  The pretrain+fine-tune paradigm is foundational in deploying large language
models (LLMs) across a diverse range of downstream applications. Among these,
Low-Rank Adaptation (LoRA) stands out for its parameter-efficient fine-tuning
(PEFT), producing numerous off-the-shelf task-specific LoRA adapters. However,
this approach requires explicit task intention selection, posing challenges for
automatic task sensing and switching during inference with multiple existing
LoRA adapters embedded in a single LLM. In this work, we introduce MeteoRA
(Multiple-Tasks embedded LoRA), a scalable multi-knowledge LoRA fusion
framework designed for LLMs. MeteoRA integrates various LoRA adapters in a
Mixture-of-Experts (MoE) style into the base LLM, enabling the model to
automatically select the most pertinent adapter based on the task input. This
advancement significantly enhances the LLM's capability to handle composite
tasks that require different adapters to solve various components of the
problem. Our evaluations, featuring the LlaMA2-13B and LlaMA3-8B base models
equipped with off-the-shelf 28 LoRA adapters through MeteoRA, demonstrate
equivalent performance with the individual adapters. Furthermore, both base
models equipped with MeteoRA achieve superior performance in sequentially
solving composite tasks with ten problems in only a single inference process,
highlighting the ability of timely intention switching in MeteoRA embedded
LLMs.


  We present a novel longitudinal multimodal corpus of physiological and
behavioral data collected from direct clinical providers in a hospital
workplace. We designed the study to investigate the use of off-the-shelf
wearable and environmental sensors to understand individual-specific constructs
such as job performance, interpersonal interaction, and well-being of hospital
workers over time in their natural day-to-day job settings. We collected
behavioral and physiological data from $n = 212$ participants through
Internet-of-Things Bluetooth data hubs, wearable sensors (including a
wristband, a biometrics-tracking garment, a smartphone, and an audio-feature
recorder), together with a battery of surveys to assess personality traits,
behavioral states, job performance, and well-being over time. Besides the
default use of the data set, we envision several novel research opportunities
and potential applications, including multi-modal and multi-task behavioral
modeling, authentication through biometrics, and privacy-aware and
privacy-preserving machine learning.


  Since the discovery of differential calculus by Newton and Leibniz and the
subsequent continuous growth of its applications to physics, mechanics,
geometry, etc, it was observed that partial derivatives in the study of various
natural problems are (self-)organized in certain structures usually called
geometric. Tensors, connections, jets, etc, are commonly known examples of
them. This list of classical geometrical structures is sporadically and
continuously widening. For instance, Lie algebroids and BV-bracket are popular
recent additions into it. Our goal is to show that the "zoo" of all geometrical
structures has a common source in the calculus of functors of differential
calculus over commutative algebras, which surprisingly comes from a due
mathematical formalization of observability mechanism in classical physics. We
also use this occasion for some critical remarks and discussion of some
perspectives.


  Particle filters (PFs) are powerful sampling-based inference/learning
algorithms for dynamic Bayesian networks (DBNs). They allow us to treat, in a
principled way, any type of probability distribution, nonlinearity and
non-stationarity. They have appeared in several fields under such names as
"condensation", "sequential Monte Carlo" and "survival of the fittest". In this
paper, we show how we can exploit the structure of the DBN to increase the
efficiency of particle filtering, using a technique known as
Rao-Blackwellisation. Essentially, this samples some of the variables, and
marginalizes out the rest exactly, using the Kalman filter, HMM filter,
junction tree algorithm, or any other finite dimensional optimal filter. We
show that Rao-Blackwellised particle filters (RBPFs) lead to more accurate
estimates than standard PFs. We demonstrate RBPFs on two problems, namely
non-stationary online regression with radial basis function networks and robot
localization and map building. We also discuss other potential application
areas and provide references to some finite dimensional optimal filters.


  We use an updated version of {\it SimProp}, a Monte Carlo simulation scheme
for the propagation of ultra-high energy cosmic rays, to compute cosmogenic
neutrino fluxes expected on Earth in various scenarios. These fluxes are
compared with the newly detected IceCube events at PeV energies and with recent
experimental limits at EeV energies of the Pierre Auger Observatory. This
comparison allows us to draw some interesting conclusions about the source
models for ultra-high energy cosmic rays. We will show how the available
experimental observations are almost at the level of constraining such models,
mainly in terms of the injected chemical composition and cosmological evolution
of sources. The results presented here will also be important in the evaluation
of the discovery capabilities of the future planned ultra-high energy cosmic
ray and neutrino observatories.


  The article concerns the subalgebra U_v^+(w) of the quantized universal
enveloping algebra of the complex Lie algebra sl_{n+1} associated with a
particular Weyl group element of length 2n. We verify that U_v^+(w) can be
endowed with the structure of a quantum cluster algebra of type A_n. The
quantum cluster algebra is a deformation of the ordinary cluster algebra
Geiss-Leclerc-Schroeer attached to w using the representation theory of the
preprojective algebra. Furthermore, we prove that the quantum cluster variables
are, up to a power of v, elements in the dual of Lusztig's canonical basis
under Kashiwara's bilinear form.


  The proposed numerical method, "FLAME-slab," solves electromagnetic wave
scattering problems for aperiodic slab structures by exploiting short-range
regularities in these structures. The computational procedure involves special
difference schemes with high accuracy even on coarse grids. These schemes are
based on Trefftz approximations, utilizing functions that locally satisfy the
governing differential equations, as is done in the Flexible Local
Approximation Method (FLAME). Radiation boundary conditions are implemented via
Fourier expansions in the air surrounding the slab. When applied to ensembles
of slab structures with identical short-range features, such as amorphous or
quasicrystalline lattices, the method is significantly more efficient, both in
runtime and in memory consumption, than traditional approaches. This efficiency
is due to the fact that the Trefftz functions need to be computed only once for
the whole ensemble.


  We study the magnetohydrostatic equilibrium of magnetic flux tubes with
circular cross sections embedded in a magnetic surrounding atmosphere. We solve
the static momentum equation in 2.5D to obtain the thermodynamics that are
consistent with a prescribed velocity and magnetic fields. We show that force
balance is roughly satisfied if the flux tube's magnetic field is aligned with
its axis. Equilibrium is guaranteed if this magnetic field possesses a
transverse component. Several forms of this transverse field are investigated.
The resulting magnetic field configurations are critically reviewed in terms of
the results from spectropolarimetric observations. The thermodynamic structure
that allows the flux tube to be in mechanical equilibrium is also calculated.
We show that the inferred pressure, density and temperature stratification
reproduce intensity features similar to dark core penumbral filaments and
penumbral grains.


  This paper analyses the set of iris codes stored or used in an iris
recognition system as an f-granular space. The f-granulation is given by
identifying in the iris code space the extensions of the fuzzy concepts wolves,
goats, lambs and sheep (previously introduced by Doddington as 'animals' of the
biometric menagerie) - which together form a partitioning of the iris code
space. The main question here is how objective (stable / stationary) this
partitioning is when the iris segments are subject to noisy acquisition. In
order to prove that the f-granulation of iris code space with respect to the
fuzzy concepts that define the biometric menagerie is unstable in noisy
conditions (is sensitive to noise), three types of noise (localvar, motion
blur, salt and pepper) have been alternatively added to the iris segments
extracted from University of Bath Iris Image Database. The results of 180
exhaustive (all-to-all) iris recognition tests are presented and commented
here.


  Traditional Time Delay Neural Networks (TDNN) have achieved state-of-the-art
performance at the cost of high computational complexity and slower inference
speed, making them difficult to implement in an industrial environment. The
Densely Connected Time Delay Neural Network (D-TDNN) with Context Aware Masking
(CAM) module has proven to be an efficient structure to reduce complexity while
maintaining system performance. In this paper, we propose a fast and
lightweight model, LightCAM, which further adopts a depthwise separable
convolution module (DSM) and uses multi-scale feature aggregation (MFA) for
feature fusion at different levels. Extensive experiments are conducted on
VoxCeleb dataset, the comparative results show that it has achieved an EER of
0.83 and MinDCF of 0.0891 in VoxCeleb1-O, which outperforms the other
mainstream speaker verification methods. In addition, complexity analysis
further demonstrates that the proposed architecture has lower computational
cost and faster inference speed.


  A Kinetic Inductance Traveling Wave amplifier (KIT) utilizes the nonlinear
kinetic inductance of superconducting films, particularly Niobium Titanium
Nitride (NbTiN), for parametric amplification. These amplifiers achieve
remarkable performance in terms of gain, bandwidth, compression power, and
frequently approach the quantum limit for noise. However, most KIT
demonstrations have been isolated from practical device readout systems. Using
a KIT as the first amplifier in the readout chain of an unoptimized microwave
SQUID multiplexer coupled to a transition-edge sensor microcalorimeter we see
an initial improvement in the flux noise. One challenge in KIT integration is
the considerable microwave pump power required to drive the non-linearity. To
address this, we have initiated efforts to reduce the pump power by using
thinner NbTiN films and an inverted microstrip transmission line design. In
this article, we present the new transmission line design, fabrication
procedure, and initial device characterization -- including gain and added
noise. These devices exhibit over 10 dB of gain with a 3 dB bandwidth of
approximately 5.5-7.25 GHz, a maximum practical gain of 12 dB and typical gain
ripple under 4 dB peak-to-peak. We observe an appreciable impedance mismatch in
the NbTiN transmission line, which is likely the source of the majority of the
gain ripple. Finally we perform an initial noise characterization and
demonstrate system-added noise of three quanta or less over nearly the entire 3
dB bandwidth.


  The antidynamical Casimir effect (ADCE) is a term coined to designate the
coherent annihilation of excitations due to resonant external perturbation of
system parameters, allowing for extraction of quantum work from nonvacuum
states of some field. Originally proposed for a two-level atom (qubit) coupled
to a single cavity mode in the context of nonstationary quantum Rabi model, it
suffered from very low transition rate and correspondingly narrow resonance
linewidth. In this paper we show analytically and numerically that the ADCE
rate can be increased by at least one order of magnitude by replacing the qubit
by an artificial three-level atom (qutrit) in a properly chosen configuration.
For the cavity thermal state we demonstrate that the dynamics of the average
photon number and atomic excitation is completely different from the qubit's
case, while the behavior of the total number of excitations is qualitatively
similar yet significantly faster.


  It is commonly assumed that if the optical metric of a dielectric medium is
identical to the metric of a vacuum space-time then light propagation through
the dielectric mimics light propagation in the vacuum. However, just as the
curved surface of the Earth cannot be mapped into a flat plane without
distortion of some surface features, so too is it impossible to project the
behavior of light from the vacuum into a dielectric analog residing in
Minkowski space-time without introducing distortions. We study the covariance
properties of dielectric analog space-times and the kinematics of a congruence
of light in the analog, and show how certain features can be faithfully
emulated in the analog depending on the choice of projection, but that not all
features can be simultaneously emulated without distortion. These findings
indicate conceptual weaknesses in the idea of using analog space-times as a
basis for transformation optics, and we show that a certain formulation of
transformation optics closely related to analog space-times resolves these
issues.


  The theory of self-adjoint extensions of first and second order elliptic
differential operators on manifolds with boundary is studied via its most
representative instances: Dirac and Laplace operators.
  The theory is developed by exploiting the geometrical structures attached to
them and, by using an adapted Cayley transform on each case, the space
$\mathcal{M}$ of such extensions is shown to have a canonical group composition
law structure.
  The obtained results are compared with von Neumann's Theorem characterising
the self-adjoint extensions of densely defined symmetric operators on Hilbert
spaces. The 1D case is thoroughly investigated.
  The geometry of the submanifold of elliptic self-adjoint extensions
$\mathcal{M}_\mathrm{ellip}$ is studied and it is shown that it is a Lagrangian
submanifold of the universal Grassmannian $\mathbf{Gr}$. The topology of
$\mathcal{M}_\mathrm{ellip}$ is also explored and it is shown that there is a
canonical cycle whose dual is the Maslov class of the manifold. Such cycle,
called the Cayley surface, plays a relevant role in the study of the phenomena
of topology change.
  Self-adjoint extensions of Laplace operators are discussed in the path
integral formalism, identifying a class of them for which both treatments leads
to the same results.
  A theory of dissipative quantum systems is proposed based on this theory and
a unitarization theorem for such class of dissipative systems is proved.
  The theory of self-adjoint extensions with symmetry of Dirac operators is
also discussed and a reduction theorem for the self-adjoint elliptic
Grasmmannian is obtained.
  Finally, an interpretation of spontaneous symmetry breaking is offered from
the point of view of the theory of self-adjoint extensions.


  Though impressive performance has been achieved in specific visual realms
(e.g. faces, dogs, and places), an omni-vision representation generalizing to
many natural visual domains is highly desirable. But, existing benchmarks are
biased and inefficient to evaluate the omni-vision representation -- these
benchmarks either only include several specific realms, or cover most realms at
the expense of subsuming numerous datasets that have extensive realm
overlapping. In this paper, we propose Omni-Realm Benchmark (OmniBenchmark). It
includes 21 realm-wise datasets with 7,372 concepts and 1,074,346 images.
Without semantic overlapping, these datasets cover most visual realms
comprehensively and meanwhile efficiently. In addition, we propose a new
supervised contrastive learning framework, namely Relational Contrastive
learning (ReCo), for a better omni-vision representation. Beyond pulling two
instances from the same concept closer -- the typical supervised contrastive
learning framework -- ReCo also pulls two instances from the same semantic
realm closer, encoding the semantic relation between concepts, and facilitating
omni-vision representation learning. We benchmark ReCo and other advances in
omni-vision representation studies that are different in architectures (from
CNNs to transformers) and in learning paradigms (from supervised learning to
self-supervised learning) on OmniBenchmark. We illustrate the superior of ReCo
to other supervised contrastive learning methods and reveal multiple practical
observations to facilitate future research.


  The dramatic slowdown of glass-forming liquids has been variously linked to
increasing dynamic and static correlation lengths. Yet, empirical evidence is
insufficient to decide among competing theories. The random first order theory
(RFOT) links the dynamic slowdown to the growth of amorphous static order,
whose range depends on a balance between configurational entropy and surface
tension. This last quantity is expected to vanish when the temperature
surpasses a spinodal point beyond which there are no metastable states. Here we
measure for the first time the surface tension in a model glass-former, and
find that it vanishes at the energy separating minima from saddles,
demonstrating the existence of a spinodal point for amorphous metastable order.
Moreover, the fluctuations of surface tension become smaller for lower
temperatures, in quantitative agreement with recent theoretical speculation
that spatial correlations in glassy systems relax nonexponentially because of
the narrowing of the surface tension distribution.


  The strongest type of coloring of pairs of countable ordinals, gotten by
Todorcevic from a strongly Luzin set, is shown to be equivalent to the
existence of a nonmeager set of reals of size $\aleph_1$. In the other
direction, it is shown that the existence of both a strongly Luzin set and a
coherent Souslin tree is compatible with the existence of a countable partition
of pairs of countable ordinals such that no coloring is strong over it.
  This clarifies the interaction between a gallery of coloring assertions going
back to Luzin and Sierpinski a hundred years ago.


  With N-body simulations of a planetary system with an asteroid belt we
investigate how the asteroid impact rate on the Earth is affected by the
architecture of the planetary system. We find that the $\nu_6$ secular
resonance plays an important role in the asteroid collision rate with the
Earth. Compared to exoplanetary systems, the solar system is somewhat special
in its lack of a super-Earth mass planet in the inner solar system. We
therefore first consider the effects of the presence of a super-Earth in the
terrestrial planet region. We find a significant effect for super-Earths with a
mass of around $10\,\rm M_\oplus$ and a separation greater than about $0.7\,\rm
AU$. For a super-Earth that is interior to the Earth's orbit, the number of
asteroids colliding with Earth increases the closer the super-Earth is to the
Earth's orbit. This is the result of multiple secular resonance locations
causing more asteroids to be perturbed onto Earth-crossing orbits. When the
super-Earth is placed exterior to Earth's orbit, the collision rate decreases
substantially because the $\nu_6$ resonance no longer exists in the asteroid
belt region. We also find that changing the semi-major axis of Saturn leads to
a significant decrease in the asteroid collision rate, while increasing its
mass increases the collision rate. These results may have implications for the
habitability of exoplanetary systems.


  We prove two results that together strongly suggest that obtaining a positive
answer to the Navier-Stokes global regularity question requires more than a
refinement of partial regularity theory. First we prove that there exists a
class of bilinear operators $\mathfrak{B}$, which contains the Euler bilinear
operator $\mathcal{E}(u,v):=\frac{1}{2}\mathbb{P}(u\cdot\nabla v + v\cdot\nabla
u)$, such that for any $B\in \mathfrak{B}$, $n\geq2$, $\alpha \in (1/2,
(n+2)/4)$, and smooth solution $u$ of the pseudodifferential equation
$\partial_t u +(-\Delta)^\alpha u +B(u,u)=0$ on $\mathbb{R}^n\times [0,T)$, we
have that $u$ is also smooth at time $T$ away from a closed set of Hausdorff
dimension at most $n+2-4\alpha$. Next we prove that, for the Euclidean space
$\mathbb{R}^3$, there exists an operator $C(u,v)\in \mathfrak{B}$ that is an
averaged version of $\mathcal{E}$, that formally allows the dissipation of
energy by the "cancellation identity" $\langle C(u,u), u\rangle =0$, and whose
corresponding pseudodifferential equation $\partial_t u +(-\Delta)^\alpha u
+C(u,u)=0$ admits a solution that blows up in finite time for all $\alpha \in
(1/2,5/4)$.


  We investigate the spectral distribution of the twisted Laplacian associated
with uniform square-integrable bounded harmonic 1-form on typical hyperbolic
surfaces of high genus. First, we estimate the spectral distribution by the
supremum norm of the corresponding harmonic form. Subsequently, we show that
the square-integrable bounded harmonic form exhibits a small supremum norm for
typical hyperbolic surfaces of high genus. Based on these findings, we prove a
uniform Weyl law for the distribution of real parts of the spectrum on typical
hyperbolic surfaces.


  Levitation of objects with action at a distance has always been intriguing to
humans. Several ways to achieve this, such as aerodynamic, acoustic, or
electromagnetic methods, including radiation pressure, stable potential wells,
and quantum Casimir-Lifshitz forces, exist. A fascinating approach for
levitation is that of magnets over superconductors based on the Meissner effect
-the expulsion of the magnetic field by a superconductor. With the advent of
metamaterials -designed structures with electromagnetic properties that may not
be found in nature- we ask whether a material may be conceived exhibiting
similar field expulsion, but involving the electric field. We show how a
special subcategory of metamaterials, called epsilon-near-zero materials,
exhibits such electric classic analog to the Meissner effect, exerting a
repulsion on nearby sources. Repulsive forces using anisotropic and chiral
metamaterials have been investigated, but our proposal uses a different
mechanism based on field expulsion, and is very robust to both losses and
material dispersion.


  We introduce DeepNash, an autonomous agent capable of learning to play the
imperfect information game Stratego from scratch, up to a human expert level.
Stratego is one of the few iconic board games that Artificial Intelligence (AI)
has not yet mastered. This popular game has an enormous game tree on the order
of $10^{535}$ nodes, i.e., $10^{175}$ times larger than that of Go. It has the
additional complexity of requiring decision-making under imperfect information,
similar to Texas hold'em poker, which has a significantly smaller game tree (on
the order of $10^{164}$ nodes). Decisions in Stratego are made over a large
number of discrete actions with no obvious link between action and outcome.
Episodes are long, with often hundreds of moves before a player wins, and
situations in Stratego can not easily be broken down into manageably-sized
sub-problems as in poker. For these reasons, Stratego has been a grand
challenge for the field of AI for decades, and existing AI methods barely reach
an amateur level of play. DeepNash uses a game-theoretic, model-free deep
reinforcement learning method, without search, that learns to master Stratego
via self-play. The Regularised Nash Dynamics (R-NaD) algorithm, a key component
of DeepNash, converges to an approximate Nash equilibrium, instead of 'cycling'
around it, by directly modifying the underlying multi-agent learning dynamics.
DeepNash beats existing state-of-the-art AI methods in Stratego and achieved a
yearly (2022) and all-time top-3 rank on the Gravon games platform, competing
with human expert players.


  The presence of losses in nonlinear photonic structures is a crucial issue
for modern applications. Active parts are introduced for wave power
compensation resulting in unbalanced gain and loss landscapes where localized
beam propagation is, in general, dynamically unstable. Here we provide generic
sufficient conditions for the relation between the gain-loss and the refractive
index profiles in order to ensure efficient wave trapping and stable
propagation for a wide range of beam launching conditions such as initial
power, angle of incidence and position. The stability is a consequence of an
underlying dynamic power balance mechanism related to a conserved quantity of
wave dynamics.


  Successful cyber attacks on power systems cause severe disruptions. One
possible manipulation strategy is the utilization of distributed energy
resources (DERs) to disturb power system operation. In addition to the impact
on bulk power system frequency, local cascading effects caused by DER control
and protection can increase the severity of this strategy. To investigate these
effects, manipulation scenarios including the disconnection as well as the
manipulation of active (P) and reactive power (Q) setpoints of DERs are
derived. The impact is analyzed using time-domain simulations and quantified
using assessment criteria such as voltage band violation and plant protection
triggering. Though DER disconnection leads to high amounts of lost P injection
the manipulation of Q setpoints offers potential to disconnect additional DERs
through local cascading effects. To mitigate the impact of the manipulation
scenarios automated tap changer operation as well as a limitation of remotely
accessible Q is suitable.


  In this work we discuss a parameter $\sigma$ on weighted $k$-element
multisets of $[n]= \{1,\dots ,n\}$. The sums of weighted $k$-multisets are
related to $k$-subsets, $k$-multisets, as well as special instances of
truncated interpolated multiple zeta values. We study properties of this
parameter using symbolic combinatorics. We rederive and extend certain
identities for $\zeta^{t}_n(\{m\}_k)$. Moreover, we introduce random variables
on the $k$-element multisets and derive their distributions, as well as limit
laws for $k$ or $n$ tending to infinity.


  Based on first principles calculations we investigate the electronic and
magnetic properties of Pt layers in Pd$(001)$/Co/Pt thin film structures
exposed to an external electric field. Due to the Co underlayer, the surface Pt
layers have induced moments that are modified by an external electric field.
The field induced changes can be explained by the modified spin-dependent
orbital hybridization that varies non-linearly with the field strength. We
calculate the x-ray absorption and the x-ray magnetic circular dichroism
spectra for an applied external electric field and examine its impact on the
spectra in the Pt layer around the L$_{2}$ and L$_{3}$ edges. We also determine
the layer dependent magneto-crystalline anisotropy and show that the anisotropy
can be tuned easily in the different layers by the external electric field.


  Rumour is a collective emergent phenomenon with a potential for provoking a
crisis. Modelling approaches have been deployed since five decades ago;
however, the focus was mostly on epidemic behaviour of the rumours which does
not take into account the differences of the agents. We use social practice
theory to model agent decision making in organizational rumourmongering. Such
an approach provides us with an opportunity to model rumourmongering agents
with a layer of cognitive realism and study the impacts of various intervention
strategies for prevention and control of rumours in organizations.


  Repeated reading (RR) helps learners, who have little to no experience with
reading fluently to gain confidence, speed and process words automatically. The
benefits of repeated readings include helping all learners with fact recall,
aiding identification of learners' main ideas and vocabulary, increasing
comprehension, leading to faster reading as well as increasing word recognition
accuracy, and assisting struggling learners as they transition from
word-by-word reading to more meaningful phrasing. Thus, RR ultimately helps in
improvements of learners' oral fluency and narrative production. However, there
are no open audio datasets available on oral responses of learners based on
their RR practices. Therefore, in this paper, we present our dataset, discuss
its properties, and propose a method to assess oral fluency and narrative
production for learners of English using acoustic, prosodic, lexical and
syntactical characteristics. The results show that a CALL system can be
developed for assessing the improvements in learners' oral fluency and
narrative production.


  Recent progress on salient object detection (SOD) mainly benefits from
multi-scale learning, where the high-level and low-level features collaborate
in locating salient objects and discovering fine details, respectively.
However, most efforts are devoted to low-level feature learning by fusing
multi-scale features or enhancing boundary representations. High-level
features, which although have long proven effective for many other tasks, yet
have been barely studied for SOD. In this paper, we tap into this gap and show
that enhancing high- level features is essential for SOD as well. To this end,
we introduce an Extremely-Downsampled Network (EDN), which employs an extreme
downsampling technique to effectively learn a global view of the whole image,
leading to accurate salient object localization. To accomplish better
multi-level feature fusion, we construct the Scale-Correlated Pyramid
Convolution (SCPC) to build an elegant decoder for recovering object details
from the above extreme downsampling. Extensive experiments demonstrate that EDN
achieves state-of-the-art performance with real-time speed. Our efficient
EDN-Lite also achieves competitive performance with a speed of 316fps. Hence,
this work is expected to spark some new thinking in SOD. Code is available at
https://github.com/yuhuan-wu/EDN.


  One of the major challenges in studying the cosmic evolution of relativistic
jets is the identification of the high-redshift ($z>3$) BL Lacertae objects, a
class of jetted active galactic nuclei characterized by their quasi-featureless
optical spectra. Here we report the identification of the first $\gamma$-ray
emitting BL Lac object, 4FGL~J1219.0+3653 (J1219), beyond $z=3$, i.e., within
the first two billion years of the age of the Universe. The optical and
near-infrared spectra of J1219 taken from 10.4 m Gran Telescopio Canarias
exhibit no emission lines down to an equivalent width of $\sim$3.5 A supporting
its BL Lac nature. The detection of a strong Lyman-$\alpha$ break at $\sim$5570
A, on the other hand, confirms that J2119 is indeed a high-redshift
($z\sim3.59$) quasar. Based on the prediction of a recent BL Lac evolution
model, J1219 is one of the only two such objects expected to be present within
the comoving volume at $z=3.5$. Future identifications of more $z>3$
$\gamma$-ray emitting BL Lac sources, therefore, will be crucial to verify the
theories of their cosmic evolution.


  The behavior of a newly introduced overlap parameter is analyzed, measuring
the correlation between intensity fluctuations of waves in random media in
different physical regimes, with varying amount of disorder and non-linearity.
Its relationship is established to the standard Parisi overlap order parameter
in replica theory for spin-glasses. In the complex spherical spin-glass model,
describing the onset and behavior of random lasers, replica symmetry breaking
in the intensity fluctuation overlap is shown to occur at high pumping or low
temperature. This order parameter identifies the laser transition in random
media and describes its glassy nature in terms of emission spectra data, the
only data so far accessible in random laser measurements. The theoretical
analysis is, eventually, compared to recent intensity fluctuation overlap
measurements demonstrating the validity of the theory and providing a
straightforward interpretation of different spectral behaviors in different
random lasers.


  We demonstrate experimentally an optical system for under-sampling several
bandwidth limited signals with carrier frequencies that are not known apriori
that can be located anywhere within a very broad frequency region between 0-18
GHz. The system is based on under-sampling asynchronously at three different
sampling rates. The pulses required for the under-sampling are generated by a
combination of an electrical comb generator and an electro-absorption
modulator. To reduce loss and improve performance the implementation of the
optical system is based on a wavelength division multiplexing technique. An
accurate reconstruction of both the phase and the amplitude of the signals was
obtained when two chirped signals generated simultaneously were sampled.


  In this paper, we study the influence of the selective pressure on the
performance of cellular genetic algorithms. Cellular genetic algorithms are
genetic algorithms where the population is embedded on a toroidal grid. This
structure makes the propagation of the best so far individual slow down, and
allows to keep in the population potentially good solutions. We present two
selective pressure reducing strategies in order to slow down even more the best
solution propagation. We experiment these strategies on a hard optimization
problem, the quadratic assignment problem, and we show that there is a value
for of the control parameter for both which gives the best performance. This
optimal value does not find explanation on only the selective pressure,
measured either by take over time and diversity evolution. This study makes us
conclude that we need other tools than the sole selective pressure measures to
explain the performances of cellular genetic algorithms.


  For an abelian category C and a filtrant preordered set Lambda, we prove that
the derived category of the quasi-abelian category of filtered objects in C
indexed by Lambda is equivalent to the derived category of the abelian category
of functors from Lambda to C. We apply this result to the study of the category
of filtered modules over a filtered ring in a tensor category.


  We have assumed the FRW universe in loop quantum cosmology (LQC) model filled
with the dark matter and the Generalized Cosmic Chaplygin gas (GCCG) type dark
energy where dark matter follows the linear equation of state. We present the
Hubble parameter in terms of the observable parameters $\Omega_{m0}$ and
$H_{0}$ with the redshift $z$ and the other parameters like $A$, $B$, $w_{m}$,
$ \omega$ and $\alpha$ which coming from our model. From Stern data set (12
points)\& SNe Type Ia 292 data (from \cite{Riess1,Riess2,Astier}) we have
obtained the bounds of the arbitrary parameters by minimizing the $\chi^{2}$
test. The best-fit values of the parameters are obtained by 66\%, 90\% and 99\%
confidence levels. Next due to joint analysis with Stern+BAO and Stern+BAO+CMB
observations, we have also obtained the bounds of the parameters ($A,B$) by
fixing some other parameters $\alpha$, $w_{m}$ and $\omega$. From the best fit
values of the parameters, we have obtained the distance modulus $\mu(z)$ for
our theoretical GCCG model in LQC and from Supernovae Type Ia (union2 sample
552 data from [\cite{Amanullah}] \& Riess 292 data from
[\cite{Riess1,Riess2,Astier}]), we have concluded that our model is in
agreement with the Supernovae Type Ia sample data. In addition, we have
investigated in details about the various types of Future Singularities that
may be formed in this model and it is notable that our model is completely free
from any types of future singularities.


  Affine su(3) and su(4) fusion multiplicities are characterised as discretised
volumes of certain convex polytopes. The volumes are measured explicitly,
resulting in multiple sum formulas. These are the first polytope-volume
formulas for higher-rank fusion multiplicities. The associated threshold levels
are also discussed. For any simple Lie algebra we derive an upper bound on the
threshold levels using a refined version of the Gepner-Witten depth rule.


  We consider the so-called simplest correlation function of four infinitely
heavy half-BPS operators in planar N=4 SYM in the limit when the operators are
light-like separated in a sequential manner. We find a closed-form expression
for the correlation function in this limit as a function of the 't Hooft
coupling and residual cross ratios. Our analysis heavily relies on the
factorization of the correlation function into the product of null octagons and
on the recently established determinant representation for the latter. We show
that the null octagon is given by a Fredholm determinant of a certain integral
operator which has a striking similarity to those previously encountered in the
study of two-point correlation functions in exactly solvable models at finite
temperature and of level spacing distributions for random matrices. This allows
us to compute the null octagon exactly by employing a method of differential
equations.


  An inifinite-dimensional representation of the double affine Hecke algebra of
rank 1 and type $(C_1^{\vee},C_1)$ in which all generators are tridiagonal is
presented. This representation naturally leads to two systems of polynomials
that are orthogonal on the unit circle. These polynomials can be considered as
circle analogs of the Askey-Wilson polynomials. The corresponding polynomials
orthogonal on an interval are constructed and discussed.


  AMD Xilinx's new Versal Adaptive Compute Acceleration Platform (ACAP) is an
FPGA architecture combining reconfigurable fabric with other on-chip hardened
compute resources. AI engines are one of these and, by operating in a highly
vectorized manner, they provide significant raw compute that is potentially
beneficial for a range of workloads including HPC simulation. However, this
technology is still early-on, and as yet unproven for accelerating HPC codes,
with a lack of benchmarking and best practice.
  This paper presents an experience report, exploring porting of the Piacsek
and Williams (PW) advection scheme onto the Versal ACAP, using the chip's AI
engines to accelerate the compute. A stencil-based algorithm, advection is
commonplace in atmospheric modelling, including several Met Office codes who
initially developed this scheme. Using this algorithm as a vehicle, we explore
optimal approaches for structuring AI engine compute kernels and how best to
interface the AI engines with programmable logic. Evaluating performance using
a VCK5000 against non-AI engine FPGA configurations on the VCK5000 and Alveo
U280, as well as a 24-core Xeon Platinum Cascade Lake CPU and Nvidia V100 GPU,
we found that whilst the number of channels between the fabric and AI engines
are a limitation, by leveraging the ACAP we can double performance compared to
an Alveo U280.


  The geoid is the true physical figure of the Earth, a particular
equipotential surface of the gravity field of the Earth that accounts for the
effect of all subsurface density variations. Its shape approximates best (in
the sense of least squares) the mean level of oceans, but the geoid is more
difficult to determine over continents. Satellite missions carry out distance
measurements and derive the gravity field to provide geoid maps over the entire
globe. However, they require calibration and extensive computations including
integration, which is a non-unique operation. Here we propose a direct method
and a new tool that directly measures geopotential differences on continents
using atomic clocks. General Relativity Theory predicts constant clock rate at
sea level, and faster (resp. slower) clock rate above (resp. below) sea level.
The technology of atomic clocks is on the doorstep of reaching an accuracy
level in clock rate that is equivalent to 1 cm in determining equipotential
surface (including geoid) height. We discuss the value and future applicability
of such measurements including direct geoid mapping on continents, and joint
gravity and geopotential surveying to invert for subsurface density anomalies.
Our synthetic calculations show that the geoid perturbation caused by a 1.5 km
radius sphere with 20% density anomaly buried at 2 km depth in the crust of the
Earth is already detectable by atomic clocks of achievable accuracy. Therefore
atomic clock geopotential surveys, used together with relative gravity data to
benefit from their different depth sensitivities, can become a useful tool in
mapping density anomalies within the Earth.


  This study proposes a quantum secret authentication code for protecting the
integrity of secret quantum states. Since BB84[1] was first proposed, the
eavesdropper detection strategy in almost all quantum cryptographic protocols
is based on the random sample discussion, in which the probability of
eavesdropper detection is depending on the number of check qubits eavesdropped
by the eavesdropper. Hence, if the eavesdropper interferes only a few qubits of
the transmitted quantum sequence, then the detection probability will be very
low. This study attempts to propose a quantum secret authentication code to
solve this problem. With the use of quantum secret authentication code, not
only is the probability of eavesdropper detection guaranteed to be evenly
distributed no matter how many qubits had been eavesdropped, but also can the
quantum transmission efficiency be highly enhanced.


  A symplectic or orthogonal bundle $V$ of rank $2n$ over a curve has an
invariant $t(V)$ which measures the maximal degree of its isotropic subbundles
of rank $n$. This invariant $t$ defines stratifications on moduli spaces of
symplectic and orthogonal bundles. We study this stratification by relating it
to another one given by secant varieties in certain extension spaces.
  We give a sharp upper bound on $t(V)$, which generalizes the classical Nagata
bound for ruled surfaces and the Hirschowitz bound for vector bundles, and
study the structure of the stratifications on the moduli spaces. In particular,
we compute the dimension of each stratum. We give a geometric interpretation of
the number of maximal Lagrangian subbundles of a general symplectic bundle,
when this is finite. We also observe some interesting features of orthogonal
bundles which do not arise for symplectic bundles, essentially due to the
richer topological structure of the moduli space in the orthogonal case.


  We provide here a thermodynamic analog of the Braess road-network paradox
with irreversible engines working between reservoirs that are placed at
vertices of the network. Paradoxes of different kinds reappear, emphasizing the
specialty of the network.


  Polarization singularities and topological polarization structures are
generic features of inhomogeneous vector wave fields of any nature. However,
their experimental studies mostly remain restricted to optical waves. Here we
report observation of polarization singularities, topological Mobius-strip
structures and skyrmionic textures in 3D polarization fields of inhomogeneous
sound waves. Our experiments are made in the ultrasonic domain using
nonparaxial propagating fields generated by space-variant 2D acoustic sources.
We also retrieve distributions of the 3D spin density in these fields. Our
results open the avenue to investigations and applications of topological
features and nontrivial 3D vector properties of structured sound waves.


  Fractal-like nanopatterned DNA thin films have been fabricated on mica
substrate by Langmuir-Blodgett (LB) technique. Structures and components of DNA
nanopatterns were investigated using atomic force microscopy (AFM) and X-ray
photoelectron spectroscopy (XPS). The effect of surface pressure on the
transferred DNA composite films has been studied. Scanning force microscopic
observations revealed that the surface structure and morphology of DNA
nanopatterns can be well controlled by changing the surface pressure. The
growth mechanism of the fractal-like nanopatterns is discussed in terms of the
diffusion-limited aggregation (DLA) model. The formation of large-scale DNA
networks provided a well-defined template for the construction of nanocomposite
films. Patterns of silver metal were prepared on DNA networks by subsequent
metallization process.


  The present paper originated from a problem in Financial Mathematics
concerned with calculating the value of a European call option based on
multiple assets each following the binomial model. The model led to an
interesting family of polytopes $P(b)$ associated with the power-set
$\mathcal{L} = \wp\{1,\dots,m\}$ and parameterized by $b \in \mathbb{R}^m$,
each of which is a collection of probability density function on $\mathcal{L}$.
For each non-empty $P(b)$ there results a family of probability measures on
$\mathcal{L}^n$ and, given a function $F \colon \mathcal{L}^n \to \mathbb{R}$,
our goal is to find among these probability measures one which maximises (resp.
minimises) the expectation of $F$. In this paper we identify a family of such
functions $F$, all of whose expectations are maximised (resp. minimised under
some conditions) by the same {\em product} probability measure defined by a
distinguished vertex of $P(b)$ called the supervertex (resp. the subvertex).
The pay-offs of European call options belong to this family of functions.


  We prove a genuine analogue of Wiener Tauberian theorem for hypergeometric
transforms. As an application we prove analogue of Furstenberg theorem on
Harmonic functions.


  We show how the massive data compression algorithm MOPED can be used to
reduce, by orders of magnitude, the number of simulated datasets that are
required to estimate the covariance matrix required for the analysis of
gaussian-distributed data. This is relevant when the covariance matrix cannot
be calculated directly. The compression is especially valuable when the
covariance matrix varies with the model parameters. In this case, it may be
prohibitively expensive to run enough simulations to estimate the full
covariance matrix throughout the parameter space. This compression may be
particularly valuable for the next-generation of weak lensing surveys, such as
proposed for Euclid and LSST, for which the number of summary data (such as
band power or shear correlation estimates) is very large, $\sim 10^4$, due to
the large number of tomographic redshift bins that the data will be divided
into. In the pessimistic case where the covariance matrix is estimated
separately for all points in an MCMC analysis, this may require an unfeasible
$10^9$ simulations. We show here that MOPED can reduce this number by a factor
of 1000, or a factor of $\sim 10^6$ if some regularity in the covariance matrix
is assumed, reducing the number of simulations required to a manageable $10^3$,
making an otherwise intractable analysis feasible.


  Active walker models have proved to be extremely effective in understanding
the evolution of a large class of systems in biology like ant trail formation
and pedestrian trails. We propose a simple model of a random walker which
modifies its local environment that in turn influences the motion of the walker
at a {\em later} time. We perform direct numerical simulations of the walker in
a discrete lattice with the walker actively depositing a chemical which
attracts the walker trajectory and also evaporates in time. We propose a method
to look at the structural transitions of the trajectory using radius of
gyration for finite time walks. The extension over a definite time-window shows
a non-monotonic change with the deposition rate characteristic of a
coil-globule transition. At certain regions of the parameter space of the
chemical deposition and evaporation rates, the extensions of the walker shows a
re-entrant behavior. The dynamics, characterised by the mean-squared
displacement, shows deviation from diffusive scaling at intermediate time
scales, returning to diffusive behavior asymptotically. A mean field theory
captures the variation of the asymptotic diffusivity.


  The problem of the origin of cosmic rays in the shocks produced by supernova
explosions at energies below the so called 'knee' (at ~3*10$^6$ GeV) in the
energy spectrum is addressed, with special attention to the propagation of the
particles through the inhomogenious interstellar medium and the need to explain
recent anisotropy results, [1]. It is shown that the fractal character of the
matter density and magnetic field distribution leads to the likelihood of a
substantial increase of spatial fluctuations in the cosmic ray energy spectra.
While the spatial distribution of cosmic rays in the vicinity of their sources
(eg. inside the Galactic disk) does not depend much on the character of
propagation and is largely determined by the distribution of their sources, the
distribution at large distances from the Galactic disk depends strongly on the
character of the propagation. In particular, the fractal character of the ISM
leads to what is known as 'anomalous diffusion' and such diffusion helps us to
understand the formation of Cosmic Ray Halo. Anomalous diffusion allows an
explanation of the recent important result from the Chacaltaya extensive air
shower experiment [1], viz. a Galactic Plane Enhancement of cosmic ray
intensity in the Outer Galaxy, which is otherwise absent for the case of the
so-called 'normal' diffusion. All these effects are for just one reason:
anomalous diffusion emphasizes the role of local phenomena in the formation of
cosmic ray characteristics in our Galaxy and elsewhere.


  Training-free network architecture search (NAS) aims to discover
high-performing networks with zero-cost proxies, capturing network
characteristics related to the final performance. However, network rankings
estimated by previous training-free NAS methods have shown weak correlations
with the performance. To address this issue, we propose AZ-NAS, a novel
approach that leverages the ensemble of various zero-cost proxies to enhance
the correlation between a predicted ranking of networks and the ground truth
substantially in terms of the performance. To achieve this, we introduce four
novel zero-cost proxies that are complementary to each other, analyzing
distinct traits of architectures in the views of expressivity, progressivity,
trainability, and complexity. The proxy scores can be obtained simultaneously
within a single forward and backward pass, making an overall NAS process highly
efficient. In order to integrate the rankings predicted by our proxies
effectively, we introduce a non-linear ranking aggregation method that
highlights the networks highly-ranked consistently across all the proxies.
Experimental results conclusively demonstrate the efficacy and efficiency of
AZ-NAS, outperforming state-of-the-art methods on standard benchmarks, all
while maintaining a reasonable runtime cost.


  Computationally efficient and accurate quantum mechanical approximations to
solve the many-electron Schr\"odinger equation are at the heart of
computational materials science. In that respect the coupled cluster hierarchy
of methods plays a central role in molecular quantum chemistry because of its
systematic improvability and computational efficiency. In this hierarchy,
coupled cluster singles and doubles (CCSD) is one of the most important steps
in moving towards chemical accuracy and, in recent years, its scope has
successfully been expanded to the study of insulating surfaces and solids.
Here, we show that CCSD theory can also be applied to real metals. In so doing,
we overcome the limitation of needing extremely large supercells to capture
long range electronic correlation effects. An effective Hamiltonian can be
found using the transition structure factor--a map of electronic excitations
from the Hartree--Fock wavefunction--which has fewer finite size effects than
conventional periodic boundary conditions. This not only paves the way of
applying coupled cluster methods to real metals but also reduces the
computational cost by two orders of magnitude compared to previous methods. Our
applications to phases of lithium and silicon show a resounding success in
reaching the thermodynamic limit, taking the first step towards a truly
universal quantum chemical treatment of solids.


This paper has been withdrawn by the author.


  This paper concerns autonomous boundary value problems for 1D semilinear
hyperbolic PDEs. For time-periodic classical solutions, which satisfy a certain
non-resonance condition, we show the following: If the PDEs are continuous with
respect to the space variable $x$ and $C^\infty$-smooth with respect to the
unknown function $u$, then the solution is $C^\infty$-smooth with respect to
the time variable $t$, and if the PDEs are $C^\infty$-smooth with respect to
$x$ and $u$, then the solution is $C^\infty$-smooth with respect to $t$ and
$x$. The same is true for appropriate weak solutions.
  Moreover, we show examples of time-periodic functions, which do not satisfy
the non-resonance condition, such that they are weak, but not classical
solutions, and such that they are classical solutions, but not
$C^\infty$-smooth, neither with respect to $t$ nor with respect to $x$, even if
the PDEs are $C^\infty$-smooth with respect to $x$ and $u$.
  For the proofs we use Fredholm solvability properties of linear time-periodic
hyperbolic PDEs and a result of E. N. Dancer about regularity of solutions to
abstract equivariant equations.


  We consider the dynamical properties of density fluctuations in the
cigar-shaped Bose-Einstein condensate described by the logarithmic wave
equation with a constant nonlinear coupling by using the Thomas-Fermi and
linear approximations. It is shown that the propagation of small density
fluctuations along the long axis of a condensed lump in a strongly anisotropic
trap is essentially one-dimensional, while the trapping potential can be
disregarded in the linear regime. Depending on the sign of nonlinear coupling,
the fluctuations either take the form of translationally symmetric pulses and
standing waves, or become oscillations with varying amplitudes. We also study
the condensate in an axial harmonic trap, by using elasticity theory's notions.
Linear particle density and energy also behave differently depending on the
nonlinear coupling's value. If it is negative, the density monotonously grows
along with lump's radius, while energy is a monotonous function of density. For
the positive coupling, the density is bound from above, whereas energy grows
monotonously as a function of density until it reaches its global maximum.


  The WorldWide Telescope(WWT) is a scientific visualization platform which can
browse deep space images, star catalogs, and planetary remote sensing data from
different observation facilities in a three-dimensional virtual scene. First
launched and then open-sourced by Microsoft Research, the WWT is now managed by
the American Astronomical Society (AAS). Hierarchical Progressive Survey (HiPS)
is an astronomical data release scheme proposed by Centre de Donn\'ees
astronomiques de Strasbourg (CDS) and has been accepted as a recommendation by
International Virtual Observatory Alliance (IVOA). The HiPS solution has been
adopted widely by many astronomical institutions for data release. Since WWT
selected Hierarchical Triangular Mesh (HTM) as the standard for data
visualization in the early stage of development, data released by HiPS cannot
be visualized in WWT, which significantly limits the application of WWT. This
paper introduces the implementation method for HiPS dataset visualization in
WWT, and introduces HiPS data projection, mesh rendering, and data index
implementation in WWT. Taking Chang'E-2 lunar probe data as an example, this
paper introduces how to convert planetary remote sensing data into a HiPS
dataset and integrate it into WWT. This paper also compares the efficiency and
memory consumption of WWT loading its native data and HiPS data, and
illustrates the application of HiPS in scientific data visualization and
science education in WWT.


  Designing plausible network models typically requires scholars to form a
priori intuitions on the key drivers of network formation. Oftentimes, these
intuitions are supported by the statistical estimation of a selection of
network evolution processes which will form the basis of the model to be
developed. Machine learning techniques have lately been introduced to assist
the automatic discovery of generative models. These approaches may more broadly
be described as "symbolic regression", where fundamental network dynamic
functions, rather than just parameters, are evolved through genetic
programming. This chapter first aims at reviewing the principles, efforts and
the emerging literature in this direction, which is very much aligned with the
idea of creating artificial scientists. Our contribution then aims more
specifically at building upon an approach recently developed by us [Menezes \&
Roth, 2014] in order to demonstrate the existence of families of networks that
may be described by similar generative processes. In other words, symbolic
regression may be used to group networks according to their inferred genotype
(in terms of generative processes) rather than their observed phenotype (in
terms of statistical/topological features). Our empirical case is based on an
original data set of 238 anonymized ego-centered networks of Facebook friends,
further yielding insights on the formation of sociability networks.


  Various work has suggested that the memorability of an image is consistent
across people, and thus can be treated as an intrinsic property of an image.
Using computer vision models, we can make specific predictions about what
people will remember or forget. While older work has used now-outdated deep
learning architectures to predict image memorability, innovations in the field
have given us new techniques to apply to this problem. Here, we propose and
evaluate five alternative deep learning models which exploit developments in
the field from the last five years, largely the introduction of residual neural
networks, which are intended to allow the model to use semantic information in
the memorability estimation process. These new models were tested against the
prior state of the art with a combined dataset built to optimize both
within-category and across-category predictions. Our findings suggest that the
key prior memorability network had overstated its generalizability and was
overfit on its training set. Our new models outperform this prior model,
leading us to conclude that Residual Networks outperform simpler convolutional
neural networks in memorability regression. We make our new state-of-the-art
model readily available to the research community, allowing memory researchers
to make predictions about memorability on a wider range of images.


  We reveal a generic mechanism of generating sign-alternating inter-site
interactions mediated by strongly correlated lattice bosons. The ground state
phase diagram of the two-component hard-core Bose-Hubbard model on a square
lattice at half-integer filling factor for each component, obtained by worm
algorithm Monte Carlo simulations, is strongly modified by these interactions
and features the solid+superfluid phase for strong anisotropy between the
hopping amplitudes. The new phase is a direct consequence of the effective
nearest-neighbor repulsion between "heavy" atoms mediated by the "light"
superfluid component. Due to their sign-alternating character, mediated
interactions lead to a rich variety of yet to be discovered quantum phases.
quantum phases.


  Automating the analysis of imagery of the Gastrointestinal (GI) tract
captured during endoscopy procedures has substantial potential benefits for
patients, as it can provide diagnostic support to medical practitioners and
reduce mistakes via human error. To further the development of such methods, we
propose a two-stream model for endoscopic image analysis. Our model fuses two
streams of deep feature inputs by mapping their inherent relations through a
novel relational network model, to better model symptoms and classify the
image. In contrast to handcrafted feature-based models, our proposed network is
able to learn features automatically and outperforms existing state-of-the-art
methods on two public datasets: KVASIR and Nerthus. Our extensive evaluations
illustrate the importance of having two streams of inputs instead of a single
stream and also demonstrates the merits of the proposed relational network
architecture to combine those streams.


  Unranked trees can be represented using their minimal dag (directed acyclic
graph). For XML this achieves high compression ratios due to their repetitive
mark up. Unranked trees are often represented through first child/next sibling
(fcns) encoded binary trees. We study the difference in size (= number of
edges) of minimal dag versus minimal dag of the fcns encoded binary tree. One
main finding is that the size of the dag of the binary tree can never be
smaller than the square root of the size of the minimal dag, and that there are
examples that match this bound. We introduce a new combined structure, the
hybrid dag, which is guaranteed to be smaller than (or equal in size to) both
dags. Interestingly, we find through experiments that last child/previous
sibling encodings are much better for XML compression via dags, than fcns
encodings. We determine the average sizes of unranked and binary dags over a
given set of labels (under uniform distribution) in terms of their exact
generating functions, and in terms of their asymptotical behavior.


  As a vital stage of automated rule checking (ARC), rule interpretation of
regulatory texts requires considerable effort. However, interpreting regulatory
clauses with implicit properties or complex computational logic is still
challenging due to the lack of domain knowledge and limited expressibility of
conventional logic representations. Thus, LLM-FuncMapper, an approach to
identifying predefined functions needed to interpret various regulatory clauses
based on the large language model (LLM), is proposed. First, by systematically
analysis of building codes, a series of atomic functions are defined to capture
shared computational logics of implicit properties and complex constraints,
creating a database of common blocks for interpreting regulatory clauses. Then,
a prompt template with the chain of thought is developed and further enhanced
with a classification-based tuning strategy, to enable common LLMs for
effective function identification. Finally, the proposed approach is validated
with statistical analysis, experiments, and proof of concept. Statistical
analysis reveals a long-tail distribution and high expressibility of the
developed function database, with which almost 100% of computer-processible
clauses can be interpreted and represented as computer-executable codes.
Experiments show that LLM-FuncMapper achieve promising results in identifying
relevant predefined functions for rule interpretation. Further proof of concept
in automated rule interpretation also demonstrates the possibility of
LLM-FuncMapper in interpreting complex regulatory clauses. To the best of our
knowledge, this study is the first attempt to introduce LLM for understanding
and interpreting complex regulatory clauses, which may shed light on further
adoption of LLM in the construction domain.


  We predict a novel quantum interference based on the negative refraction
across a semiconductor P-N junction: with a local pump on one side of the
junction, the response of a local probe on the other side behaves as if the
disturbance emanates not from the pump but instead from its mirror image about
the junction. This phenomenon is guaranteed by translational invariance of the
system and matching of Fermi surfaces of the constituent materials, thus it is
robust against other details of the junction (e.g., junction width, potential
profile, and even disorder). The recently fabricated P-N junctions in 2D
semiconductors provide ideal platforms to explore this phenomenon and its
applications to dramatically enhance charge and spin transport as well as
carrier-mediated long-range correlation.


  Decompilation is a well-studied area with numerous high-quality tools
available. These are frequently used for security tasks and to port legacy
code. However, they regularly generate difficult-to-read programs and require a
large amount of engineering effort to support new programming languages and
ISAs. Recent interest in neural approaches has produced portable tools that
generate readable code. However, to-date such techniques are usually restricted
to synthetic programs without optimization, and no models have evaluated their
portability. Furthermore, while the code generated may be more readable, it is
usually incorrect. This paper presents SLaDe, a Small Language model Decompiler
based on a sequence-to-sequence transformer trained over real-world code. We
develop a novel tokenizer and exploit no-dropout training to produce
high-quality code. We utilize type-inference to generate programs that are more
readable and accurate than standard analytic and recent neural approaches.
Unlike standard approaches, SLaDe can infer out-of-context types and unlike
neural approaches, it generates correct code. We evaluate SLaDe on over 4,000
functions from ExeBench on two ISAs and at two optimizations levels. SLaDe is
up to 6 times more accurate than Ghidra, a state-of-the-art,
industrial-strength decompiler and up to 4 times more accurate than the large
language model ChatGPT and generates significantly more readable code than
both.


  We show results of Monte Carlo simulations of an array of monodispersed
magnetic monodomain particles, in a square lattice with dipolar interactions
and perpendicular uniaxial anisotropy. We first show the equilibrium phase
diagram of the system, which shows three phases, superparamagnetic (SP),
out-of-plane antiferromagnetic and in-plane antiferromagnetic with a
reorientation transition between the last two. We then employ a recently
introduced time quantified Monte Carlo method to study the relaxation of
autocorrelations of the particle array for different ratios of dipolar to
anisotropy energies. In the non-interacting case we show that relaxation is
exponential in time with characteristic times obeying a classic result by
Brown. When dipolar interactions are switched on, the relaxation is very well
described by stretched exponential forms in the whole time window and in both
the SP and ordered phases. Relaxation times still obey a nearly Arrhenius
behaviour, with a single effective energy barrier that decreases as the dipolar
interaction increases, a result that must be interpreted within the dynamics
protocol. No signs of glassy behaviour were found, in agreement with the
absence of disorder in the model system.


  Near the corotation resonance of a transient spiral arm, stellar orbital
angular momenta may be changed without inducing significant kinematic heating,
resulting in what has come to be known as radial migration. When radial
migration is very efficient, a large fraction of disk stars experiences
significant, permanent changes to their individual orbital angular momenta over
the lifetime of the disk, having strong implications for the evolution of disk
galaxies. The first step for a star in a spiral disk to migrate radially is to
be captured in a "trapped" orbit, associated with the corotation resonance of
the spiral pattern. An analytic criterion for determining whether or not a star
is in a trapped orbit has previously been derived only for stars with zero
random orbital energy in the presence of a spiral with fixed properties. In
this first paper in a series, we derive an analytic criterion appropriate for a
star that is on an orbit of finite random orbital energy. Our new criterion
demonstrates that whether or not a star is in a "trapped" orbit primarily
depends on the star's orbital angular momentum. This criterion could be a
powerful tool in the interpretation of the results of N-body simulations. In
future papers of this series, we apply our criterion to explore the physical
parameters important to determining the efficiency of radial migration and its
potential importance to disk evolution.


  Massive scalar fields provide excellent dark matter candidates, whose
dynamics are often explored analytically and numerically using nonrelativistic
Schr\"{o}dinger-Poisson (SP) equations in a cosmological context. In this
paper, starting from the nonlinear and fully relativistic Klein-Gordon-Einstein
(KGE) equations in an expanding universe, we provide a systematic framework for
deriving the SP equations, as well as relativistic corrections to them, by
integrating out `fast modes' and including nonlinear metric and matter
contributions. We provide explicit equations for the leading-order relativistic
corrections, which provide insight into deviations from the SP equations as the
system approaches the relativistic regime. Upon including the leading-order
corrections, our equations are applicable beyond the domain of validity of the
SP system, and are simpler to use than the full KGE case in some contexts. As a
concrete application, we calculate the mass-radius relationship of solitons in
scalar dark matter and accurately capture the deviations of this relationship
from the SP system towards the KGE one.


  We prove global existence of nonnegative weak solutions to a degenerate
parabolic system which models the interaction of two thin fluid films in a
porous medium. Furthermore, we show that these weak solutions converge at an
exponential rate towards flat equilibria.


  We propose the concept of SLOCC-equivalent basis (SEB) in the multiqubit
space. In particular, two special SEBs, the GHZ-type and the W-type basis are
introduced. They can make up a more general family of multiqubit states, the
GHZ-W-type states, which is a useful kind of entanglement for quantum
teleporatation and error correction. We completely characterize the property of
this type of states, and mainly classify the GHZ-type states and the W-type
states in a regular way, which is related to the enumerative combinatorics.
Many concrete examples are given to exhibit how our method is used for the
classification of these entangled states.


  We study the effects of anisotropic hopping amplitudes on quantum phases of
ultracold fermions in optical lattices described by the repulsive Fermi-Hubbard
model. In particular, using dynamical mean-field theory (DMFT) we investigate
the dimensional crossover between the isotropic square and the isotropic cubic
lattice. We analyze the phase transition from the antiferromagnetic to the
paramagnetic state and observe a significant change in the critical
temperature: Depending on the interaction strength, the anisotropy can lead to
both a suppression or increase. We also investigate the localization properties
of the system, such as the compressibility and double occupancy. Using the
local density approximation in combination with DMFT we conclude that density
profiles can be used to detect the mentioned anisotropy-driven transitions.


  In this paper we investigate the game chromatic number for complete
multipartite graphs. We devise several strategies for Alice, and one strategy
for Bob, and we prove their optimality in all complete multipartite graphs with
no singletons. All the strategies presented are computable in linear time, and
the values of the game chromatic number depend directly only on the number and
the sizes of sets in the partition.


  Recently Arm introduced a new instruction set called Scalable Vector
Extension (SVE), which supports vector lengths up to 2048 bits. While SVE
hardware will not be generally available until about 2021, we believe that
future SVE-based architectures will have great potential for Lattice QCD. In
this contribution we discuss key aspects of SVE and describe how we implemented
SVE in the Grid Lattice QCD framework.


  Applying a non-diagonal spherically symmetric tetrad field having arbitrary
function, $S(r)$, that is corresponding to local Lorentz transformation, to the
field equations of f(T) gravity theories.
  An analytic vacuum solutions with constants of integration are derived. These
constants are studied by calculating the total conserved charge associated to
each solution. The study has shown that the obtained solutions represent
Schwarzschild-Ads spacetime.


  Compton scattering of X-rays in the bulk flow of the accretion column in
magnetic cataclysmic variables (mCVs) can significantly shift photon energies.
We present Monte Carlo simulations based on a nonlinear algorithm demonstrating
the effects of Compton scattering on the H-like, He-like and neutral Fe K alpha
lines produced in the post-shock region of the accretion column. The peak line
emissivities of the photons in the post-shock flow are taken into consideration
and frequency shifts due to Doppler effects are also included. We find that
line profiles are most distorted by Compton scattering effects in strongly
magnetized mCVs with a low white dwarf mass and high mass accretion rate and
which are viewed at an oblique angle with respect to the accretion column. The
resulting line profiles are most sensitive to the inclination angle. We have
also explored the effects of modifying the accretion column width and using a
realistic emissivity profile. We find that these do not have a significant
overall effect on the resulting line profiles. A comparison of our simulated
line spectra with high resolution Chandra/HETGS observations of the mCV GK Per
indicates that a wing feature redward of the 6.4 keV line may result from
Compton recoil near the base of the accretion column.


  We study a two-species competition model in a patchy advective environment,
where the species are subject to both directional drift and undirectional
random dispersal between patches and there are losses of individuals in the
downstream end (e.g., due to the flow into a lake or ocean). The two competing
species are assumed to have the same growth rates but different advection and
random dispersal rates. We focus our studies on the properties of an associated
eigenvalue problem which characterizes the extinction/persistence dynamics of
the underlying patch population model. We also derive conditions on the
advection and random dispersal rates under which a mutating species can or
cannot invade the resident species.


  The unitary Cayley graph $C_R$ of a finite unital ring $R$ is the simple
graph with vertex set $R$ in which two elements $x$ and $y$ are connected by an
edge if and only if $x-y$ is a unit of $R$. We characterize the unitary Cayley
graph $C_{T_n (\mathbb{F})}$ of the ring of all upper triangular matrices
$T_n(\mathbb{F})$ over a finite field $\mathbb{F}$. We show that $C_{T_n
(\mathbb{F})}$ is isomorphic to the semistrong product of the complete graph
$K_m$ and the antipodal graph of the Hamming graph $A(H(n,p^k))$, where
$m=p^{\frac{kn(n-1)}{2}}$ and $|\mathbb{F}|=p^k$. In particular, if
$|\mathbb{F}|=2$, then the graph $C_{T_n (\mathbb{F})}$ has $2^{n-1}$ connected
components, each component is isomorphic to the complete bipartite graph
$K_{m,m}$, where $m=2^{\frac{n(n-1)}{2}}$. We also compute the diameter,
triameter, and clique number of the graph $C_{T_n (\mathbb{F})}$.


  To address the coordination issue of connected automated vehicles (CAVs) at
urban scenarios, a game-theoretic decision-making framework is proposed that
can advance social benefits, including the traffic system efficiency and
safety, as well as the benefits of individual users. Under the proposed
decision-making framework, in this work, a representative urban driving
scenario, i.e. the unsignalized intersection, is investigated. Once the vehicle
enters the focused zone, it will interact with other CAVs and make
collaborative decisions. To evaluate the safety risk of surrounding vehicles
and reduce the complexity of the decision-making algorithm, the driving risk
assessment algorithm is designed with a Gaussian potential field approach. The
decision-making cost function is constructed by considering the driving safety
and passing efficiency of CAVs. Additionally, decision-making constraints are
designed and include safety, comfort, efficiency, control and stability. Based
on the cost function and constraints, the fuzzy coalitional game approach is
applied to the decision-making issue of CAVs at unsignalized intersections. Two
types of fuzzy coalitions are constructed that reflect both individual and
social benefits. The benefit allocation in the two types of fuzzy coalitions is
associated with the driving aggressiveness of CAVs. Finally, the effectiveness
and feasibility of the proposed decision-making framework are verified with
three test cases.


  For the fifth Painlev\'e equation it is known that a general solution is
represented asymptotically by an elliptic function in cheese-like strips near
the point at infinity. We present an explicit asymptotic formula for the error
term of this expression, which leads to an estimate for its magnitude as was
conjectured. Analogous formula is obtained for the error term of the correction
function associated with the Lagrangian.


  Let $G \leq \operatorname{SL}_{n+1}(\mathbb{C})$ act on $R = \mathbb{C}[X_1,
\ldots, X_{n+1}]$ by change of variables. Then, the skew-group algebra $R \ast
G$ is bimodule $(n+1)$-Calabi-Yau. Under certain circumstances, the algebra
admits a locally finite-dimensional grading of Gorenstein parameter $1$, in
which case it is the $(n+1)$-preprojective algebra of its $n$-representation
infinite degree $0$ piece, as defined by Herschend, Iyama and Oppermann. If the
group $G$ is abelian, the $(n+1)$-preprojective algebra is said to be of type
$\~A$. For a given group $G$, it is not obvious whether $R \ast G$ admits such
a grading making it into an $(n+1)$-preprojective algebra. We study the case
when $n=2$ and $G$ is abelian. We give an explicit classification of groups
such that $R \ast G$ is $3$-preprojective by constructing such gradings. This
is possible as long as $G$ is not a subgroup of
$\operatorname{SL}_2(\mathbb{C})$ and not $C_2 \times C_2$. For a fixed $G$,
the algebra $R \ast G$ admits different $3$-preprojective gradings, so we
associate a type to a grading and classify all types. Then we show that
gradings of the same type are related by a certain kind of mutation. This gives
a classification of $2$-representation infinite algebras of type $\~A$. The
involved quivers are those arising from hexagonal dimer models on the torus,
and the gradings we consider correspond to perfect matchings on the dimer, or
equivalently to periodic lozenge tilings of the plane. Consequently, we
classify these tilings up to flips, which correspond to our mutation.


  We propose a simple model in which the baryon asymmetry and dark matter are
created via the decays and inverse decays of QCD-triplet scalars, at least one
of which must be in the TeV mass range. Singlet fermions produced in these
decays constitute the dark matter. The singlets never reach equilibrium, and
their coherent production, propagation, and annihilation generates a baryon
asymmetry. We find that that the out-of-equilibrium condition and the dark
matter density constraint typically require the lightest scalar to be
long-lived, giving good prospects for detection or exclusion in current and
upcoming colliders. In generalizing the leptogenesis mechanism of Akhmedov,
Rubakov and Smirnov, our model expands the phenomenological possibilities for
low-scale baryogenesis.


  Large language models (LLMs) are used for long-form question answering
(LFQA), which requires them to generate paragraph-length answers to complex
questions. While LFQA has been well-studied in English, this research has not
been extended to other languages. To bridge this gap, we introduce CaLMQA, a
collection of 1.5K complex culturally specific questions spanning 23 languages
and 51 culturally agnostic questions translated from English into 22 other
languages. We define culturally specific questions as those uniquely or more
likely to be asked by people from cultures associated with the question's
language. We collect naturally-occurring questions from community web forums
and hire native speakers to write questions to cover under-resourced,
rarely-studied languages such as Fijian and Kirundi. Our dataset contains
diverse, complex questions that reflect cultural topics (e.g. traditions, laws,
news) and the language usage of native speakers. We automatically evaluate a
suite of open- and closed-source models on CaLMQA by detecting incorrect
language and token repetitions in answers, and observe that the quality of
LLM-generated answers degrades significantly for some low-resource languages.
Lastly, we perform human evaluation on a subset of models and languages. Manual
evaluation reveals that model performance is significantly worse for culturally
specific questions than for culturally agnostic questions. Our findings
highlight the need for further research in non-English LFQA and provide an
evaluation framework.


  Stellar evolution theory is most uncertain for massive stars. For reliable
predictions of the evolution of massive stars and their final fate, solid
constraints on the physical parameters, and their changes along the evolution
and in different environments, are required. Massive stars evolve through a
variety of short transition phases, in which they can experience large
mass-loss either in the form of dense winds or via sudden eruptions. The B[e]
supergiants comprise one such group of massive transition objects. They are
characterized by dense, dusty disks of yet unknown origin. In the Milky Way,
identification and classification of B[e] supergiants is usually hampered by
their uncertain distances hence luminosities, and by the confusion of
low-luminosity candidates with massive pre-main sequence objects. The
extragalactic objects are often mistaken as quiescent or candidate luminous
blue variables, with whom B[e] supergiants share a number of spectroscopic
characteristics. In this review, proper criteria are provided, based on which
B[e] supergiants can be unambiguously classified and separated from other high
luminosity post-main sequence stars and pre-main sequence stars. Using these
criteria, the B[e] supergiant samples in diverse galaxies are critically
inspected, to achieve a reliable census of the current population.


  Universal domain adaptation (UniDA) is a practical but challenging problem,
in which information about the relation between the source and the target
domains is not given for knowledge transfer. Existing UniDA methods may suffer
from the problems of overlooking intra-domain variations in the target domain
and difficulty in separating between the similar known and unknown class. To
address these issues, we propose a novel Mutual Learning Network (MLNet) with
neighborhood invariance for UniDA. In our method, confidence-guided invariant
feature learning with self-adaptive neighbor selection is designed to reduce
the intra-domain variations for more generalizable feature representation. By
using the cross-domain mixup scheme for better unknown-class identification,
the proposed method compensates for the misidentified known-class errors by
mutual learning between the closed-set and open-set classifiers. Extensive
experiments on three publicly available benchmarks demonstrate that our method
achieves the best results compared to the state-of-the-arts in most cases and
significantly outperforms the baseline across all the four settings in UniDA.
Code is available at https://github.com/YanzuoLu/MLNet.


  Reconstructed jets in heavy ion collisions are a crucial tool for
understanding the quark-gluon plasma. The separation of jets from the
underlying event is necessary particularly in central heavy ion reactions in
order to quantify medium modifications of the parton shower and the response of
the surrounding medium itself. There have been many methods proposed and
implemented for studying the underlying event substructure in proton-proton and
heavy ion collisions. In this paper, we detail a method for understanding
underlying event contributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV
utilizing the HIJING event generator. This method, extended from previous work
by the ATLAS collaboration, provides a well-defined association of "truth jets"
from the fragmentation of hard partons with "reconstructed jets" using the
anti-$k_T$ algorithm. Results presented here are based on an analysis of 750M
minimum bias HIJING events. We find that there is a substantial range of jet
energies and radius parameters where jets are well separated from the
background fluctuations (often termed "fake jets") that make jet measurements
at RHIC a compelling physics program.


  I discuss the time evolution of quantum entanglement in presence of
non-collapsing interactions. In the case of relativistic systems, the
correlation between entangled processes is defined by the equality of the
correspondent invariant intervals. As an example, the entanglement between the
products of a particle decay is revisited, leading to correlations in precise
agreement with the muon $g-2$ experimental results. The extension of such a
postulate to the curved space-time is also used to discuss the survival of
entanglement in the presence of horizons.


  The solution of Boltzmann equation for plasma in magnetic field, with
arbitrarily degenerate electrons and non-degenerate nuclei, is obtained by
Chapman-Enskog method. Functions, generalizing Sonin polynomials are used for
obtaining an approximate solution. Fully ionized plasma is considered. The
tensor of the heat conductivity coefficients in non-quantized magnetic field is
calculated. For non-degenerate and strongly degenerate plasma the asymptotic
analytic formulas are obtained, which are compared with results of previous
authors. The Lorentz approximation, with neglecting of electron-electron
encounters, is asymptotically exact for strongly degenerate plasma.
  We obtain, for the first time, in three polynomial approximation, with
account of electron-electron collisions, analytical expressions for the heat
conductivity tensor for non-degenerate electrons, in presence of a magnetic
field. Account of the third polynomial improved substantially the precision of
results.
  In two polynomial approximation our solution coincides with the published
results. For strongly degenerate electrons we obtain, for the first time, an
asymptotically exact analytical solution for the heat conductivity tensor in
presence of a magnetic field. This solution has considerably more complicated
dependence on the magnetic field than those in previous publications, and gives
several times smaller relative value of a thermal conductivity across the
magnetic field at $\omega\tau\gtrsim 0.8$.


  The concepts of apartments and buildings were suggested by Tits for
description of the Weyl-Coxeter reflection groups. We use these and many
additional facts from the theory of reflection and pseudo-reflection groups
along with results from the algebraic and symplectic geometry of toric
varieties in order to obtain the tachyon-free Veneziano-like multiparticle
scattering amplitudes and the partition function generating these
amplitudes.Although the obtained amplitudes reproduce the tachyon-free spectra
of both open and closed boisonic string, the generating (partition) function is
not that of the traditional bosonic string. It is argued that it is directly
related to the N=2 sypersymmetric quantum mechanical model proposed by Witten
in 1982 in connection with his development of the Morse theory.Such partition
function can be independently obtained with help of the results by Solomon
(published in 1963) on invariants of finite (pseudo) reflection groups.
Although the formalism developed in this work is also applicable to conformal
field theories (CFT), it leaves all CFT results unchanged


  We propose a new estimator for the integrated covariance of two Ito
semimartingales observed at a high-frequency. This new estimator, which we call
the pre-averaged truncated Hayashi-Yoshida estimator, enables us to separate
the sum of the co-jumps from the total quadratic covariation even in the case
that the sampling schemes of two processes are nonsynchronous and the
observation data is polluted by some noise. It is the first estimator which can
simultaneously handle these three issues, which are fundamental to empirical
studies of high-frequency financial data. We also show the asymptotic mixed
normality of this estimator under some mild conditions allowing infinite
activity jump processes with finite variations, some dependency between the
sampling times and the observed processes as well as a kind of endogenous
observation errors. We examine the finite sample performance of this estimator
using a Monte Carlo study.


  This paper gives a priori estimates for the positve solutions of Kirchhoff
type equation without variational structure.


  Let $\mathcal{M}$ be a smooth submanifold of $\mathbb{R}^n$ equipped with the
Euclidean (chordal) metric. This note considers the smallest dimension $m$ for
which there exists a bi-Lipschitz function $f: \mathcal{M} \mapsto
\mathbb{R}^m$ with bi-Lipschitz constants close to one. The main result bounds
the embedding dimension $m$ below in terms of the bi-Lipschitz constants of $f$
and the reach, volume, diameter, and dimension of $\mathcal{M}$. This new lower
bound is applied to show that prior upper bounds by Eftekhari and Wakin
(arXiv:1306.4748) on the minimal low-distortion embedding dimension of such
manifolds using random matrices achieve near-optimal dependence on both reach
and volume. This supports random linear maps as being nearly as efficient as
the best possible nonlinear maps at reducing the ambient dimension for manifold
data. In the process of proving our main result, we also prove similar results
concerning the impossibility of achieving better nonlinear measurement maps
with the Restricted Isometry Property (RIP) in compressive sensing
applications.


  We present a novel and simple picture of the generation dynamics of coherent
longitudinal optical (LO) phonons and LO-phonon-plasmon-coupled (LOPC) modes by
the ultrafast infrared pump-pulses in gallium arsenide (GaAs) employing the
low-temperature approximation. LO phonons exhibit a pronounced coupling with
plasmons formed by the optically excited electrons in the excited states of
GaAs. This coupling results in the coherent oscillation of the LOPC modes in
the excited states. The pump pulse also induces stimulated Raman scattering,
which generates the coherent LO-phonon oscillation in the ground state. This
picture is incorporated into a simplified model, and the time evolution of the
density operator is calculated using the Lindblad-type quantum master equation.
The theoretical results explain well the reported experimental results on the
coherent oscillation of LO phonons and LOPC modes observed through transient
reflection measurements. Above all, our model provides a natural reason for the
simultaneous manifestation of the LO phonons and the LOPC modes.


  We consider unique continuation properties of solutions to a family of
evolution equations. Our interest is mainly on nonlinear non-local models. This
class contains the Benjamin-Ono, the Intermediate Long Wave, the Camassa-Holm,
the dispersion generalized Benjamin-Ono and non-local Schr\"odinger equations
as well as their generalizations. We shall review, discuss, expand, and comment
on several results. In addition, we shall state some open questions concerning
these results and their techniques.


  A novel canonical Hamiltonian formalism is developed for long internal waves
in a rotating environment. This includes the effects of background vorticity
and shear on the waves. By restricting consideration to flows in hydrostatic
balance, superimposed on a horizontally uniform background of vertical shear
and vorticity, a particularly simple Hamiltonian structure arises, which can be
thought of as describing a nonlinearly coupled infinite collection of shallow
water systems. The kinetic equation describing the time evolution of the
spectral energy of internal waves is subsequently derived, and a stationary
Kolmogorov solution is found in the high frequency limit. This is surprisingly
close to the Garrett--Munk spectrum of oceanic internal waves.


  To revisit the long-standing problem of possible inconsistency concerning the
oxygen composition in the current galactic gas and in the solar atmosphere
(i.e., the former being appreciably lower by ~0.3 dex) apparently contradicting
the galactic chemical evolution, we carried out oxygen abundance determinations
for 64 mid- through late-B stars by using the O I 6156-8 lines while taking
into account the non-LTE effect, and compared them with the solar O abundance
established in the same manner. The resulting mean oxygen abundance was <A(O)>
= 8.71 (+/- 0.06), which means that [O/H] (star-Sun differential abundance) is
~-0.1, the difference being less significant than previously thought. Moreover,
since the 3D correction may further reduce the reference solar oxygen abundance
(8.81) by ~0.1 dex, we conclude that the photospheric O abundances of these B
stars are almost the same as that of the Sun. We also determined the non-LTE
abundances of neon for the sample B stars from Ne I 6143/6163 lines to be
<A(Ne)> = 8.02 (+/- 0.09), leading to the Ne-to-O ratio of ~0.2 consistent with
the recent studies. This excludes a possibility of considerably high Ne/O ratio
once proposed as a solution to the confronted solar model problem.


  The existing QCD predictions for the Deeply Virtual Compton Scattering (DVCS)
depend on the convention used for the skewedness parameter and on the reference
frame used to define helicity amplitudes. These ambiquities are formally
power-suppressed but numerically significant. They are cancelled by finite-$t$
and target mass corrections that have been calculated recently to the $1/Q^2$
accuracy. It turns out that these corrections can be minimized, at least for
unpolarized observables, by choosing a specific reference frame where
longitudinal directions are defined by the photon momenta.


  In a celebrated unpublished manuscript Beilinson and Drinfeld quantize the
Hitchin integrable system by showing that the global sections of critically
twisted differential operators on the moduli stack of G-bundles on an algebraic
curve is identified with the ring of regular functions on the space of G-opers;
they deduce existence of an automorphic D-module corresponding to a local
system carrying a structure of an oper. In this note we show for G=GL(n) that
those results admit a short proof by reduction to positive characteristic,
where they are deduced from generic Langlands duality established earlier by
the first author and A. Braverman. The appendix contains a proof of some
properties of the p-curvature map restricted to the space of opers.


  Assuming Lorentz symmetry is broken by some fixed vector background, we study
the spinor electrodynamics modified by two dimension-five Lorentz-violating
interactions between fermions and photons. The effective polarization and
magnetization are identified from the modified Maxwell equations, and the
theoretical consequences are investigated. We also compute the corrections to
the relativistic energy levels of hydrogen atom induced by these
Lorentz-violating operators in the absence and presence of uniform external
fields in first-order perturbation theory. We find that the hydrogen spectrum
is insensitive to the breakdown of Lorentz boost symmetry.


  We prove that every finite symmetric integral tensor category $\mathcal{C}$
with the Chevalley property over an algebraically closed field $k$ of
characteristic $p>2$ admits a symmetric fiber functor to $\text{sVec}$. This
proves Ostrik's conjecture \cite[Conjecture 1.3]{o} in this case. Equivalently,
we prove that there exists a unique finite supergroup scheme $\mathcal{G}$ over
$k$ and a grouplike element $\epsilon\in k[\mathcal{G}]$ of order $\le 2$,
whose action by conjugation on $\mathcal{G}$ coincides with the parity
automorphism of $\mathcal{G}$, such that $\mathcal{C}$ is symmetric tensor
equivalent to $\Rep(\mathcal{G},\epsilon)$. In particular, when $\mathcal{C}$
is unipotent, the functor lands in $\Vect$, so $\mathcal{C}$ is symmetric
tensor equivalent to $\Rep(U)$ for a unique finite unipotent group scheme $U$
over $k$. We apply our result and the results of \cite{g} to classify certain
finite dimensional triangular Hopf algebras with the Chevalley property over
$k$ (e.g., local), in group scheme-theoretical terms. Finally, we compute the
Sweedler cohomology of restricted enveloping algebras over an algebraically
closed field $k$ of characteristic $p>0$, classify associators for their duals,
and study finite dimensional (not necessarily triangular) local quasi-Hopf
algebras and finite (not necessarily symmetric) unipotent tensor categories
over an algebraically closed field $k$ of characteristic $p>0$.
  The appendix by K. Coulembier and P. Etingof gives another proof of the above
classification results using the recent paper \cite{Co}, and, more generally,
shows that the maximal Tannakian and super-Tannakian subcategory of a symmetric
tensor category over a field of characteristic $\ne 2$ is always a Serre
subcategory.


  The mass and width of the W boson are measured using e+e- -> W+W- events from
the data sample collected by the OPAL experiment at LEP at centre-of-mass
energies between 170 GeV and 209 GeV. The mass (mw) and width (gw) are
determined using direct reconstruction of the kinematics of W+W- -> qqbarlv and
W+W- -> qqbarqqbar events. When combined with previous OPAL measurements using
W+W- -> lvlv events and the dependence on mw of the WW production cross-section
at threshold, the results are determined to be mw = 80.415 +- 0.042 +- 0.030 +-
0.009 GeV gw = 1.996 +- 0.096 +- 0.102 +- 0.003 GeV where the first error is
statistical, the second systematic and the third due to uncertainties in the
value of the LEP beam energy. By measuring mw with several different jet
algorithms in the qqbarqqbar channel, a limit is also obtained on possible
final-state interactions due to colour reconnection effects in W+W- ->
qqbarqqbar events. The consistency of the results for the W mass and width with
those inferred from other electroweak parameters provides an important test of
the Standard Model of electroweak interactions