  Assume we are given (finitely many) mutually independent variables and
(finitely many) "undesirable" events, each depending on a subset of the
variables of at most $k$ elements, called the scope of the event. Assume that
the probability of a variable belonging to the scope of an occurring event is
bounded by $q$. We prove that if $ekq \leq 1$ then there exists at least one
assignment to the variables for which none of the events occurs. Examples are
given where the criterion $ekq \leq 1$ is applicable, whereas that of the
classical version of the Lov\'asz local lemma is not. The proof of the result
is through an interactive, private-coin implementation of the algorithm by
Moser. The original implementation, which yields the classical result, finds
efficiently, but probabilistically, an assignment to the events that avoids all
undesirable events. Interestingly, the interactive implementation given in this
work does not constitute an efficient, even if probabilistic, algorithm to find
an assignment as desired under the weaker assumption $ekq \leq 1$. We can only
conclude that under the hypothesis that $ekq \leq 1$, the interactive protocol
will produce an assignment as desired within $n$ rounds, with probability high
with respect to $n$; however, the provers' choices remain non-deterministic.
Plausibly finding such an assignment is inherently hard, as the situation is
reminiscent, in a probabilistic framework, of problems complete for syntactic
subclasses of TFNP.


  The analysis of two-ordinary-meson scattering amplitudes in the limit of a
large number $N_{\rm c}$ of the colour degrees of freedom of quantum
chromodynamics, with suitably decreasing strong coupling and all quarks
transforming according to the gauge group's fundamental representation, enables
us to establish a set of rigorous consistency conditions for the emergence of a
tetraquark (i.e., a bound state of two quarks and two antiquarks) as a pole in
these amplitudes. For genuinely flavour-exotic tetraquarks, these constraints
require the existence of two tetraquark states distinguishable by their
preferred couplings to two ordinary mesons, whereas, for cryptoexotic
tetraquarks, our constraints may be satisfied by a single tetraquark state,
which then, however, may mix with ordinary mesons. For elucidation of the
tetraquark features, the consideration of the subleading contributions proves
to be mandatory: for both variants of tetraquarks, their decay widths fall off
like $1/N_{\rm c}^2$ for large $N_{\rm c}.$


  Left ventricular diastolic dysfunction (LVDD) is a group of diseases that
adversely affect the passive phase of the cardiac cycle and can lead to heart
failure. While left ventricular end-diastolic pressure (LVEDP) is a valuable
prognostic measure in LVDD patients, traditional invasive methods of measuring
LVEDP present risks and limitations, highlighting the need for alternative
approaches. This paper investigates the possibility of measuring LVEDP
non-invasively using inverse in-silico modeling. We propose the adoption of
patient-specific cardiac modeling and simulation to estimate LVEDP and
myocardial stiffness from cardiac strains. We have developed a high-fidelity
patient-specific computational model of the left ventricle. Through an inverse
modeling approach, myocardial stiffness and LVEDP were accurately estimated
from cardiac strains that can be acquired from in vivo imaging, indicating the
feasibility of computational modeling to augment current approaches in the
measurement of ventricular pressure. Integration of such computational
platforms into clinical practice holds promise for early detection and
comprehensive assessment of LVDD with reduced risk for patients.


  Assembly101 is a new procedural activity dataset featuring 4321 videos of
people assembling and disassembling 101 "take-apart" toy vehicles. Participants
work without fixed instructions, and the sequences feature rich and natural
variations in action ordering, mistakes, and corrections. Assembly101 is the
first multi-view action dataset, with simultaneous static (8) and egocentric
(4) recordings. Sequences are annotated with more than 100K coarse and 1M
fine-grained action segments, and 18M 3D hand poses. We benchmark on three
action understanding tasks: recognition, anticipation and temporal
segmentation. Additionally, we propose a novel task of detecting mistakes. The
unique recording format and rich set of annotations allow us to investigate
generalization to new toys, cross-view transfer, long-tailed distributions, and
pose vs. appearance. We envision that Assembly101 will serve as a new challenge
to investigate various activity understanding problems.


  The interplay of Coulomb repulsion and geometrical frustration on
charge-driven quantum phase transitions is explored. The ground state phase
diagram of an extended Hubbard model on an anisotropic triangular lattice
relevant to quarter-filled layered organic materials contains homogeneous
metal, 'pinball' and three-fold charge ordered metallic phases. The stability
of the 'pinball' phase occurring for strong Coulomb repulsions is found to be
strongly influenced by geometrical frustration. A comparison with a spinless
model reproduces the transition from the homogeneous metallic phase to a
pinball liquid, which indicates that the spin correlations should play a much
smaller role than the charge correlations in the metallic phase close to the
charge ordering transition. Spin degeneracy is, however, essential to describe
the dependence of the system on geometrical frustration. Based on finite
temperature Lanczos diagonalization we find that the effective Fermi
temperature scale, T*, of the homogeneous metal vanishes at the quantum phase
transition to the ordered metallic phase driven by the Coulomb repulsion. Above
this temperature scale 'bad' metallic behavior is found which is robust against
geometrical frustration in general. Quantum critical phenomena are not found
whenever nesting of the Fermi surface is strong, possibly indicating a first
order transition instead. 'Reentrant' behavior in the phase diagram is
encountered whenever the 2kF-CDW instability competes with the Coulomb driven
three-fold charge order transition. The relevance of our results to the family
of quarter-filled materials: theta-(BEDT-TTF)2X is discussed.


  The reductions of the Heun equation to the hypergeometric equation by
polynomial transformations of its independent variable are enumerated and
classified. Heun-to-hypergeometric reductions are similar to classical
hypergeometric identities, but the conditions for the existence of a reduction
involve features of the Heun equation that the hypergeometric equation does not
possess; namely, its cross-ratio and accessory parameters. The reductions
include quadratic and cubic transformations, which may be performed only if the
singular points of the Heun equation form a harmonic or an equianharmonic
quadruple, respectively; and several higher-degree transformations. This result
corrects and extends a theorem in a previous paper, which found only the
quadratic transformations. [See K. Kuiken, "Heun's equation and the
hypergeometric equation", SIAM Journal on Mathematical Analysis 10:3 (1979),
655-657.]


  The interaction of a single quantum emitter with its environment is a central
theme in quantum optics. When placed in highly confined optical fields, such as
those created in optical cavities or plasmonic structures, the optical
properties of the emitter can change drastically. In particular, photonic
crystal (PC) cavities show high quality factors combined with an extremely
small mode volume. Efficiently coupling a single quantum emitter to a PC cavity
is challenging because of the required positioning accuracy. Here, we
demonstrate deterministic coupling of single Nitrogen-Vacancy (NV) centers to
high-quality gallium phosphide PC cavities, by deterministically positioning
their 50 nm-sized host nanocrystals into the cavity mode maximum with
few-nanometer accuracy. The coupling results in a 25-fold enhancement of NV
center emission at the cavity wavelength. With this technique, the NV center
photoluminescence spectrum can be reshaped allowing for efficient generation of
coherent photons, providing new opportunities for quantum science.


  Full Stokes filter-polarimeters are key instruments for investigating the
rapid evolution of magnetic structures on the solar surface. To this end, the
image quality is routinely improved using a-posteriori image reconstruction
methods. We analyze the robustness of circular polarization asymmetries to
phase-diversity image reconstruction techniques. We use snapshots of
magneto-hydrodynamical simulations carried out with different initial
conditions to synthesize spectra of the magnetically sensitive Fe I line at
5250.2 A. We degrade the synthetic profiles spatially and spectrally to
simulate observations with the IMaX full Stokes filter-polarimeter. We also
simulate the focused/defocused pairs of images used by the phase-diversity
algorithm for reconstruction and the polarimetric modulation scheme. We assume
that standard optimization methods are able to infer the projection of the
wavefront on the Zernike polynomials with 10% precision. We also consider the
less favorable case of 25% precision. We obtain reconstructed monochromatic
modulated images that are later demodulated and compared with the original
maps. Although asymmetries are often difficult to define in the quiet Sun due
to the complexity of the Stokes V profiles, we show how asymmetries are
degraded with spatial and spectral smearing. The results indicate that,
although image reconstruction techniques reduce the spatial smearing, they can
modify the asymmetries of the profiles, mainly caused by the appearance of
spatially-correlated noise.


  We construct an explicit one-to-one correspondence between non-relativistic
stochastic processes and solutions of the Schrodinger equation and between
relativistic stochastic processes and solutions of the Klein-Gordon equation.
The existence of this equivalence suggests that the Lorentzian path integral
can be defined as an Ito integral, similar to the definition of the Euclidean
path integral in terms of the Wiener integral. Moreover, the result implies a
stochastic interpretation of quantum theories.


  In the hexagonal columnar phase of chiral polymers a bias towards cholesteric
twist competes with braiding along an average direction. When the chirality is
strong, topological defects proliferate, leading to either a tilt grain
boundary phase or a new ``moire state'' with twisted bond order. This moire
phase can melt leading to a new phase: the chiral hexatic. I will discuss some
recent experimental results from the NIH on DNA liquid crystals in the context
of these theories.


  A novel approach to shock capturing for high-order flux reconstruction
schemes is derived based on the mathematical formalism of the filtered
governing equations. While the latter perspective is only typically used for
turbulence modeling in the context of Large-Eddy Simulations (LES), the novel
Legendre Spectral Viscosity (LSV) sub-filter scale (SFS) closure model is
capable of performing simulations in the presence of shock-discontinuities. The
LSV method exploits the set of hierarchical basis functions formed by the
Legendre polynomials to extract the information on the energy content near the
resolution limit and estimate the overall magnitude of the required SFS
dissipative terms, resulting in a scheme that dynamically activates only in
cells where nonlinear behavior is important. Additionally, the modulation of
such terms in the Legendre spectral space allows for the concentration of the
dissipative action at small scales. The proposed method is tested in canonical
shock-dominated flow setups in both one and two dimensions. These include the
1D Burgers' problem, a 1D shock tube, a 1D shock-entropy wave interaction, a 2D
inviscid shock-vortex interaction and a 2D double Mach reflection. Results
showcase a high-degree of resolution power, achieving accurate results with a
small number of degrees of freedom, and robustness, being able to capture
shocks associated with the Burgers' equation and the 1D shock tube within a
single cell with orders 120 and higher.


  In this paper, we will give an improvement on the lower bound for the
counterfeit coins problem in the case that the number of false coins is unknown
in advance


  The caterpillar associahedron $\mathcal{A}(G)$ is a polytope arising from the
rotation graph of search trees on a caterpillar tree $G$, generalizing the
rotation graph of binary search trees (BSTs) and thus the conventional
associahedron. We show that the diameter of $\mathcal{A}(G)$ is $\Theta(n + m
\cdot (H+1))$, where $n$ is the number of vertices, $m$ is the number of
leaves, and $H$ is the entropy of the leaf distribution of $G$.
  Our proofs reveal a strong connection between caterpillar associahedra and
searching in BSTs. We prove the lower bound using Wilber's first lower bound
for dynamic BSTs, and the upper bound by reducing the problem to searching in
static BSTs.


  The Qweak experiment which ran at Jefferson Lab in Newport News, VA, measured
the weak charge of the proton $Q_W^p$ via elastic electron-proton scattering.
Longitudinally polarized electrons were scattered from an unpolarized liquid
hydrogen target. The Standard Model predicts a small parity-violating asymmetry
of scattering rates between electron right and left helicity states due to the
weak interaction. An initial result using 4% of the data was published in
October 2013 with a measured parity-violating asymmetry of $-279\pm
35(\text{stat})\pm 31$ (syst) parts per billion (ppb). This asymmetry, along
with other data from parity-violating electron scattering experiments, provided
the world's first determination of the weak charge of the proton. The weak
charge of the proton was found to be $Q_W^p=0.064\pm0.012$, in agreement with
the Standard Model prediction of $Q_W^p(SM)=0.0708\pm0.0003$.
  The results of the full dataset are expected to decrease the statistical
error from the initial publication by a factor of 4-5. The level of precision
of the final result makes it a useful test of Standard Model predictions and
particularly of the "running" of $\sin^2\theta_W$ from the Z-mass to low
energies. This thesis focuses on reduction of systematic error in two key
systematics for the Qweak experiment. First, techniques for measuring and
removing false asymmetries arising from helicity-correlated electron beam
properties at the few ppb level are discussed. Second, as a parity-violating
experiment, Qweak relies on accurate knowledge of electron beam polarimetry. To
help address the requirement of accurate polarimetry, a Compton polarimeter
built specifically for Qweak. Compton polarimetry requires accurate knowledge
of laser polarization inside a Fabry-Perot cavity enclosed in the electron beam
pipe. A new technique was developed for Qweak that nearly eliminates this
systematic error.


  We propose a way of detecting dark matter axion by using two slabs of
conductor. The flat surfaces are put to meet face to face so that they are
parallel to each other. External magnetic field $B$ parallel to the surfaces is
impressed. Radiations converted from the axion arise between two slabs. When we
tune the spacing $l$ between two surfaces such as $l=\pi/m_a$ with axion mass
$m_a$, a resonance occurs so that the radiations become strong. Furthermore,
electric current flowing on the surface of the slabs is enhanced. We show that
the electric current is large enough to be detectable at the resonance. It
reaches $0.7\times
10^{-9}$A$(10^{-5}\mbox{eV}/m_a)^{1/2}(B/5\mbox{T})(L/10\mbox{cm})(\sigma/3.3\times
10^7\rm eV)$, using $6$N copper of the square slab with side length $L$ and
high electrical conductivity $\sigma$ at temperature $T\sim 1$K. The power of
the Joule heating is
$0.3\times10^{-22}\mbox{W}(B/5\mbox{T})^2(10^{-5}\mbox{eV}/m_a)^{1/2}(L/10\mbox{cm})^2(\sigma/3.3\times
10^7\rm eV)$. When we amplify the power using LC circuit with $Q$ value, the
signal to noise ratio is $4.5\times
10^4(Q/10^6)(B/5\mbox{T})^2(t_{obs}/1\sec)^{1/2}\,(10^{-5}\mbox{eV}/m_a)
(L/10\mbox{cm})^2(\sigma/3.3\times 10^7\rm eV)$ with $t_{obs}$ observational
time.


  Understanding the interaction between different road users is critical for
road safety and automated vehicles (AVs). Existing mathematical models on this
topic have been proposed based mostly on either cognitive or machine learning
(ML) approaches. However, current cognitive models are incapable of simulating
road user trajectories in general scenarios, and ML models lack a focus on the
mechanisms generating the behavior and take a high-level perspective which can
cause failures to capture important human-like behaviors. Here, we develop a
model of human pedestrian crossing decisions based on computational
rationality, an approach using deep reinforcement learning (RL) to learn
boundedly optimal behavior policies given human constraints, in our case a
model of the limited human visual system. We show that the proposed combined
cognitive-RL model captures human-like patterns of gap acceptance and crossing
initiation time. Interestingly, our model's decisions are sensitive to not only
the time gap, but also the speed of the approaching vehicle, something which
has been described as a "bias" in human gap acceptance behavior. However, our
results suggest that this is instead a rational adaption to human perceptual
limitations. Moreover, we demonstrate an approach to accounting for individual
differences in computational rationality models, by conditioning the RL policy
on the parameters of the human constraints. Our results demonstrate the
feasibility of generating more human-like road user behavior by combining RL
with cognitive models.


  It is well known that the optical Kerr effect can be a source of highly
squeezed light, however the analytical limit of the noise suppression has not
been found yet. The process is reconsidered and an analytical estimation of the
optimal quadrature noise level is presented. The validity of the new scaling
law is checked numerically and analytically.


  Quantum computation is conventionally performed using quantum operations
acting on two-level quantum bits, or qubits. Qubits in modern quantum computers
suffer from inevitable detrimental interactions with the environment that cause
errors during computation, with multi-qubit operations often being a primary
limitation. Most quantum devices naturally have multiple accessible energy
levels beyond the lowest two traditionally used to define a qubit. Qudits offer
a larger state space to store and process quantum information, reducing
complexity of quantum circuits and improving efficiency of quantum algorithms.
Here, we experimentally demonstrate a ternary decomposition of a multi-qubit
operation on cloud-enabled fixed-frequency superconducting transmons.
Specifically, we realize an order-preserving Toffoli gate consisting of four
two-transmon operations, whereas the optimal order-preserving binary
decomposition uses eight \texttt{CNOT}s on a linear transmon topology. Both
decompositions are benchmarked via truth table fidelity where the ternary
approach outperforms on most sets of transmons on \texttt{ibmq\_jakarta}, and
is further benchmarked via quantum process tomography on one set of transmons
to achieve an average gate fidelity of 78.00\% $\pm$ 1.93\%.


  We are developing a beam line which compresses the phase space of a standard
surface $\mu^+$ beam by 10 orders of magnitude with an efficiency of $10^{-3}$.
Phase space compression occurs in a He gas target and consists of three
consecutive stages: Transverse (perpendicular to the beam axis) compression,
longitudinal compression and re-extraction into vacuum. Transverse compression
was observed for the first time and longitudinal compression has been measured
to occur within 2.5 $\mu$s with high efficiency.


  To guarantee the availability and reliability of data source in Magnetic
Confinement Fusion (MCF) devices, incorrect diagnostic data, which cannot
reflect real physical properties of measured objects, should be sorted out
before further analysis and study. Traditional data sorting cannot meet the
growing demand of MCF research because of the low-efficiency, time-delay, and
lack of objective criteria. In this paper, a Time-Domain Global Similarity
(TDGS) method based on machine learning technologies is proposed for the
automatic data cleaning of MCF devices. Traditional data sorting aims to the
classification of original diagnostic data sequences, which are different in
both length and evolution properties under various discharge parameters. Hence
the classification criteria are affected by many discharge parameters and vary
shot by shot. The focus of TDGS method is turned to the physical similarity
between data sequences from different channels, which are more essential and
independent of discharge parameters. The complexity arisen from real discharge
parameters during data cleaning is avoided in the TDGS method by transforming
the general data sorting problem into a binary classification problem about the
physical similarity between data sequences. As a demonstration of its
application to multi-channel measurement systems, the TDGS method is applied to
the EAST POlarimeter-INterferomeTer (POINT) system. The optimized performance
of the method has reached 0.9871.


  This paper provides an overview of the new features of the finite element
library deal.II version 8.1.


  Electrocardiogram (ECG) is a simple non-invasive measure to identify
heart-related issues such as irregular heartbeats known as arrhythmias. While
artificial intelligence and machine learning is being utilized in a wide range
of healthcare related applications and datasets, many arrhythmia classifiers
using deep learning methods have been proposed in recent years. However, sizes
of the available datasets from which to build and assess machine learning
models is often very small and the lack of well-annotated public ECG datasets
is evident. In this paper, we propose a deep transfer learning framework that
is aimed to perform classification on a small size training dataset. The
proposed method is to fine-tune a general-purpose image classifier ResNet-18
with MIT-BIH arrhythmia dataset in accordance with the AAMI EC57 standard. This
paper further investigates many existing deep learning models that have failed
to avoid data leakage against AAMI recommendations. We compare how different
data split methods impact the model performance. This comparison study implies
that future work in arrhythmia classification should follow the AAMI EC57
standard when using any including MIT-BIH arrhythmia dataset.


  The imaginary-time Green's function is a building block of various numerical
methods for correlated electron systems. Recently, it was shown that a
model-independent compact orthogonal representation of the Green's function can
be constructed by decomposing its spectral representation. We investigate the
performance of this so-called \textit{intermedaite representation} (IR) from
several points of view. First, for two simple models, we study the number of
coefficients necessary to achieve a given tolerance in expanding the Green's
function. We show that the number of coefficients grows only as $O(\log \beta)$
for fermions, and converges to a constant for bosons as temperature $T=1/\beta$
decreases. Second, we show that this remarkable feature is ascribed to the
properties of the physically constructed basis functions. The fermionic basis
functions have features in the spectrum whose width is scaled as $O(T)$, which
are consistent with the low-$T$ properties of quasiparticles in a Fermi liquid
state. On the other hand, the properties of the bosonic basis functions are
consistent with those of spin/orbital susceptibilities at low $T$. These
results demonstrate the potential wide application of the IR to calculations of
correlated systems.


  Ultrashort x-ray pulses can be used to disentangle magnetic and structural
dynamics and are accordingly utilized here to study the photoexcitation of
NdNiO$_3$ (NNO), a model nickelate exhibiting structural and magnetic dynamics
that conspire to induce an IMT. During the course of the photoinduced insulator
to metal transition (IMT) with above gap excitation, we observe an ultrafast
($<$ 180 fs) quenching of magnetic order followed by a time delayed collapse of
the insulating phase probed by X-ray absorption and THz transmission (~ 450 fs)
that correlates with the slowest optical phonon mode involved in the structural
transition. A simultaneous order-disorder response at the Ni site and
displacive response at the Nd site coexist in the ultrafast magnetic response.
Crucially, we observe the optical phonon through its coherent coupling with Nd
magnetic order, demonstrating that the magnetic and structural degrees of
freedom both contribute in driving the IMT. Density functional theory (DFT)
calculations reveal a consistent scenario where optically driven inter-site
charge transfer (ICT) drives a collapse of antiferromagnetic order that in turn
destabilizes the charge-ordered phase resulting in an IMT. These experiments
provide new modalities for control of electronic phase transitions in quantum
materials based on ultrafast interplay between structural and magnetic orders
created by femtosecond photoexcitation.


  Low-shot relation extraction~(RE) aims to recognize novel relations with very
few or even no samples, which is critical in real scenario application.
Few-shot and zero-shot RE are two representative low-shot RE tasks, which seem
to be with similar target but require totally different underlying abilities.
In this paper, we propose Multi-Choice Matching Networks to unify low-shot
relation extraction. To fill in the gap between zero-shot and few-shot RE, we
propose the triplet-paraphrase meta-training, which leverages triplet
paraphrase to pre-train zero-shot label matching ability and uses meta-learning
paradigm to learn few-shot instance summarizing ability. Experimental results
on three different low-shot RE tasks show that the proposed method outperforms
strong baselines by a large margin, and achieve the best performance on
few-shot RE leaderboard.


  The research described herewith is to re-visit the classical doubly robust
estimation of average treatment effect by conducting a systematic study on the
comparisons, in the sense of asymptotic efficiency, among all possible
combinations of the estimated propensity score and outcome regression. To this
end, we consider all nine combinations under, respectively, parametric,
nonparametric and semiparametric structures. The comparisons provide useful
information on when and how to efficiently utilize the model structures in
practice. Further, when there is model-misspecification, either propensity
score or outcome regression, we also give the corresponding comparisons. Three
phenomena are observed. Firstly, when all models are correctly specified, any
combination can achieve the same semiparametric efficiency bound, which
coincides with the existing results of some combinations. Secondly, when the
propensity score is correctly modeled and estimated, but the outcome regression
is misspecified parametrically or semiparametrically, the asymptotic variance
is always larger than or equal to the semiparametric efficiency bound. Thirdly,
in contrast, when the propensity score is misspecified parametrically or
semiparametrically, while the outcome regression is correctly modeled and
estimated, the asymptotic variance is not necessarily larger than the
semiparametric efficiency bound. In some cases, the "super-efficiency"
phenomenon occurs. We also conduct a small numerical study.


  Software Engineering researchers are increasingly using Natural Language
Processing (NLP) techniques to automate Software Vulnerabilities (SVs)
assessment using the descriptions in public repositories. However, the existing
NLP-based approaches suffer from concept drift. This problem is caused by a
lack of proper treatment of new (out-of-vocabulary) terms for the evaluation of
unseen SVs over time. To perform automated SVs assessment with concept drift
using SVs' descriptions, we propose a systematic approach that combines both
character and word features. The proposed approach is used to predict seven
Vulnerability Characteristics (VCs). The optimal model of each VC is selected
using our customized time-based cross-validation method from a list of eight
NLP representations and six well-known Machine Learning models. We have used
the proposed approach to conduct large-scale experiments on more than 100,000
SVs in the National Vulnerability Database (NVD). The results show that our
approach can effectively tackle the concept drift issue of the SVs'
descriptions reported from 2000 to 2018 in NVD even without retraining the
model. In addition, our approach performs competitively compared to the
existing word-only method. We also investigate how to build compact
concept-drift-aware models with much fewer features and give some
recommendations on the choice of classifiers and NLP representations for SVs
assessment.


  A new asymptotic theory is proposed for the peripheral sub- and above-barrier
transfer $A$($x$, $y$)$B$ reaction within the three-body ($A$, $a$ and $y$)
model, where $ x$= $y$ + $a$, $B$= $A$ + $a$ and $ a$ is a transferred
particle. In the asymptotic theory, the allowance of the contribution of the
three-body ($A$, $a$ and $y$) Coulomb dynamics of the transfer mechanism to the
peripheral partial amplitudes for the partial wave $l_i>>$ 1 and of the
Coulomb-nuclear distorted effects in the entrance and exit channels is done in
a correct manner within the framework of the dispersion theory and the
conventional distorted-wave Born approximation (DWBA), respectively. It is
shown that the proposed asymptotic theory makes it possible to test the
accuracy of taking into account the the three-body Coulomb dynamics of the
transfer mechanism in the modified DWBA. The results of the analysis of the
differential cross sections of the specific proton and triton transfer
reactions at above- and sub-barrier energies are presented. New estimates and
their uncertainties are obtained for values of the asymptotic normalization
coefficients for ${\rm{^9Be}} \,+p \to\,{\rm{^{10}B}}$,
${\rm{^{11}B}}\,+\,p\to\,{\rm{^{12}C}}$, ${\rm{^{16}O}} \,+\,p \to\,
{\rm{^{17}F}}$ and ${\rm{^{19}F}}\to\, {\rm{^{16}O}} \,+\,t$ as well as for the
direct astrophysical $S$ factors at stellar energy of the radiative capture
${\rm{^9Be(}}p,\,\gamma{\rm{)^{10}B}} $,
${\rm{^{11}B(}}p,\,\gamma{\rm{)^{12}C}} $ and
${\rm{^{16}O(}}p,\,\gamma{\rm{)^{17}F}}$ reactions.


  We study the ramification of fierce cyclic Galois extensions of a local field
$K$ of characteristic zero with a one-dimensional residue field of
characteristic $p>0$. Using Kato's theory of the refined Swan conductor, we
associate to such an extension a ramification datum, consisting of a sequence
of pairs $(\delta_i,\omega_i)$, where $\delta_i$ is a positive rational number
and $\omega_i$ a differential form on the residue field of $K$. Our main result
gives necessary and sufficient conditions on such sequences to occur as a
ramification datum of a fierce cyclic extension of $K$.


  The muon $(g-2)_\mu$ and $b\to s \bar \mu \mu$ induced $B$ anomalies as hints
of new physics beyond the standard model (SM) have attracted much attention.
These two anomalies indicate that there may exist new interaction specifically
related to muon. A lot of theoretical ideas have been proposed to explain these
anomalies. Gauged flavor specific $U(1)_{B_q-L_\mu}$ is among the promising
ones. The new gauge boson $Z'$ from $U(1)_{B_q-L_\mu}$ interacts with muon and
provides necessary ingredient to solve the $(g-2)_\mu$ anomaly. The $Z'$-quark
coupling can generate flavor changing interactions after diagonalization of
quark mass matrix between weak eigen-state and mass eigen-state basis. We
revisit challenges for such models attempting to explain the $(g-2)_\mu$ and
$B$ anomalies separately or simultaneously. We find although for
$U(1)_{B_q-L_\mu}$ models there is still parameter space to provide solutions
for separately explaining the $(g-2)_\mu$ and $B$ anomalies, there exists no
parameter space for such models to solve both the anomalies simultaneously,
after taking into account existing constraints from $\tau \to \mu \gamma$,
$\tau \to 3 \mu$, neutrino trident and $B_s - \bar B_s$ data. Among them
leptonic processes restrict $Z^\prime$ mass to be less than a few hundred MeV
if required to solve the $(g-2)_\mu$ anomaly, which causes conflict between
data from $B_s - \bar B_s$, $D^0 - \bar D^0$ mixing and also hadron decays with
$Z^\prime$ in the final states. The effects of $U(1)_Y$ and $U(1)_{B_q-L_\mu}$
kinetic mixing on these anomalies are also studied. We find that neither can
these effects do much to bring the two anomalies together to be solved
simultaneously.


  The heavy fermion compound Ce$_{3}$Pd$_{20}$Si$_{6}$ displays unconventional
quantum criticality as the lower of two consecutive phase transitions is fully
suppressed by magnetic field. Here we report on the effects of pressure as
additional tuning parameter. Specific heat and electrical resistivity
measurements reveal a converse effect of pressure on the two transitions,
leading to the merging of both transitions at 6.2 kbar. The field-induced
quantum criticality is robust under pressure tuning. We rationalize our
findings within an extended version of the global phase diagram for
antiferromagnetic heavy fermion quantum criticality.


  We generalize the spherical harmonics for l=1 and give the differential
equation that the generalized forms satisfy. The new forms have an obvious
interpretation in the context of quantum mechanics.


  Polymer-like structures are ubiquitous in nature and synthetic materials.
Their configurational and migration properties are often affected by crowded
environments leading to non-thermal fluctuations. Here, we study an ideal Rouse
chain in contact with a non-homogeneous active bath, characterized by the
presence of active self-propelled agents which exert time-correlated forces on
the chain. By means of a coarse-graining procedure, we derive an effective
evolution for the center of mass of the chain and show its tendency to migrate
towards and preferentially localize in regions of high/low bath activity
depending on the model parameters. In particular, we demonstrate that an active
bath with non-uniform activity can be used to separate efficiently polymeric
species with different lengths and/or connectivity.


  Consistency models are promising generative models as they distill the
multi-step sampling of score-based diffusion in a single forward pass of a
neural network. Without access to sampling trajectories of a pre-trained
diffusion model, consistency training relies on proxy trajectories built on an
independent coupling between the noise and data distributions. Refining this
coupling is a key area of improvement to make it more adapted to the task and
reduce the resulting randomness in the training process. In this work, we
introduce a novel coupling associating the input noisy data with their
generated output from the consistency model itself, as a proxy to the
inaccessible diffusion flow output. Our affordable approach exploits the
inherent capacity of consistency models to compute the transport map in a
single step. We provide intuition and empirical evidence of the relevance of
our generator-induced coupling (GC), which brings consistency training closer
to score distillation. Consequently, our method not only accelerates
consistency training convergence by significant amounts but also enhances the
resulting performance. The code is available at:
https://github.com/thibautissenhuth/consistency_GC.


  We show that in a topological dynamical system $(X,T)$ of positive entropy
there exist proper (positively) asymptotic pairs, that is, pairs $(x,y)$ such
that $x\not= y$ and $\lim_{n\to +\infty} d(T^n x,T^n y)=0$. More precisely we
consider a $T$-ergodic measure $\mu$ of positive entropy and prove that the set
of points that belong to a proper asymptotic pair is of measure $1$. When $T$
is invertible, the stable classes (i.e., the equivalence classes for the
asymptotic equivalence) are not stable under $T^{-1}$: for $\mu$-almost every
$x$ there are uncountably many $y$ that are asymptotic with $x$ and such that
$(x,y)$ is a Li-Yorke pair with respect to $T^{-1}$. We also show that
asymptotic pairs are dense in the set of topological entropy pairs.


  Phenomenologically relevant electroweak precision pseudo-observables related
to Z-boson physics are discussed in the context of the strong experimental
demands of future $e^+e^-$ colliders. The recent completion of two-loop Z-boson
results is summarized and a prospect for the 3-loop Standard Model calculation
of the Z-boson decay pseudo-observable is given.


  Using a recently introduced algebraic framework for the classification of
fragments of first-order logic, we study the complexity of the satisfiability
problem for several ordered fragments of first-order logic, which are obtained
from the ordered logic and the fluted logic by modifying some of their
syntactical restrictions.


  In this note we give several characterisations of weights for two-weight
Hardy inequalities to hold on general metric measure spaces possessing polar
decompositions. Since there may be no differentiable structure on such spaces,
the inequalities are given in the integral form in the spirit of Hardy's
original inequality. We give examples obtaining new weighted Hardy inequalities
on $\mathbb R^n$, on homogeneous groups, on hyperbolic spaces, and on
Cartan-Hadamard manifolds.


  We show that for a wide class of functions $F$ that: $$ {\lim_{\epsilon
\downarrow 0} {\frac{1}{\epsilon}} \int_0^t \Big\{F(s, X_s) - F(s, X_s -
\epsilon)\Big\} d\big<X,X\big>_s} = - \int_0^t\int_{\R} F(s, x) d L_s^x $$
where $X_t$ is a continuous semi-martingale, $(L_t^x, x \in \R, t \geq 0)$ its
local time process and $(\big<X,X\big>_t, t \geq 0)$ its quadratic variation
process.


  Dislocation slip and deformation twin are widely regarded as two important
mechanisms of active competition in the process of plastic deformation.
Calculating and comparing the critical resolved shear stress (CRSS) of two
deformation modes are the key to discussing the mechanical properties reflected
by different mechanisms in crystals. Here, the paper proposes a model to
predict the CRSS of discrete twins, resembling thin layers, using the elastic
anisotropy theory and a macroscopic energy perspective. In addition, the
directionality of deformation twinning is also verified. We investigated
twinning in FCC crystals to illustrate the methodology, and predicted the CRSS
of twinning under different variables such as temperature and strain rate, both
of which were in excellent agreement with experimental and other theory
results. It draws the conclusion that we can promote twinning nucleation by
applying shear stress along the <112> direction to reduce the interface energy
as a resistance term and increase the difference in strain energy for twinning
nucleation. This conclusion provides a guiding direction for exploring and
accurately predicting the conditions of twinning in FCC crystals in future.


  Single particle momentum spectra are calculated within three micro-canonical
statistical ensembles, namely, with conserved system energy, system momentum,
as well as system energy and momentum. Deviations from the exponential spectrum
of the grand canonical ensemble are quantified and discussed. For mean particle
multiplicity and temperature, typical for p+p interactions at the LHC energies,
the effect of the conservation laws extends to transverse momenta as low as
about 3 GeV/c. The results may help to interpret spectra measured in nuclear
collisions at high energies, in particular, their system size dependence.


  Gaussian pentachoron weights can be used for constructing algebraic
realizations of four-dimensional Pachner moves. Here, we consider a natural
`gauge equivalence' for such weights with one and two bosonic - i.e., commuting
- variables on 3-faces. For the one-boson case, all generic weights turn out to
be gauge equivalent. For the two-boson case, and generic weights, their gauge
equivalence classes are parameterized by multiplicative 2-cocycles. Moreover, a
generic two-boson weight can be reduced by a gauge transformation to a
delta-function form.


  The streaming instability concentrates solid particles in protoplanetary
disks, leading to gravitational collapse into planetesimals. Despite its key
role in producing particle clumping and determining critical length scales in
the instability's linear regime, the influence of the disk's radial pressure
gradient on planetesimal properties has not been examined in detail. Here, we
use streaming instability simulations that include particle self-gravity to
study how the planetesimal initial mass function depends on the radial pressure
gradient. Fitting our results to a power-law, ${\rm d}N / {\rm d}M_p \propto
M_p^{-p}$, we find a single value $p \approx 1.6$ describes simulations in
which the pressure gradient varies by $\gtrsim 2$. An exponentially truncated
power-law provides a significantly better fit, with a low mass slope of
$p^\prime \approx 1.3$ that weakly depends on the pressure gradient. The
characteristic truncation mass is found to be $\sim M_G = 4 \pi^5 G^2
\Sigma_p^3 / \Omega^4$. We exclude the cubic dependence of the characteristic
mass with pressure gradient suggested by linear considerations, finding instead
a linear scaling. These results strengthen the case for a streaming-derived
initial mass function that depends at most weakly on the aerodynamic properties
of the disk and participating solids. A simulation initialized with zero
pressure gradient---which is {\em not} subject to the streaming
instability---also yields a top-heavy mass function but with modest evidence
for a different shape. We discuss the consistency of the theoretically
predicted mass function with observations of Kuiper Belt planetesimals, and
describe implications for models of early stage planet formation..


  We present a scheme for finding all roots of an analytic function in a square
domain in the complex plane. The scheme can be viewed as a generalization of
the classical approach to finding roots of a function on the real line, by
first approximating it by a polynomial in the Chebyshev basis, followed by
diagonalizing the so-called ''colleague matrices''. Our extension of the
classical approach is based on several observations that enable the
construction of polynomial bases in compact domains that satisfy three-term
recurrences and are reasonably well-conditioned. This class of polynomial bases
gives rise to ''generalized colleague matrices'', whose eigenvalues are roots
of functions expressed in these bases. In this paper, we also introduce a
special-purpose QR algorithm for finding the eigenvalues of generalized
colleague matrices, which is a straightforward extension of the recently
introduced componentwise stable QR algorithm for the classical cases (See
[Serkh]). The performance of the schemes is illustrated with several numerical
examples.


  Automatic facial age estimation can be used in a wide range of real-world
applications. However, this process is challenging due to the randomness and
slowness of the aging process. Accordingly, in this paper, we propose a
comprehensive framework aimed at overcoming the challenges associated with
facial age estimation. First, we propose a novel age encoding method, referred
to as 'Soft-ranking', which encodes two important properties of facial age,
i.e., the ordinal property and the correlation between adjacent ages.
Therefore, Soft-ranking provides a richer supervision signal for training deep
models. Moreover, we also carefully analyze existing evaluation protocols for
age estimation, finding that the overlap in identity between the training and
testing sets affects the relative performance of different age encoding
methods. Finally, since existing face databases for age estimation are
generally small, deep models tend to suffer from an overfitting problem. To
address this issue, we propose a novel regularization strategy to encourage
deep models to learn more robust features from facial parts for age estimation
purposes. Extensive experiments indicate that the proposed techniques improve
the age estimation performance; moreover, we achieve state-of-the-art
performance on the three most popular age databases, $i.e.$, Morph II,
CLAP2015, and CLAP2016.


  In this note we prove that a (anti-)self dual quasi Yamabe soliton with
positive sectional curvature is rotationally symmetric. This generalizes a
recent result of G. Huang and H. Li in dimension four. Whence, (anti-) self
dual gradient Yamabe solitons with positive sectional curvature is rotationally
symmetric. We also prove that half conformally flat gradient Yamabe soliton has
a special warped product structure provided that the potential function has no
critical point.


  The modern accuracy of measurements allows the residual/peculiar
(Galactocentric) velocity of the supermassive black hole (SMBH) in our Galaxy,
Sgr A*, on the order of several kilometers per second. We integrate possible
orbits of the SMBH along with the surrounding nuclear star cluster (NSC) for a
barred model of the Galaxy using modern constraints on the components of the
SMBH Galactocentric velocity. Is is shown that the range of oscillations of the
SMBH + NSC in a regular Galactic field in the plane of the Galaxy allowed by
these constraints strongly depends on the set of central components of the
Galactic potential. If the central components are represented only by a
bulge/bar, for a point estimate of the SMBH Galactocentric velocity, the
oscillation amplitude does not exceed 7 pc in the case that a classical bulge
is present and reaches 25 pc if there is no bulge; with SMBH velocity
components within the $2\sigma$ significance level, the amplitude can reach 15
and 50 pc, respectively. However, when taking into account the nuclear stellar
disk (NSD), even in the absence of a bulge, the oscillation amplitude is only 5
pc for the point estimate of the SMBH velocity, and 10 pc for the $2\sigma$
significance level. Thus, the possible oscillations of the SMBH + NSC complex
from the confirmed components of the Galaxy's potential are mostly limited by
the NSD, and even taking into account the uncertainty of the mass of the
latter, the oscillation amplitude can hardly exceed $13\,\text{pc}=6'$.


  Efficiently running federated learning (FL) on resource-constrained devices
is challenging since they are required to train computationally intensive deep
neural networks (DNN) independently. DNN partitioning-based FL (DPFL) has been
proposed as one mechanism to accelerate training where the layers of a DNN (or
computation) are offloaded from the device to the server. However, this creates
significant communication overheads since the intermediate activation and
gradient need to be transferred between the device and the server during
training. While current research reduces the communication introduced by DNN
partitioning using local loss-based methods, we demonstrate that these methods
are ineffective in improving the overall efficiency (communication overhead and
training speed) of a DPFL system. This is because they suffer from accuracy
degradation and ignore the communication costs incurred when transferring the
activation from the device to the server. This article proposes EcoFed - a
communication efficient framework for DPFL systems. EcoFed eliminates the
transmission of the gradient by developing pre-trained initialization of the
DNN model on the device for the first time. This reduces the accuracy
degradation seen in local loss-based methods. In addition, EcoFed proposes a
novel replay buffer mechanism and implements a quantization-based compression
technique to reduce the transmission of the activation. It is experimentally
demonstrated that EcoFed can reduce the communication cost by up to 133x and
accelerate training by up to 21x when compared to classic FL. Compared to
vanilla DPFL, EcoFed achieves a 16x communication reduction and 2.86x training
time speed-up. EcoFed is available from https://github.com/blessonvar/EcoFed.


  By analyzing $2.93\ \rm fb^{-1}$ of data taken at a center-of-mass energy of
3.773~GeV with the BESIII detector, we measure the branching fractions of the
Cabibbo-favored hadronic decays $D^0\to K^-\pi^+\eta^\prime$, $D^0\to
K^0_S\pi^0\eta^\prime$ and $D^+\to K^0_S\pi^+\eta^\prime$, which are determined
to be $(6.43 \pm 0.15_{\rm stat.} \pm 0.31_{\rm syst.})\times 10^{-3}$, $(2.52
\pm 0.22_{\rm stat.} \pm 0.15_{\rm syst.})\times 10^{-3}$ and $(1.90 \pm
0.17_{\rm stat.} \pm 0.13_{\rm syst.})\times 10^{-3}$, respectively. The
precision of the branching fraction of $D^0\to K^-\pi^+\eta^\prime$ is
significantly improved, and the processes $D^0\to K^0_S\pi^0\eta^\prime$ and
$D^+\to K^0_S\pi^+\eta^\prime$ are observed for the first time.


  Using recently derived results for one-loop hadronic splitting functions from
a nonlocal implementation of chiral effective theory, we study the
contributions from pseudoscalar meson loops to flavor asymmetries in the
proton. Constraining the parameters of the regulating functions by inclusive
production of $n$, $\Delta^{++}$, $\Lambda$ and $\Sigma^{*+}$ baryons in $pp$
collisions, we compute the shape of the light antiquark asymmetry
$\bar{d}-\bar{u}$ in the proton and the strange asymmetry $s-\bar{s}$ in the
nucleon sea. With these constraints, the magnitude of the $\bar{d}-\bar{u}$
asymmetry is found to be compatible with that extracted from the Fermilab E866
Drell-Yan measurement, with no indication of a sign change at large values of
$x$, and an integrated value in the range $\langle \bar d-\bar u \rangle
\approx 0.09-0.17$. The $s-\bar s$ asymmetry is predicted to be positive at $x
> 0$, with compensating negative contributions at $x=0$, and an integrated
$x$-weighted moment in the range $\langle x (s-\bar s) \rangle \approx
(0.9-2.5) \times 10^{-3}$.


  We give a finite presentation by generators and relations of the unitary
operators expressible over the {CNOT, T, X} gate set, also known as
CNOT-dihedral operators. To this end, we introduce a notion of normal form for
CNOT-dihedral circuits and prove that every CNOT-dihedral operator admits a
unique normal form. Moreover, we show that in the presence of certain
structural rules only finitely many circuit identities are required to reduce
an arbitrary CNOT-dihedral circuit to its normal form.
  By appropriately restricting our relations, we obtain a finite presentation
of unitary operators expressible over the {CNOT, T} gate set as a corollary.


  We determine the cumulative spectral energy distribution (SED) of local AGN
in the 3-300 keV band and compare it with the spectrum of the cosmic X-ray
background (CXB) in order to test the widely accepted paradigm that the CXB is
a superposition of AGN and to place constraints on AGN evolution. We performed
a stacking analysis of the hard X-ray spectra of AGN detected in two recent
all-sky surveys, performed by the IBIS/ISGRI instrument aboard INTEGRAL and by
the PCA instrument aboard RXTE, taking into account the space densities of AGN
with different luminosities and absorption column densities. We derived the
collective SED of local AGN in the 3-300 keV energy band. Those AGN with
luminosities below 10^43.5 erg/s (17-60 keV) provide the main contribution to
the local volume hard X-ray emissivity, at least 5 times more than more
luminous objects. The cumulative spectrum exhibits (although with marginal
significance) a cutoff at energies above 100-200 keV and is consistent with the
CXB spectrum if AGN evolve over cosmic time in such a way that the SED of their
collective high-energy emission has a constant shape and the relative fraction
of obscured AGN remains nearly constant, while the AGN luminosity density
undergoes strong evolution between z~1 and z=0, a scenario broadly consistent
with results from recent deep X-ray surveys. The first direct comparison
between the collective hard X-ray SED of local AGN and the CXB spectrum
demonstrates that the popular concept of the CXB being a superposition of AGN
is generally correct. By repeating this test using improved AGN statistics from
current and future hard X-ray surveys, it should be possible to tighten the
constraints on the cosmic history of black hole growth.


  Most existing word embedding methods can be categorized into Neural Embedding
Models and Matrix Factorization (MF)-based methods. However some models are
opaque to probabilistic interpretation, and MF-based methods, typically solved
using Singular Value Decomposition (SVD), may incur loss of corpus information.
In addition, it is desirable to incorporate global latent factors, such as
topics, sentiments or writing styles, into the word embedding model. Since
generative models provide a principled way to incorporate latent factors, we
propose a generative word embedding model, which is easy to interpret, and can
serve as a basis of more sophisticated latent factor models. The model
inference reduces to a low rank weighted positive semidefinite approximation
problem. Its optimization is approached by eigendecomposition on a submatrix,
followed by online blockwise regression, which is scalable and avoids the
information loss in SVD. In experiments on 7 common benchmark datasets, our
vectors are competitive to word2vec, and better than other MF-based methods.


  We present a transformer-based image anomaly detection and localization
network. Our proposed model is a combination of a reconstruction-based approach
and patch embedding. The use of transformer networks helps to preserve the
spatial information of the embedded patches, which are later processed by a
Gaussian mixture density network to localize the anomalous areas. In addition,
we also publish BTAD, a real-world industrial anomaly dataset. Our results are
compared with other state-of-the-art algorithms using publicly available
datasets like MNIST and MVTec.


  For microscale heterogeneous PDEs, this article further develops novel theory
and methodology for their macroscale mathematical/asymptotic homogenization.
This article specifically encompasses the case of quasi-periodic heterogeneity
with finite scale separation: no scale separation limit is required. Dynamical
systems theory frames the homogenization as a slow manifold of the ensemble of
all phase-shifts of the heterogeneity. Depending upon any perceived scale
separation within the quasi-periodic heterogeneity, the homogenization may be
done in either one step, or two sequential steps: the results are equivalent.
The theory not only assures us of the existence and emergence of the
homogenization, it also provides a practical systematic method to construct the
homogenization to any specified order. For a class of heterogeneities, we show
that the macroscale homogenization is potentially valid down to lengths which
are just twice that of the microscale heterogeneity! This methodology provides
a new rigorous and flexible approach to homogenization that potentially also
provides correct initial and boundary conditions, treatment of forcing and
control, and analysis of uncertainty.


  We present a distributed Lagrange multiplier formulation of the Finite
Element Immersed Boundary Method to couple incompressible fluids with
compressible solids. This is a generalization of the formulation presented in
Heltai and Costanzo (2012), that offers a cleaner variational formulation,
thanks to the introduction of distributed Lagrange multipliers, that acts as
intermediary between the fluid and solid equations, keeping the two formulation
mostly separated. Stability estimates and a brief numerical validation are
presented.


  We report the direct detection of the kinetic Sunyaev-Zel'dovich (kSZ) effect
in galaxy clusters with a 3.5 sigma significance level. The measurement was
performed by stacking the Planck map at 217 GHz at the positions of galaxy
clusters from the Wen-Han-Liu (WHL) catalog. To avoid the cancelation of
positive and negative kSZ signals, we used the large-scale distribution of the
Sloan Digital Sky Survey (SDSS) galaxies to estimate the peculiar velocities of
the galaxy clusters along the line of sight and incorporated the sign in the
velocity-weighted stacking of the kSZ signals. Using this technique, we were
able to measure the kSZ signal around galaxy clusters beyond 3R500. Assuming a
standard beta-model, we also found that the gas fraction within R500 is
fgas,500 = 0.12 +- 0.04 for the clusters with the mass of M500 ~ 1e14 Msun/h.
We compared this result to predictions from the Magneticum cosmological
hydrodynamic simulations as well as other kSZ and X-ray measurements, most of
which show a lower gas fraction than the universal baryon fraction for the same
mass of clusters. Our value is statistically consistent with results from the
measurements and simulations and also with the universal value within our
measurement uncertainty.


  In recent years, advancements in the field of speech processing have led to
cutting-edge deep learning algorithms with immense potential for real-world
applications. The automated identification of stuttered speech is one of such
applications that the researchers are addressing by employing deep learning
techniques. Recently, researchers have utilized Wav2vec2.0, a speech
recognition model to classify disfluency types in stuttered speech. Although
Wav2vec2.0 has shown commendable results, its ability to generalize across all
disfluency types is limited. In addition, since its base model uses 12 encoder
layers, it is considered a resource-intensive model. Our study unravels the
capabilities of Whisper for the classification of disfluency types in stuttered
speech. We have made notable contributions in three pivotal areas: enhancing
the quality of SEP28-k benchmark dataset, exploration of Whisper for
classification, and introducing an efficient encoder layer freezing strategy.
The optimized Whisper model has achieved the average F1-score of 0.81, which
proffers its abilities. This study also unwinds the significance of deeper
encoder layers in the identification of disfluency types, as the results
demonstrate their greater contribution compared to initial layers. This
research represents substantial contributions, shifting the emphasis towards an
efficient solution, thereby thriving towards prospective innovation.


  In this work, we present two alternative yet equivalent representation
formulae for Whitney forms that are valid for any choice of coordinates, and
generalizes the original characterization of Whitney forms in Whitney (1957)
that requires the use of barycentric coordinates. In addition, we demonstrate
that these formulae appropriately generalize the notion of Whitney forms and
barycentric coordinates to Minkowski spacetime, and naturally to any other flat
pseudo-Riemannian manifold. These alternate forms are related to each other
through a duality between the exterior algebras on vectors and covectors. In
addition, these two formulae have a geometrically intuitive interpretation
which provide interesting insights into their structure. Furthermore, we obtain
an explicit characterization of the Hodge dual of the space of Whitney forms on
Minkowski spacetime, and this opens the door to treating the theory of
classical electromagnetism in a fully covariant fashion through the combination
of multisymplectic variational integration and spacetime finite-element
exterior calculus (FEEC) techniques. We conclude the paper with the results
from an $\mathbb{R}^{1+1}$ wave equation simulation, as a proof-of-concept of
the spacetime formulation described herein.


  The spectrum of the fermion zero modes in the vicinity of the vortex with
fractional winding number is discussed. This is inspired by the observation of
the 1/2 vortex in high-temperature superconductors (Kirtley, et al, Phys. Rev.
Lett. 76 (1996) 1336). The fractional value of the winding number leads to the
fractional value of the invariant, which describes the topology of the energy
spectrum of fermions. This results in the phenomenon of the "half-crossing":
the spectrum approaches zero but does not cross it, being captured at the zero
energy level. The similarity with the phenomenon of the fermion condensation is
discussed.


  The aim of this paper is to give a unified definition of a large class of
discriminants arising in algebraic geometry using the discriminant of a
morphism of locally free sheaves. The discriminant of a morphism of locally
free sheaves has a geometric definition in terms of grassmannian bundles,
tautological sequences and projections and is a simultaneous generalization of
the discriminant of a morphism of schemes, the discriminant of a linear system
on a smooth projective scheme and the classical discriminant of degree $d$
polynomials. We study the discriminant of a morphism in various situations: The
discriminant of a finite morphism of schemes, the discriminant of a linear
system on the projective line and the discriminant of a linear system on a flag
variety. The main result of the paper is that the discrimiant of any linear
system on any flag variety is irreducible.


  It has recently been proposed that if the Galactic dark matter halo were
triaxial it would induce lumpiness in the velocity distribution of halo stars
in the Solar Neighbourhood through orbital resonances. These substructures
could therefore provide a way of measuring its shape. We explore the robustness
of this proposal by integrating numerically orbits starting from a realistic
set of initial conditions in dark halo potentials of different shape. We have
analysed the resulting velocity distributions in Solar neighbourhood-like
volumes, and have performed statistical tests for the presence of kinematic
substructures. Furthermore, we have characterized the particles' orbits using a
Fourier analysis. The local velocity distributions obtained are relatively
smooth, statistically consistent with being devoid of substructures even for a
dark halo potential with significant but plausible triaxiality. Although
resonances are indeed present and associated with specific regions of velocity
space, the fraction of stars associated to these is relatively minor. The most
significant imprint of the triaxiality of the dark halo is in fact, a variation
in the shape of the velocity ellipsoid with spatial location.


  In this paper, we use support vector machines (SVM) to develop a machine
learning framework to discover phase space structures that distinguish between
distinct reaction pathways. The SVM model is trained using data from
trajectories of Hamilton's equations and works well even with relatively few
trajectories. Moreover, this framework is specifically designed to require
minimal a priori knowledge of the dynamics in a system. This makes our approach
computationally better suited than existing methods for high-dimensional
systems and systems where integrating trajectories is expensive. We benchmark
our approach on Chesnavich's CH$_4^+$ Hamiltonian.


  In this paper we focus on a general type of mean-field stochastic control
problem with partial observation, in which the coefficients depend in a
non-linear way not only on the state process $X_t$ and its control $u_t$ but
also on the conditional law $E[X_t|\mathcal{F}_t^Y]$ of the state process
conditioned with respect to the past of observation process $Y$. We first
deduce the well-posedness of the controlled system by showing weak existence
and uniqueness in law. Neither supposing convexity of the control state space
nor differentiability of the coefficients with respect to the control variable,
we study Peng's stochastic maximum principle for our control problem. The
novelty and the difficulty of our work stem from the fact that, given an
admissible control $u$, the solution of the associated control problem is only
a weak one. This has as consequence that also the probability measure in the
solution $P^{u}=L^{u}_TQ$ depends on $u$ and has a density $L^{u}_T$ with
respect to a reference measure $Q$. So characterizing an optimal control leads
to the differentiation of non-linear functions
$f(P^{u}\circ\{E^{P^{u}}[X_t|\mathcal{F}_t^Y]\}^{-1})$ with respect to
$(L^{u}_T,X_t)$. This has as consequence for the study of Peng's maximum
principle that we get a new type of first and second order variational
equations and adjoint backward stochastic differential equations, all with new
mean-field terms and with coefficients which are not Lipschitz. For their
estimates and for those for the Taylor expansion new techniques have had to be
introduced and rather technical results have had to be established. The
necessary optimality condition we get extends Peng's one with new, non-trivial
terms.


  In the context of change-point detection, addressed by Total Variation
minimization strategies, an efficient on-the-fly algorithm has been designed
leading to exact solutions for univariate data. In this contribution, an
extension of such an on-the-fly strategy to multivariate data is investigated.
The proposed algorithm relies on the local validation of the Karush-Kuhn-Tucker
conditions on the dual problem. Showing that the non-local nature of the
multivariate setting precludes to obtain an exact on-the-fly solution, we
devise an on-the-fly algorithm delivering an approximate solution, whose
quality is controlled by a practitioner-tunable parameter, acting as a
trade-off between quality and computational cost. Performance assessment shows
that high quality solutions are obtained on-the-fly while benefiting of
computational costs several orders of magnitude lower than standard iterative
procedures. The proposed algorithm thus provides practitioners with an
efficient multivariate change-point detection on-the-fly procedure.


  In the present paper, we propose integrable semi-discrete and full-discrete
analogues of the short pulse (SP) equation. The key of the construction is the
bilinear forms and determinant structure of solutions of the SP equation. We
also give the determinant formulas of N-soliton solutions of the semi-discrete
and full-discrete analogues of the SP equations, from which the multi-loop and
multi-breather solutions can be generated. In the continuous limit, the
full-discrete SP equation converges to the semi-discrete SP equation, then to
the continuous SP equation. Based on the semi-discrete SP equation, an
integrable numerical scheme, i.e., a self-adaptive moving mesh scheme, is
proposed and used for the numerical computation of the short pulse equation.


  We extract the black hole (BH) static tidal deformability coefficients (Love
numbers) and their spin-0 and spin-1 analogs by comparing on-shell amplitudes
for fields to scatter off a spinning BH in the worldline effective field theory
(EFT) and in general relativity (GR). We point out that the GR amplitudes due
to tidal effects originate entirely from the BH potential region. Thus, they
can be separated from gravitational non-linearities in the wave region, whose
proper treatment requires higher order EFT loop calculations. In particular,
the elastic scattering in the near field approximation is produced exclusively
by tidal effects. We find this contribution to vanish identically, which
implies that the static Love numbers of Kerr BHs are zero for all types of
perturbations. We also reproduce the known behavior of scalar Love numbers for
higher dimensional BHs. Our results are manifestly gauge-invariant and
coordinate-independent, thereby providing a valuable consistency check for the
commonly used off-shell methods.


  This paper proposes convolutional filtering for data whose structure can be
modeled by a simplicial complex (SC). SCs are mathematical tools that not only
capture pairwise relationships as graphs but account also for higher-order
network structures. These filters are built by following the shift-and-sum
principle of the convolution operation and rely on the Hodge-Laplacians to
shift the signal within the simplex. But since in SCs we have also
inter-simplex coupling, we use the incidence matrices to transfer the signal in
adjacent simplices and build a filter bank to jointly filter signals from
different levels. We prove some interesting properties for the proposed filter
bank, including permutation and orientation equivariance, a computational
complexity that is linear in the SC dimension, and a spectral interpretation
using the simplicial Fourier transform. We illustrate the proposed approach
with numerical experiments.


  We study slowly rotating four-dimensional black holes with flat horizon
structure in scale-dependent gravity. First we obtain the solution, and then we
study thermodynamic properties as well as the invariants of the theory. The
impact of the scale-dependent parameter is investigated in detail. We find that
the scale-dependent solution exhibits a single singularity at the origin, also
present in the classical solution.


  The Finite Volume method (FVM) is widely adopted in many different
applications because of its built-in conservation properties, its ability to
deal with arbitrary mesh and its computational efficiency. In this work, we
consider the Rhie-Chow stabilized Box Method (RCBM) for the approximation of
the Stokes problem. The Box Method (BM) is a piecewise linear Petrov-Galerkin
formulation on the Voronoi dual mesh of a Delaunay triangulation, whereas the
Rhie-Chow (RC) stabilization is a well known stabilization technique for FVM.
The first part of the paper provides a variational formulation of the RC
stabilization and discusses the validity of crucial properties relevant for the
well-posedeness and convergence of RCBM. Moreover, a numerical exploration of
the convergence properties of the method on 2D and 3D test cases is presented.
The last part of the paper considers the theoretically justification of the
well-posedeness of RCBM and the experimentally observed convergence rates. This
latter justification hinges upon suitable assumptions, whose validity is
numerically explored.


  We study the problem of irreversibility when the dynamical evolution of a
many-body system is described by a stochastic quantum circuit. Such evolution
is more general than a Hamiltonian one, and since energy levels are not well
defined, the well-established connection between the statistical fluctuations
of the energy spectrum and irreversibility cannot be made. We show that the
entanglement spectrum provides a more general connection. Irreversibility is
marked by a failure of a disentangling algorithm and is preceded by the
appearance of Wigner-Dyson statistical fluctuations in the entanglement
spectrum. This analysis can be done at the wave-function level and offers an
alternative route to study quantum chaos and quantum integrability.


  Hybrid beamforming for Terahertz (THz) ultra-massive multiple-input
multiple-output (UM-MIMO) systems is a promising technology for 6G
space-air-ground integrated networks, which can overcome huge propagation loss
and offer unprecedented data rates. With ultra-wide bandwidth and
ultra-large-scale antennas array in THz band, the beam squint becomes one of
the critical problems which could reduce the array gain and degrade the data
rate substantially. However, the traditional phase-shifters-based hybrid
beamforming architectures cannot tackle this issue due to the frequency-flat
property of the phase shifters. In this paper, to combat the beam squint while
keeping high energy efficiency, a novel dynamic-subarray with fixed
true-time-delay (DS-FTTD) architecture is proposed. Compared to the existing
studies which use the complicated adjustable TTDs, the DS-FTTD architecture has
lower power consumption and hardware complexity, thanks to the low-cost FTTDs.
Furthermore, a low-complexity row-decomposition (RD) algorithm is proposed to
design hybrid beamforming matrices for the DS-FTTD architecture. Extensive
simulation results show that, by using the RD algorithm, the DS-FTTD
architecture achieves near-optimal array gain and significantly higher energy
efficiency than the existing architectures. Moreover, the spectral efficiency
of DS-FTTD architecture with the RD algorithm is robust to the imperfect
channel state information.


  We report on a 350-ks NuSTAR observation of the magnetar 1E 1841-045 taken in
2013 September. During the observation, NuSTAR detected six bursts of short
duration, with $T_{90}<1$ s. An elevated level of emission tail is detected
after the brightest burst, persisting for $\sim$1 ks. The emission showed a
power-law decay with a temporal index of 0.5 before returning to the persistent
emission level. The long observation also provided detailed phase-resolved
spectra of the persistent X-ray emission of the source. By comparing the
persistent spectrum with that previously reported, we find that the source
hard-band emission has been stable over approximately 10 years. The persistent
hard X-ray emission is well fitted by a coronal outflow model, where $e^{+/-}$
pairs in the magnetosphere upscatter thermal X-rays. Our fit of phase-resolved
spectra allowed us to estimate the angle between the rotational and magnetic
dipole axes of the magnetar, $\alpha_{mag}=0.25$, the twisted magnetic flux,
$2.5\times10^{26}\rm \ G\ cm^2$, and the power released in the twisted
magnetosphere, $L_j=6\times10^{36}\rm \ erg\ s^{-1}$. Assuming this model for
the hard X-ray spectrum, the soft X-ray component is well fit by a
two-blackbody model, with the hotter blackbody consistent with the footprint of
the twisted magnetic field lines on the star. We also report on the 3-year
Swift monitoring observations obtained since 2011 July. The soft X-ray spectrum
remained stable during this period, and the timing behavior was noisy, with
large timing residuals.


  In the study of open quantum systems, information exchange between system and
its surrounding environment plays an eminent and important role in analysing
the dynamics of open quantum system. In this work, by making use of the quantum
information theory and intrinsic properties such as \emph{entropy exchange},
\emph{coherent information} and using the notion of \emph{quantum loss} as a
criterion of the amount of lost information, we will propose a new witness,
based on information exchange, to detect non-Markovianity. Also a measure for
determining the degree of non-Markovianity, will be introduced by using our
witness. The characteristic of non-Markovianity is clarified by means of our
witness, and we emphasize that this measure is constructed based on the loss of
information or in other word the rate of \emph{quantum loss} in the
environment. It is defined in term of reducing correlation between system and
ancillary. Actually, our focus is on the information which be existed in the
environment and it has been entered to the environment due to its interaction
with the system. Remarkably, due to choosing the situation which the "system
+ancillary" in maximal entangled pure state, optimization procedure does not
need in calculation of our measure, such that the degree of non-Markovianity is
computed analytically by straightforward calculations.


  The 16 Myr-old A0V star HD 156623 in the Scorpius--Centaurus association
hosts a high-fractional-luminosity debris disk, recently resolved in scattered
light for the first time by the Gemini Planet Imager (GPI) in polarized
intensity. We present new analysis of the GPI H-band polarimetric detection of
the HD 156623 debris disk, with particular interest in its unique morphology.
This debris disk lacks a visible inner clearing, unlike the majority of
low-inclination disks in the GPI sample and in Sco-Cen, and it is known to
contain CO gas, positioning it as a candidate ``hybrid'' or ``shielded'' disk.
We use radiative transfer models to constrain the geometric parameters of the
disk based on scattered light data and thermal models to constrain the
unresolved inner radius based on the system's spectral energy distribution
(SED). We also compute a measurement of the polarized scattering phase
function, adding to the existing sample of empirical phase function
measurements. We find that HD 156623's debris disk inner radius is constrained
to less than 26.6 AU from scattered light imagery and less than 13.4 AU from
SED modeling at a 99.7% confidence interval, and suggest that gas drag may play
a role in retaining sub-blowout size dust grains so close to the star.


  In this work, I review some aspects concerning the evolution of quantum
low-energy fields in a foamlike spacetime, with involved topology at the Planck
scale but with a smooth metric structure at large length scales, as follows.
Quantum gravitational fluctuations may induce a minimum length thus introducing
an additional source of uncertainty in physics. The existence of this
resolution limit casts doubts on the metric structure of spacetime at the
Planck scale and opens a doorway to nontrivial topologies, which may dominate
Planck scale physics. This foamlike structure of spacetime may show up in
low-energy physics through loss of quantum coherence and mode-dependent energy
shifts, for instance, which might be observable. Spacetime foam introduces
nonlocal interactions that can be modeled by a quantum bath, and low-energy
fields evolve according to a master equation that displays such effects.
Similar laws are also obtained for quantum mechanical systems evolving
according to good real clocks, although the underlying Hamiltonian structure in
this case establishes serious differences among both scenarios. Contents.---
Quantum fluctuations of the gravitational field; Spacetime foam; Loss of
quantum coherence; Quantum bath; Low-energy effective evolution; Real clocks;
Conclusions.


  It is by now well known that pyramid based wavefront sensors, once in closed
loop, have the capability to improve more and more the gain as the reference
natural star image size is getting smaller on the pyramid pin. Especially in
extreme adaptive optics applications, in order to correct the non-common path
aberrations between the scientific and sensing channel, it is common use to
inject a certain amount of offset wavefront deformation into the DM(s),
departing at the same time the pyramid from the optimal working condition. In
this paper we elaborate on the possibility to correct the low order non-common
path aberrations at the pyramid wavefront sensor level by means of an adaptive
refractive lens placed on the optical path before the pyramid itself, allowing
the mitigation of the gain loss.


  We present general results on fluctuations and spatial correlations of the
coarse-grained empirical density and current of Markovian diffusion in
equilibrium or non-equilibrium steady states on all time scales. We unravel a
deep connection between current fluctuations and generalized time-reversal
symmetry, providing new insight into time-averaged observables. We highlight
the essential role of coarse graining in space from mathematical,
thermodynamical, and experimental points of view. Spatial coarse graining is
required to uncover salient features of currents that break detailed balance,
and a thermodynamically "optimal" coarse graining ensures the most precise
inference of dissipation. Defined without coarse graining, the fluctuations of
empirical density and current are proven to diverge on all time scales in
dimensions higher than one, which has far-reaching consequences for the
central-limit regime in continuous space. We apply the results to examples of
irreversible diffusion. Our findings provide new intuition about time-averaged
observables and allow for a more efficient analysis of single-molecule
experiments.


  The semiclassical Einstein equations are solved to first order in $\epsilon =
\hbar/M^2$ for the case of an extreme or nearly extreme Reissner-Nordstr\"{o}m
black hole perturbed by the vacuum stress-energy of quantized free fields. It
is shown that, for realistic fields of spin 0, 1/2, or 1, any zero temperature
black hole solution to the equations must have an event horizon at $r_h < |Q|$,
with $Q$ the charge of the black hole. It is further shown that no black hole
solutions with $r_h < |Q|$ can be obtained by solving the semiclassical
Einstein equations perturbatively.


  A two dimensional electronic system with novel electronic properties forms at
the interface between the insulators LaAlO$_3$ and SrTiO$_3$. Samples
fabricated until now have been found to be either magnetic or superconducting,
depending on growth conditions. We combine transport measurements with
high-resolution magnetic torque magnetometry and report here evidence of
magnetic ordering of the two-dimensional electron liquid at the interface. The
magnetic ordering exists from well below the superconducting transition to up
to 200 K, and is characterized by an in-plane magnetic moment. Our results
suggest that there is either phase separation or coexistence between magnetic
and superconducting states. The coexistence scenario would point to an
unconventional superconducting phase in the ground state.


  Decoder-only language models (LMs) have been successfully adopted for
speech-processing tasks including automatic speech recognition (ASR). The LMs
have ample expressiveness and perform efficiently. This efficiency is a
suitable characteristic for streaming applications of ASR. In this work, we
propose to use a decoder-only architecture for blockwise streaming ASR. In our
approach, speech features are compressed using CTC output and context embedding
using blockwise speech subnetwork, and are sequentially provided as prompts to
the decoder. The decoder estimates the output tokens promptly at each block. To
this end, we also propose a novel training scheme using random-length prefix
prompts to make the model robust to the truncated prompts caused by blockwise
processing. An experimental comparison shows that our proposed decoder-only
streaming ASR achieves 8% relative word error rate reduction in the LibriSpeech
test-other set while being twice as fast as the baseline model.


  We consider the $\theta$-deformed quantum three sphere $S^3_\theta$ and study
its Chern--Simons theory from a spectral point of view. We first construct a
spectral triple on $S^3_\theta$ as a generalization of the Dirac geometry on
$S^3 $. Since the choice of Dirac operator is not unique, we give two more
natural spectral triples on $S^3_\theta$ related to the standard round metric.
We then compute the Chern--Simons action with respect to the three spectral
triples, it turns out that it is not a topological invariant, that is, it
depends on the choice of Dirac operators.


  Scattering scanning near-field optical microscopy (s-SNOM) is a promising
technique for overcoming Abbe diffraction limit and substantially enhancing the
spatial resolution in spectroscopic imaging. The s-SNOM works by exposing an
atomic force microscope (AFM) tip to an optical electromagnetic (EM) field,
while the tip is so close to a dielectric sample that the incident beam lies
within the near-field regime and displays nonlinear behaviour. We replace the
incident EM field by photons generated by a single photon emitter, and propose
a quantum model for the suggested system by employing electric-dipole
approximation, image theory, and perturbation theory. Quantum state of
scattered photons from the AFM tip is extracted from the proposed model, which
contains information about electrical permittivity of the dielectric material
beneath the tip. The permittivity of the sample can be extracted through
spectroscopic setups. Our proposed scheme has potential applications for
high-resolution quantum sensing and metrology, especially for quantum imaging
and quantum spectroscopy.


  We study a modified version of an equation of the continuous Toda type in 1+1
dimensions. This equation contains a friction-like term which can be switched
off by annihilating a free parameter $\ep$. We apply the prolongation method,
the symmetry and the approximate symmetry approach. This strategy allows us to
get insight into both the equations for $\ep =0$ and $\ep \ne 0$, whose
properties arising in the above frameworks are mutually compared. For $\ep =0$,
the related prolongation equations are solved by means of certain series
expansions which lead to an infinite- dimensional Lie algebra. Furthermore,
using a realization of the Lie algebra of the Euclidean group $E_{2}$, a
connection is shown between the continuous Toda equation and a linear wave
equation which resembles a special case of a three-dimensional wave equation
that occurs in a generalized Gibbons-Hawking ansatz \cite{lebrun}. Nontrivial
solutions to the wave equation expressed in terms of Bessel functions are
determined.
  For $\ep\,\ne\,0,$ we obtain a finite-dimensional Lie algebra with four
elements. A matrix representation of this algebra yields solutions of the
modified continuous Toda equation associated with a reduced form of a
perturbative Liouville equation. This result coincides with that achieved in
the context of the approximate symmetry approach. Example of exact solutions
are also provided. In particular, the inverse of the exponential-integral
function turns out to be defined by the reduced differential equation coming
from a linear combination of the time and space translations. Finally, a Lie
algebra characterizing the approximate symmetries is discussed.


  Precision measurements of the cosmic microwave background temperature
anisotropy on scales $\ell > 500$ will be available in the near future.
Successful interpretation of these data is dependent on a detailed
understanding of the damping tail and cosmological recombination of both
hydrogen and helium. This paper and two companion papers are devoted to a
precise calculation of helium recombination. We discuss several aspects of the
standard recombination picture, and then include feedback, radiative transfer
in HeI lines with partial redistribution, and continuum opacity from HI
photoionization. In agreement with past calculations, we find that HeII
recombination proceeds in Saha equilibrium, whereas HeI recombination is
delayed relative to Saha due to the low rates connecting excited states of HeI
to the ground state. However, we find that at $z<2200$ the continuum absorption
by the rapidly increasing HI population becomes effective at destroying photons
in the HeI $2^1P^o-1^1S$ line, causing HeI recombination to finish around
$z\approx 1800$, much earlier than previously estimated.


  Spectrum sensing is an essential component of modern wireless networks as it
offers a tool to characterize spectrum usage and better utilize it. Deep
Learning (DL) has become one of the most used techniques to perform spectrum
sensing as they are capable of delivering high accuracy and reliability.
However, current techniques suffer from ad-hoc implementations and high
complexity, which makes them unsuited for practical deployment on wireless
systems where flexibility and fast inference time are necessary to support
real-time spectrum sensing. In this paper, we introduce DeepSweep, a novel
DL-based transceiver design that allows scalable, accurate, and fast spectrum
sensing while maintaining a high level of customizability to adapt its design
to a broad range of application scenarios and use cases. DeepSweep is designed
to be seamlessly integrated with well-established transceiver designs and
leverages shallow convolutional neural network (CNN) to "sweep" the spectrum
and process captured IQ samples fast and reliably without interrupting ongoing
demodulation and decoding operations. DeepSweep reduces training and inference
times by more than 2 times and 10 times respectively, achieves up to 98 percent
accuracy in locating spectrum activity, and produces outputs in less than 1 ms,
thus showing that DeepSweep can be used for a broad range of spectrum sensing
applications and scenarios.


  We present a realization of the idea that the Higgs boson is mainly a bound
state of neutrinos induced by strong four-fermion interactions. The conflicts
of this idea with the measured values of the top quark and Higgs boson masses
are overcome by introducing, in addition to the right-handed neutrino, a new
fermion singlet, which, at low energies, implements the inverse see-saw
mechanism. The singlet fermions also develop a scalar bound state which mixes
with the Higgs boson. This allows us to obtain a small Higgs boson mass even if
the couplings are large, as required in composite scalar scenarios. The model
gives the correct masses for the top quark and Higgs boson for compositeness
scales below the Planck scale and masses of the new particles above the
electroweak scale, so that we obtain naturally a low-scale see-saw scenario for
neutrino masses. The theory contains additional scalar particles coupled to the
neutral fermions, which could be tested in present and near future experiments.


  Image acquisition and segmentation are likely to introduce noise. Further
image processing such as image registration and parameterization can introduce
additional noise. It is thus imperative to reduce noise measurements and boost
signal. In order to increase the signal-to-noise ratio (SNR) and smoothness of
data required for the subsequent random field theory based statistical
inference, some type of smoothing is necessary. Among many image smoothing
methods, Gaussian kernel smoothing has emerged as a de facto smoothing
technique among brain imaging researchers due to its simplicity in numerical
implementation. Gaussian kernel smoothing also increases statistical
sensitivity and statistical power as well as Gausianness. Gaussian kernel
smoothing can be viewed as weighted averaging of voxel values. Then from the
central limit theorem, the weighted average should be more Gaussian.


  We explicitly compute \'etale covers of the smooth Fermat curves $Y_{p+1} =
\Proj k[u,v,w]/(u^{p+1} + v^{p+1} - w^{p+1})$ which trivialise the vector
bundles $\Syz(u^2, v^2, w^2)(3)$, where $k$ is a field of characteristic $p
\geq 3$.


  Starfinder is an IDL code for the deep analysis of stellar fields, designed
for well-sampled images with high and low Strehl factor. An important feature
is represented by the possibility to measure the anisoplanatic effect in
wide-field Adaptive Optics observations and exploit this knowledge to improve
the analysis of the observed field. A description of the method and
applications to real AO data are presented.


  In today's fast-paced world, accurately monitoring stress levels is crucial.
Sensor-based stress monitoring systems often need large datasets for training
effective models. However, individual-specific models are necessary for
personalized and interactive scenarios. Traditional methods like Ecological
Momentary Assessments (EMAs) assess stress but struggle with efficient data
collection without burdening users. The challenge is to timely send EMAs,
especially during stress, balancing monitoring efficiency and user convenience.
This paper introduces a novel context-aware active reinforcement learning (RL)
algorithm for enhanced stress detection using Photoplethysmography (PPG) data
from smartwatches and contextual data from smartphones. Our approach
dynamically selects optimal times for deploying EMAs, utilizing the user's
immediate context to maximize label accuracy and minimize intrusiveness.
Initially, the study was executed in an offline environment to refine the label
collection process, aiming to increase accuracy while reducing user burden.
Later, we integrated a real-time label collection mechanism, transitioning to
an online methodology. This shift resulted in an 11% improvement in stress
detection efficiency. Incorporating contextual data improved model accuracy by
4%. Personalization studies indicated a 10% enhancement in AUC-ROC scores,
demonstrating better stress level differentiation. This research marks a
significant move towards personalized, context-driven real-time stress
monitoring methods.


  For a given projective variety $X$, the high rank loci are the closures of
the sets of points whose $X$-rank is higher than the generic one. We show
examples of strict inclusion between two consecutive high rank loci. Our first
example is for the Veronese surface of plane quartics. Although Piene had
already shown an example when $X$ is a curve, we construct infinitely many
curves in $\mathbb P^4$ for which such strict inclusion appears. For space
curves, we give two criteria to check whether the locus of points of maximal
rank 3 is finite (possibly empty).


  We present a 4-bit Arithmetic Logic Unit (ALU) utilizing superconductor
technology. The ALU serves as the central processing unit of a processor,
performing crucial arithmetic and logical operations. We have adopted a
bit-parallel architecture to ensure an efficient and streamlined design with
minimal fanin/fanout and optimal latency. In terms of fabrication, the ALU has
been fabricated using a standard commercial process. It operates at an
impressive clock frequency exceeding 30 GHz while consuming a mere 4.75 mW of
power, including applied reverse current, encompassing static and dynamic
components. The ALU contains over 9000 Josephson junctions, with approximately
7000 JJs dedicated to wiring, delay lines, and path balancing, and it has over
18% bias margin. Designed as a co-processor, this arithmetic logic unit will
work with external CMOS memory and processors via interface circuits. Thorough
testing and validation of the ALU's functionality have been conducted with
digital and analog simulations, and all the components were fabricated and
measured within a 4K pulse-tube cryocooler. Experimental verification has
confirmed the successful operation of both the arithmetic and logic units.
These results have been analyzed and are presented alongside the experimental
data to provide comprehensive insights into the ALU's behavior and
capabilities.


  In this paper, a general model of wireless channels is established based on
the physics of wave propagation. Then the problems of inverse scattering and
channel prediction are formulated as nonlinear filtering problems. The
solutions to the nonlinear filtering problems are given in the form of dynamic
evolution equations of the estimated quantities. Finally, examples are provided
to illustrate the practical applications of the proposed theory.


  Complex networks are ubiquitous in nature and play a role of paramount
importance in many contexts. Internet and the cyberworld, which permeate our
everyday life, are self-organized hierarchical graphs. Urban traffic flows on
intricate road networks, which impact both transportation design and epidemic
control. In the brain, neurons are cabled through heterogeneous connections,
which support the propagation of electric signals. In all these cases, the true
challenge is to unveil the mechanisms through which specific dynamical features
are modulated by the underlying topology of the network. Here, we consider
agents randomly hopping along the links of a graph, with the additional
possibility of performing long-range hops to randomly chosen disconnected nodes
with a given probability. We show that an optimal combination of the two jump
rules exists that maximises the efficiency of target search, the optimum
reflecting the topology of the network.


  Should we input known genome sequence features or input sequence itself in
deep learning framework? As deep learning more popular in various applications,
researchers often come to question whether to generate features or use raw
sequences for deep learning. To answer this question, we study the prediction
accuracy of precursor miRNA prediction of feature-based deep belief network and
sequence-based convolution neural network. Tested on a variant of six-layer
convolution neural net and three-layer deep belief network, we find the raw
sequence input based convolution neural network model performs similar or
slightly better than feature based deep belief networks with best accuracy
values of 0.995 and 0.990, respectively. Both the models outperform existing
benchmarks models. The results shows us that if provided large enough data,
well devised raw sequence based deep learning models can replace feature based
deep learning models. However, construction of well behaved deep learning model
can be very challenging. In cased features can be easily extracted,
feature-based deep learning models may be a better alternative.


  The $A^{(1)}_{n-1}$-face model with boundary reflection is considered on the
basis of the boundary CTM bootstrap. We construct the fused boundary Boltzmann
weights to determine the normalization factor. We derive difference equations
of the quantum Knizhnik-Zamolodchikov type for correlation functions of the
boundary model. The simplest difference equations are solved the in the case of
the free boundary condition.


  We construct a minimal four-band model for the two-dimensional (2D)
topological insulators and quantum anomalous Hall insulators based on the
$p_x$- and $p_y$-orbital bands in the honeycomb lattice. The multiorbital
structure allows the atomic spin-orbit coupling which lifts the degeneracy
between two sets of on-site Kramers doublets $j_z=\pm\frac{3}{2}$ and
$j_z=\pm\frac{1}{2}$. Because of the orbital angular momentum structure of
Bloch-wave states at $\Gamma$ and $K(K^\prime)$ points, topological gaps are
equal to the atomic spin-orbit coupling strengths, which are much larger than
those based on the mechanism of the $s$-$p$ band inversion. In the weak and
intermediate regime of spin-orbit coupling strength, topological gaps are the
global gap. The energy spectra and eigen wave functions are solved analytically
based on Clifford algebra. The competition among spin-orbit coupling $\lambda$,
sublattice asymmetry $m$ and the N\'eel exchange field $n$ results in band
crossings at $\Gamma$ and $K (K^\prime)$ points, which leads to various
topological band structure transitions. The quantum anomalous Hall state is
reached under the condition that three gap parameters $\lambda$, $m$, and $n$
satisfy the triangle inequality. Flat bands also naturally arise which allow a
local construction of eigenstates. The above mechanism is related to several
classes of solid state semiconducting materials.