  Physics-Informed Neural Networks (PINNs) have been widely used for solving
partial differential equations (PDEs) of different types, including fractional
PDEs (fPDES) [29]. Herein, we propose a new general (quasi) Monte Carlo PINN
for solving fPDEs on irregular domains. Specifically, instead of approximating
fractional derivatives by Monte Carlo approximations of integrals as was done
previously in [31], we use a more general Monte Carlo approximation method to
solve different fPDEs, which is valid for fractional differentiation under any
definition. Moreover, based on the ensemble probability density function, the
generated nodes are all located in denser regions near the target point where
we perform the differentiation. This has an unexpected connection with known
finite difference methods on non-equidistant or nested grids, and hence our
method inherits their advantages. At the same time, the generated nodes exhibit
a block-like dense distribution, leading to a good computational efficiency of
this approach. We present the framework for using this algorithm and apply it
to several examples. Our results demonstrate the effectiveness of GMC-PINNs in
dealing with irregular domain problems and show a higher computational
efficiency compared to the original fPINN method. We also include comparisons
with the Monte Carlo fPINN [31]. Finally, we use examples to demonstrate the
effectiveness of the method in dealing with fuzzy boundary location problems,
and then use the method to solve the coupled 3D fractional Bloch-Torrey
equation defined in the ventricular domain of the human brain, and compare the
results with classical numerical methods.


  We study the unconventional insulating state in A_4C_{60} with a variety of
approaches, including density functional calculations and dynamical mean-field
theory. While the former predicts a metallic state, in disagreement with
experiment, the latter yields a (paramagnetic) Mott-Jahn-Teller insulator. In
that state, conduction between molecules is blocked by on-site Coulomb
repulsion, magnetism is suppressed by intra-molecular Jahn-Teller effect, and
important excitations (such as optical and spin gap) should be essentially
intra-molecular. Experimental gaps of 0.5 eV and 0.1 eV respectively compare
well with molecular ion values, in agreement with this picture.


  Two recent experiments from Cornell and Columbia have reported
insulator-to-metal transitions in two-dimensional (2D) moir\'e transition metal
dichalcogenides (mTMD) induced by doping around half-filling, where the system
is a Mott insulator. In the current work, we consider the temperature dependent
resistivity of this metallic phase in the doped situation away from
half-filling, arguing that it arises from the strongly temperature dependent 2D
Friedel oscillations (i.e. finite momentum screening) associated with random
quenched charged impurities, leading to the observed strongly increasing
linear-in-$T$ resistivity in the metallic phase. Our theory appears to account
for the temperature-dependent metallic resistivity for doping around
half-filling of the effective moir\'e TMD band, showing that
temperature-dependent screened Coulomb disorder is an essential ingredient of
doped 2D mTMD physics.


  Integral-field-spectroscopy and multi-object-spectroscopy provide the high
multiplex gain required for efficient use of the upcoming generation of
extremely large telescopes. We present instrument developments and designs for
both concepts, and how these designs can be applied to cryogenic near-infrared
instrumentation. Specifically, the fiber-based concept stands out the
possibility to expand it to any number of image points, and its modularity
predestines it to become the new concept for multi-field-spectroscopy. Which of
the three concepts --- integral-field-, multi-object-, or
multi-field-spectroscopy --- is best suited for the largest telescopes is
discussed considering the size of the objects and their density on the sky.


  (Abridged) We explore, by means of a large ensemble of SPH simulations, how
the level of turbulence affects the collapse and fragmentation of a
star-forming core. All our simulated cores have the same, except that we vary
(a) the initial level of turbulence (as measured by the ratio of turbulent to
gravitational energy, $\alpha_{\rm turb} \equiv U_{\rm turb}/|\Omega| = 0,
0.01, 0.025, 0.05, 0.10 {\rm and} 0.25$) and (b), for fixed $\alpha_{\rm
turb}$, the details of the initial turbulent velocity field (so as to obtain
good statistics).
  A low level of turbulence ($\alpha_{\rm turb} \sim 0.05$) suffices to produce
multiple systems. As $\alpha_{\rm turb}$ is increased, the number of objects
formed and the companion frequency both increase. The mass function is bimodal,
with a flat low-mass segment representing single objects ejected from the core
before they can accrete much, and a Gaussian high-mass segment representing
objects which because they remain in the core grow by accretion and tend to
pair up in multiple systems.


  We consider the problem of secure communications in a MIMO setting in the
presence of an adversarial jammer equipped with $n_j$ transmit antennas and an
eavesdropper equipped with $n_e$ receive antennas. A multiantenna transmitter,
equipped with $n_t$ antennas, desires to secretly communicate a message to a
multiantenna receiver equipped with $n_r$ antennas. We propose a transmission
method based on artificial noise and linear precoding and a two-stage receiver
method employing beamforming. Under this strategy, we first characterize the
achievable secrecy rates of communication and prove that the achievable secure
degrees-of-freedom (SDoF) is given by $d_s = n_r - n_j$ in the perfect channel
state information (CSI) case. Second, we consider quantized CSI feedback using
Grassmannian quantization of a function of the direct channel matrix and derive
sufficient conditions for the quantization bit rate scaling as a function of
transmit power for maintaining the achievable SDoF $d_s$ with perfect CSI and
for having asymptotically zero secrecy rate loss due to quantization. Numerical
simulations are also provided to support the theory.


  At the LHC, for the first time, laboratory energies are sufficiently large to
reproduce the kind of reactions that occur when energetic cosmic rays strike
the top of the atmosphere. The reaction products of interest for cosmic ray
studies are produced at small angles, even with colliding beams. Most of the
emphasis at the LHC is on rare processes that are studied with detectors at
large angles. It is precision measurements at large angles that are expected to
lead to discoveries of Higgs bosons and super symmetric particles. CMS
currently has two small angle detectors, CASTOR and a Zero Degree Calorimeter
(ZDC). CASTOR, at $0.7^{\circ}$ down to $0.08^{\circ}$, is designed to study
"Centauro" and "long penetrating" events, observed in VHE cosmic-ray data. As a
general purpose detector it also makes measurements of reaction products at
forward angles from p-p collisions, which provide input for cosmic ray shower
codes. The ZDC is small, 9 cm. wide, between the incoming and outgoing beam
pipes out at a distance of 140 m. The ZDC measures neutral objects that follow
the direction of the beam at the interaction point. If the long penetrating
objects are spectators they could be seen in the ZDC if their charge to mass
ratio, Z/A, is less than 0.2.


  Facial expression recognition (FER), aiming to classify the expression
present in the facial image or video, has attracted a lot of research interests
in the field of artificial intelligence and multimedia. In terms of video based
FER task, it is sensible to capture the dynamic expression variation among the
frames to recognize facial expression. However, existing methods directly
utilize CNN-RNN or 3D CNN to extract the spatial-temporal features from
different facial units, instead of concentrating on a certain region during
expression variation capturing, which leads to limited performance in FER. In
our paper, we introduce a Graph Convolutional Network (GCN) layer into a common
CNN-RNN based model for video-based FER. First, the GCN layer is utilized to
learn more significant facial expression features which concentrate on certain
regions after sharing information between extracted CNN features of nodes.
Then, a LSTM layer is applied to learn long-term dependencies among the GCN
learned features to model the variation. In addition, a weight assignment
mechanism is also designed to weight the output of different nodes for final
classification by characterizing the expression intensities in each frame. To
the best of our knowledge, it is the first time to use GCN in FER task. We
evaluate our method on three widely-used datasets, CK+, Oulu-CASIA and MMI, and
also one challenging wild dataset AFEW8.0, and the experimental results
demonstrate that our method has superior performance to existing methods.


  Turbo compressed sensing (Turbo-CS) is an efficient iterative algorithm for
sparse signal recovery with partial orthogonal sensing matrices. In this paper,
we extend the Turbo-CS algorithm to solve compressed sensing problems involving
more general signal structure, including compressive image recovery and
low-rank matrix recovery. A main difficulty for such an extension is that the
original Turbo-CS algorithm requires prior knowledge of the signal distribution
that is usually unavailable in practice. To overcome this difficulty, we
propose to redesign the Turbo-CS algorithm by employing a generic denoiser that
does not depend on the prior distribution and hence the name denoising-based
Turbo-CS (D-Turbo-CS). We then derive the extrinsic information for a generic
denoiser by following the Turbo-CS principle. Based on that, we optimize the
parametric extrinsic denoisers to minimize the output mean-square error (MSE).
Explicit expressions are derived for the extrinsic SURE-LET denoiser used in
compressive image denoising and also for the singular value thresholding (SVT)
denoiser used in low-rank matrix denoising. We find that the dynamics of
D-Turbo-CS can be well described by a scaler recursion called MSE evolution,
similar to the case for Turbo-CS. Numerical results demonstrate that D-Turbo-CS
considerably outperforms the counterpart algorithms in both reconstruction
quality and running time.


  We present the decomposition of the stellar velocity ellipsoid using stellar
velocity dispersions within a 40 deg wedge about the major-axis (sigma_maj),
the epicycle approximation, and the asymmetric drift equation. Thus, we employ
no fitted forms for sigma_maj and escape interpolation errors resulting from
comparisons of the major and minor axes. We apply the theoretical construction
of the method to integral field data taken for NGC 3949 and NGC 3982. We derive
the vertical-to-radial velocity dispersion ratio (sigma_z / sigma_R) and find
(1) our decomposition method is accurate and reasonable, (2) NGC 3982 appears
to be rather typical of an Sb type galaxy with sigma_z / sigma_R = 0.73
(+0.13/-0.11) despite its high surface brightness and small size, and (3) NGC
3949 has a hot disk with sigma_z / sigma_R = 1.18 (+0.36/-0.28).


  We study the rationality properties of the moduli space $\mathcal{A}_g$ of
principally polarised abelian $g$-folds over $\mathbb{Q}$ and apply the results
to arithmetic questions. In particular we show that any principally polarised
abelian threefold over $\mathbb{F}_p$ may be lifted to an abelian variety over
$\mathbb{Q}$. This is a phenomenon of low dimension: assuming the Bombieri-Lang
conjecture we also show that this is not the case for abelian varieties of
dimension at least seven. About moduli spaces, we show that $\mathcal{A}_g$ is
unirational over $\mathbb{Q}$ for $g \leq 5$ and stably rational for $g=3$.
This also allows us to make unconditional one of the results of Masser and
Zannier about the existence of abelian varieties over $\mathbb{Q}$ that are not
isogenous to Jacobians.


  Periodically driven systems with internal and spatial symmetries can exhibit
a variety of anomalous boundary behaviors at both the zero and $\pi$
quasienergies despite the trivial bulk Floquet bands. These phenomena are
called anomalous Floquet topology (AFT) as they are unconnected from their
static counterpart, arising from the winding of the time evolution unitary
rather than the bulk Floquet bands at the end of the driving period. In this
paper, we systematically derive the first and inversion-symmetric second-order
AFT bulk-boundary correspondence for Altland-Zirnbauer (AZ) classes BDI, D,
DIII, AII. For each AZ class, we start a dimensional hierarchy with a parent
dimension having $\mathbb{Z}$ classification, then use it as an interpolating
map to classify the lower-dimensional descendants. From the Atiyah-Hirzebruch
spectral sequence (AHSS), we identify the subspace that contains topological
information and faithfully derive the AFT bulk-boundary correspondence for both
the parent and descendants. Our theory provides analytic tools for
out-of-equilibrium topological phenomena.


  In this paper, we introduce a new attack called controller manipulation
attack (CMA) on a Reconfigurable Intelligent Surface (RIS) assisted
communication system between a transmitter and a receiver. An attacker has the
capability to manipulate the RIS controller and modify the phase shift induced
by the RIS elements. The goal of the attacker is to minimize the data rate at
the receiver, subject to a constraint on the attack detection probability at
the receiver. We consider a number of attack detection models: (i) composite
hypothesis testing based attack detection in a given fading block for known
channel gains, (ii) sequential quickest detection of CMA in a given fading
block for known channel gains, (iii) nonparametric hypothesis test to detect
CMA for unknown channel gains over a fading block, and (iv)
signal-to-noise-ratio (SNR) moment based detection over possibly multiple
fading blocks. In the first case, a simple energy detector turns out to be
uniformly most powerful (UMP). In the second case, simplification of the
standard CUSUM test and its performance bounds are obtained. In the third case,
non-parametric Kolmogorov-Smirnov test is further simplified to a simple
per-sample double threshold test. The attack against these three detectors are
designed via novel optimization formulations and semidefinite relaxation based
solutions. In the fourth case, we consider threshold detection using moments of
SNR; various SNR moments under no attack are obtained analytically for large
RIS and then used to formulate the attack design problem as a linear program.
Finally, numerical results illustrate the performance and trade-offs associated
with the attack schemes, and also demonstrate their efficacy.


  We prove Rubin's conjecture on the structure of local units in the
anticyclotomic $\mathbb{Z}_p$-extension of unramified quadratic extension of
$\mathbb{Q}_p$ in $p=3$ case by extending Burungale-Kobayashi-Ota's work.


  Quasi-monochromatic complex reductions of a number of physically important
equations are obtained. Starting from the cubic nonlinear Klein-Gordon (NLKG),
the Korteweg-deVries (KdV) and water wave equations, it is shown that the
leading order asymptotic approximation can be transformed to the well-known
integrable AKNS system [6] associated with second order (in space) nonlinear
wave equations. This in turn establishes, for the first time, an important
physical connection between the recently discovered nonlocal integrable
reductions of the AKNS system and physically interesting equations. Reductions
include the parity-time, reverse space-time and reverse time nonlocal nonlinear
Schrodinger equations.


  This article provides an overview of intimate threats: a class of privacy
threats that can arise within our families, romantic partnerships, close
friendships, and caregiving relationships. Many common assumptions about
privacy are upended in the context of these relationships, and many otherwise
effective protective measures fail when applied to intimate threats. Those
closest to us know the answers to our secret questions, have access to our
devices, and can exercise coercive power over us. We survey a range of intimate
relationships and describe their common features. Based on these features, we
explore implications for both technical privacy design and policy, and offer
design recommendations for ameliorating intimate privacy risks.


  The eigenvalues and eigenvectors of the connectivity matrix of complex
networks contain information about its topology and its collective behavior. In
particular, the spectral density $\rho(\lambda)$ of this matrix reveals
important network characteristics: random networks follow Wigner's semicircular
law whereas scale-free networks exhibit a triangular distribution. In this
paper we show that the spectral density of hierarchical networks follow a very
different pattern, which can be used as a fingerprint of modularity. Of
particular importance is the value $\rho(0)$, related to the homeostatic
response of the network: it is maximum for random and scale free networks but
very small for hierarchical modular networks. It is also large for an actual
biological protein-protein interaction network, demonstrating that the current
leading model for such networks is not adequate.


  The fundamental theorem of the theory of optimal control, the Pontryagin
maximum principle (PMP), is extended to the setting of almost Lie (AL)
algebroids, geometrical objects generalizing Lie algebroids. This formulation
of the PMP yields, in particular, a scheme comprising reductions of optimal
control problems similar to the reduction for the rigid body in analytical
mechanics. On the other hand, in the presented approach the reduced and
unreduced PMPs are parts of the same universal formalism. The framework is
based on a very general concept of homotopy of measurable paths and the
geometry of AL algebroids.


  In this work the methods of comparison of digitized copies of administrative
documents were considered. This problem arises, for example, when comparing two
copies of documents signed by two parties in order to find possible
modifications made by one party, in the banking sector at the conclusion of
contracts in paper form. The proposed method of document image comparison is
based on a combination of several ways of image comparison of words that are
descriptors of text feature points. Testing was conducted on public Payslip
Dataset (French). The results showed the high quality and the reliability of
finding differences in two images that are versions of the same document.


  The voltage oscillations which occur in an ideally current-biased Josephson
junction, were proposed to make a current standard for metrology. We
demonstrate similar oscillations in a more complex Josephson circuit derived
from the Cooper pair box: the quantronium. When a constant current I is
injected in the gate capacitor of this device, oscillations develop at the
frequency fB=I/2e, with e the electron charge. We detect these oscillations
through the sidebands induced at multiples of fB in the spectrum of a microwave
signal reflected on the circuit, up to currents I exceeding 100 pA. We discuss
the potential interest of this current to frequency conversion experiment for
metrology.


  The Nuclear Spectroscopic Telescope Array (NuSTAR) mission is the first
focusing X-ray telescope in the hard X-ray (3-79 keV) band. Among the phenomena
that can be studied in this energy band, some require high time resolution and
stability: rotation-powered and accreting millisecond pulsars, fast variability
from black holes and neutron stars, X-ray bursts, and more. Moreover, a good
alignment of the timestamps of X-ray photons to UTC is key for multi-instrument
studies of fast astrophysical processes. In this Paper, we describe the timing
calibration of the NuSTAR mission. In particular, we present a method to
correct the temperature-dependent frequency response of the on-board
temperature-compensated crystal oscillator. Together with measurements of the
spacecraft clock offsets obtained during downlinks passes, this allows a
precise characterization of the behavior of the oscillator. The calibrated
NuSTAR event timestamps for a typical observation are shown to be accurate to a
precision of ~65 microsec.


  Several independent lines of evidence reveal that a relatively strong and
highly ordered magnetic field is present throughout the Galaxy's central
molecular zone (CMZ). The field within dense clouds of the central molecular
zone is predominantly parallel to the Galactic plane, probably as a result of
the strong tidal shear in that region. A second magnetic field system is
present outside of clouds, manifested primarily by a population of vertical,
synchrotron-emitting filamentary features aligned with the field. Whether or
not the strong vertical field is uniform throughout the CMZ remains
undetermined, but is a key central issue for the overall energetics and the
impact of the field on the Galactic center arena. The interactions between the
two field systems are considered, as they are likely to drive some of the
activity within the CMZ. As a proxy for other gas-rich galaxies in the local
group and beyond, the Galactic center region reveals that magnetic fields are
likely to be an important diagnostic, if not also a collimator, of the flow of
winds and energetic particles out of the nucleus.


  In this article, a new natural discrete analog of the one parameter
polynomial exponential(OPPE) distribution as a mixture of a number of negative
binomial distributions has been proposed and is called as a natural discrete
one parameter polynomial exponential (NDOPPE) distribution. This distribution
is a generalized version of natural discrete Lindley (NDL) distribution,
proposed and studied by Ahmed and Afify (2019). Two estimators viz., MLE and
UMVUE of the PMF and the CDF of a NDOPPE distribution have been derived. The
estimators have been compared with respect to their MSEs. Simulation study has
been conducted to verify the consistency of the estimators. A real data
illustration has been reported.


  Linearized flow past a submerged obstacle with an elastic sheet resting on
the flow surface are studied in the limit that the bending length is small
compared to the obstacle depth, in two and three dimensions. Gravitational
effects are included in the two-dimensional geometry, but absent in the
three-dimensional geometry; the Froude number is chosen so that gravitational
and elastic restoring forces are comparable in size. In each of these problems,
the waves are exponentially small in the asymptotic limit, and can be computed
using exponential asymptotic methods. In the two-dimensional problem, flow past
a submerged step is considered. It is found that the relative strength of the
gravitational and elastic restoring forces produce two distinct classes of
elastic sheet behaviour. In one parameter regime, constant-amplitude elastic
waves and gravity waves extend indefinitely upstream and downstream from the
obstacle. In the other parameter regime, all waves decay exponentially away
from the obstacle. The equivalent nonlinear two-dimensional geometry is then
studied; this asymptotic analysis predicts the existence of a third
intermediate regime in which waves persist indefinitely only in one direction,
depending on whether the submerged step rises or falls. In the
three-dimensional geometry, it is predicted that the elastic waves extend ahead
of the submerged source, decaying algebraically in space. The form of these
elastic waves is computed, and validated by comparison with numerical
computations of the elastic sheet behaviour.


  We propose the first unified theoretical analysis of mixed sample data
augmentation (MSDA), such as Mixup and CutMix. Our theoretical results show
that regardless of the choice of the mixing strategy, MSDA behaves as a
pixel-level regularization of the underlying training loss and a regularization
of the first layer parameters. Similarly, our theoretical results support that
the MSDA training strategy can improve adversarial robustness and
generalization compared to the vanilla training strategy. Using the theoretical
results, we provide a high-level understanding of how different design choices
of MSDA work differently. For example, we show that the most popular MSDA
methods, Mixup and CutMix, behave differently, e.g., CutMix regularizes the
input gradients by pixel distances, while Mixup regularizes the input gradients
regardless of pixel distances. Our theoretical results also show that the
optimal MSDA strategy depends on tasks, datasets, or model parameters. From
these observations, we propose generalized MSDAs, a Hybrid version of Mixup and
CutMix (HMix) and Gaussian Mixup (GMix), simple extensions of Mixup and CutMix.
Our implementation can leverage the advantages of Mixup and CutMix, while our
implementation is very efficient, and the computation cost is almost
neglectable as Mixup and CutMix. Our empirical study shows that our HMix and
GMix outperform the previous state-of-the-art MSDA methods in CIFAR-100 and
ImageNet classification tasks. Source code is available at
https://github.com/naver-ai/hmix-gmix


  We prove Lieb-Thirring inequalities for Schr\"odinger operators with a
homogeneous magnetic field in two and three space dimensions. The inequalities
bound sums of eigenvalues by a semi-classical approximation which depends on
the strength of the magnetic field, and hence quantifies the diamagnetic
behavior of the system. For a harmonic oscillator in a homogenous magnetic
field, we obtain the sharp constants in the inequalities.


  In this article we study the subgroup of the Picard group of Voevodsky's
category of geometric motives generated by the reduced motives of affine
quadrics. Our main tools here are the functors of Bachmann, but we also provide
an alternative method. We show that the group in question can be described in
terms of indecomposable direct summands in the motives of projective quadrics.
In particular, we describe all the relations among the reduced motives of
affine quadrics. We also extend the Criterion of motivic equivalence of
projective quadrics.


  Generative adversarial networks (GANs) have made great success in image
inpainting yet still have difficulties tackling large missing regions. In
contrast, iterative probabilistic algorithms, such as autoregressive and
denoising diffusion models, have to be deployed with massive computing
resources for decent effect. To achieve high-quality results with low
computational cost, we present a novel pixel spread model (PSM) that
iteratively employs decoupled probabilistic modeling, combining the
optimization efficiency of GANs with the prediction tractability of
probabilistic models. As a result, our model selectively spreads informative
pixels throughout the image in a few iterations, largely enhancing the
completion quality and efficiency. On multiple benchmarks, we achieve new
state-of-the-art performance. Code is released at
https://github.com/fenglinglwb/PSM.


  As quantum computers become real, it is high time we come up with effective
techniques that help programmers write correct quantum programs. Inspired by
Hoare Type Theory in classical computing, we propose Quantum Hoare Type Theory
(QHTT), in which precise specifications about the modification to the quantum
state can be provided within the type of computation. These specifications
within a Hoare type are given in the form of Hoare-logic style pre- and
postconditions following the propositions-as-types principle. The type-checking
process verifies that the implementation conforms to the provided
specification. QHTT has the potential to be a unified system for programming,
specifying, and reasoning about quantum programs.


  Physical notions of stochastic resonance for potential diffusions in
periodically changing double-well potentials such as the spectral power
amplification have proved to be defective. They are not robust for the passage
to their effective dynamics: continuous-time finite-state Markov chains
describing the rough features of transitions between different domains of
attraction of metastable points. In the framework of one-dimensional diffusions
moving in periodically changing double-well potentials we design a new notion
of stochastic resonance which refines Freidlin's concept of quasi-periodic
motion. It is based on exact exponential rates for the transition probabilities
between the domains of attraction which are robust with respect to the reduced
Markov chains. The quality of periodic tuning is measured by the probability
for transition during fixed time windows depending on a time scale parameter.
Maximizing it in this parameter produces the stochastic resonance points.


  We present new photometry and spectroscopy of the eclipsing white dwarf -
M-dwarf binary star RR Cae. We use timings of the primary eclipse from
white-light photo-electric photometry to derive a new ephemeris for the
eclipses. We find no evidence for any period change greater than Pdot/P ~ 5E-12
over a timescale of 10 years. We have measured the effective temperature of the
white dwarf, T_WD, from an analysis of two high resolution spectra of RR Cae
and find T_WD = (7540 +- 175)K. We estimate a spectral type of M4 for the
companion from the same spectra. We have combined new spectroscopic orbits for
the white dwarf and M-dwarf with an analysis of the primary eclipse and cooling
models for helium white dwarfs to measure the mass and radius of the M-dwarf.
The mass of the M-dwarf is (0.182 - 0.183) +- 0.013 Msun and the radius is
(0.203 - 0.215) +- 0.013 Rsun, where the ranges quoted for these values reflect
the range of white dwarf models used. In contrast to previous studies, which
lacked a spectroscopic orbit for the white dwarf, we find that the mass and
radius of the M-dwarf are normal for an M4 dwarf. The mass of the white dwarf
is (0.440 +-0.022) Msun. With these revised masses and radii we find that RR
Cae will become a cataclysmic variable star when the orbital period is reduced
from its current value of 7.3 hours to 121 minutes by magnetic braking in 9-20
Gyr. We note that there is night-to-night variability of a few seconds in the
timing of primary eclipse caused by changes to the shape of the primary
eclipse. We speculate as to the possible causes of this phenomenon. (Abridged)


  We study the ability of transformer-based language models (LMs) to understand
social media language. Social media (SM) language is distinct from standard
written language, yet existing benchmarks fall short of capturing LM
performance in this socially, economically, and politically important domain.
We quantify the degree to which social media language differs from conventional
language and conclude that the difference is significant both in terms of token
distribution and rate of linguistic shift. Next, we introduce a new benchmark
for Social MedIa Language Evaluation (SMILE) that covers four SM platforms and
eleven tasks. Finally, we show that learning a tokenizer and pretraining on a
mix of social media and conventional language yields an LM that outperforms the
best similar-sized alternative by 4.2 points on the overall SMILE score.


  Mergers of compact objects (binary neutron stars, BNS, or neutron star-black
hole, NSBH) with a substantial mass ratio ($q>1.5$) are expected to produce a
mildly relativistic ejecta within $\sim20^\circ$ from the orbital plane. We
present a semi-analytic approach to calculate the expected synchrotron emission
observed from various viewing angles, along with the corresponding radio maps,
that are produced by a collisionless shock driven by such ejecta into the
interstellar medium. This method is supported by 2D numerical calculations of
the full relativistic hydrodynamics with an agreement in the observed emission
of $\sim30\%$. We consider a toroid ejecta with an opening angle of
$15^\circ\leq\theta_ \text{open}\leq30^\circ$ and broken power-law mass
distribution, $M(>\gamma\beta)\propto(\gamma\beta)^{-s}$ with $s=s_{\rm KN}$ at
$\gamma\beta<\gamma_0\beta_0$ and $s=s_{\rm ft}$ at
$\gamma\beta>\gamma_0\beta_0$ (where $\gamma$ is the Lorentz factor). While the
peak flux is dimmer by a factor of $\sim$2-3, and the peak time remains roughly
the same (within $20\%$), for various viewing angles compared to isotropic
equivalent ejecta ($\theta_\text{open}=90^\circ$) considered in preceding
papers, the radio maps are significantly different from the spherical case. The
semi-analytic method can provide information on the ejecta geometry and viewing
angle from future radio map observations and, consequently, constrain the
ejection mechanism. Due to the larger ejected mass in NSBH merger, this late
non-thermal signal can be observed to distances of $\lesssim 200$Mpc for
typical parameter values.


  The source of high-energy protons (>500 MeV) responsible for the so-called
ground level enhancements (GLEs) remains an open question in solar physics. One
of the candidates is a shock wave driven by a coronal mass ejection, which is
thought to accelerate particles via diffusive-shock acceleration. We perform
physics-based simulations of proton acceleration using information on the shock
and ambient plasma parameters derived from the observation of a real GLE event.
We analyse the simulation results with the aim to find out which of the
parameters are significant in controlling the acceleration efficiency and to
get a better understanding of the conditions under which the shock can produce
relativistic protons. We use results of the recently developed technique to
determine the shock and ambient plasma parameters, applied to the 17 May 2012
GLE event, and carry out proton acceleration simulations with the Coronal Shock
Acceleration model. We have performed proton acceleration simulations for nine
individual magnetic field lines characterised by various plasma conditions.
Analysis of the simulation results shows that the acceleration efficiency of
the shock, i.e., its ability to accelerate particles to high energies, tends to
be higher for those shock portions that are characterised by larger values of
the scattering-centre compression ratio and/or the fast-mode Mach number. At
the same time, the acceleration efficiency can be strengthened due to enhanced
plasma density in the flux tube. Analysis of the delays between the flare onset
and the production times of protons of 1 GV rigidity for different field lines
in our simulations, and a subsequent comparison of those with the observed
values indicate a possibility that quasi-perpendicular portions of the shock
play the main role in producing relativistic protons.


  In this paper we obtain the central limit theorem for triangular arrays of
non-homogeneous Markov chains under a condition imposed to the maximal
coefficient of correlation. The proofs are based on martingale techniques and a
sharp lower bound estimate for the variance of partial sums. The results
complement an important central limit theorem of Dobrushin based on the
contraction coefficient.


  In recent years, there has been a considerable amount of interest in
stability of equations and their corresponding groups. Here, we initiate the
systematic study of the quantitative aspect of this theory. We develop a novel
method, inspired by the Ornstein-Weiss quasi-tiling technique, to prove that
abelian groups are polynomially stable with respect to permutations, under the
normalized Hamming metrics on the groups $\operatorname{Sym}(n)$. In
particular, this means that there exists $D\geq 1$ such that for $A,B\in
\operatorname{Sym}(n)$, if $AB$ is $\delta$-close to $BA$, then $A$ and $B$ are
$\epsilon$-close to a commuting pair of permutations, where $\epsilon\leq
O(\delta^{1/D})$. We also observe a property-testing reformulation of this
result, yielding efficient testers for certain permutation properties.


  GRS 1758-258 is one of the few persistent hard X-ray emitters (E>100 keV) in
the Galaxy. Using the ASCA satellite, we have obtained the first detailed data
on GRS 1758-258 in the 1-10 keV range, where previous observations were
affected by confusion problems caused by the nearby strong source GX5-1. The
spectrum is well described by a power law with photon index 1.7 without strong
Fe emission lines. A prominent soft excess, as observed with ROSAT when the
hard X-ray flux was in a lower intensity state, was not detected. However, the
presence of a soft spectral component, accounting for at most 5% of the 0.1-300
keV flux, cannot be excluded. The accurate measurement of interstellar
absorption (N_H=(1.5+-0.1) x 10^22 cm -2) corresponds to an optical extinction
which definitely excludes the presence of a massive companion.


  We give an overview of a program of Stochastic Deformation of Classical
Mechanics and the Calculus of Variations, strongly inspired by the quantization
method.


  Recent observations suggest that some high-velocity clouds may be confined by
massive dark matter halos. In particular, the proximity and proposed dark
matter content of the Smith Cloud make it a tempting target for the indirect
detection of dark matter annihilation. We argue that the Smith Cloud may be a
better target than some Milky Way dwarf spheroidal satellite galaxies and use
gamma-ray observations from the Fermi Large Area Telescope to search for a dark
matter annihilation signal. No significant gamma-ray excess is found coincident
with the Smith Cloud, and we set strong limits on the dark matter annihilation
cross section assuming a spatially-extended dark matter profile consistent with
dynamical modeling of the Smith Cloud. Notably, these limits exclude the
canonical thermal relic cross section ($\sim 3\times10^{-26}{\rm cm}^{3}{\rm
s}^{-1}$) for dark matter masses $\lesssim 30$ GeV annihilating via the $b \bar
b$ or $\tau^{+}\tau^{-}$ channels for certain assumptions of the dark matter
density profile; however, uncertainties in the dark matter content of the Smith
Cloud may significantly weaken these constraints.


  Multi-view clustering aims at exploiting information from multiple
heterogeneous views to promote clustering. Most previous works search for only
one optimal clustering based on the predefined clustering criterion, but
devising such a criterion that captures what users need is difficult. Due to
the multiplicity of multi-view data, we can have meaningful alternative
clusterings. In addition, the incomplete multi-view data problem is ubiquitous
in real world but has not been studied for multiple clusterings. To address
these issues, we introduce a deep incomplete multi-view multiple clusterings
(DiMVMC) framework, which achieves the completion of data view and multiple
shared representations simultaneously by optimizing multiple groups of decoder
deep networks. In addition, it minimizes a redundancy term to simultaneously
%uses Hilbert-Schmidt Independence Criterion (HSIC) to control the diversity
among these representations and among parameters of different networks. Next,
it generates an individual clustering from each of these shared
representations. Experiments on benchmark datasets confirm that DiMVMC
outperforms the state-of-the-art competitors in generating multiple clusterings
with high diversity and quality.


  A recent work [Y. Huang and B.-Q. Ma, Commun. Phys. {\bf 1}, 62 (2018)]
associated all four PeV neutrinos observed by IceCube to gamma-ray bursts
(GRBs), and revealed a regularity which indicates a Lorentz violation scale
$E_{\rm LV}=(6.5\pm0.4)\times10^{17}$ GeV with opposite sign factors $s=\pm 1$
between neutrinos and antineutrinos. The association of "time delay" and "time
advance" events with neutrinos and antineutrinos (or vice versa) is only a
hypothesis since the IceCube detector cannot tell the chirality of the
neutrinos, and further experimental tests are needed to verify this hypothesis.
We derive the values of the CPT-odd Lorentz violating parameters in the
standard-model extension (SME) framework, and perform a threshold analysis on
the electron-positron pair emission of the superluminal neutrinos (or
antineutrinos). We find that different neutrino/antineutrino propagation
properties, suggested by Y. Huang and B.-Q. Ma, can be described in the SME
framework with both Lorentz invariance and CPT symmetry violation, but with a
threshold energy constraint. A viable way on testing the CPT symmetry violation
between neutrinos and antineutrinos is suggested.


  How does one compute the Bondi mass on an arbitrary cut of null infinity
$\scri$ when it is not presented in a Bondi system? What then is the correct
definition of the mass aspect? How does one normalise an asymptotic translation
computed on a cut which is not equipped with the unit-sphere metric? These are
questions which need to be answered if one wants to calculate the Bondi-Sachs
energy-momentum for a space-time which has been determined numerically. Under
such conditions there is not much control over the presentation of $\scri$ so
that most of the available formulations of the Bondi energy-momentum simply do
not apply. The purpose of this article is to provide the necessary background
for a manifestly conformally invariant and gauge independent formulation of the
Bondi energy-momentum. To this end we introduce a conformally invariant version
of the GHP formalism to rephrase all the well-known formulae. This leads us to
natural definitions for the space of asymptotic translations with its
Lorentzian metric, for the Bondi news and the mass-aspect. A major role in
these developments is played by the "co-curvature", a naturally appearing
quantity closely related to the Gau{\ss} curvature on a cut of~$\scri$.


  Analyzing and reasoning about safety properties of software systems becomes
an especially challenging task for programs with complex flow and, in
particular, with loops or recursion. For such programs one needs additional
information, for example in the form of loop invariants, expressing properties
to hold at intermediate program points. In this paper we study program loops
with non-trivial arithmetic, implementing addition and multiplication among
numeric program variables. We present a new approach for automatically
generating all polynomial invariants of a class of such programs. Our approach
turns programs into linear ordinary recurrence equations and computes closed
form solutions of these equations. These closed forms express the most precise
inductive property, and hence invariant. We apply Gr\"obner basis computation
to obtain a basis of the polynomial invariant ideal, yielding thus a finite
representation of all polynomial invariants. Our work significantly extends the
class of so-called P-solvable loops by handling multiplication with the loop
counter variable. We implemented our method in the Mathematica package Aligator
and showcase the practical use of our approach.


  This paper introduces a novel unified framework for calculating the first
arrival position (FAP) density in diffusion-based molecular communication (MC)
systems with fully-absorbing receivers, applicable to any spatial dimension or
receiver shape. We validate the effectiveness of our proposed method by
presenting two concrete examples from the MC literature: the 2D line receiver
and 3D spherical receiver. Our approach successfully reproduces existing
results on FAP density and further enhances the original formula for the 2D
line receiver by accommodating arbitrary drift directions. The proposed
framework offers a comprehensive and versatile solution for determining FAP
density in diffusive MC channels with fully-absorbing receivers, paving the way
for more robust and efficient system designs.


  Online Bin Stretching is a semi-online variant of bin packing in which the
algorithm has to use the same number of bins as an optimal packing, but is
allowed to slightly overpack the bins. The goal is to minimize the amount of
overpacking, i.e., the maximum size packed into any bin.
  We give an algorithm for Online Bin Stretching with a stretching factor of
1.5 for any number of bins. We build on previous algorithms and use a two-phase
approach. However, our analysis is technically more complicated and uses
amortization over the bins with the help of two weight functions.


  While the $\mathbb{Z}_3$ symmetric dark matter models have shown tremendous
prospects in addressing a number of (astro-)particle physics problems, they can
leave interesting imprints on cosmological observations as well. We consider
two such promising models: semi-annihilating dark matter (SADM) and Co-SIMP
$2\rightarrow 3$ interaction, and investigate their effects on the global 21-cm
signal. SADM alone cannot address the EDGES dip but can perform better with the
aid of an excess radio background, whereas Co-SIMP can naturally explain the
EDGES absorption feature by virtue of an intrinsic cooling effect without
invoking any such excess radiation. Hence, the latter model turns out to be a
rare model within the domain of CDM, that uses leptophilic interaction to
achieve the EDGES dip. Further, keeping in mind the ongoing debate between
EDGES and SARAS 3 on the global 21-cm signal, we demonstrate that our chosen
models can still remain viable in this context, even if the EDGES data requires
reassessment in future. We then extend our investigation to possible
reflections on the Dark Ages, followed by a consistency check with the CMB and
BAO observations via Planck 2018(+BAO) datasets. This work thus presents a
compelling case of exploring these interesting particle physics models in the
light of different cosmological observations.


  We show that a measurable function $g:\mathbb{S}^{d-1}\to\mathbb{R}$, with
$d\geq 3$, satisfies the functional relation \begin{equation*}
g(\omega)+g(\omega_*)=g(\omega')+g(\omega_*'), \end{equation*} for all
admissible $\omega,\omega_*,\omega',\omega_*'\in\mathbb{S}^{d-1}$ in the sense
that \begin{equation*} \omega+\omega_*=\omega'+\omega_*', \end{equation*} if
and only if it can be written as \begin{equation*} g(\omega)=A+B\cdot\omega,
\end{equation*} for some constants $A\in \mathbb{R}$ and $B\in\mathbb{R}^d$.
  Such functions form a family of quantized collision invariants which play a
fundamental role in the study of hydrodynamic regimes of the
Boltzmann--Fermi--Dirac equation near Fermionic condensates, i.e., at low
temperatures. In particular, they characterize the elastic collisional dynamics
of Fermions near a statistical equilibrium where quantum effects are
predominant.


  The cross section of the process $e^+e^-\to \pi^+D^0D^{*-}$ for
center-of-mass energies from 4.05 to 4.60~GeV is measured precisely using data
samples collected with the BESIII detector operating at the BEPCII storage
ring.
  Two enhancements are clearly visible in the cross section around 4.23 and
4.40~GeV.
  Using several models to describe the dressed cross section yields stable
parameters for the first enhancement, which has a mass of $4228.6 \pm 4.1 \pm
6.3 \un{MeV}/c^2$ and a width of $77.0 \pm 6.8 \pm 6.3 \un{MeV}$, where the
first uncertainties are statistical and the second ones are systematic.
  Our resonant mass is consistent with previous observations of the $Y(4220)$
state and the theoretical prediction of a $D\bar{D}_1(2420)$ molecule.
  This result is the first observation of $Y(4220)$ associated with an
open-charm final state.
  Fits with three resonance functions with additional $Y(4260)$, $Y(4320)$,
$Y(4360)$, $\psi(4415)$, or a new resonance, do not show significant
contributions from either of these resonances. The second enhancement is not
from a single known resonance. It could contain contributions from $\psi(4415)$
and other resonances, and a detailed amplitude analysis is required to better
understand this enhancement.


  A subclass of the Horndeski modified gravity theory we call No Slip Gravity
has particularly interesting properties: 1) a speed of gravitational wave
propagation equal to the speed of light, 2) equality between the effective
gravitational coupling strengths to matter and light, $G_{\rm matter}$ and
$G_{\rm light}$, hence no slip between the metric potentials, yet difference
from Newton's constant, and 3) suppressed growth to give better agreement with
galaxy clustering observations. We explore the characteristics and implications
of this theory, and project observational constraints. We also give a simple
expression for the ratio of the gravitational wave standard siren distance to
the photon standard candle distance, in this theory and others, and enable a
direct comparison of modified gravity in structure growth and in gravitational
waves, an important crosscheck.


  Deligne's regularity criterion for an integrable connection $\nabla$ on a
smooth complex algebraic variety $X$ says that $\nabla$ is regular along the
irreducible divisors at infinity in some fixed normal compactification of $X$
if and only if the restriction of $\nabla$ to every smooth curve on $X$ is
regular ({\it i. e.} has only regular singularities at infinity). The ``only
if" part is the difficult implication. Deligne's proof is transcendental, and
uses Hironaka's resolution of singularities. We give here an elementary and
purely algebraic proof of this implication: it is, as far as we know, the first
algebraic proof of Deligne's regularity criterion.


  The results of first principles electronic structure calculations for the
metallic rutile and the insulating monoclinic M1 phase of vanadium dioxide are
presented. In addition, the insulating M2 phase is investigated for the first
time. The density functional calculations allow for a consistent understanding
of all three phases. In the rutile phase metallic conductivity is carried by
metal t_2g orbitals, which fall into the one-dimensional d_parallel band, and
the isotropically dispersing e_g^pi bands. Hybridization of both types of bands
is weak. In the M1 phase splitting of the d_parallel band due to metal-metal
dimerization and upshift of the e_g^pi bands due to increased p-d overlap lead
to an effective separation of both types of bands. Despite incomplete opening
of the optical band gap due to the shortcomings of the local density
approximation, the metal-insulator transition can be understood as a
Peierls-like instability of the d_parallel band in an embedding background of
e_g^pi electrons. In the M2 phase, the metal-insulator transition arises as a
combined embedded Peierls-like and antiferromagnetic instability. The results
for VO2 fit into the general scenario of an instability of the rutile-type
transition-metal dioxides at the beginning of the d-series towards dimerization
or antiferromagnetic ordering within the characteristic metal chains. This
scenario was successfully applied before to MoO2 and NbO2. In the d^1
compounds, the d_parallel and e_g^pi bands can be completely separated, which
leads to the observed metal-insulator transitions.


  We show that the norm of the Riemann curvature tensor of any smooth solution
to the Ricci flow can be explicitly estimated in terms of its initial values on
a given ball, a local uniform bound on the Ricci tensor, and the elapsed time.
This provides a new, direct proof of a result of Sesum, which asserts that the
curvature of a solution on a compact manifold cannot blow up while the Ricci
curvature remains bounded, and extends its conclusions to the noncompact
setting. We also prove that the Ricci curvature must blow up at least linearly
along a subsequence at a finite time singularity.


  The search for undiscovered excited states of the nucleon continues to be a
focus of experiments at Jefferson Lab.Recent LQCD calculations have confirmed
long-standing quark-model predictions of many more states than have so far been
identified.A large effort for the N-star program has been launched using the
CLAS detector to provide the database that will allow nearly model-independent
partial wave analyses to be carried out in the search for such states.
Polarization observables play a crucial role in this effort, as they are
essential in disentangling overlapping resonant and non-resonant amplitudes. In
2010, double-polarization data were taken at JLab using circularly polarized
photons incident on a transversely polarized frozen-spin butanol target. Our
current analysis yields preliminary data of the T and F asymmetries for kaon
photoproduction final states, which are compared to predictions of recent
multipole analyses. This work is the first of its kind and will significantly
broaden the world database for these reactions.


  We explore the use of applied electrical potentials to induce band flattening
in graphene for bands near zero energy. We consider various families of doubly
periodic potentials and simulate their effect on the electronic band structure
using a tight-binding and a continuum approach. From these families, we find
that an applied potential with symmetries of wallpaper group 17, in particular
a Kagome potential, works best for inducing a high degree of band flattening
for a range of realistic potential amplitudes and periods. Our work indicates
that it should be possible to engineer the band structure of graphene using
electrostatic gating, thus enabling a new approach to the development of
graphene-based metamaterials.


  We consider budget feasible mechanisms for procurement auctions with additive
valuation functions. For the divisible case, where agents can be allocated
fractionally, there exists an optimal mechanism with approximation guarantee
$e/(e-1)$ under the small bidder assumption. We study the divisible case
without the small bidder assumption, but assume that the true costs of the
agents are bounded by the budget. This setting lends itself to modeling
economic situations in which the goods represent time and the agents' true
costs are not necessarily small compared to the budget. Non-trivially, we give
a mechanism with an approximation guarantee of 2.62, improving the result of 3
for the indivisible case. Additionally, we give a lower bound on the
approximation guarantee of 1.25. We then study the problem in more competitive
markets and assume that the agents' value over cost efficiencies are bounded by
some $\theta \ge 1$. For $\theta \le 2$, we give a mechanism with an
approximation guarantee of 2 and a lower bound of 1.18. Both results can be
extended to settings with different agent types with a linear capped valuation
function for each type. Finally, if each agent type has a concave valuation, we
give a mechanism for which the approximation guarantee grows linearly with the
number of agent types.


  Soil erosion by water is a widespread phenomenon throughout Europe and has
the potentiality, with his on-site and off-site effects, to affect water
quality, food security and floods. Despite the implementation of numerous and
different models for estimating soil erosion by water in Europe, there is still
a lack of harmonization of assessment methodologies.
  Often, different approaches result in soil erosion rates significantly
different. Even when the same model is applied to the same region the results
may differ. This can be due to the way the model is implemented (i.e. with the
selection of different algorithms when available) and/or to the use of datasets
having different resolution or accuracy. Scientific computation is emerging as
one of the central topic of the scientific method, for overcoming these
problems there is thus the necessity to develop reproducible computational
method where codes and data are available.
  The present study illustrates this approach. Using only public available
datasets, we applied the Revised Universal Soil loss Equation (RUSLE) to locate
the most sensitive areas to soil erosion by water in Europe.
  A significant effort was made for selecting the better simplified equations
to be used when a strict application of the RUSLE model is not possible. In
particular for the computation of the Rainfall Erosivity factor (R) the
reproducible research paradigm was applied. The calculation of the R factor was
implemented using public datasets and the GNU R language. An easily
reproducible validation procedure based on measured precipitation time series
was applied using MATLAB language. Designing the computational modelling
architecture with the aim to ease as much as possible the future reuse of the
model in analysing climate change scenarios is also a challenging goal of the
research.


  Optical fibers containing multiple cores are being developed towards capacity
enhancement in space-division multiplexed optical communication networks. In
many cases, the fibers are designed for negligible direct coupling of optical
power among the cores. The cores remain, however, embedded in a single,
mechanically-unified cladding. Elastic (or acoustic) modes supported by the
fiber cladding geometry are in overlap with multiple cores. Acoustic waves may
be stimulated by light in any core through electrostriction. Once excited, the
acoustic waves may induce photo-elastic perturbations to optical waves in other
cores as well. Such opto-mechanical coupling gives rise to inter-core
cross-phase modulation effects, even when direct optical crosstalk is very
weak. The cross-phase modulation spectrum reaches hundreds of megahertz
frequencies. It may consist of discrete and narrow peaks, or may become
quasi-continuous, depending on the geometric layout. The magnitude of the
effect at the resonance frequencies is comparable with that of intra-core
cross-phase modulation due to Kerr nonlinearity. Two potential applications are
demonstrated: single-frequency opto-electronic oscillators that do not require
radio-frequency electrical filters, and point-sensing of liquids outside the
cladding of multi-core fibers, where light cannot reach.


  In this paper, we prove Conjecture 4.8 of "Cluster algebras IV" by S. Fomin
and A. Zelevinsky, stating that the mutation classes of rectangular matrices
associated with cluster algebras of finite type are precisely those classes
which are finite.


  An off-shell generalization of the Abbott-Deser-Tekin (ADT) conserved charge
was recently proposed by Kim et al. They achieved this by introducing off-shell
Noether currents and potentials. In this paper, we construct the crucial
off-shell Noether current by the variation of the Bianchi identity for the
expression of motion equation, with the help of the property of Killing vector.
Our Noether current, which contains an additional term that is just one half of
the Lie derivative of a surface term with respect to the Killing vector, takes
a different form in comparison with the one in their work. Then we employ the
generalized formulation to calculate the quasi-local conserved charges for the
most general charged spherically symmetric and the dyonic rotating black holes
with AdS asymptotics in four-dimensional conformal Weyl gravity, as well as the
charged spherically symmetric black holes in arbitrary dimensional
Einstein-Gauss-Bonnet gravity coupled to Maxwell or nonlinear electrodynamics
in AdS spacetime. Our results confirm those through other methods in the
literature.


  We apply a new formalism to derive the higher-order quantum kinetic expansion
(QKE) for studying dissipative dynamics in a general quantum network coupled
with an arbitrary thermal bath. The dynamics of system population is described
by a time-convoluted kinetic equation, where the time-nonlocal rate kernel is
systematically expanded on the order of off-diagonal elements of the system
Hamiltonian. In the second order, the rate kernel recovers the expression of
the noninteracting-blip approximation (NIBA) method. The higher-order
corrections in the rate kernel account for the effects of the multi-site
quantum coherence and the bath relaxation. In a quantum harmonic bath, the rate
kernels of different orders are analytically derived. As demonstrated by four
examples, the higher-order QKE can reliably predict quantum dissipative
dynamics, comparing well with the hierarchic equation approach. More
importantly, the higher-order rate kernels can distinguish and quantify
distinct nontrivial quantum coherent effects, such as long-range energy
transfer from quantum tunneling and quantum interference arising from the phase
accumulation of interactions.


  We present a preferential attachment growth model to obtain the distribution
$P(K)$ of number of units $K$ in the classes which may represent business firms
or other socio-economic entities. We found that $P(K)$ is described in its
central part by a power law with an exponent $\phi=2+b/(1-b)$ which depends on
the probability of entry of new classes, $b$. In a particular problem of city
population this distribution is equivalent to the well known Zipf law. In the
absence of the new classes entry, the distribution $P(K)$ is exponential. Using
analytical form of $P(K)$ and assuming proportional growth for units, we derive
$P(g)$, the distribution of business firm growth rates. The model predicts that
$P(g)$ has a Laplacian cusp in the central part and asymptotic power-law tails
with an exponent $\zeta=3$. We test the analytical expressions derived using
heuristic arguments by simulations. The model might also explain the
size-variance relationship of the firm growth rates.


  Let G and F be finitely generated groups with infinitely many ends and let A
and B be graph of groups decompositions of F and G such that all edge groups
are finite and all vertex groups have at most one end. We show that G and F are
quasi-isometric if and only if every one-ended vertex group of A is
quasi-isometric to some one-ended vertex group of B and every one-ended vertex
group of B is quasi-isometric to some one-ended vertex group of A. From our
proof it also follows that if G is any finitely generated group, of order at
least three, the groups: G*G, G*Z,G*G*G and G* Z/2Z are all quasi-isometric.


  In the present paper we discuss antenna miniaturization using
magneto-dielectric substrates. Recent results found in the literature reveal
that advantages over conventional dielectric substrates can only be achieved if
natural magnetic inclusions are embedded into the substrate. This observation
is revised and the physical background is clarified. We present a detailed
discussion concerning magnetic materials available in the microwave regime and
containing natural magnetic constituents. The effects of magnetic dispersion
and loss are studied: constraints on the microwave permeability are used to
estimate the effect of magnetic substrates on the achievable impedance
bandwidth. Microwave composites filled with thin ferromagnetic films are
considered as a prospective antenna substrate. We calculate the impedance
bandwidth for a $\lambda/2$-patch antenna loaded with the proposed substrate,
and challenge the results against those obtained with conventional dielectric
substrates. It is shown that the radiation quality factor is strongly minimized
with the proposed substrate even in the presence of realistic losses. Estimates
for the radiation efficiency are given as a function of the magnetic loss
factor.


  We use (1+1$'$) resonance-enhanced multiphoton photodissociation (REMPD) to
detect the population in individual rovibronic states of trapped HfF$^+$ with a
single-shot absolute efficiency of 18%, which is over 200 times better than
that obtained with fluorescence detection. The first photon excites a specific
rotational level to an intermediate vibronic band at 35,000-36,500 cm$^{-1}$,
and the second photon, at 37,594 cm$^{-1}$ (266 nm), dissociates HfF$^+$ into
Hf$^+$ and F. Mass-resolved time-of-flight ion detection then yields the number
of state-selectively dissociated ions. Using this method, we observe
rotational-state heating of trapped HfF$^+$ ions from collisions with neutral
Ar atoms. Furthermore, we measure the lifetime of the $^3\Delta_1$ $v=0,\, J=1$
state to be 2.1(2) s. This state will be used for a search for a permanent
electric dipole moment of the electron.


  The nonlinear absorption of radio waves (200 - 800 MHz) in a noncollinear
cubic antiferromagnet Mn3Al2Ge3O12 in an external magnetic field H || [001] has
been studied in the temperature range of 1.2 - 4.2 K. We attribute the observed
dissipation of the electromagnetic energy to the parametric excitation of
inhomogeneous surface waves at the boundaries of antiferromagnetic domains.


  In this paper, we study the stochastic convergence of regularized solutions
for backward heat conduction problems. These problems are recognized as
ill-posed due to the exponential decay of eigenvalues associated with the
forward problems. We derive an error estimate for the least-squares regularized
minimization problem within the framework of stochastic convergence. Our
analysis reveals that the optimal error of the Tikhonov-type least-squares
optimization problem depends on the noise level, the number of sensors, and the
underlying ground truth. Moreover, we propose a self-adaptive algorithm to
identify the optimal regularization parameter for the optimization problem
without requiring knowledge of the noise level or any other prior information,
which will be very practical in applications. We present numerical examples to
demonstrate the accuracy and efficiency of our proposed method. These numerical
results show that our method is efficient in solving backward heat conduction
problems.


  Peer-to-peer ridesharing (P2P-RS) enables people to arrange one-time rides
with their own private cars, without the involvement of professional drivers.
It is a prominent collective intelligence application producing significant
benefits both for individuals (reduced costs) and for the entire community
(reduced pollution and traffic), as we showed in a recent publication where we
proposed an online approximate solution algorithm for large-scale P2P-RS. In
this paper we tackle the fundamental question of assessing the benefit of
predicting ridesharing requests in the context of P2P-RS optimisation. Results
on a public real-world show that, by employing a perfect predictor, the total
reward can be improved by 5.27% with a forecast horizon of 1 minute. On the
other hand, a vanilla long short-term memory neural network cannot improve upon
a baseline predictor that simply replicates the previous day's requests, whilst
achieving an almost-double accuracy.


  We present results of a series of magnetohydrodynamic (MHD) and hydro-
dynamic (HD) 2.5D simulations of the morphology of outflows driven by nested
wide-angle winds - i.e. winds which eminate from a central star as well as from
an orbiting accretion disk. While our results are broadly relevent to nested
wind systems we have tuned the parameters of the simulations to touch on issues
in both Young Stellar Objects and Planetary Nebula studies. In particular our
studies connect to open issues in the early evolution of Planetary Nebulae. We
find that nested MHD winds exhibit marked morphological differences from the
single MHD wind case along both dimensions of the flow. Nested HD winds on the
other hand give rise mainly to geometric distortions of an outflow that is
topologically similar to the flow arising from a single stellar HD wind. Our
MHD results are insensitive to changes in ambient temperature between ionized
and un-ionized circumstellar environments. The results are sensitive to the
relative mass-loss rates, and to the relative speeds of the stellar and disk
winds. We also present synthetic emission maps of both nested MHD and HD
simulations. We find that nested MHD winds show knots of emission appearing
on-axis that do not appear in the HD case.


  Dilute superconductivity survives in bulk strontium titanate when the Fermi
temperature falls well below the Debye temperature. Here, we show that the
onset of the superconducting dome is dopant-dependent. When mobile electrons
are introduced by removing oxygen atoms, the superconducting transition
survives down to $2 \times 10^{17}$ cm$^{-3}$, but when they are brought by
substituting Nb with Ti, the threshold density for superconductivity is an
order of magnitude higher. Our study of quantum oscillations reveals a
significant difference in the band dispersion between the dilute metals made by
these doping routes and our band calculations demonstrate that the rigid band
approximation does not hold when mobile electrons are introduced by oxygen
vacancies. We identify the band sculpted by theses vacancies as the exclusive
locus of superconducting instability in the ultra-dilute limit.


  Quantum computers will need effective error-correcting codes. Current quantum
processors require precise control of each particle, so having fewer particles
to control might be beneficial. Although traditionally quantum computers are
considered as using qubits (2-level systems), qudits (systems with more than
2-levels) are appealing since they can have an equivalent computational space
using fewer particles, meaning fewer particles need to be controlled. In this
work we prove how to construct codes with parameters $[[2^N,2^N-1-2N,\geq
3]]_q$ for any choice of prime $q$ and natural number $N$. This is accomplished
using the technique of local-dimension-invariant (LDI) codes. Generally LDI
codes have the drawback of needing large local-dimensions to ensure the
distance is at least preserved, and so this work also reduces this requirement
by utilizing the structure of CSS codes, allowing for the aforementioned code
family to be imported for any local-dimension choice.


  This article proposes a new numerical algorithm for second order elliptic
equations in non-divergence form. The new method is based on a discrete weak
Hessian operator locally constructed by following the weak Galerkin strategy.
The numerical solution is characterized as a minimization of a non-negative
quadratic functional with constraints that mimic the second order elliptic
equation by using the discrete weak Hessian. The resulting Euler-Lagrange
equation offers a symmetric finite element scheme involving both the primal and
a dual variable known as the Lagrange multiplier, and thus the name of
primal-dual weak Galerkin finite element method. Optimal order error estimates
are derived for the finite element approximations in a discrete $H^2$-norm, as
well as the usual $H^1$- and $L^2$-norms. Some numerical results are presented
for smooth and non-smooth coefficients on convex and non-convex domains.


  The classification of the optical spectra of active galactic nuclei (AGN)
into different types is well founded on AGN physics, but it involves some
degree of human oversight and cannot be reliably scaled to large data sets.
Machine learning (ML) tackles such a classification problem in a fast and
reproducible way, but is often perceived as a black box. However, ML
interpretability and explainability are active research areas in computer
science, increasingly providing us with tools to alleviate this issue. We
applied ML interpretability tools to a classifier trained to predict AGN type
from spectra, to demonstrate the use of such tools in this context. We trained
a support-vector machine on 3346 high-quality, low redshift AGN spectra from
SDSS DR15 with an existing reliable classification as type 1, type 2, or
intermediate type. On a selection of test-set spectra, we computed the gradient
of the predicted class probability and we built saliency maps. We also
visualized the high-dimensional space of AGN spectra using t-distributed
stochastic neighbor embedding (t-SNE), showing where the spectra for which we
computed a saliency map are located. Regions that affect the predicted AGN type
often coincide with physically relevant features, such as spectral lines. t-SNE
visualization shows good separability of type 1 and type 2 spectra, while
intermediate-type spectra either lie in-between as expected or appear mixed
with type 2 spectra. Saliency maps show why a given AGN type was predicted by
our classifier, resulting in a physical interpretation in terms of regions of
the spectrum that affected its decision, making it no longer a black box. These
regions coincide with those used by human experts such as relevant spectral
lines, and are even used in a similar way, with the classifier e.g. effectively
measuring the width of a line by weighing its center and its tails oppositely.


  In our previous work with Grifo and H\`a, we showed the stable
Harbourne-Huneke containment and Chudnovsky's conjecture for the defining ideal
of sufficiently many general points in $\mathbb{P}^N$. In this paper, we
establish the conjectures for all remaining cases, and hence, give the
affirmative answer to Harbourne-Huneke containment and Chudnovsky's conjecture
for any number of general points in $\mathbb{P}^N$ for all $N$. Our new
technique is to develop the Cremona reduction process that provides effective
lower bounds for the Waldschmidt constant of the defining ideals of generic
points in projective spaces.


  The charmonium and bottomonium mass spectra are investigated in potential
nonrelativistic QCD (pNRQCD) with the heavy quark potential computed by lattice
QCD simulations. The potential consists of a static potential and relativistic
corrections classified in powers of the inverse of heavy quark mass m, and the
effects of the O(1/m) and O(1/m^{2}) spin-orbit corrections on the mass spectra
are examined systematically. The pattern of the mass spectra is found to be in
fairly good agreement with experimental data, in which the O(1/m) correction
gives an important contribution.


  Let $X$ be a compact complex, not necessarily K\"ahler, manifold of dimension
$n$. We characterise the volume of any holomorphic line bundle $L\to X$ as the
supremum of the Monge-Amp\`ere masses $\int_X T_{ac}^n$ over all closed
positive currents $T$ in the first Chern class of $L$, where $T_{ac}$ is the
absolutely continuous part in the Lebesgue decomposition. This result, new in
the non-K\"ahler context, can be seen as holomorphic Morse inequalities for the
cohomology of high tensor powers of line bundles endowed with arbitrarily
singular Hermitian metrics. It gives, in particular, a new bigness criterion
for line bundles in terms of existence of singular Hermitian metrics satisfying
positivity conditions. The proof is based on the construction of a new
regularisation for closed $(1, 1)$-currents with a control of the
Monge-Amp\`ere masses of the approximating sequence. To this end, we prove a
potential-theoretic result in one complex variable and study the growth of
multiplier ideal sheaves associated with increasingly singular metrics.


  In this report we review the method of explicit calculations of interatomic
exchange interactions of magnetic materials. This involves exchange mechanisms
normally referred to as Heisenberg exchange, Dzyaloshinskii-Moriya interaction
and anisotropic symmetric exchange. The connection between microscopic theories
of the electronic structure, such as density functional theory or dynamical
mean field theory, and interatomic exchange, is given in detail. The different
aspects of extracting information for an effective spin Hamiltonian that
involves thousands of atoms, from electronic structure calculations considering
significantly fewer atoms (1-50) is highlighted. Examples of exchange
interactions of a large group of materials is presented, which involves heavy
elements of the 3d period, alloys between transition metals, Heusler compounds,
multilayer systems as well as overlayers and adatoms on a substrate, transition
metal oxides, 4f elements, magnetic materials in two dimensions and molecular
magnets. Where possible, a comparison to experimental data is made, that
naturally becomes focused on the magnon dispersion. The influence of relativity
is reviewed for a few cases, as is the importance of dynamical correlations.
Development to theories that handle out of equilibrium conditions is also
described here. The review ends with a short description of extensions of the
theories behind explicit calculations of interatomic exchange, to non-magnetic
situations, e.g. that describe chemical (charge) order and superconductivity.


  We show that quantum effects dramatically enhance the production of fermions
following preheating after inflation in the early Universe in the presence of
high excitations of bosonic quanta. As a consequence fermions rapidly approach
a quasistationary distribution with a thermal occupancy in the infrared, while
the inflaton enters a turbulent scaling regime. The failure of standard
semiclassical descriptions based on the Dirac equation with a homogeneous
background field is caused by nonperturbatively high boson occupation numbers.
During preheating the inflaton occupation number increases, thus leading to a
dynamical mechanism for the enhanced production of fermions from the
rescattering of the inflaton quanta. We comment on related phenomena in
heavy-ion collisions for the production of quark matter fields from highly
occupied gauge bosons.


  Electron density $\rho(\vec{r})$ is the fundamental variable in the
calculation of ground state energy with density functional theory (DFT). Beyond
total energy, features and changes in $\rho(\vec{r})$ distributions are often
used to capture critical physicochemical phenomena in functional materials. We
present a machine learning framework for the prediction of $\rho(\vec{r})$. The
model is based on equivariant graph neural networks and the electron density is
predicted at special query point vertices that are part of the message passing
graph, but only receive messages. The model is tested across multiple data sets
of molecules (QM9), liquid ethylene carbonate electrolyte (EC) and
LixNiyMnzCo(1-y-z)O2 lithium ion battery cathodes (NMC). For QM9 molecules, the
accuracy of the proposed model exceeds typical variability in $\rho(\vec{r})$
obtained from DFT done with different exchange-correlation functionals. The
accuracy on all three datasets is beyond state of the art and the computation
time is orders of magnitude faster than DFT.


  The purpose of this paper is two-fold. First, we characterize the existence
of binary self-orthogonal codes meeting the Griesmer bound by employing
Solomon-Stiffler codes and some related residual codes. Second, using such a
characterization, we determine the exact value of $d_{so}(n,7)$ except for five
special cases and the exact value of $d_{so}(n,8)$ except for 41 special cases,
where $d_{so}(n,k)$ denotes the largest minimum distance among all binary
self-orthogonal $[n, k]$ codes. Currently, the exact value of $d_{so}(n,k)$ $(k
\le 6)$ was determined by Shi et al. (2022). In addition, we develop a general
method to prove the nonexistence of some binary self-orthogonal codes by
considering the residual code of a binary self-orthogonal code.


  Graph processing is used extensively in areas from social networking mining
to web indexing. We demonstrate that the performance and dependability of such
applications critically hinges on the graph data structure used, because a
fixed, compile-time choice of data structure can lead to poor performance or
applications unable to complete. To address this problem, we introduce an
approach that helps programmers transform regular, off-the-shelf graph
applications into adaptive, more dependable applications where adaptations are
performed via runtime selection from alternate data structure representations.
Using our approach, applications dynamically adapt to the input graph's
characteristics and changes in available memory so they continue to run when
faced with adverse conditions such as low memory. Experiments with graph
algorithms on real-world (e.g., Wikipedia metadata, Gnutella topology) and
synthetic graph datasets show that our adaptive applications run to completion
with lower execution time and/or memory utilization in comparison to their
non-adaptive versions.


  Using a network of seismometers and sets of optimal filters, we implemented a
feed-forward control technique to minimize the seismic contribution to multiple
interferometric degrees of freedom of the LIGO interferometers. The filters are
constructed by using the Levinson-Durbin recursion relation to approximate the
optimal Wiener filter. By reducing the RMS of the interferometer feedback
signals below \sim10 Hz, we have improved the stability and duty cycle of the
joint network of gravitational wave detectors. By suppressing the large control
forces and mirror motions, we have dramatically reduced the rate of
non-Gaussian transients in the gravitational wave signal stream.


  We study the interplay between quantum Hall ordering and spontaneous
sublattice symmetry breaking in multiple Chern number bands at fractional
fillings. Primarily we study fermions with repulsive interactions near half
filling in a family of square lattice models with flat C=2 bands and a wide
band gap. By perturbing about the particularly transparent limit of two
decoupled C=1 bands and by exact diagonalization studies of small systems in
the more general case, we show that the system generically breaks sublattice
symmetry with a transition temperature $T_c>0$ and additionally exhibits a
quantized Hall conductance of $e^2/h$ as $T \rightarrow 0$. We note the close
analogy to quantum Hall ferromagnetism in the multi-component problem and the
connection to topological Mott insulators. We also discuss generalizations to
other fillings and higher Chern numbers.


  We show joint convergence of the Lukasiewicz path and height process for
slightly supercritical Galton-Watson forests. This shows that the height
processes for supercritical continuous state branching processes as constructed
by Lambert (2002) are the limit under rescaling of their discrete counterparts.
Unlike for (sub-)critical Galton-Watson forests, the height process does not
encode the entire metric structure of a supercritical Galton-Watson forest. We
demonstrate that this result is nonetheless useful, by applying it to the
configuration model with an i.i.d. power-law degree sequence in the critical
window, of which we obtain the metric space scaling limit in the product
Gromov-Hausdorff-Prokhorov topology, which is of independent interest.


  A persistent challenge to table question answering (TableQA) by generating
executable programs has been adapting to varied table structures, typically
requiring domain-specific logical forms. In response, this paper introduces a
unified TableQA framework that: (1) provides a unified representation for
structured tables as multi-index Pandas data frames, (2) uses Python as a
powerful querying language, and (3) uses few-shot prompting to translate NL
questions into Python programs, which are executable on Pandas data frames.
Furthermore, to answer complex relational questions with extended program
functionality and external knowledge, our framework allows customized APIs that
Python programs can call. We experiment with four TableQA datasets that involve
tables of different structures -- relational, multi-table, and hierarchical
matrix shapes -- and achieve prominent improvements over past state-of-the-art
systems. In ablation studies, we (1) show benefits from our multi-index
representation and APIs over baselines that use only an LLM, and (2)
demonstrate that our approach is modular and can incorporate additional APIs.


  We introduce a class of regular unit Hadamard matrices whose entries consist
of two complex numbers and their conjugates for a total of four complex
numbers. We then show that these matrices are contained in the Bose-Mesner
algebra of an association scheme arising from skew Paley matrices.


  This study introduces an uncertainty-aware, mesh-free numerical method for
solving Kolmogorov PDEs. In the proposed method, we use Gaussian process
regression (GPR) to smoothly interpolate pointwise solutions that are obtained
by Monte Carlo methods based on the Feynman-Kac formula. The proposed method
has two main advantages: 1. uncertainty assessment, which is facilitated by the
probabilistic nature of GPR, and 2. mesh-free computation, which allows
efficient handling of high-dimensional PDEs. The quality of the solution is
improved by adjusting the kernel function and incorporating noise information
from the Monte Carlo samples into the GPR noise model. The performance of the
method is rigorously analyzed based on a theoretical lower bound on the
posterior variance, which serves as a measure of the error between the
numerical and true solutions. Extensive tests on three representative PDEs
demonstrate the high accuracy and robustness of the method compared to existing
methods.


  Normal incidence ion irradiation at elevated temperatures, when amorphization
is prevented, induces novel nanoscale patterns of crystalline structures on
elemental semiconductors by a reverse epitaxial growth mechanism: on Ge
surfaces irradiation at temperatures above the recrystallization temperature of
250{\deg}C leads to self-organized patterns of inverse pyramids. Checkerboard
patterns with fourfold symmetry evolve on the Ge (100) surface, whereas on the
Ge (111) surface, isotropic patterns with a sixfold symmetry emerge. After high
fluence irradiations these patterns exhibit well developed facets. A
deterministic nonlinear continuum equation accounting for the effective surface
currents due to an Ehrlich-Schwoebel barrier for diffusing vacancies reproduces
remarkably well our experimental observations.


  In this study, we give an alternative and elementary proof to Tsuji's
criterion for a Cartier divisor to be numerically trivial.


  Compared to general document analysis tasks, form document structure
understanding and retrieval are challenging. Form documents are typically made
by two types of authors; A form designer, who develops the form structure and
keys, and a form user, who fills out form values based on the provided keys.
Hence, the form values may not be aligned with the form designer's intention
(structure and keys) if a form user gets confused. In this paper, we introduce
Form-NLU, the first novel dataset for form structure understanding and its key
and value information extraction, interpreting the form designer's intent and
the alignment of user-written value on it. It consists of 857 form images, 6k
form keys and values, and 4k table keys and values. Our dataset also includes
three form types: digital, printed, and handwritten, which cover diverse form
appearances and layouts. We propose a robust positional and logical
relation-based form key-value information extraction framework. Using this
dataset, Form-NLU, we first examine strong object detection models for the form
layout understanding, then evaluate the key information extraction task on the
dataset, providing fine-grained results for different types of forms and keys.
Furthermore, we examine it with the off-the-shelf pdf layout extraction tool
and prove its feasibility in real-world cases.


  We give a new proof of the "weakly admissible implies admissible" theorem of
Colmez and Fontaine describing the semi-stable p-adic representations. We study
Banach-Colmez spaces, i.e. p-adic Banach spaces with the extra data of a
C_p-algebra of analytic functions. The "weakly admissible" theorem is then a
result of the existence of dimension and height functions on these objects.
Furthermore, we show that the subcategory of Banach-Colmez spaces corresponding
to crystalline representations is naturally filtered by the positive rationals.


  Let $D_j\subset\Bbb C^{n_j}$ be a pseudoconvex domain and let $A_j\subset
D_j$ be a locally pluriregular set, $j=1,...,N$. Put $$ X:=\bigcup_{j=1}^N
A_1\times...\times A_{j-1}\times D_j\times A_{j+1}\times ...\times
A_N\subset\Bbb C^{n_1}\times...\times\Bbb C^{n_N}=\Bbb C^n. $$ Let
$U\subset\Bbb C^n$ be an open neighborhood of $X$ and let $M\subset U$ be a
relatively closed subset of $U$. For $j\in\{1,...,N\}$ let $\Sigma_j$ be the
set of all $(z',z'')\in(A_1\times...\times A_{j-1})
\times(A_{j+1}\times...\times A_N)$ for which the fiber
$M_{(z',\cdot,z'')}:=\{z_j\in\Bbb C^{n_j}\: (z',z_j,z'')\in M\}$ is not
pluripolar. Assume that $\Sigma_1,...,\Sigma_N$ are pluripolar. Put $$
X':=\bigcup_{j=1}^N\{(z',z_j,z'')\in(A_1\times...\times A_{j-1})\times D_j
\times(A_{j+1}\times...\times A_N)\: (z',z'')\notin\Sigma_j\}. $$ Then there
exists a relatively closed pluripolar subset $\hat M\subset\hat X$ of the
`envelope of holomorphy' $\hat X\subset\Bbb C^n$ of $X$ such that: $\hat M\cap
X'\subset M$, for every function $f$ separately holomorphic on $X\setminus M$
there exists exactly one function $\hat f$ holomorphic on $\hat X\setminus\hat
M$ with $\hat f=f$ on $X'\setminus M$, and $\hat M$ is singular with respect to
the family of all functions $\hat f$. Some special cases were previously
studied in \cite{Jar-Pfl 2001c}.


  We develop a general theory of electric polarization induced by inhomogeneity
in crystals. We show that contributions to polarization can be classified in
powers of the gradient of the order parameter. The zeroth order contribution
reduces to the well-known result obtained by King-Smith and Vanderbilt for
uniform systems. The first order contribution, when expressed in a two-point
formula, takes the Chern-Simons 3-form of the vector potentials derived from
the Bloch wave functions. Using the relation between polarization and charge
density, we demonstrate our formula by studying charge fractionalization in a
two-dimensional dimer model recently proposed.


  We consider first-passage percolation on a ladder, i.e. the graph
{0,1,...}*{0,1} where nodes at distance 1 are joined by an edge, and the times
are exponentially i.i.d. with mean 1. We find an appropriate Markov chain to
calculate an explicit expression for the time constant whose numerical value is
approximately 0.6827. This time constant is the long-term average inverse speed
of the process. We also calculate the average residual time.


  Using a combined quantum mechanical/classical method, we study the collisions
of small Na clusters on large Ar clusters as a model for cluster deposit. We
work out basic mechanisms by systematic variation of collision energy, system
sizes, and orientations. The soft Ar material is found to serve as an extremely
efficient shock absorber. The collisional energy is quickly transfered at first
impact and the Na clusters are always captured by the Ar surface. The
distribution of the collision energy into the Ar system proceeds very fast with
velocity of sound. The relaxation of shapes goes at a slower pace using times
of several ps. It produces a substantial rearrangement of the Ar system while
the Na cluster remains rather robust.


  In this study, a perceptually hidden object-recognition method is
investigated to generate secure images recognizable by humans but not machines.
Hence, both the perceptual information hiding and the corresponding object
recognition methods should be developed. Block-wise image scrambling is
introduced to hide perceptual information from a third party. In addition, an
adaptation network is proposed to recognize those scrambled images.
Experimental comparisons conducted using CIFAR datasets demonstrated that the
proposed adaptation network performed well in incorporating simple perceptual
information hiding into DNN-based image classification.


  We present the next-to-next-to-leading order (NNLO) QCD corrections to dijet
production in the purely gluonic channel retaining the full dependence on the
number of colours. The sub-leading colour contribution in this channel first
appears at NNLO and, as expected, increases the NNLO correction by around 10%
and exhibits a pT dependence, rising from 8% at low pT to 15% at high pT . The
present calculation demonstrates the utility of the antenna subtraction method
for computing the full colour NNLO corrections to dijet production at the Large
Hadron Collider.


  Is shown that any separable superreflexive Banach space X may be
isometrically embedded in a separable superreflexive Banach space Z=Z(X)
(which, in addition, is of the same type and cotype as X) such that its
conjugate admits a continuous surjection on each its subspace. This gives an
affirmative answer on S. Banach problem: Whether there exists a Banach space X,
non isomorphic to a Hilbert space, which admits a continuous linear surjection
on each its subspace and is essentially different from l_1?


  Ab initio density functional theory calculations are carried out to predict
the electronic properties and relative stability of gallium sulfide nanoribbons
(Ga2S2-NRs) with either zigzag- or armchair-terminated edges. It is found that
the electronic properties of the nanoribbons are very sensitive to the edge
structure. The zigzag nanoribbons (Ga2S2-ZNRs) are metallic with spin-polarized
edge states regardless of the H-passivation,whereas the bare armchair ones
(Ga2S2-ANRs) are semiconducting with an indirect band gap. This band gap
exhibits an oscillation behavior as the width increases and finally converges
to a constant value. Similar behavior is also found in H-saturated Ga2S2-ANRs,
although the band gap converges to a larger value. The relative stabilities of
the bare ANRs and ZNRs are investigated by calculating their binding energies.
It is found that for a similar width the ANRs are more stable than the ZNRs,
and both are more stable than some Ga2S2 nanocluters with stable
configurations.


  We study the Hall effect in diluted plasmas within the two-fluids theory.
Composed by two distinct species with opposite charge, such as electrons and
ions in fully ionised hydrogen, the plasma is driven by an electric field
through a channel in the presence of a transversal magnetic field. As a
consequence, a separation of charge is induced producing an electric potential
difference. We have found a general relation for the Hall voltage as function
of the mass and viscosity ratios, which converges to the usual expression in
the limit of solid matter, i.e. when ions are much more massive than electrons.
All the simulations have been performed using a three-dimensional
Lattice-Boltzmann model, which has been also validated for some relevant
applications. Finally, we discuss the importance of our findings in the light
of recent developments in plasma physics, in particular in magnetic
reconnection.


  We describe a unified approach to estimating the dimension of $f^{-1}(A)$ for
any $G$-equivariant map $f \colon X \to Y$ and any closed $G$-invariant subset
$A\subseteq Y$ in terms of connectivity of $X$ and dimension of $Y$, where $G$
is either a cyclic group of order $p^k$, a $p$-torus ($p$ a prime), or a torus.


  Industrial recommender systems usually hold data from multiple business
scenarios and are expected to provide recommendation services for these
scenarios simultaneously. In the retrieval step, the topK high-quality items
selected from a large number of corpus usually need to be various for multiple
scenarios. Take Alibaba display advertising system for example, not only
because the behavior patterns of Taobao users are diverse, but also
differentiated scenarios' bid prices assigned by advertisers vary
significantly. Traditional methods either train models for each scenario
separately, ignoring the cross-domain overlapping of user groups and items, or
simply mix all samples and maintain a shared model which makes it difficult to
capture significant diversities between scenarios. In this paper, we present
Adaptive Domain Interest network that adaptively handles the commonalities and
diversities across scenarios, making full use of multi-scenarios data during
training. Then the proposed method is able to improve the performance of each
business domain by giving various topK candidates for different scenarios
during online inference. Specifically, our proposed ADI models the
commonalities and diversities for different domains by shared networks and
domain-specific networks, respectively. In addition, we apply the
domain-specific batch normalization and design the domain interest adaptation
layer for feature-level domain adaptation. A self training strategy is also
incorporated to capture label-level connections across domains.ADI has been
deployed in the display advertising system of Alibaba, and obtains 1.8%
improvement on advertising revenue.


  Sequential Recommendation aims to predict the next item based on user
behaviour. Recently, Self-Supervised Learning (SSL) has been proposed to
improve recommendation performance. However, most of existing SSL methods use a
uniform data augmentation scheme, which loses the sequence correlation of an
original sequence. To this end, in this paper, we propose a Learnable Model
Augmentation self-supervised learning for sequential Recommendation (LMA4Rec).
Specifically, LMA4Rec first takes model augmentation as a supplementary method
for data augmentation to generate views. Then, LMA4Rec uses learnable Bernoulli
dropout to implement model augmentation learnable operations. Next,
self-supervised learning is used between the contrastive views to extract
self-supervised signals from an original sequence. Finally, experiments on
three public datasets show that the LMA4Rec method effectively improves
sequential recommendation performance compared with baseline methods.


  We present measurements and calculations of the trap loss rate for laser
cooled Rb atoms confined in either a magneto-optic or a magnetic quadrupole
trap when exposed to a room temperature background gas of Ar. We study the loss
rate as a function of trap depth and find that copious glancing elastic
collisions, which occur in the so-called quantum-diffractive regime and impart
very little energy to the trapped atoms, result in significant differences in
the loss rate for the MOT compared to a pure magnetic trap due solely to the
difference in potential depth. This finding highlights the importance of
knowing the trap depth when attempting to infer the total collision cross
section from measurements of trap loss rates. Moreover, this variation of trap
loss rate with trap depth can be used to extract information about the
differential cross section.


  We use the time-dependent variational of Balian and Veneroni to derive a set
of equations governing the dynamics of a trapped Bose gas at finite
temperature. We show that this dynamics generalizes the Gross-Pitaevskii
equations in that it introduces a consistent coupling between the evolution of
the condensate density, the thermal cloud and the anomalous density.


  We improve upon a recent result of Culler and Dunfield on orderability of
certain Dehn fillings by removing a difficult condition they required.