  The Web is an important resource for understanding and diagnosing medical
conditions. Based on exposure to online content, people may develop undue
health concerns, believing that common and benign symptoms are explained by
serious illnesses. In this paper, we investigate potential strategies to mine
queries and searcher histories for clues that could help search engines choose
the most appropriate information to present in response to exploratory medical
queries. To do this, we performed a longitudinal study of health search
behavior using the logs of a popular search engine. We found that query
variations which might appear innocuous (e.g. "bad headache" vs "severe
headache") may hold valuable information about the searcher which could be used
by search engines to improve performance. Furthermore, we investigated how
medically concerned users respond differently to search engine result pages
(SERPs) and find that their disposition for clicking on concerning pages is
pronounced, potentially leading to a self-reinforcement of concern. Finally, we
studied to which degree variations in the SERP impact future search and
real-world health-seeking behavior and obtained some surprising results (e.g.,
viewing concerning pages may lead to a short-term reduction of real-world
health seeking).


  The role of a super-Alfv\'enic plasmoid instability in the onset of fast
reconnection is studied by means of the largest Hall magnetohydrodynamics
simulations to date, with system sizes up to $10^{4}$ ion skin depths
($d_{i}$). It is demonstrated that the plasmoid instability can facilitate the
onset of rapid Hall reconnection, in a regime where the onset would otherwise
be inaccessible because the Sweet-Parker width is significantly above $d_{i}$.
However, the topology of Hall reconnection is not inevitably a single stable
X-point. There exists an intermediate regime where the single X-point topology
itself exhibits instability, causing the system to alternate between a single
X-point geometry and an extended current sheet with multiple X-points produced
by the plasmoid instability. Through a series of simulations with various
system sizes relative to $d_{i}$, it is shown that system size affects the
accessibility of the intermediate regime. The larger the system size is, the
easier it is to realize the intermediate regime. Although our Hall MHD model
lacks many important physical effects included in fully kinetic models, the
fact that a single X-point geometry is not inevitable raises the interesting
possibility for the first time that Hall MHD simulations may have the potential
to realize reconnection with geometrical features similar to those seen in
fully kinetic simulations, namely, extended current sheets and plasmoid
formation.


  Quantum-enhanced metrology is boosting interferometer sensitivities to
extraordinary levels, up to the point where table-top experiments have been
proposed to measure Planck-scale effects predicted by quantum gravity theories.
In setups involving multiple photon interferometers, as those for measuring the
so-called holographic fluctuations, entanglement provides substantial
improvements in sensitivity. Entanglement is however a fragile resource and may
be endangered by decoherence phenomena. We analyze how noisy effects arising
either from the weak coupling to an external environment or from the
modification of the canonical commutation relations in photon propagation may
affect this entanglement enhanced gain in sensitivity.


  Heating of polar coronal holes during solar minimum and acceleration of the
fast solar wind issuing therefrom lack comprehensive theoretical understanding.
Wave particle interactions are considered to have crucial effects on the
extreme properties of heavy ions in the collision-less region of the polar
coronal holes. In this article, we have presented a novel sensitivity analysis
to investigate plasma heating by radio waves at lower hybrid frequencies. We
have employed a three fluid Maxwell model comprising electrons, protons, and
alpha particles at around two solar radius heliocentric distance in the polar
coronal holes and derived a dispersion relation as a thirteenth order
polynomial for the frequency. Our model provides indications of preferential
heating of alpha particles in comparison with protons by means of lower hybrid
instabilities. We have employed the electron velocity and spatial charge
distribution as our basic study tools so as to show the effects of alpha proton
differential mass and differential perpendicular velocity on the preferential
heating of alpha particles.


  In this article, we study the order of a positive pluriharmonic current and
we compare it with either the order of the concurrent slices or the
directionnel orders of the current. Therefore some estimates of the growth of
the \textsc{Lelong} function are established and the problem of algebraicity of
the current is treated as a result.


  In this paper, we study some quantum properties of a superposition of
displaced squeezed two-mode vacuum and single-photon states, such as the
second-order correlation function, the Cauchy-Schwartz inequality, quadrature
squeezing, quasiprobability distribution functions and purity. This type of
states includes two mechanisms, namely, interference in phase space and
entanglement. We show that these states can exhibit sub-Piossonian statistics,
squeezing and deviate from the classical Cauchy-Schwartz inequality. Moreover,
the amount of entanglement in the system can be increased by increasing the
squeezing mechanism. In the framework of the quasiprobability distribution
functions we show that the single-mode state can tend to thermal state based on
the correlation mechanism. Generation scheme for such states is given.


  In the current Industrial 4.0 revolution, Prognostics and Health Management
(PHM) is an emerging field of research. The difficulty of obtaining data from
electromechanical systems in an industrial setting increases proportionally
with the scale and accessibility of the automated industry, resulting in a less
interpolated PHM system. To put it another way, the development of an accurate
PHM system for each industrial system necessitates a unique dataset acquired
under specified conditions. In most circumstances, obtaining this one-of-a-kind
dataset is difficult, and the resulting dataset has a significant imbalance, a
lack of certain useful information, and multi-domain knowledge. To address
this, this paper provides a fault detection and diagnosis system that evaluates
and pre-processes Imbalanced, Scarce, Multi-Domain (ISMD) data acquired from an
industrial robot utilizing Signal Processing (SP) techniques and Deep
Learning-based (DL) domain knowledge transfer. The domain knowledge transfer is
used to produce a synthetic dataset with a high interpolation rate that
contains all the useful information about each domain. For domain knowledge
transfer and data generation, Continuous Wavelet Transform (CWT) with
Generative Adversarial Network (GAN) was used, as well as Convolutional Neural
Network (CNN) to test the suggested methodology using transfer learning and
categorize several faults. The proposed methodology was tested on a real
experimental bench that included an industrial robot created by Hyundai
Robotics Co. This development resulted in a satisfactory resolution with 99.7%
(highest) classification accuracy achieved by transfer learning on several CNN
benchmark models.


  Emphasis Selection is a newly proposed task which focuses on choosing words
for emphasis in short sentences. Traditional methods only consider the sequence
information of a sentence while ignoring the rich sentence structure and word
relationship information. In this paper, we propose a new framework that
considers sentence structure via a sentence structure graph and word
relationship via a word similarity graph. The sentence structure graph is
derived from the parse tree of a sentence. The word similarity graph allows
nodes to share information with their neighbors since we argue that in emphasis
selection, similar words are more likely to be emphasized together. Graph
neural networks are employed to learn the representation of each node of these
two graphs. Experimental results demonstrate that our framework can achieve
superior performance.


  The axino and the gravitino are well-motivated candidates for the lightest
supersymmetric particle (LSP) and also for cold dark matter in the Universe.
Assuming that a charged slepton is the next-to-lightest supersymmetric particle
(NLSP), we show how the NLSP decays can be used to probe the axino LSP scenario
in hadronic axion models as well as the gravitino LSP scenario at the Large
Hadron Collider and the International Linear Collider. We show how one can
identify experimentally the scenario realized in nature. In the case of the
axino LSP, the NLSP decays will allow one to estimate the value of the axino
mass and the Peccei-Quinn scale.


  Traditionally introduced in terms of advanced topological constructions, many
link invariants may also be defined in much simpler terms given their values on
a few initial links and a recursive formula on a skein triangle. Then the
crucial question to ask is how many initial values are necessary to completely
determine such a link invariant. We focus on a specific class of invariants
known as nonzero determinant link invariants, defined only for links which do
not evaluate to zero on the link determinant. We restate our objective by
considering a set $\mathcal{S}$ of links subject to the condition that if any
three nonzero determinant links belong to a skein triangle, any two of these
belonging to $\mathcal{S}$ implies that the third also belongs to
$\mathcal{S}$. Then we aim to determine a minimal set of initial generators so
that $\mathcal{S}$ is the set of all links with nonzero determinant. We show
that only the unknot is required as a generator if the skein triangle is
unoriented. For oriented skein triangles, we show that the unknot and Hopf link
orientations form a set of generators.


  We present an extended comparison of contextualized language models for
Hungarian. We compare huBERT, a Hungarian model against 4 multilingual models
including the multilingual BERT model. We evaluate these models through three
tasks, morphological probing, POS tagging and NER. We find that huBERT works
better than the other models, often by a large margin, particularly near the
global optimum (typically at the middle layers). We also find that huBERT tends
to generate fewer subwords for one word and that using the last subword for
token-level tasks is generally a better choice than using the first one.


  We present three-dimensional simulations on a new mechanism for the
detonation of a sub-Chandrasekhar CO white dwarf in a dynamically unstable
system where the secondary is either a pure He white dwarf or a He/CO hybrid.
For dynamically unstable systems where the accretion stream directly impacts
the surface of the primary, the final tens of orbits can have mass accretion
rates that range from $10^{-5}$ to $10^{-3} M_{\odot}$ s$^{-1}$, leading to the
rapid accumulation of helium on the surface of the primary. After $\sim
10^{-2}$ $M_{\odot}$ of helium has been accreted, the ram pressure of the hot
helium torus can deflect the accretion stream such that the stream no longer
directly impacts the surface. The velocity difference between the stream and
the torus produces shearing which seeds large-scale Kelvin-Helmholtz
instabilities along the interface between the two regions. These instabilities
eventually grow into dense knots of material that periodically strike the
surface of the primary, adiabatically compressing the underlying helium torus.
If the temperature of the compressed material is raised above a critical
temperature, the timescale for triple-$\alpha$ reactions becomes comparable to
the dynamical timescale, leading to the detonation of the primary's helium
envelope. This detonation drives shockwaves into the primary which tend to
concentrate at one or more focal points within the primary's CO core. If a
relatively small amount of mass is raised above a critical temperature and
density at these focal points, the CO core may itself be detonated.


  The pion-nucleon $\sigma$-term can be stringently constrained by the
combination of analyticity, unitarity, and crossing symmetry with
phenomenological information on the pion-nucleon scattering lengths. Recently,
lattice calculations at the physical point have been reported that find lower
values by about $3\sigma$ with respect to the phenomenological determination.
We point out that a lattice measurement of the pion-nucleon scattering lengths
could help resolve the situation by testing the values extracted from
spectroscopy measurements in pionic atoms.


  Controlling interlayer excitons in van der Waals heterostructures holds
promise for exploring Bose-Einstein condensates and developing novel
optoelectronic applications, such as excitonic integrated circuits. Despite
intensive studies, several key fundamental properties of interlayer excitons,
such as their binding energies and interactions with charges, remain not well
understood. Here we report the formation of momentum-direct interlayer excitons
in a high-quality MoSe2/hBN/MoSe2 heterostructure under an electric field,
characterized by bright photoluminescence (PL) emission with high quantum yield
and a narrow linewidth of less than 4 meV. These interlayer excitons show
electrically tunable emission energy spanning ~180 meV through the Stark
effect, and exhibit a sizable binding energy of ~81 meV in the intrinsic
regime, along with trion binding energies of a few millielectronvolts.
Remarkably, we demonstrate the long-range transport of interlayer excitons with
a characteristic diffusion length exceeding ten micrometers, which can be
attributed, in part, to their dipolar repulsive interactions. Spatially and
polarization-resolved spectroscopic studies reveal rich exciton physics in the
system, such as valley polarization, local trapping, and the possible existence
of dark interlayer excitons. The formation and transport of tightly bound
interlayer excitons with narrow linewidth, coupled with the ability to
electrically manipulate their properties, open exciting new avenues for
exploring quantum many-body physics, including excitonic condensate and
superfluidity, and for developing novel optoelectronic devices, such as exciton
and photon routers.


  The quantum imaginary time evolution (QITE) methodology was developed to
overcome a critical issue as regards non-unitarity in the implementation of
imaginary time evolution on a quantum computer. QITE has since been used to
approximate ground states of various physical systems. In this paper, we
demonstrate a practical application of QITE as a quantum numerical solver for
linear partial differential equations. Our algorithm takes inspiration from
QITE in that the quantum state follows the same normalised trajectory in both
algorithms. However, it is our QITE methodology's ability to track the scale of
the state vector over time that allows our algorithm to solve differential
equations. We demonstrate our methodology with numerical simulations and use it
to solve the heat equation in one and two dimensions using six and ten qubits,
respectively.


  Due to its great importance for applications, we generalize and extend the
approach of our previous papers to study aspects of the quantum and classical
dynamics of a $4$-body system with equal masses in {\it $d$}-dimensional space
with interaction depending only on mutual (relative) distances. The study is
restricted to solutions in the space of relative motion which are functions of
mutual (relative) distances only. The ground state (and some other states) in
the quantum case and some trajectories in the classical case are of this type.
We construct the quantum Hamiltonian for which these states are eigenstates.
For $d \geq 3$, this describes a six-dimensional quantum particle moving in a
curved space with special $d$-independent metric in a certain $d$-dependent
singular potential, while for $d=1$ it corresponds to a three-dimensional
particle and coincides with the $A_3$ (4-body) rational Calogero model; the
case $d=2$ is exceptional and is discussed separately. The kinetic energy of
the system has a hidden $sl(7,{\bf R})$ Lie (Poisson) algebra structure, but
for the special case $d=1$ it becomes degenerate with hidden algebra $sl(4,R)$.
We find an exactly-solvable four-body $S_4$-permutationally invariant,
generalized harmonic oscillator-type potential as well as a
quasi-exactly-solvable four-body sextic polynomial type potential with singular
terms. Naturally, the tetrahedron whose vertices correspond to the positions of
the particles provides pure geometrical variables, volume variables, that lead
to exactly solvable models. Their generalization to the $n$-body system as well
as the case of non-equal masses is briefly discussed.


  We study the three-dimensional stable matching problem with cyclic
preferences. This model involves three types of agents, with an equal number of
agents of each type. The types form a cyclic order such that each agent has a
complete preference list over the agents of the next type. We consider the open
problem of the existence of three-dimensional matchings in which no triple of
agents prefer each other to their partners. Such matchings are said to be
weakly stable. We show that contrary to published conjectures, weakly stable
three-dimensional matchings need not exist. Furthermore, we show that it is
NP-complete to determine whether a weakly stable three-dimensional matchings
exists. We achieve this by reducing from the variant of the problem where
preference lists are allowed to be incomplete. Our results can be generalized
to the $k$-dimensional stable matching problem with cyclic preferences for $k
\geq 3$.


  We are concerned with the Cauchy problem on the Boltzmann equation in the
whole space. The goal is to construct global-in-time bounded mild solutions
near Maxwellians with the perturbation admitting a polynomial tail in large
velocities. The proof is based on the Caflisch's decomposition together with
the $L^2- L^\infty$ interplay technique developed by Guo. The full range of
both hard and soft potentials under the Grad's cutoff assumption can be
covered. The main difficulty to be overcome in case of the whole space is the
polynomial time decay of solutions which is much slower than the exponential
rate in contrast with the torus case.


  There are many reasons to believe that there is a fundamental minimum length
scale below which distances cannot be reliably resolved. One method of
constructing a quantum field with a finite minimum length scale is to use
bandlimited quantum field theory, where the spacetime is mathematically both
continuous and discrete. This is a modification to the field, which has been
shown to have many consequences at the level of the field. We consider an
operational approach and use a pair of particle detectors (two-level qubits) as
a local probe of the field, which are coupled to the vacuum of the bandlimited
massless scalar field in a time dependent way through a switching function. We
show that, mathematically, the bandlimit modifies the spatial profile of the
detectors so that they are only quasi-local. We explore two different types of
switching functions, Gaussian and Dirac delta. We find that with Gaussian
switching, the bandlimit exponentially suppresses the de-excitation of the
detectors when the energy gap between the two levels is larger than the
bandlimit. If the detectors are prepared in ground state, in certain regions of
the parameter space they are able to extract more entanglement from the field
than if there was no bandlimit. When the detectors couple with Dirac-delta
switching, we show that a particle detector is most sensitive to the bandlimit
when it couples to a small but finite region of spacetime. We find that the
effects of a bandlimit are detectable using local probes. This work is
important because it illustrates the possible observable consequences of a
fundamental bandlimit in a quantum field.


  A classical problem in the theory of projective curves is the classification
of all their possible genera in terms of the degree and the dimension of the
space where they are embedded. Fixed integers $r,d,s$, Castelnuovo-Halphen's
theory states a sharp upper bound for the genus of a non-degenerate, reduced
and irreducible curve of degree $d$ in $\mathbb P^r$, under the condition of
being not contained in a surface of degree $<s$. This theory can be generalized
in several ways. For instance, fixed integers $r,d,k$, one may ask for the
maximal genus of a curve of degree $d$ in $\mathbb P^r$, not contained in a
hypersurface of a degree $<k$. In the present paper we examine the genus of
curves $C$ of degree $d$ in $\mathbb P^r$ not contained in quadrics (i.e.
$h^0(\mathbb P^r, \mathcal I_C(2))=0$). When $r=4$ and $r=5$, and $d\gg0$, we
exhibit a sharp upper bound for the genus. For certain values of $r\geq 7$, we
are able to determine a sharp bound except for a constant term, and the
argument applies also to curves not contained in cubics.


  Properties of non-canonical GC Base Pairs and their relation with
mechanochemical cleavage of DNA are analyzed. A hypothesis of the involvement
of the Transient GC Wobble Base Pairs in the mechanisms of the mechanochemical
cleavage of DNA and epigenetic mechanisms with participation of
5-methylcytosine is proposed. The hypothesis explains the increase in the
frequency of the breaks of the sugar-phosphate backbone of DNA after cytosines,
asymmetric character of these breaks, and an increase in the frequency of
breaks in CpG after cytosine methylation.


  Vision Language Models (VLMs) demonstrate remarkable proficiency in
addressing a wide array of visual questions, which requires strong perception
and reasoning faculties. Assessing these two competencies independently is
crucial for model refinement, despite the inherent difficulty due to the
intertwined nature of seeing and reasoning in existing VLMs. To tackle this
issue, we present Prism, an innovative framework designed to disentangle the
perception and reasoning processes involved in visual question solving. Prism
comprises two distinct stages: a perception stage that utilizes a VLM to
extract and articulate visual information in textual form, and a reasoning
stage that formulates responses based on the extracted visual information using
a Large Language Model (LLM). This modular design enables the systematic
comparison and assessment of both proprietary and open-source VLM for their
perception and reasoning strengths. Our analytical framework provides several
valuable insights, underscoring Prism's potential as a cost-effective solution
for vision-language tasks. By combining a streamlined VLM focused on perception
with a powerful LLM tailored for reasoning, Prism achieves superior results in
general vision-language tasks while substantially cutting down on training and
operational expenses. Quantitative evaluations show that Prism, when configured
with a vanilla 2B LLaVA and freely accessible GPT-3.5, delivers performance on
par with VLMs $10 \times$ larger on the rigorous multimodal benchmark MMStar.
The project is released at: https://github.com/SparksJoe/Prism.


  The adoption of advanced deep learning architectures in stuttering detection
(SD) tasks is challenging due to the limited size of the available datasets. To
this end, this work introduces the application of speech embeddings extracted
from pre-trained deep learning models trained on large audio datasets for
different tasks. In particular, we explore audio representations obtained using
emphasized channel attention, propagation, and aggregation time delay neural
network (ECAPA-TDNN) and Wav2Vec2.0 models trained on VoxCeleb and LibriSpeech
datasets respectively. After extracting the embeddings, we benchmark with
several traditional classifiers, such as the K-nearest neighbour (KNN),
Gaussian naive Bayes, and neural network, for the SD tasks. In comparison to
the standard SD systems trained only on the limited SEP-28k dataset, we obtain
a relative improvement of 12.08%, 28.71%, 37.9% in terms of unweighted average
recall (UAR) over the baselines. Finally, we have shown that combining two
embeddings and concatenating multiple layers of Wav2Vec2.0 can further improve
the UAR by up to 2.60% and 6.32% respectively.


  We present a numerical evidence supporting the scenario that the peculiar
alignments of the galaxy stellar spins with the major principal axes of the
local tidal tensors are produced during the quiescent evolution period when the
galaxies experience no recent merger events. Analyzing the merger tree from the
TNG300-1 simulation of the IllustrisTNG project, we find the latest merger
epochs, $a(z_{m})$, of the galaxies, and create four $a(z_{m})$-selected
samples that are controlled to share the identical mass and density
distributions. For each sample, we determine the spin and shape vectors of the
galaxy stellar, cold and hot gas, and dark matter components separately, and
compute the average strengths of their alignments with the principal directions
of the local tidal fields as well as their mutual alignment tendencies. It is
found that the stellar (cold gas) spin axes of the galaxies whose latest merger
events occur at earlier epochs are more strongly aligned (weakly anti-aligned)
with the major principal axes of the tidal fields. It is also shown that
although the mass-dependent transition of the galaxy DM spins have little
connection with the merger events, the morphologies, spin-shape and shape-shear
alignment strengths of the galaxy four components sensitively depend on
$a(z_{m})$. Noting that the stellar components of the galaxies which undergo
long quiescent evolution have distinctively oblate shapes and very strong
spin-shape alignments, we suggest that the local tidal field might be traced by
using the stellar shapes of galaxies without signatures of mergers as a proxy
of their stellar spins.


  We propose a simple model in the type-III seesaw framework to explain the
neutrino mass, asymmetric dark matter, baryon asymmetry of the Universe, and
the recently reported W-mass anomaly by CDF-II collaboration. We extend the
standard model with a vector-like singlet lepton ($\chi$) and a hypercharge
zero scalar triplet ($\Delta$) in addition to three hypercharge zero triplet
fermions($\Sigma_i~,i=1,2,3$). A $Z_2$ symmetry is imposed under which $\chi$
and $\Delta$ are odd, while all other particles are even. As a result, the
lightest $Z_2$ odd particle $\chi$ behaves as a candidate of dark matter. In
the early Universe, the CP-violating out-of-equilibrium decay of heavy triplet
fermions to the Standard Model lepton ($L$) and Higgs ($H$) generate a net
lepton asymmetry, while that of triplet fermions to $\chi$ and $\Delta$
generate a net asymmetric dark matter. The lepton asymmetry is converted to the
required baryon asymmetry of the Universe via the electroweak sphalerons, while
the asymmetry in $\chi$ remains as a dark matter relic that we observe today.
We introduce a singlet scalar $\phi$, with mass $m_\phi < m_\chi$, which not
only assists to deplete the symmetric component of $\chi$ through the
annihilation process: $\bar{\chi} \chi \to \phi \phi$ but also paves a path to
detect dark matter $\chi$ at direct search experiments through $\phi-H$ mixing.
The $Z_2$ symmetry is broken softly resulting in an unstable asymmetric dark
matter with mass ranging from a few MeV to a few tens of GeV. The softly broken
$Z_2$ symmetry also induces a vacuum expectation value (vev) of $\Delta$ due to
which the asymmetry in $\Delta$ disappears. Moreover, the vev of $\Delta$
enhances the W-boson mass as reported by CDF-II collaboration with $7\sigma$
statistical significance, while keeping the $Z$-boson mass intact.


  Low-rank matrix recovery from structured measurements has been a topic of
intense study in the last decade and many important problems like matrix
completion and blind deconvolution have been formulated in this framework. An
important benchmark method to solve these problems is to minimize the nuclear
norm, a convex proxy for the rank. A common approach to establish recovery
guarantees for this convex program relies on the construction of a so-called
approximate dual certificate. However, this approach provides only limited
insight in various respects. Most prominently, the noise bounds exhibit
seemingly suboptimal dimension factors. In this paper we take a novel, more
geometric viewpoint to analyze both the matrix completion and the blind
deconvolution scenario. We find that for both these applications the dimension
factors in the noise bounds are not an artifact of the proof, but the problems
are intrinsically badly conditioned. We show, however, that bad conditioning
only arises for very small noise levels: Under mild assumptions that include
many realistic noise levels we derive near-optimal error estimates for blind
deconvolution under adversarial noise.


  Virtual assistants such as Google Assistant, Amazon Alexa, and Apple Siri
enable users to interact with a large number of services and APIs on the web
using natural language. In this work, we investigate two methods for Natural
Language Generation (NLG) using a single domain-independent model across a
large number of APIs. First, we propose a schema-guided approach which
conditions the generation on a schema describing the API in natural language.
Our second method investigates the use of a small number of templates, growing
linearly in number of slots, to convey the semantics of the API. To generate
utterances for an arbitrary slot combination, a few simple templates are first
concatenated to give a semantically correct, but possibly incoherent and
ungrammatical utterance. A pre-trained language model is subsequently employed
to rewrite it into coherent, natural sounding text. Through automatic metrics
and human evaluation, we show that our method improves over strong baselines,
is robust to out-of-domain inputs and shows improved sample efficiency.


  We improve QCD calculations of the $B_{d, s} \to \pi, K$ form factors at
large hadronic recoil by implementing the next-to-leading-logarithmic
resummation for the obtained leading-power light-cone sum rules in the
soft-collinear effective theory (SCET) framework. Additionally, we endeavour to
investigate a variety of the subleading-power contributions to these
heavy-to-light form factors at ${\cal O}(\alpha_s^0)$, by including the
higher-order terms in the heavy-quark expansion of the hard-collinear quark
propagator, by evaluating the desired effective matrix element of the
next-to-leading-order term in the ${\rm SCET_{I}}$ representation of the weak
transition current, by taking into account the off-light-cone contributions of
the two-body heavy-quark effective theory matrix elements as well as the
three-particle higher-twist corrections from the subleading bottom-meson
light-cone distribution amplitudes, and by computing the twist-five and
twist-six four-body higher-twist effects with the aid of the factorization
approximation. Having at our disposal the SCET sum rules for the exclusive
$B$-meson decay form factors, we further explore in detail numerical
implications of the newly computed subleading-power corrections by employing
the three-parameter model for both the leading-twist and higher-twist $B$-meson
distribution amplitudes. Taking advantage of the customary
Bourrely-Caprini-Lellouch parametrization for the semileptonic $B_{d, s} \to
\pi, K$ form factors, we then determine the correlated numerical results for
the interesting series coefficients, by carrying out the simultaneous fit of
the exclusive $B$-meson decay form factors to both the achieved SCET sum rule
predictions and the available lattice QCD results.


  Thanks to the single-photon interference at a third untrusted party, the
twin-field quantun key distribution (TF-QKD) protocol and its variants can beat
the well-known rate-loss bound without quantum repeaters, and related
experiments have been implemented recently. Generally, quantum states in these
schemes should be randomly switched between the code mode and test mode. To
adopt the standard decoy-state method, phases of coherent state sources in the
test mode are assumed to be continuously randomized. However, such a crucial
assumption cannot be well satisfied in experimental implementations. In this
paper, to bridge the gap between theory and practice, we propose a TF-QKD
variant with discrete-phase-randomized sources both in the code mode and test
mode, and prove its security against collective attacks. Our simulation results
indicate that, with only a small number of discrete phases, the performance of
discrete-phase-randomized sources can overcome the rate-loss bound and approach
that of continuous-phase-randomized sources.


  Recent developments relevant to the formation of globular cluster systems in
galaxies are discussed, including (1) The age distribution of the oldest Milky
Way clusters, (2) Subgroups and possible accretion and merger remnants in the
Galactic halo, (3) Key features of globular cluster systems in giant elliptical
galaxies (metallicity distribution functions, luminosity distribution
functions, specific frequencies). Processes contributing to the formation of
giant ellipticals are summarized.


  The study of taxonomies and hypernymy relations has been extensive on the
Natural Language Processing (NLP) literature. However, the evaluation of
taxonomy learning approaches has been traditionally troublesome, as it mainly
relies on ad-hoc experiments which are hardly reproducible and manually
expensive. Partly because of this, current research has been lately focusing on
the hypernymy detection task. In this paper we reflect on this trend, analyzing
issues related to current evaluation procedures. Finally, we propose three
potential avenues for future work so that is-a relations and resources based on
them play a more important role in downstream NLP applications.


  We investigate inflation models in Jordan frame supergravity, in which an
inflaton non-minimally couples to the scalar curvature. By imposing the
condition that an inflaton would have the canonical kinetic term in the Jordan
frame, we construct inflation models with asymptotically flat potential through
pole inflation technique and discuss their relation to the models based on
Einstein frame supergravity. We also show that the model proposed by Ferrara et
al. has special position and the relation between the K\"ahler potential and
the frame function is uniquely determined by requiring that scalars take the
canonical kinetic terms in the Jordan frame and that a frame function consists
only of a holomorphic term (and its anti-holomorphic counterpart) for symmetry
breaking terms. Our case corresponds to relaxing the latter condition.


  Non-equilibrium photon correlations of coherently excited single quantum
systems can reveal their internal quantum dynamics and provide spectroscopic
access. Here we propose and discuss the fundamentals of a coherent photon
coincidence spectroscopy based on the application of laser pulses with variable
delay and the detection of an time-averaged two-photon coincidence rate. For
demonstration, two simple but important cases, i.e., an exciton - biexciton in
a quantum dot and two coupled quantum emitters, are investigated based on
quantum dynamics simulations demonstrating that this nonlinear spectroscopy
reveals information specific to the particular single quantum system.


  The nontrivial topology of the electronic structure of iron pnictides can
lead to the appearance of surface states. We study such states in various strip
geometries with a focus on the superconducting phase. In the presence of
unconventional superconducting pairing with $s_\pm$-wave gap structure, the
topological states are quite robust and partly remain in the superconducting
gap. Furthermore, Andreev bound states appear, which coexist with the
topological states for small superconducting gaps and merge with them for
larger gap values. The bulk and surface dispersions are obtained from exact
diagonalization for two-orbital and five-orbital models in strip geometries.


  Beam dynamics applications at the Swiss Light Source (SLS) have benefitted
from a distributed computing environment in which the Common Object Request
Broker Architecture (CORBA) forms the middleware layer and access point to
several different software components.A suite of remote CORBA server objects
provides the client with a convenient and uniform interface to the CDEV (Common
DEVice) controls library, the TRACY accelerator physics package, the Oracle
database, and en event logging facility. Use is made of methods provided by the
CORBA Portable Object Adaptor for accessing ORB functions, such as object
activation and object persistence, the Implementation Repository for the
automatic reactivation of servers, and the CORBA Event Service for the
propagation of controls and physics data. An account of the CORBA framework, as
used by applications in the commissioning and first operation of the SLS, is
presented.


  One of the distinguishing features of quantum theory is that its measurement
outcomes are usually unpredictable or, equivalently, random. Moreover, this
randomness is certifiable with minimal assumptions in the so-called
device-independent (DI) paradigm, where a device's behavior does not need to be
presupposed but can be verified through the statistics it produces. In this
work, we explore various forms of randomness that are certifiable in this
setting, where two users can perform two binary-outcome measurements on their
shared entangled state. In this case, even though the
Clauser-Horne-Shimony-Holt (CHSH) Bell-inequality violation is a pre-requisite
for the generation of DI certifiable randomness, the CHSH value alone does not
generally give a tight bound on the certifiable randomness. Here, we determine
the certifiable randomness when zero-probability constraints are incorporated
into the task of DI randomness expansion for the standard local and global
randomness and the so-called "blind" randomness. Asymptotically, we observe
consistent improvements in the amount of DI certifiable randomness (of all
kinds) as we increase the number zero constraints for a wide range of given
CHSH Bell violations. However, if we further optimize over the allowed CHSH
values, then benefits of these additional constraints over the standard
CHSH-based protocol are only found in the case of global and blind randomness.
In contrast, in the regimes of finite data, these zero constraints only give a
slight improvement in the local randomness rate when compared with all existing
protocols.


  We present an approach to generate novel computer game levels that blend
different game concepts in an unsupervised fashion. Our primary contribution is
an analogical reasoning process to construct blends between level design models
learned from gameplay videos. The models represent probabilistic relationships
between elements in the game. An analogical reasoning process maps features
between two models to produce blended models that can then generate new level
chunks. As a proof-of-concept we train our system on the classic platformer
game Super Mario Bros. due to its highly-regarded and well understood level
design. We evaluate the extent to which the models represent stylistic level
design knowledge and demonstrate the ability of our system to explain levels
that were blended by human expert designers.


  I consider the natural infinitary variations of the games Wordle and
Mastermind, as well as their game-theoretic variations Absurdle and
Madstermind, considering these games with infinitely long words and infinite
color sequences and allowing transfinite game play. For each game, a secret
codeword is hidden, which the codebreaker attempts to discover by making a
series of guesses and receiving feedback as to their accuracy. In Wordle with
words of any size from a finite alphabet of $n$ letters, including infinite
words or even uncountable words, the codebreaker can nevertheless always win in
$n$ steps. Meanwhile, the mastermind number, defined as the smallest winning
set of guesses in infinite Mastermind for sequences of length $\omega$ over a
countable set of colors without duplication, is uncountable, but the exact
value turns out to be independent of ZFC, for it is provably equal to the
eventually different number $\frak{d}({\neq^*})$, which is the same as the
covering number of the meager ideal $\text{cov}(\mathcal{M})$. I thus place all
the various mastermind numbers, defined for the natural variations of the game,
into the hierarchy of cardinal characteristics of the continuum.


  The stability of persistent currents in a two-component Bose-Einstein
condensate in a toroidal trap is studied both in the miscible and immiscible
regimes. In the miscible regime we show that superflow decay is related to
linear instabilities of the spin-density Bogoliubov mode. We find a region of
partial stability, where the flow is stable in the majority component while it
decays in the minority component. We also characterize the dynamical
instability appearing for a large relative velocity between the two components.
In the immiscible regime the stability criterion is modified and depends on the
specific density distribution of the two components. The effect of a coherent
coupling between the two components is also discussed.


  We describe an experimental protocol to characterize magnetic field dependent
microwave losses in superconducting niobium microstrip resonators. Our approach
provides a unified view that covers two well-known magnetic field dependent
loss mechanisms: quasiparticle generation and vortex motion. We find that
quasiparticle generation is the dominant loss mechanism for parallel magnetic
fields. For perpendicular fields, the dominant loss mechanism is vortex motion
or switches from quasiparticle generation to vortex motion, depending on
cooling procedures. In particular, we introduce a plot of the quality factor
versus the resonance frequency as a general method for identifying the dominant
loss mechanism. We calculate the expected resonance frequency and the quality
factor as a function of the magnetic field by modeling the complex resistivity.
Key parameters characterizing microwave loss are estimated from comparisons of
the observed and expected resonator properties. Based on these key parameters,
we find a niobium resonator whose thickness is similar to its penetration depth
is the best choice for X-band electron spin resonance applications. Finally, we
detect partial release of the Meissner current at the vortex penetration field,
suggesting that the interaction between vortices and the Meissner current near
the edges is essential to understand the magnetic field dependence of the
resonator properties.


  As we have shown several years ago [Y2], zeros of $L(s, \Delta )$ and
$L^(2)(s, \Delta )$ can be calculated quite efficiently by a certain
experimental method. Here $\Delta$ denotes the cusp form of weight 12 with
respect to SL$(2, Z)$ and $L(s, \Delta )$ (resp. $L^(2)(s, \Delta )$) denotes
the standard (resp. symmetric square) $L$-function attached to $\Delta$. The
purpose of this paper is to show that this method can be applied to a wide
class of $L$-functions so that we can obtain precise numerical values of their
zeros.


  We focus on very general, very large U, doped Mott Insulators with arbitrary
hopping and interactions. We provide simple testimony to the competition
between magnetic and superconducting orders in these systems. By mapping hard
core bosons, spinless, and spinful fermions onto XXZ models, we aim to make
very simple precise statements. We try to address optimal and expected filling
fractions of holes within the plane and on stripes in a variety of hole and
hole pair geometries. We examine the role of attractions/repulsion amongst hole
pairs and single holes, and provide trivial expected numerical values for
filling fractions in various scenarios. We demnostrate that plaquette states
seem to naturally provide the correct stripe filling fractions.


  Quantum devices characterized by non-Hermitian topology are predicted to show
highly robust and potentially useful properties, but realizing them has
remained a daunting experimental task. This is because non-Hermiticity is often
associated with gain and loss, which would require precise tailoring to produce
the signatures of nontrivial topology. Here, instead of gain/loss, we use the
nonreciprocity of the quantum Hall edge states to directly observe
non-Hermitian topology in a multi-terminal quantum Hall ring. Our transport
measurements evidence a robust, non-Hermitian skin effect: currents and
voltages show an exponential profile, which persists also across Hall plateau
transitions away from the regime of maximum non-reciprocity. Our observation of
non-Hermitian topology in a quantum device introduces a scalable experimental
approach to construct and investigate generic non-Hermitian systems.


  We analyze spectral properties of a leaky wire model with a potential bias.
It describes a two-dimensional quantum particle exposed to a potential
consisting of two parts. One is an attractive $\delta$-interaction supported by
a non-straight, piecewise smooth curve $\mathcal{L}$ dividing the plane into
two regions of which one, the `interior', is convex. The other interaction
component is a constant positive potential $V_0$ in one of the regions. We show
that in the critical case, $V_0=\alpha^2$, the discrete spectrum is non-void if
and only if the bias is supported in the interior. We also analyze the
non-critical situations, in particular, we show that in the subcritical case,
$V_0<\alpha^2$, the system may have any finite number of bound states provided
the angle between the asymptotes of $\mathcal{L}$ is small enough.


  A system-bath entanglement theorem (SBET) with Gaussian environments was
established previously in J. Chem. Phys. 152, 034102 (2020) in terms of linear
response functions. This theorem connects the system-bath entanglement
responses to the local system and bare bath ones. In this work, we generalize
it to correlation functions. Key steps in derivation are the generalized
Langevin dynamics for the hybridizing bath modes as in the previous work,
together with the Bogoliubov transformation mapping the original
finite-temperature canonical reservoir to an effective zero-temperature vacuum
via an auxiliary bath. With the theorem, the system-bath entangled correlations
and the bath modes correlations in the full composite space can be evaluated as
long as the bare-bath statistical properties are known and the reduced system
correlations are obtained. Numerical demonstrations are carried out for the
evaluation of the solvation free energy of an electron transfer system with a
certain intramolecular vibrational modes.


  A family of exact upper bounds interpolating between Chebyshev's and
Cantelli's is presented.


  In this paper, we study the codebook-based near-field beam training for
intelligent reflecting surfaces (IRSs) aided wireless system. In the considered
model, the near-field beam training is critical to focus signals at the
location of user equipment (UE) to obtain prominent IRS array gain. However,
existing codebook schemes cannot achieve low training overhead and high
receiving power simultaneously. To tackle this issue, a novel two-layer
codebook based beam training scheme is proposed. The layer-1 codebook is
designed based on the omnidirectionality of a random-phase beam pattern, which
estimates the UE distance with training overhead equivalent to that of one DFT
codeword. Then, based on the estimated UE distance, the layer-2 codebook is
generated to scan candidate UE locations and obtain the optimal codeword for
IRS beamforming. Numerical results show that compared with benchmarks, the
proposed two-layer beam training scheme achieves more accurate UE distance and
angle estimation, higher data rate, and smaller training overhead.


  This paper targets unsupervised skeleton-based action representation learning
and proposes a new Hierarchical Contrast (HiCo) framework. Different from the
existing contrastive-based solutions that typically represent an input skeleton
sequence into instance-level features and perform contrast holistically, our
proposed HiCo represents the input into multiple-level features and performs
contrast in a hierarchical manner. Specifically, given a human skeleton
sequence, we represent it into multiple feature vectors of different
granularities from both temporal and spatial domains via sequence-to-sequence
(S2S) encoders and unified downsampling modules. Besides, the hierarchical
contrast is conducted in terms of four levels: instance level, domain level,
clip level, and part level. Moreover, HiCo is orthogonal to the S2S encoder,
which allows us to flexibly embrace state-of-the-art S2S encoders. Extensive
experiments on four datasets, i.e., NTU-60, NTU-120, PKU-MMD I and II, show
that HiCo achieves a new state-of-the-art for unsupervised skeleton-based
action representation learning in two downstream tasks including action
recognition and retrieval, and its learned action representation is of good
transferability. Besides, we also show that our framework is effective for
semi-supervised skeleton-based action recognition. Our code is available at
https://github.com/HuiGuanLab/HiCo.


  The sparse transformer can reduce the computational complexity of the
self-attention layers to $O(n)$, whilst still being a universal approximator of
continuous sequence-to-sequence functions. However, this permutation variant
operation is not appropriate for direct application to sets. In this paper, we
proposed an $O(n)$ complexity sampled transformer that can process point set
elements directly without any additional inductive bias. Our sampled
transformer introduces random element sampling, which randomly splits point
sets into subsets, followed by applying a shared Hamiltonian self-attention
mechanism to each subset. The overall attention mechanism can be viewed as a
Hamiltonian cycle in the complete attention graph, and the permutation of point
set elements is equivalent to randomly sampling Hamiltonian cycles. This
mechanism implements a Monte Carlo simulation of the $O(n^2)$ dense attention
connections. We show that it is a universal approximator for continuous
set-to-set functions. Experimental results on point-clouds show comparable or
better accuracy with significantly reduced computational complexity compared to
the dense transformer or alternative sparse attention schemes.


  Motivated by the theory of quantum waveguides, we investigate the spectrum of
the Laplacian, subject to Dirichlet boundary conditions, in a curved strip of
constant width that is defined as a tubular neighbourhood of an infinite curve
in a two-dimensional Riemannian manifold. Under the assumption that the strip
is asymptotically straight in a suitable sense, we localise the essential
spectrum and find sufficient conditions which guarantee the existence of
geometrically induced bound states. In particular, the discrete spectrum exists
for non-negatively curved strips which are studied in detail. The general
results are used to recover and revisit the known facts about quantum strips in
the plane. As an example of non-positively curved quantum strips, we consider
strips on ruled surfaces.


  We have studied the effect of one-loop logarithmic electroweak radiative
corrections on WZ and $W\gamma$ production processes at the LHC. We present
analytical results for the leading-logarithmic electroweak corrections to the
corresponding partonic processes du -> WZ, Wgamma. Using the leading-pole
approximation we implement these corrections into Monte Carlo programs for
$pp\to l\nu_l l'\bar l', l\nu_l\gamma$. We find that electroweak corrections
lower the predictions by 5-20% in the physically interesting region of large
transverse momentum and small rapidity separation of the gauge bosons.


  This paper considers the optimal decentralized control for networked control
systems (NCSs) with asymmetric partial information sharing between two
controllers. In this NCSs model, the controller 2 (C2) shares its observations
and part of its historical control inputs with the controller 1 (C1), whereas
C2 cannot obtain the information of C1 due to network constraints. We present
the optimal estimators for C1 and C2 respectively based on asymmetric
observations. Since the information for C1 and C2 are asymmetric, the
estimation error covariance (EEC) is coupled with the controller which means
that the classical separation principle fails. By applying the Pontryagin's
maximum principle, we obtain a solution to the forward and backward stochastic
difference equations. Based on this solution, we derive the optimal controllers
to minimize a quadratic cost function. Combining the optimal controllers with
the EEC, the controller C1 is decoupled from the ECC. It should be emphasized
that the control gain is dependent on the estimation gain. What's more, the
estimation gain satisfies the forward Riccati equation and the control gain
satisfies the backward Riccati equation which makes the problem more
challenging. We propose iterative solutions to the Riccati equations and give a
suboptimal solution to the optimal decentralized control problem.


  The 2011 Tohoku tsunami entered the Kitakami river and propagated there as a
train of shock waves, recorded with a 1-min interval at water level stations at
Fukuchi, Iino, and the weir 17.2 km from the mouth, where the bulk of the wave
was reflected back. The records showed that each bore kept its shape and
identity as it traveled a 10.9-km-path Fukuchi-Iino-weir-Iino. Shock handling
based on the cross-river integrated classical shock conditions was applied to
reconstruct the flow velocity time histories at the measurement sites, to
estimate inflow into the river at each site, to evaluate the wave heights of
incident and reflected tsunami bores near the weir, and to estimate propagation
speed of the individual bores. Theoretical predictions are verified against the
measurements. We discuss experiences of exercising the shock conditions with
actual tsunami measurements in the Kitakami river, and test applicability of
the shallow-water approximation for describing tsunami bores with heights
ranging from 0.3 m to 4 m in a river segment with a depth of 3-4 m.


  We give a new, elementary proof of a key inequality used by Rudelson in the
derivation of his well-known bound for random sums of rank-one operators. Our
approach is based on Ahlswede and Winter's technique for proving operator
Chernoff bounds. We also prove a concentration inequality for sums of random
matrices of rank one with explicit constants.


  Whether aftershocks originate directly from the mainshock and surrounding
stress environment or from afterslip dynamics is crucial to the understanding
of the nature of aftershocks. We build on a classical description of the fault
and creeping regions as two blocks connected elastically, subject to different
friction laws. We show analytically that, upon introduction of variability in
the fault plane's static friction threshold, a non trivial stick-slip dynamics
ensues. In particular we support the hypothesis \citep{PA04} that the
aftershock occurrence rate is proportional to the afterslip rate, up to a
corrective factor that is also computed. Thus, the Omori law originates from
the afterslip's logarithmic evolution in the velocity-strengthening region. We
confirm these analytical results with numerical simulations, generating
synthetic catalogs with statistical features in good agreement with
instrumental catalogs. In particular we recover the Gutenberg-Richter law with
a realistic $b$-value ($b\simeq 1$) when Coulomb stress thresholds obey a power
law distribution.


  We describe a procedure based on the Krawczyk method to compute a verified
enclosure for the stabilizing solution of a continuous-time algebraic Riccati
equation $A^*X+XA+Q=XGX$ building on the work of [B.~Hashemi, \emph{SCAN} 2012]
and adding several modifications to the Krawczyk procedure. We show that after
these improvements the Krawczyk method reaches results comparable with the
current state-of-the-art algorithm [Miyajima, \emph{Jpn. J. Ind. Appl. Math}
2015], and surpasses it in some examples. Moreover, we introduce a new direct
method for verification which has a cubic complexity in term of the dimension
of $X$, employing a fixed-point formulation of the equation inspired by the ADI
procedure. The resulting methods are tested on a number of standard benchmark
examples.


  We report an investigation of the heterogeneity in super-cooled liquids and
glasses using the non-Gaussianity parameter. We simulate selenium and a binary
Lennard-Jones system by molecular dynamics. In the non-Gaussianity three time
domains can be distinguished. First there is an increase on the ps-scale due to
the vibrational (ballistic) motion of the atoms. This is followed, on an
intermediate time-scale, by a growth, due to local relaxations
(beta-relaxation) at not too high temperatures. A maximum is reached at times
corresponding to long range diffusion (alpha-relaxation). At long times the
non-Gaussianity slowly drops, the system becoming homogeneous on these
time-scales. In both systems studied, the non-Gaussianity follows in the
intermediate time domain, corresponding to the beta-relaxations, a law ~ t^1/2.
This general behavior is explained by collective hopping and dynamic
heterogeneity. We support this finding by a model calculation.


  In this paper the inverse problem of determining the fractional orders in
mixed-type equations is considered. In one part of the domain the considered
equation is the subdiffusion equation with a fractional derivative in the sense
of Gerasimov-Caputo of the order 0<a<1 , and in the other part - a wave
equation with a fractional derivative of the order 1<b<2 . The elliptic part of
the equation is a second-order operator, considered in a N - dimensional domain
D. Assuming the parameters a and b to be unknown, additional conditions are
found that provide an unambiguous determination of the required parameters.


  The phase distribution in a Bose-Einstein condensate can realize various
topological states classified by distinct winding numbers. While states with
different winding numbers are topologically protected in the linear
Schr\"odinger equation, when nonlinearities are introduced, violations of the
topological protection can occur, leading to unwinding. Exciton-polariton
condensates constitute a nonlinear open-dissipative system that is well suited
to studying such physics. Here we show that a one-dimensional array of
exciton-polariton condensates displays a spontaneous phase unwinding from a
$\pi$- to zero-state. We clarify that this collective mode transition is caused
by the combined effect of nonlinearity and topological defects in the
condensates. While the mode-switching phenomenon observed in our previous
experiment was interpreted as the single-particle mode competition, we offer an
alternative explanation in terms the collective phase unwinding and find its
evidence by reanalyzing the experimental data. Our results open a route towards
active control of the mode switching by manipulating the topological defects in
prospective quantum polaritonic devices.


  Direct measurements of the trilinear gauge boson couplings by the CDF and D0
collaborations at Fermilab are reviewed. Limits on the anomalous couplings were
obtained at a 95 % CL from four diboson production processes: W-gamma
production with the subsequent W boson decay to e-nu or mu-nu, WW production
with both the W boson decaying to e-nu or mu-nu, WW/WZ production with one of
the gauge bosons decaying leptonically and the other gauge boson decaying to
two jets, and Z-gamma production with the subsequent Z boson decay to e-e,
mu-mu, or nu-nu. Limits were also obtained by a combined fit to W-gamma, WW to
dileptons and WW/WZ semileptonic data samples.


  The processing of Visually-Rich Documents (VRDs) is highly important in
information extraction tasks associated with Document Intelligence. We
introduce DI-Metrics, a Python library devoted to VRD model evaluation
comprising text-based, geometric-based and hierarchical metrics for information
extraction tasks. We apply DI-Metrics to evaluate information extraction
performance using publicly available CORD dataset, comparing performance of
three SOTA models and one industry model. The open-source library is available
on GitHub.


  This paper is concerned with a novel regularisation technique for solving
linear ill-posed operator equations in Hilbert spaces from data that is
corrupted by white noise. We combine convex penalty functionals with
extreme-value statistics of projections of the residuals on a given set of
sub-spaces in the image-space of the operator. We prove general consistency and
convergence rate results in the framework of Bregman-divergences which allows
for a vast range of penalty functionals. Various examples that indicate the
applicability of our approach will be discussed. We will illustrate in the
context of signal and image processing that the presented method constitutes a
locally adaptive reconstruction method.


  We present a coinductive framework for defining infinitary analogues of
equational reasoning and rewriting in a uniform way. We define the relation
=^infty, notion of infinitary equational reasoning, and ->^infty, the standard
notion of infinitary rewriting as follows:
  =^infty := nu R. ( <-_root + ->_root + lift(R) )^*
  ->^infty := mu R. nu S. ( ->_root + lift(R) )^* ; lift(S)
  where
  lift(R) := { (f(s_1,...,s_n), f(t_1,...,t_n)) | s_1 R t_1,...,s_n R t_n } +
id ,
  and where mu is the least fixed point operator and nu is the greatest fixed
point operator.
  The setup captures rewrite sequences of arbitrary ordinal length, but it has
neither the need for ordinals nor for metric convergence. This makes the
framework especially suitable for formalizations in theorem provers.


  This book chapter describes how spectral correlations in scattered light
fields can be utilized for high-precision time-of-flight sensing. The chapter
should serve as a gentle introduction and is intended for computational imaging
scientists and students new to the fascinating topic of synthetic wavelength
imaging. Technical details (such as detector or light source specifications)
will be largely omitted. Instead, the similarities between different methods
will be emphasized to "draw the bigger picture."


  Define $|n|$ to be the complexity of $n$, the smallest number of 1's needed
to write $n$ using an arbitrary combination of addition and multiplication.
John Selfridge showed that $|n|\ge 3\log_3 n$ for all $n$. Define the defect of
$n$, denoted $\delta(n)$, to be $|n|-3\log_3 n$; in this paper we present a
method for classifying all $n$ with $\delta(n)<r$ for a given $r$. From this,
we derive several consequences. We prove that $|2^m 3^k|=2m+3k$ for $m\le 21$
with $m$ and $k$ not both zero, and present a method that can, with more
computation, potentially prove the same for larger $m$. Furthermore, defining
$A_r(x)$ to be the number of $n$ with $\delta(n)<r$ and $n\le x$, we prove that
$A_r(x)=\Theta_r((\log x)^{\lfloor r \rfloor+1})$, allowing us to conclude that
the values of $|n|-3\log_3 n$ can be arbitrarily large.


  This work presents a study on the nonrelativistic quantum motion of a charged
particle in a rotating frame, considering the Aharonov-Bohm effect and a
uniform magnetic field. We derive the equation of motion and the corresponding
radial equation to describe the system. The Schr\"odinger equation with minimal
coupling incorporates rotation effects by substituting the momentum operator
with an effective four-potential. Additionally, a radial potential term,
dependent on the average radius of the ring, is introduced. The analysis is
restricted to motion in a two-dimensional plane, neglecting the degree of
freedom in the $z$-direction. By solving the radial equation, we determine the
eigenvalues and eigenfunctions, allowing for an explicit expression of the
energy. The probability distribution is analyzed for varying rotating parameter
values, revealing a shift of the distribution as the rotation changes,
resulting in a centrifugal effect and occupation of the ring's edges.
Furthermore, numerical analysis demonstrates the significant rotational effects
on energy levels and optical properties, including optical absorption and
refractive coefficients.


  Suppose a path $\alpha$ factors through an $\mathbb{R}$-tree $T$ as $\alpha=q
\circ p $. Let $r$ parameterize the unique geodesic in $T$ joining the
endpoints of $p$. Then we say that the path $\beta=q \circ r$ is obtained from
$\alpha$ by "geodesic $\mathbb{R}$-tree reduction." Essentially, $\beta$ is
obtained from $\alpha$ by deleting one-dimensional back-tracking. In this
paper, we show that any two homotopic paths are geodesic $\mathbb{R}$-tree
reductions of some single common path. Hence, the equivalence relation on paths
generated by geodesic $\mathbb{R}$-tree reduction is precisely path-homotopy.
The common path is explicitly constructed and is necessarily space-filling in
the image of a given path-homotopy.


  We consider the problem of classifying graphs using graph kernels. We define
a new graph kernel, called the generalized shortest path kernel, based on the
number and length of shortest paths between nodes. For our example
classification problem, we consider the task of classifying random graphs from
two well-known families, by the number of clusters they contain. We verify
empirically that the generalized shortest path kernel outperforms the original
shortest path kernel on a number of datasets. We give a theoretical analysis
for explaining our experimental results. In particular, we estimate
distributions of the expected feature vectors for the shortest path kernel and
the generalized shortest path kernel, and we show some evidence explaining why
our graph kernel outperforms the shortest path kernel for our graph
classification problem.


  In an era of rapid climate change and its adverse effects on food production,
technological intervention to monitor pollinator conservation is of paramount
importance for environmental monitoring and conservation for global food
security. The survival of the human species depends on the conservation of
pollinators. This article explores the use of Computer Vision and Object
Recognition to autonomously track and report bee behaviour from images. A novel
dataset of 9664 images containing bees is extracted from video streams and
annotated with bounding boxes. With training, validation and testing sets
(6722, 1915, and 997 images, respectively), the results of the COCO-based YOLO
model fine-tuning approaches show that YOLOv5m is the most effective approach
in terms of recognition accuracy. However, YOLOv5s was shown to be the most
optimal for real-time bee detection with an average processing and inference
time of 5.1ms per video frame at the cost of slightly lower ability. The
trained model is then packaged within an explainable AI interface, which
converts detection events into timestamped reports and charts, with the aim of
facilitating use by non-technical users such as expert stakeholders from the
apiculture industry towards informing responsible consumption and production.


  Given a finite group $G$, the commuting graph of $G$ is the simple graph
whose vertex set is $G$, and two distinct vertices are adjacent if they
commute. In this paper, we classify all finite groups whose commuting graph is
split and threshold. We also investigate the structure of a group whose
commuting graph is either a cograph or a chordal graph, and determine all
non-abelian finite simple groups whose commuting graph is a cograph. The
results partly answer a question by Peter J. Cameron established in 2022 in his
survey paper on graphs defined on groups.


  A recurring motif in gene regulatory networks is transcription factors (TFs)
that regulate each other, and then bind to overlapping sites on DNA, where they
interact and synergistically control transcription of a target gene. Here, we
suggest that this motif maximizes information flow in a noisy network. Gene
expression is an inherently noisy process due to thermal fluctuations and the
small number of molecules involved. A consequence of multiple TFs interacting
at overlapping binding-sites is that their binding noise becomes correlated.
Using concepts from information theory, we show that in general a signaling
pathway transmits more information if 1) noise of one input is correlated with
that of the other, 2) input signals are not chosen independently. In the case
of TFs, the latter criterion hints at up-stream cross-regulation. We
demonstrate these ideas for competing TFs and feed-forward gene regulatory
modules, and discuss generalizations to other signaling pathways. Our results
challenge the conventional approach of treating biological noise as
uncorrelated fluctuations, and present a systematic method for understanding TF
cross-regulation networks either from direct measurements of binding noise, or
bioinformatic analysis of overlapping binding-sites.


  We show that the automorphisms of the flag space associated with a
3-dimensional projective space can be characterized as bijections preserving a
certain binary relation on the set of flags in both directions. From this we
derive that there are no other automorphisms of the flag space than those
coming from collineations and dualities of the underlying projective space.
Further, for a commutative ground field, we discuss the corresponding flag
variety and characterize its group of automorphic collineations.


  Aumann's celebrated theorem says that a group of agents who once shared a
common prior probability distribution cannot assign different posteriors to a
given proposition, should these agents have common knowledge about their
posteriors. In other words, rational agents cannot agree to disagree. Aumann's
agreement theorem was one of the first attempts to formalise and explore the
role played by common knowledge in decision theory. Recently, we have seen a
resurfacing of the debate around possible (quantum) extensions of Aumann's
results. This paper contributes to this discussion. First, as expected, we
argue that agreeing to disagree is impossible in quantum theory. Secondly, and
based on the quantum argument, we show that agreeing to disagree is also
forbidden in any generalised probability theory.


  Handling multimodality that commonly arises from complicated statistical
models remains a challenge. Current Markov chain Monte Carlo (MCMC) methodology
tackling this subject is based on an ensemble of chains targeting a product of
power-tempered distributions. Despite the theoretical validity of such methods,
practical implementations typically suffer from bad mixing and slow convergence
due to the high-computation cost involved. In this work we study novel
extensions of the t-walk algorithm, an existing MCMC method that is inexpensive
and invariant to affine transformations of the state space, for dealing with
multimodal distributions. We acknowledge that the effectiveness of the new
method will be problem dependent and might struggle in complex scenarios; for
such cases we propose a post-processing technique based on pseudo-marginal
theory for combining isolated samples.


  Fulling-Davies-Unruh effect contains great amount of theoretical importance
in various branches of physics. Requirement of very high acceleration hinders
its experimental evidence. We propose a novel model to capture this effect
experimentally through measuring the Pancharatnam-Berry phase (PBP) of the
accelerated quantum system. We find that allowing the qubit's motion along one
of the parallel directions of two parallel mirrors and by keeping it in between
them, PBP can be greatly enhanced. Our investigation shows that for the current
measurable PBP ($\sim 10^{-6}$ rad), energy gap $\sim1$ GHz of the qubit,
distance between two mirrors $L\sim150$ (or $300)\,m$ and detector's position
$z_0 \sim3.3\,m$ the required acceleration of the qubit can be as low as $a\sim
10^9~ m/s^2$. This value is potentially very achievable within the current
technology and thereby providing a very close to realistic model for
experimentally verify the aforesaid quantum phenomenon.


  A new solution to the requirement of two-loop finiteness of the soft
supersymmetry breaking terms (SSB) parameters is found in Finite-Gauge-Yukawa
unified theories. The new solution has the form of a sum rule for the relevant
scalar masses, relaxing the universality required by the previously known
solution, which leads to models with unpleasant phenomenological consequences.
Using the sum rule we investigate two Finite-Gauge-Yukawa unified models and we
determine their spectrum in terms of few parameters. Some characteristic
features of the models are that a) the old agreement of the top quark mass
prediction with the measured value remains unchanged, b) the lightest Higgs
mass is predicted around 120 GeV, c) the s-spectrum starts above 200 GeV.


  Computer-assisted reading and analysis of text has various applications in
the humanities and social sciences. The increasing size of many electronic text
archives has the advantage of a more complete analysis but the disadvantage of
taking longer to obtain results. On-Line Analytical Processing is a method used
to store and quickly analyze multidimensional data. By storing text analysis
information in an OLAP system, a user can obtain solutions to inquiries in a
matter of seconds as opposed to minutes, hours, or even days. This analysis is
user-driven allowing various users the freedom to pursue their own direction of
research.


  We present the first investigation on the effect of highly charged ion
bombardment on a manganese arsenide thin film. The MnAs films, 150 nm thick,
are irradiated with 90 keV Ne$^{9+}$ ions with a dose varying from
$1.6\times10^{12}$ to $1.6\times10^{15}$ ions/cm$^2$. The structural and
magnetic properties of the film after irradiation are investigated using
different techniques, namely, X-ray diffraction, magneto-optic Kerr effect and
magnetic force microscope. Preliminary results are presented. From the study of
the lattice spacing, we measure a change on the film structure that depends on
the received dose, similarly to previous studies with other materials.
Investigations on the surface show a strong modification of its magnetic
properties.


  Comparing and aligning large datasets is a pervasive problem occurring across
many different knowledge domains. We introduce and study MREC, a recursive
decomposition algorithm for computing matchings between data sets. The basic
idea is to partition the data, match the partitions, and then recursively match
the points within each pair of identified partitions. The matching itself is
done using black box matching procedures that are too expensive to run on the
entire data set. Using an absolute measure of the quality of a matching, the
framework supports optimization over parameters including partitioning
procedures and matching algorithms. By design, MREC can be applied to extremely
large data sets. We analyze the procedure to describe when we can expect it to
work well and demonstrate its flexibility and power by applying it to a number
of alignment problems arising in the analysis of single cell molecular data.


  By means of a relativistic effective potential, we have analytically
researched competition between the quark-antiquark condensates $<\bar{q}q>$ and
the diquark condensates $<qq>$ in vacuum in ground state of a two-flavor
Nambu-Jona-Lasinio (NJL) model and obtained the $G_S-H_S$ phase diagram, where
$G_S$ and $H_S$ are the respective four-fermion coupling constants in scalar
quark-antiquark channel and scalar color anti-triplet diquark channel. The
results show that, in the chiral limit, there is only the pure $<\bar{q}q>$
phase when $G_S/H_S>2/3$, and as $G_S/H_S$ decreases to $2/3>G_S/H_S\geq 0$ one
will first have a coexistence phase of the condensates $<\bar{q}q>$ and $<qq>$
and then a pure $<qq>$ phase. In non-zero bare quark mass case, the critical
value of $G_S/H_S$ at which the pure $<\bar{q}q>$ phase will transfer to the
coexistence phase of the condensates $<\bar{q}q>$ and $<qq>$ will be less than
2/3. Our theoretical results, combined with present phenomenological fact that
there is no diquark condensates in the vacuum of QCD, will also impose a real
restriction to any given two-flavor NJL model which is intended to simulate
QCD, i.e. in such model the resulting smallest ratio $G_S/H_S$ after the Fierz
transformations in the Hartree approximation must be larger than 2/3. A few
phenomenological QCD-like NJL models are checked and analyzed.


  We summarize the original formulation of the free energy principle, and
highlight some technical issues. We discuss how these issues affect related
results involving generalised coordinates and, where appropriate, mention
consequences for and reveal, up to now unacknowledged, differences to newer
formulations of the free energy principle. In particular, we reveal that
various definitions of the "Markov blanket" proposed in different works are not
equivalent. We show that crucial steps in the free energy argument which
involve rewriting the equations of motion of systems with Markov blankets, are
not generally correct without additional (previously unstated) assumptions. We
prove by counterexample that the original free energy lemma, when taken at face
value, is wrong. We show further that this free energy lemma, when it does
hold, implies equality of variational density and ergodic conditional density.
The interpretation in terms of Bayesian inference hinges on this point, and we
hence conclude that it is not sufficiently justified. Additionally, we
highlight that the variational densities presented in newer formulations of the
free energy principle and lemma are parameterised by different variables than
in older works, leading to a substantially different interpretation of the
theory. Note that we only highlight some specific problems in the discussed
publications. These problems do not rule out conclusively that the general
ideas behind the free energy principle are worth pursuing.


  Time series prediction can be generalized as a process that extracts useful
information from historical records and then determines future values. Learning
long-range dependencies that are embedded in time series is often an obstacle
for most algorithms, whereas Long Short-Term Memory (LSTM) solutions, as a
specific kind of scheme in deep learning, promise to effectively overcome the
problem. In this article, we first give a brief introduction to the structure
and forward propagation mechanism of the LSTM model. Then, aiming at reducing
the considerable computing cost of LSTM, we put forward the Random Connectivity
LSTM (RCLSTM) model and test it by predicting traffic and user mobility in
telecommunication networks. Compared to LSTM, RCLSTM is formed via stochastic
connectivity between neurons, which achieves a significant breakthrough in the
architecture formation of neural networks. In this way, the RCLSTM model
exhibits a certain level of sparsity, which leads to an appealing decrease in
the computational complexity and makes the RCLSTM model become more applicable
in latency-stringent application scenarios. In the field of telecommunication
networks, the prediction of traffic series and mobility traces could directly
benefit from this improvement as we further demonstrate that the prediction
accuracy of RCLSTM is comparable to that of the conventional LSTM no matter how
we change the number of training samples or the length of input sequences.


  Elliptic flow ($v_2$) and hexadecupole flow ($v_4$) of light clusters have
been studied in details for 25 MeV/nucleon $^{86}$Kr + $^{124}$Sn at large
impact parameters by Quantum Molecular Dynamics model with different potential
parameters. Four parameter sets which include soft or hard equation of state
(EOS) with/without symmetry energy term are used. Both number-of-nucleon ($A$)
scaling of the elliptic flow versus transverse momentum ($p_t$) and the scaling
of $v_4/A^{2}$ versus $(p_t/A)^2$ have been demonstrated for the light clusters
in all above calculation conditions. It was also found that the ratio of
$v_4/{v_2}^2$ keeps a constant of 1/2 which is independent of $p_t$ for all the
light fragments. By comparisons among different combinations of EOS and
symmetry potential term, the results show that the above scaling behaviors are
solid which do not depend the details of potential, while the strength of flows
is sensitive to EOS and symmetry potential term.


  Over the past century, rooted in the theory of general relativity, cosmology
has developed a very successful physical model of the universe: the {\em
big-bang model}. Its construction followed different stages to incorporate
nuclear processes, the understanding of the matter present in the universe, a
description of the early universe and of the large scale structure. This model
has been confronted to a variety of observations that allow one to reconstruct
its expansion history, its thermal history and the structuration of matter.
Hence, what we refer to as the big-bang model today is radically different from
what one may have had in mind a century ago. This construction changed our
vision of the universe, both on observable scales and for the universe as a
whole. It offers in particular physical models for the origins of the atomic
nuclei, of matter and of the large scale structure. This text summarizes the
main steps of the construction of the model, linking its main predictions to
the observations that back them up. It also discusses its weaknesses, the open
questions and problems, among which the need for a dark sector including dark
matter and dark energy.


  In this paper, novel methods are presented to measure the optical properties
of muon detectors (MDs) in the Large High-Altitude Air Shower Observatory
(LHAASO), which can also be used by other experiments. Each MD consists of a
cylindrical water Cherenkov detector, with a Tyvek liner containing pure water,
and a photomultiplier tube (PMT) mounted on the top. The time distribution of
the photons collected by the PMT in the water Cherenkov detector have an
approximately exponential distribution, and their decay factor is determined by
the photon absorption length in the water, the reflectivity of the inner Tyvek
surface, the mean reflecting step length of photons reflected by the inner
surface, and the ratio of reflectional Tyvek area to the total inner surface
area. By considering the principles of photon propagation in the water
Cherenkov detector, we have developed novel methods to measure the water
absorption length, the Tyvek reflectivity, and the mean step length of photons.
The step length of photons can be determined by measuring the time distribution
of the reflected photons hitting the PMT after multiple photons with single
wavelength are generated in the tank, with slightly different ratios of the
inner Tyvek to the total inner area. The water absorption length and Tyvek
reflectivity can be measured simultaneously by the PMT by changing the height
of the water, while the step length and Tyvek reflectivity in air can also be
measured simultaneously. The proposed novel methods are supported by deduction
of formulae and verified by GEANT4 simulations and the prototype experiment.


  Automatic evaluation of essay (AES) and also called automatic essay scoring
has become a severe problem due to the rise of online learning and evaluation
platforms such as Coursera, Udemy, Khan academy, and so on. Researchers have
recently proposed many techniques for automatic evaluation. However, many of
these techniques use hand-crafted features and thus are limited from the
feature representation point of view. Deep learning has emerged as a new
paradigm in machine learning which can exploit the vast data and identify the
features useful for essay evaluation. To this end, we propose a novel
architecture based on recurrent networks (RNN) and convolution neural network
(CNN). In the proposed architecture, the multichannel convolutional layer
learns and captures the contextual features of the word n-gram from the word
embedding vectors and the essential semantic concepts to form the feature
vector at essay level using max-pooling operation. A variant of RNN called
Bi-gated recurrent unit (BGRU) is used to access both previous and subsequent
contextual representations. The experiment was carried out on eight data sets
available on Kaggle for the task of AES. The experimental results show that our
proposed system achieves significantly higher grading accuracy than other deep
learning-based AES systems and also other state-of-the-art AES systems.


  We study the integrable and supersymmetric massive $\hat\phi_{(1,3)}$
deformation of the tricritical Ising model in the presence of a boundary. We
use constraints from supersymmetry in order to compute the exact boundary
$S$-matrices, which turn out to depend explicitly on the topological charge of
the supersymmetry algebra. We also solve the general boundary Yang-Baxter
equation and show that in appropriate limits the general reflection matrices go
over the supersymmetry preserving solutions. Finally, we briefly discuss the
possible connection between our reflection matrices and boundary perturbations
within the framework of perturbed boundary conformal field theory.


  We introduce GCIS, a grammar compression algorithm based on the induced
suffix sorting algorithm SAIS, introduced by Nong et al. in 2009. Our solution
builds on the factorization performed by SAIS during suffix sorting. We
construct a context-free grammar on the input string which can be further
reduced into a shorter string by substituting each substring by its
correspondent factor. The resulting grammar is encoded by exploring some
redundancies, such as common prefixes between suffix rules, which are sorted
according to SAIS framework. When compared to well-known compression tools such
as Re-Pair and 7-zip, our algorithm is competitive and very effective at
handling repetitive string regarding compression ratio, compression and
decompression running time.


  The open-source multiphysics suite SU2 features discrete adjoints by means of
operator overloading automatic differentiation (AD). While both primal and
discrete adjoint solvers support MPI parallelism, hybrid parallelism using both
MPI and OpenMP has only been introduced for the primal solvers so far. In this
work, we enable hybrid parallel discrete adjoint solvers. Coupling SU2 with
OpDiLib, an add-on for operator overloading AD tools that extends AD to OpenMP
parallelism, marks a key step in this endeavour. We identify the affected parts
of SU2's advanced AD workflow and discuss the required changes and their
tradeoffs. Detailed performance studies compare MPI parallel and hybrid
parallel discrete adjoints in terms of memory and runtime and unveil key
performance characteristics. We showcase the effectiveness of performance
optimizations and highlight perspectives for future improvements. At the same
time, this study demonstrates the applicability of OpDiLib in a large code base
and its scalability on large test cases, providing valuable insights for future
applications both within and beyond SU2.


  In this paper, we establish a Liouville type theorem for the homogeneous dual
fractional parabolic equation \begin{equation}
  \partial^\alpha_t u(x,t)+(-\Delta)^s u(x,t) = 0\ \ \mbox{in}\ \
\mathbb{R}^n\times\mathbb{R} . \end{equation} where $0<\alpha,s<1$. Under an
asymptotic assumption
$$\liminf_{|x|\rightarrow\infty}\frac{u(x,t)}{|x|^\gamma}\geq 0 \; ( \mbox{or}
\; \leq 0) \,\,\mbox{for some} \;0\leq\gamma\leq 1, $$ in the case
$\frac{1}{2}<s < 1$, we prove that all solutions in the sense of distributions
of above equation must be constant by employing a method of Fourier analysis.
Our result includes the previous Liouville theorems on harmonic functions
\cite{ABR} and on $s$-harmonic functions \cite{CDL} as special cases and it is
still novel even restricted to one-sided Marchaud fractional equations, and our
methods can be applied to a variety of dual nonlocal parabolic problems.
  In the process of deriving our main result, through very delicate
calculations, we obtain an optimal estimate on the decay rate of $\left[D_{\rm
right}^\alpha+(-\Delta)^s\right] \varphi(x,t)$ for functions in Schwartz space.
This sharp estimate plays a crucial role in defining the solution in the sense
of distributions and will become a useful tool in the analysis of this family
of equations.


  We examine the problem of allocating a given total storage budget in a
distributed storage system for maximum reliability. A source has a single data
object that is to be coded and stored over a set of storage nodes; it is
allowed to store any amount of coded data in each node, as long as the total
amount of storage used does not exceed the given budget. A data collector
subsequently attempts to recover the original data object by accessing only the
data stored in a random subset of the nodes. By using an appropriate code,
successful recovery can be achieved whenever the total amount of data accessed
is at least the size of the original data object. The goal is to find an
optimal storage allocation that maximizes the probability of successful
recovery. This optimization problem is challenging in general because of its
combinatorial nature, despite its simple formulation. We study several
variations of the problem, assuming different allocation models and access
models. The optimal allocation and the optimal symmetric allocation (in which
all nonempty nodes store the same amount of data) are determined for a variety
of cases. Our results indicate that the optimal allocations often have
nonintuitive structure and are difficult to specify. We also show that
depending on the circumstances, coding may or may not be beneficial for
reliable storage.


  We study the performance of generalized polar (GP) codes when they are used
for coding schemes involving erasure. GP codes are a family of codes which
contains, among others, the standard polar codes of Ar{\i}kan and Reed-Muller
codes. We derive a closed formula for the zero-undetected-error capacity
$I_0^{GP}(W)$ of GP codes for a given binary memoryless symmetric (BMS) channel
$W$ under the low complexity successive cancellation decoder with erasure. We
show that for every $R<I_0^{GP}(W)$, there exists a generalized polar code of
blocklength $N$ and of rate at least $R$ where the undetected-error probability
is zero and the erasure probability is less than
$2^{-N^{\frac{1}{2}-\epsilon}}$. On the other hand, for any GP code of rate
$I_0^{GP}(W)<R<I(W)$ and blocklength $N$, the undetected error probability
cannot be made less than $2^{-N^{\frac{1}{2}+\epsilon}}$ unless the erasure
probability is close to $1$.


  We studied the B meson decays $B\to J/\Psi K_1(1270,1400)$ in the pQCD
approach beyond the leading order. With the vertex corrections and the NLO
Wilson coefficients included, the branching ratios of the considered decays are
$Br(B^+\to J/\Psi K_1(1270)^+)=1.76^{+0.65}_{-0.69}\times10^{-3}, Br(B^+\to
J/\Psi K_1(1400)^+)=7.03^{+2.70}_{-2.52}\times10^{-4}$, and $Br(B^0\to J/\Psi
K_1(1270)^0)=(1.63^{+0.60}_{-0.64})\times10^{-3}$ with the mixing angle
$\theta_{K_1}=33^\circ$, which can agree well with the data or the present
experimental upper limit within errors. So we support the opinion that
$\theta_{K_1}\sim33^\circ$ is much more favored than $58^{\circ}$. Furthermore,
we also give the predictions for the polarization fractions, direct CP
violations from the different polarization components, the relative phase
angles for the considered decays with the mixing angle $\theta_{K_1}=33^\circ$
and $58^\circ$, respectively. The direct CP violations of the two charged
decays $B^+\to J/\Psi K_1(1270,1400)^+$ are very small $(10^{-4}\sim10^{-5})$,
because there is no weak phase until up to $\mathcal{O}(\lambda^4)$ with the
Wolfenstein parameter $\lambda=0.22537$. These results can be tested at the
running LHCb and forthcoming Super-B experiments.


  There is a one-to-one correspondence between natural numbers and rooted
trees; the number is called the Matula number of the rooted tree. We show how a
large number of properties of trees can be obtained directly from the
corresponding Matula number.


  We consider a homogeneous heteronuclear Bose mixture with contact
interactions at the mean-field collapse, i.e. with interspecies attraction
equal to the mean geometrical intraspecies repulsion. We show that the
Lee-Huang-Yang (LHY) energy functional is accurately approximated by an
expression that has the same functional form as in the homonuclear case. The
approximated energy functional is characterized by two exponents, which can be
treated as fitting parameters. We demonstrate that the values of these
parameters which preserve the invariance under permutation of the two atomic
species are exactly those of the homonuclear case. Deviations from the exact
expression of LHY energy functional are discussed quantitatively and a specific
application is described.


  In this note we prove that finitely generated virtually free groups are
stable with respect to a normalized $p$-Schatten norm for $1\leq p < \infty$.
In particular, this implies that virtually free groups are Hilbert-Schmidt
stable.


  We model the large scale late time universe as a Lambda-CDM cosmology driven
by cosmological constant and perfect dust fluid. Our aim is to find new
solutions in the matter and Lambda epoch consistent with inflationary initial
conditions, namely that to the far past in the matter era the cosmology tends
to a flat FLRW solution. We identify the moduli degrees of freedom that
parametrize the flat Lambda-dust FLRW solution and then promote these moduli to
slowly varying functions of the spatial coordinates and show how to solve the
Einstein equations in a comoving gradient expansion, controlled by the
cosmological constant length scale. Our initial conditions ensure that the
approximation remains under control to the far past of the matter era, and to
the far future of Lambda domination. The solution is fully non-perturbative in
the amplitude of the metric deformation, and we explicitly construct it to
fourth order in derivatives. A general Lambda-dust universe dominated by Lambda
in the future is characterized by a 3-metric and a stress tensor (with positive
trace) defined on the future conformal boundary. The new cosmologies with
inflationary initial conditions are characterized only by the boundary
3-metric, the stress tensor being locally determined entirely in terms of that
metric.


  The problem of matching different regions of spacetime in order to construct
inhomogeneous cosmological models is investigated in the context of Lagrangian
theories of gravity constructed from general analytic functions f(R), and from
non-analytic theories with f(R)=R^n. In all of the cases studied, we find that
it is impossible to satisfy the required junction conditions without the
large-scale behaviour reducing to that expected from Einstein's equations with
a cosmological constant. For theories with analytic f(R) this suggests that the
usual treatment of weak-field systems as perturbations about Minkowski space
may not be compatible with late-time acceleration driven by anything other than
a constant term of the form f(0), which acts like a cosmological constant. In
the absence of Minkowski space as a suitable background for weak-field systems,
one must then choose and justify some other solution to perform perturbative
analyses around. For theories with f(R)=R^n we find that no known spherically
symmetric vacuum solutions can be matched to an expanding FLRW background. This
includes the absence of any Einstein-Straus-like embeddings of the
Schwarzschild exterior solution in FLRW spacetimes.


  We present a hyperconcentration scheme for nonlocal $N$-photon hyperentangled
Greenberger-Horne-Zeilinger states. The maximally hyperentangled state, in
which $N$ particles are entangled simultaneously in the polarization and the
spatial mode, can be obtained with a certain probability from two partially
hyperentangled states. The hyperconcentration scheme is based on one
polarization parity check measurement, one spatial mode parity check
measurement and N-2 single-photon two-qubit measurements. The concentration
only requires linear optical elements, which makes it feasible and practical
with current technology.


  We consider a coloring problem on dynamic, one-dimensional point sets: points
appearing and disappearing on a line at given times. We wish to color them with
k colors so that at any time, any sequence of p(k) consecutive points, for some
function p, contains at least one point of each color.
  We prove that no such function p(k) exists in general. However, in the
restricted case in which points appear gradually, but never disappear, we give
a coloring algorithm guaranteeing the property at any time with p(k)=3k-2. This
can be interpreted as coloring point sets in R^2 with k colors such that any
bottomless rectangle containing at least 3k-2 points contains at least one
point of each color. Here a bottomless rectangle is an axis-aligned rectangle
whose bottom edge is below the lowest point of the set. For this problem, we
also prove a lower bound p(k)>ck, where c>1.67. Hence for every k there exists
a point set, every k-coloring of which is such that there exists a bottomless
rectangle containing ck points and missing at least one of the k colors.
  Chen et al. (2009) proved that no such function $p(k)$ exists in the case of
general axis-aligned rectangles. Our result also complements recent results
from Keszegh and Palvolgyi on cover-decomposability of octants (2011, 2012).


  Schemes for optical-state truncation of two cavity modes are analysed. The
systems, referred to as the nonlinear quantum scissors devices, comprise two
coupled nonlinear oscillators (Kerr nonlinear coupler) with one or two of them
pumped by external classical fields. It is shown that the quantum evolution of
the pumped couplers can be closed in a two-qubit Hilbert space spanned by
vacuum and single-photon states only. Thus, the pumped couplers can behave as a
two-qubit system. Analysis of time evolution of the quantum entanglement shows
that Bell states can be generated. A possible implementation of the couplers is
suggested in a pumped double-ring cavity with resonantly enhanced Kerr
nonlinearities in an electromagnetically-induced transparency scheme. The
fragility of the generated states and their entanglement due to the standard
dissipation and phase damping are discussed by numerically solving two types of
master equations.