  Learning-based controllers have demonstrated superior performance compared to
classical controllers in various tasks. However, providing safety guarantees is
not trivial. Safety, the satisfaction of state and input constraints, can be
guaranteed by augmenting the learned control policy with a safety filter. Model
predictive safety filters (MPSFs) are a common safety filtering approach based
on model predictive control (MPC). MPSFs seek to guarantee safety while
minimizing the difference between the proposed and applied inputs in the
immediate next time step. This limited foresight can lead to jerky motions and
undesired oscillations close to constraint boundaries, known as chattering. In
this paper, we reduce chattering by considering input corrections over a longer
horizon. Under the assumption of bounded model uncertainties, we prove
recursive feasibility using techniques from robust MPC. We verified the
proposed approach in both extensive simulation and quadrotor experiments. In
experiments with a Crazyflie 2.0 drone, we show that, in addition to preserving
the desired safety guarantees, the proposed MPSF reduces chattering by more
than a factor of 4 compared to previous MPSF formulations.


  Full waveform inversion (FWI) aims at reconstructing unknown physical
coefficients in wave equations using the wave field data generated from
multiple incoming sources. In this work, we propose an offline-online
computational strategy for coupling classical least-squares based computational
inversion with modern deep learning based approaches for FWI to achieve
advantages that can not be achieved with only one of the components. In a
nutshell, we develop an offline learning strategy to construct a robust
approximation to the inverse operator and utilize it to design a new objective
function for the online inversion with new datasets. We demonstrate through
numerical simulations that our coupling strategy improves the computational
efficiency of FWI with reliable offline training on moderate computational
resources (in terms of both the size of the training dataset and the
computational cost needed).


  We consider the Casimir interaction between (non-magnetic) dielectric bodies
or conductors. Our main result is a proof that the Casimir force between two
bodies related by reflection is always attractive, independent of the exact
form of the bodies or dielectric properties. Apart from being a fundamental
property of fields, the theorem and its corollaries also rule out a class of
suggestions to obtain repulsive forces, such as the two hemisphere repulsion
suggestion and its relatives.


  In an earlier paper [1] it was shown that the Frobenius compound characters
for the symmetric groups are related to the irreducible characters by a linear
relation that involves a unitriagular coupling matrix that gives the Frobenius
characters in terms of linear combinations of the irreducible characters. It is
desirable to invert this relationship since we have formulas for the Frobenius
characters and want the values for the irreducible characters. This inversion
is straightforward and yields both the irreducible characters but also the
coupling matrix that turns out to be the Kostka matrix in the original
direction. We show that if the Frobenius monomial identity is applied a
modification of it, equation (22), produces a monomial formula that produces
the Kostka matrix inverse without involving the characters of either type.
However it is a formidable task to execute this procedure for symmetric groups
of even modest order. Alternatively the inversion by means of the unitriangular
coupling matrix produces the Kostka matrix and the irreducible characters
simultaneously and with much less effort than required for the monomial
approach. Moreover there is a surprise.


  For n even, we prove Pozhidaev's conjecture on the existence of associative
enveloping algebras for simple n-Lie algebras. More generally, for n even and
any (n+1)-dimensional n-Lie algebra L, we construct a universal associative
enveloping algebra U(L) and show that the natural map from L to U(L) is
injective. We use noncommutative Grobner bases to present U(L) as a quotient of
the free associative algebra on a basis of L and to obtain a monomial basis of
U(L). In the last section, we provide computational evidence that the
construction of U(L) is much more difficult for n odd.


  A Puiseux monoid is an additive submonoid of the nonnegative cone of the
rational numbers. We say that a Puiseux monoid $M$ is exponential provided that
there exist a positive rational $r$ and a set $S$ consisting of nonnegative
integers, which contains $0$, such that $M$ is generated by the set $\{r^s \mid
s \in S\}$. If $M$ is multiplicatively closed then we say that $M$ is an
exponential Puiseux semiring. Here we study the atomic properties of
exponential Puiseux monoids and semirings. First, we characterize atomic
exponential Puiseux monoids, and we prove that the finite factorization
property, the bounded factorization property, and the ACCP coincide in this
context. Then we proceed to offer a necessary condition and a sufficient
condition for an exponential Puiseux monoid to satisfy the ACCP. We conclude by
describing the exponential Puiseux monoids that are semirings.


  User-centric (UC) based cell-free (CF) structures can provide the benefits of
coverage enhancement for millimeter wave (mmWave) multiple input multiple
output (MIMO) systems, which is regarded as the key technology of the reliable
and high-rate services. In this paper, we propose a new beam selection scheme
and precoding algorithm for the UC CF mmWave MIMO system, where a weighted
sum-rate maximization problem is formulated. Since the joint design of beam
selection and precoding is non-convex and tractable with high complexity, this
paper designs the beam selection and precoding separately. Particularly, the
proposed beam selection aims at reducing the inter-cluster inter-beam
interference, then we also propose a precoding algorithm based on the weighted
sum mean-square error (WSMSE) framework, where the precoding matrix can be
updated in a distributed manner. We further employ the low-rank decomposition
and Neumann series expansion (NSE) to reduce the computational complexity of
the precoding. Simulations and complexity analysis verify the effectiveness of
the proposed algorithm with a considerable reduction in computational
complexity.


  Most black hole binaries show large changes in X-ray luminosity caused
primarily by variations in mass accretion rate. An important question for
understanding black hole accretion and jet production is whether the inner edge
of the accretion disk recedes at low accretion rate. Measurements of the
location of the inner edge (Rin) can be made using iron emission lines that
arise due to fluorescence of iron in the disk, and these indicate that Rin is
very close to the black hole at high and moderate luminosities (near 1% of the
Eddington luminosity, Ledd). Here, we report on X-ray observations of the black
hole GX 339-4 in the hard state by Suzaku and the Rossi X-ray Timing Explorer
(RXTE) that extend iron line studies to 0.14% Ledd and show that Rin increases
by a factor of >27 over the value found when GX 339-4 was bright. The exact
value of Rin depends on the inclination of the inner disk (i), and we derive
90% confidence limits of Rin > 35 Rg at i = 0 degrees and Rin > 175 Rg at i =
30 degrees. This provides direct evidence that the inner portion of the disk is
not present at low luminosity, allowing for the possibility that the inner disk
is replaced by advection- or magnetically-dominated accretion flows.


  We formulate a damped oscillating particle method to solve the stationary
nonlinear Schr\"{o}dinger equation (NLSE). The ground state solutions are found
by a converging damped oscillating evolution equation that can be discretized
with symplectic numerical techniques. The method is demonstrated for three
different cases: for the single-component NLSE with an attractive
self-interaction, for the single-component NLSE with a repulsive self
interaction and a constraint on the angular momentum, and for the two-component
NLSE with a constraint on the total angular momentum. We reproduce the so
called yrast curve for the single-component case, described in [A. D. Jackson
et al., Europhys. Lett. 95, 30002 (2011)], and produce for the first time an
analogous curve for the two-component NLSE. The numerical results are compared
with analytic solutions and competing numerical methods. Our method is well
suited to handle a large class of equations and can easily be adapted to
further constraints and components.


  It has been shown that only certain neutrino mass matrices with texture zeros
are compatible with existing data. We discuss the stability of phenomenological
consequences of texture zeros under radiative corrections in the type-I see-saw
scenario. We show that under certain conditions additional patterns are allowed
due to these effects.


  This paper present our work in the DSAA 2023 Challenge about Link Prediction
for Wikipedia Articles. We use traditional machine learning models with POS
tags (part-of-speech tags) features extracted from text to train the
classification model for predicting whether two nodes has the link. Then, we
use these tags to test on various machine learning models. We obtained the
results by F1 score at 0.99999 and got 7th place in the competition. Our source
code is publicly available at this link:
https://github.com/Tam1032/DSAA2023-Challenge-Link-prediction-DS-UIT_SAT


  Simulations of gauge theories on quantum computers require the digitization
of continuous field variables. Digitization schemes that uses the minimum
amount of qubits are desirable. We present a practical scheme for digitizing
$SU(3)$ gauge theories via its discrete subgroup $S(1080)$. The $S(1080)$
standard Wilson action cannot be used since a phase transition occurs as the
coupling is decreased, well before the scaling regime. We proposed a modified
action that allows simulations in the scaling window and carry out classical
Monte Carlo calculations down to lattice spacings of order $a\approx 0.08$ fm.
We compute a set of observables with sub-percent precision at multiple lattice
spacings and show that the continuum extrapolated value agrees with the full
$SU(3)$ results. This suggests that this digitization scheme provides
sufficient precision for NISQ-era QCD simulations.


  We analyze two large datasets from technological networks with location and
social data: user location records from an online location-based social
networking service, and anonymized telecommunications data from a European
cellphone operator, in order to investigate the differences between individual
and group behavior with respect to physical location. We discover agreements
between the two datasets: firstly, that individuals are more likely to meet
with one friend at a place they have not visited before, but tend to meet at
familiar locations when with a larger group. We also find that groups of
individuals are more likely to meet at places that their other friends have
visited, and that the type of a place strongly affects the propensity for
groups to meet there. These differences between group and solo mobility has
potential technological applications, for example, in venue recommendation in
location-based social networks.


  This paper quantifies the information rate of multiple-input multiple-output
(MIMO) systems with finite rate channel state feedback and power on/off
strategy. In power on/off strategy, a beamforming vector (beam) is either
turned on (denoted by on-beam) with a constant power or turned off. We prove
that the ratio of the optimal number of on-beams and the number of antennas
converges to a constant for a given signal-to-noise ratio (SNR) when the number
of transmit and receive antennas approaches infinity simultaneously and when
beamforming is perfect. Based on this result, a near optimal strategy, i.e.,
power on/off strategy with a constant number of on-beams, is discussed. For
such a strategy, we propose the power efficiency factor to quantify the effect
of imperfect beamforming. A formula is proposed to compute the maximum power
efficiency factor achievable given a feedback rate. The information rate of the
overall MIMO system can be approximated by combining the asymptotic results and
the formula for power efficiency factor. Simulations show that this
approximation is accurate for all SNR regimes.


  In this paper, we propose a vector total variation (VTV) of feature image
model for image restoration. The VTV imposes different smoothing powers on
different features (e.g. edges and cartoons) based on choosing various
regularization parameters. Thus, the model can simultaneously preserve edges
and remove noises. Next, the existence of solution for the model is proved and
the split Bregman algorithm is used to solve the model. At last, we use the
wavelet filter banks to explicitly define the feature operator and present some
experimental results to show its advantage over the related methods in both
quality and efficiency.


  The physical mechanisms responsible for pulsar timing glitches are thought to
excite quasi-normal mode oscillations in their parent neutron star that couple
to gravitational wave emission. In August 2006, a timing glitch was observed in
the radio emission of PSR B0833-45, the Vela pulsar. At the time of the glitch,
the two co-located Hanford gravitational wave detectors of the Laser
Interferometer Gravitational-wave observatory (LIGO) were operational and
taking data as part of the fifth LIGO science run (S5). We present the first
direct search for the gravitational wave emission associated with oscillations
of the fundamental quadrupole mode excited by a pulsar timing glitch. No
gravitational wave detection candidate was found. We place Bayesian 90%
confidence upper limits of 6.3e-21 to 1.4e-20 on the peak intrinsic strain
amplitude of gravitational wave ring-down signals, depending on which spherical
harmonic mode is excited. The corresponding range of energy upper limits is
5.0e44 to 1.3e45 erg.


  We study singular hypersurfaces in tensor multi-scalar theories of gravity.
We derive in a distributional and then in an intrinsic way, the general
equations of junction valid for all types of hypersurfaces, in particular for
lightlike shells and write the general equations of evolution for these
objects. We apply this formalism to various examples in static spherically
symmetric spacetimes, and to the study of planar domain walls and plane
impulsive waves.


  With the recent success of artificial intelligence in neuroscience, a number
of deep learning (DL) models were proposed for classification, anomaly
detection, and pattern recognition tasks in electroencephalography (EEG). EEG
is a multi-channel time-series that provides information about the individual
brain activity for diagnostics, neuro-rehabilitation, and other applications
(including emotions recognition). Two main issues challenge the existing
DL-based modeling methods for EEG: the high variability between subjects and
the low signal-to-noise ratio making it difficult to ensure a good quality in
the EEG data. In this paper, we propose two variational autoencoder models,
namely vEEGNet-ver3 and hvEEGNet, to target the problem of high-fidelity EEG
reconstruction. We properly designed their architectures using the blocks of
the well-known EEGNet as the encoder, and proposed a loss function based on
dynamic time warping. We tested the models on the public Dataset 2a - BCI
Competition IV, where EEG was collected from 9 subjects and 22 channels.
hvEEGNet was found to reconstruct the EEG data with very high-fidelity,
outperforming most previous solutions (including our vEEGNet-ver3 ).
Furthermore, this was consistent across all subjects. Interestingly, hvEEGNet
made it possible to discover that this popular dataset includes a number of
corrupted EEG recordings that might have influenced previous literature
results. We also investigated the training behaviour of our models and related
it with the quality and the size of the input EEG dataset, aiming at opening a
new research debate on this relationship. In the future, hvEEGNet could be used
as anomaly (e.g., artefact) detector in large EEG datasets to support the
domain experts, but also the latent representations it provides could be used
in other classification problems and EEG data generation.


  Battery energy storage systems (ESS) are widely used in microgrids to
complement high renewables. However, the real-time energy management of
microgrids with battery ESS is challenging in two aspects: 1) the evolution
process of battery energy level is across-time coupled; 2) uncertainties
unavoidably arise in the forecasting process for renewable generation. In this
paper, a tube-based model predictive control (MPC) approach is innovatively
proposed in accommodating the real-time energy management of microgrids with
battery ESS. Firstly, a real-time operation model of battery, including the
degradation cost and time-aware SoC range, is proposed for the battery ESS. In
particular, the battery feature shallower-cheaper is depicted and the terminal
SoC requirement is achieved. Secondly, two cascaded MPC controllers are
designed in the proposed tube-based MPC, in which reference trajectories are
generated by the nominal MPC without uncertainties, and then the ancillary MPC
steers the actual trajectories to the nominal ones upon the realization of
uncertainties. Specifically, in this paper, the battery SoC is viewed as the
state variable of the system, while the generator power output and exchange
power with the utility are seen as control variables. Lastly, numerous case
studies demonstrate the effectiveness of the proposed approach, including both
the low and high penetration level of renewables. Additional Monte Carlo
simulations of consecutive 365 days show that the competitive ratio of the
proposed approach is excellently below 1.10.


  Traditional image recognition methods only consider objects belonging to
already learned classes. However, since training a recognition model with every
object class in the world is unfeasible, a way of getting information on
unknown objects (i.e., objects whose class has not been learned) is necessary.
A way for an image recognition system to learn new classes could be asking a
human about objects that are unknown. In this paper, we propose a method for
generating questions about unknown objects in an image, as means to get
information about classes that have not been learned. Our method consists of a
module for proposing objects, a module for identifying unknown objects, and a
module for generating questions about unknown objects. The experimental results
via human evaluation show that our method can successfully get information
about unknown objects in an image dataset. Our code and dataset are available
at https://github.com/mil-tokyo/vqg-unknown.


  The PEP-II interaction region is designed to accommodate asymmetric beam
energies, head-on collisions, small bunch spacing and provide low beta* for
high luminosity. Local correction schemes are implemented to compensate
non-linear chromaticity from the IP doublets as well as coupling, orbit and
focusing effects from the 6 Tm asymmetric detector solenoid. The main IR optics
features and local correction schemes are presented. MAD code is used for the
optics calculations.


  There has been significant progress made in the field of autonomous vehicles.
Object detection and tracking are the primary tasks for any autonomous vehicle.
The task of object detection in autonomous vehicles relies on a variety of
sensors like cameras, and LiDAR. Although image features are typically
preferred, numerous approaches take spatial data as input. Exploiting this
information we present an approach wherein, using a novel encoding of the LiDAR
point cloud we infer the location of different classes near the autonomous
vehicles. This approach does not implement a bird's eye view approach, which is
generally applied for this application and thus saves the extensive
pre-processing required. After studying the numerous networks and approaches
used to solve this approach, we have implemented a novel model with the
intention to inculcate their advantages and avoid their shortcomings. The
output is predictions about the location and orientation of objects in the
scene in form of 3D bounding boxes and labels of scene objects.


  Many empirical studies have demonstrated the performance benefits of
conditional computation in neural networks, including reduced inference time
and power consumption. We study the fundamental limits of neural conditional
computation from the perspective of memorization capacity. For Rectified Linear
Unit (ReLU) networks without conditional computation, it is known that
memorizing a collection of $n$ input-output relationships can be accomplished
via a neural network with $O(\sqrt{n})$ neurons. Calculating the output of this
neural network can be accomplished using $O(\sqrt{n})$ elementary arithmetic
operations of additions, multiplications and comparisons for each input. Using
a conditional ReLU network, we show that the same task can be accomplished
using only $O(\log n)$ operations per input. This represents an almost
exponential improvement as compared to networks without conditional
computation. We also show that the $\Theta(\log n)$ rate is the best possible.
Our achievability result utilizes a general methodology to synthesize a
conditional network out of an unconditional network in a
computationally-efficient manner, bridging the gap between unconditional and
conditional architectures.


  (abridged) [...] Methods: In a continued study of the molecular core
population of the Pipe Nebula, we present a molecular-line survey of 52 cores.
Previous research has shown a variety of different chemical evolutionary stages
among the cores. Using the Mopra radio telescope, we observed the ground
rotational transitions of HCO+, H13CO+, HCN, H13CN, HNC, and N2H+. These data
are complemented with near-infrared extinction maps to constrain the column
densities, effective dust temperatures derived from Herschel data, and
NH3-based gas kinetic temperatures. Results: The target cores are located
across the nebula, span visual extinctions between 5 and 67 mag, and effective
dust temperatures (averaged along the lines of sight) between 13 and 19 K. The
extinction-normalized integrated line intensities, a proxy for the abundance in
constant excitation conditions of optically thin lines, vary within an order of
magnitude for a given molecule. The effective dust temperatures and gas kinetic
temperatures are correlated, but the effective dust temperatures are
consistently higher than the gas kinetic temperatures. Combining the molecular
line and temperature data, we find that N2H+ is only detected toward the
coldest and densest cores while other lines show no correlation with these core
properties. Conclusions: Within this large sample, N2H+ is the only species to
exclusively trace the coldest and densest cores, in agreement with chemical
considerations. In contrast, the common high-density tracers HCN and HNC are
present in a majority of cores, demonstrating the utility of these molecules to
characterize cores over a large range of extinctions. The correlation between
the effective dust temperatures and the gas kinetic temperatures suggests that
the former are dominated by dust that is both dense and thermodynamically
coupled to the dense gas traced by NH3. [...]


  Local unitary invariants allow one to test whether multipartite states are
equivalent up to local basis changes. Equivalently, they specify the geometry
of the "orbit space" obtained by factoring out local unitary action from the
state space. This space is of interest because of its intimate relationship to
entanglement. Unfortunately, the dimension of the orbit space grows
exponentially with the number of subsystems, and the number of invariants
needed to characterise orbits grows at least as fast. This makes the study of
entanglement via local unitary invariants seem very daunting. I point out here
that there is a simplifying principle: Invariants fall into families related by
the tracing-out of subsystems, and these families grow exponentially with the
number of subsystems. In particular, in the case of pure qubit systems, there
is a family whose size is about half the dimension of orbit space. These
invariants are closely related to cumulants and to multipartite separability.
Members of the family have been repeatedly discovered in the literature, but
the fact that they are related to cumulants and constitute a family has
apparently not been observed.


  Currently, there is a growing trend of outsourcing the execution of DNNs to
cloud services. For service providers, managing multi-tenancy and ensuring
high-quality service delivery, particularly in meeting stringent execution time
constraints, assumes paramount importance, all while endeavoring to maintain
cost-effectiveness. In this context, the utilization of heterogeneous
multi-accelerator systems becomes increasingly relevant. This paper presents
RELMAS, a low-overhead deep reinforcement learning algorithm designed for the
online scheduling of DNNs in multi-tenant environments, taking into account the
dataflow heterogeneity of accelerators and memory bandwidths contentions. By
doing so, service providers can employ the most efficient scheduling policy for
user requests, optimizing Service-Level-Agreement (SLA) satisfaction rates and
enhancing hardware utilization. The application of RELMAS to a heterogeneous
multi-accelerator system composed of various instances of Simba and Eyeriss
sub-accelerators resulted in up to a 173% improvement in SLA satisfaction rate
compared to state-of-the-art scheduling techniques across different workload
scenarios, with less than a 1.5% energy overhead.


  We study cross-Kerr (CK) effect on an optomechanical system driven by
two-tone fields. We show that in the presence of the CK effect, a bistable
behavior of the mean photon number in the cavity becomes more robust against
the fluctuations of the frequency detuning between the cavity mode and the
control field. The bistability can also be turned into a tri-stability within
the experimentally accessible range of the system parameters. Also, we find
that the symmetric profile of the optomechanically induced transparency is
broken and the zero-absorption point is shifted in the presence of the CK
effect. This shift can be used to measure the strength of the CK effect, and
the asymmetric absorption profiles can be employed to engineer a high quality
factor of the cavity.


  We present an experimental proposal for the rapid preparation of the center
of mass of a levitated particle in a macroscopic quantum state, that is a state
delocalized over a length scale much larger than its zero-point motion and that
has no classical analog. This state is prepared by letting the particle evolve
in a static double-well potential after a sudden switchoff of the harmonic
trap, following initial center-of-mass cooling to a sufficiently pure quantum
state. We provide a thorough analysis of the noise and decoherence that is
relevant to current experiments with levitated nano- and microparticles. In
this context, we highlight the possibility of using two particles, one evolving
in each potential well, to mitigate the impact of collective sources of noise
and decoherence. The generality and scalability of our proposal make it
suitable for implementation with a wide range of systems, including single
atoms, ions, and Bose-Einstein condensates. Our results have the potential to
enable the generation of macroscopic quantum states at unprecedented scales of
length and mass, thereby paving the way for experimental exploration of the
gravitational field generated by a source mass in a delocalized quantum state.


  It has been suggested that secondary CMB anisotropies generated by neutral
lithium could open a new observational window into the universe around the
redshift z ~ 400, and permit a determination of the primordial lithium
abundance. The effect is due to resonant scattering in the allowed LiI doublet
(2s ^2S_{1/2} - 2p ^2P_{1/2,3/2}), so its observability depends on the
formation history of neutral lithium. Here we show that the ultraviolet photons
produced during hydrogen recombination are sufficient to keep lithium in the
LiII ionization stage in the relevant redshift range and suppress the neutral
fraction by ~3 orders of magnitude from previous calculations, making the
lithium signature unobservable.


  We study oscillations of slowly rotating relativistic barotropic as well as
non-barotropic polytropic stars in the Cowling approximation, including first
order rotational corrections. By taking into account the coupling between the
polar and axial equations, we find that, in contrast to previous results, the
$m=2$ $r$ modes are essentially unaffected by the continuous spectrum and exist
even for very relativistic stellar models. We perform our calculations both in
the time and frequency domain. In order to numerically solve the infinite
system of coupled equations, we truncate it at some value $l_{\rm max}$.
Although the time dependent equations can be numerically evolved without any
problems, the eigenvalue equations possess a singular structure, which is
related to the existence of a continuous spectrum. This prevents the numerical
computation of an eigenmode if its eigenfrequency falls inside the continuous
spectrum. The properties of the latter depend strongly on the cut-off value
$l_{\rm max}$ and it can consist of several either disconnected or overlapping
patches, which are the broader the more relativistic the stellar model is. By
discussing the dependence of the continuous spectrum as a function of both the
cut-off value $l_{\rm max}$ and the compactness $M/R$, we demonstrate how it
affects the inertial modes. Through the time evolutions we are able to show
that some of the inertial modes can actually exist inside the continuous
spectrum, but some cannot. For more compact and therefore more relativistic
stellar models, the width of the continuous spectrum strongly increases and as
a consequence, some of the inertial modes, which exist in less relativistic
stars, disappear.


  Learning and memory may rely on the ability of neuronal circuits to
reorganize by dendritic spine remodeling. We have looked for geometrical
parameters of cortical circuits, which maximize information storage capacity
associated with this mechanism. In particular, we calculated optimal volume
fractions of various neuropil components. The optimal axonal and dendritic
volume fractions are not significantly different from anatomical measurements
in the mouse and rat neocortex, and the rat hippocampus. This has led us to
propose that the maximization of information storage capacity associated with
dendritic spine remodeling may have been an important driving force in the
evolution of the cortex.


  The uniform states of a model for one-dimensional chains of thin magnetic
islands on a nonmagnetic substrate coupled via dipolar interactions are
described here. Magnetic islands oriented with their long axes perpendicular to
the chain direction are assumed, whose shape anisotropy imposes a preference
for the dipoles to point perpendicular to the chain. The competition between
anisotropy and dipolar interactions leads to three types of uniform states of
distinctly different symmetries, including metastable transverse or remanent
states, transverse antiferromagnetic states, and longitudinal states where all
dipoles align with the chain direction. The stability limits and normal modes
of oscillation are found for all three types of states, even including infinite
range dipole interactions. The normal mode frequencies are shown to be
determined from the eigenvalues of the stability problem.


  We study a fully decentralized federated learning algorithm, which is a novel
gradient descent algorithm executed on a communication-based network. For
convenience, we refer to it as a network gradient descent (NGD) method. In the
NGD method, only statistics (e.g., parameter estimates) need to be
communicated, minimizing the risk of privacy. Meanwhile, different clients
communicate with each other directly according to a carefully designed network
structure without a central master. This greatly enhances the reliability of
the entire algorithm. Those nice properties inspire us to carefully study the
NGD method both theoretically and numerically. Theoretically, we start with a
classical linear regression model. We find that both the learning rate and the
network structure play significant roles in determining the NGD estimator's
statistical efficiency. The resulting NGD estimator can be statistically as
efficient as the global estimator, if the learning rate is sufficiently small
and the network structure is well balanced, even if the data are distributed
heterogeneously. Those interesting findings are then extended to general models
and loss functions. Extensive numerical studies are presented to corroborate
our theoretical findings. Classical deep learning models are also presented for
illustration purpose.


  The MAGIC 17m diameter Cherenkov telescope will be upgraded with a second
telescope within the year 2007. The camera of MAGIC-II will include several new
features compared to the MAGIC-I camera. Photomultipliers with the highest
available photon collection efficiency have been selected. A modular design
allows easier access and flexibility to test new photodetector technologies.
The camera will be uniformly equipped with 0.1 degree diamter pixels, which
allows the use of an increased trigger area. Finally, the overall signal chain
features a large bandwidth to retain the shape of the very fast Cherenkov
signals.


  Automatic radiology report generation has attracted enormous research
interest due to its practical value in reducing the workload of radiologists.
However, simultaneously establishing global correspondences between the image
(e.g., Chest X-ray) and its related report and local alignments between image
patches and keywords remains challenging. To this end, we propose an Unify,
Align and then Refine (UAR) approach to learn multi-level cross-modal
alignments and introduce three novel modules: Latent Space Unifier (LSU),
Cross-modal Representation Aligner (CRA) and Text-to-Image Refiner (TIR).
Specifically, LSU unifies multimodal data into discrete tokens, making it
flexible to learn common knowledge among modalities with a shared network. The
modality-agnostic CRA learns discriminative features via a set of orthonormal
basis and a dual-gate mechanism first and then globally aligns visual and
textual representations under a triplet contrastive loss. TIR boosts
token-level local alignment via calibrating text-to-image attention with a
learnable mask. Additionally, we design a two-stage training procedure to make
UAR gradually grasp cross-modal alignments at different levels, which imitates
radiologists' workflow: writing sentence by sentence first and then checking
word by word. Extensive experiments and analyses on IU-Xray and MIMIC-CXR
benchmark datasets demonstrate the superiority of our UAR against varied
state-of-the-art methods.


  Bevan established that the growth rate of a monotone grid class of
permutations is equal to the square of the spectral radius of a related
bipartite graph. We give an elementary and self-contained proof of a
generalization of this result using only Stirling's Formula, the method of
Lagrange multipliers, and the singular value decomposition of matrices.


  Besides the astrometric mission of the Gaia satellite, its repeated and
high-precision measurements serve also as an all-sky photometric transient
survey. The sudden brightenings of the sources are published as Gaia
Photometric Science Alerts and are made publicly available allowing the
community to photometrically and spectroscopically follow-up the object. The
goal of this paper was to analyze the nature and derive the basic parameters of
Gaia18aen, transient detected at the beginning of 2018. It coincides with the
position of the emission line star WRAY 15-136. The brightening was classified
as a "nova?" on the basis of subsequent spectroscopic observation. We have
analyzed two spectra of Gaia18aen and collected the available photometry of the
object covering the brightenings in 2018 and also the preceding and following
periods of quiescence. Based on this observational data, we have derived the
parameters of Gaia18aen and discussed the nature of the object. Gaia18aen is
the first symbiotic star discovered by the Gaia satellite. The system is an
S-type symbiotic star and consists of an M giant of a slightly super-solar
metallicity, with Teff ~3500 K, a radius of ~230 R$\odot$, and a high
luminosity L ~7400 L$\odot$. The hot component is a hot white dwarf. We
tentatively determined the orbital period of the system ~487 days. The main
outburst of Gaia18aen in 2018 was accompanied by a decrease in the temperature
of the hot component. The first phase of the outburst was characterized by the
high luminosity L ~27000 L$\odot$, which remained constant for about three
weeks after the optical maximum, later followed by the gradual decline of
luminosity and increase of temperature. Several re-brightenings have been
detected on the timescales of hundreds of days.


  An ab initio potential for the interaction of the neutral helium atom with
antiprotons and protons is calculated using the Born-Oppenheimer approximation.
Using this potential, the annihilation cross section for antiprotons in the
energy range 0.01 microvolt to 1 eV is calculated.


  Pairwise alignment of DNA sequencing data is a ubiquitous task in
bioinformatics and typically represents a heavy computational burden. A
standard approach to speed up this task is to compute "sketches" of the DNA
reads (typically via hashing-based techniques) that allow the efficient
computation of pairwise alignment scores. We propose a rate-distortion
framework to study the problem of computing sketches that achieve the optimal
tradeoff between sketch size and alignment estimation distortion. We consider
the simple setting of i.i.d. error-free sources of length $n$ and introduce a
new sketching algorithm called "locational hashing." While standard approaches
in the literature based on min-hashes require $B = (1/D) \cdot O\left( \log n
\right)$ bits to achieve a distortion $D$, our proposed approach only requires
$B = \log^2(1/D) \cdot O(1)$ bits. This can lead to significant computational
savings in pairwise alignment estimation.


  A comparison-based search algorithm lets a user find a target item $t$ in a
database by answering queries of the form, ``Which of items $i$ and $j$ is
closer to $t$?'' Instead of formulating an explicit query (such as one or
several keywords), the user navigates towards the target via a sequence of such
(typically noisy) queries.
  We propose a scale-free probabilistic oracle model called $\gamma$-CKL for
such similarity triplets $(i,j;t)$, which generalizes the CKL triplet model
proposed in the literature. The generalization affords independent control over
the discriminating power of the oracle and the dimension of the feature space
containing the items.
  We develop a search algorithm with provably exponential rate of convergence
under the $\gamma$-CKL oracle, thanks to a backtracking strategy that deals
with the unavoidable errors in updating the belief region around the target.
  We evaluate the performance of the algorithm both over the posited oracle and
over several real-world triplet datasets. We also report on a comprehensive
user study, where human subjects navigate a database of face portraits.


  As the first-line diagnostic imaging modality, radiography plays an essential
role in the early detection of developmental dysplasia of the hip (DDH).
Clinically, the diagnosis of DDH relies on manual measurements and subjective
evaluation of different anatomical features from pelvic radiographs. This
process is inefficient and error-prone and requires years of clinical
experience. In this study, we propose a deep learning-based system that
automatically detects 14 keypoints from a radiograph, measures three anatomical
angles (center-edge, T\"onnis, and Sharp angles), and classifies DDH hips as
grades I-IV based on the Crowe criteria. Moreover, a novel data-driven scoring
system is proposed to quantitatively integrate the information from the three
angles for DDH diagnosis. The proposed keypoint detection model achieved a mean
(95% confidence interval [CI]) average precision of 0.807 (0.804-0.810). The
mean (95% CI) intraclass correlation coefficients between the center-edge,
Tonnis, and Sharp angles measured by the proposed model and the ground-truth
were 0.957 (0.952-0.962), 0.947 (0.941-0.953), and 0.953 (0.947-0.960),
respectively, which were significantly higher than those of experienced
orthopedic surgeons (p<0.0001). In addition, the mean (95% CI) test diagnostic
agreement (Cohen's kappa) obtained using the proposed scoring system was 0.84
(0.83-0.85), which was significantly higher than those obtained from diagnostic
criteria for individual angle (0.76 [0.75-0.77]) and orthopedists (0.71
[0.63-0.79]). To the best of our knowledge, this is the first study for
objective DDH diagnosis by leveraging deep learning keypoint detection and
integrating different anatomical measurements, which can provide reliable and
explainable support for clinical decision-making.


  This paper reports on the design, fabrication, and characterization of an
edge-coupled magnetostatic forward volume wave bandpass filter. Using
micromachining techniques, the filter is fabricated from a yttrium iron garnet
(YIG) film grown on a gadolinium gallium garnet (GGG) substrate with inductive
transducers. By adjusting an out-of-plane magnetic field, we demonstrate linear
center frequency tuning for a $4^{\text{th}}$-order filter from 4.5 GHz to 10.1
GHz while retaining a fractional bandwidth of 0.3%, an insertion loss of 6.94
dB, and a -35dB rejection. We characterize the filter nonlinearity in the
passband and stopband with IIP3 measurements of -4.85 dBm and 25.84 dBm,
respectively. When integrated with a tunable magnetic field, this device is an
octave tunable narrowband channel-select filter.


  This manuscript studies statistical properties of linear classifiers obtained
through minimization of an unregularized convex risk over a finite sample.
Although the results are explicitly finite-dimensional, inputs may be passed
through feature maps; in this way, in addition to treating the consistency of
logistic regression, this analysis also handles boosting over a finite weak
learning class with, for instance, the exponential, logistic, and hinge losses.
In this finite-dimensional setting, it is still possible to fit arbitrary
decision boundaries: scaling the complexity of the weak learning class with the
sample size leads to the optimal classification risk almost surely.


  We present a quantum theory of dielectric energy loss arising from the
piezoelectric coupling between photons and phonons in superconducting devices.
Photon loss is shown to occur predominantly at the interface, where the
piezoelectric effect is non-zero even when the materials are perfectly
crystalline (epitaxial) and free of two-level system defects. We present
explicit numerical calculations for the value of the intrinsic loss tangent at
several interfaces to conclude that the $T_1$ of superconducting qubits may
reach $10^{4}$ $\mu$s if the device is made with defect-free interfaces.


  To study the bulk properties of the quark-gluon-plasma (QGP) produced at the
beam energy scan (BES) energies at the Relativistic Heavy Ion Collider (RHIC),
we extend the (3+1)-dimensional viscous hydrodynamics CLVisc to include net
baryon number conservation and Israel-Stewart-like equation for baryon
diffusion with the NEOS-BQS equation of state, fluctuating initial conditions
from Monte-Carlo Glauber model, and the afterburner SMASH. This integrated
framework is shown to provide a good description of identified particle
spectra, mean transverse momenta and anisotropic flows for different
centralities and over a wide range of collision energies (7.7-62.4 GeV). It is
found that the mean momenta of identified particles and anisotropic flows
increases mildly with the collision energy due to larger radial flow. We
further compute the multiple-particle cumulant ratio $v_2\{4\}/v_2\{2\}$ of
elliptic flow across BES energies, and find that the relative fluctuations of
elliptic flow are insensitive to the collision energy, consistent with the
preliminary STAR data. Our model provides a benchmark for understanding the
RHIC-BES data and studying the critical properties and phase structure of hot
and dense QCD matter.


  We report on the melting dynamics of ice suspended in fresh water and subject
to natural convective flows. Using direct numerical simulations we investigate
the melt rate of ellipsoidal objects for $2.32\times 10^4 \leq \text{Ra} \leq
7.61\times 10^8$, where \text{Ra} is the Rayleigh number defined with the
temperature difference between the ice and the surrounding water. We reveal
that the system exhibits non-monotonic behavior in three control parameters. As
a function of the aspect ratio of the ellipsoidal, the melting time shows a
distinct minimum that is different from a disk which has the minimum perimeter.
Furthermore, also with \text{Ra} the system shows a non-monotonic trend, since
for large \text{Ra} and large aspect ratio the flow separates, leading to
distinctly different dynamics. Lastly, since the density of water is
non-monotonic with temperature, the melt rate depends non-monotonically also on
the ambient temperature, as for intermediate temperatures
($\unit{4}{\celsius}$--$\unit{7}{\celsius}$) the flow is (partially) reversed.
In general, the shape which melts the slowest is quite distinct from that of a
disk.


  I dedicated the volume $2$ of monograph 'Introduction into Noncommutative
Algebra' to studying of module over non-commutative algebra.


  This paper shows how mesoscopic nonequilibrium thermodynamics can be applied
to condensation and evaporation. By extending the normal set of thermodynamic
variables with two internal variables, we are able to give a new theoretical
foundation for a mechanism of condensation that has been proposed from
molecular simulation results. The flux does not follow a simple Arrhenius
formula for small activation energies which are relevant here.


  We study curvature flows in the locally homogeneous case (e.g. compact
quotients of Lie groups, solvmanifolds, nilmanifolds) in a unified way, by
considering a generic flow under just a few natural conditions on the broad
class of almost-hermitian structures. As a main tool, we use an ODE system
defined on the variety of 2n-dimensional Lie algebras, called the bracket flow,
whose solutions differ from those to the original curvature flow by only
pull-back by time-dependent diffeomorphisms. The approach, which has already
been used to study the Ricci flow on homogeneous manifolds, is useful to better
visualize the possible pointed limits of solutions, under diverse rescalings,
as well as to address regularity issues. Immortal, ancient and self-similar
solutions arise naturally from the qualitative analysis of the bracket flow.
The Chern-Ricci flow and the symplectic curvature flow are considered in more
detail.


  Linear complexity is an important parameter for arrays that are used in
applications related to information security. In this work we survey
constructions of two and three dimensional arrays, and present new results on
the multidimensional linear complexity of periodic arrays obtained using the
definition and method proposed in \cite{ArCaGoMoOrRuTi,GoHoMoRu,MoHoRu}. The
results include a generalization of a bound for the linear complexity, a
comparison with the measure of complexity for multisequences, and computations
of the complexity of arrays with periods that are not relatively prime for
which the ``unfolding method'' does not work. Conjectures for exact formulas
and the asymptotic behavior of the complexity of some array constructions are
formulated. We also present open source software for constructing
multidimensional arrays and for computing their multidimensional linear
complexity.


  We use the formalism of Szapudi(2004} to derive full explicit expressions for
the linear two-point correlation function, including redshift space distortions
and large angle effects. We take into account a non-perturbative geometric term
in the Jacobian, which is still linear in terms of the dynamics. This term had
been identified previously (Kaiser 1987,Hamilton and Culhane 1996), but has
been neglected in all subsequent explicit calculations of the linear redshift
space two-point correlation function. Our results represent a significant
correction to previous explicit expressions and are in excellent agreement with
our measurements in the Hubble Volume Simulation.


  We study the initial properties and positron annihilation within a small
electron-positron plasma drop formed by intense laser pulse. Such QED cascade
initiated plasma is, in general, far below the chemical (particle yield)
equilibrium. We find that the available electrons and positrons equilibrate
kinetically, yet despite relatively high particle density, the
electron-positron annihilation is very slow, suggesting a rather long lifespan
of the plasma drop.


  Atomic and electronic structures of a polar surface of MgO formed on Ag(111)
was investigated by using reflection high energy electron diffraction (RHEED),
Auger electron spectroscopy, electron energy loss spectroscopy (EELS), and
ultraviolet photoemission spectroscopy (UPS). A rather flat unreconstructed
polar MgO(111) 1$\times$1 surface could be grown by alternate adsorption of Mg
and O$_{2}$ on Ag(111). The stability of the MgO(111) surface was discussed in
terms of interaction between Ag and Mg atoms at the interface, and charge state
of the surface atoms. EELS of this surface did not show a band gap region, and
finite density of states appeared at the Fermi level in UPS. These results
suggest that a polar MgO(111) surface was not an insulating surface but a
semiconducting or metallic surface.


  This work advances knowledge of the threshold of prox-boundedness of a
function; an important concern in the use of proximal point optimization
algorithms and in determining the existence of the Moreau envelope of the
function. In finite dimensions, we study general prox-bounded functions and
then focus on some useful families such as piecewise functions and Lipschitz
continuous functions. The thresholds are explicitly determined when possible
and bounds are established otherwise. Some calculus rules are constructed; we
consider functions with known thresholds and find the thresholds of their sum
and composition.


  In this paper we address the consensus problem in the context of networked
agents whose communication graph can be split into a certain number of clusters
in such a way that interactions between agents in the same clusters are
cooperative, while interactions between agents belonging to different clusters
are antagonistic. This problem set-up arises in the context of social networks
and opinion dynamics, where reaching consensus means that the opinions of the
agents in the same cluster converge to the same decision. The consensus problem
is here investigated under the assumption that agents in the same cluster have
the same constant and pre-fixed amount of trust (/distrust) to be distributed
among their cooperators (/adversaries). The proposed solution establishes how
much agents in the same group must be conservative about their opinions in
order to converge to a common decision.


  The representation of politics in media influences societal perceptions and
attitudes. Video games, as a pervasive form of media, contribute significantly
to this phenomenon. In this work, we explore political themes within video
games by analyzing politically-themed games on game distribution platforms
including Steam. We conducted a statistical examination of games with political
context to identify patterns and use this as a basis to introduce a first
taxonomy to categorize and better understand the interplay between politics and
video games. This taxonomy offers a first framework for analyzing political
content in games and also sets a foundation for future research in this field.


  Objectives: We introduce a new method for reducing crime in hot spots and
across cities through ridge estimation. In doing so, our goal is to explore the
application of density ridges to hot spots and patrol optimization, and to
contribute to the policing literature in police patrolling and crime reduction
strategies.
  Methods: We make use of the subspace-constrained mean shift algorithm, a
recently introduced approach for ridge estimation further developed in
cosmology, which we modify and extend for geospatial datasets and hot spot
analysis. Our experiments extract density ridges of Part I crime incidents from
the City of Chicago during the year 2018 and early 2019 to demonstrate the
application to current data.
  Results: Our results demonstrate nonlinear mode-following ridges in agreement
with broader kernel density estimates. Using early 2019 incidents with
predictive ridges extracted from 2018 data, we create multi-run confidence
intervals and show that our patrol templates cover around 94% of incidents for
0.1-mile envelopes around ridges, quickly rising to near-complete coverage. We
also develop and provide researchers, as well as practitioners, with a
user-friendly and open-source software for fast geospatial density ridge
estimation.
  Conclusions: We show that ridges following crime report densities can be used
to enhance patrolling capabilities. Our empirical tests show the stability of
ridges based on past data, offering an accessible way of identifying routes
within hot spots instead of patrolling epicenters. We suggest further research
into the application and efficacy of density ridges for patrolling.


  In this paper we present an algorithm for computing a matrix representation
for a surface in P^3 parametrized over a 2-dimensional toric variety T. This
algorithm follows the ideas of [Botbol-Dickenstein-Dohm-09] and it was
implemented in Macaulay2. We showed in [BDD09] that such a surface can be
represented by a matrix of linear syzygies if the base points are finite in
number and form locally a complete intersection, and in [Botbol-09] we
generalized this to the case where the base locus is not necessarily a local
complete intersection. The key point consists in exploiting the sparse
structure of the parametrization, which allows us to obtain significantly
smaller matrices than in the homogeneous case.


  Time4sys is a formalism developed by Thales, realizing a graphical
specification for real-time systems. However, this formalism does not allow to
perform formal analyses for real-time systems. So a translation of this tool to
a formalism equipped with a formal semantics is needed. We present here
Time4sys2imi, a tool translating Time4sys models into parametric timed automata
in the input language of IMITATOR. This translation allows not only to check
the schedulability of real-time systems, but also to infer some timing
constraints (e.g., deadlines, offsets) guaranteeing schedulability. We
successfully applied Time4sys2imi to various examples.


  For many new accelerator applications, superconducting radio frequency (SRF)
systems are the enabling technology. In particular for CW applications, much
effort is being expended to minimize the power dissipation (surface resistance)
of niobium cavities. Starting in 2009, we suggested a means of reducing the
residual resistance by performing a thermal cycle [1], a procedure of warming
up a cavity after initial cooldown to about 20K and cooling it down again. In
subsequent studies [2], this technique was used to manipulate the residual
resistance by more than a factor of 2. It was postulated that thermocurrents
during cooldown generate additional trapped magnetic flux that impacts the
cavity quality factor. Here, we present a more extensive study that includes
measurements of two additional passband modes and that confirms the effect. In
this paper, we also discuss simulations that support the claim. While the
layout of the cavity LHe tank system is cylindrically symmetric, we show that
the temperature dependence of the material parameters results in a
non-symmetric current distribution. Hence a significant amount of magnetic flux
can be generated at the RF surface.


  Using a variety of methods developed in the literature (in particular, the
theory of weak Hopf algebras), we prove a number of general results about
fusion categories in characteristic zero. We show that the global dimension of
a fusion category is always positive, and that the S-matrix of any modular
category (not necessarily hermitian) is unitary. We also show that the category
of module functors between two module categories over a fusion category is
semisimple, and that fusion categories and tensor functors between them are
undeformable (generalized Ocneanu rigidity). In particular the number of such
categories (functors) realizing a given fusion datum is finite. Finally, we
develop the theory of Frobenius-Perron dimensions in an arbitrary fusion
category and classify categories of prime dimension.


  Let $\mathcal{C}$ be a small category. In this paper, we mainly study the
category of modules $\mathfrak{M}\mbox{od-}\mathfrak{R}$ on ringed sites
$(\mathbf{C},\mathfrak{R})$. We firstly reprove the Theorem A of the paper (M.
Wu and F. Xu. Skew category algebras and modules on ringed finite sites. J. A.
631, 2023), then we characterize $\mathfrak{M}\mbox{od-}\mathfrak{R}$ in terms
of the torsion presheaves on $Gr(\mathfrak{R})$, where $Gr(\mathfrak{R})$ is
the linear Grothendieck construction of $\mathfrak{R}$. Finally, we investigate
the hereditary torsion pairs, TTF triples and Abelian recollements of
$\mathfrak{M}\mbox{od-}\mathfrak{R}$. When $\mathcal{C}$ is finite, the
complete classifications of all these are given respectively.


  We develop a generalization of quantitative $K$-theory, which we call
controlled $K$-theory. It is powerful enough to study the $K$-theory of crossed
product of $C^*$-algebras by action of \'etale groupoids and discrete quantum
groups. In this article, we will use it to study groupoids crossed products. We
define controlled assembly maps, which factorize the Baum-Connes assembly maps,
and define the controlled Baum-Connes conjecture. We relate the controlled
conjecture for groupoids to the classical conjecture, and to the coarse
Baum-Connes conjecture. This allows to give applications to Coarse Geometry. In
particular, we can prove that the maximal version of the controlled coarse
Baum-Connes conjecture is satisfied for a coarse space which admits a fibred
coarse embedding, which is a stronger version of a result of M. Finn-Sell.


  In this paper, we consider Ising-Vannimenus model on a Cayley tree for order
two with competing nearest-neighbor, prolonged next-nearest neighbor
interactions. We stress that the mentioned model was investigated only
numerically, without rigorous (mathematical) proofs. One of the main point of
this paper is to propose a measure-theoretical approach the considered model.
We find certain conditions for the existence of Gibbs measures corresponding to
the model. Then we establish the existence of the phase transition. Moreover,
the free energies of the found Gibbs measures are calculated.


  We report interferometric measurements of [NII] 205 um fine-structure line
emission from a representative sample of three galaxies at z=5-6 using the
Atacama Large (sub)Millimeter Array (ALMA). These galaxies were previously
detected in [CII] and far-infrared continuum emission and span almost two
orders of magnitude in star formation rate (SFR). Our results show at least two
different regimes of ionized inter-stellar medium properties for galaxies in
the first billion years of cosmic time, separated by their L_[CII]/L_[NII]
ratio. We find extremely low [NII] emission compared to [CII] (L_
[CII]/L_[NII]=68 [+200/-28]) from a "typical" L*_UV star-forming galaxy, likely
directly or indirectly (by its effect on the radiation field) related to low
dust abundance and low metallicity. The infrared-luminous modestly star-forming
Lyman Break Galaxy (LBG) in our sample is characterized by an ionized-gas
fraction (L_[CII]/L_[NII]<=20) typical of local star-forming galaxies and shows
evidence for spatial variations in its ionized-gas fraction across an extended
gas reservoir. The extreme SFR, warm and compact dusty starburst AzTEC-3 shows
an ionized fraction higher than expected given its star-formation rate surface
density (L_[CII]/L_[NII]=22+/-8) suggesting that [NII] dominantly traces a
diffuse ionized medium rather than star-forming HII regions in this type of
galaxy. This highest redshift sample of [NII] detections provides some of the
first constraints on ionized and neutral gas modeling attempts and on the
structure of the inter-stellar medium at z=5-6 in "normal" galaxies and
starbursts.


  Axions and axion-like particles are well-motivated dark matter candidates. We
propose an experiment that uses single photon detection interferometry to
search for axions and axion-like particles in the galactic halo. We show that
photon counting with a dark rate of 6E-6 Hz can improve the quantum sensitivity
of axion interferometry by a factor of 50 compared to the quantum-enhanced
heterodyne readout for 5-m long optical resonators. The proposed experimental
method has the potential to be scaled up to kilometer-long facilities, enabling
the detection or setting of constraints on the axion-photon coupling
coefficient of 1E-17 - 1E-16 GeV-1 for axion masses ranging from 0.1 to 1 neV.


  Thermal frequency fluctuations in optical cavities limit the sensitivity of
precision experiments ranging from gravitational wave observatories to optical
atomic clocks. Conventional modeling of these noises assumes a linear response
of the optical field to the fluctuations of cavity frequency. Fundamentally,
however, this response is nonlinear. Here we show that nonlinearly transduced
thermal fluctuations of cavity frequency can dominate the broadband noise in
photodetection, even when the magnitude of fluctuations is much smaller than
the cavity linewidth. We term this noise "thermal intermodulation noise" and
show that for a resonant laser probe it manifests as intensity fluctuations. We
report and characterize thermal intermodulation noise in an optomechanical
cavity, where the frequency fluctuations are caused by mechanical Brownian
motion, and find excellent agreement with our developed theoretical model. We
demonstrate that the effect is particularly relevant to quantum optomechanics:
using a phononic crystal $Si_3N_4$ membrane with a low mass, soft-clamped
mechanical mode we are able to operate in the regime where measurement quantum
backaction contributes as much force noise as the thermal environment does.
However, in the presence of intermodulation noise, quantum signatures of
measurement are not revealed in direct photodetectors. The reported noise
mechanism, while studied for an optomechanical system, can exist in any optical
cavity.


  An approximation scheme for model disordered solids is proposed that leads to
the fully analytical evaluation of the elastic constants under explicit account
of the inhomogeneity (nonaffinity) of the atomic displacements. The theory is
in quantitative agreement with simulations for central-force systems and
predicts the vanishing of the shear modulus at the isostatic point with the
linear law {\mu} ~ (z - 2d), where z is the coordination number. The vanishing
of rigidity at the isostatic point is shown to be a consequence of the
canceling out of positive affine and negative nonaffine terms.


  Unsupervised Domain Adaptive Object Detection (DAOD) could adapt a model
trained on a source domain to an unlabeled target domain for object detection.
Existing unsupervised DAOD methods usually perform feature alignments from the
target to the source. Unidirectional domain transfer would omit information
about the target samples and result in suboptimal adaptation when there are
large domain shifts. Therefore, we propose a pairwise attentive adversarial
network with a Domain Mixup (DomMix) module to mitigate the aforementioned
challenges. Specifically, a deep-level mixup is employed to construct an
intermediate domain that allows features from both domains to share their
differences. Then a pairwise attentive adversarial network is applied with
attentive encoding on both image-level and instance-level features at different
scales and optimizes domain alignment by adversarial learning. This allows the
network to focus on regions with disparate contextual information and learn
their similarities between different domains. Extensive experiments are
conducted on several benchmark datasets, demonstrating the superiority of our
proposed method.


  In this essay I begin to lay out a conceptual scheme for: (i) analysing
dualities as cases of theoretical equivalence; (ii) assessing when cases of
theoretical equivalence are also cases of physical equivalence. The scheme is
applied to gauge/gravity dualities. I expound what I argue to be their
contribution to questions about: (iii) the nature of spacetime in quantum
gravity; (iv) broader philosophical and physical discussions of spacetime.
(i)-(ii) proceed by analysing duality through four contrasts. A duality will be
a suitable isomorphism between models: and the four relevant contrasts are as
follows:
  (a) Bare theory: a triple of states, quantities, and dynamics endowed with
appropriate structures and symmetries; vs. interpreted theory: which is endowed
with, in addition, a suitable pair of interpretative maps.
  (b) Extendable vs. unextendable theories: which can, respectively cannot, be
extended as regards their domains of application.
  (c) External vs. internal intepretations: which are constructed,
respectively, by coupling the theory to another interpreted theory vs. from
within the theory itself.
  (d) Theoretical vs. physical equivalence: which contrasts formal equivalence
with the equivalence of fully interpreted theories.
  I apply this scheme to answering questions (iii)-(iv) for gauge/gravity
dualities. I argue that the things that are physically relevant are those that
stand in a bijective correspondence under duality: the common core of the two
models. I therefore conclude that most of the mathematical and physical
structures that we are familiar with, in these models, are largely, though
crucially never entirely, not part of that common core. Thus, the
interpretation of dualities for theories of quantum gravity compels us to
rethink the roles that spacetime, and many other tools in theoretical physics,
play in theories of spacetime.


  The entanglement quantification and classification of multipartite quantum
states are two important research fields in quantum information. In this work,
we study the entanglement of arbitrary-dimensional multipartite pure states by
looking at the averaged partial entropies of various bipartite partitions of
the system, namely, the so-called Manhattan distance ($l_1$ norm) of averaged
partial entropies (MAPE), and it is proved to be an entanglement measure for
pure states. We connected the MAPE with the coefficient matrices, which are
important tools in entanglement classification and reexpressed the MAPE for
arbitrary-dimensional multipartite pure states by the nonzero singular values
of the coefficient matrices. The entanglement properties of the $n$-qubit Dicke
states, arbitrary-dimensional Greenberger-Horne-Zeilinger states, and $D_3^n$
states are investigated in terms of the MAPE, and the relation between the rank
of the coefficient matrix and the degree of entanglement is demonstrated for
symmetric states by two examples.


  Radio interferometers have the ability to precisely localize and better
characterize the properties of sources. This ability is having a powerful
impact on the study of fast radio transients, where a few milliseconds of data
is enough to pinpoint a source at cosmological distances. However, recording
interferometric data at millisecond cadence produces a terabyte-per-hour data
stream that strains networks, computing systems, and archives. This challenge
mirrors that of other domains of science, where the science scope is limited by
the computational architecture as much as the physical processes at play. Here,
we present a solution to this problem in the context of radio transients:
realfast, a commensal, fast transient search system at the Jansky Very Large
Array. Realfast uses a novel architecture to distribute fast-sampled
interferometric data to a 32-node, 64-GPU cluster for real-time imaging and
transient detection. By detecting transients in situ, we can trigger the
recording of data for those rare, brief instants when the event occurs and
reduce the recorded data volume by a factor of 1000. This makes it possible to
commensally search a data stream that would otherwise be impossible to record.
This system will search for millisecond transients in more than 1000 hours of
data per year, potentially localizing several Fast Radio Bursts, pulsars, and
other sources of impulsive radio emission. We describe the science scope for
realfast, the system design, expected outcomes, and ways real-time analysis can
help in other fields of astrophysics.


  In this paper we prove that for numbers $n = 8k+1$, such that $8k-1$ is
prime, there exists the coloring of all 3-element subsets of {1, ..., n} such
that any sets $A, B: |A\cap B|=2$ have different colors.


  Dynamic Epistemic Logic (DEL) is a logical framework in which one can
describe in great detail how actions are perceived by the agents, and how they
affect the world. DEL games were recently introduced as a way to define classes
of games with imperfect information where the actions available to the players
are described very precisely. This framework makes it possible to define
easily, for instance, classes of games where players can only use public
actions or public announcements. These games have been studied for reachability
objectives, where the aim is to reach a situation satisfying some epistemic
property expressed in epistemic logic; several (un)decidability results have
been established. In this work we show that the decidability results obtained
for reachability objectives extend to a much more general class of winning
conditions, namely those expressible in the epistemic temporal logic LTLK. To
do so we establish that the infinite game structures generated by DEL public
actions are regular, and we describe how to obtain finite representations on
which we rely to solve them.


  We propose a purely data-driven model predictive control (MPC) scheme to
control unknown linear time-invariant systems with guarantees on stability and
constraint satisfaction in the presence of noisy data. The scheme predicts
future trajectories based on data-dependent Hankel matrices, which span the
full system behavior if the input is persistently exciting. This paper extends
previous work on data-driven MPC by including a suitable constraint tightening
which ensures that the closed-loop trajectory satisfies desired
pointwise-in-time output constraints. Furthermore, we provide estimation
procedures to compute system constants related to controllability and
observability, which are required to implement the constraint tightening. The
practicality of the proposed approach is illustrated via a numerical example.


  In the approach of the effective field theory of modified gravity, we derive
the equations of motion for linear perturbations in the presence of a
barotropic perfect fluid on the flat isotropic cosmological background. In a
simple version of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, which is
the minimum extension of Horndeski theories, we show that a slight deviation of
the tensor propagation speed squared $c_{\rm t}^2$ from 1 generally leads to
the large modification to the propagation speed squared $c_{\rm s}^2$ of a
scalar degree of freedom $\phi$. This problem persists whenever the kinetic
energy $\rho_X$ of the field $\phi$ is much smaller than the background energy
density $\rho_m$, which is the case for most of dark energy models in the
asymptotic past. Since the scaling solution characterized by the constant ratio
$\rho_X/\rho_m$ is one way out for avoiding such a problem, we study the
evolution of perturbations for a scaling dark energy model in the framework of
GLPV theories in the Jordan frame. Provided the oscillating mode of scalar
perturbations is fine-tuned so that it is initially suppressed, the anisotropic
parameter $\eta=-\Phi/\Psi$ between the two gravitational potentials $\Psi$ and
$\Phi$ significantly deviates from 1 for $c_{\rm t}^2$ away from 1. For other
general initial conditions, the deviation of $c_{\rm t}^2$ from 1 gives rise to
the large oscillation of $\Psi$ with the frequency related to $c_{\rm s}^2$. In
both cases, the model can leave distinct imprints for the observations of CMB
and weak lensing.


  Brownian ratchet has emerged as a promising tool for understanding motion
mechanism of molecules and proteins, and dynamically manipulating particles in
non-equilibrium thermodynamics state. Here, we propose and experimentally
demonstrate a new type of optical Brownian ratchets, which is generated by
using controllable phase profiles in holographic optical trapping system. The
potential energy profiles are dynamically switched in on-off mode, controlled
by Labview software. Experimental results reveal that not only high speed but
also large step distance can be easily achieved in Brownian ratchet, in which
the average velocity of forward motion is about 28 {\mu}m/s and step distance
is about 42 {\mu}m. More importantly, its motion path, step distance and
velocity can be easily changed by manipulating its holograms, which exhibits
high flexibility, easy control and excellent capability. This technique
provides new opportunities for exploring non-equilibrium dynamics at the
nanoscale level, and developing novel nanoparticle manipulation.


  We study decay properties for solutions to the initial value problem
associated with the one-dimensional Zakharov-Rubenchik/Benney-Roskes system. We
prove time-integrability in growing compact intervals of size $t^{r}$, $r<2/3$,
centered on some characteristic curves coming from the underlying transport
equations associated with the ZR/BR system. Additionally, we prove decay to
zero of the local energy-norm in so-called far-field regions. Our results are
independent of the size of the initial data and do not require any parity
condition.


  The developed computational approach is capable of initiating and propagating
cracks inside materials and along material interfaces of general multi-domain
structures under quasi-static conditions. Special attention is paid to
particular situation of a solid with inhomogeneities. Description of the
fracture processes are based on the theory of material damage. It introduces
two independent damage parameters to distinguish between interface and internal
cracks. The parameter responsible for interface cracks is defined in a thin
adhesive layer of the interface and renders relation between stress and strain
quantities in fashion of cohesive zone models.The second parameter is defined
inside material domains and it is founded on the theory of phase-field fracture
guaranteeing the material damage to occur in a thin material strip introducing
a regularised model of internal cracks. Additional property of both interface
and phase-field damage is their capability to distinguish between fracture
modes which is useful if the structures is subjected to combined loading. The
solution methodology is based on a variational approach which allows
implementation of non-linear programming optimisation into standard methods of
finite-element discretisation and time stepping method.Computational
implementation is prepared in MATLAB whose numerical data validate developed
formulation for analysis of problems of fracture in multi-domain elements of
structures.


  In this work, we establish the existence and decay of {\em plasmons}, the
quantum of Langmuir's oscillatory waves found in plasma physics, for the
linearized Hartree equations describing an interacting gas of infinitely many
fermions near general translation-invariant steady states, including compactly
supported Fermi gases at zero temperature, in the whole space $\RR^d$ for $d\ge
2$. Notably, these plasmons exist precisely due to the long-range pair
interaction between the particles. Next, we provide a survival threshold of
spatial frequencies, below which the plasmons purely oscillate and disperse
like a Klein-Gordon's wave, while at the threshold they are damped by {\em
Landau damping}, the classical decaying mechanism due to their resonant
interaction with the background fermions. The explicit rate of Landau damping
is provided for general radial homogenous equilibria. Above the threshold, the
density of the excited fermions is well approximated by that of the free gas
dynamics and thus decays rapidly fast for each Fourier mode via {\em phase
mixing}. Finally, pointwise bounds on the Green function and dispersive
estimates on the density are established.


  We present an annotation scheme for argumentative and domain-specific aspects
of scholarly articles on the theory of International Relations. At
argumentation level we identify Claims and Support/Attack relations. At domain
level we model discourse content in terms of Theory and Data-related
statements. We annotate Waltz's 1993 text on structural realism and show that
our scheme can be reliably applied by domain experts enables insights on two
research questions on justifications of claims.


  Text-based reinforcement learning involves an agent interacting with a
fictional environment using observed text and admissible actions in natural
language to complete a task. Previous works have shown that agents can succeed
in text-based interactive environments even in the complete absence of semantic
understanding or other linguistic capabilities. The success of these agents in
playing such games suggests that semantic understanding may not be important
for the task. This raises an important question about the benefits of LMs in
guiding the agents through the game states. In this work, we show that rich
semantic understanding leads to efficient training of text-based RL agents.
Moreover, we describe the occurrence of semantic degeneration as a consequence
of inappropriate fine-tuning of language models in text-based reinforcement
learning (TBRL). Specifically, we describe the shift in the semantic
representation of words in the LM, as well as how it affects the performance of
the agent in tasks that are semantically similar to the training games. We
believe these results may help develop better strategies to fine-tune agents in
text-based RL scenarios.


  Densification and multi-band operation in 5G and beyond pose an unprecedented
challenge for mobility management, particularly for inter-frequency handovers.
The challenge is aggravated by the fact that the impact of key inter-frequency
mobility parameters, namely A5 time to trigger (TTT), A5 threshold1 and A5
threshold2 on the system's performance is not fully understood. These
parameters are fixed to a gold standard value or adjusted through hit and
trial. This paper presents a first study to analyze and optimize A5 parameters
for jointly maximizing two key performance indicators (KPIs): Reference signal
received power (RSRP) and handover success rate (HOSR). As analytical modeling
cannot capture the system-level complexity, a data driven approach is used. By
developing XGBoost based model, that outperforms other models in terms of
accuracy, we first analyze the concurrent impact of the three parameters on the
two KPIs. The results reveal three key insights: 1) there exist optimal
parameter values for each KPI; 2) these optimal values do not necessarily
belong to the current gold standard; 3) the optimal parameter values for the
two KPIs do not overlap. We then leverage the Sobol variance-based sensitivity
analysis to draw some insights which can be used to avoid the parametric
conflict while jointly maximizing both KPIs. We formulate the joint RSRP and
HOSR optimization problem, show that it is non-convex and solve it using the
genetic algorithm (GA). Comparison with the brute force-based results show that
the proposed data driven GA-aided solution is 48x faster with negligible loss
in optimality.


  Mobility edges (ME), i.e. critical energies which separate absolutely
continuous spectrum and purely point spectrum, is an important issue in quantum
physics. So far there are two experimentally feasible 1D quasiperiodic models
that have been discovered to have exact mobility edge. However, all the
theoretical studies have remained at the numerical level. In this paper, we
rigorously prove the existence and give the precise location of the MEs for
these models.


  We introduce an operator on classes of regular languages, the star-free
closure. Our motivation is to generalize standard results of automata theory
within a unified framework. Given an arbitrary input class $C$, the star-free
closure operator outputs the least class closed under Boolean operations and
language concatenation, and containing all languages of $C$ as well as all
finite languages. We establish several equivalent characterizations of
star-free closure: in terms of regular expressions, first-order logic, pure
future and future-past temporal logic, and recognition by finite monoids. A key
ingredient is that star-free closure coincides with another closure operator,
defined in terms of regular operations where Kleene stars are allowed in
restricted~contexts.
  A consequence of this first result is that we can decide membership of a
regular language in the star-free closure of a class whose separation problem
is decidable. Moreover, we prove that separation itself is decidable for the
star-free closure of any finite class, and of any class of group languages
having itself decidable separation (plus mild additional properties). We
actually show decidability of a stronger property, called covering.


  Two approaches are presented to coupling explicit Goldstone modes to $N_f$
flavors of massless quarks preserving exact $SU(N_f) \times SU(N_f)$ chiral
symmetry on the lattice. The first approach is a generalization a chiral
extension to QCD (aka XQCD) proposed by Brower, Shen and Tan consistent with
the Ginsparg-Wilson relation. The second approach based on the Callan,Coleman,
Wess and Zumino coset construction has a real determinant atzero quark axial
coupling, $g_A = 0$.


  Sampling-based motion planning is the predominant paradigm in many real-world
robotic applications, but its performance is immensely dependent on the quality
of the samples. The majority of traditional planners are inefficient as they
use uninformative sampling distributions as opposed to exploiting structures
and patterns in the problem to guide better sampling strategies. Moreover, most
current learning-based planners are susceptible to posterior collapse or mode
collapse due to the sparsity and highly varying nature of C-Space and motion
plan configurations. In this work, we introduce a conditional normalising flow
based distribution learned through previous experiences to improve sampling of
these methods. Our distribution can be conditioned on the current problem
instance to provide an informative prior for sampling configurations within
promising regions. When we train our sampler with an expert planner, the
resulting distribution is often near-optimal, and the planner can find a
solution faster, with less invalid samples, and less initial cost. The
normalising flow based distribution uses simple invertible transformations that
are very computationally efficient, and our optimisation formulation explicitly
avoids mode collapse in contrast to other existing learning-based planners.
Finally, we provide a formulation and theoretical foundation to efficiently
sample from the distribution; and demonstrate experimentally that, by using our
normalising flow based distribution, a solution can be found faster, with less
samples and better overall runtime performance.


  Power operations in the homology of infinite loop spaces, and $H_\infty$ or
$E_\infty$ ring spectra have a long history in Algebraic Topology. In the case
of ordinary mod p homology for a prime p, the power operations of Kudo, Araki,
Dyer and Lashof interact with Steenrod operations via the Nishida relations,
but for many purposes this leads to complicated calculations once iterated
applications of these functions are required.On the other hand, the homology
coaction turns out to provide tractable formulae better suited to exploiting
multiplicative structure.
  We show how to derive suitable formulae for the interaction between power
operations and homology coactions in a wide class of examples; our approach
makes crucial use of modern frameworks for spectra with well behaved smash
products. In the case of mod $p$ homology, our formulae extend those of Bisson
and Joyal to odd primes. We also show how to exploit our results in sample
calculations, and produce some apparently new formulae for the Dyer-Lashof
action on the dual Steenrod algebra.


  The solution to fine tuning is one of the principal motivations for
supersymmetry. However constraints on the parameter space of the Minimal
Supersymmetric Standard Model (MSSM) suggest it may also require fine tuning
(although to a much lesser extent). To compare this tuning with different
extensions of the Standard Model (including other supersymmetric models) it is
essential that we have a reliable, quantitative measure of tuning. We review
the measures of tuning used in the literature and propose an alternative
measure. We apply this measure to several toy models and the MSSM with some
intriguing results.


  To grow precisely aligned graphene on h-BN without metal catalyst is
extremely important, which allows for intriguing physical properties and
devices of graphene/h-BN hetero-structure to be studied in a controllable
manner. In this report, such hetero-structures were fabricated and investigated
by atomic resolution scanning probe microscopy. Moirre patterns are observed
and the sensitivity of moirre interferometry proves that the graphene grains
can align precisely with the underlying h-BN lattice within an error of less
than 0.05 degree. The occurrence of moirre pattern clearly indicates that the
graphene locks into h-BN via van der Waals epitaxy with its interfacial stress
greatly released. It is worthy to note that the edges of the graphene grains
are primarily oriented along the armchair direction. The field effect mobility
in such graphene flakes exceeds 20,000 cm2/V.s at ambient condition. This work
opens the door of atomic engineering of graphene on h-BN, and sheds light on
fundamental research as well as electronic applications based on graphene/h-BN
hetero-structure.


  We have investigated the nature and origin of the Fe K emission lines in
Mrk~205 using observations with {\it Suzaku} and {\it XMM-Newton}, aiming to
resolve the ambiguity between a broad emission line and multiple unresolved
lines of higher ionization. We detect the presence of a narrow Fe K$\alpha$
emission line along with a broad band Compton reflection hump at energies $E>10
\rm \, keV$. These are consistent with reflected emission of hard X-ray photons
off a Compton thick material of $N_{\rm H} \ge 2.15\times 10^{24} \rm cm^{-2}$.
In addition we detect a partially covering ionized absorption with ionization
parameter $\log(\xi/\rm erg\, cm\, s^{-1})=1.9_{-0.5}^{+0.1}$, column density
$N_{\rm H}=(5.6_{-1.9}^{+2.0})\times 10^{22}\rm cm^{-2}$ and a covering factor
of $0.22_{-0.06}^{+0.09}$. We detect the presence of emission arising out of
ionized disk reflection contributing in the soft and the hard X-rays
consistently in all the observations. We however, could not definitely
ascertain the presence of a relativistically broadened Fe line in the X-ray
spectra. Using relativistic reflection model, we found that the data are unable
to statistically distinguish between the scenarios when the super-massive black
hole is non-rotating and when it is maximally spinning. Using the disk
reflection model we also find that the accretion disk of the AGN may be
truncated at a distance $6R_{\rm G}<R<12R_{\rm G}$, which may suggest why there
may not be any broad Fe line. The Eddington rate of the source is low
($\lambda_{\rm Edd}=0.03$), which points to an inefficient accretion, possibly
due to a truncated disk.


  Using functional and harmonic analysis methods, we study Kazhdan sets in
topological groups which do not necessarily have Property (T). We provide a new
criterion for a generating subset $Q$ of a group $G$ to be a Kazhdan set; it
relies on the existence of a positive number $\varepsilon$ such that every
unitary representation of $G$ with a $(Q,\varepsilon )$-invariant vector has a
finite dimensional subrepresentation. Using this result, we give an
equidistribution criterion for a generating subset of $G$ to be a Kazhdan set.
In the case where $G=\mathbb{Z}$, this shows that if $(n_{k})_{k\ge 1}$ is a
sequence of integers such that $(e^{2i\pi \theta n_{k}})_{k\ge 1}$ is uniformly
distributed in the unit circle for all real numbers $\theta $ except at most
countably many, then $\{n_{k}\,;\,k\ge 1\}$ is a Kazhdan set in $\mathbb{Z}$ as
soon as it generates $\mathbb{Z}$. This answers a question of Y. Shalom from
[B.~Bekka, P.~de la~Harpe, A.~Valette, Kazhdan's property (T), Cambridge Univ.
Press, 2008]. We also obtain characterizations of Kazhdan sets in second
countable locally compact abelian groups, in the Heisenberg groups and in the
group $\textrm{Aff}_{+}(\mathbb{R})$. This answers in particular a question
from [B.~Bekka, P.~de la~Harpe, A.~Valette, Kazhdan's property (T), op. cit.].


  We construct Narain CFTs from self-dual codes on the finite field $F_p$
through even self-dual lattices for any prime $p>2$. Using this correspondence,
we can relate the spectral gap and the partition function of the CFT to the
error correction capability and the extended enumerator polynomial of the code.
In particular, we calculate specific spectral gaps of CFTs constructed from
codes and compare them with the largest spectral gap among all Narain CFTs.


  We obtain a new Liouville comparison principle for entire weak solutions
$(u,v)$ of semilinear parabolic second-order partial differential inequalities
of the form $$ u_t -{\mathcal L}u- |u|^{q-1}u\geq v_t -{\mathcal L}v-
|v|^{q-1}v (*) $$ in the half-space ${\mathbb S} = {\mathbb R}^1_+ \times
\mathbb R^n$. Here $n\geq 1$, $q>0$ and $$ {\mathcal
L}=\sum\limits_{i,j=1}^n\frac{\partial}{{\partial}x_i} [ a_{ij}(t, x)
\frac{\partial}{{\partial}x_j}],$$ where $a_{ij}(t,x)$, $i,j=1,...,n$, are
functions defined, measurable and locally bounded in $\mathbb S$, and such that
$a_{ij}(t,x)=a_{ji}(t,x)$ and $$ \sum_{i,j=1}^n a_{ij}(t,x)\xi_i\xi_j\geq 0 $$
for almost all $(t,x)\in \mathbb S$ and all $\xi \in \mathbb R^n$. The critical
exponents in the Liouville comparison principle obtained, which responsible for
the non-existence of non-trivial (i.e., such that $u\not \equiv v$) entire weak
solutions to (*) in $\mathbb S$, depend on the behaviour of the coefficients of
the operator $\mathcal L$ at infinity. As direct corollaries we obtain a new
Fujita comparison principle for entire weak solutions $(u,v)$ of the Cauchy
problem for the inequality (*), as well as new Liouville-type and Fujita-type
theorems for non-negative entire weak solutions $u$ of the inequality (*) in
the case when $v\equiv 0$. All the results obtained are new and sharp.


  We demonstrate through numerical simulations and a mean field calculation
that immiscible two-phase flow in a porous medium behaves effectively as a
Bingham viscoplastic fluid. This leads to a generalized Darcy equation where
the volumetric flow rate depends quadratically on an excess pressure difference
in the range of flow rates where the capillary forces compete with the viscous
forces. At higher rates, the flow is Newtonian.


  Accurate automatic evaluation metrics for open-domain dialogs are in high
demand. Existing model-based metrics for system response evaluation are trained
on human annotated data, which is cumbersome to collect. In this work, we
propose to use information that can be automatically extracted from the next
user utterance, such as its sentiment or whether the user explicitly ends the
conversation, as a proxy to measure the quality of the previous system
response. This allows us to train on a massive set of dialogs with weak
supervision, without requiring manual system turn quality annotations.
Experiments show that our model is comparable to models trained on human
annotated data. Furthermore, our model generalizes across both spoken and
written open-domain dialog corpora collected from real and paid users.


  The hadronic decay rate of the tau lepton serves as one of the most precise
determinations of the QCD coupling alpha_s. The dominant theoretical source of
uncertainty at present resides in the seeming disparity of two approaches to
improving the perturbative expansion with the help of the renormalisation
group, namely fixed-order and contour-improved perturbation theory. In this
work it is demonstrated that in fact both approaches yield compatible results.
However, the fixed-order series is found to oscillate around the
contour-improved result with an oscillation frequency of approximately six
perturbative orders, approaching it until about the 30th order, after which the
expansion reveals its asymptotic nature. Additionally, the renormalisation
scale and scheme dependencies of the perturbative series for the tau hadronic
width are investigated in detail.


  Heavy-to-light transition form factors at large recoil energy of the light
meson have been conjectured to obey a factorization formula, where the set of
form factors is reduced to a smaller number of universal form factors up to
hard-scattering corrections. In this paper we extend our previous investigation
of heavy-to-light currents in soft-collinear effective theory to final states
with invariant mass Lambda^2 as is appropriate to exclusive B meson decays. The
effective theory contains soft modes and two collinear modes with virtualities
of order m_b*Lambda (`hard-collinear') and Lambda^2. Integrating out the
hard-collinear modes results in the hard spectator-scattering contributions to
exclusive B decays. We discuss the representation of heavy-to-light currents in
the effective theory after integrating out the hard-collinear scale, and show
that the previously conjectured factorization formula is valid to all orders in
perturbation theory. The naive factorization of matrix elements in the
effective theory into collinear and soft matrix elements may be invalidated by
divergences in convolution integrals. In the factorization proof we circumvent
the explicit regularization of endpoint divergences by a definition of the
universal form factors that includes hard-collinear, collinear and soft
effects.


  The paper describes the observations and first results of studying the
mesosphere temperature and dust based on twilight wide-field polarization
analysis using original all-sky camera started in 2015 in Apatity, northern
Russia (67.6 deg N, 33.4 deg E). It is the first twilight polarization
measurements session conducted in the polar region and the first measurements
during the winter and early spring season. The general polarization properties
of twilight sky and the separation procedure of single scattering are
described. The Boltzmann temperature decrease above 70 km and lack of
mesosphere dust that is typical for this season are the key results of the
study.


  We examine the evolution of the IGM Ly-alpha optical depth distribution using
the transmitted flux probability distribution function (PDF) in a sample of 63
QSOs spanning absorption redshifts 1.7 < z < 5.8. The data are compared to two
theoretical optical depth distributions: a model distribution based on the
density distribution of Miralda-Escude et al. (2000) (MHR00), and a lognormal
distribution. We assume a uniform UV background and an isothermal IGM for the
MHR00 model, as has been done in previous works. Under these assumptions, the
MHR00 model produces poor fits to the observed flux PDFs at redshifts where the
optical depth distribution is well sampled, unless large continuum corrections
are applied. However, the lognormal optical depth distribution fits the data at
all redshifts with only minor continuum adjustments. We use a simple
parametrization for the evolution of the lognormal parameters to calculate the
expected mean transmitted flux at z > 5.4. The lognormal optical depth
distribution predicts the observed Ly-alpha and Ly-beta effective optical
depths at z > 5.7 while simultaneously fitting the mean transmitted flux down
to z = 1.6. If the evolution of the lognormal distribution at z < 5 reflects a
slowly-evolving density field, temperature, and UV background, then no sudden
change in the IGM at z ~ 6 due to late reionization appears necessary. We have
used the lognormal optical depth distribution without any assumption about the
underlying density field. If the MHR00 density distribution is correct, then a
non-uniform UV background and/or IGM temperature may be required to produce the
correct flux PDF. We find that an inverse temperature-density relation greatly
improves the PDF fits, but with a large scatter in the equation of state index.
[Abridged]


  Among many Bechgaard salts, TMTSF2NO3 exhibits very anomalous low temperature
properties. Unlike conventional spin density wave (SDW), TMTSF2NO3 undergoes
the SDW transition at $\T_SDW\approx 9.5$ K and the low temperature
quasiparticle excitations are gapless. Also, it is known that TMTSF2NO3 does
not exhibit superconductivity even under pressure, while FISDW is found in
TMTSF2NO3 only for P=8.5 kbar and B>20 T. Here we shall show that both the
angle dependent magnetoresistance data and the nonlinear Hall resistance of
TMTSF2NO3 at ambient pressure are interpreted satisfactory in terms of
unconventional spin density wave (USDW). Based on these facts, we propose a new
phase diagram for Bechgaards salts.