  Recent years have seen an increasing use of Signal Temporal Logic (STL) as a
formal specification language for symbolic control, due to its expressiveness
and closeness to natural language. Furthermore, STL specifications can be
encoded as cost functions using STL's robust semantics, transforming the
synthesis problem into an optimization problem. Unfortunately, these cost
functions are non-smooth and non-convex, and exact solutions using
mixed-integer programming do not scale well. Recent work has focused on using
smooth approximations of robustness, which enable faster gradient-based methods
to find local maxima, at the expense of soundness and/or completeness. We
propose a novel robustness approximation that is smooth everywhere, sound, and
asymptotically complete. Our approach combines the benefits of existing
approximations, while enabling an explicit tradeoff between conservativeness
and completeness.


  The Bethe-Salpeter equation (BSE) can provide an accurate description of
low-energy optical spectra of insulating crystals - even when excitonic effects
are important. However, due to high computational costs it is only possible to
include a few bands in the BSE Hamiltonian. As a consequence, the dielectric
screening given by the real part of the dielectric function can be
significantly underestimated by the BSE. Here we show that universally accurate
optical response functions can be obtained by combining a four-point BSE-like
equation for the irreducible polarisability with a two-point Dyson equation
which includes the higher-lying transitions within the random phase
approximation (RPA). The new method is referred to as BSE+. It has a
computational cost comparable to the BSE but a much faster convergence with
respect to the size of the electron-hole basis. We use the method to calculate
refractive indices and electron energy loss spectra for a test set of
semiconductors and insulators. In all cases the BSE+ yields excellent agreement
with experimental data across a wide frequency range and outperforms both BSE
and RPA.


  We consider spin dynamics for implementation in an atomistic framework and we
address the feasibility of capturing processes in the femtosecond regime by
inclusion of moment of inertia. In the spirit of an {\it s-d} -like interaction
between the magnetization and electron spin, we derive a generalized equation
of motion for the magnetization dynamics in the semi-classical limit, which is
non-local in both space and time. Using this result we retain a generalized
Landau-Lifshitz-Gilbert equation, also including the moment of inertia, and
demonstrate how the exchange interaction, damping, and moment of inertia, all
can be calculated from first principles.


  We describe the first method to automatically estimate the 3D pose of the
human body as well as its 3D shape from a single unconstrained image. We
estimate a full 3D mesh and show that 2D joints alone carry a surprising amount
of information about body shape. The problem is challenging because of the
complexity of the human body, articulation, occlusion, clothing, lighting, and
the inherent ambiguity in inferring 3D from 2D. To solve this, we first use a
recently published CNN-based method, DeepCut, to predict (bottom-up) the 2D
body joint locations. We then fit (top-down) a recently published statistical
body shape model, called SMPL, to the 2D joints. We do so by minimizing an
objective function that penalizes the error between the projected 3D model
joints and detected 2D joints. Because SMPL captures correlations in human
shape across the population, we are able to robustly fit it to very little
data. We further leverage the 3D model to prevent solutions that cause
interpenetration. We evaluate our method, SMPLify, on the Leeds Sports,
HumanEva, and Human3.6M datasets, showing superior pose accuracy with respect
to the state of the art.


  This paper reports on an all-sky search for periodic gravitational waves from
sources such as deformed isolated rapidly-spinning neutron stars. The analysis
uses 840 hours of data from 66 days of the fifth LIGO science run (S5). The
data was searched for quasi-monochromatic waves with frequencies f in the range
from 50 Hz to 1500 Hz, with a linear frequency drift \dot{f} (measured at the
solar system barycenter) in the range -f/\tau < \dot{f} < 0.1 f/\tau, for a
minimum spin-down age \tau of 1000 years for signals below 400 Hz and 8000
years above 400 Hz. The main computational work of the search was distributed
over approximately 100000 computers volunteered by the general public. This
large computing power allowed the use of a relatively long coherent integration
time of 30 hours while searching a large parameter space. This search extends
Einstein@Home's previous search in LIGO S4 data to about three times better
sensitivity. No statistically significant signals were found. In the 125 Hz to
225 Hz band, more than 90% of sources with dimensionless gravitational-wave
strain tensor amplitude greater than 3e-24 would have been detected.


  The phenomenon of the large phase shift of the strongly nonlocal spatial
optical soliton was predicted by Guo et al. within the phenomenological
framework [Q. Guo, et al., Phys. Rev. E 69, 016602 (2004)], but has not been
experimentally confirmed so far. We theoretically and experimentally
investigate the large phase shift of that propagating in the lead glass. It is
verified that the change of the optical power carried by the optical beam about
10 mW around the critical power for the soliton can lead to a {\pi} phase
shift, which would be of its potential in the application of all-optical
switchings.


  Historical user-item interaction datasets are essential in training modern
recommender systems for predicting user preferences. However, the arbitrary
user behaviors in most recommendation scenarios lead to a large volume of noisy
data instances being recorded, which cannot fully represent their true
interests. While a large number of denoising studies are emerging in the
recommender system community, all of them suffer from highly dynamic data
distributions. In this paper, we propose a Deep Reinforcement Learning (DRL)
based framework, AutoDenoise, with an Instance Denoising Policy Network, for
denoising data instances with an instance selection manner in deep recommender
systems. To be specific, AutoDenoise serves as an agent in DRL to adaptively
select noise-free and predictive data instances, which can then be utilized
directly in training representative recommendation models. In addition, we
design an alternate two-phase optimization strategy to train and validate the
AutoDenoise properly. In the searching phase, we aim to train the policy
network with the capacity of instance denoising; in the validation phase, we
find out and evaluate the denoised subset of data instances selected by the
trained policy network, so as to validate its denoising ability. We conduct
extensive experiments to validate the effectiveness of AutoDenoise combined
with multiple representative recommender system models.


  We present a novel analysis of the internal kinematics of the Fornax dwarf
spheroidal galaxy. Our results are based on the largest sample of spectroscopic
data for Fornax stars presently available ($> 2500$ stars), for which we have
chemical and kinematic information. We introduce new software, Beacon, designed
to detect chemo-kinematic patterns among stars of different stellar populations
using their metallicity and velocity along the line of sight. Applying Beacon
to Fornax we have detected non-negligible rotation signals around main optical
axes of the galaxy, characteristic for a triaxial system partially supported by
rotation. The dominant rotation pattern is relatively strong ($\sim 12$ km
s$^{-1}$), but the galaxy also shows additional weaker albeit complex rotation
patterns. Using the information available from the star formation history of
Fornax we have also derived the average age of the different chemo-kinematic
components found by Beacon, which has allowed us to obtain its kinematic
history. Our results point to a possible major merger suffered by Fornax at
redshift $z\sim1$, in agreement with previous works.


  We present analytic solutions to the spatially homogeneous axion field
equation, using a model potential which strongly resembles the standard
anharmonic $(1-\cos N\theta)$ potential, but contains only a piece-wise second
order term. Our exactly soluble model for $\theta(t)$ spans the entire range
$[-\pi/N,\pi/N]$. In particular, we are able to confirm (i) Turner's numeric
correction factors \cite{Turner} to the adiabatic and harmonic analytic
treatments of homogeneous axion oscillations, and (ii) Lyth's estimate
\cite{Lyth} valid near the metastable misalignment angle $\pi/N$ at the peak of
the potential. We compute the enhancement of axion density fluctuations that
occurs when the axion mass becomes significant at $T\sim 1$ GeV. We find that
the anharmonicity amplifies density \mbox{f}luctuations, but only significantly
for relatively large initial misalignment angles. The enhancement factor is
$\sim$ (2,3,4,13) for $\theta_{\rm in}\sim (0.85,0.90,0.95,0.99)\times\pi$.


  In this work, we establish new rigidity results for the Maslov class of
Lagrangian submanifolds in large classes of closed and convex symplectic
manifolds. Our main result establishes upper bounds for the minimal Maslov
number of displaceable Lagrangian submanifolds which are product manifolds
whose factors each admit a metric of negative sectional curvature. Such
Lagrangian submanifolds exist in every symplectic manifold of dimension greater
than six or equal to four.
  The proof utilizes the relations between closed geodesics on the Lagrangian,
the periodic orbits of geometric Hamiltonian flows supported near the
Lagrangian, and the length minimizing properties of these flows with respect to
the negative Hofer length functional.


  We report a closed-form expression for the Kullback-Leibler divergence
between Cauchy distributions which involves the calculation of a novel definite
integral. The formula shows that the Kullback-Leibler divergence between Cauchy
densities is always finite and symmetric.


  Generalizations of symplectic and metric structures for supermanifolds are
analyzed. Two types of structures are possible according to the even/odd
character of the corresponding quadratic tensors. In the even case one has a
very rich set of geometric structures: even symplectic supermanifolds (or,
equivalently, supermanifolds with non-degenerate Poisson structures), even
Fedosov supermanifolds and even Riemannian supermanifolds. The existence of
relations among those structures is analyzed in some details. In the odd case,
we show that odd Riemannian and Fedosov supermanifolds are characterized by a
scalar curvature tensor. However, odd Riemannian supermanifolds can only have
constant curvature.


  We explore the commonalities between methods for assuring the security of
computer systems (cybersecurity) and the mechanisms that have evolved through
natural selection to protect vertebrates against pathogens, and how insights
derived from studying the evolution of natural defenses can inform the design
of more effective cybersecurity systems. More generally, security challenges
are crucial for the maintenance of a wide range of complex adaptive systems,
including financial systems, and again lessons learned from the study of the
evolution of natural defenses can provide guidance for the protection of such
systems.


  According to the correspondence principle, classical mechanics and quantum
mechanics agree in the semiclassical limit, although presently it has become
more and more clear how intriguing would be to try to fix a boundary between
them. Here we give a significant example in which the agreement concerns
Newtonian trajectories of an electron with initial data corresponding to a
quantum ground state. The example is the simplest case in which a chemical bond
occurs, i.e. the $H_2^+$ ion. By molecular dynamics simulations for the full
system (two protons and one electron) we show that there exist initial data
producing an ``effective potential'' among the protons, which superposes in a
surprisingly good way the quantum one computed in the Born-Oppenheimer
approximation (Fig~1). Preliminarily, following the perturbation procedure
first exhibited by Born and Heisenberg in the year 1924, we recall why an
effective potential should exist in a classical frame, and also describe the
numerical procedure employed in computing it.


  Data used to train machine learning models can be adversarial--maliciously
constructed by adversaries to fool the model. Challenge also arises by privacy,
confidentiality, or due to legal constraints when data are geographically
gathered and stored across multiple learners, some of which may hold even an
"anonymized" or unreliable dataset. In this context, the distributionally
robust optimization framework is considered for training a parametric model,
both in centralized and federated learning settings. The objective is to endow
the trained model with robustness against adversarially manipulated input data,
or, distributional uncertainties, such as mismatches between training and
testing data distributions, or among datasets stored at different workers. To
this aim, the data distribution is assumed unknown, and lies within a
Wasserstein ball centered around the empirical data distribution. This robust
learning task entails an infinite-dimensional optimization problem, which is
challenging. Leveraging a strong duality result, a surrogate is obtained, for
which three stochastic primal-dual algorithms are developed: i) stochastic
proximal gradient descent with an $\epsilon$-accurate oracle, which invokes an
oracle to solve the convex sub-problems; ii) stochastic proximal gradient
descent-ascent, which approximates the solution of the convex sub-problems via
a single gradient ascent step; and, iii) a distributionally robust federated
learning algorithm, which solves the sub-problems locally at different workers
where data are stored. Compared to the empirical risk minimization and
federated learning methods, the proposed algorithms offer robustness with
little computation overhead. Numerical tests using image datasets showcase the
merits of the proposed algorithms under several existing adversarial attacks
and distributional uncertainties.


  In recent years, Large Language Models (LLMs) have made significant strides
towards Artificial General Intelligence. However, training these models from
scratch requires substantial computational resources and vast amounts of text
data. In this paper, we explore an alternative approach to constructing an LLM
for a new language by continually pretraining (CPT) from existing pretrained
LLMs, instead of using randomly initialized parameters. Based on parallel
experiments on 40 model sizes ranging from 40M to 5B parameters, we find that
1) CPT converges faster and saves significant resources in a scalable manner;
2) CPT adheres to an extended scaling law derived from Hoffmann et al. (2022)
with a joint data-parameter scaling term; 3) The compute-optimal data-parameter
allocation for CPT markedly differs based on our estimated scaling factors; 4)
The effectiveness of transfer at scale is influenced by training duration and
linguistic properties, while robust to data replaying, a method that
effectively mitigates catastrophic forgetting in CPT. We hope our findings
provide deeper insights into the transferability of LLMs at scale for the
research community.


  Maximum likelihood principle is shown to be the best measure for relating the
experimental data with the predictions of quantum theory.


  We give a variational proof of the existence and uniqueness of a convex cap
with the given upper boundary. The proof uses the concavity of the total scalar
curvature functional on the space of generalized convex caps. As a byproduct,
we prove that generalized convex caps with the fixed boundary are globally
rigid, that is uniquely determined by their curvatures.


  In this article, we propose a programmable plasmonic waveguide system (PPWS)
to achieve several different functions based on metal coding metamaterials
(MCMs) and inverse design technology. There is no need to spend much time on
considering the relation between the function and the structure because the
MCMs in the PPWS are reprogrammable. In order to demonstrate the effectiveness
of the PPWS, we utilize it to achieve several filtering functions, including
bandstop and bandpass filters. The simulation results exhibit that the
performance of filters is improved based on genetic algorithm, particle swarm
optimization, multi-traversal direct-binary search and simulated annealing.
Especially, the bandwidth and quality factor for the narrow-band filter can
reach 6.5 nm and 200.5. In addition to the simple filtering functions, some
relatively complex transmission characteristics can be obtained by using the
PPWS, such as plasmon-induced transparency-like effects. In conclusion, genetic
algorithm is considered as the most efficient inverse design method for our
system due to its less optimization time and stable performance. In comparison
with the previous works, our proposed PPWS not only provides a general
framework for obtaining an effective, flexible and compact plasmonic device but
also shows the applications of inverse design on photonics devices.


  For any geodesic current we associated a quasi-metric space. For a subclass
of geodesic currents, called filling, it defines a metric and we study the
critical exponent associated to this space. We show that is is equal to the
exponential growth rate of the intersection function for closed curves.


  In this paper, we report progress on answering the open problem presented by
Pagh~[14], who considered the nearest neighbor search without false negatives
for the Hamming distance. We show new data structures for solving the
$c$-approximate nearest neighbors problem without false negatives for Euclidean
high dimensional space $\mathcal{R}^d$. These data structures work for any $c =
\omega(\sqrt{\log{\log{n}}})$, where $n$ is the number of points in the input
set, with poly-logarithmic query time and polynomial preprocessing time. This
improves over the known algorithms, which require $c$ to be $\Omega(\sqrt{d})$.
  This improvement is obtained by applying a sequence of reductions, which are
interesting on their own. First, we reduce the problem to $d$ instances of
dimension logarithmic in $n$. Next, these instances are reduced to a number of
$c$-approximate nearest neighbor search instances in $\big(\mathbb{R}^k\big)^L$
space equipped with metric $m(x,y) = \max_{1 \le i \le L}(\lVert x_i -
y_i\rVert_2)$.


  Radio communication through attenuating media necessitates the use of
very-low frequency (VLF) and ultra-low frequency (ULF) carrier bands, which are
frequently used in underwater and under-ground communication applications.
Quantum sensing techniques can be used to circumvent hard constraints on the
size, weight and noise floor of classical signal transducers. In this
low-frequency range, an optically pumped atomic sample can be used to detect
carrier wave modulation resonant with ground-state Zeeman splitting of alkali
atoms. Using a compact, self-calibrating system we demonstrate a resonant
atomic transducer for digital data encoded using binary phase- and
frequency-keying of resonant carrier waves in the 200 Hz -200 kHz range. We
present field trial data showing sensor noise floor, decoded data and received
bit error rate, and calculate the projected range of sub-sea communication
using this device.


  We associate all small subgraph counting problems with a systematic graph
encoding/representation system which makes a coherent use of graphlet
structures. The system can serve as a unified foundation for studying and
connecting many important graph problems in theory and practice. We describe
topological relations among graphlets (graph elements) in rigorous mathematics
language and from the perspective of graph encoding. We uncover, characterize
and utilize algebraic and numerical relations in graphlet counts/frequencies.
We present a novel algorithm for efficiently counting small subgraphs as a
practical product of our theoretical findings.


  We present an approach to learn voice-face representations from the talking
face videos, without any identity labels. Previous works employ cross-modal
instance discrimination tasks to establish the correlation of voice and face.
These methods neglect the semantic content of different videos, introducing
false-negative pairs as training noise. Furthermore, the positive pairs are
constructed based on the natural correlation between audio clips and visual
frames. However, this correlation might be weak or inaccurate in a large amount
of real-world data, which leads to deviating positives into the contrastive
paradigm. To address these issues, we propose the cross-modal prototype
contrastive learning (CMPC), which takes advantage of contrastive methods and
resists adverse effects of false negatives and deviate positives. On one hand,
CMPC could learn the intra-class invariance by constructing semantic-wise
positives via unsupervised clustering in different modalities. On the other
hand, by comparing the similarities of cross-modal instances from that of
cross-modal prototypes, we dynamically recalibrate the unlearnable instances'
contribution to overall loss. Experiments show that the proposed approach
outperforms state-of-the-art unsupervised methods on various voice-face
association evaluation protocols. Additionally, in the low-shot supervision
setting, our method also has a significant improvement compared to previous
instance-wise contrastive learning.


  Adaptive inference is a simple method for reducing inference costs. The
method works by maintaining multiple classifiers of different capacities, and
allocating resources to each test instance according to its difficulty. In this
work, we compare the two main approaches for adaptive inference, Early-Exit and
Multi-Model, when training data is limited. First, we observe that for models
with the same architecture and size, individual Multi-Model classifiers
outperform their Early-Exit counterparts by an average of 2.3%. We show that
this gap is caused by Early-Exit classifiers sharing model parameters during
training, resulting in conflicting gradient updates of model weights. We find
that despite this gap, Early-Exit still provides a better speed-accuracy
trade-off due to the overhead of the Multi-Model approach. To address these
issues, we propose SWEET (Separating Weights in Early Exit Transformers), an
Early-Exit fine-tuning method that assigns each classifier its own set of
unique model weights, not updated by other classifiers. We compare SWEET's
speed-accuracy curve to standard Early-Exit and Multi-Model baselines and find
that it outperforms both methods at fast speeds while maintaining comparable
scores to Early-Exit at slow speeds. Moreover, SWEET individual classifiers
outperform Early-Exit ones by 1.1% on average. SWEET enjoys the benefits of
both methods, paving the way for further reduction of inference costs in NLP.


  Brugia malayi are thread-like parasitic worms and one of the etiological
agents of Lymphatic filariasis (LF). Existing anthelmintic drugs to treat LF
are effective in reducing the larval microfilaria (mf) counts in human
bloodstream but are less effective on adult parasites. To test potential drug
candidates, we report a multi-parameter phenotypic assay based on tracking the
motility of adult B. malayi and mf in vitro. For adult B. malayi, motility is
characterized by the centroid velocity, path curvature, angular velocity,
eccentricity, extent, and Euler Number. These parameters are evaluated in
experiments with three anthelmintic drugs. For B. malayi mf, motility is
extracted from the evolving body skeleton to yield positional data and bending
angles at 74 key point. We achieved high-fidelity tracking of complex worm
postures (self-occlusions, omega turns, body bending, and reversals) while
providing a visual representation of pose estimates and behavioral attributes
in both space and time scales.


  High-resolution UV spectroscopy of low-z QSOs with the Space Telescope
Imaging Spectrograph and the Far Ultraviolet Spectroscopic Explorer has
indicated that O VI absorption-line systems provide a valuable probe of the
low-z intergalactic medium. These observations and their implications are
briefly reviewed. Though still uncertain due to the small sample, the number of
O VI absorbers per unit redshift is quite high, and these absorbers appear to
trace an important baryon reservoir. The O VI systems are intervening; they are
highly displaced from the background QSO redshifts and are correlated with
foreground luminous galaxies. Their physical conditions are variable and
sometimes complicated. In some cases, there is clear evidence that the
absorbers have a multiphase nature. Some appear to be photoionized by the UV
background from QSOs, while others are probably collisionally ionized. However,
the majority of the O VI lines have b-values that suggest an origin in
collisionally ionized hot gas. The observations are in agreement with
hydrodynamic simulations of cosmological structure growth, which predict
substantial quantities of shock-heated, hot intergalactic gas at low z, but
more observational and theoretical work is needed to confirm the nature of the
O VI systems.


  It is well-known that perturbative calculations in field theory can lead to
far simpler answers than the Feynman diagram approach might suggest. In some
cases scattering amplitudes can be constructed for processes with any desired
number of external legs yielding compact expressions which are inaccessible
from the point of view of conventional perturbation theory. In this thesis we
discuss some attempts to address the nature of this underlying simplicity and
then use the results to calculate some previously unknown amplitudes of
interest. Witten's twistor string theory is introduced and the CSW rules at
tree-level and one-loop are described. We use these techniques to calculate the
one-loop gluonic MHV amplitudes in N=1 super-Yang-Mills as a verification of
their validity and then proceed to evaluate the general MHV amplitudes in pure
Yang-Mills with a scalar running in the loop. This latter amplitude is a new
result in QCD. In addition to this, we review some recent on-shell recursion
relations for tree-level amplitudes in gauge theory and apply them to gravity.
As a result we present a new compact form for the n-graviton MHV amplitudes in
general relativity. The techniques and results discussed are relevant to the
understanding of the structure of field theory and gravity and the
non-supersymmetric Yang-Mills amplitudes in-particular are pertinent to
background processes at the LHC. The gravitational recursion relations provide
new techniques for perturbative gravity and have some bearing on the
ultraviolet properties of Einstein gravity.


  We present statistical analysis of a fluence limited sample of over 1100
giant pulses from the Crab pulsar, with fluence > 130 Jy ms at ~1330 MHz. These
were detected in ~260 hours of observation with the National Centre for Radio
Astrophysics (NCRA)-15m radio telescope. We find that the pulse energy
distribution follows a power law with index $\alpha\approx$-3 at least up to a
fluence of ~5 Jy s. The power law index agrees well with that found for lower
energy pulses in the range 3-30 Jy ms. The fluence distribution of the Crab
pulsar hence appears to follow a single power law over ~3 orders of magnitude
in fluence. We do not see any evidence for the flattening at high fluences
reported by earlier studies. We also find that at these fluence levels, the
rate of giant-pulse emission varies by as much as a factor of ~5 on time-scales
of a few days, although the power law index of the pulse-energy distribution
remains unchanged. The slope of the fluence distribution for Crab giant pulses
is similar to that recently determined for the repeating FRB 121102. We also
find an anti-correlation between the pulse fluence and the pulse width, so that
more energetic pulses are preferentially shorter.


  About 100 millisecond (ms) pulsars have been identified in the Galaxy, and
only ~10% of them are solitary, i.e. without a binary companion. Nothing is
known on the optical emission properties of millisecond pulsars. Observations
of solitary millisecond pulsars are the only way to detect their faint optical
radiation, otherwise buried by the brighter white dwarf companion. As in the
case of solitary, non millisecond pulsars, an X-ray detection represents the
first step for a follow-up identification campaign in the optical. Among the
X-ray detected millisecond pulsars, PSR J2124-3358 stands out as an ideal case
because it is very close (<270 pc) and little absorbed. Here, we report on
recent VLT observations of the PSR J2124-3358 aimed at the identification of
its optical counterpart. No optical emission from the pulsar has been detected
down to a limiting flux of V ~ 27.8.


  In this paper we consider Grassmannians in arbitrary characteristic.
Generalizing Kapranov's well-known characteristic-zero results we construct
dual exceptional collections on them (which are however not strong) as well as
a tilting bundle. We show that this tilting bundle has a quasi-hereditary
endomorphism ring and we identify the standard, costandard, projective and
simple modules of the latter.


  We define Hochschild cohomology of the second kind for differential graded
(dg) or curved algebras as a derived functor in a compactly generated derived
category of the second kind, and show that it is invariant under Morita
equivalence of the second kind. A bimodule version of Koszul duality is
constructed and used to show that Hochschild cohomology of the second kind is
preserved under (nonconilpotent) Koszul duality. Hochschild cohomology of the
second kind of an algebra often computes the ordinary Hochschild cohomology of
geometrically meaningful dg categories. Examples include the category of
infinity local systems on a topological space, the bounded derived category of
a complex algebraic manifold and the category of matrix factorizations.


  Given commuting $d$-tuples $\mathbb{S}_i$ and $\mathbb{T}_i$, $1\leq i\leq
2$, Banach space operators such that the tensor products pair
$(\mathbb{S}_1\otimes\mathbb{S}_2,\mathbb{T}_1\otimes\mathbb{T}_2)$ is strict
$m$-isometric (resp., $\mathbb{S}_1$, $\mathbb{S}_2$ are invertible and
$(\mathbb{S}_1 \otimes \mathbb{S}_2, \mathbb{T}_1 \otimes\mathbb{T}_2)$ is
strict $m$-symmetric), there exist integers $m_i >0$, and a non-zero scalar
$c$, such that $m=m_1+m_2-1$, $(\mathbb{S}_1, {\frac{1}{c}}\mathbb{T}_1)$ is
strict $m_1$-isometric and $(\mathbb{S}_2, c\mathbb{T}_2)$ is strict
$m_2$-isometric (resp., there exist integers $m_i >0$, and a non-zero scalar
$c$, such that $m=m_1+m_2-1$, $(\mathbb{S}_1,{\frac{1}{c}}\mathbb{T}_1)$ is
strict $m_1$-symmetric and $(\mathbb{S}_2, c\mathbb{T}_2)$ is strict
$m_2$-symmetric. However, $(\mathbb{S}_i,\mathbb{T}_i)$ is strict
$m_i$-isometric (resp., strict $m_i$-symmetric) for $1\leq i\leq 2$ implies
only that $(\mathbb{S}_1\otimes \mathbb{S}_2, \mathbb{T}_1\otimes
\mathbb{T}_2)$ is $m$-isometric (resp., $(\mathbb{S}_1 \otimes \mathbb{S}_2,
\mathbb{T}_1\otimes\mathbb{T}_2)$ is $m$-symmetric).


  The momentum dependence of the antikaon optical potential in nuclear matter
is obtained from a microscopic and self-consistent calculation using the
meson-exchange J\"ulich $\bar{K}N$ interaction. Two self-consistent schemes are
discussed, which would lead to substantially different predictions for the
width of ${\bar K}$ nuclear bound states. The effect of higher partial waves of
the $\bar{K}N$ interaction, beyond the L=0 component, is studied and found to
have moderate but non-negligible effects on the ${\bar K}$ nuclear potential at
zero momentum. At momenta as large as 500 MeV/c, relevant in the analysis of
heavy-ion collisions, the higher partial partial waves modify the ${\bar K}$
optical potential by nearly a factor of two.


  We show that the subregion entanglement Hamiltonians of excited eigenstates
of a quantum many-body system are approximately linear combinations of
subregionally (quasi)local approximate conserved quantities, with relative
commutation errors $\mathcal{O}\left(\frac{\text{subregion boundary
area}}{\text{subregion volume}}\right)$. By diagonalizing an entanglement
Hamiltonian superdensity matrix (EHSM) for an ensemble of eigenstates, we can
obtain these conserved quantities as the EHSM eigen-operators with nonzero
eigenvalues. For free fermions, we find the number of nonzero EHSM eigenvalues
is cut off around the order of subregion volume, and some of their EHSM
eigen-operators can be rather nonlocal, although subregionally quasilocal. In
the interacting XYZ model, we numerically find the nonzero EHSM eigenvalues
decay roughly in power law if the system is integrable, with the exponent
$s\approx 1$ ($s\approx 1.5\sim 2$) if the eigenstates are extended (many-body
localized). For fully chaotic systems, only two EHSM eigenvalues are
significantly nonzero, the eigen-operators of which correspond to the identity
and the subregion Hamiltonian.


  Compressing large neural networks is an important step for their deployment
in resource-constrained computational platforms. In this context, vector
quantization is an appealing framework that expresses multiple parameters using
a single code, and has recently achieved state-of-the-art network compression
on a range of core vision and natural language processing tasks. Key to the
success of vector quantization is deciding which parameter groups should be
compressed together. Previous work has relied on heuristics that group the
spatial dimension of individual convolutional filters, but a general solution
remains unaddressed. This is desirable for pointwise convolutions (which
dominate modern architectures), linear layers (which have no notion of spatial
dimension), and convolutions (when more than one filter is compressed to the
same codeword). In this paper we make the observation that the weights of two
adjacent layers can be permuted while expressing the same function. We then
establish a connection to rate-distortion theory and search for permutations
that result in networks that are easier to compress. Finally, we rely on an
annealed quantization algorithm to better compress the network and achieve
higher final accuracy. We show results on image classification, object
detection, and segmentation, reducing the gap with the uncompressed model by 40
to 70% with respect to the current state of the art.


  Neural Radiance Fields (NeRFs) have shown great potential in novel view
synthesis. However, they struggle to render sharp images when the data used for
training is affected by motion blur. On the other hand, event cameras excel in
dynamic scenes as they measure brightness changes with microsecond resolution
and are thus only marginally affected by blur. Recent methods attempt to
enhance NeRF reconstructions under camera motion by fusing frames and events.
However, they face challenges in recovering accurate color content or constrain
the NeRF to a set of predefined camera poses, harming reconstruction quality in
challenging conditions. This paper proposes a novel formulation addressing
these issues by leveraging both model- and learning-based modules. We
explicitly model the blur formation process, exploiting the event double
integral as an additional model-based prior. Additionally, we model the
event-pixel response using an end-to-end learnable response function, allowing
our method to adapt to non-idealities in the real event-camera sensor. We show,
on synthetic and real data, that the proposed approach outperforms existing
deblur NeRFs that use only frames as well as those that combine frames and
events by +6.13dB and +2.48dB, respectively.


  Obstructive sleep apnea (OSA) is a complex disease with complex etiology,
which requires multidisciplinary cooperation in diagnosis and treatment.
Mandibular retrognathia is strongly associated with OSA. Orthodontists can
either correct the mandibular retrognathia of pediatric OSA via various kinds
of orthodontic appliances, following adenoidectomy and tonsillectomy, or
enlarge upper airway by mandibular advancement device (MAD) through
repositioning the mandible and tongue of adult OSA patients. This mini review
was to investigate the therapy of MAD to adult OSA as well as orthodontic
treatment to pediatric OSA.


  Poonen and Stoll have shown that the reduced Shafarevich-Tate group of a
principally polarized abelian variety over a global field can have order twice
a square (the odd case) as well as a square (the even case). For a curve over a
global field, they give a local diophantine criterion for its jacobian to be
even or odd. In this note we use the Cherednik-Drinfeld p-adic uniformization
to study the local points and divisors on certain Atkin-Lehner quotients of
Shimura curves. We exhibit an explicit family of such quotient curves over the
rationals with odd jacobians, with genus going to infinity, and with at most
finitely many hyperelliptic members.


  Camouflaged object detection (COD) is the challenging task of identifying
camouflaged objects visually blended into surroundings. Albeit achieving
remarkable success, existing COD detectors still struggle to obtain precise
results in some challenging cases. To handle this problem, we draw inspiration
from the prey-vs-predator game that leads preys to develop better camouflage
and predators to acquire more acute vision systems and develop algorithms from
both the prey side and the predator side. On the prey side, we propose an
adversarial training framework, Camouflageator, which introduces an auxiliary
generator to generate more camouflaged objects that are harder for a COD method
to detect. Camouflageator trains the generator and detector in an adversarial
way such that the enhanced auxiliary generator helps produce a stronger
detector. On the predator side, we introduce a novel COD method, called
Internal Coherence and Edge Guidance (ICEG), which introduces a camouflaged
feature coherence module to excavate the internal coherence of camouflaged
objects, striving to obtain more complete segmentation results. Additionally,
ICEG proposes a novel edge-guided separated calibration module to remove false
predictions to avoid obtaining ambiguous boundaries. Extensive experiments show
that ICEG outperforms existing COD detectors and Camouflageator is flexible to
improve various COD detectors, including ICEG, which brings state-of-the-art
COD performance.


  We describe the superconducting proximity effect taking place in a contact
between a noncentrosymmetric superconductor and a diffusive
normal/ferromagnetic metal within the quasiclassical theory of
superconductivity. By solving numerically the Usadel equation with boundary
conditions valid for arbitrary interface transparency, we show that the
analysis of the proximity-modified local density of states in the normal side
can be used to obtain information about the exotic superconductivity of
noncentrosymmetric materials. We point out the signatures of triplet pairing,
the coexistence of triplet and singlet pairing, and particular orbital
symmetries of the pair potential. Exploiting the directional dependence of the
spin polarization pair breaking effect on the triplet correlations, we show how
the order relation between triplet and singlet gaps can be discriminated and
that an estimation of the specific gap ratio is possible in some cases.


  Crosscorrelation structures in the Green function retrieval by
crosscorrelating wavefields are revealed using rigorous mathematical theory on
integral equations. The previous practice on extracting the Green function by
crosscorrelating the wavefields recorded at two locations produced by the same
source and then summing such crosscorrelations over all sources on a boundary
is inadequate and has limitations in recovering the low frequency content in
the Green function. To recover the exact Green function, we need crosscorrelate
the wavefields observed at the two locations generated by different sources,
respectively. The crosscorrelation structure can be viewed as a matrix in the
discrete case or an integral operator in the continuous case. The previous
Green function retrieval method corresponds to the identity matrix multiplying
a constant. If the matrix is diagonal, the wavefield crosscorrelation is still
within the wavefield due to the same source but different weighting should be
applied for different sources. We have derived analytically the
crosscorrelation kernels for two important cases, the plane boundary and the
circular boundary, and both kernels are symmetrical difference kernels, which
correspond to convolutional operations. For high frequency waves or far-field
sources, the kernels reduce to the know result which is the Dirac delta
distribution (or an identity matrix). For other boundaries of general geometric
shapes, numerical schemes like the boundary element method can be used to solve
for the kernel matrix.


  For quantum particles in a Boltzmann state, we derive an inequality between
momentum uncertainty $\Delta p$ and thermal de Broglie wavelength $\lambda_{\rm
th}$, expressed as $\Delta p \geq \sqrt{2\pi}\hbar/\lambda_{\rm th}$, as a
corollary of the Boltzmann lower bound for the Heisenberg uncertainty product
proposed in the previous work [EPL, 143, 20001 (2023)]


  Seesaw models with a slightly broken lepton number symmetry can explain small
neutrino masses, and allow for low-scale leptogenesis. We make a thorough
analysis of leptogenesis within the simplest model with two right-handed (RH)
neutrinos (or with N_3 decoupled). We obtain a semi-analytical formula for the
final asymmetry in both supersymmetric and non-supersymmetric cases with a
simple dependence on each parameter. The low-energy parameters factorize from
the high-energy ones, and the high-energy phase must be non-zero. The role of
the PMNS phases is carefully studied. Moreover, we find that the breaking
parameter in the Yukawa coupling matrix must be relatively large, \epsilon_h >
10^{-3} for normal and 10^{-2} for inverted hierarchy. Therefore, leptogenesis
in our simple model is incompatible with RH neutrino signals at future
colliders or sizable lepton-flavor violation. The other breaking parameter,
\epsilon_M, which appears in the RH neutrino mass matrix, can be much smaller,
and actually needs to be so in order to have low-scale leptogenesis.


  The LEUTL FEL at the APS has achieved gain at 530 nm with peak beam current
\~100 A. In an effort to push to 120 nm and beyond, we have designed and are
commissioning a bunch compressor to increase the peak current to 600 A or more.
The bunch compressor uses a four-dipole chicane at an energy of 100 to 210 MeV.
To provide options for control of emittance growth due to coherent synchrotron
radiation (CSR), the chicane has variable R56. The central pair of dipoles is
movable, accommodating variable R56 with less concern about emittance dilution
from nonuniformity of the dipole field. The symmetry of the chicane is also
variable via longitudinal motion of the final dipole, which is predicted to
have an effect on emittance growth. Following the chicane, a three-screen
emittance measurement system should permit resolution of the difference in
emittance growth between various chicane configurations. A vertical bending
magnet analysis line is present to permit imaging of correlations between
transverse and energy coordinates. This paper reviews the features and expected
performance of the chicane. A companion paper discusses the physics design in
detail.
  Work supported by the U.S. Department of Energy, Office of Basic Energy
Sciences, under Contract No. W-31-109-ENG-38.


  In this note, a new local regularity criteria for the axisymmetric solutions
to the 3D Navier--Stokes equations is investigated. It is slightly
supercritical and implies an upper bound for the oscillation of $\Gamma=r
u^{\theta}$: for any $0< \tau<1$, there exists a constant $c>0$, $$
|\Gamma(r,x_{3},t)|\leq N e^{-c\, |\ln r|^{\tau}},\ 0<r\leq \frac{1}{4}. $$


  We study the complexity of approximating integrals of smooth functions at
absolute precision $\varepsilon > 0$ with confidence level $1 - \delta \in
(0,1)$. The optimal error rate for multivariate functions from classical
isotropic Sobolev spaces $W_p^r(G)$ with sufficient smoothness on bounded
Lipschitz domains $G \subset \mathbb{R}^d$ is determined. It turns out that the
integrability index $p$ has an effect on the influence of the uncertainty
$\delta$ in the complexity. In the limiting case $p = 1$ we see that
deterministic methods cannot be improved by randomization. In general, higher
smoothness reduces the additional effort for diminishing the uncertainty.
Finally, we add a discussion about this problem for function spaces with mixed
smoothness.


  The hard X-ray emission in a solar flare is typically characterized by a
number of discrete sources, each with its own spectral, temporal, and spatial
variability. Establishing the relationship amongst these sources is critical to
determine the role of each in the energy release and transport processes that
occur within the flare. In this paper we present a novel method to identify and
characterize each source of hard X-ray emission. The method permits a
quantitative determination of the most likely number of subsources present, and
of the relative probabilities that the hard X-ray emission in a given subregion
of the flare is represented by a complicated multiple source structure or by a
simpler single source. We apply the method to a well-studied flare on
2002~February~20 in order to assess competing claims as to the number of
chromospheric footpoint sources present, and hence to the complexity of the
underlying magnetic geometry/toplogy. Contrary to previous claims of the need
for multiple sources to account for the chromospheric hard X-ray emission at
different locations and times, we find that a simple
two-footpoint-plus-coronal-source model is the most probable explanation for
the data. We also find that one of the footpoint sources moves quite rapidly
throughout the event, a factor that presumably complicated previous analyses.
The inferred velocity of the footpoint corresponds to a very high induced
electric field, compatible with those in thin reconnecting current sheets.


  We present a theoretical investigation on the pulsational behavior of
metal-rich RR Lyrae variables over the range of evolutionary parameters
suitable for stars with metallicities Z= 0.006, 0.01 and 0.02. With the
addition of similar results for metal-poor pulsators we discuss the theoretical
pulsational scenario covering the metallicity range from Z=0.0001 to 0.02. We
find that the distribution of field ab-type RR Lyrae stars in the
period-metallicity plane can be easily understood within the framework of the
present theoretical scenario, suggesting that the Oosterhoff dichotomy also
affects field variables. Theoretical predictions concerning the
amplitude-period diagram are discussed and compared with observational data. We
find a general agreement for metal-poor ([Fe/H]<-1.4) RR Lyrae stars, whereas
more metal-rich variables show amplitudes smaller than those predicted for
pulsators originated from old, low-mass evolving stars. Alternatively, the
agreement between theory and observations would require that a substantial
fraction of metal-rich RR Lyrae variables in the Galactic field were younger
than approximately 2 Gyr. The comparison between the pulsational behavior of RR
Lyrae either in the Galactic field or in the Galactic bulge discloses the
evidence that, at least as far as RR Lyrae variables are concerned, the
metal-rich components of the bulge and of the field population appear quite
similar.


  Coronal bright points (CBP) are ubiquitous small brightenings in the solar
corona associated with small magnetic bipoles. We derive the solar differential
rotation profile by tracing the motions of CBPs detected by the Atmospheric
Imaging Assembly (AIA) instrument aboard the Solar Dynamics Observatory (SDO).
We also investigate problems related to detection of coronal bright points
resulting from instrument and detection algorithm limitations. To determine the
positions and identification of coronal bright points we used a segmentation
algorithm. A linear fit of their central meridian distance and latitude versus
time was utilised to derive velocities. We obtained 906 velocity measurements
in a time interval of only 2 days. The differential rotation profile can be
expressed as $\omega_{rot} = (14.47\pm 0.10 + (0.6\pm 1.0)\sin^{2}(b) +
(-4.7\pm 1.7)\sin^{4}(b))$\degr day$^{-1}$. Our result is in agreement with
other work and it comes with reasonable errors in spite of the very short time
interval used. This was made possible by the higher sensitivity and resolution
of the AIA instrument compared to similar equipment as well as high cadence.
The segmentation algorithm also played a crucial role by detecting so many
CBPs, which reduced the errors to a reasonable level. Data and methods
presented in this paper show a great potential to obtain very accurate velocity
profiles, both for rotation and meridional motion and, consequently, Reynolds
stresses. The amount of coronal bright point data that could be obtained from
this instrument should also provide a great opportunity to study changes of
velocity patterns with a temporal resolution of only a few months. Other
possibilities are studies of evolution of CBPs and proper motions of magnetic
elements on the Sun.


  To depict the complex relationship among nodes and the evolving process of a
complex system, a Bose-Einstein hypernetwork is proposed in this paper. Based
on two basic evolutionary mechanisms, growth and preference jumping, the
distribution of hyperedge cardinalities is studied. The Poisson process theory
is used to describe the arrival process of new node batches. And, by using the
Poisson process theory and a continuity technique, the hypernetwork is analyzed
and the characteristic equation of hyperedge cardinalities is obtained.
Additionally, an analytical expression for the stationary average hyperedge
cardinality distribution is derived by employing the characteristic equation,
from which Bose-Einstein condensation in the hypernetwork is obtained. The
theoretical analyses in this paper agree with the conducted numerical
simulations. This is the first study on the hyperedge cardinality in
hypernetworks, where Bose-Einstein condensation can be regarded as a special
case of hypernetworks. Moreover, a condensation degree is also discussed with
which Bose-Einstein condensation can be classified.


  The novel concept of non-compensated n-p codoping has made it possible to
create tunable intermediate bands in the intrinsic band gap of TiO2, making the
codoped TiO2 a promising material for developing intermediate band solar cells
(IBSCs). Here we investigate the quantum efficiency of such IBSCs within two
scenarios - with and without current extracted from the extended intermediate
band. Using the ideal equivalent circuit model, we find that the maximum
efficiency of 57% in the first scenario and 53% in the second are both much
higher than the Shockley-Queisser limit from single gap solar cells. We also
obtain various key quantities of the circuits, a useful step in realistic
development of TiO2 based solar cells invoking device integration. These
equivalent circuit results are also compared with the efficiencies obtained
directly from consideration of electron transition between the energy bands,
and both approaches reveal the intriguing existence of double peaks in the
maximum quantum efficiency as a function of the relative location of IBs.


  We investigate the deflection angle in a strong deflection limit for a
marginally unstable photon sphere in a general asymptotically flat, static and
spherically symmetric spacetime under some assumptions to calculate
observables. The deflection angle of a light ray reflected by the marginally
unstable photon sphere diverges nonlogarithmically while the one reflected by a
photon sphere diverges logarithmically. We apply our formula to a
Reissner-Nordstrom spacetime and Hayward spacetime.


  The first part of this work consists of a study of the ODE/IM correspondence
for simply-laced affine Toda field theories. It is a first step towards a full
generalisation of the results of Lukyanov and Zamolodchikov on $\hat{\mathfrak
a}_1$ to a general affine Lie-Ka\v{c}-Moody algebra $\hat{\mathfrak g}$. In
order to achieve our goal, we investigate the structure of evaluation
representations of $\hat{\mathfrak g}$ and show how their tensor products are
related by what we call projected isomorphisms. These isomorphisms are used to
construct a set of quadratic functional relations, called $\psi$-system, for
the solutions to complex differential equations associated to $\hat{\mathfrak
g}$. Finally, from the $\psi$-system for the algebras $\mathfrak a$ and
$\mathfrak d$, we derive a set of Bethe Ansatz equations satisfied by the
eigenvalues of some particular boundary problem for the above mentioned
differential equations.
  The second part of this work deals with the study of one-point functions in
sine- and sinh-Gordon models. The approach to the computation of these
quantities follows a powerful method, which we call fermionic basis, developed
by Boos et al. for the XXZ, quantum Liouville and quantum sine-Gordon models.
We show how the determinant formula for one-point functions obtained there can
be generalised to the sinh-Gordon model. In doing so we give an interpretation
of the fermionic basis in terms of certain symmetries of the system. This new
perspective will also allow us to solve trivially the reflection relations
introduced by Fateev et al. We then provide analytical and numerical results
supporting our finding.


  How to explore useful features from images as prompts to guide the deep image
restoration models is an effective way to solve image restoration. In contrast
to mining spatial relations within images as prompt, which leads to
characteristics of different frequencies being neglected and further remaining
subtle or undetectable artifacts in the restored image, we develop a Frequency
Prompting image restoration method, dubbed FPro, which can effectively provide
prompt components from a frequency perspective to guild the restoration model
address these differences. Specifically, we first decompose input features into
separate frequency parts via dynamically learned filters, where we introduce a
gating mechanism for suppressing the less informative elements within the
kernels. To propagate useful frequency information as prompt, we then propose a
dual prompt block, consisting of a low-frequency prompt modulator (LPM) and a
high-frequency prompt modulator (HPM), to handle signals from different bands
respectively. Each modulator contains a generation process to incorporate
prompting components into the extracted frequency maps, and a modulation part
that modifies the prompt feature with the guidance of the decoder features.
Experimental results on commonly used benchmarks have demonstrated the
favorable performance of our pipeline against SOTA methods on 5 image
restoration tasks, including deraining, deraindrop, demoir\'eing, deblurring,
and dehazing. The source code and pre-trained models will be available at
https://github.com/joshyZhou/FPro.


  We compute charmonium spectral functions in 2-flavor QCD on anisotropic
lattices using the maximum entropy method. Our results suggest that the S-waves
(J/psi and eta_c) survive up to temperatures close to 2Tc, while the P-waves
(chi_c0 and chi_c1) melt away below 1.2Tc.


  We formulate a general, signature-independent form of the law of the excluded
middle and prove that a logic is semisimple if and only if it enjoys this law,
provided that it satisfies a weak form of the so-called inconsistency lemma of
Raftery. We then show that this equivalence can be used to provide simple
syntactic proofs of the theorems of Kowalski and Kracht characterizing the
semisimple varieties of FLew-algebras and Boolean algebras with operators, and
to extend them to FLe-algebras and Heyting algebras with operators. Moreover,
under stronger assumptions this correspondence works at the level of individual
models: the semisimple models of such a logic are precisely those which satisfy
an axiomatic form of the law of the excluded middle, and a Glivenko-like
connection obtains between the logic and its extension by the axiom of the
excluded middle. This in particular subsumes the well-known Glivenko theorems
relating intuitionistic and classical logic and the modal logics S4 and S5. As
a consequence, we also obtain a description of the subclassical substructural
logics which are Glivenko related to classical logic.


  The ordinal approach to evaluate time series due to innovative works of Bandt
and Pompe has increasingly established itself among other techniques of
nonlinear time series analysis. In this paper, we summarize and generalize the
theory of determining the Kolmogorov-Sinai entropy of a measure-preserving
dynamical system via increasing sequences of order generated partitions of the
state space. Our main focus are measuring processes without information loss.
Particularly, we consider the question of the minimal necessary number of
measurements related to the properties of a given dynamical system.


  The discovery of $\gamma$-ray emission from some radio-loud narrow-line
Seyfert 1 galaxies (RLNLS1s) indicated the presence of a relativistic beamed
jet in these objects. This immediately opened a new question about their parent
population: is how do they look like when observed at large angles? The study
of the parent population has provided important new insights on the physical
properties of this fascinating class of active galactic nuclei (AGN). In this
work, I will review the most recent advances in the study of parent sources,
and I will show the impact that a recent continuum survey carried out with the
Karl G. Jansky Very Large Array had on this topic. Finally, I will show how all
these new results point toward a new unification model for young jetted AGN.


  Hidden Rashba and Dresselhaus spin-splittings in centrosymmetric crystals
with subunits (sectors) having non-centrosymmetric symmetries (the R-2 and D-2
effects) have been predicted and observed experimentally, but the microscopic
mechanism remains unclear. Here we demonstrate that the spin-splitting in R-2
is enforced by specific symmetries (such as the non-symmorphic in the present
example) which ensures that the pertinent spin wavefunctions segregate
spatially on just one of the two inversion-partner sectors and thus avoid
compensation. This finding establishes a common fundamental source for the
conventional Rashba (R-1) effect and the R-2 effect, both originating from the
local sector symmetries, rather than from the global crystal asymmetry alone
for R-1 per se. We further show that the effective Hamiltonian for the R-1
effect is also applicable for the R-2 effect, but applying a symmetry-breaking
electric field to an R-2 compound produces different spin-splitting pattern
than applying a field to a trivial (non-R-2) centrosymmetric compound.


  Magnetic Resonance Image (MRI) pre-processing is a critical step for
neuroimaging analysis. However, the computational cost of MRI pre-processing
pipelines is a major bottleneck for large cohort studies and some clinical
applications. While High-Performance Computing (HPC) and, more recently, Deep
Learning have been adopted to accelerate the computations, these techniques
require costly hardware and are not accessible to all researchers. Therefore,
it is important to understand the performance bottlenecks of MRI pre-processing
pipelines to improve their performance. Using Intel VTune profiler, we
characterized the bottlenecks of several commonly used MRI-preprocessing
pipelines from the ANTs, FSL, and FreeSurfer toolboxes. We found that few
functions contributed to most of the CPU time, and that linear interpolation
was the largest contributor. Data access was also a substantial bottleneck. We
identified a bug in the ITK library that impacts the performance of ANTs
pipeline in single-precision and a potential issue with the OpenMP scaling in
FreeSurfer recon-all. Our results provide a reference for future efforts to
optimize MRI pre-processing pipelines.


  The Sturm-Liouville operator on a star-shaped graph is considered. We assume
that the potential is known a priori on all the edges except one, and study the
partial inverse problem, which consists in recovering the potential on the
remaining edge from the part of the spectrum. A constructive method is
developed for the solution of this problem, based on the Riesz-basicity of some
sequence of vector functions. The local solvability of the inverse problem and
the stability of its solution are proved.


  Barium stars are one of the important probes to understand the origin and
evolution of slow neutron-capture process elements in the Galaxy. These are
extrinsic stars, where the observed s-process element abundances are believed
to have an origin in the now invisible companions that produced these elements
at their Asymptotic Giant Branch phase of evolution. We have attempted to
understand the s-process nucleosynthesis, as well as the physical properties of
the companion stars through a detailed comparison of observed elemental
abundances of 10 barium stars with the predictions from AGB nucleosynthesis
models, FRUITY. For these stars, we have presented estimates of abundances of
several elements, C, N, O, Na, Al, $\alpha$-elements, Fe-peak elements and
neutron-capture elements Rb, Sr, Y, Zr, Ba, La, Ce, Pr, Nd, Sm and Eu. The
abundance estimates are based on high resolution spectral analysis.
Observations of Rb in four of these stars have allowed us to put a limit to the
mass of the companion AGB stars. Our analysis clearly shows that the former
companions responsible for the surface abundance peculiarities of these stars
are low-mass AGB stars. Kinematic analysis have shown the stars to be members
of Galactic disk population.


  We demonstrate a 13-fold increase in hard x-ray bremsstrahlung (10 - 200 keV)
emitted by a copper plasma created by 100 fs, 806 nm pulses at
$10^{14}-10^{15}$ Wcm$^{-2}$. This enhancement is achieved by roughening the
target surface with copper nanoparticles of ~15 nm size. A simple model that
invokes local field modifications by surface plasmon excitation and `lightning
rod' effects explains the observed enhancement quantitatively and provides
pointers to the design of structured surfaces for maximizing the emission.


  Existing state-of-the-art 3D point cloud understanding methods merely perform
well in a fully supervised manner. To the best of our knowledge, there exists
no unified framework that simultaneously solves the downstream high-level
understanding tasks including both segmentation and detection, especially when
labels are extremely limited. This work presents a general and simple framework
to tackle point cloud understanding when labels are limited. The first
contribution is that we have done extensive methodology comparisons of
traditional and learned 3D descriptors for the task of weakly supervised 3D
scene understanding, and validated that our adapted traditional PFH-based 3D
descriptors show excellent generalization ability across different domains. The
second contribution is that we proposed a learning-based region merging
strategy based on the affinity provided by both the traditional/learned 3D
descriptors and learned semantics. The merging process takes both low-level
geometric and high-level semantic feature correlations into consideration.
Experimental results demonstrate that our framework has the best performance
among the three most important weakly supervised point clouds understanding
tasks including semantic segmentation, instance segmentation, and object
detection even when very limited number of points are labeled. Our method,
termed Region Merging 3D (RM3D), has superior performance on ScanNet
data-efficient learning online benchmarks and other four large-scale 3D
understanding benchmarks under various experimental settings, outperforming
current arts by a margin for various 3D understanding tasks without complicated
learning strategies such as active learning.


  We introduce the concept of quasirational relation modules for discrete and
pro-$p$ presentations of discrete and pro-$p$ groups and show that aspherical
presentations and their subpresentations are quasirational. In the pro-$p$-case
quasirationality of pro-$p$-groups with a single defining relation holds. For
every quasirational (pro-$p$)relation module we construct the so called
$p$-adic rationalization, which is a pro-fd-module
$\overline{R}\widehat{\otimes}\mathbb{Q}_p= \varprojlim
R/[R,R\mathcal{M}_n]\otimes\mathbb{Q}_p$. We provide the isomorphisms
$\overline{R^{\wedge}_w}(\mathbb{Q}_p)=\overline{R}\widehat{\otimes}\mathbb{Q}_p$
and $\overline{R_u}(\mathbb{Q}_p)=\mathcal{O}(G_u)^*$, where $R^{\wedge}_w$ and
$R^{\wedge}_u$ stands for continuous prounipotent completions and corresponding
prounipotent presentations correspondingly. We show how
$\overline{R^{\wedge}_{w}}$ embeds into a sequence of abelian prounipotent
groups. This sequence arises naturally from a certain prounipotent crossed
module, the latter bring concrete examples of proalgebraic homotopy types. The
old-standing open problem of Serre, slightly corrected by Gildenhuys, in its
modern form states that pro-$p$-groups with a single defining relation are
aspherical. Our results give a positive feedback to the question of Serre.


  This paper discusses recent results and near-term prospects of the
long-baseline neutrino experiments MINOS, MINOS+, T2K and NOvA. The non-zero
value of the third neutrino mixing angle {\theta}13 allows experimental
analysis in a manner which explicitly exhibits appearance and disappearance
dependencies on additional parameters associated with mass-hierarchy, CP
violation, and any non-maximal {\theta}23. These current and near-future
experiments begin the era of precision accelerator long-baseline measurements
and lay the framework within which future experimental results will be
interpreted.


  The widespread use of Deep Learning (DL) applications in science and industry
has created a large demand for efficient inference systems. This has resulted
in a rapid increase of available Hardware Accelerators (HWAs) making comparison
challenging and laborious. To address this, several DL hardware benchmarks have
been proposed aiming at a comprehensive comparison for many models, tasks, and
hardware platforms. Here, we present our DL hardware benchmark which has been
specifically developed for inference on embedded HWAs and tasks required for
autonomous driving. In addition to previous benchmarks, we propose a new
granularity level to evaluate common submodules of DL models, a twofold
benchmark procedure that accounts for hardware and model optimizations done by
HWA manufacturers, and an extended set of performance indicators that can help
to identify a mismatch between a HWA and the DL models used in our benchmark.


  Anisotropic magnetoresistance is the change tendency of resistance of a
material on the mutual orientation of the electric current and the external
magnetic field. Here, we report experimental observations in the Dirac
semimetal Cd3As2 of giant anisotropic magnetoresistance and its transverse
version, called the planar Hall effect. The relative anisotropic
magnetoresistance is negative and up to -68% at 2 K and 10 T. The high
anisotropy and the minus sign in this isotropic and nonmagnetic material are
attributed to a field-dependent current along the magnetic field, which may be
induced by the Berry curvature of the band structure. This observation not only
reveals unusual physical phenomena in Weyl and Dirac semimetals, but also finds
additional transport signatures of Weyl and Dirac fermions other than negative
magnetoresistance.


  We discuss the observational properties of pulsar wind nebulae (PWNe) linking
them to the injected (at the termination shock) electron spectral energy
distribution and parameters of pulsar magnetospheres. In particular, we (1)
present spatially-resolved Chandra ACIS spectral maps of twelve PWNe and
measure the slopes of the uncooled PWN spectra just downstream of the
termination shock obtained from these maps, (2) consider the connections
between PWN morphologies and predictions of the magnetospheric emission models
and (3) discuss the limits on the maximum energies of particles in PWNe from
X-ray and gamma-ray observations.


  Flattened liquid drops poured on a very hot surface evaporate quite slowly
and float on a film of their own vapour. In the cavities of a surface, an
unusual type of vibrational motions occurs. Large vibrations take place and
different forms of dynamic drops are possible. They form elliptic patterns with
two lobes or hypotrochoid patterns with three lobes or more. The lobes are
turning relatively to the hot surface. We present a model of vibrating motions
of the drops. Frequencies of the vibrations are calculated regarding the number
of lobes. The computations agree with experiments.


  This volume contains the proceedings of the Second International Workshop on
Developments in Implicit Computational complExity (DICE 2011), which took place
on April 2-3 2011 in Saarbruecken, Germany, as a satellite event of the Joint
European Conference on Theory and Practice of Software, ETAPS 2011. Implicit
Computational Complexity aims at studying computational complexity without
referring to external measuring conditions or particular machine models, but
instead by considering restrictions on programming languages or logical
principles implying complexity properties. The aim of this workshop was to
bring together researchers working on implicit computational complexity, from
its logical and semantics aspects to those related to the static analysis of
programs, so as to foster their interaction and to give newcomers an overview
of the current trends in this area.
  The first DICE workshop was held in 2010 at ETAPS and published in EPTCS,
volume 23 (http://eptcs.org/content.cgi?DICE2010).


  The multiplicative semigroup $M_n(F)$ of $n\times n$ matrices over a field
$F$ is well understood, in particular, it is a regular semigroup. This paper
considers semigroups of the form $M_n(S)$, where $S$ is a semiring, and the
subsemigroups $UT_n(S)$ and $U_n(S)$ of $M_n(S)$ consisting of upper triangular
and unitriangular matrices. Our main interest is in the case where $S$ is an
idempotent semifield, where we also consider the subsemigroups $UT_n(S^*)$ and
$U_n(S^*)$ consisting of those matrices of $UT_n(S)$ and $U_n(S)$ having all
elements on and above the leading diagonal non-zero. Our guiding examples of
such $S$ are the 2-element Boolean semiring $\mathbb{B}$ and the tropical
semiring $\mathbb{T}$. In the first case, $M_n(\mathbb{B})$ is isomorphic to
the semigroup of binary relations on an $n$-element set, and in the second,
$M_n(\mathbb{T})$ is the semigroup of $n\times n$ tropical matrices.
  Il'in has proved that for any semiring $R$ and $n>2$, the semigroup $M_n(R)$
is regular if and only if $R$ is a regular ring. We therefore base our
investigations for $M_n(S)$ and its subsemigroups on the analogous but weaker
concept of being Fountain (formerly, weakly abundant). These notions are
determined by the existence and behaviour of idempotent left and right
identities for elements, lying in particular equivalence classes. We show that
certain subsemigroups of $M_n(S)$, including several generalisations of
well-studied monoids of binary relations (Hall relations, reflexive relations,
unitriangular Boolean matrices), are Fountain. We give a detailed study of a
family of Fountain semigroups arising in this way that has particularly
interesting and unusual properties.


  Two ideal polygons, $(p_1,\ldots,p_n)$ and $(q_1,\ldots,q_n)$, in the
hyperbolic plane or in hyperbolic space are said to be $\alpha$-related if the
cross-ratio $[p_i,p_{i+1},q_i,q_{i+1}] = \alpha$ for all $i$ (the vertices lie
on the projective line, real or complex, respectively). For example, if $\alpha
= -1$, the respective sides of the two polygons are orthogonal. This relation
extends to twisted ideal polygons, that is, polygons with monodromy, and it
descends to the moduli space of M\"obius-equivalent polygons. We prove that
this relation, which is, generically, a 2-2 map, is completely integrable in
the sense of Liouville. We describe integrals and invariant Poisson structures,
and show that these relations, with different values of the constants $\alpha$,
commute, in an appropriate sense. We investigate the case of small-gons,
describe the exceptional ideal polygons, that possess infinitely many
$\alpha$-related polygons, and study the ideal polygons that are
$\alpha$-related to themselves (with a cyclic shift of the indices).


  It is of paramount importance to uncover influential nodes to control
diffusion phenomena in a network. In recent works, there is a growing trend to
investigate the role of the community structure to solve this issue. Up to now,
the vast majority of the so-called community-aware centrality measures rely on
non-overlapping community structure. However, in many real-world networks, such
as social networks, the communities overlap. In other words, a node can belong
to multiple communities. To overcome this drawback, we propose and investigate
the "Overlapping Modularity Vitality" centrality measure. This extension of
"Modularity Vitality" quantifies the community structure strength variation
when removing a node. It allows identifying a node as a hub or a bridge based
on its contribution to the overlapping modularity of a network. A comparative
analysis with its non-overlapping version using the
Susceptible-Infected-Recovered (SIR) epidemic diffusion model has been
performed on a set of six real-world networks. Overall, Overlapping Modularity
Vitality outperforms its alternative. These results illustrate the importance
of incorporating knowledge about the overlapping community structure to
identify influential nodes effectively. Moreover, one can use multiple ranking
strategies as the two measures are signed. Results show that selecting the
nodes with the top positive or the top absolute centrality values is more
effective than choosing the ones with the maximum negative values to spread the
epidemic.


  Recent developments in ``Einstein Dehn filling'' allow the construction of
infinitely many Einstein manifolds that have different topologies but are
geometrically close to each other. Using these results, we show that for many
spatial topologies, the Hartle-Hawking wave function for a spacetime with a
negative cosmological constant develops sharp peaks at certain calculable
geometries. The peaks we find are all centered on spatial metrics of constant
negative curvature, suggesting a new mechanism for obtaining local homogeneity
in quantum cosmology.


  Solving image and video jigsaw puzzles poses the challenging task of
rearranging image fragments or video frames from unordered sequences to restore
meaningful images and video sequences. Existing approaches often hinge on
discriminative models tasked with predicting either the absolute positions of
puzzle elements or the permutation actions applied to the original data.
Unfortunately, these methods face limitations in effectively solving puzzles
with a large number of elements. In this paper, we propose JPDVT, an innovative
approach that harnesses diffusion transformers to address this challenge.
Specifically, we generate positional information for image patches or video
frames, conditioned on their underlying visual content. This information is
then employed to accurately assemble the puzzle pieces in their correct
positions, even in scenarios involving missing pieces. Our method achieves
state-of-the-art performance on several datasets.


  We introduce and study algebraic dynamical systems generated by triangular
systems of rational functions. We obtain several results about the degree
growth and linear independence of iterates as well as about possible lengths of
trajectories generated by such dynamical systems over finite fields. Some of
these results are generalisations of those known in the polynomial case, some
are new even in this case.


  In recent work [quant-ph/0405174] by Schumacher and Werner was discussed an
abstract algebraic approach to a model of reversible quantum cellular automata
(CA) on a lattice. It was used special model of CA based on partitioning scheme
and so there is a question about quantum CA derived from more general, standard
model of classical CA. In present work is considered an approach to definition
of a scheme with "history", valid for quantization both irreversible and
reversible classical CA directly using local transition rules. It is used
language of vectors in Hilbert spaces instead of C*-algebras, but results may
be compared in some cases. Finally, the quantum lattice gases, quantum walk and
"bots" are also discussed briefly.


  Current radio frequency (RF) sensors at the Edge lack the computational
resources to support practical, in-situ training for intelligent spectrum
monitoring, and sensor data classification in general. We propose a solution
via Deep Delay Loop Reservoir Computing (DLR), a processing architecture that
supports general machine learning algorithms on compact mobile devices by
leveraging delay-loop reservoir computing in combination with innovative
electrooptical hardware. With both digital and photonic realizations of our
design of the loops, DLR delivers reductions in form factor, hardware
complexity and latency, compared to the State-of-the-Art (SoA). The main impact
of the reservoir is to project the input data into a higher dimensional space
of reservoir state vectors in order to linearly separate the input classes.
Once the classes are well separated, traditionally complex, power-hungry
classification models are no longer needed for the learning process. Yet, even
with simple classifiers based on Ridge regression (RR), the complexity grows at
least quadratically with the input size. Hence, the hardware reduction required
for training on compact devices is in contradiction with the large dimension of
state vectors. DLR employs a RR-based classifier to exceed the SoA accuracy,
while further reducing power consumption by leveraging the architecture of
parallel (split) loops. We present DLR architectures composed of multiple
smaller loops whose state vectors are linearly combined to create a lower
dimensional input into Ridge regression. We demonstrate the advantages of using
DLR for two distinct applications: RF Specific Emitter Identification (SEI) for
IoT authentication, and wireless protocol recognition for IoT situational
awareness.


  We propose a $B-L$ model combined with the $S_4\times Z_3\times Z_4$ discrete
symmetry which successfully explains the recent $3+1$ sterile - active neutrino
data. The smallness of neutrino mass is obtained through the type-I seesaw
mechanism. The active-active and sterile-active neutrino mixing angles are
predicted to be consistent with the recent constraints in which $0.3401\,
(0.3402) \leq \sin^2\theta_{12}\leq 0.3415\, (0.3416), \, 0.456\, (0.433) \leq
\sin^2\theta_{23}\leq 0.544\, (0.545), \, 2.00\, (2.018) \leq 10^2\times
\sin^2\theta_{13}\leq 2.405\, (2.424),\,\, 156 \, (140.8) \leq
\delta^{(\circ)}_{CP}\leq 172\, (167.2)$ for normal (inverted) ordering of the
three neutrino scenario, and $0.015 \,(0.022) \leq s^2_{14}\leq 0.045
\,(0.029), \, 0.005 (0.0095)\leq s^2_{24}\leq 0.012\, (0.012), \, 0.003
\,(0.009)\leq s^2_{34} \leq 0.011$ for normal (inverted) ordering of the $3+1$
neutrino scenario. Our model predicts flavour conserving leptonic neutral
scalar interactions and successfully explains the muon $g-2$ anomaly.


  We formulate the composite fermions in the presence of an in-plane magnetic
field. As the in-plane field increases, if we assume the state at $\nu=5/2$
turns into the mixed state between the unidirectional charge density wave
domains and paired Hall state, we can phenomenologically fit the theoretically
defined gap to the experimental measured results. We explain the destruction of
the paired Hall states and then a phase transition from the paired Hall state
to the unidirectional charge density wave from a symmetry point of view.


  We study the diameter of the graph $G(w)$ of reduced words of an element $w$
in a Coxeter group $W$ whose edges correspond to applications of the Coxeter
relations. We resolve conjectures of Reiner--Roichman and Dahlberg--Kim by
proving a tight lower bound on this diameter when $W=S_n$ is the symmetric
group and by characterizing the equality cases. We also give partial results in
other classical types which illustrate the limits of current techniques.


  Quantum key distribution uses public discussion protocols to establish shared
secret keys. In the exploration of ultimate limits to such protocols, the
property of symmetric extendibility of underlying bipartite states $\rho_{AB}$
plays an important role. A bipartite state $\rho_{AB}$ is symmetric extendible
if there exits a tripartite state $\rho_{ABB'}$, such that the $AB$ marginal
state is identical to the $AB'$ marginal state, i.e. $\rho_{AB'}=\rho_{AB}$.
For a symmetric extendible state $\rho_{AB}$, the first task of the public
discussion protocol is to break this symmetric extendibility. Therefore to
characterize all bi-partite quantum states that possess symmetric extensions is
of vital importance. We prove a simple analytical formula that a two-qubit
state $\rho_{AB}$ admits a symmetric extension if and only if
$\tr(\rho_B^2)\geq \tr(\rho_{AB}^2)-4\sqrt{\det{\rho_{AB}}}$. Given the
intimate relationship between the symmetric extension problem and the quantum
marginal problem, our result also provides the first analytical necessary and
sufficient condition for the quantum marginal problem with overlapping
marginals.


  While large language models based on the transformer architecture have
demonstrated remarkable in-context learning (ICL) capabilities, understandings
of such capabilities are still in an early stage, where existing theory and
mechanistic understanding focus mostly on simple scenarios such as learning
simple function classes. This paper takes initial steps on understanding ICL in
more complex scenarios, by studying learning with representations. Concretely,
we construct synthetic in-context learning problems with a compositional
structure, where the label depends on the input through a possibly complex but
fixed representation function, composed with a linear function that differs in
each instance. By construction, the optimal ICL algorithm first transforms the
inputs by the representation function, and then performs linear ICL on top of
the transformed dataset. We show theoretically the existence of transformers
that approximately implement such algorithms with mild depth and size.
Empirically, we find trained transformers consistently achieve near-optimal ICL
performance in this setting, and exhibit the desired dissection where lower
layers transforms the dataset and upper layers perform linear ICL. Through
extensive probing and a new pasting experiment, we further reveal several
mechanisms within the trained transformers, such as concrete copying behaviors
on both the inputs and the representations, linear ICL capability of the upper
layers alone, and a post-ICL representation selection mechanism in a harder
mixture setting. These observed mechanisms align well with our theory and may
shed light on how transformers perform ICL in more realistic scenarios.


  We present a model independent method of reconstructing the Lagrangian for
the k-essence field driving the present acceleration of the universe. We
consider the simplest k-essence model for which the potential is constant.
Later we use three parametrizations for the Hubble parameter $H(z)$, consistent
with the recent SN1a data, to yield the Lagrangian $F$. Our reconstruction
program does not generate any physically realistic Lagrangian for models that
allow phantom crossing, whereas models without phantom crossing, yield well
behaved Lagrangian.


  An outstanding challenge in large-scale quantum platforms is to
simultaneously achieve strong interactions, giving rise to the most interesting
behaviors, and local addressing -that can probe them. In the context of
correlated phases, local addressing enables one to directly probe the nature of
the system's order. Meanwhile, for out-ofequilibrium dynamics, such addressing
allows the study of quantum information spreading and operator growth. Here, we
introduce a novel technique that enables the measurement of local correlation
functions, down to single-site resolution, despite access to only global
controls. Our approach leverages the intrinsic disorder present in a
solid-state spin ensemble to dephase the nonlocal components of the correlation
function. Utilizing this toolset, we measure both the spin and energy transport
in nuclear spin chains. By tuning the interaction Hamiltonian via Floquet
engineering, we investigate the cross-over between ballistic and diffusive
hydrodynamics. Interestingly, when the system is both interacting and
(nearly-)integrable, we observe the coexistence of diffusive spin transport
with ballistic energy transport.


  Drawing from a thought experiment that we conduct, we propose that a virtual
graviton gives rise to a black hole geometry when its momentum surpasses a
certain threshold value on the Planck scale. This hypothesis implies that the
propagator of a virtual graviton, that possesses momentum surpassing this
threshold, vanishes. Consequently, a Feynman diagram containing this type of
graviton propagator does not add to the overall amplitude. This mechanism
suggests the feasibility of formulating an ultraviolet-finite four-dimensional
quantum gravitational theory. The elementary particles including the gravitons
are treated as point particles in this formulation.


  We study the geometry and topology of Hilbert schemes of points on the
orbifold surface [C^2/G], respectively the singular quotient surface C^2/G,
where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition
of the (equivariant) Hilbert scheme of the orbifold into affine space strata
indexed by a certain combinatorial set, the set of Young walls. The generating
series of Euler characteristics of Hilbert schemes of points of the singular
surface of type A or D is computed in terms of an explicit formula involving a
specialized character of the basic representation of the corresponding affine
Lie algebra; we conjecture that the same result holds also in type E. Our
results are consistent with known results in type A, and are new for type D.


  Lookup table decoding is fast and distance-preserving, making it attractive
for near-term quantum computer architectures with small-distance quantum
error-correcting codes. In this work, we develop several optimization tools
that can potentially reduce the space and time overhead required for flag
fault-tolerant quantum error correction (FTQEC) with lookup table decoding on
Calderbank-Shor-Steane (CSS) codes. Our techniques include the compact lookup
table construction, the Meet-in-the-Middle technique, the adaptive time
decoding for flag FTQEC, the classical processing technique for flag
information, and the separated $X$ and $Z$ counting technique. We evaluate the
performance of our tools using numerical simulation of hexagonal color codes of
distances 3, 5, 7, and 9 under circuit-level noise. Combining all tools can
result in more than an order of magnitude increase in pseudothreshold for the
hexagonal color code of distance 9, from $(1.34 \pm 0.01) \times 10^{-4}$ to
$(1.42 \pm 0.12) \times 10^{-3}$.


  Let $M$ be a closed $3$-dimensional Riemann manifold and let $3\le r\le
\infty$. We prove that there exists an open dense subset in the space of $C^r$
volume-preserving Anosov flows on $M$ such that all the flows in it are
exponentially mixing.


  In the cooperative cellular network, relay-like base stations are connected
to the central processor (CP) via rate-limited fronthaul links and the joint
processing is performed at the CP, which thus can effectively mitigate the
multiuser interference. In this paper, we consider the joint beamforming and
compression problem with per-antenna power constraints in the cooperative
cellular network. We first establish the equivalence between the considered
problem and its semidefinite relaxation (SDR). Then we further derive the
partial Lagrangian dual of the SDR problem and show that the objective function
of the obtained dual problem is differentiable. Based on the differentiability,
we propose two efficient projected gradient ascent algorithms for solving the
dual problem, which are projected exact gradient ascent (PEGA) and projected
inexact gradient ascent (PIGA). While PEGA is guaranteed to find the global
solution of the dual problem (and hence the global solution of the original
problem), PIGA is more computationally efficient due to the lower complexity in
inexactly computing the gradient. Global optimality and high efficiency of the
proposed algorithms are demonstrated via numerical experiments.


  LiV$_2$O$_4$ is a mixed-valent spinel oxide and one of a few transition-metal
compounds to host a heavy fermion phase at low temperatures. While numerous
experimental studies have attempted to elucidate how its 3$d$ electrons undergo
giant mass renormalization, spectroscopic probes that may provide crucial
hints, such as scanning tunneling microscopy (STM), remain to be applied. A
prerequisite is atomically flat and pristine surfaces, which, in the case of
LiV$_2$O$_4$, are difficult to obtain by cleavage of small, three-dimensional
crystals. We report the epitaxial growth of LiV$_2$O$_4$ thin films with
bulklike properties on SrTiO$_3$(111) via pulsed laser deposition and stable
STM imaging of the LiV$_2$O$_4$(111) surface. The as-grown films were
transferred $ex$ $situ$ to a room-temperature STM, where subsequent annealing
with optional sputtering in ultrahigh vacuum enabled compact islands with
smooth surfaces and a hexagonal 1$\times$1 atomic lattice to be resolved. Our
STM measurements provide insights into growth mechanisms of LiV$_2$O$_4$ on
SrTiO$_3$(111), as well as demonstrate the feasibility of performing
surface-sensitive measurements of this heavy fermion compound.


  We show that the Hausdorff dimension of any slice of the graph of the Takagi
function is bounded above by the Assouad dimension of the graph minus one, and
that the bound is sharp. The result is deduced from a statement on more general
self-affine sets, which is of independent interest. We also prove that the
Marstrand's slicing theorem on the graph of the Takagi function extends to all
slices if and only if the upper pointwise dimension of every projection of the
length measure on the $x$-axis lifted to the graph is at least one.


  In this paper we describe and evaluate new spectral line polarisation
observations obtained with the goal of mapping the surfaces of magnetic Ap
stars in great detail. One hundred complete or partial Stokes IQUV sequences,
corresponding to 297 individual polarised spectra, have been obtained for 7
bright Ap stars using the ESPaDOnS and NARVAL spectropolarimeters. The targets
span a range of mass from approximately 1.8 to 3.4 solar mass, a range of
rotation period from 2.56 to 6.80 days, and a range of maximum longitudinal
magnetic field strength from 0.3 to over 4 kG. For 3 of the 7 stars, we have
obtained dense phase coverage sampling the entire rotational cycle. These
datasets are suitable for immediate magnetic and chemical abundance surface
mapping using Magnetic Doppler Imaging (MDI). For the 4 remaining stars,
partial phase coverage has been obtained, and additional observations will be
required in order to map the surfaces of these stars. The median
signal-to-noise ratio of the reduced observations is over 700 per 1.8 km\s
pixel. Spectra of all stars show Stokes V Zeeman signatures in essentially all
individual lines, and most stars show clear Stokes QU signatures in many
individual spectral lines. The observations provide a vastly improved data set
compared to previous generations of observations in terms of signal-to-noise
ratio, resolving power and measurement uncertainties. Measurement of the
longitudinal magnetic field demonstrates that the data are internally
consistent within computed uncertainties typically at the 50 to 100 sigma
level. Data are also shown to be in excellent agreement with published
observations and in qualitative agreement with the predictions of published
surface structure models. This study establishes the performance and stability
of the ESPaDOnS and NARVAL high-resolution spectropolarimeters during the
period 2006-2010.


  Effects of a new triple-{\alpha} reaction rate on the s-process during the
evolution of a massive star of 25 M\odot are investigated for the first time.
Although the s-process in massive stars has been believed to be established
with only minor change, we find that the s-process with use of the new rate
during the core He-burning is very inefficient compared to the case with the
previous triple-{\alpha} rate. However, the difference of the overproduction is
found to be largely compensated by the subsequent C-burning. Since the
s-process in massive stars has been attributed so far to the neutron
irradiation during core He-burning, our finding reveals the importance of
C-burning for the s-process during the evolution of massive stars.


  Multilevel autonomous quantum thermal machines are discussed. In particular,
we explore the relation between the size of the machine (captured by Hilbert
space dimension), and the performance of the machine. Using the concepts of
virtual qubits and virtual temperatures, we show that higher dimensional
machines can outperform smaller ones. For instance, by considering
refrigerators with more levels, lower temperatures can be achieved, as well as
higher power. We discuss the optimal design for refrigerators of a given
dimension. As a consequence we obtain a statement of the third law in terms of
Hilbert space dimension: reaching absolute zero temperature requires infinite
dimension. These results demonstrate that Hilbert space dimension should be
considered a thermodynamic resource.


  High-resolution angle-resolved photoemission (ARPES) data show that a
metal-insulator Mott transition occurs at the surface of the quasi-two
dimensional compound TaSe$_2$. The transition is driven by the narrowing of the
Ta $5d$ band induced by a temperature-dependent modulation of the atomic
positions. A dynamical mean-field theory calculation of the spectral function
of the half-filled Hubbard model captures the main qualitative feature of the
data, namely the rapid transfer of spectral weight from the observed
quasiparticle peak at the Fermi surface to the Hubbard bands, as the
correlation gap opens up.


  The slope filtration of Euclidean lattices was introduced in works by Stuhler
in the late 1970s, extended by Grayson a few years later, as a new tool for
reduction theory and its applications to the study of arithmetic groups.
Lattices with trivial filtration are called semistable, in keeping with a
classical terminology. In 1997, Bost conjectured that the tensor product of
semistable lattices should be semistable itself. Our aim in this work is to
study these questions for the restricted class of isodual lattices. Such
lattices appear in a wide range of contexts, and it is rather natural to study
their slope filtration. We exhibit specific properties in this case, which
allow, in turn, to prove some new particular cases of Bost's conjecture.


  This paper explores the evolution of China's Personal Information Protection
Law (PIPL) and situates it within the context of global data protection
development. It draws inspiration from the theory of 'Brussels Effect' and
provides a critical account of its application in non-Western jurisdictions,
taking China as a prime example. Our objective is not to provide a comparative
commentary on China's legal development but to illuminate the intricate
dynamics between the Chinese law and the EU's GDPR. We argue that the
trajectory of China's Personal Information Protection Law calls into question
the applicability of the Brussels Effect: while the GDPR's imprint on the PIPL
is evident, a deeper analysis unveils China's nuanced, non-linear adoption that
diverges from many assumptions of the Brussels Effect and similar theories. The
evolution of the GDPR-inspired PIPL is not as a straightforward outcome of the
Brussels Effect but as a nuanced, intricate interplay of external influence and
domestic dynamics. We introduce a complementary theory of 'gravity assist',
which portrays China's strategic instrumentalisation of the GDPR as a template
to shape its unique data protection landscape. Our theoretical framework
highlights how China navigates through a patchwork of internal considerations,
international standards, and strategic choices, ultimately sculpting a data
protection regime that has a similar appearance to the GDPR but aligns with its
distinct political, cultural and legal landscape. With a detailed historical
and policy analysis of the PIPL, coupled with reasonable speculations on its
future avenues, our analysis presents a pragmatic, culturally congruent
approach to legal development in China. It signals a trajectory that, while
potentially converging at a principled level, is likely to diverge
significantly in practice [...]