  \newcommand{\GLn}{\operatorname{GL}_n} \newcommand{\GL}{\GLn(C)}
  Let $F$ be a differential field with algebraically closed field of constants
$C$. We prove that $F< Y_{ij}>(X_{ij})\supset F< Y_{ij}>$ is a generic
Picard-Vessiot extension of $F$ for $\GL$. If $E\supset F$ is any
Picard-Vessiot extension with differential Galois group $\GL$ then $E\cong
F(X_{ij})$ as $F$- and $\GL$-modules and there are $f_{ij}\in F$ such that $F<
Y_{ij}>(X_{ij})\supset F< Y_{ij}>$ specializes to $E\supset F$ via $
Y_{ij}\mapsto f_{ij}$. The $[f_{ij}]\in M_n(F)$ for which the image of the map
$ Y_{ij}\mapsto f_{ij}$ is a Picard-Vessiot extension of $F$ with group $\GL$
can be characterized as those $[f_{ij}]\in M_n(F)$ for which the wronskians of
the monomials in $F< Y_{ij}>(X_{ij})$ of degree less than or equal to $k$ all
map to non-zero elements under $ Y_{ij}\mapstof_{ij}$.


  A possibility to describe magnetism in the iron pnictide parent compounds in
terms of the two-dimensional frustrated Heisenberg $J_1$-$J_2$ model has been
actively discussed recently. However, recent neutron scattering data has shown
that the pnictides have a relatively large spin wave dispersion in the
direction perpendicular to the planes. This indicates that the third dimension
is very important. Motivated by this observation we study the $J_1$-$J_2$-$J_c$
model that is the three dimensional generalization of the $J_1$-$J_2$
Heisenberg model for $S = 1/2$ and S = 1. Using self-consistent spin wave
theory we present a detailed description of the staggered magnetization and
magnetic excitations in the collinear state. We find that the introduction of
the interlayer coupling $J_c$ suppresses the quantum fluctuations and
strengthens the long range ordering. In the $J_1$-$J_2$-$J_c$ model, we find
two qualitatively distinct scenarios for how the collinear phase becomes
unstable upon increasing $J_1$. Either the magnetization or one of the spin
wave velocities vanishes. For $S = 1/2$ renormalization due to quantum
fluctuations is significantly stronger than for S=1, in particular close to the
quantum phase transition. Our findings for the $J_1$-$J_2$-$J_c$ model are of
general theoretical interest, however, the results show that it is unlikely
that the model is relevant to undoped pnictides.


  We introduce EELBERT, an approach for compression of transformer-based models
(e.g., BERT), with minimal impact on the accuracy of downstream tasks. This is
achieved by replacing the input embedding layer of the model with dynamic, i.e.
on-the-fly, embedding computations. Since the input embedding layer accounts
for a significant fraction of the model size, especially for the smaller BERT
variants, replacing this layer with an embedding computation function helps us
reduce the model size significantly. Empirical evaluation on the GLUE benchmark
shows that our BERT variants (EELBERT) suffer minimal regression compared to
the traditional BERT models. Through this approach, we are able to develop our
smallest model UNO-EELBERT, which achieves a GLUE score within 4% of fully
trained BERT-tiny, while being 15x smaller (1.2 MB) in size.


  Charge-parity (CP) asymmetries in charm decays are extremely suppressed in
the Standard Model and may well be dominated by new-physics contributions. The
LHCb collaboration reported the results of direct CP asymmetry measurements in
$D^0\to K^+ K^-$ and $D^0\to \pi^+\pi^-$ decays with unprecedented accuracy:
$a_{\rm{CP}}(K^+ K^-)=(7.7\pm5.7)\times 10^{-4}$ and
$a_{\rm{CP}}(\pi^+\pi^-)=(23.2\pm6.1)\times 10^{-4}$, with the latter quantity
inferred from the precise measurement of $\Delta a_{\rm{CP}} =\,
a_{\rm{CP}}(K^+ K^-) -a_{\rm{CP}}(\pi^+\pi^-) =\, (-15.7\pm2.9)\times 10^{-4}$.
When interpreted within the Standard Model, these values indicate a breakdown
of the approximate $U$-spin symmetry of QCD. If, however, this symmetry holds
and the data stem from new physics, other CP asymmetries should be enhanced as
well. We derive CP asymmetry sum rules based on $\rm{SU}(3)$ flavor symmetry
for $D$ meson decays into a pair of pseudoscalar mesons as well as a pair of a
pseudoscalar and a vector meson for two generic scenarios, with $\Delta U=0$
and $|\Delta U|=1$ interactions, respectively. The correlations implied by the
sum rules can be used to check the consistency between different measurements
and to discriminate between these scenarios with future data. For instance, we
find $a_{\mathrm{CP}}(\pi^{+}K^{* 0}) + a_{\mathrm{CP}}(K^{+}\overline{K}^{*
0}) = 0$ for $\Delta U=0$ new physics and the opposite relative sign for the
$|\Delta U|=1$ case. One sum rule, connecting four decay modes, holds in both
scenarios. We further extend our sum rules to certain differences of CP
asymmetries from which the $D$ production asymmetries drop out.


  In this demonstration, we put ourselves in the place of a website manager who
seeks to use browser fingerprinting for web authentication. The first step is
to choose the attributes to implement among the hundreds that are available. To
do so, we developed BrFAST, an attribute selection platform that includes
FPSelect, an algorithm that rigorously selects the attributes according to a
trade-off between security and usability. BrFAST is configured with a set of
parameters for which we provide values for BrFAST to be usable as is. We
notably include the resources to use two publicly available browser fingerprint
datasets. BrFAST can be extended to use other parameters: other attribute
selection methods, other measures of security and usability, or other
fingerprint datasets. BrFAST helps visualize the exploration of the
possibilities during the search of the best attributes to use, compare the
properties of attribute sets, and compare several attribute selection methods.
During the demonstration, we compare the attributes selected by FPSelect with
these selected by the usual methods according to the properties of the
resulting browser fingerprints (e.g., their usability, their unicity).


  Generalization to unseen tasks is an important ability for few-shot learners
to achieve better zero-/few-shot performance on diverse tasks. However, such
generalization to vision-language tasks including grounding and generation
tasks has been under-explored; existing few-shot VL models struggle to handle
tasks that involve object grounding and multiple images such as visual
commonsense reasoning or NLVR2. In this paper, we introduce GRILL, GRounded
vIsion Language aLigning, a novel VL model that can be generalized to diverse
tasks including visual question answering, captioning, and grounding tasks with
no or very few training instances. Specifically, GRILL learns object grounding
and localization by exploiting object-text alignments, which enables it to
transfer to grounding tasks in a zero-/few-shot fashion. We evaluate our model
on various zero-/few-shot VL tasks and show that it consistently surpasses the
state-of-the-art few-shot methods.


  For both the Poisson model problem and the Stokes problem in any dimension,
this paper proves that the enriched Crouzeix-Raviart elements are actually
identical to the first order Raviart-Thomas elements in the sense that they
produce the same discrete stresses. This result improves the previous result in
literature which, for two dimensions, states that the piecewise constant
projection of the stress by the first order Raviart-Thomas element is equal to
that by the Crouzeix-Raviart element. For the eigenvalue problem of Laplace
operator, this paper proves that the error of the enriched Crouzeix-Raviart
element is equivalent to that of the Raviart-Thomas element up to higher order
terms.


  In 1950, Forsythe and Leibler (1950) introduced a statistical technique for
finding the inverse of a matrix by characterizing the elements of the matrix
inverse as expected values of a sequence of random walks. Barto and Duff (1994)
subsequently showed relations between this technique and standard dynamic
programming and temporal differencing methods. The advantage of the Monte Carlo
matrix inversion (MCMI) approach is that it scales better with respect to
state-space size than alternative techniques. In this paper, we introduce an
algorithm for performing reinforcement learning policy evaluation using MCMI.
We demonstrate that MCMI improves on runtime over a maximum likelihood
model-based policy evaluation approach and on both runtime and accuracy over
the temporal differencing (TD) policy evaluation approach. We further improve
on MCMI policy evaluation by adding an importance sampling technique to our
algorithm to reduce the variance of our estimator. Lastly, we illustrate
techniques for scaling up MCMI to large state spaces in order to perform policy
improvement.


  Purpose: Recent work highlights the breadth of reported spin-lattice
relaxation rates ($R_1$) for individual tissues. One potential source of
variation is the protocol used to determine $R_1$. The methodological
dependence of R1 and relaxivity $r_1$ are investigated.
  Methods: $R_1$ is quantified in gel phantoms with varying concentration of
MnCl2, and a small cohort of three healthy volunteers using different
acquisition methods. Siemens inversion recovery (IR) and saturation recovery
(SR) protocols are applied to phantoms and volunteers. Variable flip angle
(VFA) protocols are additionally applied to phantoms. $R_1$ is quantified using
single voxel fits, and distributions examined for regions in the thalamus, and
cerebellum as well as grey and white matter. Phantoms exclude boundary fits and
relaxivity is quantified across the full concentration range. Normality of
$R_1$ distributions is assessed by Kolmogorov-Smirnov score, and inter-sequence
agreement by two-sample t-test.
  Results: Phantom relaxivity is found to be 7.16 Hz/mM, 9.22 Hz/mM and 10.65
Hz/mM to 11.91 Hz/mM for IR, SR and VFA methods, respectively. In vivo $R_1$
exhibit low intra-participant variation for IR. SR $R_1$ are lower than IR
values with inter- and intra-participant variation on the same order. Brain
regions and phantoms mapped with different protocols varied significantly with
t-test p-values between 0 and 5E-10.
  Conclusion: Results suggest a significant protocol dependence of $R_1$, and
corresponding relaxivity, suggesting inter-method comparisons should be
attempted tentatively, if at all.


  We introduce 21CMMC: a parallelized, Monte Carlo Markov Chain analysis tool,
incorporating the epoch of reionization (EoR) seminumerical simulation
21CMFAST. 21CMMC estimates astrophysical parameter constraints from 21 cm EoR
experiments, accommodating a variety of EoR models, as well as priors on model
parameters and the reionization history. To illustrate its utility, we consider
two different EoR scenarios, one with a single population of galaxies (with a
mass-independent ionizing efficiency) and a second, more general model with two
different, feedback-regulated populations (each with mass-dependent ionizing
efficiencies). As an example, combining three observations (z=8, 9 and 10) of
the 21 cm power spectrum with a conservative noise estimate and uniform model
priors, we find that interferometers with specifications like the Low Frequency
Array/Hydrogen Epoch of Reionization Array (HERA)/Square Kilometre Array 1
(SKA1) can constrain common reionization parameters: the ionizing efficiency
(or similarly the escape fraction), the mean free path of ionizing photons and
the log of the minimum virial temperature of star-forming haloes to within
45.3/22.0/16.7, 33.5/18.4/17.8 and 6.3/3.3/2.4 per cent, ~$1\sigma$ fractional
uncertainty, respectively. Instead, if we optimistically assume that we can
perfectly characterize the EoR modelling uncertainties, we can improve on these
constraints by up to a factor of ~few. Similarly, the fractional uncertainty on
the average neutral fraction can be constrained to within $\lesssim10$ per cent
for HERA and SKA1. By studying the resulting impact on astrophysical
constraints, 21CMMC can be used to optimize (i) interferometer designs; (ii)
foreground cleaning algorithms; (iii) observing strategies; (iv) alternative
statistics characterizing the 21 cm signal; and (v) synergies with other
observational programs.


  We report the characterization of the FBK ``NUV-HD-Cryo'' SiPMs at 10 K
temperature. With 405 nm and 530 nm light, we measured the photo-detection
efficiency (PDE) at the bias voltages between 6 to 11 V overvoltage (OV). The
PDE reaches $\sim$ 40\% for 405 nm and 530 nm light with a bias voltage of OV 9
V. A bias voltage higher than 9 V leads to a slightly greater PDE. We also
measured the SiPMs' PDE at room temperature (RT). The results are consistent
with the measurements on the similar model SiPMs by other groups. The I-V curve
of the SiPMs differs significantly from the conventional one measured at RT.
The dark current ratio (DCR) is tested to be $\sim$ 1 Hz for the 92 mm$^2$
SiPMs, or 0.01 Hz/mm$^2$, which is $\sim$ 7 orders lower than the ratio tested
at RT. The SiPMs' performance at 10 K demonstrated that it could be equipped on
a liquid helium detector as the photosensor to search for rare events,
including but not limited to dark matter searches.


  We consider the bounds for the values of higgs mass $m_H$ and the mass of the
extra quarks and leptons $m_{extra}$ derived from the stability of electroweak
vacuum and from the absence of Landau pole in Higgs potential. We find that in
the case of the absence of new physics up to the GUT scale the bounds on masses
of 4th generation are so strong that one can hope to discover it at LEP2.


  We calculate the main observables in $B_{u,d}\to (\rho,\omega,K^*)\gamma$ and
$B_s\to (\bar K^*,\phi)\gamma$ decays, i.e. branching ratios and CP and isospin
asymmetries. We include QCD factorisation results and also the dominant
contributions beyond QCD factorisation, namely long-distance photon emission
and soft-gluon emission from quark loops. All contributions beyond QCD
factorisation are estimated from light-cone sum rules. We devise in particular
a method for calculating soft-gluon emission, building on earlier ideas
developed for analogous contributions in non-leptonic decays. Our results are
relevant for new-physics searches at the $B$ factories, the LHC and a future
super-flavour factory. Using current experimental data, we also extract
$|V_{td}/V_{ts}|$ and the angle $\gamma$ of the unitarity triangle. We give
detailed tables of theoretical uncertainties of the relevant quantities which
facilitates future determinations of these CKM parameters from updated
experimental results.


  We present an on-device real-time hand gesture recognition (HGR) system,
which detects a set of predefined static gestures from a single RGB camera. The
system consists of two parts: a hand skeleton tracker and a gesture classifier.
We use MediaPipe Hands as the basis of the hand skeleton tracker, improve the
keypoint accuracy, and add the estimation of 3D keypoints in a world metric
space. We create two different gesture classifiers, one based on heuristics and
the other using neural networks (NN).


  In recent work we have presented a novel algorithm for mesh refinement which
utilizes a reduced model. In particular, the reduced model is used to monitor
the transfer of activity (e.g. mass, energy) from larger to smaller scales.
When the activity transfer rate exceeds a prescribed tolerance, the algorithm
refines the mesh accordingly. The algorithm was applied to the inviscid Burgers
and focusing Schr\"odinger equations to detect singularities. We offer here a
simple proof of why the use of a reduced model for mesh refinement is a good
idea. We do so by showing that by controlling the transfer of activity rate one
controls the error caused inevitably by a finite resolution.


  The main objective of this work is to study the existence of Lagrange
multipliers for infinite dimensional problems under G\^ateux differentiability
assumptions on the data. Our investigation follows two main steps: the proof of
the existence of Lagrange multipliers under a calmness assumption on the
constraints and the study of sufficient conditions, which only use the
G\^ateaux derivative of the function defining the constraint, that ensure this
assumption.


  This is the first in a series of two papers concerned with relative
birational geometry of algebraic spaces. In this paper, we study Pr\"ufer
spaces and Pr\"ufer pairs of algebraic spaces that generalize spectra of
Pr\"ufer rings. As a particular case of Pr\"ufer spaces we introduce valuation
algebraic spaces, and use them to establish valuative criterion of universal
closedness that sharpens the standard criterion. In the sequel paper, we will
introduce a version of Riemann-Zariski spaces, and will prove Nagata
compactification theorem for algebraic spaces.


  We present a simple approach for sensor registration in target tracking
applications. The proposed method uses targets of opportunity and, without
making assumptions on their dynamical models, allows simultaneous calibration
of multiple three- and two-dimensional sensors. Whereas for two-sensor
scenarios only relative registration is possible, in practical cases with three
or more sensors unambiguous absolute calibration may be achieved. The derived
algorithms are straightforward to implement and do not require tuning of
parameters. The performance of the algorithms is tested in a numerical study.


  Concerns over reproducibility in science extend to research using existing
healthcare data; many observational studies investigating the same topic
produce conflicting results, even when using the same data. To address this
problem, we propose a paradigm shift. The current paradigm centers on
generating one estimate at a time using a unique study design with unknown
reliability and publishing (or not) one estimate at a time. The new paradigm
advocates for high-throughput observational studies using consistent and
standardized methods, allowing evaluation, calibration, and unbiased
dissemination to generate a more reliable and complete evidence base. We
demonstrate this new paradigm by comparing all depression treatments for a set
of outcomes, producing 17,718 hazard ratios, each using methodology on par with
state-of-the-art studies. We furthermore include control hypotheses to evaluate
and calibrate our evidence generation process. Results show good transitivity
and consistency between databases, and agree with four out of the five findings
from clinical trials. The distribution of effect size estimates reported in
literature reveals an absence of small or null effects, with a sharp cutoff at
p = 0.05. No such phenomena were observed in our results, suggesting more
complete and more reliable evidence.


  We consider a model consisting of a quintessence coupled to the Ricci scalar
and the Gauss-Bonnet invariant. We propose a mechanism for the rising of dark
energy in the matter era, alleviating the coincidence problem. The role of the
Gauss-Bonnet invariant is to restore the initial $Z_2$ symmetry. The Ricci
scalar breaks this symmetry during the Universe's expansion and activates the
quintessence. In our model, the observational constraint on gravitational wave
speed is respected.


  We introduce an analytically solvable model for a fragmented object that,
despite of a low degree of randomness and of the extreme simplicity of the
breaking process, displays non self-averaging effects in its thermodynamic
limit.


  In this work, we define cost-free learning (CFL) formally in comparison with
cost-sensitive learning (CSL). The main difference between them is that a CFL
approach seeks optimal classification results without requiring any cost
information, even in the class imbalance problem. In fact, several CFL
approaches exist in the related studies, such as sampling and some
criteria-based pproaches. However, to our best knowledge, none of the existing
CFL and CSL approaches are able to process the abstaining classifications
properly when no information is given about errors and rejects. Based on
information theory, we propose a novel CFL which seeks to maximize normalized
mutual information of the targets and the decision outputs of classifiers.
Using the strategy, we can deal with binary/multi-class classifications
with/without abstaining. Significant features are observed from the new
strategy. While the degree of class imbalance is changing, the proposed
strategy is able to balance the errors and rejects accordingly and
automatically. Another advantage of the strategy is its ability of deriving
optimal rejection thresholds for abstaining classifications and the
"equivalent" costs in binary classifications. The connection between rejection
thresholds and ROC curve is explored. Empirical investigation is made on
several benchmark data sets in comparison with other existing approaches. The
classification results demonstrate a promising perspective of the strategy in
machine learning.


  Only a few years ago, it was realized that the zero-area Sagnac
interferometer topology is able to perform quantum nondemolition measurements
of position changes of a mechanical oscillator. Here, we experimentally show
that such an interferometer can also be efficiently enhanced by squeezed light.
We achieved a nonclassical sensitivity improvement of up to 8.2 dB, limited by
optical loss inside our interferometer. Measurements performed directly on our
squeezed-light laser output revealed squeezing of 12.7 dB. We show that the
sensitivity of a squeezed-light enhanced Sagnac interferometer can surpass the
standard quantum limit for a broad spectrum of signal frequencies without the
need for filter cavities as required for Michelson interferometers. The Sagnac
topology is therefore a powerful option for future gravitational-wave
detectors, such as the Einstein Telescope, whose design is currently being
studied.


  We define a new quantum Hermitian operator (namely, the energy variance
operator) which is simply duplicated from the statistical definition of energy
variance in classical physics. Its expectation value yields the standard
deviation of the energy about the mean value of this latter. We show by use of
an exact Hamiltonian description that this standard deviation is due to the
high-frequeny energy oscillations which are usually discarded in the rotating
wave aproximation. We check the present theory by recovering the duration of an
abrupt quantum jump that has been described in a recent experiment.


  The article is a lightly edited version of my habilitation thesis at the
University Wuerzburg. My aim is to give a self contained, if concise,
introduction to the formal methods used when off-line learning in feedforward
networks is analyzed by statistical physics. However, due to its origin, the
article is not a comprehensive review of the field but is highly skewed towards
reporting my own research.


  We introduce a scheme to coherently suppress second-rank tensor frequency
shifts in atomic clocks, relying on the continuous rotation of an external
magnetic field during the free atomic state evolution in a Ramsey sequence. The
method retrieves the unperturbed frequency within a single interrogation cycle
and is readily applicable to various atomic clock systems. For the frequency
shift due to the electric quadrupole interaction, we experimentally demonstrate
suppression by more than two orders of magnitude for the ${}^2S_{1/2} \to
{}^2D_{3/2}$ transition of a single trapped ${}^{171}\text{Yb}^+$ ion. The
scheme provides particular advantages in the case of the ${}^{171}\text{Yb}^+$
${}^2S_{1/2} \to {}^2F_{7/2}$ electric octupole (E3) transition. For an
improved estimate of the residual quadrupole shift for this transition, we
measure the excited state electric quadrupole moments $\Theta({}^2D_{3/2}) =
1.95(1)~ea_0^2$ and $\Theta({}^2F_{7/2}) = -0.0297(5)~ea_0^2$ with $e$ the
elementary charge and $a_0$ the Bohr radius, improving the measurement
uncertainties by one order of magnitude.


  Underwater acoustic transducers often include a stack of thickness polarized
piezoelectric material pieces of alternating polarity interspersed with
electrodes, bonded together and electrically connected in parallel. The stack
is normally much shorter than a quarter wavelength at the fundamental resonance
frequency, so that the mechanical behavior of the transducer is not affected by
the segmentation. When the transducer bandwidth is less than a half octave, as
has conventionally been the case, stack segmentation has no significant effect
on the mechanical behavior of the device. However, when a high coupling
coefficient material such as PMN-PT is used to achieve a wider bandwidth, the
difference between a segmented stack and a similar piezoelectric section with
electrodes only at the two ends can be significant. This paper investigates the
effects of stack segmentation on the performance of wideband underwater
acoustic transducers, particularly tonpilz transducer elements. Included is
discussion of transducer designs using single crystal piezoelectric material
with high coupling coefficient compared with more traditional PZT ceramics.


  Particle dark matter near the galactic center is accreted by the central
black hole into a dense spike, strongly enhancing its annihilation rate.
Searching for its annihilation products may give us information on the presence
or absence of a central cusp in the dark halo profile. We summarize our paper
Phys Rev Lett 83, 1719 (1999), and use an updated limit on the neutrino
emission from the galactic center.


  The current status of the theoretical and observational cosmology is
reviewed.


  We present, using a novel technique, a study of the angular distribution of
satellite galaxies around a sample of isolated, blue host galaxies selected
from the sixth data release of the Sloan Digital Sky Survey. As a complement to
previous studies we subdivide the sample of galaxies into bins of differing
inclination and use the systematic differences that would exist between the
different bins as the basis for our approach. We parameterize the cumulative
distribution function of satellite galaxies and apply a maximum likelihood,
Monte-Carlo technique to determine allowable distributions, which we show as an
exclusion plot. We find that the allowed distributions of the satellites of
spiral hosts are very nearly isotropic. We outline our formalism and our
analysis and discuss how this technique may be refined for future studies and
future surveys.


  In this paper, we formulate a distributed optimal control problem related to
the evolution of two isothermal, incompressible, immiscible fluids in a two
dimensional bounded domain. The distributed optimal control problem is framed
as the minimization of a suitable cost functional subject to the controlled
nonlocal Cahn-Hilliard-Navier-Stokes equations. We describe the first order
necessary conditions of optimality via Pontryagin's minimum principle and prove
second order necessary and sufficient conditions of optimality for the problem.


  Few real-world hybrid systems are amenable to formal verification, due to
their complexity and black box components. Optimization-based falsification---a
methodology of search-based testing that employs stochastic optimization---is
attracting attention as an alternative quality assurance method. Inspired by
the recent works that advocate coverage and exploration in falsification, we
introduce a two-layered optimization framework that uses Monte Carlo tree
search (MCTS), a popular machine learning technique with solid mathematical and
empirical foundations. MCTS is used in the upper layer of our framework; it
guides the lower layer of local hill-climbing optimization, thus balancing
exploration and exploitation in a disciplined manner.


  Recently, it has been determined that there are 242 Wilf classes of triples
of 4-letter permutation patterns by showing that there are 32 non-singleton
Wilf classes. Moreover, the generating function for each triple lying in a
non-singleton Wilf class has been explicitly determined. In this paper, toward
the goal of enumerating avoiders for the singleton Wilf classes, we obtain the
generating function for all but one of the triples containing 1324. (The
exceptional triple is conjectured to be intractable.) Our methods are both
combinatorial and analytic, including generating trees, recurrence relations,
and decompositions by left-right maxima. Sometimes this leads to an algebraic
equation for the generating function, sometimes to a functional equation or a
multi-index recurrence amenable to the kernel method.


  We examine the dynamics induced on the four dimensional boundary of a five
dimensional anti-deSitter spacetime by the five dimensional Chern-Simons theory
with gauge group the direct product of SO(4,2) with U(1). We show that, given
boundary conditions compatible with the geometry of 5d AdS spacetime in the
asymptotic region, the induced surface theory is the $WZW_4$ model.


  In this remark, we give another approach to the local well-posedness of
quadratic Schr\"odinger equation with nonlinearity $u\bar u$ in $H^{-1/4}$,
which was already proved by Kishimoto \cite{kis}. Our resolution space is
$l^1$-analogue of $X^{s,b}$ space with low frequency part in a weaker space
$L^{\infty}_{t}L^2_x$. Such type spaces was developed by Guo. \cite{G} to deal
the KdV endpoint $H^{-3/4}$ regularity.


  In their seminal paper "Double zeta values and modular forms" Gangl, Kaneko
and Zagier defined a double Eisenstein series and used it to study the
relations between double zeta values. One of their key ideas is to study the
formal double space and apply the double shuffle relations. They also proved
the double shuffle relations for the double Eisenstein series. More recently,
Kaneko and Tasaka extended the double Eisenstein series to level 2, proved its
double shuffle relations and studied the double zeta values of level 2.
Motivated by the above works, we define in this paper the corresponding objects
at higher levels and prove that the double Eisenstein series of level N
satisfies the double shuffle relations for every positive integer N. In order
to obtain our main theorem we prove a key result on the multiple divisor
functions of level N and then use it to solve a complicated under-determined
system of linear equations by some standard techniques from linear algebra.


  In this paper we study the convex envelopes of a new class of functions.
Using this approach, we are able to unify two important classes of regularizers
from unbiased non-convex formulations and weighted nuclear norm penalties. This
opens up for possibilities of combining the best of both worlds, and to
leverage each methods contribution to cases where simply enforcing one of the
regularizers are insufficient.
  We show that the proposed regularizers can be incorporated in standard
splitting schemes such as Alternating Direction Methods of Multipliers (ADMM),
and other subgradient methods. Furthermore, we provide an efficient way of
computing the proximal operator.
  Lastly, we show on real non-rigid structure-from-motion (NRSfM) datasets, the
issues that arise from using weighted nuclear norm penalties, and how this can
be remedied using our proposed method.


  When sensors collect spatio-temporal data in a large geographical area, the
existence of missing data cannot be escaped. Missing data negatively impacts
the performance of data analysis and machine learning algorithms. In this
paper, we study deep autoencoders for missing data imputation in
spatio-temporal problems. We propose a convolution bidirectional-LSTM for
capturing spatial and temporal patterns. Moreover, we analyze an autoencoder's
latent feature representation in spatio-temporal data and illustrate its
performance for missing data imputation. Traffic flow data are used for
evaluation of our models. The result shows that the proposed convolution
recurrent neural network outperforms state-of-the-art methods.


  In this paper we consider the problem of a measure that allows us to describe
the spatial and temporal dependence structure of multivariate time series with
innovations having infinite variance. By using recent results obtained in the
problem of temporal dependence structure of univariate stochastic processes,
where the auto-codifference was used, we extend its idea and propose a
cross-codifference measure for a general vector autoregressive model of order 1
(VAR(1)). Next, we derive an analytical results for VAR(1) model with Gaussian
and sub-Gaussian innovations, that are characterized by finite and infinite
variance, respectively. We emphasize that obtained expressions perfectly agree
with the empirical counterparts. Moreover, we show that for the considered
processes the cross-codifference simplifies to the well-established
cross-covariance measure in case of Gaussian white noise. Last part of the work
is devoted to the statistical estimation of VAR(1) parameters based on the
empirical cross-codifference. Again, we demonstrate via Monte Carlo simulations
that proposed methodology works correctly.


  Aims.We study the dependence of the halo abundance function (AF) on different
environments in a whole-sky $\Lambda$CDM light-cone halo catalogue extending to
z < 0.65, using a simple and well-defined halo isolation criterion. Methods.
The isolation status of each individual dark matter halo is determined by the
distance to its nearest neighbour, which defines the maximum spherical region
devoid of halos above a threshold mass around it (although the true size of
such region may be much larger since it is not necessarily spherical). A
versatile double power-law Schechter function is used to fit the dark matter
halo AF, and its derived parameters are studied as a function of halo isolation
status. Results. (a) Our function fits the halo abundances for all halo
isolation statuses extremely well, while the well-established theoretical mass
functions, integrated over the volume of the light-cone, provide an adequate
but poorer fit than our phenomenological model. (b) As expected, and in
agreement with other studies based on snap-shot simulations, we find
significant differences of the halo abundance function as a function of halo
isolation, indicating different rates of halo formation. The slope of the power
law and the characteristic mass of the Schechter-like fitting function decrease
with isolation, a result consistent with the formation of less massive haloes
in lower density regions. (c) We find an unexpected upturn of the
characteristic mass of the most isolated haloes of our sample. This upturn
originates and characterises only the higher redshift regime (z > 0.45), which
probably implies a significant and recent evolution of the isolation status of
the most isolated and most massive haloes.


  For a given graph $G$, let $f:V(G)\to \{1,2,\ldots,n\}$ be a bijective
mapping. For a given edge $uv \in E(G)$, $\sigma(uv)=+$, if $f(u)$ and $f(v)$
have the same parity and $\sigma(uv)=-$, if $f(u)$ and $f(v)$ have opposite
parity. The resultant signed graph is called a parity signed graph and the
mapping $\sigma$ is called a parity signature of $G$. Let us denote a parity
signed graph $S=(G,\sigma)$ by $G_\sigma$. Let $E^-(G_\sigma)$ be a set of
negative edges in a parity signed graph and let $Si(G)$ be the set of all
parity signatures for the underlying graph $G$. We define the \textit{rna}
number of $G$ as $\sigma^-(G)=\min\{|E^-(G_\sigma)|:\sigma \in Si(G)\}$. In
this paper, we prove a non-trivial upper bound in the case of trees:
$\sigma^-(T)\leq \lceil\frac{n}{2}\rceil$, where $T$ is a tree of order $n+1$.
We have found families of trees whose \textit{rna} numbers are bounded above by
$\lceil\frac{\Delta}{2}\rceil$ and also we have shown that for any $i\leq
\lceil\frac{n}{2}\rceil$, there exists a tree $T$ (of order $n+1$) with
$\sigma^-(T)=i$. This paper gives a characterization of graphs with
\textit{rna} number 1 in terms of its spanning trees and also a
characterization of graphs with \textit{rna} number 2.


  The paper studies query evaluation in parallel constant time in the PRAM
model. While it is well-known that all relational algebra queries can be
evaluated in constant time on an appropriate CRCW-PRAM, this paper is
interested in the efficiency of evaluation algorithms, that is, in the number
of processors or, asymptotically equivalent, in the work. Naive evaluation in
the parallel setting results in huge (polynomial) bounds on the work of such
algorithms and in presentations of the result sets that can be extremely
scattered in memory. The paper first discusses some obstacles for constant time
PRAM query evaluation. It presents algorithms for relational operators that are
considerably more efficient than the naive approaches. Further it explores
three settings, in which efficient sequential query evaluation algorithms
exist: acyclic queries, semi-join algebra queries, and join queries -- the
latter in the worst-case optimal framework. Under natural assumptions on the
representation of the database, the work of the given algorithms matches the
best sequential algorithms in the case of semi-join queries, and it comes close
in the other two settings. An important tool is the compaction technique from
Hagerup (1992).


  The object of this paper is to prove that the standard categories in which
homotopy theory is done, such as topological spaces, simplicial sets, chain
complexes of abelian groups, and any of the various good models for spectra,
are all homotopically self-contained. The left half of this statement
essentially means that any functor that looks like it could be a tensor product
(or product, or smash product) with a fixed object is in fact such a tensor
product, up to homotopy. The right half says any functor that looks like it
could be Hom into a fixed object is so, up to homotopy. More precisely, suppose
we have a closed symmetric monoidal category (resp. Quillen model category) M.
Then the functor T_{B} that takes A to A tensor B is an M-functor and a left
adjoint. The same is true if B is an E-E'-bimodule, where E and E' are monoids
in M, and T_{B} takes an E-module A to A tensored over E with B. Define a
closed symmetric monoidal category (resp. model category) to be left
self-contained (resp. homotopically left self-contained) if every functor F
from E-modules to E'-modules that is an M-functor and a left adjoint (resp. and
a left Quillen functor) is naturally isomorphic (resp. naturally weakly
equivalent) to T_{B} for some B. The classical Eilenberg-Watts theorem in
algebra then just says that the category of abelian groups is left
self-contained, so we are generalizing that theorem.


  The space-air-ground integrated network (SAGIN), one of the key technologies
for next-generation mobile communication systems, can facilitate data
transmission for users all over the world, especially in some remote areas
where vast amounts of informative data are collected by Internet of remote
things (IoRT) devices to support various data-driven artificial intelligence
(AI) services. However, training AI models centrally with the assistance of
SAGIN faces the challenges of highly constrained network topology, inefficient
data transmission, and privacy issues. To tackle these challenges, we first
propose a novel topology-aware federated learning framework for the SAGIN,
namely Olive Branch Learning (OBL). Specifically, the IoRT devices in the
ground layer leverage their private data to perform model training locally,
while the air nodes in the air layer and the ring-structured low earth orbit
(LEO) satellite constellation in the space layer are in charge of model
aggregation (synchronization) at different scales.To further enhance
communication efficiency and inference performance of OBL, an efficient
Communication and Non-IID-aware Air node-Satellite Assignment (CNASA) algorithm
is designed by taking the data class distribution of the air nodes as well as
their geographic locations into account. Furthermore, we extend our OBL
framework and CNASA algorithm to adapt to more complex multi-orbit satellite
networks. We analyze the convergence of our OBL framework and conclude that the
CNASA algorithm contributes to the fast convergence of the global model.
Extensive experiments based on realistic datasets corroborate the superior
performance of our algorithm over the benchmark policies.


  We describe an external electron injection scheme for the AWAKE experiment.
We use scattering in two foils, that are necessary as vacuum window and laser
beam dump, to decrease the betatron function of the incoming electron beam for
injection and matching into plasma wakefields driven by a self-modulated proton
bunch. We show that, for a total aluminum foil thickness of $\sim 280\, \mu$m,
multiple Coulomb scattering increases the beam emittance by a factor of $\sim
10$ and decreases the betatron function by a factor of $\sim 3$. The plasma in
the accelerator is created by a ionizing laser pulse, counter-propagating with
respect to the electron beam. This allows for the electron bunch to enter the
plasma through an "infinitely" sharp vapor-plasma boundary, away from the
foils.


  The Neyman and Scott (1948) model is widely used to demonstrate a serious
weakness of the Maximum Likelihood (ML) method: it can give rise to
inconsistent estimators. The primary objective of this paper is to revisit this
example with a view to demonstrate that the culprit for the inconsistent
estimation is not the ML method but an ill-defined statistical model. It is
also shown that a simple recasting of this model renders it well-defined and
the ML method gives rise to consistent and asymptotically efficient estimators.


  The mass reduction of satellite solar arrays results in significant panel
flexibility. When such structures are launched there is a possible striking at
one with another dynamically, leading ultimately to structural damage during
the launch stage. To prevent this, rubber snubbers are mounted at well chosen
points of the structure and they act as one sided linear spring; as a negative
consequence, the dynamic of these panels becomes nonlinear. In this paper a
solar array and a snubber are simply modeled as a linear Euler-Bernoulli beam
with a one sided linear spring respectively. In this investigation, a numerical
and an experimental study of a beam striking a one-sided spring under harmonic
excitation is presented. The finite element approximation is used to solve the
partial differential equations governing the structural dynamics. The models
are subsequently validated and updated with experiments.


  Neutrino--antineutrino ($\nu\bar\nu$) pair production is one of the main
processes responsible for the energy loss of stars. Apart from the collision of
two ($\gamma\gamma\to\nu\bar\nu$) or three ($\gamma\gamma\gamma\to\nu\bar\nu$)
real photons, pair creation from a photon and photon collisions in the presence
of nuclear Coulomb fields or external magnetic fields have been considered
previously. Here, we study a pair production of neutrino and antineutrino from
a low-energy photon in the presence of a combined homogeneous magnetic field
and the Coulomb field of a nucleus with charge number $Z$.


  We report on the synthesis and superconductivity of high-entropy-alloy-type
(HEA-type) compounds TrZr2 (Tr = Fe, Co, Ni, Rh, Ir), in which the Tr site
satisfies the criterion of HEA. Polycrystalline samples of HEA-type TrZr2 with
four different compositions at the Tr site were synthesized by arc melting
method. The phase purity and crystal structure were examined by Rietveld
refinement of X-ray diffraction profile. It has been confirmed that the
obtained samples have a CuAl2-type tetragonal structure. From analyses of
elemental composition and mixing entropy at the Tr site, the HEA state for the
Tr site was confirmed. The physical properties of obtained samples were
characterized by electrical resistivity and magnetization measurements. All the
samples show bulk superconductivity with various transition temperature (Tc).
The Tc varied according to the compositions and showed correlations with the
lattice constant c and Tr-Zr bond lengths. Introduction of an HEA site in TrZr2
is useful to achieve systematic tuning of Tc with a wide temperature range,
which would be a merit for superconductivity application.


  The massive streams of Internet of Things (IoT) data require a timely
analysis to retain data usefulness. Stream processing systems (SPSs) enable
this task, deriving knowledge from the IoT data in real-time. Such real-time
analytics benefits many applications but can also be used to violate user
privacy, as the IoT data collected from users or their vicinity is inherently
sensitive. In this paper, we present our systematic look into privacy issues
arising from the intersection of SPSs and IoT, identifying key research
challenges towards achieving holistic privacy protection in SPSs and proposing
the solutions.


  We describe a method for calculating the exchange and correlation (XC)
contributions to the total energy, effective potential, and stress tensor in
the generalized gradient approximation. We avoid using the analytical
expressions for the functional derivatives of E_xc*rho, which depend on
discontinuous second-order derivatives of the electron density rho. Instead, we
first approximate E_xc by its integral in a real space grid, and then we
evaluate its partial derivatives with respect to the density at the grid
points. This ensures the exact consistency between the calculated total energy,
potential, and stress, and it avoids the need of second-order derivatives. We
show a few applications of the method, which requires only the value of the
(spin) electron density in a grid (possibly nonuniform) and returns a
conventional (local) XC potential.


  Image super-resolution is a challenging task and has attracted increasing
attention in research and industrial communities. In this paper, we propose a
novel end-to-end Attention-based DenseNet with Residual Deconvolution named as
ADRD. In our ADRD, a weighted dense block, in which the current layer receives
weighted features from all previous levels, is proposed to capture valuable
features rely in dense layers adaptively. And a novel spatial attention module
is presented to generate a group of attentive maps for emphasizing informative
regions. In addition, we design an innovative strategy to upsample residual
information via the deconvolution layer, so that the high-frequency details can
be accurately upsampled. Extensive experiments conducted on publicly available
datasets demonstrate the promising performance of the proposed ADRD against the
state-of-the-arts, both quantitatively and qualitatively.


  Late-type galaxies falling into a cluster would evolve being influenced by
the interactions with both the cluster and the nearby cluster member galaxies.
Most numerical studies, however, tend to focus on the effects of the former
with little work done on those of the latter. We thus perform a numerical study
on the evolution of a late-type galaxy interacting with neighboring early-type
galaxies at high speed, using hydrodynamic simulations. Based on the
information obtained from the Coma cluster, we set up the simulations for the
case where a Milky Way-like late-type galaxy experiences six consecutive
collisions with twice as massive early-type galaxies having hot gas in their
halos at the closest approach distances of 15-65 kpc/h at the relative
velocities of 1500-1600 km/s. Our simulations show that the evolution of the
late-type galaxy can be significantly affected by the accumulated effects of
the high-speed multiple collisions with the early-type galaxies, such as on
cold gas content and star formation activity of the late-type galaxy,
particularly through the hydrodynamic interactions between cold disk and hot
gas halos. We find that the late-type galaxy can lose most of its cold gas
after the six collisions and have more star formation activity during the
collisions. By comparing our simulation results with those of galaxy-cluster
interactions, we claim that the role of the galaxy-galaxy interactions on the
evolution of late-type galaxies in clusters could be comparable with that of
the galaxy-cluster interactions, depending on the dynamical history.


  Based on duality, we previously proposed to use rich informations on pi p
total cross sections below N=10GeV in addition to high-energy data in order to
discriminate whether these cross sections increase like log nu or log2 nu at
high energies. We then arrived at the conclusion that our analysis prefers the
log2 nu behaviours. Using the FESR as a constraint for high energy parameters
also for the pp, pbar p scattering, we search for the simultaneous best fit to
the data points of sigma(tot) and rho ratio up to some energy (e.g., ISR,
Tevatron) to determine the high-energy parameters. We then predict sigma(tot)
and rho in the LHC and high-energy cosmic-ray regions. Using the data up to
E=1.8TeV (Tevatron), we predict sigma(tot)pp and rho(pp) at the LHC energy
(E=14TeV) as 106.3+- 5.1syst +- 2.4stat mb and 0.126 +- 0.007syst +- 0.004stat,
respectively. The predicted values of sigma(tot) in terms of the same
parameters are in good agreement with the cosmic-ray experimental data up to
Plab = 10 (8--9) GeV.


  The considerable mathematical knowledge encoded by the Flyspeck project is
combined with external automated theorem provers (ATPs) and machine-learning
premise selection methods trained on the proofs, producing an AI system capable
of answering a wide range of mathematical queries automatically. The
performance of this architecture is evaluated in a bootstrapping scenario
emulating the development of Flyspeck from axioms to the last theorem, each
time using only the previous theorems and proofs. It is shown that 39% of the
14185 theorems could be proved in a push-button mode (without any high-level
advice and user interaction) in 30 seconds of real time on a fourteen-CPU
workstation. The necessary work involves: (i) an implementation of sound
translations of the HOL Light logic to ATP formalisms: untyped first-order,
polymorphic typed first-order, and typed higher-order, (ii) export of the
dependency information from HOL Light and ATP proofs for the machine learners,
and (iii) choice of suitable representations and methods for learning from
previous proofs, and their integration as advisors with HOL Light. This work is
described and discussed here, and an initial analysis of the body of proofs
that were found fully automatically is provided.


  Increasingly, artificial intelligence (AI) and machine learning (ML) are used
in eScience applications [9]. While these approaches have great potential, the
literature has shown that ML-based approaches frequently suffer from results
that are either incorrect or unreproducible due to mismanagement or misuse of
data used for training and validating the models [12, 15]. Recognition of the
necessity of high-quality data for correct ML results has led to data-centric
ML approaches that shift the central focus from model development to creation
of high-quality data sets to train and validate the models [14, 20]. However,
there are limited tools and methods available for data-centric approaches to
explore and evaluate ML solutions for eScience problems which often require
collaborative multidisciplinary teams working with models and data that will
rapidly evolve as an investigation unfolds [1]. In this paper, we show how data
management tools based on the principle that all of the data for ML should be
findable, accessible, interoperable and reusable (i.e. FAIR [26]) can
significantly improve the quality of data that is used for ML applications.
When combined with best practices that apply these tools to the entire life
cycle of an ML-based eScience investigation, we can significantly improve the
ability of an eScience team to create correct and reproducible ML solutions. We
propose an architecture and implementation of such tools and demonstrate
through two use cases how they can be used to improve ML-based eScience
investigations.


  Mobile code presents a number of threats to machines that execute it. We
introduce an approach for protecting machines and the resources they hold from
mobile code, and describe a system based on our approach for protecting host
machines from Java 1.1 applets. In our approach, each Java applet downloaded to
the protected domain is rerouted to a dedicated machine (or set of machines),
the {\em playground}, at which it is executed. Prior to execution the applet is
transformed to use the downloading user's web browser as a graphics terminal
for its input and output, and so the user has the illusion that the applet is
running on her own machine. In reality, however, mobile code runs only in the
sanitized environment of the playground, where user files cannot be mounted and
from which only limited network connections are accepted by machines in the
protected domain. Our playground thus provides a second level of defense
against mobile code that circumvents language-based defenses. The paper
presents the design and implementation of a playground for Java 1.1 applets,
and discusses extensions of it for other forms of mobile code including Java
1.2.


  Josephson junctions in two-dimensional topological insulators with embedded
magnetic domains can host a number of topological phases, in particular,
Jackiw-Rebbi solitons and Majorana zero modes. These different non-trivial
phases appear in such junctions for multiple-domain magnetic islands, showing a
rich multi-gap structure. Features related to the interplay between
superconductivity and magnetism in these systems cannot be easily discerned
looking at behavior of the Andreev spectrum and the concomitant dc Josephson
effect. Instead, the thermal conductance is very sensitive to the nature of the
junction and the domain structure of the magnetic island. We present a detailed
analysis of these properties in the case of a topological Josephson junction
with a single and two-domain magnetic island. Configurations hosting soliton
magnetic modes lead to a peculiar behavior of the thermal conductance relative
to the thermal quantum, characterized by a negative slope as a function of the
temperature, just above the superconducting critical temperature. At low
temperatures, these junctions also show characteristic coherence patters in the
behavior of the thermal conductance as function of the Josephson phase bias and
the angle between the magnetizations of the domains.


  Experimental results related to charged particle and $\pi^{0}$ suppression
obtained at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven for Au-Au
(Cu-Cu) collisions and at the Large Hadron Collider (LHC) at CERN for Pb-Pb
(Xe-Xe) collisions are compiled in terms of the usual nuclear modification
factors, $R_{AA} $ and $R_{CP}$, and of the newly introduced $R^{N}_{AA}$ and
$R^{N}_{CP}$ as a function of $\langle N_{part} \rangle$ and $\langle
dN_{ch}/d\eta\rangle$. The studies are focused on a $p_T$ range in the region
of maximum suppression evidenced in the experiments. The core contribution to
$R_{AA}$ is presented. Considerations on the missing suppression in high
charged particle multiplicity events for pp collisions at 7 TeV are presented.
The trends of $R_{CP}$ and $R^N_{CP}$ for charged particles and
$R_{AA}^{\pi^0}$ and $(R_{AA}^N)^{\pi^0}$ as a function of $\sqrt{s_{NN}}$,
measured at RHIC in Au-Au collisions and at LHC in Pb-Pb collisions, show a
suppression that becomes larger from $\sqrt{s_{NN}}$ = 39 GeV up to
$\sqrt{s_{NN}}$=200 GeV, followed by a saturation up to the highest energy of
$\sqrt{s_{NN}}$ =5.02 TeV in Pb-Pb collisions. A clear change in the dependence
of $(1-R_{AA}^{\pi^0})/\langle dN/dy \rangle$ for the most central collisions
as a function of collision energy is evidenced in the region of $\sqrt{s_{NN}}$
=62.4 - 130 GeV.


  We propose PolyVoice, a language model-based framework for speech-to-speech
translation (S2ST) system. Our framework consists of two language models: a
translation language model and a speech synthesis language model. We use
discretized speech units, which are generated in a fully unsupervised way, and
thus our framework can be used for unwritten languages. For the speech
synthesis part, we adopt the existing VALL-E X approach and build a unit-based
audio language model. This grants our framework the ability to preserve the
voice characteristics and the speaking style of the original speech. We examine
our system on Chinese $\rightarrow$ English and English $\rightarrow$ Spanish
pairs. Experimental results show that our system can generate speech with high
translation quality and audio quality. Speech samples are available at
https://speechtranslation.github.io/polyvoice.


  Hyperbolic-spaces are better suited to represent data with underlying
hierarchical relationships, e.g., tree-like data. However, it is often
necessary to incorporate, through alignment, different but related
representations meaningfully. This aligning is an important class of machine
learning problems, with applications as ontology matching and cross-lingual
alignment. Optimal transport (OT)-based approaches are a natural choice to
tackle the alignment problem as they aim to find a transformation of the source
dataset to match a target dataset, subject to some distribution constraints.
This work proposes a novel approach based on OT of embeddings on the Poincar\'e
model of hyperbolic spaces. Our method relies on the gyrobarycenter mapping on
M\"obius gyrovector spaces. As a result of this formalism, we derive extensions
to some existing Euclidean methods of OT-based domain adaptation to their
hyperbolic counterparts. Empirically, we show that both Euclidean and
hyperbolic methods have similar performances in the context of retrieval.


  Pyro is a probabilistic programming language built on Python as a platform
for developing advanced probabilistic models in AI research. To scale to large
datasets and high-dimensional models, Pyro uses stochastic variational
inference algorithms and probability distributions built on top of PyTorch, a
modern GPU-accelerated deep learning framework. To accommodate complex or
model-specific algorithmic behavior, Pyro leverages Poutine, a library of
composable building blocks for modifying the behavior of probabilistic
programs.


  We study the intra-planar tunneling between quantum Hall samples separated by
a quasi one-dimensional barrier, induced through the interaction of edge
degrees of freedom with the charge density waves of a Hall crystal defined in a
parallel layer. A field theory formulation is set up in terms of bosonic
(2+1)-dimensional excitations coupled to (1+1)-dimensional fermions. Parity
symmetry is broken at the quantum level by the confinement of
soliton-antisoliton pairs near the tunneling region. The usual Peierls argument
allows to estimate the critical temperature $T_c$, so that for $T > T_c$ mass
corrections due to longitudinal density fluctuations disappear from the edge
spectrum. We compute the gap dependence upon the random global phase of the
pinned charge density wave, as well as the effects of a voltage bias applied
across the tunneling junction.


  Converting the traction power of kites into electricity can be a low cost
solution for wind energy. Reliable control of both trajectory and tether
reeling is crucial. The present study proposes a modelling framework describing
the dynamic behaviour of the interconnected system components, suitable for
design and optimization of the control systems. The wing, bridle, airborne
control unit and tether are represented as a particle system using
spring-damper elements to describe their mechanical properties. Two kite models
are proposed: a point mass model and a four point model. Reeling of the tether
is modelled by varying the lengths of constituent tether elements. Dynamic
behaviour of the ground station is included. The framework is validated by
combining it with the automatic control system used for the operation of a kite
power system demonstrator. The simulation results show that the point mass
model can be adjusted to match the measured behaviour during a pumping cycle.
The four point model can better predict the influence of gravity and inertia on
the steering response and remains stable also at low tether forces. Compared to
simple one point models, the proposed framework is more accurate and robust
while allowing real-time simulations of the complete system.


  We discuss the coherent oscillations between two coupled quantum states of a
Bose-Einstein condensate in two-dimensional space at zero temperature. In the
system we consider, weak interparticle repulsive interactions occur between the
particles in state one only, while the state two particles remain
non-interacting. Analytical as well as numerical solution of the coupled
Gross-Pitaevskii and Schroedinger equations reveals various regimes of
oscillational dynamics for the relative quantum phase and population imbalance
between the two subsystems of the condensate. We show that, depending on the
energy detuning between the two states, the system can exhibit modified
harmonic and anharmonic Rabi oscillations or can transit to the regime
analogous to internal a.c. Josephson effect. Morover, at a certain value of
energy detuning, the internal oscillations are fully suppressed.


  We briefly review the young field of spectropolarimetry of core-collapse
supernovae (SNe). Spectropolarimetry provides the only direct known probe of
early-time supernova (SN) geometry. The fundamental result is that asphericity
is a ubiquitous feature of young core-collapse SNe. However, the nature and
degree of the asphericity vary considerably. The best predictor of
core-collapse SN polarization seems to be the mass of the hydrogen envelope
that is intact at the time of the explosion: those SNe that arise from
progenitors with large, intact envelopes (e.g., Type II-plateau) have very low
polarization, while those that result from progenitors that have lost part (SN
IIb, SN IIn) or all (SN Ib) of their hydrogen (or even helium; SN Ic) layers
prior to the explosion tend to show substantial polarization. Thus, the deeper
we probe into core-collapse events, the greater the asphericity seems to be,
suggesting a fundamentally asymmetric explosion with the asymmetry damped by
the addition of envelope material.


  Meyer and Reisner had proved the Mahler conjecture for rovelution bodies. In
this paper, using a new method, we prove that among origin-symmetric bodies of
revolution in R^3, cylinders have the minimal Mahler volume. Further, we prove
that among parallel sections homothety bodies in R^3, 3-cubes have the minimal
Mahler volume.


  We review several linear algebraic aspects of the Dehn-Sommerville relations
and relate redundant analogues of the f- and h-vectors describing the subsets
of a simplex 2^{1,...,m} that satisfy Dehn-Sommerville type relations to
integer points contained in some rational polytopes.


  A latent internal process describes the state of some system, e.g. the social
tension in a political conflict, the strength of an industrial component or the
health status of a person. When this process reaches a predefined threshold,
the process terminates and an observable event occurs, e.g. the political
conflict finishes, the industrial component breaks down or the person has a
heart attack. Imagine an intervention, e.g., a political decision, maintenance
of a component or a medical treatment, is initiated to the process before the
event occurs. How can we evaluate whether the intervention had an effect?
  To answer this question we describe the effect of the intervention through
parameter changes of the law governing the internal process. Then, the time
interval between the start of the process and the final event is divided into
two subintervals: the time from the start to the instant of intervention,
denoted by $S$, and the time between the intervention and the threshold
crossing, denoted by $R$. The first question studied here is: What is the joint
distribution of $(S,R)$? The theoretical expression is provided and serves as a
basis to answer the main question: Can we estimate the parameters of the model
from observations of $S$ and $R$ and compare them statistically? Maximum
likelihood estimators are illustrated on simulated data under the assumption
that the process before and after the intervention is described by the same
type of model, i.e. a Brownian motion, but with different parameters.


  Dual-function radar-communication (DFRC) is a key enabler of location-based
services for next-generation communication systems. In this paper, we
investigate the problem of designing constant modulus waveforms for DFRC
systems. For high-precision radar sensing, we consider joint optimization of
the correlation properties and spatial beam pattern. For communication, we
employ constructive interference-based block-level precoding (CI-BLP) to
leverage distortion induced by multiuser multiple-input multiple-output
(MU-MIMO) and radar transmission on a block level. We propose two solution
algorithms based on the alternating direction method of multipliers (ADMM) and
majorization-minimization (MM) principles, which are effective for small and
large block sizes, respectively. The proposed ADMM-based solution decomposes
the nonconvex formulated problem into multiple tractable subproblems, each of
which admits a closed-form solution. To accelerate convergence of the MM-based
solution, we propose an improved majorizing function that leverages a novel
diagonal matrix structure. After majorization, we decompose the approximated
problem into independent subproblems for parallelization, mitigating the
complexity that increases with block size. We then evaluate the performance of
the proposed algorithms through a series of numerical experiments. Simulation
results demonstrate that the proposed methods can substantially enhance
spatial/temporal sidelobe suppression through block-level optimization.


  We present an analysis of a scalar field model of dark energy with an
exponential potential using the Dark Energy Task Force (DETF) simulated data
models. Using Markov Chain Monte Carlo sampling techniques we examine the
ability of each simulated data set to constrain the parameter space of the
exponential potential for data sets based on a cosmological constant and a
specific exponential scalar field model. We compare our results with the
constraining power calculated by the DETF using their ``$w_0-w_a$''
parametrization of the dark energy. We find that respective increases in
constraining power from one stage to the next produced by our analysis give
results consistent with DETF results. To further investigate the potential
impact of future experiments, we also generate simulated data for an
exponential model background cosmology which can not be distinguished from a
cosmological constant at DETF ``Stage 2'', and show that for this cosmology
good DETF Stage 4 data would exclude a cosmological constant by better than
3$\sigma$.


  This work investigates the task-oriented dialogue problem in mixed-domain
settings. We study the effect of alternating between different domains in
sequences of dialogue turns using two related state-of-the-art dialogue
systems. We first show that a specialized state tracking component in multiple
domains plays an important role and gives better results than an end-to-end
task-oriented dialogue system. We then propose a hybrid system which is able to
improve the belief tracking accuracy of about 28% of average absolute point on
a standard multi-domain dialogue dataset. These experimental results give some
useful insights for improving our commercial chatbot platform FPT.AI, which is
currently deployed for many practical chatbot applications.


  We use Poisson summation formula to calculate integrals of producs of sinc
functions (cf. [4]) and related integrals as in [5] and [3]. We also generalize
the one in [5] and introduce other remarkable integrals.
  Finally we give a sum version of Siegel-type lower bound. (cf. [2], Theorem
3)


  We investigate the mechanism in the tunneling dynamics of open ultracold
few-boson systems by numerically solving the time-dependent few-boson
Schr\"{o}dinger equation exactly. By starting from a weakly repulsive,
initially coherent two-boson system we demonstrate that the decay dynamics
incorporate fragmentation. The wavefunction of the tunneling state exhibits a
pronounced dynamically-stable pattern which we explain by an analytical model.
By studying more bosons and stronger interactions we arrive to the conclusion
that the decay by tunneling is not a coherent process and exhibits a wealth of
phenomena depending on the interaction between the particles.


  The vast and growing number of publications in all disciplines of science
cannot be comprehended by a single human researcher. As a consequence,
researchers have to specialize in narrow sub-disciplines, which makes it
challenging to uncover scientific connections beyond the own field of research.
Thus access to structured knowledge from a large corpus of publications could
help pushing the frontiers of science. Here we demonstrate a method to build a
semantic network from published scientific literature, which we call SemNet. We
use SemNet to predict future trends in research and to inspire new,
personalized and surprising seeds of ideas in science. We apply it in the
discipline of quantum physics, which has seen an unprecedented growth of
activity in recent years. In SemNet, scientific knowledge is represented as an
evolving network using the content of 750,000 scientific papers published since
1919. The nodes of the network correspond to physical concepts, and links
between two nodes are drawn when two physical concepts are concurrently studied
in research articles. We identify influential and prize-winning research topics
from the past inside SemNet thus confirm that it stores useful semantic
knowledge. We train a deep neural network using states of SemNet of the past,
to predict future developments in quantum physics research, and confirm high
quality predictions using historic data. With the neural network and
theoretical network tools we are able to suggest new, personalized,
out-of-the-box ideas, by identifying pairs of concepts which have unique and
extremal semantic network properties. Finally, we consider possible future
developments and implications of our findings.


  We have used a stringy model of quantum space-time foam to suggest that the
vacuum may exhibit a non-trivial refractive index depending linearly on
gamma-ray energy: eta -1 ~ E_gamma/M_QG1, where M_QG1 is some mass scale
typical of quantum gravity that may be ~ 10^18 GeV: see Phys. Lett. B 665, 412
(2008) and references therein. The MAGIC, HESS and Fermi gamma-ray telescopes
have recently probed the possible existence of such an energy-dependent vacuum
refractive index. All find indications of time-lags for higher-energy photons,
but cannot exclude the possibility that they are due to intrinsic delays at the
sources. However, the MAGIC and HESS observations of time-lags in emissions
from AGNs Mkn 501 and PKS 2155-304 are compatible with each other and a
refractive index depending linearly on the gamma-ray energy, with M_QG1 ~ 10^18
GeV. We combine their results to estimate the time-lag Delta t to be expected
for the highest-energy photon from GRB 080916c measured by the Fermi telescope,
which has an energy ~ 13.2 GeV, assuming the redshift z = 4.2 \pm 0.3 measured
by GROND. In the case of a refractive index depending linearly on the gamma-ray
energy we predict Delta t = 25 \pm 11 s. This is compatible with the time-lag
Delta t <= 16.5 s reported by the Fermi Collaboration, whereas the time-lag
would be negligible in the case of a refractive index depending quadratically
on the gamma-ray energy. We suggest a strategy for future observations that
could distinguish between a quantum-gravitational effect and other
interpretations of the time-lags observed by the MAGIC, HESS and Fermi
gamma-ray telescopes.


  In this study a systematical analysis of various polarization asymmetries in
inclusive $b \rar s \ell^+ \ell^-$ decay in the standard model (SM) with four
generation of quarks is carried out. We found that the various asymmetries are
sensitive to the new mixing and quark masses for both of the $\mu$ and $\tau$
channels. Sizeable deviations from the SM values are obtained. Hence, $b \rar s
\ell^+ \ell^-$ decay is a valuable tool for searching physics beyond the SM,
especially in the indirect searches for the fourth-generation of quarks ($t',
b')$.


  This paper presents a deep learning-based de-homogenization method for
structural compliance minimization. By using a convolutional neural network to
parameterize the mapping from a set of lamination parameters on a coarse mesh
to a one-scale design on a fine mesh, we avoid solving the least square
problems associated with traditional de-homogenization approaches and save time
correspondingly. To train the neural network, a two-step custom loss function
has been developed which ensures a periodic output field that follows the local
lamination orientations. A key feature of the proposed method is that the
training is carried out without any use of or reference to the underlying
structural optimization problem, which renders the proposed method robust and
insensitive wrt. domain size, boundary conditions, and loading. A
post-processing procedure utilizing a distance transform on the output field
skeleton is used to project the desired lamination widths onto the output field
while ensuring a predefined minimum length-scale and volume fraction. To
demonstrate that the deep learning approach has excellent generalization
properties, numerical examples are shown for several different load and
boundary conditions. For an appropriate choice of parameters, the
de-homogenized designs perform within $7-25\%$ of the homogenization-based
solution at a fraction of the computational cost. With several options for
further improvements, the scheme may provide the basis for future interactive
high-resolution topology optimization.


  We study and implement a simple method, based on the Perfectly Matched Layer
approach, to treat non reflecting boundary conditions with the Smoothed
Particles Hydrodynamics numerical algorithm. The method is based on the concept
of physical damping. We illustrate how it works in the case of 1D and 2D time
dependent waves propagating in a finite domain.


  In the context of F-theory, we study the related eight dimensional
super-Yang-Mills theory and reveal the underlying supersymmetric quantum
mechanics algebra that the fermionic fields localized on the corresponding
defect theory are related to. Particularly, the localized fermionic fields
constitute a graded vector space, and in turn this graded space enriches the
geometric structures that can be built on the initial eight-dimensional space.
We construct the implied composite fibre bundles, which include the graded
affine vector space and demonstrate that the composite sections of this fibre
bundle are in one-to-one correspondence to the sections of the square root of
the canonical bundle corresponding to the submanifold on which the zero modes
are localized.


  Boolean networks is a well-established formalism for modelling biological
systems. A vital challenge for analysing a Boolean network is to identify all
the attractors. This becomes more challenging for large asynchronous Boolean
networks, due to the asynchronous updating scheme. Existing methods are
prohibited due to the well-known state-space explosion problem in large Boolean
networks. In this paper, we tackle this challenge by proposing a SCC-based
decomposition method. We prove the correctness of our proposed method and
demonstrate its efficiency with two real-life biological networks.


  Recall that an algebraic module is a KG-module that satisfies a polynomial
with integer coefficients, with addition and multiplication given by direct sum
and tensor product. In this article we prove that non-periodic algebraic
modules are very rare, and that if the complexity of an algebraic module is at
least 3, then it is the only algebraic module on its component of the (stable)
Auslander--Reiten quiver. We include a strong conjecture on the relationship
between periodicity and algebraicity.


  In this paper we prove that on a simple surface where the metric is $C^{17}$,
the scattering relation determines the Dirichlet to Neumann map (DN map) - a
known result for the case when the metric is smooth. For metrics with finite
differentiability we had to modified each technical result used in the original
proof; such as properties of the exit time function and the characterization of
$C_\alpha$ space. Moreover, surjectivity of $I^*$ in the original proof
required the use of microlocal analysis on the normal operator $I^*I$ - which
is not a standard pseudodifferential operator for metrics with finite
regularity. Finally, using the injectivity of $I$ on Lipschitz one forms for
simple $C^{1,1}$ manifolds we prove an equivalent characterization of harmonic
conjugacy using operators defined by the scattering relation to prove the
titular result. We also prove that the boundary distance function determines
the metric at the boundary (which in turns determines the scattering relation)
for a closed disk even when the metric is only $C^{1,1}$ and the exponential
map is only Lipschitz and does not preserve tangent vectors or differentials
pointwise.


  Detailed deterministic derivation of the kinetic equations for the
relativistic plasmas is given. Focus is made on the dynamic of one-coordinate
distribution functions of various tensor dimensions, but the closed set of
kinetic equations is constructed of three functions: the scalar distribution
function, the vector distribution function of dipole moment, and the vector
distribution function of velocity (or the dipole moment in the momentum space).
All two-coordinate distributions functions are discussed as well. They are
presented together with their limits existing in the self-consistent field
approximation. The dynamics of the small amplitude spin-electron-acoustic waves
in the dense degenerate plasmas is are studied within the kinetic model. This
work presents the deterministic approach to the derivation and interpretation
of the kinetic equations. So, no probability is introduced during the
transition from the level of individual particles to the collective functions.
Problem of thermalization is not considered, but we can see that the structure
of kinetic equations is kept for the system before and after thermalization.
Hence, the kinetic equations can be used to approach this item.


  Despite of the pain and limited accuracy of blood tests for early recognition
of cardiovascular disease, they dominate risk screening and triage. On the
other hand, heart rate variability is non-invasive and cheap, but not
considered accurate enough for clinical practice. Here, we tackle heart beat
interval based classification with deep learning. We introduce an end to end
differentiable hybrid architecture, consisting of a layer of biological neuron
models of cardiac dynamics (modified FitzHugh Nagumo neurons) and several
layers of a standard feed-forward neural network. The proposed model is
evaluated on ECGs from 474 stable at-risk (coronary artery disease) patients,
and 1172 chest pain patients of an emergency department. We show that it can
significantly outperform models based on traditional heart rate variability
predictors, as well as approaching or in some cases outperforming clinical
blood tests, based only on 60 seconds of inter-beat intervals.


  Methane (CH$_4$) is the chief contributor to global climate change. Recent
Airborne Visible-Infrared Imaging Spectrometer-Next Generation (AVIRIS-NG) has
been very useful in quantitative mapping of methane emissions. Existing methods
for analyzing this data are sensitive to local terrain conditions, often
require manual inspection from domain experts, prone to significant error and
hence are not scalable. To address these challenges, we propose a novel
end-to-end spectral absorption wavelength aware transformer network,
MethaneMapper, to detect and quantify the emissions. MethaneMapper introduces
two novel modules that help to locate the most relevant methane plume regions
in the spectral domain and uses them to localize these accurately. Thorough
evaluation shows that MethaneMapper achieves 0.63 mAP in detection and reduces
the model size (by 5x) compared to the current state of the art. In addition,
we also introduce a large-scale dataset of methane plume segmentation mask for
over 1200 AVIRIS-NG flight lines from 2015-2022. It contains over 4000 methane
plume sites. Our dataset will provide researchers the opportunity to develop
and advance new methods for tackling this challenging green-house gas detection
problem with significant broader social impact. Dataset and source code are
public


  The inelastic scattering of electrons is one route to study the vibrational
and electronic properties of materials. Such experiments, also called electron
energy-loss spectroscopy, are particularly useful for the investigation of the
collective excitations in metals, the charge carrier plasmons. These plasmons
are characterized by a specific dispersion (energy-momentum relationship),
which contains information on the sometimes complex nature of the conduction
electrons in topical materials. In this review we highlight the improvements of
the electron energy-loss spectrometer in the last years, summarize current
possibilities with this technique, and give examples where the investigation of
the plasmon dispersion allows insight into the interplay of the conduction
electrons with other degrees of freedom.


  Semantic segmentation is a computer vision task that associates a label with
each pixel in an image. Modern approaches tend to introduce class embeddings
into semantic segmentation for deeply utilizing category semantics, and regard
supervised class masks as final predictions. In this paper, we explore the
mechanism of class embeddings and have an insight that more explicit and
meaningful class embeddings can be generated based on class masks purposely.
Following this observation, we propose ECENet, a new segmentation paradigm, in
which class embeddings are obtained and enhanced explicitly during interacting
with multi-stage image features. Based on this, we revisit the traditional
decoding process and explore inverted information flow between segmentation
masks and class embeddings. Furthermore, to ensure the discriminability and
informativity of features from backbone, we propose a Feature Reconstruction
module, which combines intrinsic and diverse branches together to ensure the
concurrence of diversity and redundancy in features. Experiments show that our
ECENet outperforms its counterparts on the ADE20K dataset with much less
computational cost and achieves new state-of-the-art results on PASCAL-Context
dataset. The code will be released at https://gitee.com/mindspore/models and
https://github.com/Carol-lyh/ECENet.


  In this paper we prove the following: Take any "small Mandelbrot set" and
zoom in a neighborhood of a parabolic or Misiurewicz parameter in it, then we
can see a quasiconformal image of a Cantor Julia set which is a perturbation of
a parabolic or Misiurewicz Julia set. Furthermore, zoom in its middle part,
then we can see a certain nested structure ("decoration") and finally another
"smaller Mandelbrot set" appears. A similar nested structure exists in the
Julia set for any parameter in the "smaller Mandelbrot set". We can also find
images of a Julia sets by quasiconformal maps with dilatation arbitrarily close
to 1. This answers a question by Adrian Douady. All the parameters belonging to
these images are semihyperbolic and this leads to the fact that the set of
semihyperbolic but non-Misiurewicz and non-hyperbolic parameters is dense with
Hausdorff dimension 2 in the boundary of the Mandelbrot set.


  Advancements in the implementation of quantum hardware have enabled the
acquisition of data that are intractable for emulation with classical
computers. The integration of classical machine learning (ML) algorithms with
these data holds potential for unveiling obscure patterns. Although this hybrid
approach extends the class of efficiently solvable problems compared to using
only classical computers, this approach has been realized for solving
restricted problems because of the prevalence of noise in current quantum
computers. Here, we extend the applicability of the hybrid approach to problems
of interest in many-body physics, such as predicting the properties of the
ground state of a given Hamiltonian and classifying quantum phases. By
performing experiments with various error-reducing procedures on
superconducting quantum hardware with 127 qubits, we managed to acquire refined
data from the quantum computer. This enabled us to demonstrate the successful
implementation of classical ML algorithms for systems with up to 44 qubits. Our
results verify the scalability and effectiveness of the classical ML algorithms
for processing quantum experimental data.


  Context. It has become evident that one-zone synchrotron self-Compton models
are not always adequate for very-high-energy (VHE) gamma-ray emitting blazars.
While two-component models are performing better, they are difficult to
constrain due to the large number of free parameters. Aims. In this work, we
make a first attempt to take into account the observational constraints from
Very Long Baseline Interferometry (VLBI) data, long-term light curves (radio,
optical, and X-rays) and optical polarisation to limit the parameter space for
a two-component model and test if it can still reproduce the observed spectral
energy distribution (SED) of the blazars. Methods. We selected five TeV BL Lac
objects based on the availability of VHE gamma-ray and optical polarisation
data. We collected constraints for the jet parameters from VLBI observations.
We evaluated the contributions of the two components to the optical flux by
means of decomposition of long-term radio and optical light curves as well as
modeling of the optical polarisation variability of the objects. We selected
eight epochs for these five objects, based on the variability observed at VHE
gamma rays, for which we constructed the SEDs that we then modeled with a
two-component model. Results. We found parameter sets which can reproduce the
broadband SED of the sources in the framework of two-component models
considering all available observational constraints from VLBI observations.
Moreover, the constraints obtained from the long-term behavior of the sources
in the lower energy bands could be used to determine the region where the
emission in each band originates. Finally, we attempted to use optical
polarisation data to shed new light on the behavior of the two components in
the optical band. Our observationally constrained two zone model allows
explanation of the entire SED from radio to VHE with two co-located emission
regions.


  We study scattering processes on $p$-adic multiloop surfaces represented as
multiloop infinite graphs with total valence in each vertex equal $p+1$. They
all are spaces of the constant negative curvature since they are quotients of
the $p$-adic hyperbolic plane over free acting discrete subgroup of $PGL(2,
{\bf Q}_p)$. Releasing the closed part of this graph containing all loops which
is called reduced graph $T_{red}$ we can obtain $L$-function corresponding to
this closed graph. For the total graph we introduce the notion of the spherical
functions being eigenfunctions of the Laplace operator acting on the graph and
consider $s$--wave scattering processes therefore defining scattering matrices
$c_i$. The number of possibilities coincides with $|\T_{red}|$ --- the number
of vertices of the reduced graph. Taking the product over all $c_i$ we define
the total scattering matrix which appears to be essentially presented as a
ratio of $L$--functions: $C\sim L(\alpha_+)/L(\alpha_-)$, where the function
$L$ itself depends only on the shape of $\Tr$ and not on the initial infinite
graph, and the only dependence of initial $p$ is contained in arguments
$\alpha_\pm$ defined by $p$ and eigenvalue $t$ of the Laplacian. We also
present a proof by H.Bass of the theorem expressing $L$--functions on arbitrary
finite graphs via determinants of some local operators on these graphs.


  The supermassive black hole Sgr A* at the center of our galaxy produces
repeating near-infrared flares that are observed by ground and space based
instruments. This activity has been simulated in the past with Magnetically
Arrested Disk (MAD) models which include stable jet formations. The present
study uses a different approach in that it considers a Standard and Normal
Evolution (SANE) multi-loop model that lacks a stable jet structure. The main
objective of this research is to identify regions that contain current sheets
and high magnetic turbulence, and to subsequently generate a 2.2 micron light
curve generated from non-thermal particles. Additionally, we investigate the
properties of the flares, in particular, their evolution during flare events,
and the similarity of flare characteristics between the generated and observed
light curves. 2D GRMHD simulation data from a SANE multi-loop model is
employed, and thermal radiation is introduced to generate a 230 GHz light
curve. Physical variables are calibrated to align with the 230 GHz
observations. Current sheets are identified by analyzing toroidal currents,
magnetization, plasma beta, density, and dimensionless temperatures. The
evolution of current sheets during flare events is studied, and higher-energy
non-thermal light curves are calculated, focusing on the 2.2 micron
near-infrared range. We obtain promising 2.2 micron light curves whose flare
duration and spectral index behavior align well with observations. Our findings
support the association of flares with particle acceleration and nonthermal
emission in current sheet plasmoid chains and in the boundary of the disk
inside the funnel above and below the central black hole.


  Robust PCA is a widely used statistical procedure to recover a underlying
low-rank matrix with grossly corrupted observations. This work considers the
problem of robust PCA as a nonconvex optimization problem on the manifold of
low-rank matrices, and proposes two algorithms (for two versions of
retractions) based on manifold optimization. It is shown that, with a proper
designed initialization, the proposed algorithms are guaranteed to converge to
the underlying low-rank matrix linearly. Compared with a previous work based on
the Burer-Monterio decomposition of low-rank matrices, the proposed algorithms
reduce the dependence on the conditional number of the underlying low-rank
matrix theoretically. Simulations and real data examples confirm the
competitive performance of our method.


  The coma of comet C/2016 R2 (PanSTARRS) is one of the most chemically
peculiar ever observed, in particular due to its extremely high CO/H2O and
N2+/H2O ratios}, and unusual trace volatile abundances. However, the complex
shape of its CO emission lines, as well as uncertainties in the coma structure
and excitation, has lead to ambiguities in the total CO production rate. We
performed high resolution, spatially, spectrally and temporally resolved CO
observations using the James Clerk Maxwell Telescope (JCMT) and Submillimeter
Array (SMA) to elucidate the outgassing behaviour of C/2016 R2. Results are
analyzed using a new, time-dependent, three dimensional radiative transfer code
(SUBLIME), incorporating for the first time, accurate state-to-state
collisional rate coefficients for the CO--CO system. The total CO production
rate was found to be in the range $(3.8-7.6)\times10^{28}$ s$^{-1}$ between
2018-01-13 and 2018-02-01, with a mean value of $(5.3\pm0.6)\times10^{28}$
s$^{-1}$ at r_H = 2.8-2.9 au. The emission is concentrated in a near-sunward
jet, with an outflow velocity $0.51\pm0.01$ km/s, compared to $0.25\pm0.01$
km/s in the ambient (and night-side) coma. Evidence was also found for an
extended source of CO emission, possibly due to icy grain sublimation around
$1.2\times10^5$ km from the nucleus. Based on the coma molecular abundances, we
propose that the nucleus ices of C/2016 R2 can be divided into a rapidly
sublimating apolar phase, rich in CO, CO2, N2 and CH3OH, and a predominantly
frozen (or less abundant), polar phase containing more H2O, CH4, H2CO and HCN.


  The interplay of superconductivity, magnetic fields, and spin-orbit
interaction lies at the heart of topological superconductivity. Remarkably, the
recent experimental discovery of $\varphi_{0}$ Josephson junctions by Szombati
et al., Nat. Phys. 12, 568 (2016), characterized by a finite phase offset in
the supercurrent, require the same ingredients as topological superconductors,
which suggests a profound connection between these two distinct phenomena.
Here, we theoretically show that a quantum dot $\varphi_{0}$ Josephson junction
can serve as a new qualitative indicator for topological superconductivity:
Microscopically, we find that the phase shift in a junction of $s-$wave
superconductors is due to the spin-orbit induced mixing of singly occupied
states on the qantum dot, while for a topological superconductor junction it is
due to singlet-triplet mixing. Because of this important difference, when the
spin-orbit vector of the quantum dot and the external Zeeman field are
orthogonal, the $s$-wave superconductors form a $\pi$ Josephson junction while
the topological superconductors have a finite offset $\varphi_{0}$ by which
topological superconductivity can be distinguished from conventional
superconductivity. Our prediction can be immediately tested in nanowire systems
currently used for Majorana fermion experiments and thus offers a new and
realistic approach for detecting topological bound states.


  Several numerical radius inequalities are studied by developing an extension
of the Buzano's inequality. It is shown that if $T$ is a bounded linear
operator on a complex Hilbert space, then
  \begin{eqnarray*}
  w^n(T) &\leq& \frac{1}{2^{n-1}} w(T^n)+ \sum_{k=1}^{n-1} \frac{1}{2^{k}}
\left\|T^k \right\| \left\|T \right\|^{n-k}, \end{eqnarray*} for every positive
integer $n\geq 2.$ This is a non-trivial improvement of the classical
inequality $w(T)\leq \|T\|.$ The above inequality gives an estimation for the
numerical radius of the nilpotent operators, i.e., if $T^n=0$ for some least
positive integer $n\geq 2$, then \begin{eqnarray*}
  w(T) &\leq& \left(\sum_{k=1}^{n-1} \frac{1}{2^{k}} \left\|T^k \right\|
\left\|T \right\|^{n-k}\right)^{1/n}
  \leq \left( 1- \frac{1}{2^{n-1}}\right)^{1/n} \|T\|. \end{eqnarray*}
  Also, we deduce a reverse inequality for the numerical radius power
inequality $w(T^n)\leq w^n(T)$. We show that if $\|T\|\leq 1$, then
  \begin{eqnarray*}
  w^n(T) &\leq& \frac{1}{2^{n-1}} w(T^n)+ 1- \frac{1}{2^{n-1}},
  \end{eqnarray*}
  for every positive integer $n\geq 2.$ This inequality is sharp.


  It is well known the adversarial optimization of GAN-based image
super-resolution (SR) methods makes the preceding SR model generate unpleasant
and undesirable artifacts, leading to large distortion. We attribute the cause
of such distortions to the poor calibration of the discriminator, which hampers
its ability to provide meaningful feedback to the generator for learning
high-quality images. To address this problem, we propose a simple but
non-travel diffusion-style data augmentation scheme for current GAN-based SR
methods, known as DifAugGAN. It involves adapting the diffusion process in
generative diffusion models for improving the calibration of the discriminator
during training motivated by the successes of data augmentation schemes in the
field to achieve good calibration. Our DifAugGAN can be a Plug-and-Play
strategy for current GAN-based SISR methods to improve the calibration of the
discriminator and thus improve SR performance. Extensive experimental
evaluations demonstrate the superiority of DifAugGAN over state-of-the-art
GAN-based SISR methods across both synthetic and real-world datasets,
showcasing notable advancements in both qualitative and quantitative results.


  This note is concerned with concentration inequalities for extrema of
stationary Gaussian processes. It provides non-asymptotic tail inequalities
which fully reflect the fluctuation rate, and as such improve upon standard
Gaussian concentration. The arguments rely on the hypercontractive approach
developed by Chatterjee for superconcentration variance bounds. Some
statistical illustrations complete the exposition.


  We present the temperature dependence of the specific heat, without external
magnetic field and with H= 9 T, for LaMnO3, La1.35Sr1.65Mn2O7, La1.5Sr0.5NiO4
and La1.5Sr0.5CoO4 single crystals. We found that spin-wave excitations in the
ferromagnetic and bilayer-structure La1.35Sr1.65Mn2O7 were suppressed by the 9
T magnetic field. On the other hand, the external magnetic field had no effect
in the specific heat of the other three antiferromagnetic samples. Also, the
electronic part of the interactions were removed at very low temperatures in
the La1.5Sr0.5NiO4 single crystal, even with a zero applied magnetic field.
Below 4 K, we found that the specific heat data for La1.35Sr1.65Mn2O7 and
La1.5Sr0.5NiO4 crystals could be fitted to an exponential decay law. Detailed
magnetization measurements in this low temperature interval showed the
existence of a peak close to 2 K. Both results, magnetizations and specific
heat suggest the existence of an anisotropy gap in the energy spectrum of
La1.35Sr1.65Mn2O7 and La1.5Sr0.5NiO4 compounds.