractional quantum Hall effect,
both for fermions and bosons.


  Prototype Generation (PG) methods are typically considered for improving the
efficiency of the $k$-Nearest Neighbour ($k$NN) classifier when tackling
high-size corpora. Such approaches aim at generating a reduced version of the
corpus without decreasing the classification performance when compared to the
initial set. Despite their large application in multiclass scenarios, very few
works have addressed the proposal of PG methods for the multilabel space. In
this regard, this work presents the novel adaptation of four multiclass PG
strategies to the multilabel case. These proposals are evaluated with three
multilabel $k$NN-based classifiers, 12 corpora comprising a varied range of
domains and corpus sizes, and different noise scenarios artificially induced in
the data. The results obtained show that the proposed adaptations are capable
of significantly improving -- both in terms of efficiency and classification
performance -- the only reference multilabel PG work in the literature as well
as the case in which no PG method is applied, also presenting a statistically
superior robustness in noisy scenarios. Moreover, these novel PG strategies
allow prioritising either the efficiency or efficacy criteria through its
configuration depending on the target scenario, hence covering a wide area in
the solution space not previously filled by other works.


  Recently Dzhafarov and Kon published the paper advertising the possibility to
use the coupling technique of classical probability theory to model
incompatible observables in quantum physics and quantum-like models of
psychology. Here I present comments on this paper by stressing advantages and
disadvantages.


  It is an established fact that a finite difference operator approximates a
derivative with a fixed algebraic rate of convergence. Nevertheless, we exhibit
a new finite difference operator and prove it has spectral accuracy. Its rate
of convergence is not fixed and improves with the function's regularity. For
example, the rate of convergence is exponential for analytic functions. Our new
framework is conceptually nonstandard, making no use of polynomial
interpolation, nor any other expansion basis, such as typically considered in
approximation theory. Our new method arises solely from the numerical
manipulation of singular integrals, through an accurate quadrature for Cauchy
Principal Value convolutions. The kernel is a distribution which gives rise to
multi-resolution grid coefficients. The respective distributional finite
difference scheme is spatially structured having stencils of different support
widths. These multi-resolution stencils test/estimate function variations in a
nonlocal fashion, giving rise to a highly accurate distributional finite
difference operator. Computational illustrations are presented, where the
accuracy and roundoff error structure are compared with the respective Fourier
based method. We also compare our method with a recent and popular complex-step
method.


  In order to facilitate the application of standard renormalization
techniques, gravitation should be decribed, if possible, in pure connection
formalism, as a Yang-Mills theory of a certain spacetime group, say the
Poincare or the affine group. This embodies the translational as well as the
linear connection. However, the coframe is not the standard Yang-Mills type
gauge field of the translations, since it lacks the inhomogeneous gradient term
in the gauge transformations. By explicitly restoring the "hidden" piece
responsible for this behavior within the framework of nonlinear realizations,
the usual geometrical interpretation of the dynamical theory becomes possible,
and in addition one can avoid the metric or coframe degeneracy which would
otherwise interfere with the integrations within the path integral. We claim
that nonlinear realizations provide a general mathematical scheme clarifying
the foundations of gauge theories of spacetime symmetries. When applied to
construct the Yang-Mills theory of the affine group, tetrads become identified
with nonlinear translational connections; the anholonomic metric does not
constitute any more an independent gravitational potential, since its degrees
of freedom reveal to correspond to eliminable Goldstone bosons. This may be an
important advantage for quantization.


  We establish existence and regularity results for normal Coulomb frames in
the normal bundle of two-dimensional surfaces of disc-type embedded in
Euclidean spaces of higher dimensions.


  The transition from monolayers to multilayered structures in bacterial
colonies is a fundamental step in biofilm development. Observed across
different morphotypes and species, this transition is triggered within freely
growing bacterial microcolonies comprising a few hundred cells. Using a
combination of numerical simulations and analytical modeling, here we
demonstrate that this transition originates from the competition between
growth-induced in-plane active stresses and vertical restoring forces, due to
the cell-substrate interactions. Using a simple chainlike colony of laterally
confined cells, we show that the transition sets when individual cells become
unstable to rotations, thus it is localized and mechanically deterministic.
Asynchronous cell division renders the process stochastic, so that all the
critical parameters that control the onset of the transition are continuously
distributed random variables. Here we demonstrate that the occurrence of the
first division in the colony can be approximated as a Poisson process in the
limit of large cells numbers. This allows us to approximately calculate the
probability distribution function of the position and time associated with the
first extrusion. The rate of such a Poisson process can be identified as the
order parameter of the transition, thus highlighting its mixed
deterministic-stochastic nature.


  In this paper, the shadow casted by the rotating black hole inspired by
noncommutative geometry is investigated. In addition to the dimensionless spin
parameter $a/M_{0}$ with $M_{0}$ black hole mass and inclination angle $i$, the
dimensionless noncommutative parameter $\sqrt{\vartheta}/M_{0}$ is also found
to affect the shape of the black hole shadow. The result shows that the size of
the shadow slightly decreases with the parameter $\sqrt{\vartheta}/M_{0}$,
while the distortion increases with it. Compared to the Kerr black hole, the
parameter $\sqrt{\vartheta}/M_{0}$ increases the deformation of the shadow.
This may offer a way to distinguish noncommutative geometry inspired black hole
from Kerr one via astronomical instruments in the near future.


  Applying the Helmholtz Decomposition theorem to linearized General Relativity
leads to a gauge-invariant formulation where the transverse-traceless part of
the metric perturbation describes gravitational waves in matter. Gravitational
waves incident on a superconductor can be described by a linear London-like
constituent equation characterized by a "gravitational shear modulus" and a
corresponding plasma frequency and penetration depth. Electric-like and
magnetic-like gravitational tensor fields are defined in terms of the strain
field of a gravitational wave. It is shown that in the DC limit, the
magnetic-like tensor field is expelled from the superconductor in a
gravitational Meissner-like effect. The Cooper pair density is described by the
GinzburgLandau free energy density embedded in curved spacetime. The ionic
lattice is modeled by quantum harmonic oscillators coupled to gravitational
waves and characterized by quasi-energy eigenvalues for the phonon modes. The
formulation predicts the possibility of a dynamical Casimir effect since the
zero-point energy of the ionic lattice phonons is found to be modulated by the
gravitational wave, in a quantum analog of a "Weber-bar effect." Applying
periodic thermodynamics and the Debye model in the low-temperature limit leads
to a free energy density for the ionic lattice. Lastly, we relate the
gravitational strain of space to the strain of matter to show that the response
to a gravitational wave is far less for the Cooper pair density than for the
ionic lattice. This predicts a charge separation effect in the superconductor
as a result of the gravitational wave.


  We combine theory and experiment to investigate five-body recombination in an
ultracold gas of atomic cesium at negative scattering length. A refined
theoretical model, in combination with extensive laboratory tunability of the
interatomic interactions, enables the five-body resonant recombination rate to
be calculated and measured. The position of the new observed recombination
feature agrees with a recent theoretical prediction and supports the prediction
of a family of universal cluster states at negative $a$ that are tied to an
Efimov trimer.


  We prove the existence of a successful coupling for $n$ particles in the
symmetric inclusion process. As a consequence we characterize the ergodic
measures with finite moments, and obtain sufficient conditions for a measure to
converge in the course of time to an invariant product measure.


  This is an introductory course on nonlinear integrable partial differential
and differential-difference equ\-a\-ti\-ons based on lectures given for
students of Moscow Institute of Physics and Technology and Higher School of
Economics. The typical examples of Korteweg-de Vries (KdV),
Kadomtsev-Petviashvili (KP) and Toda lattice equations are studied in detail.
We give a detailed description of the Lax representation of these equations and
their hierarchies in terms of pseudo-differential or pseudo-difference
operators and also of different classes of the solutions including famous
soliton solutions. The formulation in terms of tau-function and Hirota bilinear
differential and difference equations is also discussed. Finally, we give a
representation of tau-functions as vacuum expectation values of certain
operators composed of free fermions.


  Using first and second order supersymmetry formalism we obtain a class of
exactly solvable potentials subject to moving boundary conditions.


  The objective of this work is to report on the influence of muon interactions
on the development of air showers initiated by astroparticles. We make a
comparative study of the different theoretical approaches to muon
bremsstrahlung and muonic pair production interactions. A detailed algorithm
that includes all the relevant characteristics of such processes has been
implemented in the AIRES air shower simulation system. We have simulated ultra
high energy showers in different conditions in order to measure the influence
of these muonic electromagnetic interactions. We have found that during the
late stages of the shower development (well beyond the shower maximum) many
global observables are significantly modified in relative terms when the
mentioned interactions are taken into account. This is most evident in the case
of the electromagnetic component of very inclined showers. On the other hand,
our simulations indicate that the studied processes do not induce significant
changes either in the position of the shower maximum or the structure of the
shower front surface.


  If F is an infinitely differentiable function whose composition with a
blowing-up belongs to a Denjoy-Carleman class C_M (determined by a log convex
sequence M=(M_k)), then F, in general, belongs to a larger shifted class C_N,
where N_k = M_2k; i.e., there is a loss of regularity. We show that this loss
of regularity is sharp. In particular, loss of regularity of Denjoy-Carleman
classes is intrinsic to arguments involving resolution of singularities.


  The presence of asymmetry between fermions of opposite handedness in plasmas
of relativistic particles can lead to exponential growth of a helical magnetic
field via a small-scale chiral dynamo instability known as the chiral magnetic
effect. Here, we show, using dimensional arguments and numerical simulations,
that this process produces through the Lorentz force chiral magnetically driven
turbulence. A k^{-2} magnetic energy spectrum emerges via inverse transfer over
a certain range of wavenumbers k. The total chirality (magnetic helicity plus
normalized chiral chemical potential) is conserved in this system. Therefore,
as the helical magnetic field grows, most of the total chirality gets
transferred into magnetic helicity until the chiral magnetic effect terminates.
Quantitative results for height, slope, and extent of the spectrum are
obtained. Consequences of this effect for cosmic magnetic fields are discussed.


  We employ a variational Monte Carlo approach to efficiently obtain the
dynamical structure factor for the spin-1/2 $J_1-J_2$ Heisenberg model on the
square lattice. Upon increasing the frustrating ratio $J_2/J_1$, the ground
state undergoes a continuous transition from a N\'eel antiferromagnet to a
$\mathbb{Z}_{2}$ gapless spin liquid. We identify the characteristic spectral
features in both phases and highlight the existence of a broad continuum of
excitations in the proximity of the spin-liquid phase. The magnon branch, which
dominates the spectrum of the unfrustrated Heisenberg model, gradually loses
its spectral weight, thus releasing nearly-deconfined spinons, whose signatures
are visible even in the magnetically ordered state. Our results show how free
spinons emerge across a quantum critical point, providing evidence for the
fractionalization of magnons into deconfined spinons.


  We used the ESO VLT-FORS2 facility to collect low-resolution spectra of 51
targets distributed along the Horizontal Branch. We determined atmospheric
parameters by comparison with theoretical models through standard fitting
routines, and masses by basic equations. Results are in general in good
agreement with previous works, although not always with theoretical
expectations for cooler stars (Teff<15000 K). The calculated color excess is
systematically lower than literature values, pointing towards a possible
underestimation of effective temperatures. Moreover, we find two groups of
stars at Teff=14000 K and at Teff=27000$ K that present anomalies with respect
to the general trend and expectations. We suppose that the three peculiar
bright stars at Teff=14000 K are probably affected by an enhanced stellar wind.
For the eight Extreme Horizontal Branch stars at Teff=27000 K which show
unusually high masses we find no plausible explanation. While most of our
results agree well with the predictions of standard horizontal branch
evolution, we still have problems with the low masses we derive in certain
temperature ranges. We believe that Kurucz ATLAS9 LTE model atmospheres with
solar-scaled abundances are probably inadequate for these temperature ranges.
Concerning the group of anomalous stars at Teff=27000 K, a Kolmogorov-Smirnov
test indicates that there is only an 8.4% probability that these stars are
randomly drawn from the general distribution in the color-magnitude diagram.
This is not conclusive but points out that these stars could be both (and
independently) spectroscopically and photometrically peculiar with respect to
the general Extreme Horizontal Branch population.


  Differently from animals, robots can record its experience correctly for long
time. We propose a novel algorithm that runs a particle filter on the time
sequence of the experience. It can be applied to some teach-and-replay tasks.
In a task, the trainer controls a robot, and the robot records its sensor
readings and its actions. We name the sequence of the record an episode, which
is derived from the episodic memory of animals. After that, the robot executes
the particle filter so as to find a similar situation with the current one from
the episode. If the robot chooses the action taken in the similar situation, it
can replay the taught behavior. We name this algorithm the particle filter on
episode (PFoE). The robot with PFoE shows not only a simple replay of a
behavior but also recovery motion from skids and interruption. In this paper,
we evaluate the properties of PFoE with a small mobile robot.


  The discretization of Cahn-Hilliard equation with obstacle potential leads to
a block 2 by 2 non-linear system, where the p1, 1q block has a non-linear and
non-smooth term. Recently a globally convergent Newton Schur method was
proposed for the non-linear Schur complement corresponding to this non-linear
system. The solver may be seen as an inexact Uzawa method which has the falvour
of an active set method in the sense that the active sets are first identified
by solving a quadratic obstacle problem corresponding to the p1, 1q block of
the block 2 by 2 nonlinear system, and a new decent direction is obtained after
discarding the active set region. The problem becomes linear on nonactive set,
and corresponds to solving a linear saddle point problem on truncated domains.
For solving the quadratic obstacle problem, various optimal multigrid like
methods have been proposed. In this paper solvers for the truncated saddle
point problem is considered. Three preconditioners are considered, two of them
have block diagonal structure, and the third one has block tridiagonal
structure. One of the block diagonal preconditioners is obtained by adding
certain scaling of stiffness and mass matrices, whereas, the remaining two
involves Schur complement. Eigenvalue bound and condition number estimates are
derived for the preconditioned untruncated problem. It is shown that the
extreme eigenvalues of the preconditioned truncated system remain bounded by
the extreme eigenvalues of the preconditioned untruncated system. Numerical
experiments confirm the optimality of the solvers.


  We consider a system of hardcore particles advected by a fluctuating
potential energy landscape, whose dynamics is in turn affected by the
particles. Earlier studies have shown that as a result of two-way coupling
between the landscape and the particles, the system shows an interesting phase
diagram as the coupling parameters are varied. The phase diagram consists of
various different kinds of ordered phases and a disordered phase. We introduce
a relative timescale $\omega$ between the particle and landscape dynamics, and
study its effect on the steady state properties. We find there exists a
critical value $\omega = \omega_{c}$ when all configurations of the system are
equally likely in the steady state. We prove this result exactly in a discrete
lattice system and obtain an exact expression for $\omega_c$ in terms of the
coupling parameters of the system. We show that $\omega_c$ is finite in the
disordered phase, diverges at the boundary between the ordered and disordered
phase, and is undefined in the ordered phase. We also derive $\omega_c$ from a
coarse-grained level description of the system using linear hydrodynamics. We
start with the assumption that there is a specific value $\omega^\ast$ of the
relative timescale when correlations in the system vanish, and mean-field
theory gives exact expressions for the current Jacobian matrix $A$ and
compressibility matrix $K$. Our exact calculations show that Onsager-type
current symmetry relation $AK = KA^{T}$ can be satisfied if and only if
$\omega^\ast = \omega_c$ . Our coarse-grained model calculations can be easily
generalized to other coupled systems.


  Starting from the $0^{++}$ glueball mass and wave function computed from
lattice QCD, we compute the local potential between two constituent gluons.
Since the properties of constituent gluons are still a matter of research, we
allow for them to be either massless, or massive with a mass around 0.7 GeV.
Both pictures are actually used in the literature. When the gluons are
massless, the corresponding local potential is shown to be compatible with a
Cornell form, that is a linear confinement plus a short-range Coulomb part,
with standard values for the flux tube energy density and for the strong
coupling constant. When the gluons are massive, the confining potential is a
saturating one, commonly used to simulate string-breaking effects. These
results fill a gap between lattice QCD and phenomenological models: The picture
of the scalar glueball as a bound state of two constituent gluons interacting
via a phenomenological potential is shown to emerge from pure gauge lattice QCD
computations. Moreover, we show that the allowed potential shape is constrained
by the mass of the constituent gluons.


  In the present paper several bounds on multiplicities of eigenvalues of the
Laplacian operator on surfaces are generalized from the case of either closed
surface or simply-connected planar domain to the case of a surface of positive
genus with holes.


  The rate of quasi-stationary, two-dimensional magnetic reconnection is
calculated in the framework of incompressible Hall magnetohydrodynamics (MHD).
The calculation is based on the solution of Hall-MHD equations that include
Hall and electron pressure terms for electric current. These equations are
solved in a local region across the reconnection electron layer, including only
the upstream region and the layer center. In the case when the ion inertial
length d_i is larger than the Sweet-Parker reconnection layer thickness, the
dimensionless reconnection rate is found to be independent of the electrical
resistivity and equal to d_i/L, where L is the scale length of the external
magnetic field in the upstream region outside the electron layer.


  This whitepaper presents the research priorities decided on by attendees of
the 2022 Town Meeting for Fundamental Symmetries, Neutrons and Neutrinos, which
took place December 13-15, 2022 in Chapel Hill, NC, as part of the Nuclear
Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of
275 scientists registered for the meeting. The whitepaper makes a number of
explicit recommendations and justifies them in detail.


  Since the Russian invasion of Ukraine, a large volume of biased and partisan
news has been spread via social media platforms. As this may lead to wider
societal issues, we argue that understanding how partisan news sharing impacts
users' communication is crucial for better governance of online communities. In
this paper, we perform a measurement study of partisan news sharing. We aim to
characterize the role of such sharing in influencing users' communications. Our
analysis covers an eight-month dataset across six Reddit communities related to
the Russian invasion. We first perform an analysis of the temporal evolution of
partisan news sharing. We confirm that the invasion stimulates discussion in
the observed communities, accompanied by an increased volume of partisan news
sharing. Next, we characterize users' response to such sharing. We observe that
partisan bias plays a role in narrowing its propagation. More biased media is
less likely to be spread across multiple subreddits. However, we find that
partisan news sharing attracts more users to engage in the discussion, by
generating more comments. We then built a predictive model to identify users
likely to spread partisan news. The prediction is challenging though, with
61.57% accuracy on average. Our centrality analysis on the commenting network
further indicates that the users who disseminate partisan news possess lower
network influence in comparison to those who propagate neutral news.


  Robust synchronization is indispensable for stable operation of a power grid.
Recently, it has been reported that a large number of decentralized generators,
rather than a small number of large power plants, provide enhanced
synchronization together with greater robustness against structural failures.
In this paper, we systematically control the spatial uniformity of the
geographical distribution of generators, and conclude that the more uniformly
generators are distributed, the more enhanced synchronization occurs. In the
presence of temporal failures of power sources, we observe that spatial
uniformity helps the power grid to recover stationarity in a shorter time. We
also discuss practical implications of our results in designing the structure
of a power-grid network.


  Protein-surface interactions cause the desirable effect of controlled protein
adsorption onto biodevices as well as the undesirable effect of protein
fouling. The key to controlling protein-surface adsorptions is to identify and
quantify the main adsorption mechanisms: adsorptions that occur (1) while
depositing a protein solution onto dry surfaces and (2) after the deposition
onto wet surfaces. Bulk measurements cannot reveal the dynamic protein
adsorption pathways and thus cannot differentiate between the two adsorption
mechanisms. We imaged the interactions of single streptavidin molecules with
hydrophobic fused-silica surfaces in real-time. We observed both adsorbed
proteins on surfaces and diffusing proteins near surfaces and analyzed their
adsorption kinetics. Our analysis shows that the protein solution deposition
process is the primary mechanism of streptavidin adsorption onto surfaces at
the sub-nanomolar to nanomolar protein concentrations. Furthermore, we found
that hydrophilic fused-silica surfaces can prevent the adsorption of
streptavidin molecules.


  This paper studies crystalline representations of G_K with coefficients of
any dimension, where K is the unramified extension of Q_p of degree a. We prove
a theorem of Fontaine-Laffaille type when \sigma-invariant Hodge-Tate weight
less than p-1, which establishes the bijection between Galois stable lattices
in crystalline representations and strongly divisible \phi-lattice. In
generalizing Breuil's work, we classify all reducible and irreducible
crystalline representations of G_K of dimensional 2, then describe their mod p
reductions. We generalize some results (of Deligne, Fontaine-Serre, and
Edixhoven) to representations arising from Hilbert modular forms when
\sigma-invariant Hodge-Tate weight less than p-1.


  In this work we investigate the effects of the short range magnetic
correlations on the gap opening of the topological Kondo insulators. We
consider an additional narrow band to the otherwise completely localized
f-electrons, by adding a term to the periodic Anderson model which allows a
small hopping of the localized electrons between neighboring sites of the
lattice. This new model is adequate to study a novel class of intermetallic 4f
and 5f orbitals materials: the Kondo topological insulators, whose paradigmatic
material is the compound SmB6.
  For simplicity, we consider a version of the periodic Anderson model on a two
dimensional square lattice. The starting point of the model is the 4f-Ce ions
orbitals, with J=5/2 multiplet in the presence of spin-orbit coupling. We
present results of the correlation functions and we show that the short range
antiferromagnetic correlations favors the formation of magnetic moments on the
atoms, and at the same time the existence of these moments opens the
possibility of the spin-flip scattering by the conduction electrons, generating
the Kondo effect, which contribute to the opening of a gap in the density of
states of the system. We also calculate the phase diagram which shows that, as
we vary the Ef level position from the empty regime to the Kondo regime, the
system develops several phases: metallic, band insulator and Kondo topological
insulator. The band structure calculated shows that the model develops a strong
topological insulator.


  The Cohen-Lenstra-Martinet Heuristics gives a prediction of the distribution
of $\operatorname{Cl}_K[p^\infty]$ whne $K$ runs over $\Gamma$-fields and
$p\nmid|\Gamma|$. In this paper, we prove several results on the distribution
of ideal class groups for some $p||\Gamma|$, and show that the behaviour is
qualitatively different than what is predicted by the heuristics when
$p\nmid|\Gamma|$.We do this by using genus theory and the invariant part of the
class group to investigate the algebraic structure of the class group. For
general number fields, our result is conditional on a natural conjecture on
counting fields. For abelian or $D_4$-fields, our result is unconditional.


  We present a novel facial expression recognition network, called Distract
your Attention Network (DAN). Our method is based on two key observations.
Firstly, multiple classes share inherently similar underlying facial
appearance, and their differences could be subtle. Secondly, facial expressions
exhibit themselves through multiple facial regions simultaneously, and the
recognition requires a holistic approach by encoding high-order interactions
among local features. To address these issues, we propose our DAN with three
key components: Feature Clustering Network (FCN), Multi-head cross Attention
Network (MAN), and Attention Fusion Network (AFN). The FCN extracts robust
features by adopting a large-margin learning objective to maximize class
separability. In addition, the MAN instantiates a number of attention heads to
simultaneously attend to multiple facial areas and build attention maps on
these regions. Further, the AFN distracts these attentions to multiple
locations before fusing the attention maps to a comprehensive one. Extensive
experiments on three public datasets (including AffectNet, RAF-DB, and SFEW
2.0) verified that the proposed method consistently achieves state-of-the-art
facial expression recognition performance. Code will be made available at
https://github.com/yaoing/DAN.


  A necessary and sufficient condition is found for a graph $G$, which
satisfies the equality $\mu_{21}(G)=|V(G)|$.


  Singular Gordon potentials are defined to be distributions from the space
W^{-1}_{2,unif}(R) that are sufficiently fast approximated by periodic ones. We
prove that Schr\"odinger operators with singular Gordon potentials have no
point spectrum and show that a rich class of quasiperiodic distributions
consists of singular Gordon potentials.


  New phases of matter can be stabilized by a combination of diverging
electronic density of states, strong interactions, and spin-orbit coupling.
Recent experiments in magic-angle twisted bilayer graphene (TBG) have uncovered
a wealth of novel phases as a result of interaction-driven spin-valley flavour
polarization. In this work, we explore correlated phases appearing due to the
combined effect of spin-orbit coupling-enhanced valley polarization and large
density of states below half filling ($\nu \lesssim 2$) of the moir\'e band in
a TBG coupled to tungsten diselenide. We observe anomalous Hall effect,
accompanied by a series of Lifshitz transitions, that are highly tunable with
carrier density and magnetic field. Strikingly, the magnetization shows an
abrupt sign change in the vicinity of half-filling, confirming its orbital
nature. The coercive fields reported are about an order of magnitude higher
than previous studies in graphene-based moir\'e systems, presumably aided by a
Stoner instability favoured by the van Hove singularities in the malleable
bands. While the Hall resistance is not quantized at zero magnetic fields,
indicative of a ground state with partial valley polarization, perfect
quantization and complete valley polarization are observed at finite fields.
Our findings illustrate that singularities in the flat bands in the presence of
spin-orbit coupling can stabilize ordered phases even at non-integer moir\'e
band fillings.


  Spin systems with honeycomb structures have recently attracted a great deal
of attention in connection with the Kitaev quantum spin liquid state (QSL)
predicted theoretically. One possible Kitaev QSL candidate is
Na$_2$Co$_2$TeO$_6$ realizing a honeycomb lattice of pseudo-spin-1/2.
Field-dependent single-crystal neutron diffraction technique allows us to
determine the microscopic spin-spin correlations across the field induced phase
transitions for H//a and H//a* in plane field directions. Our results reveal
phase transitions, initially to a canted zigzag antiferromagnetic state at
approximately 60 kOe, followed by a possible transition to a partially
polarized state over the range of 90-120 kOe, and finally to a field-induced
fully polarized state above 120 kOe. We observe distinct field dependencies of
the magnetic peak intensities for H//a and H//a*. In addition, low-temperature
electron spin resonance in magnetic fields H//c yields a complete softening for
one of the antiferromagnetic resonances at ~ 40 kOe, revealing a field-induced
phase transition. The present work, thus, provides new insights into the field
evolution of the important Kitaev-Heisenberg spin system Na$_2$Co$_2$TeO$_6$.


  The random reversal graph offers new perspectives, allowing to study the
connectivity of genomes as well as their most likely distance as a function of
the reversal rate. Our main result shows that the structure of the random
reversal graph changes dramatically at $\lambda_n=1/\binom{n+1}{2}$. For
$\lambda_n=(1-\epsilon)/\binom{n+1}{2}$, the random graph consists of
components of size at most $O(n\ln(n))$ a.s. and for
$(1+\epsilon)/\binom{n+1}{2}$, there emerges a unique largest component of size
$\sim \wp(\epsilon) \cdot 2^n\cdot n$!$ a.s.. This "giant" component is
furthermore dense in the reversal graph.


  We prove matching direct and inverse theorems for (algebraic) polynomial
approximation with doubling weights $w$ having finitely many zeros and
singularities (i.e., points where $w$ becomes infinite) on an interval and not
too ``rapidly changing'' away from these zeros and singularities. This class of
doubling weights
  is rather wide and, in particular, includes the classical Jacobi weights,
generalized Jacobi weights and generalized Ditzian-Totik weights.
  We approximate in the weighted $L_p$ (quasi) norm $\|f\|_{p, w}$ with
$0<p<\infty$, where $\|f\|_{p, w} := \left(\int_{-1}^1 |f(u)|^p w(u) du
\right)^{1/p}$. Equivalence type results involving related realization
functionals are also discussed.


  Object counting is a challenging task with broad application prospects in
security surveillance, traffic management, and disease diagnosis. Existing
object counting methods face a tri-fold challenge: achieving superior
performance, maintaining high generalizability, and minimizing annotation
costs. We develop a novel training-free class-agnostic object counter,
TFCounter, which is prompt-context-aware via the cascade of the essential
elements in large-scale foundation models. This approach employs an iterative
counting framework with a dual prompt system to recognize a broader spectrum of
objects varying in shape, appearance, and size. Besides, it introduces an
innovative context-aware similarity module incorporating background context to
enhance accuracy within messy scenes. To demonstrate cross-domain
generalizability, we collect a novel counting dataset named BIKE-1000,
including exclusive 1000 images of shared bicycles from Meituan. Extensive
experiments on FSC-147, CARPK, and BIKE-1000 datasets demonstrate that
TFCounter outperforms existing leading training-free methods and exhibits
competitive results compared to trained counterparts.