  The 15 puzzle is a classic reconfiguration puzzle with fifteen uniquely
labeled unit squares within a $4 \times 4$ board in which the goal is to slide
the squares (without ever overlapping) into a target configuration. By
generalizing the puzzle to an $n \times n$ board with $n^2-1$ squares, we can
study the computational complexity of problems related to the puzzle; in
particular, we consider the problem of determining whether a given end
configuration can be reached from a given start configuration via at most a
given number of moves. This problem was shown NP-complete in Ratner and Warmuth
(1990). We provide an alternative simpler proof of this fact by reduction from
the rectilinear Steiner tree problem.


  We propose two experimentally feasible methods based on atom interferometry
to measure the quantum state of the kicked rotor.


  This paper resolves one of the longest standing basic problems in the
streaming computational model. Namely, optimal construction of quantile
sketches. An $\varepsilon$ approximate quantile sketch receives a stream of
items $x_1,\ldots,x_n$ and allows one to approximate the rank of any query up
to additive error $\varepsilon n$ with probability at least $1-\delta$. The
rank of a query $x$ is the number of stream items such that $x_i \le x$. The
minimal sketch size required for this task is trivially at least
$1/\varepsilon$. Felber and Ostrovsky obtain a
$O((1/\varepsilon)\log(1/\varepsilon))$ space sketch for a fixed $\delta$. To
date, no better upper or lower bounds were known even for randomly permuted
streams or for approximating a specific quantile, e.g.,\ the median. This paper
obtains an $O((1/\varepsilon)\log \log (1/\delta))$ space sketch and a matching
lower bound. This resolves the open problem and proves a qualitative gap
between randomized and deterministic quantile sketching. One of our
contributions is a novel representation and modification of the widely used
merge-and-reduce construction. This subtle modification allows for an analysis
which is both tight and extremely simple. Similar techniques should be useful
for improving other sketching objectives and geometric coreset constructions.


  This paper studies the resource allocation algorithm design for secure
information and renewable green energy transfer to mobile receivers in
distributed antenna communication systems. In particular, distributed remote
radio heads (RRHs/antennas) are connected to a central processor (CP) via
capacity-limited backhaul links to facilitate joint transmission. The RRHs and
the CP are equipped with renewable energy harvesters and share their energies
via a lossy micropower grid for improving the efficiency in conveying
information and green energy to mobile receivers via radio frequency (RF)
signals. The considered resource allocation algorithm design is formulated as a
mixed non-convex and combinatorial optimization problem taking into account the
limited backhaul capacity and the quality of service requirements for
simultaneous wireless information and power transfer (SWIPT). We aim at
minimizing the total network transmit power when only imperfect channel state
information of the wireless energy harvesting receivers, which have to be
powered by the wireless network, is available at the CP. In light of the
intractability of the problem, we reformulate it as an optimization problem
with binary selection, which facilitates the design of an iterative resource
allocation algorithm to solve the problem optimally using the generalized
Bender's decomposition (GBD). Furthermore, a suboptimal algorithm is proposed
to strike a balance between computational complexity and system performance.
Simulation results illustrate that the proposed GBD based algorithm obtains the
global optimal solution and the suboptimal algorithm achieves a
close-to-optimal performance. Besides, the distributed antenna network for
SWIPT with renewable energy sharing is shown to require a lower transmit power
compared to a traditional system with multiple co-located antennas.


  We consider the Gaudin model associated to a point z in C^n with pairwise
distinct coordinates and to the subspace of singular vectors of a given weight
in the tensor product of irreducible finite-dimensional sl_2-representations,
[G]. The Bethe equations of this model provide the critical point system of a
remarkable rational symmetric function. Any critical orbit determines a common
eigenvector of the Gaudin hamiltonians called a Bethe vector.
  In [ReV], it was shown that for generic z the Bethe vectors span the space of
singular vectors, i.e. that the number of critical orbits is bounded from below
by the dimension of the space of singular vectors. The upper bound by the same
number is one of the main results of [SV].
  In the present paper we get this upper bound in another, ``less technical'',
way. The crucial observation is that the symmetric function defining the Bethe
equations can be interpreted as the generating function of the map sending a
pair of complex polynomials into their Wronski determinant: the critical orbits
determine the preimage of a given polynomial under this map. Within the
framework of the Schubert calculus, the number of critical orbits can be
estimated by the intersection number of special Schubert classes. Relations to
the sl_2 representation theory [F] imply that this number is the dimension of
the space of singular vectors.
  We prove also that the spectrum of the Gaudin hamiltonians is simple for
generic z.


  Let $\mathcal{I}_{d,g,r}$ be the union of irreducible components of the
Hilbert scheme whose general points correspond to smooth irreducible
non-degenerate curves of degree $d$ and genus $g$ in $\mathbb{P}^r$. We use
families of curves on cones to show that under certain numerical assumptions
for $d$, $g$ and $r$, the scheme $\mathcal{I}_{d,g,r}$ acquires generically
smooth components whose general points correspond to curves that are double
covers of irrational curves. In particular, in the case $\rho(d,g,r) :=
g-(r+1)(g-d+r) \geq 0$ we construct explicitly a regular component that is
different from the distinguished component of $\mathcal{I}_{d,g,r}$ dominating
the moduli space $\mathcal{M}_g$.


  It is challenging to develop two thoughts at the same time or perform two
uncorrelated motions simultaneously. This work looks specifically towards
training humans to perform a 2:3 polyrhythmic bimanual ratio using haptic force
feedback devices (SensAble Phantom OMNI). We implemented an interactive
training session to help participants learn to decouple their hand motions
quickly. Three subjects (2 Females, 1 Male) were tested and have successfully
increased their scores after adaptive training durations of under five minutes.


  The quantum worldsheet dynamics of vortex strings contains information about
the 4d non-Abelian gauge theory in which the string lives. Here I tell this
story. The string worldsheet theory is typically some variant of the CP^{N-1}
sigma-model, describing the orientation of the string in a U(N) gauge group.
Qualitative parallels between 2d sigma-models and 4d non-Abelian gauge theories
have been known since the 1970s. The vortex string provides a quantitative link
between the two. In 4d theories with N=2 supersymmetry, the exact BPS spectrum
of the worldsheet coincides with the bulk spectrum in 4d. Moreover, by tuning
parameters, the CP^{N-1} sigma-model can be coaxed to flow to an interacting
conformal fixed point which is related to the 4d Argyres-Douglas fixed point.
For theories with N=1 supersymmetry, the worldsheet theory suffers dynamical
supersymmetry breaking and, more interestingly, supersymmetry restoration, in a
way which captures the physics of Seiberg's quantum deformed moduli space.


  In this II, a probability to detect the neutrino produced in a high-energy
pion decay is shown to receive the large finite-size correction. The neutrino
interacts extremely weakly with matters and is described with a many-body wave
function together with the pion and charged lepton. This wave function slowly
approaches to an asymptotic form, which is probed by the neutrino. The whole
process is described by an S-matrix of a finite-time interval, which couples
with states of non-conserving kinetic energy, and the final states of a broad
spectrum specific to a relativistic invariant system contribute to the positive
semi-definite correction similar to diffraction of waves through a hole. This
diffraction component for the neutrino becomes long range and stable under
changes of the pion's energy.
  Moreover, it has a universal form that depends on the absolute neutrino mass.
Thus a new method of measuring the absolute neutrino mass is suggested.


  Domain shift is a very challenging problem for semantic segmentation. Any
model can be easily trained on synthetic data, where images and labels are
artificially generated, but it will perform poorly when deployed on real
environments. In this paper, we address the problem of domain adaptation for
semantic segmentation of street scenes. Many state-of-the-art approaches focus
on translating the source image while imposing that the result should be
semantically consistent with the input. However, we advocate that the image
semantics can also be exploited to guide the translation algorithm. To this
end, we rethink the generative model to enforce this assumption and strengthen
the connection between pixel-level and feature-level domain alignment. We
conduct extensive experiments by training common semantic segmentation models
with our method and show that the results we obtain on the synthetic-to-real
benchmarks surpass the state-of-the-art.


  Existing approaches to video understanding, mainly designed for short videos
from a third-person perspective, are limited in their applicability in certain
fields, such as robotics. In this paper, we delve into open-ended
question-answering (QA) in long, egocentric videos, which allows individuals or
robots to inquire about their own past visual experiences. This task presents
unique challenges, including the complexity of temporally grounding queries
within extensive video content, the high resource demands for precise data
annotation, and the inherent difficulty of evaluating open-ended answers due to
their ambiguous nature. Our proposed approach tackles these challenges by (i)
integrating query grounding and answering within a unified model to reduce
error propagation; (ii) employing large language models for efficient and
scalable data synthesis; and (iii) introducing a close-ended QA task for
evaluation, to manage answer ambiguity. Extensive experiments demonstrate the
effectiveness of our method, which also achieves state-of-the-art performance
on the QaEgo4D and Ego4D-NLQ benchmarks. Code, data, and models are available
at https://github.com/Becomebright/GroundVQA.


  As a neuromorphic sensor with high temporal resolution, spike camera can
generate continuous binary spike streams to capture per-pixel light intensity.
We can use reconstruction methods to restore scene details in high-speed
scenarios. However, due to limited information in spike streams, low-light
scenes are difficult to effectively reconstruct. In this paper, we propose a
bidirectional recurrent-based reconstruction framework, including a
Light-Robust Representation (LR-Rep) and a fusion module, to better handle such
extreme conditions. LR-Rep is designed to aggregate temporal information in
spike streams, and a fusion module is utilized to extract temporal features.
Additionally, we have developed a reconstruction benchmark for high-speed
low-light scenes. Light sources in the scenes are carefully aligned to
real-world conditions. Experimental results demonstrate the superiority of our
method, which also generalizes well to real spike streams. Related codes and
proposed datasets will be released after publication.


  Exact solutions of a magnetized plasma in a vorticity containing shear flow
for constant temperature are presented. This is followed by the modification of
these solutions by thermomagnetic currents in the presence of temperature
gradients. It is shown that solutions which are unstable for a subsonic flow,
are stable if the flow is supersonic.
  The results are applied to the problem of vorticity shear flow stabilization
of a linear z-pinch discharge.


  This work constructs symbolic dynamics for non-uniformly hyperbolic surface
maps with a set of discontinuities $D$. We allow the derivative of points
nearby $D$ to be unbounded, of the order of a negative power of the distance to
$D$. Under natural geometrical assumptions on the underlying space $M$, we code
a set of non-uniformly hyperbolic orbits that do not converge exponentially
fast to $D$. The results apply to non-uniformly hyperbolic planar billiards,
e.g. Bunimovich stadia.


  The Feynman quantum-classical isomorphism between classical statistical
mechanics in 3+1 dimensions and quantum statistical mechanics in 3 dimensions
is used to connect classical polymer self-consistent field theory with quantum
time-dependent density functional theory. This allows the theorems of density
functional theory to relate non-relativistic quantum mechanics back to a
classical statistical mechanical derivation of polymer self-consistent field
theory for ring polymers in a 4 dimensional thermal-space. One dynamic
postulate is added to two static postulates which allows for a complete
description of quantum physics from a 5 dimensional thermal-space-time ensemble
perspective which also removes the measurement problem. In the classical limit,
a cylinder condition naturally arises as the thermal dimension becomes
irrelevant, providing a justification for using 5 dimensions and a cylinder
condition in general relativity, which is known to produce 4 dimensional
space-time gravity and Maxwell's equations. Thus, in this approach, the
postulates of electromagnetism become derived results of a special case of a
ring polymer interpretation of quantum foundations.


  Estimates of national immunization coverage are crucial for guiding policy
and decision-making in national immunization programs and setting the global
immunization agenda. WHO and UNICEF estimates of national immunization coverage
(WUENIC) are produced annually for various vaccine-dose combinations and all
WHO Member States using information from multiple data sources and a
deterministic computational logic approach. This approach, however, is
incapable of characterizing the uncertainties inherent in coverage measurement
and estimation. It also provides no statistically principled way of exploiting
and accounting for the interdependence in immunization coverage data collected
for multiple vaccines, countries and time points. Here, we develop Bayesian
hierarchical modeling approaches for producing accurate estimates of national
immunization coverage and their associated uncertainties. We propose and
explore two candidate models: a balanced data single likelihood (BDSL) model
and an irregular data multiple likelihood (IDML) model, both of which differ in
their handling of missing data and characterization of the uncertainties
associated with the multiple input data sources. We provide a simulation study
that demonstrates a high degree of accuracy of the estimates produced by the
proposed models, and which also shows that the IDML model is the better model.
We apply the methodology to produce coverage estimates for select vaccine-dose
combinations for the period 2000-2019. A contributed R package {\tt imcover}
implementing the No-U-Turn Sampler (NUTS) in the Stan programming language
enhances the utility and reproducibility of the methodology.


  A Variable Parameter (VP) analysis aims to give precise time complexity
expressions of algorithms with exponents appearing solely in terms of variable
parameters. A variable parameter is the number of objects with specific
properties. Here we describe two VP-algorithms, an implicit enumeration and a
polynomial-time approximation scheme for a strongly $NP$-hard problem of
scheduling $n$ independent jobs with release and due times on one machine to
minimize the maximum job completion time $C_{\max}$. Our variable parameters
are the amounts of some specially defined types of jobs. A partial solution
without these jobs is constructed in a low degree polynomial time, and an
exponential time procedure (in the number of variable parameters) is carried
out to augment it to a complete optimal solution. In the alternative time
complexity expressions, the exponential dependence is solely on the some job
parameters. Applying the fixed parameter analysis to these estimations, a
polynomial-time dependence is achieved. Both, the intuitive probabilistic
estimations and our extensive experimental study support our conjecture that
the total number of the variable parameters is far less than $n$ and its ratio
to $n$ converges to 0 asymptotically.


  Solitons in nematic liquid crystals offer intriguing opportunities for
transport and sensing in microfluidic systems. Little is known about the
elementary conditions that are needed to create solitons in nematic materials.
In this work, theory, simulations and experiments are used to study the
generation and propagation of solitary waves (or "solitons") in nematic liquid
crystals upon the application of an alternating current (AC) electric field. We
find that these solitary waves exhibit "butterfly"-like or "bullet"-like
structures that travel in the direction perpendicular to the applied electric
field. Such structures propagate over long distances without losing their
initial shape. The theoretical model adopted here serves to identify some of
the key requirements that are needed to generate solitons in the absence of
electrostatic interactions. These include surface imperfections that introduce
a twist in the director, unequal elastic constants, and negative anisotropic
dielectric permittivity. The results of simulations are shown to be in good
agreement with our own experimental observations, serving to establish the
validity of the theoretical concepts advanced in this work.


  Auroral classification plays a crucial role in polar research. However,
current auroral classification studies are predominantly based on images taken
at a single wavelength, typically 557.7 nm. Images obtained at other
wavelengths have been comparatively overlooked, and the integration of
information from multiple wavelengths remains an underexplored area. This
limitation results in low classification rates for complex auroral patterns.
Furthermore, these studies, whether employing traditional machine learning or
deep learning approaches, have not achieved a satisfactory trade-off between
accuracy and speed. To address these challenges, this paper proposes a
lightweight auroral multi-wavelength fusion classification network, MLCNet,
based on a multi-view approach. Firstly, we develop a lightweight feature
extraction backbone, called LCTNet, to improve the classification rate and cope
with the increasing amount of auroral observation data. Secondly, considering
the existence of multi-scale spatial structures in auroras, we design a novel
multi-scale reconstructed feature module named MSRM. Finally, to highlight the
discriminative information between auroral classes, we propose a lightweight
attention feature enhancement module called LAFE. The proposed method is
validated using observational data from the Arctic Yellow River Station during
2003-2004. Experimental results demonstrate that the fusion of multi-wavelength
information effectively improves the auroral classification performance. In
particular, our approach achieves state-of-the-art classification accuracy
compared to previous auroral classification studies, and superior results in
terms of accuracy and computational efficiency compared to existing multi-view
methods.


  Resistive random-access memory (RRAM) is widely recognized as a promising
emerging hardware platform for deep neural networks (DNNs). Yet, due to
manufacturing limitations, current RRAM devices are highly susceptible to
hardware defects, which poses a significant challenge to their practical
applicability. In this paper, we present a machine learning technique that
enables the deployment of defect-prone RRAM accelerators for DNN applications,
without necessitating modifying the hardware, retraining of the neural network,
or implementing additional detection circuitry/logic. The key idea involves
incorporating a drop-connect inspired approach during the training phase of a
DNN, where random subsets of weights are selected to emulate fault effects
(e.g., set to zero to mimic stuck-at-1 faults), thereby equipping the DNN with
the ability to learn and adapt to RRAM defects with the corresponding fault
rates. Our results demonstrate the viability of the drop-connect approach,
coupled with various algorithm and system-level design and trade-off
considerations. We show that, even in the presence of high defect rates (e.g.,
up to 30%), the degradation of DNN accuracy can be as low as less than 1%
compared to that of the fault-free version, while incurring minimal
system-level runtime/energy costs.


  Coupled oscillator networks often display transitions between qualitatively
different phase-locked solutions -- such as synchrony and rotating wave
solutions -- following perturbation or parameter variation. In the limit of
weak coupling, these transitions can be understood in terms of commonly studied
phase approximations. As the coupling strength increases, however, predicting
the location and criticality of transition, whether continuous or
discontinuous, from the phase dynamics may depend on the order of the phase
approximation -- or a phase description of the network dynamics that neglects
amplitudes may become impossible altogether. Here we analyze synchronization
transitions and their criticality systematically for varying coupling strength
in theory and experiments with coupled electrochemical oscillators. First, we
analyze bifurcations analysis of synchrony and splay states in an abstract
phase model and discuss conditions under which synchronization transitions with
different criticalities are possible. Second, we illustrate that transitions
with different criticality indeed occur in experimental systems. Third, we
highlight that the amplitude dynamics observed in the experiments can be
captured in a numerical bifurcation analysis of delay-coupled oscillators. Our
results showcase that reduced order phase models may miss important features
that one would expect in the dynamics of the full system.


  We study the motion of an elastic rigid rod which is radially free-falling
towards a Schwarzschild black hole. This is accomplished by reducing the
corresponding free-boundary PDE problem to a sequence of ODEs, which we
integrate numerically. Starting with a rod at rest, we show that it is possible
to choose its initial compression profile so that its midpoint falls
substantially faster, or slower, than a free-falling particle with the same
initial conditions. This seems to be a purely kinematic effect, since on
average there is no net transfer of elastic to mechanical energy.


  Theory of Mind (ToM) is the cognitive capability to perceive and ascribe
mental states to oneself and others. Recent research has sparked a debate over
whether large language models (LLMs) exhibit a form of ToM. However, existing
ToM evaluations are hindered by challenges such as constrained scope,
subjective judgment, and unintended contamination, yielding inadequate
assessments. To address this gap, we introduce ToMBench with three key
characteristics: a systematic evaluation framework encompassing 8 tasks and 31
abilities in social cognition, a multiple-choice question format to support
automated and unbiased evaluation, and a build-from-scratch bilingual inventory
to strictly avoid data leakage. Based on ToMBench, we conduct extensive
experiments to evaluate the ToM performance of 10 popular LLMs across tasks and
abilities. We find that even the most advanced LLMs like GPT-4 lag behind human
performance by over 10% points, indicating that LLMs have not achieved a
human-level theory of mind yet. Our aim with ToMBench is to enable an efficient
and effective evaluation of LLMs' ToM capabilities, thereby facilitating the
development of LLMs with inherent social intelligence.


  In particle accelerators, particle losses to surrounding components must be
minimized. These particles usually have been driven into an undesired "halo"
outside the desired distribution before being lost. The processes involved and
physical identification of such halo is an intense research topic especially
when the nonlinear space charge effect is taken into account. In order to
present a method, firmly based on the physics of the transient beam state, for
determining when a particle may be defined as being in a halo, the particular
example of an initially rms matched beam injected into a resonance of an
alternating-gradient (AG) focusing lattice is studied, in which the resonance
between the collective mode and single particle motion pushes some particles
into a halo defined by extending the halo description to the action-angle
frame. In this new frame of description, the halo particles can be physically
defined as those with larger actions affected by the outer quasi hyperbolic
tori, which contains the halo particles observed in the traditional approaches
on projected 2D phase space, as well as some particles still hidden in the
core.


  On-policy imitation learning algorithms such as DAgger evolve a robot control
policy by executing it, measuring performance (loss), obtaining corrective
feedback from a supervisor, and generating the next policy. As the loss between
iterations can vary unpredictably, a fundamental question is under what
conditions this process will eventually achieve a converged policy. If one
assumes the underlying trajectory distribution is static (stationary), it is
possible to prove convergence for DAgger. However, in more realistic models for
robotics, the underlying trajectory distribution is dynamic because it is a
function of the policy. Recent results show it is possible to prove convergence
of DAgger when a regularity condition on the rate of change of the trajectory
distributions is satisfied. In this article, we reframe this result using
dynamic regret theory from the field of online optimization and show that
dynamic regret can be applied to any on-policy algorithm to analyze its
convergence and optimality. These results inspire a new algorithm, Adaptive
On-Policy Regularization (AOR), that ensures the conditions for convergence. We
present simulation results with cart-pole balancing and locomotion benchmarks
that suggest AOR can significantly decrease dynamic regret and chattering as
the robot learns. To our knowledge, this the first application of dynamic
regret theory to imitation learning.


  A Mythen detector has been equipped at the beamline 4B9A of Beijing
Synchrotron Radiation Facility, which can be used for in-situ real-time
measurement of X-ray diffraction (XRD) full profiles. In this paper, the
thermal expansion behavior of metal indium has been studied by using the
in-situ XRD technique with the Mythen detector. The indium film was heated from
30 to 160 {\deg}C with a heating rate of 2 {\deg}C/min. The in-situ XRD
full-profiles were collected with a rate of one profile per 10 seconds.
Rietveld refinement was used to extract the structural parameters. The results
demonstrate that the thermal expansion of metal indium is nonlinear especially
when the sample temperature was close to its melting point (156.5 {\deg}C). The
expansion of a-axis and the contraction of c-axis of the tetragonal unit cell
of metallic indium can be well described by biquadratic and cubic polynomials,
respectively. The tetragonal unit cell presents a tendency to become cubic one
with the increase of temperature but without detectable phase change. This
study is not only beneficial to the application of metal indium, but also
exhibits the capacity of in-situ time-resolved XRD experiments at the X-ray
diffraction station of BSRF.


  The extended Wild sums considered in this article generalize the classi- cal
Wild sums of statistical physics. We first show how to obtain explicit
solutions for the evolution equation of a large system where the interactions
are given by a single, but general, interacting kernel which involves m
components, for a fixed m >= 2. We then show how to retain the explicit
formulas for the case of OTC market models where the dynamics is more directly
described by two (or more) kernels.


  Correlating neuropathology with neuroimaging findings provides a multiscale
view of pathologic changes in the human organ spanning the meso- to
micro-scales, and is an emerging methodology expected to shed light on numerous
disease states. To gain the most information from this multimodal, multiscale
approach, it is desirable to identify precisely where a histologic tissue
section was taken from within the organ in order to correlate with the tissue
features in exactly the same organ region. Histology-to-organ registration
poses an extra challenge, as any given histologic section can capture only a
small portion of a human organ. Making use of the capabilities of
state-of-the-art deep learning models, we unlock the potential to address and
solve such intricate challenges. Therefore, we create the ATOM benchmark
dataset, sourced from diverse institutions, with the primary objective of
transforming this challenge into a machine learning problem and delivering
outstanding outcomes that enlighten the biomedical community. The performance
of our RegisMCAN model demonstrates the potential of deep learning to
accurately predict where a subregion extracted from an organ image was obtained
from within the overall 3D volume. The code and dataset can be found at:
https://github.com/haizailache999/Image-Registration/tree/main


  Stochastic hybrid systems involve a coupling between a discrete Markov chain
and a continuous stochastic process. If the latter evolves deterministically
between jumps in the discrete state, then the system reduces to a piecewise
deterministic Markov process (PDMP). Well known examples include stochastic
gene expression, voltage fluctuations in neurons, and motor-driven
intracellular transport. In this paper we use coherent spin states to construct
a new path integral representation of the probability density functional for
stochastic hybrid systems, which holds outside the weak noise regime. We use
the path integral to derive a system of Langevin equations in the
semi-classical limit, which extends previous diffusion approximations based on
a quasi-steady-state reduction. We then show how in the weak noise limit the
path integral is equivalent to an alternative representation that was
previously derived using Doi-Peliti operators. The action functional of the
latter is related to a large deviation principle for stochastic hybrid systems.


  Different mechanisms for the creation of strange non-chaotic dynamics in the
quasiperiodically forced logistic map are studied. These routes to strange
nonchaos are characterised through the behavior of the largest nontrivial
Lyapunov exponent, as well as through the characteristic distributions of
finite time Lyapunov exponents. Strange nonchaotic attractors can be created at
a saddle-node bifurcation when the dynamics shows Type-I intermittency; this
intermittent transition, which is studied in detail, is characterised through
scaling exponents. Band-merging crises through which dynamics remains
nonchaotic are also studied, and correspondence is made with analogous behavior
in the unforced logistic map. Robustness of these phenomena with respect to
additive noise is investigated.


  We present a complete set of generators for the rank 5 special unitary group,
SU(6), to unify strong, weak and electromagnetic interactions. The unification
is realized through the breaking pattern of SU)6) -> SU(3)_C x SU(3)_H x U(1)_C
followed by SU(3)_H -> SU(2)_L x U(1)_B. All known elementary particles and its
quantum numbers are well accomodated in its {6} and {15} multiplets. These
multiplets require a new neutral fermion which should be assigned as the heavy
Majorana neutrino to realize the seesaw mechanism naturally in the minimal
scenario of this model.


  Let $X_{1}$ be a projective, smooth and geometrically connected curve over
$\mathbb{F}_{q}$ with $q=p^{n}$ elements where $p$ is a prime number, and let
$X$ be its base change to an algebraic closure of $\mathbb{F}_{q}$. We give a
formula for the number of irreducible $\ell$-adic local systems ($\ell\neq p$)
with a fixed rank over $X$ fixed by the Frobenius endomorphism. We prove that
this number behaves like a Lefschetz fixed point formula for a variety over
$\mathbb{F}_q$, which generalises a result of Drinfeld in rank $2$ and proves a
conjecture of Deligne. To do this, we pass to the automorphic side by Langlands
correspondence, then use Arthur's non-invariant trace formula and link this
number to the number of $\mathbb{F}_q$-points of the moduli space of stable
Higgs bundles.


  Balancing passenger demand and vehicle availability is crucial for ensuring
the sustainability and effectiveness of urban transportation systems. To
address this challenge, we propose a novel hierarchical strategy for the
efficient distribution of empty vehicles in urban areas. The proposed approach
employs a data-enabled predictive control algorithm to develop a high-level
controller, which guides the inter-regional allocation of idle vehicles. This
algorithm utilizes historical data on passenger demand and vehicle supply in
each region to construct a non-parametric representation of the system,
enabling it to determine the optimal number of vehicles to be repositioned or
retained in their current regions without modeling the system. At the low
level, a coverage control-based controller is designed to provide
inter-regional position guidance, determining the desired road intersection
each vehicle should target. With the objective of optimizing area coverage, it
aligns the vehicle distribution with the demand across different districts
within a single region. The effectiveness of the proposed method is validated
through simulation experiments on the real road network of Shenzhen, China. The
integration of the two layers provides better performance compared to applying
either layer in isolation, demonstrating its potential to reduce passenger
waiting time and answer more requests, thus promoting the development of more
efficient and sustainable transportation systems.


  Overlap coincidence in a self-affine tiling in $\R^d$ is equivalent to pure
point dynamical spectrum of the tiling dynamical system. We interpret the
overlap coincidence in the setting of substitution Delone set in $\R^d$ and
find an efficient algorithm to check the pure point dynamical spectrum. This
algorithm is easy to implement into a computer program. We give the program and
apply it to several examples. In the course the proof of the algorithm, we show
a variant of the conjecture of Urba\'nski (Solomyak \cite{Solomyak:08}) on the
Hausdorff dimension of the boundaries of fractal tiles.


  We consider closed orientable surfaces $S$ of genus $g>1$ and homeomorphisms
$f:S\rightarrow S$ homotopic to the identity. A set of hypotheses is presented,
called fully essential system of curves $\mathscr{C}$ and it is shown that
under these hypotheses, the natural lift of $f$ to the universal cover of $S$
(the Poincar\'e disk $\mathbb{D}),$ denoted $\widetilde{f},$ has complicated
and rich dynamics. In this context we generalize results that hold for
homeomorphisms of the torus homotopic to the identity when their rotation sets
contain zero in the interior. In particular, we prove that if $f$ is a
$C^{1+\epsilon }$ diffeomorphism for some $\epsilon >0$ and $\pi
:\mathbb{D}\rightarrow S$ is the covering map, then there exists a contractible
hyperbolic $f$-periodic saddle point $p\in S$ such that for any
$\widetilde{p}\in \pi ^{-1}(p),$ $$W^u(\widetilde{p}) \pitchfork
W^s(g(\widetilde{p})) $$ for all deck transformations $g\in Deck(\pi ).$ By
$\pitchfork,$ we mean a topologically transverse intersection between the
manifolds, see the precise definition in subsection 1.1. We also show that the
homological rotation set of such a $f$ is a compact convex subset of
$\mathbb{R}^{2g}$ with maximal dimension and all points in its interior are
realized by compact $f$-invariant sets, periodic orbits in the rational case,
and $f$ has uniformly bounded displacement with respect to rotation vectors in
the boundary of the rotation set. Something that implies, in case $f$ is
area-preserving, that the rotation vector of Lebesgue measure belongs to the
interior of the rotation set.


  Quite much recent studies has been attracted to the operated algebra since it
unifies various notions such as the differential algebra and the Rota-Baxter
algebra. An $\Omega$-operated algebra is a an (associative) algebra equipped
with a set $\Omega$ of linear operators which might satisfy certain operator
identities such as the Leibniz rule. A free $\Omega$-operated algebra $B$ can
be generated on an algebra $A$ similar to a free algebra generated on a set. If
$A$ has a Gr\"{o}bner-Shirshov basis $G$ and if the linear operators $\Omega$
satisfy a set $\Phi$ of operator identities, it is natural to ask when the
union $G\cup \Phi$ is a Gr\"{o}bner-Shirshov basis of $B$. A previous work
answers this question affirmatively under a mild condition, and thereby obtains
a canonical linear basis of $B$.
  In this paper, we answer this question in the general case of multiple linear
operators. As applications we get operated Gr\"{o}bner-Shirshov bases for free
differential Rota-Baxter algebras and free integro-differential algebras over
algebras as well as their linear bases. One of the key technical difficulties
is to introduce new monomial orders for the case of two operators, which might
be of independent interest.


  We have developed a new approach based on matrix product representations of
ground states to study Quantum Phase Transitions (QPT). As confirmation of the
power of our approach we have analytically analyzed the XXZ spin-one chain with
uniaxial single-ion-type anisotropy and our results compare favourably with
previous numerical studies. In addition, our description lets to know which
part of parameters space of the Hamiltonian is most likely to be exactly
solvable.


  We show how the C*-algebras of quantum complex projective spaces (standard or
nonstandard) are related to groupoids.


  Finding the structure of a graphical model has been received much attention
in many fields. Recently, it is reported that the non-Gaussianity of data
enables us to identify the structure of a directed acyclic graph without any
prior knowledge on the structure. In this paper, we propose a novel
non-Gaussianity based algorithm for more general type of models; chain graphs.
The algorithm finds an ordering of the disjoint subsets of variables by
iteratively evaluating the independence between the variable subset and the
residuals when the remaining variables are regressed on those. However, its
computational cost grows exponentially according to the number of variables.
Therefore, we further discuss an efficient approximate approach for applying
the algorithm to large sized graphs. We illustrate the algorithm with
artificial and real-world datasets.


  Semi-supervised semantic segmentation aims to learn from a small amount of
labeled data and plenty of unlabeled ones for the segmentation task. The most
common approach is to generate pseudo-labels for unlabeled images to augment
the training data. However, the noisy pseudo-labels will lead to cumulative
classification errors and aggravate the local inconsistency in prediction. This
paper proposes a Region Relevance Network (RRN) to alleviate the problem
mentioned above. Specifically, we first introduce a local pseudo-label
filtering module that leverages discriminator networks to assess the accuracy
of the pseudo-label at the region level. A local selection loss is proposed to
mitigate the negative impact of wrong pseudo-labels in consistency
regularization training. In addition, we propose a dynamic region-loss
correction module, which takes the merit of network diversity to further rate
the reliability of pseudo-labels and correct the convergence direction of the
segmentation network with a dynamic region loss. Extensive experiments are
conducted on PASCAL VOC 2012 and Cityscapes datasets with varying amounts of
labeled data, demonstrating that our proposed approach achieves
state-of-the-art performance compared to current counterparts.


  We propose a new chiral model of metastable supersymmetry breaking in the
conformal window via chiral/nonchiral Seiberg duality, which is focused on
Spin(7)/SU(N_f-4) duality in this letter. Following the approach of
Intriligator-Seiberg-Shih model, a small mass perturbation in the nonchiral
theory leads to supersymmetry breaking by rank condition in the chiral dual
description.


  A sunflower with $k$ petals, or $k$-sunflower, is a family of $k$ sets every
two of which have a common intersection. Known since 1960, the sunflower
conjecture states that a family ${\mathcal F}$ of sets each of cardinality $m$
includes a $k$-sunflower if $|{\mathcal F}| \ge c_k^m$ for some $c_k \in
{\mathbb R}_{>0}$ depending only on $k$. The case $k=3$ of the conjecture was
especially emphasized by Erd\"os, for which Kostochka's bound $c m! \left(
\frac{\log \log \log m}{\log \log m} \right)^m$ on $|{\mathcal F}|$ without a
3-sunflower had been the best-known since 1997 until the recent development to
update it to $c \log m$. This paper proves with an entirely different
combinatorial approach that ${\mathcal F}$ includes three mutually disjoint
sets if it satisfies the $\Gamma \left( c m^{\frac{1}{2}+ \delta}
\right)$-condition for any given $\delta \in (0, 1/2)$. Here $c$ is a constant
depending only on $\delta$, and the $\Gamma$-condition refers to \[ | \left\{
U~:~ U \in {\mathcal F} \textrm{~and~} S \subset U \right\}| < \left( c
m^{\frac{1}{2}+ \delta} \right)^{-|S|} |{\mathcal F}|, \] for every nonempty
set $S$. This poses an alternative proof of the 3-sunflower bound $\left( c
m^{\frac{1}{2}+ \delta} \right)^m$.


  Realizations of algebras in terms of canonical or bosonic variables can often
be used to simplify calculations and to exhibit underlying properties. There is
a long history of using such methods in order to study symmetry groups related
to collective motion, for instance in nuclear shell models. Here, related
questions are addressed for algebras obtained by turning the quantum commutator
into a Poisson bracket on moments of a quantum state, truncated to a given
order. In this application, canonical realizations allow one to express the
quantum back-reaction of moments on basic expectation values by means of
effective potentials. In order to match degrees of freedom, faithfulness of the
realization is important, which requires that, at least locally, the space of
moments as a Poisson manifold is realized by a complete set of Casimir-Darboux
coordinates in local charts. A systematic method to derive such variables is
presented and applied to certain sets of moments which are important for
physical applications. If only second-order moments are considered, their
Poisson-bracket relations are isomorphic to the Lie bracket of sp(2N,R),
providing an interesting link with realizations of nuclear shell models.


  We identify 42 candidate groups lying between 1.8<z<3.0 from a sample of 3502
galaxies with spectroscopic redshifts in the zCOSMOS-deep redshift survey
within the same redshift interval. These systems contain three to five
spectroscopic galaxies that lie within 500kpc in projected distance (in
physical space) and within 700km/s in velocity. Based on extensive analysis of
mock catalogues that have been generated from the Millennium simulation, we
examine the likely nature of these systems at the time of observation, and what
they will evolve into down to the present epoch. Although few of the "member"
galaxies are likely to reside in the same halo at the epoch we observe them,
50% of the systems will eventually bring them all into the same halo, and
almost all (93%) will have at least part of the member galaxies in the same
halo by the present epoch. Most of the candidate groups can therefore be
described as "proto-groups". An estimate of the overdensities is also
consistent with the idea that these systems are being seen at the start of the
assembly process. We also examine present-day haloes and ask whether their
progenitors would have been seen amongst our candidate groups. For present-day
haloes between 10^14-10^15Msun/h, 35% should have appeared amongst our
candidate groups, and this would have risen to 70% if our survey had been
fully-sampled, so we can conclude that our sample can be taken as
representative of a large fraction of such systems. There is a clear excess of
massive galaxies above 10^10Msun around the locations of the candidate groups
in a large independent COSMOS photo-z sample, but we see no evidence in this
latter data for any colour differentiation with respect to the field. This is
however consistent with the idea that such differentiation arises in satellite
galaxies, as indicated at z<1, if the candidate groups are indeed only starting
to be assembled.


  While large language models (LLMs) have enabled learning knowledge from the
pre-training corpora, the acquired knowledge may be fundamentally incorrect or
outdated over time, which necessitates rectifying the knowledge of the language
model (LM) after the training. A promising approach involves employing a
hyper-network to generate parameter shift, whereas existing hyper-networks
suffer from inferior scalability in synchronous editing operation amount. To
mitigate the problem, we propose the MAssive Language Model Editing Network
(MALMEN), which formulates the parameter shift aggregation as the least square
problem, subsequently updating the LM parameters using the normal equation. To
accommodate editing multiple facts simultaneously with limited memory budgets,
we separate the computation on the hyper-network and LM, enabling arbitrary
batch size on both neural networks. Our method is evaluated by editing up to
thousands of facts on LMs with different architectures, i.e., BERT-base, GPT-2,
T5-XL (2.8B), and GPT-J (6B), across various knowledge-intensive NLP tasks,
i.e., closed book fact-checking and question answering. Remarkably, MALMEN is
capable of editing hundreds of times more facts than strong baselines with the
identical hyper-network architecture and outperforms editor specifically
designed for GPT. Our code is available at
https://github.com/ChenmienTan/malmen.


  We present evidence for condensed phase methane precipitation near Xanadu
using nine nights of observations from the SINFONI integral-field spectrograph
at the Very Large Telescope and imaging analysis with empirical surface
subtraction. Radiative transfer models are used to support the imaging
technique by simulating the spectrometer datacubes and testing for variations
in both the surface reflectivity spectrum and atmospheric opacity. We use the
models and observations together to argue against artifacts that may arise in
the image analysis. High phase angle observations from Cassini/VIMS are used to
test against surface scattering artifacts that may be confused with sources of
atmospheric opacity. Although changes in the surface reflectivity spectrum can
reproduce observations from a particular viewing geometry on a given night,
multiple observations are best modeled by condensed-phase methane opacity near
the surface. These observations and modeling indicate that the condensed-phase
methane opacity observed with this technique occurs predominantly near Xanadu
and is most likely due to precipitation.


  Spin-only approaches to anisotropic effects in strongly interacting materials
are often insufficient for systems close to the Mott regime. Within a model
context, here the consequences of the low-symmetry relevant
Dzyaloshinskii-Moriya (DM) interaction are studied for strongly correlated, but
overall itinerant, systems. Namely, we investigate the Hubbard bilayer model
supplemented by a DM term at half filling and in the hole-doped regime. As an
add-on, further results for the two- impurity Anderson model with DM
interaction are also provided. The model Hamiltonians are treated by means of
the rotational invariant slave boson technique at saddle point within a
(cellular) cluster approach. Already small values of the anisotropic
interaction prove to have a strong influence on the phases and correlation
functions with increasing U. An intriguing metallic spin-flop phase is found in
the doped bilayer model and a reduction of the RKKY exchange in the
two-impurity model.


  Cold compaction of ceramic powders is driven by plastic strain, during which
the elastic stiffness of the material progressively increases from values
typical of granular matter to those representative of a fully dense solid. This
increase of stiffness strongly affects the mechanical behaviour of the green
body and is crucial in the modelling of forming processes for ceramics. A
protocol for ultrasonic experimental investigation (via P and S waves
transmission) is proposed to quantify the elastic constants (Young modulus and
Poisson's ratio) as functions of the forming pressure. Experimental results
performed in uniaxial strain allow for the introduction of laws that describe
the variation of the elastic constants during densification. These laws are
motivated in terms of elastoplastic coupling through the simulation of an
isostatic pressure compaction process of alumina powder. A micromechanical
explanation of the stiffening of elastic properties during densification is
deferred to Part II of this study.


  We reconsider the two different facets of $\pi$ and $K$ mesons as $q \bar q$
bound states and approximate Nambu-Goldstone bosons. We address several topics,
including masses, mass splittings between $\pi$ and $\rho$ and between $K$ and
$K^*$, meson wavefunctions, charge radii, and the $K-\pi$ wavefunction overlap.


  We study dynamo action in a convective layer of electrically-conducting,
compressible fluid, rotating about the vertical axis. At the upper and lower
bounding surfaces, perfectly-conducting boundary conditions are adopted for the
magnetic field. Two different levels of thermal stratification are considered.
If the magnetic diffusivity is sufficiently small, the convection acts as a
small-scale dynamo. Using a definition for the magnetic Reynolds number $R_M$
that is based upon the horizontal integral scale and the horizontally-averaged
velocity at the mid-layer of the domain, we find that rotation tends to reduce
the critical value of $R_M$ above which dynamo action is observed. Increasing
the level of thermal stratification within the layer does not significantly
alter the critical value of $R_M$ in the rotating calculations, but it does
lead to a reduction in this critical value in the non-rotating cases. At the
highest computationally-accessible values of the magnetic Reynolds number, the
saturation levels of the dynamo are similar in all cases, with the mean
magnetic energy density somewhere between 4 and 9% of the mean kinetic energy
density. To gain further insights into the differences between rotating and
non-rotating convection, we quantify the stretching properties of each flow by
measuring Lyapunov exponents. Away from the boundaries, the rate of stretching
due to the flow is much less dependent upon depth in the rotating cases than it
is in the corresponding non-rotating calculations. It is also shown that the
effects of rotation significantly reduce the magnetic energy dissipation in the
lower part of the layer. We also investigate certain aspects of the saturation
mechanism of the dynamo.


  We find general non-linear lagrangians of a U(1) field invariant under
electric-magnetic duality. They are characterized by an arbitrary function and
go to the Maxwell theory in the weak field limit. We give some explicit
examples which are generalizations of the Born-Infeld theory.


  We describe the supercuspidal representations of Sp(4,F), for F a
non-archimedean local field of residual characteristic different from 2, and
determine which are generic.


  We demonstrate how to find both the color diagonal form of the squared Dirac
equation in the axial color background and the transformation of the color
space, which makes this equation diagonal.


  We consider a family of linear viscoelastic shells with thickness
$2\varepsilon$ ( $\varepsilon$ , small parameter), clamped along a portion of
their lateral face, all having the same middle surface $S$. We formulate the
three-dimensional mechanical problem in curvilinear coordinates and provide
existence and uniqueness of (weak) solution of the corresponding
three-dimensional variational problem.
  We are interested in studying the limit behavior of the three-dimensional
problems and their solutions (displacements $\mathbf{u}^\varepsilon$ of
components $u_i^\varepsilon$) when $\varepsilon$ tends to zero. To do that, we
use asymptotic analysis methods. First, we formulate the variational problem in
a fixed domain independent of $\varepsilon$. Then we assume an asymptotic
expansion of the scaled displacements field
$\mathbf{u}(\varepsilon)=(u_i(\varepsilon))$. Identifying the terms of the
proposed asymptotic expansion we characterize the zeroth order term as the
solution of a two-dimensional scaled limit problem. Moreover, on one hand, we
find that if the applied body force density is $O(1)$ with respect to
$\varepsilon$ and surface tractions density is $O(\varepsilon)$, the limit of
the field $\mathbf{u}(\varepsilon)$ is the solution of a two-dimensional system
of variational equations called viscoelastic membrane problem. On the other
hand, if the applied body force density is $O(\varepsilon^2)$ and surface
tractions density is $O(\varepsilon^3)$, the limit of the field
$\mathbf{u}(\varepsilon)$ is the solution of a system of two-dimensional
variational equations called viscoelastic flexural problem.
  In both cases, we find a model which presents a long-term memory that takes
into account the deformations at previous times. We comment on the existence
and uniqueness of solution for the two-dimensional variational problems found
and announce convergence results in forthcoming papers.


  Computational fluid dynamics (CFD) models of blood flow in the left ventricle
(LV) and aorta are important tools for analyzing the mechanistic links between
myocardial deformation and flow patterns. Typically, the use of image-based
kinematic CFD models prevails in applications such as predicting the acute
response to interventions which alter LV afterload conditions. However, such
models are limited in their ability to analyze any impacts upon LV load or key
biomarkers known to be implicated in driving remodeling processes as LV
function is not accounted for in a mechanistic sense.
  This study addresses these limitations by reporting on progress made towards
a novel electro-mechano-fluidic (EMF) model that represents the entire physics
of LV electromechanics (EM) based on first principles. A biophysically detailed
finite element (FE) model of LV EM was coupled with a FE-based CFD solver for
moving domains using an arbitrary Eulerian-Lagrangian (ALE) formulation. Two
clinical cases of patients suffering from aortic coarctations (CoA) were built
and parameterized based on clinical data under pre-treatment conditions. For
one patient case simulations under post-treatment conditions after geometric
repair of CoA by a virtual stenting procedure were compared against
pre-treatment results. Numerical stability of the approach was demonstrated by
analyzing mesh quality and solver performance under the significantly large
deformations of the LV blood pool. Further, computational tractability and
compatibility with clinical time scales were investigated by performing strong
scaling benchmarks up to 1536 compute cores. The overall cost of the entire
workflow for building, fitting and executing EMF simulations was comparable to
those reported for image-based kinematic models, suggesting that EMF models
show potential of evolving into a viable clinical research tool.


  We present a phenomenological analysis of the cos-phi and cos-2phi
asymmetries in unpolarized semi-inclusive deep inelastic scattering, based on
the recent multidimensional data released by the COMPASS and HERMES
Collaborations. In the TMD framework, valid at relatively low transverse
momenta, these asymmetries arise from intrinsic transverse momentum and
transverse spin effects, and from their correlations. The role of the Cahn and
Boer-Mulders effects in both azimuthal moments is explored up to order 1/Q. As
the kinematics of the present experiments is dominated by the low-Q^2 region,
higher-twist contributions turn out to be important, affecting the results of
our fits.


  The functional delta-method provides a convenient tool for deriving the
asymptotic distribution of a plug-in estimator of a statistical functional from
the asymptotic distribution of the respective empirical process. Moreover, it
provides a tool to derive bootstrap consistency for plug-in estimators from
bootstrap consistency of empirical processes. It has recently been shown that
the range of applications of the functional delta-method for the asymptotic
distribution can be considerably enlarged by employing the notion of
quasi-Hadamard differentiability. Here we show in a general setting that this
enlargement carries over to the bootstrap. That is, for quasi-Hadamard
differentiable functionals bootstrap consistency of the plug-in estimator
follows from bootstrap consistency of the respective empirical process. This
enlargement often requires convergence in distribution of the bootstrapped
empirical process w.r.t.\ a nonuniform sup-norm. The latter is not problematic
as will be illustrated by means of examples.


  Standard methods for multi-label text classification largely rely on
encoder-only pre-trained language models, whereas encoder-decoder models have
proven more effective in other classification tasks. In this study, we compare
four methods for multi-label classification, two based on an encoder only, and
two based on an encoder-decoder. We carry out experiments on four datasets --
two in the legal domain and two in the biomedical domain, each with two levels
of label granularity -- and always depart from the same pre-trained model, T5.
Our results show that encoder-decoder methods outperform encoder-only methods,
with a growing advantage on more complex datasets and labeling schemes of finer
granularity. Using encoder-decoder models in a non-autoregressive fashion, in
particular, yields the best performance overall, so we further study this
approach through ablations to better understand its strengths.


  The contribution of a $K^*(1430)$ $0^+$ resonance to $D^0\to K^-\pi^+$ is
calculated by applying the soft pion theorem to $D^+ \to K^* \pi^+$, and is
found to be about 30% of the measured amplitude and to be larger than the
$\Delta I=3/2$ component of this amplitude. We estimate a 70% contribution to
the total amplitude from a higher $K^*(1950)$ resonance. This implies large
deviations from factorization in D decay amplitudes, a lifetime difference
between D^0 and D^+, and an enhancement of $D^0-\bar D^0$ mixing due to SU(3)
breaking.


  In this paper we study some properties of almost abelian solvmanifolds using
minimal models associated to a fibration. In particular we state a necessary
and sufficient condition to formality and a method for finding symplectic
strucures of this kind of solvmanifolds.


  We classify tame block algebras of Hecke algebras of classical type over an
algebraically closed field of odd characteristic.


  Comparisons of the positive and negative halves of the distributions of
parity-odd event variables in particle-physics experimental data can provide
sensitivity to sources of non-standard parity violation. Such techniques
benefit from lacking first-order dependence on simulations or theoretical
models, but have hitherto lacked systematic means of enumerating all
discoverable signals. To address that issue this paper seeks to construct sets
of parity-odd event variables which may be proved to be able to reveal the
existence of any Lorentz-invariant source of non-standard parity violation
which could be visible in data consisting of groups of real non space-like
four-momenta exhibiting certain permutation symmetries.


  seNorge_2018 is an observational gridded dataset for daily aggregated
temperatures and precipitation data over the Norwegian mainland. The time
interval covered spans more than 60 years, from the 1st of January 1957 to the
present day. Version 20.05 of the historical archive (1957-2019) is described
in this document, with special emphasis on the variations in the methods with
respect to the previous version of the archive, which is version 18.12.


  This study aimed to investigate the antitumor effect of ultrasmall gold
nanoparticles (AuNPs), around 3 nm, stabilized by the anionic polysaccharide
gum arabic (GA-AuNPs). The focus was downregulation of cancer hallmarks of
aggressive tumors, using a highly metastatic model of melanoma. We first
demonstrated that GA-AuNPs showed excellent stability under biological
environment. Non-cytotoxic concentrations to seven different cell lines,
including tumorigenic and non-tumorigenic cells, were determined by standard 2D
in vitro assays. Gold concentrations below 2.4 mg L-1 were non-cytotoxic and
therefore chosen for further analyses. Cells exposed to GA-AuNPs were uptaken
by melanoma cells through endocytic processes. Next, we described remarkable
biological properties using non-cytotoxic concentrations of this nanomaterial.
Invasion through an extracellular matrix barrier as well as 3D growth capacity
(anchorage-independent colony formation and spheroids growth) were negatively
affected by 2.4 mg L-1 GA-AuNPs. Additionally, exposed spheroids showed
morphological changes, suggesting that GA-AuNPs could penetrate into the
preformed tumor and affect its integrity. All together these results
demonstrate that side effects, such as cytotoxicity, can be avoided by choosing
the right concentration, nevertheless, preserving desirable effects such as
modulation of key tumor cell malignancy features.


  We observed 17 nearby low luminosity FR I radio galaxies using the NRAO Very
Long Baseline Array (VLBA) at 1.67 GHz, as part of a multi-wavelength study of
a complete sample of 21 sources selected by radio flux density from the Uppsala
General Catalogue of Galaxies. We detected radio emission from all 17 galaxies.
At a FWHM resolution of ~ 10x4 mas, five galaxies show only an unresolved radio
core, ten galaxies show core-jet structures, and two galaxies show twin-jet
structures. Comparing these VLBA images with images previously obtained with
the NRAO VLA, we find that all detected VLBA jets are well-aligned on parsec
scales with the VLA jets on kilo parsec scales, and that the jet to counter-jet
surface brightness ratios, or the sidedness, decreases systematically with
increasing distance along the jet. We attribute the sidedness to the Doppler
boosting effect and its decline to the deceleration of the jets. We show that a
distribution of Lorentz factor centered near Gamma = 5 can reproduce our VLBA
detection statistics for core, core-jet and twin-jet sources. We also note that
the luminosity per unit length, L_j, of the VLBA jets drops quickly with
distance, r, along the jet, approximately as L_j being proportional to
r^(-2.0). We discuss three different mechanisms to explain this jet fading: (1)
the decrease of Doppler boosting due to jet deceleration, (2) synchrotron
losses, and (3) expansion losses in constant velocity but adiabatically
spreading jets. Mechanisms (1) and (2) are inconsistent with the observations,
while mechanism (3) is consistent with the observations provided the magnetic
field lines in the jets are aligned perpendicular to the jet axis. This implies
that the deceleration of the jets required by the Unified Scheme does not occur
on the tens of parsec scales, but must occur on larger scales.


  In this article, we prove exact estimates for the $W$-invariant Dunkl kernel
and heat kernel, for the root system of type $A$ with arbitrary positive
multiplicities. We apply the estimates of the $W$-invariant Dunkl heat kernel
to compute sharp estimates for the Newton kernel and for the $s$-stable
semigroups generated by a fractional power of the $W$-invariant Dunkl
Laplacian.


  Researchers investigating example hardness have increasingly focused on the
dynamics by which neural networks learn and forget examples throughout
training. Popular metrics derived from these dynamics include (i) the epoch at
which examples are first correctly classified; (ii) the number of times their
predictions flip during training; and (iii) whether their prediction flips if
they are held out. However, these metrics do not distinguish among examples
that are hard for distinct reasons, such as membership in a rare subpopulation,
being mislabeled, or belonging to a complex subpopulation. In this paper, we
propose $second$-$split$ $forgetting$ $time$ (SSFT), a complementary metric
that tracks the epoch (if any) after which an original training example is
forgotten as the network is fine-tuned on a randomly held out partition of the
data. Across multiple benchmark datasets and modalities, we demonstrate that
$mislabeled$ examples are forgotten quickly, and seemingly $rare$ examples are
forgotten comparatively slowly. By contrast, metrics only considering the first
split learning dynamics struggle to differentiate the two. At large learning
rates, SSFT tends to be robust across architectures, optimizers, and random
seeds. From a practical standpoint, the SSFT can (i) help to identify
mislabeled samples, the removal of which improves generalization; and (ii)
provide insights about failure modes. Through theoretical analysis addressing
overparameterized linear models, we provide insights into how the observed
phenomena may arise. Code for reproducing our experiments can be found here:
https://github.com/pratyushmaini/ssft


  In this article we study basic properties of the mixed BV-Sobolev capacity
with variable exponent p. We give an alternative way to define mixed type
BV-Sobolev-space which was originally introduced by Harjulehto, H\"ast\"o, and
Latvala. Our definition is based on relaxing the p-energy functional with
respect to the Lebesgue space topology. We prove that this procedure produces a
Banach space that coincides with the space defined by Harjulehto et al. for
bounded domain and log-H\"older continuous exponent p. Then we show that this
induces a type of variable exponent BV-capacity and that this is a Choquet
capacity with many usual properties. Finally, we prove that this capacity has
the same null sets as the variable exponent Sobolev capacity when p is
log-H\"older continuous.


  We report the detection of Giant Pulses (GPs) in the pulsar PSR J1752+2359.
About one pulse in 270 has a peak flux density more than 40 times the peak flux
density of an average pulse (AP), and the strongest GP is as large as 260. The
energy of the strongest GP exceeds the energy of the average pulse by a factor
of 200 which is greater than in other known pulsars with GPs. PSR J1752+2359 as
well as the previously detected pulsars PSR B0031-07 and PSR B1112+50, belong
to the first group of pulsars found to have GPs without a strong magnetic field
at the light cylinder.


  The principle of the momentum computed tomography of charged particles is
presented. It may be useful for momentum spectroscopy of various beam-matter
interactions, especially when very intense beams are involved. It is able to
collect the shower of charged particles with the 4Pi solid angle, and suitable
for measuring the overall perspective of the arbitrary momentum distribution of
the outgoing charged particles induced by arbitrary beams, especially when the
other techniques are invalid. The extended collisional region, the strong field
approximation and the case without magnetic field are discussed.


  The presented paper will be proved the necessary and sufficient conditions in
order maximal operator of Walsh-N\"orlund means with non-increasing weights to
be bounded from the dyadic Hardy space $H_{p}(\mathbb{I})$\ to the space $%
L_{p}(\mathbb{I})$.


  I discuss the use of spinors in the construction of spin-foam models, in
particular the form of the closure and simplicity constraints for triangles
that are space-like, i.e. with (area)$^2=\half S^{IJ}S_{IJ}>0$, regardless of
whether they belong the tetrahedra with a space-like or time-like normal,
emphasizing the role of the light-like 4-vector $u_t\sigma^I\bar u_t$. In the
quantization of the model, with the representations of SL(2,$\mathbb{C}$)
acting on spaces of functions of light-like vectors, one may use the canonical
basis of SU(2) representations, or the pseudobasis limited to the discrete
representations of SU(1,1); in alternative it is proposed to use instead a
basis of eigenstates of $(L_3,K_3)$, which might give matrix elements and
vertex functions with the same classical limit. A detailed example of a small
triangulation is presented, which among other things indicates, on the basis of
a classical calculation, that it would be impractical to limit oneself to
tetrahedra with time-like normals.


  Several intriguing electronic phenomena and electric properties were
discovered in three-dimensional Dirac nodal line semimetals (3D-DNLSM), which
are, however, easy to be perturbed under strong spin-orbit coupling (SOC).
While two-dimensional (2D) layers are an emerging material category with many
advantages, 2D-DNLSM against SOC is yet to be uncovered. Here, we report a
2D-DNLSM in odd-atomic-layer Bi (the brick phase, another Bi allotrope), whose
robustness against SOC is protected by the little co-group C_2v \times Z^T_2,
the unique protecting symmetry we found in 2D.Specially, (4n+2) valence
electrons fill the electronic bands in the brick phase, so that the Dirac nodal
line with fourfold degeneracy locates across the Fermi level. There are almost
no other low energy states close to the Fermi level; this allows to feasibly
observe the neat DNLSM-induced phenomena in transport measurements without
being affected by other bands. In contrast, Other VA-group elements also form
the brick phases, but their DNL states are mixed with the extra states around
the Fermi level. This unprecedented category of layered materials allows for
exploring nearly isolated 2DDNL states in 2D.


  As an alternative to conventional multi-pixel cameras, single-pixel cameras
enable images to be recorded using a single detector that measures the
correlations between the scene and a set of patterns. However, to fully sample
a scene in this way requires at least the same number of correlation
measurements as there are pixels in the reconstructed image. Therefore
single-pixel imaging systems typically exhibit low frame-rates. To mitigate
this, a range of compressive sensing techniques have been developed which rely
on a priori knowledge of the scene to reconstruct images from an under-sampled
set of measurements. In this work we take a different approach and adopt a
strategy inspired by the foveated vision systems found in the animal kingdom -
a framework that exploits the spatio-temporal redundancy present in many
dynamic scenes. In our single-pixel imaging system a high-resolution foveal
region follows motion within the scene, but unlike a simple zoom, every frame
delivers new spatial information from across the entire field-of-view. Using
this approach we demonstrate a four-fold reduction in the time taken to record
the detail of rapidly evolving features, whilst simultaneously accumulating
detail of more slowly evolving regions over several consecutive frames. This
tiered super-sampling technique enables the reconstruction of video streams in
which both the resolution and the effective exposure-time spatially vary and
adapt dynamically in response to the evolution of the scene. The methods
described here can complement existing compressive sensing approaches and may
be applied to enhance a variety of computational imagers that rely on
sequential correlation measurements.


  We explore simplified models of mixed dark matter (DM), defined here to be a
stable relic composed of a singlet and an electroweak charged state. Our setup
describes a broad spectrum of thermal DM candidates that can naturally
accommodate the observed DM abundance but are subject to substantial
constraints from current and upcoming direct detection experiments. We identify
"blind spots" at which the DM-Higgs coupling is identically zero, thus
nullifying direct detection constraints on spin independent scattering.
Furthermore, we characterize the fine-tuning in mixing angles, i.e.
well-tempering, required for thermal freeze-out to accommodate the observed
abundance. Present and projected limits from LUX and XENON1T force many thermal
relic models into blind spot tuning, well-tempering, or both. This simplified
model framework generalizes bino-Higgsino DM in the MSSM, singlino-Higgsino DM
in the NMSSM, and scalar DM candidates that appear in models of extended Higgs
sectors.


  In the last decades, the blossoming of experimental breakthroughs in the
domain of electron energy loss spectroscopy (EELS) has triggered a variety of
theoretical developments. Those have to deal with completely different
situations, from atomically resolved phonon mapping to electron circular
dichroism passing by surface plasmon mapping. All of them rely on very
different physical approximations and have not yet been reconciled, despite
early attempts to do so. As an effort in that direction, we report on the
development of a scalar relativistic quantum electrodynamic (QED) approach of
the inelastic scattering of fast electrons. This theory can be adapted to
describe all modern EELS experiments, and under the relevant approximations,
can be reduced to any of the last EELS theories. In that aim, we present in
this paper the state of the art and the basics of scalar relativistic QED
relevant to the electron inelastic scattering. We then give a clear relation
between the two once antagonist descriptions of the EELS, the retarded green
Dyadic, usually applied to describe photonic excitations and the quasi-static
mixed dynamic form factor (MDFF), more adapted to describe core electronic
excitations of material. We then use this theory to establish two important
EELS-related equations. The first one relates the spatially resolved EELS to
the imaginary part of the photon propagator and the incoming and outgoing
electron beam wavefunction, synthesizing the most common theories developed for
analyzing spatially resolved EELS experiments. The second one shows that the
evolution of the electron beam density matrix is proportional to the mutual
coherence tensor, proving that quite universally, the electromagnetic
correlations in the target are imprinted in the coherence properties of the
probing electron beam.


  Combining image sensor simulation tools (e.g., ISETCam) with physically based
ray tracing (e.g., PBRT) offers possibilities for designing and evaluating
novel imaging systems as well as for synthesizing physically accurate, labeled
images for machine learning. One practical limitation has been simulating the
optics precisely: Lens manufacturers generally prefer to keep lens design
confidential. We present a pragmatic solution to this problem using a black box
lens model in Zemax; such models provide necessary optical information while
preserving the lens designer's intellectual property. First, we describe and
provide software to construct a polynomial ray transfer function that
characterizes how rays entering the lens at any position and angle subsequently
exit the lens. We implement the ray-transfer calculation as a camera model in
PBRT and confirm that the PBRT ray-transfer calculations match the Zemax lens
calculations for edge spread functions and relative illumination.


  The estimation of modal parameters from a set of noisy measured data is a
highly judgmental task, with user expertise playing a significant role in
distinguishing between estimated physical and noise modes of a test-piece.
Various methods have been developed to automate this procedure. The common
approach is to identify models with different orders and cluster similar modes
together. However, most proposed methods based on this approach suffer from
high-dimensional optimization problems in either the estimation or clustering
step. To overcome this problem, this study presents an algorithm for autonomous
modal parameter estimation in which the only required optimization is performed
in a three-dimensional space. To this end, a subspace-based identification
method is employed for the estimation and a non-iterative correlation-based
method is used for the clustering. This clustering is at the heart of the
paper. The keys to success are correlation metrics that are able to treat the
problems of spatial eigenvector aliasing and nonunique eigenvectors of
coalescent modes simultaneously. The algorithm commences by the identification
of an excessively high-order model from frequency response function test data.
The high number of modes of this model provide bases for two subspaces: one for
likely physical modes and one for its complement dubbed the subspace of noise
modes. By employing the bootstrap resampling technique, several subsets are
generated from the same basic dataset and for each of them a model is
identified to form a set of models. Then, by correlation analysis, highly
correlated modes of these models which appear repeatedly are clustered together
and the noise modes are collected in a so-called Trashbox cluster. Stray noise
modes attracted to the mode clusters are trimmed away by correlation analysis.
The final step is a fuzzy c-means clustering procedure.


  We compute the weak$^*$-dentability index of the spaces $C(K)$ where $K$ is a
countable compact space. Namely ${Dz}(C([0,\omega^{\omega^\alpha}])) =
\omega^{1+\alpha+1}$, whenever $0\le\alpha<\omega_1$. More generally,
${Dz}(C(K))=\omega^{1+\alpha+1}$ if $K$ is a scattered compact whose height
$\eta(K)$ satisfies $\omega^\alpha<\eta(K)\leq \omega^{\alpha+1}$ with an
$\alpha$ countable.


  Let $G=$SL$(2,R)\ltimes(R^2)^{\oplus k}$ and let $\Gamma$ be a congruence
subgroup of SL$(2,Z)\ltimes(Z^2)^{\oplus k}$. We prove a polynomially effective
asymptotic equidistribution result for special types of unipotent orbits in
$\Gamma\backslash G$ which project to pieces of closed horocycles in
SL$(2,Z)\backslash$SL$(2,R)$. As an application, we prove an effective
quantitative Oppenheim type result for the quadratic form
$(m_1-\alpha)^2+(m_2-\beta)^2-(m_3-\alpha)^2-(m_4-\beta)^2$, for
$(\alpha,\beta)$ of Diophantine type, following the approach by Marklof [24]
using theta sums.


  The notion of local subgroupoids as generalition of a local equivalence
relations was defined by the first author and R.Brown. Here we investigate some
relations between transitive components and coherence properties of the local
subgroupoids.


  In perturbative calculations of quantum-statistical zero-temperature path
integrals in curvilinear coordinates one encounters Feynman diagrams involving
multiple temporal integrals over products of distributions, which are
mathematically undefined. In addition, there are terms proportional to powers
of Dirac delta-functions at the origin coming from the measure of path
integration. We give simple rules for integrating products of distributions in
such a way that the results ensure coordinate independence of the path
integrals. The rules are derived by using equations of motion and partial
integration, while keeping track of certain minimal features originating in the
unique definition of all singular integrals in $1 - \epsilon$ dimensions. Our
rules yield the same results as the much more cumbersome calculations in 1-
epsilon dimensions where the limit epsilon --> 0 is taken at the end. They also
agree with the rules found in an independent treatment on a finite time
interval.


  Starting from a nonequilibrium configuration we analyse the essential role of
the direct and the inverse binary and triple interactions in reaching an
asymptotic thermal equilibrium in a homogeneous isotropic
electron-positron-photon plasma. We focus on energies in the range 0.1--10 MeV.
We numerically integrate the integro-partial differential relativistic
Boltzmann equation with the exact QED collisional integrals taking into account
all binary and triple interactions in the plasma. We show that first, when
detailed balance is reached for all binary interactions on a timescale
$t_{k}\lesssim10^{-14}$sec, photons and electron-positron pairs establish
kinetic equilibrium. Successively, when triple interactions fulfill the
detailed balance on a timescale $t_{eq}\lesssim10^{-12}$sec, the plasma reaches
thermal equilibrium. It is shown that neglecting the inverse triple
interactions prevents reaching thermal equilibrium. Our results obtained in the
theoretical physics domain also find application in astrophysics and cosmology.


  We show that nonlinear Maxwell Equations in $\R^3$ admit a convenient dual
variational formulation that permits to prove the existence of nontrivial
solutions via standard variational methods.


  As training datasets become increasingly drawn from unstructured,
uncontrolled environments such as the web, researchers and industry
practitioners have increasingly relied upon data filtering techniques to
"filter out the noise" of web-scraped data. While datasets have been widely
shown to reflect the biases and values of their creators, in this paper we
contribute to an emerging body of research that assesses the filters used to
create these datasets. We show that image-text data filtering also has biases
and is value-laden, encoding specific notions of what is counted as
"high-quality" data. In our work, we audit a standard approach of image-text
CLIP-filtering on the academic benchmark DataComp's CommonPool by analyzing
discrepancies of filtering through various annotation techniques across
multiple modalities of image, text, and website source. We find that data
relating to several imputed demographic groups -- such as LGBTQ+ people, older
women, and younger men -- are associated with higher rates of exclusion.
Moreover, we demonstrate cases of exclusion amplification: not only are certain
marginalized groups already underrepresented in the unfiltered data, but
CLIP-filtering excludes data from these groups at higher rates. The
data-filtering step in the machine learning pipeline can therefore exacerbate
representation disparities already present in the data-gathering step,
especially when existing filters are designed to optimize a specifically-chosen
downstream performance metric like zero-shot image classification accuracy.
Finally, we show that the NSFW filter fails to remove sexually-explicit content
from CommonPool, and that CLIP-filtering includes several categories of
copyrighted content at high rates. Our conclusions point to a need for
fundamental changes in dataset creation and filtering practices.


  Background: Bayesian Networks (BNs) are probabilistic graphical models that
leverage Bayes' theorem to portray dependencies and cause-and-effect
relationships between variables. These networks have gained prominence in the
field of health sciences, particularly in diagnostic processes, by allowing the
integration of medical knowledge into models and addressing uncertainty in a
probabilistic manner.
  Objectives: This review aims to provide an exhaustive overview of the current
state of Bayesian Networks in disease diagnosis and prognosis. Additionally, it
seeks to introduce readers to the fundamental methodology of BNs, emphasizing
their versatility and applicability across varied medical domains.
  Methods: Employing a meticulous search strategy with MeSH descriptors in
diverse scientific databases, we identified 190 relevant references. These were
subjected to a rigorous analysis, resulting in the retention of 60 papers for
an in-depth review. The robustness of our approach minimizes the risk of
selection bias. Results: The selected studies encompass a wide range of medical
areas, providing insights into the statistical methodology, implementation
feasibility, and predictive accuracy of BNs, as evidenced by an average AUC
exceeding 75%. The comprehensive analysis underscores the adaptability and
efficacy of Bayesian Networks in diverse clinical scenarios.
  Conclusion: The encompassing exploration of Bayesian Networks presented in
this review highlights their significance and growing impact in the realm of
disease diagnosis and prognosis. It underscores the need for further research
and development to optimize their capabilities and broaden their applicability
in addressing diverse and intricate healthcare challenges.


  Electron transport through disordered quasi one-dimensional quantum systems
is studied. Decoherence is taken into account by a spatial distribution of
virtual reservoirs, which represent local interactions of the conduction
electrons with their environment. We show that the decoherence distribution has
observable effects on the transport. If the decoherence reservoirs are
distributed randomly without spatial correlations, a minimal degree of
decoherence is necessary to obtain Ohmic conduction. Below this threshold the
system is localized and thus, a decoherence driven metal-insulator transition
is found. In contrast, for homogenously distributed decoherence, any finite
degree of decoherence is sufficient to destroy localization. Thus, the presence
or absence of localization in a disordered one-dimensional system may give
important insight about how the electron phase is randomized.


  Monolayer PtSe$_2$ is a semiconducting transition metal dichalcogenide
characterized by an indirect band gap, space inversion symmetry, and high
carrier mobility. Strong intrinsic spin-orbit coupling and the possibility to
induce extrinsic spin-orbit fields by gating make PtSe$_2$ attractive for
fundamental spin transport studies as well as for potential spintronics
applications. We perform a systematic theoretical study of the spin-orbit
coupling and spin relaxation in this material. Specifically, we employ first
principles methods to obtain the basic orbital and spin-orbital properties of
PtSe$_2$, also in the presence of an external transverse electric field. We
calculate the spin mixing parameters $b^2$ and the spin-orbit fields $\Omega$
for the Bloch states of electrons and holes. This information allows us to
predict the spin lifetimes due to the Elliott-Yafet and D'yakonov-Perel
mechanisms. We find that $b^2$ is rather large, on the order of $10^{-2}$ and
$10^{-1}$, while $\Omega$ varies strongly with doping, being about $10^{3} -
10^{4}$\,ns$^{-1}$ for %typical Fermi levels in the interval $(10-100)$ meV,
carrier density in the interval $10^{13}-10^{14}$\,cm$^{-2}$ at the electric
field of 1 V/nm. We estimate the spin lifetimes to be on the picosecond level.


  An X-ray monitoring campaign with Chandra and Swift confirms that 1RXS
J171824.2-402934 is accreting at the lowest rate among the known persistently
accreting low-mass X-ray binaries. A thermonuclear X-ray burst was detected
with the all-sky monitor on RXTE. This is only the second such burst seen in
1RXS J171824.2-402934 in more than 20 Ms of observations done over 19 years.
The low burst recurrence rate is in line with the low accretion rate. The
persistent nature and low accretion rate can be reconciled within accretion
disk theory if the binary system is ultracompact. An unprecedentedly short
orbital period of less than approximately 7 minutes would be implied. An
ultracompact nature, together with the properties of the type I X-ray burst,
suggests, in turn, that helium-rich material is accreted. Optical follow-up of
the Chandra error region does not reveal an unambiguous counterpart.


  Text discourse parsing plays an important role in understanding information
flow and argumentative structure in natural language. Previous research under
the Rhetorical Structure Theory (RST) has mostly focused on inducing and
evaluating models from the English treebank. However, the parsing tasks for
other languages such as German, Dutch, and Portuguese are still challenging due
to the shortage of annotated data. In this work, we investigate two approaches
to establish a neural, cross-lingual discourse parser via: (1) utilizing
multilingual vector representations; and (2) adopting segment-level translation
of the source content. Experiment results show that both methods are effective
even with limited training data, and achieve state-of-the-art performance on
cross-lingual, document-level discourse parsing on all sub-tasks.


  Neural network-based turbulence modeling has gained significant success in
improving turbulence predictions by incorporating high--fidelity data. However,
the interpretability of the learned model is often not fully analyzed, which
has been one of the main criticism of neural network-based turbulence modeling.
Therefore, it is increasingly demanding to provide physical interpretation of
the trained model, which is of significant interest for guiding the development
of interpretable and unified turbulence models. The present work aims to
interpret the predictive improvement of turbulence flows based on the behavior
of the learned model, represented with tensor basis neural networks. The
ensemble Kalman method is used for model learning from sparse observation data
due to its ease of implementation and high training efficiency. Two cases,
i.e., flow over the S809 airfoil and flow in a square duct, are used to
demonstrate the physical interpretation of the ensemble-based turbulence
modeling. For the flow over the S809 airfoil, our results show that the
ensemble Kalman method learns an optimal linear eddy viscosity model, which
improves the prediction of the aerodynamic lift by reducing the eddy viscosity
in the upstream boundary layer and promoting the early onset of flow
separation. For the square duct case, the method provides a nonlinear eddy
viscosity model, which predicts well secondary flows by capturing the imbalance
of the Reynolds normal stresses. The flexibility of the ensemble-based method
is highlighted to capture characteristics of the flow separation and secondary
flow by adjusting the nonlinearity of the turbulence model.


  We develop coarse-graining schemes for stochastic many-particle microscopic
models with competing short- and long-range interactions on a d-dimensional
lattice. We focus on the coarse-graining of equilibrium Gibbs states and using
cluster expansions we analyze the corresponding renormalization group map. We
quantify the approximation properties of the coarse-grained terms arising from
different types of interactions and present a hierarchy of correction terms. We
derive semi-analytical numerical schemes that are accompanied with a posteriori
error estimates for coarse-grained lattice systems with short and long-range
interactions.


  I use the fact that the radiation emitted by the accretion disk of
supermassive black hole can heat up the surrounding gas in the protogalaxy to
achieve hydrostatic equilibrium during the galaxy formation. The correlation
between the black hole mass M_BH and velocity dispersion \sigma thus naturally
arises. The result generally agrees with empirical fittings from observational
data, even with M_BH \leq 10^6M_sun. This model provides a clear picture on how
the properties of the galactic supermassive black holes are connected with the
kinetic properties of the galactic bulges.


  Large language models (LLMs) encode a vast amount of world knowledge acquired
from massive text datasets. Recent studies have demonstrated that LLMs can
assist an embodied agent in solving complex sequential decision making tasks by
providing high-level instructions. However, interactions with LLMs can be
time-consuming. In many practical scenarios, it requires a significant amount
of storage space that can only be deployed on remote cloud servers.
Additionally, using commercial LLMs can be costly since they may charge based
on usage frequency. In this paper, we explore how to enable intelligent
cost-effective interactions between a down stream task oriented agent and an
LLM. We find that this problem can be naturally formulated by a Markov decision
process (MDP), and propose When2Ask, a reinforcement learning based approach
that learns when it is necessary to query LLMs for high-level instructions to
accomplish a target task. On one side, When2Ask discourages unnecessary
redundant interactions, while on the other side, it enables the agent to
identify and follow useful instructions from the LLM. This enables the agent to
halt an ongoing plan and transition to a more suitable one based on new
environmental observations. Experiments on MiniGrid and Habitat environments
that entail planning sub-goals demonstrate that When2Ask learns to solve target
tasks with only a few necessary interactions with the LLM, significantly
reducing interaction costs in testing environments compared with baseline
methods. Our code is available at: https://github.com/ZJLAB-AMMI/LLM4RL.


  The pivot algorithm -- we also call it the pivot chain -- is an algorithm for
approximately uniform sampling from $\Omega _{N},$ the set of $N$-step
self-avoiding walks on $\mathbb{Z}^{d}$ ($N,$ $d\geq 1$). Based on this
algorithm and the $G$ method, we construct another algorithm/chain, called the
pivot$^{\text{+}}$ algorithm/chain, for approximately uniform sampling from
$\Omega _{N},$ here, $N\geq 2$. The pivot$^{\text{+}}$ algorithm samples the
pivot from the set $\left\{ 1,2,...,N-1\right\} $ according to the uniform
probability distribution on this set while the pivot algorithm samples the
pivot from the set $\left\{0,1,2,...,N-1\right\} $ according to the uniform
probability distribution on this set, so, on the pivot, the pivot$^{\text{+}}$
algorithm is better than the pivot algorithm. Further, we obtain another
important thing, namely, the pivot$^{\text{+}}$ algorithm/chain enters, at time
$1$, a set $2d$ times smaller than $\Omega _{N},$ and stays forever in this
set, so, at times $1,2,...$ we work with a chain having a state space $2d$
times smaller than $\Omega _{N}$. As to the speed of convergence, we conjecture
that the pivot$^{\text{+}}$ algorithm/chain is faster than the pivot
algorithm/chain.


  The construction and classification of super-modular categories is an ongoing
project, of interest in algebra, topology and physics. In a recent paper, Cho,
Kim, Seo and You produced two mysterious families of super-modular data, with
no known realization. We show that these data are realized by modifying the
Drinfeld centers of near-group fusion categories associated with the groups
$\mathbb Z/6$ and $\mathbb Z/2\times \mathbb Z/4$. The methods we develop have
wider applications and we describe some of these, with a view towards
understanding when near-group centers provide super-modular categories.


  We consider a one-dimensional spin chain system with quenched disorder and in
the presence of a local periodic drive. We study the time evolution of the
system in the Floquet basis and evaluate the fidelity susceptibility, which is
a measure of how a given state changes under a small perturbation, of states to
a weak periodic drive. We demonstrate that the statistical properties of the
fidelity susceptibility over different disorder realizations can be used to
identify two phases of the system: (1) the many-body localized phase, in which
the susceptibility exhibits long tails while its average value decreases
rapidly as disorder increases; and (2) the ergodic phase, in which the
susceptibility distribution is narrow and its average value weakly depends on
disorder. This distinction in the average value of the susceptibility between
the two phases develops readily for systems with ten or more spins. Therefore,
recently built networks of qubits subject to a local drive can simulate
dynamics of a system in the many-body localization regime. We also show that
the spin accumulation speed is correlated with the fidelity susceptibility and
can also be used to distinguish the two phases.


  In this paper we study global existence of weak solutions for the Quantum
Hydrodynamics System in 2-D in the space of energy. We do not require any
additional regularity and/or smallness assumptions on the initial data. Our
approach replaces the WKB formalism with a polar decomposition theory which is
not limited by the presence of vacuum regions. In this way we set up a self
consistent theory, based only on particle density and current density, which
does not need to define velocity fields in the nodal regions. The mathematical
techniques we use in this paper are based on uniform (with respect to the
approximating parameter) Strichartz estimates and the local smoothing property.


  Despite the great success of High-Level Synthesis (HLS) tools, we observe
several unresolved challenges: 1) the high-level abstraction of programming
styles in HLS sometimes conceals optimization opportunities; 2) existing HLS
tools do not provide flexible trade-off (Pareto) solutions among different
objectives and constraints; 3) the actual quality of the resulting RTL designs
is hard to predict. To address these challenges, we propose an end-to-end
framework, namelyIronMan. The primary goal is to enable a flexible and
automated design space exploration (DSE), to provide either optimal solutions
under user-specified constraints, or various trade-offs among different
objectives (such as different types of resources, area, and latency). Such DSE
either requires tedious manual efforts or is not achievable to attain these
goals through existing HLS tools. There are three components in IronMan: 1)
GPP, a highly accurate graph-neural-network-based performance and resource
predictor; 2) RLMD, a reinforcement-learning-based multi-objective DSE engine
that explores the optimal resource allocation strategy, to provide Pareto
solutions between different objectives; 3) CT, a code transformer to assist
RLMD and GPP, which extracts the data flow graph from original HLS C/C++ and
automatically generates synthesizable code with HLS directives. The
experimental results show that: 1) GPP achieves high prediction accuracy,
reducing prediction errors of HLS tools by 10.9x in resource utilization and
5.7x in timing; 2) RLMD obtains optimal or Pareto solutions that outperform the
genetic algorithm and simulated annealing by 12.7% and 12.9%, respectively; 3)
IronMan is able to find optimized solutions perfectly matching various DSP
constraints, with 2.54x fewer DSPs and up to 6x shorter latency than those of
HLS tools while being up to 400x faster than the heuristic algorithms and HLS
tools.