  We analyse special classes of biorthogonal sets of vectors in Hilbert and in
Krein spaces, and their relations with $\mathcal{G}$- quasi bases. We also
discuss their relevance in some concrete quantum mechanical system driven by
manifestly non self-adjoint Hamiltonians.


  A select collection of pseudorandom number generators is applied to a Monte
Carlo study of the two dimensional square site percolation model. A generator
suitable for high precision calculations is identified from an application
specific test of randomness. After extended computation and analysis, an
ostensibly reliable value of pc = 0.59274598(4) is obtained for the percolation
threshold.


  The semileptonic $B\to \pi l^+ \nu_l$ decay is studied starting from a simple
quark model which includes the influence of the $B^*$ pole.
  To extend the predictions of a nonrelativistic constituent quark model from
its region of applicability near $q^2_{\rm max}=(m_B-m_\pi)^2$ to all $q^2$
values accessible in the physical decay, we use a novel multiply-subtracted
Omn\`es dispersion relation, which considerably diminishes the form factor
dependence on the elastic $\pi B \to \pi B$ scattering amplitudes at high
energies. By comparison to the experimental branching fraction we extract
$|V_{ub}| = 0.0034 \pm 0.0003 ({\rm exp}) \pm 0.0007 ({\rm theory})$. To
further test our framework, we also study $D\to \pi$ and $D\to K$ decays and
find excellent results $\frac{f^+_\pi(0)}{f^+_K(0)} = 0.80 \pm 0.03, \quad
\frac{{\cal B}(D^0\to \pi^- e^+ \nu_e)}{{\cal B}(D^0\to K^- e^+ \nu_e)}= 0.079
\pm 0.008$. In particular for the $D\to \pi$ case, we reproduce, with high
accuracy, the three-flavor lattice QCD results recently obtained by the
Fermilab-MILC-HPQCD Collaboration. While for the $D\to K$ case, we successfully
describe the data for $f^+(q^2)/f^+(0)$ recently measured by the FOCUS
Collaboration.


  For each $\alpha \in (0,1)$, $A_\alpha$ denotes the universal $C^*$-algebra
generated by two unitaries $u$ and $v$, which satisfy the commutation relation
$uv=\exp (2\pi i\alpha)vu$. We consider the order four automorphism $\sigma$ of
$A_\alpha$ defined by $\sigma (u)=v$, $\sigma (v)=u^{-1}$ and describe a method
for constructing projections in the fixed point algebra $A_\alpha^\sigma$,
using Rieffel's imprimitivity bimodules and Jacobi's theta functions. In the
case $\alpha =q^{-1}$, $q\in {\mathbf Z}$, $q\geq 2$, we give explicit formulae
for such projections and find a lower bound for the norm of the Harper operator
$u+u^* +v+v^*$.


  A central goal of both knowledge tracing and traditional assessment is to
quantify student knowledge and skills at a given point in time. Deep knowledge
tracing flexibly considers a student's response history but does not quantify
epistemic uncertainty, while IRT and CDM compute measurement error but only
consider responses to individual tests in isolation from a student's past
responses. Elo and BKT could bridge this divide, but the simplicity of the
underlying models limits information sharing across skills and imposes strong
inductive biases. To overcome these limitations, we introduce Dynamic LENS, a
modeling paradigm that combines the flexible uncertainty-preserving properties
of variational autoencoders with the principled information integration of
Bayesian state-space models. Dynamic LENS allows information from student
responses to be collected across time, while treating responses from the same
test as exchangeable observations generated by a shared latent state. It
represents student knowledge as Gaussian distributions in high-dimensional
space and combines estimates both within tests and across time using Bayesian
updating. We show that Dynamic LENS has similar predictive performance to
competing models, while preserving the epistemic uncertainty - the deep
learning analogue to measurement error - that DKT models lack. This approach
provides a conceptual bridge across an important divide between models designed
for formative practice and summative assessment.


  We present the analysis of a peculiar W~Virginis (pWVir) type-II Cepheid,
OGLE-LMC-T2CEP-211 ($P_{puls}=9.393\,d$), in a double-lined binary system
($P_{orb}=242\,d$), which shed light on virtually unknown evolutionary status
and structure of pWVir stars. The dynamical mass of the Cepheid (first ever for
a type-II Cepheid) is $0.64\pm{}0.02\,M_\odot$ and the radius
$R=25.1\pm{}0.3\,R_\odot$. The companion is a massive ($5.67\,M_\odot$)
main-sequence star obscured by a disk. Such configuration suggests a mass
transfer in the system history. We found that originally the system
($P_{orb}^{init}=12\,d$) was composed of $3.5$ and $2.8\,M_\odot$ stars, with
the current Cepheid being more massive. The system age is now $\sim{}$200 My,
and the Cepheid is almost completely stripped of hydrogen, with helium mass of
$\sim{}92\%$ of the total mass. It finished transferring the mass 2.5 My ago
and is evolving towards lower temperatures passing through the instability
strip. Comparison with observations indicate a reasonable
$2.7\cdot{}10^{-8}\,M_\odot/y$ mass loss from the Cepheid. The companion is
most probably a Be main-sequence star with $T=22000\,K$ and $R=2.5\,R_\odot$.
Our results yield a good agreement with a pulsation theory model for a
hydrogen-deficient pulsator, confirming the described evolutionary scenario. We
detected a two-ring disk ($R_{disk}\sim\,116\,R_{\odot}$) and a shell
($R_{shell}\sim\,9\,R_{\odot}$) around the companion, that is probably a
combination of the matter from the past mass transfer, the mass being lost by
the Cepheid due to wind and pulsations, and a decretion disk around a rapidly
rotating secondary. Our study together with observational properties of pWVir
stars suggests that their majority are products of a similar binary evolution
interaction.


  Artificial neural nets can represent and classify many types of data but are
often tailored to particular applications -- e.g., for "fair" or "hierarchical"
classification. Once an architecture has been selected, it is often difficult
for humans to adjust models for a new task; for example, a hierarchical
classifier cannot be easily transformed into a fair classifier that shields a
protected field. Our contribution in this work is a new neural network
architecture, the concept subspace network (CSN), which generalizes existing
specialized classifiers to produce a unified model capable of learning a
spectrum of multi-concept relationships. We demonstrate that CSNs reproduce
state-of-the-art results in fair classification when enforcing concept
independence, may be transformed into hierarchical classifiers, or even
reconcile fairness and hierarchy within a single classifier. The CSN is
inspired by existing prototype-based classifiers that promote interpretability.


  The correlation between radio spectral index and redshift has long been used
to identify high redshift radio galaxies, but its cause is unknown. Traditional
explanations invoke either $(i)$ intrinsic relations between spectral index and
power, $(ii)$ environmental differences at high redshift, or $(iii)$ higher
inverse Compton losses due to the increased photon energy density of the cosmic
microwave background. In this paper we investigate whether the increased
inverse Compton losses alone can cause the observed spectral index - redshift
correlation by using spectral modelling of nearby radio galaxies to simulate
high redshift equivalents. We then apply selection effects and directly compare
the simulated radio galaxy sample with an observed sample with sufficient
redshift coverage. We find excellent agreement between the two, implying that
inverse Compton losses and selection effects alone can largely reproduce the
observed spectral index - redshift correlation.


  G290.1-0.8 (MSH 11-61A) is a supernova remnant (SNR) whose X-ray morphology
is centrally bright. However, unlike the class of X-ray composite SNRs whose
centers are dominated by nonthermal emission, presumably driven by a central
pulsar, we show that the X-ray emission from G290.1-0.8 is thermal in nature,
placing the remnant in an emerging class which includes such remnants as W44,
W28, 3C391, and others. The evolutionary sequence which leads to such X-ray
properties is not well understood. Here we investigate two scenarios for such
emission: evolution in a cloudy interstellar medium, and early-stage evolution
of a remnant into the radiative phase, including the effects of thermal
conduction. We construct models for these scenarios in an attempt to reproduce
the observed center-filled X-ray properties of G290.1-0.8, and we derive the
associated age, energy, and ambient density conditions implied by the models.
We find that for reasonable values of the explosion energy, the remnant age is
of order (1 - 2) x 10^{4} yr. This places a fairly strong constraint on any
association between G290.1-0.8 and PSR J1105-610, which would require an
anomalously large velocity for the pulsar.


  Safe motion planning for robotic systems in dynamic environments is
nontrivial in the presence of uncertain obstacles, where estimation of obstacle
uncertainties is crucial in predicting future motions of dynamic obstacles. The
worst-case characterization gives a conservative uncertainty prediction and may
result in infeasible motion planning for the ego robotic system. In this paper,
an efficient, robust, and safe motion-planing algorithm is developed by
learning the obstacle uncertainties online. More specifically, the unknown yet
intended control set of obstacles is efficiently computed by solving a linear
programming problem. The learned control set is used to compute forward
reachable sets of obstacles that are less conservative than the worst-case
prediction. Based on the forward prediction, a robust model predictive
controller is designed to compute a safe reference trajectory for the ego
robotic system that remains outside the reachable sets of obstacles over the
prediction horizon. The method is applied to a car-like mobile robot in both
simulations and hardware experiments to demonstrate its effectiveness.


  We introduce the weighted Yamabe flow $\frac{\partial g}{\partial
t}=(r^m_{\phi}-R^m_{\phi})g$, $\frac{\partial \phi}{\partial
t}=\frac{m}{2}(R^m_{\phi}-r^m_{\phi})$ on a smooth metric measure space $(M^n,
g, e^{-\phi}{\rm dvol}_g, m)$, where $R^m_{\phi}$ denotes the associated
weighted scalar curvature, and $r^m_{\phi}$ denotes the mean value of the
weighted scalar curvature. We prove long-time existence and convergence of the
weighted Yamabe flow if the dimension $n$ satisfies $n\geqslant 3$.


  Recently, ChatGPT, along with DALL-E-2 and Codex,has been gaining significant
attention from society. As a result, many individuals have become interested in
related resources and are seeking to uncover the background and secrets behind
its impressive performance. In fact, ChatGPT and other Generative AI (GAI)
techniques belong to the category of Artificial Intelligence Generated Content
(AIGC), which involves the creation of digital content, such as images, music,
and natural language, through AI models. The goal of AIGC is to make the
content creation process more efficient and accessible, allowing for the
production of high-quality content at a faster pace. AIGC is achieved by
extracting and understanding intent information from instructions provided by
human, and generating the content according to its knowledge and the intent
information. In recent years, large-scale models have become increasingly
important in AIGC as they provide better intent extraction and thus, improved
generation results. With the growth of data and the size of the models, the
distribution that the model can learn becomes more comprehensive and closer to
reality, leading to more realistic and high-quality content generation. This
survey provides a comprehensive review on the history of generative models, and
basic components, recent advances in AIGC from unimodal interaction and
multimodal interaction. From the perspective of unimodality, we introduce the
generation tasks and relative models of text and image. From the perspective of
multimodality, we introduce the cross-application between the modalities
mentioned above. Finally, we discuss the existing open problems and future
challenges in AIGC.


  Given an undirected $n$-vertex planar graph $G=(V,E,\omega)$ with
non-negative edge weight function $\omega:E\rightarrow \mathbb R$ and given an
assigned label to each vertex, a vertex-labeled distance oracle is a data
structure which for any query consisting of a vertex $u$ and a label $\lambda$
reports the shortest path distance from $u$ to the nearest vertex with label
$\lambda$. We show that if there is a distance oracle for undirected $n$-vertex
planar graphs with non-negative edge weights using $s(n)$ space and with query
time $q(n)$, then there is a vertex-labeled distance oracle with
$\tilde{O}(s(n))$ space and $\tilde{O}(q(n))$ query time. Using the
state-of-the-art distance oracle of Long and Pettie, our construction produces
a vertex-labeled distance oracle using $n^{1+o(1)}$ space and query time
$\tilde O(1)$ at one extreme, $\tilde O(n)$ space and $n^{o(1)}$ query time at
the other extreme, as well as such oracles for the full tradeoff between space
and query time obtained in their paper. This is the first non-trivial exact
vertex-labeled distance oracle for planar graphs and, to our knowledge, for any
interesting graph class other than trees.


  The Lipschitz constant of a network plays an important role in many
applications of deep learning, such as robustness certification and Wasserstein
Generative Adversarial Network. We introduce a semidefinite programming
hierarchy to estimate the global and local Lipschitz constant of a multiple
layer deep neural network. The novelty is to combine a polynomial lifting for
ReLU functions derivatives with a weak generalization of Putinar's positivity
certificate. This idea could also apply to other, nearly sparse, polynomial
optimization problems in machine learning. We empirically demonstrate that our
method provides a trade-off with respect to state of the art linear programming
approach, and in some cases we obtain better bounds in less time.


  In this paper, we present a two stage model for multi-hop question answering.
The first stage is a hierarchical graph network, which is used to reason over
multi-hop question and is capable to capture different levels of granularity
using the nature structure(i.e., paragraphs, questions, sentences and entities)
of documents. The reasoning process is convert to node classify task(i.e.,
paragraph nodes and sentences nodes). The second stage is a language model
fine-tuning task. In a word, stage one use graph neural network to select and
concatenate support sentences as one paragraph, and stage two find the answer
span in language model fine-tuning paradigm.


  Nuclear stellar clusters are common in the center of galaxies. We consider
the possibility that their progenitors assumed to be globular clusters may have
formed elsewhere, migrated to and assembled near their present location. The
main challenge for this scenario is whether globular clusters can withstand the
tidal field of their host galaxies. Our analysis suggests that provided the
mass-density distribution of background potential is relatively shallow, as in
some galaxies with relatively flat surface brightness profiles, the tidal field
near the center of galaxies may be shown to be able to compress rather than
disrupt a globular cluster at a distance from the center much smaller than the
conventionally defined `tidal disruption radius', $r_t$. To do so, we adopt a
previously constructed formalism and consider the secular evolution of star
clusters with a homogeneous mass density distribution. We analytically solve
the secular equations in the limit that the mass density of stars in the
galactic center approaches a uniform distribution. Our model indicates that a
star cluster could travel to distances much smaller than $r_t$ without
disruption, thus potentially contributing to the formation of the nuclear
cluster. However, appropriate numerical N-body simulations are needed to
confirm our analytic findings.


  Context. Massive-star formation triggered by the expansion of HII regions.
Aims. To understand if sequential star formation is taking place at the
periphery of the HII region Sh2-219. Methods. We present 12CO(2-1) line
observations of this region, obtained at the IRAM 30-m telescope (Pico Veleta,
Spain). Results. In the optical, Sh2-219 is spherically symmetric around its
exciting star; furthermore it is surrounded along three quarters of its
periphery by a ring of atomic hydrogen. This spherical symmetry breaks down at
infrared and millimetre wavelengths. A molecular cloud of about 2000\msol lies
at the southwestern border of Sh2-219, in the HI gap. Two molecular
condensations, elongated along the ionization front, probably result from the
interaction between the expanding HII region and the molecular cloud. In this
region of interaction there lies a cluster containing many highly reddened
stars, as well as a massive star exciting an ultracompact HII region. More
surprisingly, the brightest parts of the molecular cloud form a `chimney',
perpendicular to the ionization front. This chimney is closed at its south-west
extremity by H-alpha walls, thus forming a cavity. The whole structure is 7.5
pc long. A luminous H-alpha emission-line star, lying at one end of the chimney
near the ionization front, may be responsible for this structure. Confrontation
of the observations with models of HII region evolution shows that Sh2-219 is
probably 10^5 yr old. The age and origin of the near-IR cluster observed on the
border of Sh2-219 remain unknown.


  Severity of warming predicted by climate models depends on their Transient
Climate Response (TCR). Inter-model spread of TCR has persisted at ~100% of its
mean for decades. Existing observational constraints of TCR are based on
observed historical warming to historical forcing and their uncertainty spread
is just as wide, mainly due to forcing uncertainty, and especially that of
aerosols. Contrary, no aerosols are involved in solar-cycle forcing, providing
an independent, tighter, constraint. Here, we define a climate sensitivity
metric: time-dependent response regressed against time-dependent forcing,
allowing phenomena with dissimilar time variations, such as the solar cycle
with 11-year cyclic forcing, to be used to constrain TCR, which has a linear
time-dependent forcing. We find a theoretical linear relationship between the
two. The latest coupled atmosphere-ocean climate models obey the same linear
relationship statistically. The proposed observational constraint on TCR is
about 1/3 as narrow as existing constraints. The central estimate,
2.2$^\circ$C, is at the midpoint of the spread of the latest generation of
climate models, which are more sensitive than those of the previous
generations.


  Observations of soil moisture (SM) during excess and deficit monsoon seasons
between 2000 to 2021 present a unique opportunity to understand the soil water
dynamics (SWD) over core monsoon zone (CMZ) of India. This study aims to
analyse SWD by investigating the SM variability, SM memory (SMM), and the
coupling between the surface and subsurface SM levels. Particularly intriguing
are instances of concurrent monsoonal extremes, which give rise to complex SWD
patterns. Usually, it is noted that a depleted convective activity and
persistence of higher temperatures during the pre-monsoon season leads to lower
SM, while monsoon rains and post-monsoon showers support the prevalence of
higher SM conditions. The long persistent dry spells during deficit monsoon
years enhances the Bowen ratio (BR) due to the high sensible heat fluxes. On
the other hand, the availability of large latent heat flux during excess
monsoon and post-monsoon seasons tends to decrease the BR. This enhancement or
reduction in BR is due to evapotranspiration (ET), which influences the SWD by
modulating the surface subsurface SM coupling. The surface and subsurface SM
coupling analysis for CMZ exhibits significant distinction in the evolution of
wet and dry extremes. SM variations and persistence time scale is used as an
indicator of SMM, and analysed for both surface and subsurface SM observation
levels. Evidently, subsurface SM exhibits remarkably prolonged memory
timescales, approximately twice that of surface SM. Furthermore, we dissect SWD
linked to wet and dry extremes by analysing annual soil water balance (SWB).
Our findings reveal augmented (diminished) ET during deficit (excess) years,
subjected to a higher (lower) number of break events. In essence, our study
underscores the significance of surface-subsurface SM observations in
unravelling the intricate tapestry of SWD.


  We study the potential synergy between two different NLP tasks, both
confronting predicate lexical variability: identifying predicate paraphrases,
and event coreference resolution. First, we used annotations from an event
coreference dataset as distant supervision to re-score heuristically-extracted
predicate paraphrases. The new scoring gained more than 18 points in average
precision upon their ranking by the original scoring method. Then, we used the
same re-ranking features as additional inputs to a state-of-the-art event
coreference resolution model, which yielded modest but consistent improvements
to the model's performance. The results suggest a promising direction to
leverage data and models for each of the tasks to the benefit of the other.


  It is shown that the Lorentz invariant $f(T)$ gravity, defined by the
coframe-connection-multiplier form of the Lagrangian, can be gauge-fixed to the
pure coframe form. After clarifying basic aspects of the problem in the
Lagrangian formalism, a more detailed analysis of this gauge equivalence is
given relying on the Dirac Hamiltonian approach.


  We present here some results of applying the Cayley-Dickson process to
certain alternative algebras (notably built upon Galois fields and congruence
rings), in a manner which might yield new building blocks for cryptographic
systems. We focus on enumeration properties rather than the classification and
comparison questions which are extensively studied elsewhere, at least for
algebras over fields. The results presented here are technical but not
inherently difficult.


  Deep learning has achieved notable success in 3D object detection with the
advent of large-scale point cloud datasets. However, severe performance
degradation in the past trained classes, i.e., catastrophic forgetting, still
remains a critical issue for real-world deployment when the number of classes
is unknown or may vary. Moreover, existing 3D class-incremental detection
methods are developed for the single-domain scenario, which fail when
encountering domain shift caused by different datasets, varying environments,
etc. In this paper, we identify the unexplored yet valuable scenario, i.e.,
class-incremental learning under domain shift, and propose a novel 3D domain
adaptive class-incremental object detection framework, DA-CIL, in which we
design a novel dual-domain copy-paste augmentation method to construct multiple
augmented domains for diversifying training distributions, thereby facilitating
gradual domain adaptation. Then, multi-level consistency is explored to
facilitate dual-teacher knowledge distillation from different domains for
domain adaptive class-incremental learning. Extensive experiments on various
datasets demonstrate the effectiveness of the proposed method over baselines in
the domain adaptive class-incremental learning scenario.


  In this paper, we present a family of bivariate copulas by transforming a
given copula function with two increasing functions, named as transformed
copula. One distinctive characteristic of the transformed copula is its
singular component along the main diagonal. Conditions guaranteeing the
transformed function to be a copula function are provided, and several classes
of the transformed copulas are given. The singular component along the main
diagonal of the transformed copula is verified, and the tail dependence
coefficients of the transformed copulas are obtained. Finally, some properties
of the transformed copula are discussed, such as the totally positive of order
2 and the concordance order.


  For classical lattice systems, the Dobrushin-Lanford-Ruelle theory of
boundary conditions states that the restriction of a global equilibrium state
to a subsystem can be obtained as an integral over equilibrium states of the
subsystem alone. The Hamiltonians for the subsystem are obtained by fixing a
configuration for the variables in the complement of the subsystem, or more
generally, by evaluating the full interaction Hamiltonian with respect to a
state for the complement. We provide examples showing that the quantum
mechanical version of this statement is false. It fails even if the subsystem
is classical, but embedded into a quantum environment. We suggest an
alternative characterization of the local restrictions of global equilibrium
states by inequalities involving only local data.


  We review the main results from axisymmetric, time-dependent hydrodynamical
simulations of radiation driven disk winds in AGN. We illustrate the capability
of such simulations to provide useful insights into the three domains of
observational astronomy: spectroscopy, time-variability, and imaging.
Specifically, the synthetic line profiles predicted by the simulations resemble
the broad absorption lines observed in quasars. The intrinsically time
dependent nature of radiation driven disk winds that have been predicted by the
simulations can be supported by a growing number of the observed dramatic
variability in the UV absorption lines. And finally, the intensity maps
predicted by the simulations give physical and geometrical justification to the
phenomenologically deduced fact that a proper interpretation of the observed
line absorption requires the wind covering factor to be considered as being
partial, inhomogeneous, and velocity dependent.


  Annotation corpus for discourse relations benefits NLP tasks such as machine
translation and question answering. In this paper, we present SciDTB, a
domain-specific discourse treebank annotated on scientific articles. Different
from widely-used RST-DT and PDTB, SciDTB uses dependency trees to represent
discourse structure, which is flexible and simplified to some extent but do not
sacrifice structural integrity. We discuss the labeling framework, annotation
workflow and some statistics about SciDTB. Furthermore, our treebank is made as
a benchmark for evaluating discourse dependency parsers, on which we provide
several baselines as fundamental work.


  We consider the problem of estimating a low-rank signal matrix from noisy
measurements under the assumption that the distribution of the data matrix
belongs to an exponential family. In this setting, we derive generalized
Stein's unbiased risk estimation (SURE) formulas that hold for any spectral
estimators which shrink or threshold the singular values of the data matrix.
This leads to new data-driven spectral estimators, whose optimality is
discussed using tools from random matrix theory and through numerical
experiments. Under the spiked population model and in the asymptotic setting
where the dimensions of the data matrix are let going to infinity, some
theoretical properties of our approach are compared to recent results on
asymptotically optimal shrinking rules for Gaussian noise. It also leads to new
procedures for singular values shrinkage in finite-dimensional matrix denoising
for Gamma-distributed and Poisson-distributed measurements.


  To a higher rank directed graph $(\Lambda, d)$, in the sense of Kumjian and
Pask, one can associate natural noncommutative analytic Toeplitz algebras, both
weakly closed and norm closed. We introduce methods for the classification of
these algebras in the case of single vertex graphs.


  We attain a renormalized and iterative expression of the Andreev level in a
quantum-dot Josephson junction, which is bound to have significant implications
due to several significant advantages. The renormalized form of the Andreev
level not only allows us to extend beyond the limitations of small tunnel
coupling, quantum dot energy, magnetic field, and mean-field Coulomb
interaction but also enables the capturing of subgap levels that leak out of
the superconducting gap into the continuous spectrum. Furthermore, the
iterative form of the Andreev level provides an intuitive understanding of the
spin-split and superconducting proximity effects of the superconducting leads.
We find a singlet-doublet quantum phase transition (QPT) in the ground state
due to the intricate competition between the superconducting and spin-split
proximity effects, that differs from the typical QPT arising from the
competition between the superconducting proximity effect (favoring singlet
phase) and the quantum dot Coulomb interaction (favoring doublet phase). This
QPT has a diverse phase diagram owing to the spin-split proximity effects which
favors the doublet phase akin to the quantum-dot Coulomb interaction but can be
also enhanced by the tunneling coupling like the superconducting proximity
effect. Unlike the typical QPT, where tunnel coupling prefers singlet ground
state, this novel QPT enables strong tunnel coupling to suppress the singlet
ground state via the spin-split proximity effect, allowing a
singlet-doublet-singlet transition with increasing tunnel coupling. Our
renormalized and iterative formalism of the Andreev level is crucial for the
electrostatic gate, external flux, and magnetic field modulations of the
Andreev qubits.


  We introduce IFFNeRF to estimate the six degrees-of-freedom (6DoF) camera
pose of a given image, building on the Neural Radiance Fields (NeRF)
formulation. IFFNeRF is specifically designed to operate in real-time and
eliminates the need for an initial pose guess that is proximate to the sought
solution. IFFNeRF utilizes the Metropolis-Hasting algorithm to sample surface
points from within the NeRF model. From these sampled points, we cast rays and
deduce the color for each ray through pixel-level view synthesis. The camera
pose can then be estimated as the solution to a Least Squares problem by
selecting correspondences between the query image and the resulting bundle. We
facilitate this process through a learned attention mechanism, bridging the
query image embedding with the embedding of parameterized rays, thereby
matching rays pertinent to the image. Through synthetic and real evaluation
settings, we show that our method can improve the angular and translation error
accuracy by 80.1% and 67.3%, respectively, compared to iNeRF while performing
at 34fps on consumer hardware and not requiring the initial pose guess.


  The Wide Field Camera 3 is one of the instruments currently onboard the
Hubble Space Telescope and, since 2012, with the use of the spatial scanning
technique, has provided the largest number of observed exoplanetary atmosphere,
ranging from super-Earths to hot Jupiters. This technique enables the
observation of bright targets without saturating the sensitive detectors, but
at the same time requires more complicated data reduction and calibration
techniques to extract the planetary signal from the observations. In absence of
absolute calibration sources, the validation of current data analysis
techniques is not possible as the planetary signal is not known. Here, we
demonstrate how simulated observations can help us understand the effect of
different analysis processes, and potential unknown systematics on the final
transmission spectra of exoplanets. We test and validate the robustness of two
of the most precise WFC3 exoplanetary spectra - HD 209458 b and 55 Cancri e -
against three different known and potential sources of systematics. In
addition, we identify the horizontal shifts seen in WFC3 observations as the
most important source of systematic errors in the planetary spectra, concluding
that a precision better that 1% of a pixel is necessary.


  A well-studied scenario in quantum parameter estimation theory arises when
the parameter to be estimated is imprinted on the initial state by a
Hamiltonian of the form $\theta G$. For such "phase shift Hamiltonians" it has
been shown that one cannot improve the channel quantum Fisher information by
adding ancillas and letting the system interact with them. Here we investigate
the general case, where the Hamiltonian is not necessarily a phase shift, and
show that in this case in general it \emph{is} possible to increase the quantum
channel information and to reach an upper bound. This can be done by adding a
term proportional to the derivative of the Hamiltonian, or by subtracting a
term to the original Hamiltonian. Both methods do not make use of any ancillas
and show therefore that for quantum channel estimation with arbitrary
parameter-dependent Hamiltonian, entanglement with an ancillary system is not
necessary to reach the best possible sensitivity. By adding an operator to the
Hamiltonian we can also modify the time scaling of the channel quantum Fisher
information. We illustrate our techniques with NV-center magnetometry and the
estimation of the direction of a magnetic field in a given plane using a single
spin-1 as probe.


  We consider the task of certification of genuine entanglement of tripartite
states. For this purpose, we first present an "all-versus-nothing" proof of
genuine tripartite Einstein-Podolsky-Rosen (EPR) steering by demonstrating the
non-existence of a hybrid local hidden state (LHS) model in the tripartite
network as a motivation to our main result. A full logical contradiction of the
predictions of the hybrid LHS model with quantum mechanical outcome statistics
for any three-qubit generalized Greenberger-Horne-Zeilinger (GGHZ) states and
pure W-class states is shown. Using logical contradiction, we can distinguish
between the GGHZ and W-class state in a two-sided device-independent (2SDI)
steering scenario. We next formulate a 2SDI steering inequality which is a
generalization of the fine-grained steering inequality (FGI) derived in
\cite{PKM14} for the tripartite scenario. We show that the maximum quantum
violation of this tripartite FGI can be used to certify genuine entanglement of
three-qubit pure states.


  The Atmospheric Chemistry Suite (ACS) instrument onboard the ExoMars Trace
Gas Orbiter (TGO) ESA-Roscosmos mission began science operations in March 2018.
ACS Mid InfraRed (MIR) channel notably provides solar occultation observations
of the martian atmosphere in the 2.3 - 4.2 $\mu$m spectral range. Here we use
these observations to characterize water ice clouds before and during the MY 34
Global Dust Storm (GDS). We developed a method to detect water ice clouds with
mean particle size $\leq$ 2 $\mu$m, and applied it to observations gathered
between $L_s=165^\circ$ and $L_s=243^\circ$. We observe a shift in water ice
clouds maximum altitudes from about 60 km before the GDS to above 90 km during
the storm. These very high altitude, small-sized ($r_\mathrm{eff} \leq 0.3$
$\mu$m) water ice clouds are more frequent during MY34 compared to non-GDS
years at the same season. Particle size frequently decreases with altitude,
both locally within a given profile and globally in the whole dataset. We
observe that the maximum altitude at which a given size is observed can
increase during the GDS by several tens of km for certain sizes. We notably
notice some large water ice particles ($r_\mathrm{eff}\geq1.5$ $\mu$m) at
surprisingly high altitudes during the GDS (50 - 70 km). These results suggest
that GDS can significantly impact the formation and properties of high altitude
water ice clouds as compared to the usual perihelion dust activity.


  We derive equivalent linear and dynamic programs for infinite horizon
risk-sensitive control for minimization of the asymptotic growth rate of the
cumulative cost.


  In this work, three different particle sizes: the static radius $R_{s}$,
hydrodynamic radius $R_{h}$ and apparent hydrodynamic radius $ R_{h,app}$
obtained using the light scattering technique, are investigated for dilute
poly-disperse homogenous spherical particles with a simple assumption that the
hydrodynamic radius is in proportion to the static radius, when the
Rayleigh-Gans-Debye approximation is valid. The results show that the expected
values of the normalized time auto-correlation function of the scattered light
intensity $g^{(2)}(\tau) $ calculated based on the static particle size
information are consistent with the experimental data. The volume phase
transition is thus investigated using the equilibrium swelling ratios of static
radii and apparent hydrodynamic radii respectively. The changes of the static
particle size information and apparent hydrodynamic radius as a function of
temperature $T$ show the effects of the volume phase transition on optical
properties and the total influences of the volume phase transition on the
optical, hydrodynamic characteristics and size distribution of particles,
respectively. The effects of cross-linker on the volume phase transition are
also discussed.


  Unsupervised near-duplicate detection has many practical applications ranging
from social media analysis and web-scale retrieval, to digital image forensics.
It entails running a threshold-limited query on a set of descriptors extracted
from the images, with the goal of identifying all possible near-duplicates,
while limiting the false positives due to visually similar images. Since the
rate of false alarms grows with the dataset size, a very high specificity is
thus required, up to $1 - 10^{-9}$ for realistic use cases; this important
requirement, however, is often overlooked in literature. In recent years,
descriptors based on deep convolutional neural networks have matched or
surpassed traditional feature extraction methods in content-based image
retrieval tasks. To the best of our knowledge, ours is the first attempt to
establish the performance range of deep learning-based descriptors for
unsupervised near-duplicate detection on a range of datasets, encompassing a
broad spectrum of near-duplicate definitions. We leverage both established and
new benchmarks, such as the Mir-Flick Near-Duplicate (MFND) dataset, in which a
known ground truth is provided for all possible pairs over a general, large
scale image collection. To compare the specificity of different descriptors, we
reduce the problem of unsupervised detection to that of binary classification
of near-duplicate vs. not-near-duplicate images. The latter can be conveniently
characterized using Receiver Operating Curve (ROC). Our findings in general
favor the choice of fine-tuning deep convolutional networks, as opposed to
using off-the-shelf features, but differences at high specificity settings
depend on the dataset and are often small. The best performance was observed on
the MFND benchmark, achieving 96\% sensitivity at a false positive rate of
$1.43 \times 10^{-6}$.


  We give new combinatorial formulas for decomposition of the tensor product of
integrable highest weight modules over the classical Lie algebras of type $B,
C, D$, and the branching decomposition of an integrable highest weight module
with respect to a maximal Levi subalgebra of type $A$. This formula is based on
a combinatorial model of classical crystals called spinor model. We show that
our formulas extend in a bijective way various stable branching rules for
classical groups to arbitrary highest weights, including the Littlewood
restriction rules.


  CO observations of 0<z<4 radio galaxies are presented. The L_CO upper limits
for the high-redshift powerful radio galaxies (HzPRGs: z > 1, P_408MHz > 10^27
Watts/Hz) are consistent with no evolution in molecular gas (H_2) mass with
redshift and/or radio power. Of the low-redshift powerful radio galaxies
(LzPRGs: z<0.2, P_408MHz MHz > 10^23.5 W/Hz) observed, only one F-R II galaxy
has been detected in CO, whereas approximately 50% of the radio-compact (FC)
and F-R I galaxies have been detected. The CO and imaging data to date imply
that either F-R II galaxies result from mergers of gas-poor galaxies relative
to FC/F-R I galaxies, or that some FC/F-R I galaxies evolve into F-R II
galaxies. In either scenario, the radio activity in powerful radio galaxies is
most likely triggered by a merger event, and H_2 may be the fuel for the active
galactic nucleus (AGN) in the early stages of the merger.


  In this paper we investigate the parabolic-hyperbolic formulation of the
vacuum constraint equations introduced by R{\'a}cz with a view to constructing
multiple black hole initial data sets without spin. In order to respect the
natural properties of this configuration, we foliate the spatial domain with
2-spheres. It is then a consequence of these equations that they must be solved
as an initial value problem evolving outwards towards spacelike infinity.
Choosing the free data and the "strong field boundary conditions" for these
equations in a way which mimics asymptotically flat and asymptotically
spherical binary black hole initial data sets, our focus in this paper is on
the analysis of the asymptotics of the solutions. In agreement with our earlier
results, our combination of analytical and numerical tools reveals that these
solutions are in general not asymptotically flat, but have a cone geometry
instead. In order to remedy this and approximate asymptotically Euclidean data
sets, we then propose and test an iterative numerical scheme.


  Dewetting of liquid films on solid surfaces in the presence of evaporation is
a common phenomenon and has been studied by many researchers. The previous
numerical approach has revealed that evaporation accelerates the dewetting
speed of the triple contact line and established correlations between the
dewetting speed and the surface wettability and superheating. However, such a
numerical calculation is time- and resource-consuming. ,We examine dewetting
physics and propose a time-averaged approach based on the multiscale theory.
The new approach averages the dewetting process over time and consists of only
several algebraic equations, making the problem easier to solve. It can produce
time-averaged values of essential quantities, such as the dewetting speed and
contact angle as a function of superheating, which agrees with the previous
numerical results. This simple approach is valuable for many applications, such
as modeling pulsating heat pipes and describing the microlayer dynamics under
growing vapor bubbles in nucleate boiling.


  We obtain an accurate estimate for the peak intensities of multi-soliton
complexes for a Kerr-type nonlinearity in the (1+1) - dimension problem. Using
exact analytical solutions of the integrable set of nonlinear Schrodinger
equations, we establish a rigorous relationship between the eigenvalues of
incoherently-coupled fundamental solitons and the range of admissible
intensities. A clear geometrical interpretation of this effect is given.


  We propose a notion of random horseshoe for one-dimensional random dynamical
systems. We prove the abundance of random horseshoes for a class of circle
endomorphisms subject to additive noise, large enough to make the Lyapunov
exponent positive. In particular, we provide conditions which guarantee that
given any pair of disjoint intervals, for almost every noise realization, there
exists a positive density sequence of return times to these intervals such that
the induced dynamics are the full shift on two symbols.


  Globular clusters (GCs) in the Milky Way exhibit a well-observed bimodal
distribution in core radii separating the so-called "core-collapsed" and
"non-core-collapsed" clusters. Here, we use our H\'enon-type Monte Carlo code,
CMC, to explore initial cluster parameters that map into this bimodality.
Remarkably, we find that by varying the initial size of clusters (specified in
our initial conditions in terms of the initial virial radius, $r_v$) within a
relatively narrow range consistent with the measured radii of young star
clusters in the local universe ($r_v \approx 0.5-5$ pc), our models reproduce
the variety of present-day cluster properties. Furthermore, we show that
stellar-mass black holes (BHs) play an intimate role in this mapping from
initial conditions to the present-day structural features of GCs. We identify
"best-fit" models for three GCs with known observed BH candidates, NGC 3201,
M22, and M10, and show that these clusters harbor populations of $\sim 50-100$
stellar-mass BHs at present. As an alternative case, we also compare our models
to the core-collapsed cluster NGC 6752 and show that this cluster likely
contains few BHs at present. Additionally, we explore the formation of BH
binaries in GCs and demonstrate that these systems form naturally in our models
in both detached and mass-transferring configurations with a variety of
companion stellar types, including low-mass main sequence stars, white dwarfs,
and sub-subgiants.


  We consider the existence and uniqueness of bounded solutions of periodic
evolution equations of the form $u'=A(t)u+\epsilon H(t,u)+f(t)$, where $A(t)$
is, in general, an unbounded operator depending 1-periodically on $t$, $H$ is
1-periodic in $t$, $\epsilon$ is small, and $f$ is a bounded and continuous
function that is not necessarily uniformly continuous. We propose a new
approach to the spectral theory of functions via the concept of "circular
spectrum" and then apply it to study the linear equations $u'=A(t)u+f(t)$ with
general conditions on $f$. For small $\epsilon$ we show that the perturbed
equation inherits some properties of the linear unperturbed one. The main
results extend recent results in the direction, saying that if the unitary
spectrum of the monodromy operator does not intersect the circular spectrum of
$f$, then the evolution equation has a unique mild solution with its circular
spectrum contained in the circular spectrum of $f$.


  Correcting bugs using modern Automated Program Repair (APR) can be both
time-consuming and resource-expensive. We describe a program repair approach
that aims to improve the scalability of modern APR tools. The approach
leverages program reduction in the form of program slicing to eliminate code
irrelevant to fixing the bug, which improves the APR tool's overall
performance. We investigate slicing's impact on all three phases of the repair
process: fault localization, patch generation, and patch validation. Our
empirical exploration finds that the proposed approach, on average, enhances
the repair ability of the TBar APR tool, but we also discovered a few cases
where it was less successful. Specifically, on examples from the widely used
Defects4J dataset, we obtain a substantial reduction in median repair time,
which falls from 80 minutes to just under 18 minutes. We conclude that program
reduction can improve the performance of APR without degrading repair quality,
but this improvement is not universal.
  A replication package is available via Zenodo at
https://doi.org/10.5281/zenodo.13074333.
  Keywords: automated program repair, dynamic program slicing, fault
localization, test-suite reduction, hybrid techniques.


  A compact set $E\subset {\Bbb R}^d$ is said to be arithmetically thick if
there exists a positive integer $n$ so that the $n$-fold arithmetic sum of $E$
has non-empty interior. We prove the arithmetic thickness of $E$, if $E$ is
uniformly non-flat, in the sense that there exists $\epsilon_0>0$ such that for
$x\in E$ and $0<r\leq {\rm diam}(E)$, $E\cap B(x,r)$ never stays
$\epsilon_0r$-close to a hyperplane in ${\Bbb R}^d$. Moreover, we prove the
arithmetic thickness for several classes of fractal sets, including
self-similar sets, self-conformal sets in ${\Bbb R}^d$ (with $d\geq 2$) and
self-affine sets in ${\Bbb R}^2$ that do not lie in a hyperplane, and certain
self-affine sets in ${\Bbb R}^d$ (with $d\geq 3$) under specific assumptions.


  This article generalizes the work of Ballmann and \'Swiatkowski to the case
of Reflexive Banach spaces and uniformly convex Busemann spaces, thus giving a
new fixed point criterion for groups acting on simplicial complexes.


  Pyroxene is the principal host of Fe$^{3+}$ in basalt source regions, hosting
79 and 81% of the Fe$^{3+}$ in spinel and garnet lherzolite, respectively, with
opx and cpx hosting 48% and 31%, respectively, of the total Fe$^{3+}$ in spinel
peridotite. To better understand partitioning of Fe$^{3+}$ between pyroxene and
melt we conducted experiments at 100 KPa with f$_{O2}$ controlled by CO-CO$_2$
gas mixes between $\Delta$QFM -1.19 to +2.06 in a system containing andesitic
melt saturated with opx or cpx only. To produce large (100-150 $\mu$m),
homogeneous pyroxenes, we employed a dynamic cooling technique with a
5-10$\deg$C/h cooling rate, and initial and final dwell temperatures
5-10$\deg$C and 20-30$^\circ$C super and sub-liquidus, respectively. Resulting
pyroxene crystals have absolute variation in Al$_2$O$_3$ and TiO$_2$ <0.05 wt.%
and <0.02 wt.%, respectively. Fe$^{3+}$/Fe$^T$ in pyroxenes and quenched glass
were measured by XANES. We used a newly developed XANES calibration for cpx and
opx by only selecting spectra with X-ray vibrating on the optic axial plane at
$50 \pm 5^\circ$ to the crystallographic c axis. Values of DFe$^{3+}$ cpx/melt
increase from 0.03 to 0.53 as fO2 increases from $\Delta$QFM -0.44 to 2.06,
while DFe$^{3+}$ opx/melt remains unchanged at 0.26 between $\Delta$QFM -1.19
to +1.37. In comparison to natural peridotitic pyroxenes, Fe$^{3+}$/FeT in
pyroxenes crystallized in this study are lower at similar f$_{O2}$, presumably
owing to lower Al$^{3+}$ contents. This study shows that the existing
thermodynamic models implemented in pMELTS and Perple_X over-predict the
stability of Fe$^{3+}$ in pyroxenes, causing an anomalous reduced character to
spinel peridotites at calculated conditions of MORB genesis.


  The problem of two fixed centers was introduced by Euler as early as in 1760.
It plays an important role both in celestial mechanics and in the microscopic
world. In the present paper we study the spatial problem in the case of
arbitrary (both positive and negative) strengths of the centers. Combining
techniques from scattering theory and Liouville integrability, we show that
this spatial problem has topologically non-trivial scattering dynamics, which
we identify as scattering monodromy. The approach that we introduce in this
paper applies more generally to scattering systems that are integrable in the
Liouville sense.


  Efficient machine learning implementations optimized for inference in
hardware have wide-ranging benefits, depending on the application, from lower
inference latency to higher data throughput and reduced energy consumption. Two
popular techniques for reducing computation in neural networks are pruning,
removing insignificant synapses, and quantization, reducing the precision of
the calculations. In this work, we explore the interplay between pruning and
quantization during the training of neural networks for ultra low latency
applications targeting high energy physics use cases. Techniques developed for
this study have potential applications across many other domains. We study
various configurations of pruning during quantization-aware training, which we
term quantization-aware pruning, and the effect of techniques like
regularization, batch normalization, and different pruning schemes on
performance, computational complexity, and information content metrics. We find
that quantization-aware pruning yields more computationally efficient models
than either pruning or quantization alone for our task. Further,
quantization-aware pruning typically performs similar to or better in terms of
computational efficiency compared to other neural architecture search
techniques like Bayesian optimization. Surprisingly, while networks with
different training configurations can have similar performance for the
benchmark application, the information content in the network can vary
significantly, affecting its generalizability.


  This paper deals with periodic solutions of the Hamilton equation with many
parameters. Theorems on global bifurcation of solutions with periods $2\pi/j,$
$j\in\mathbb{N},$ from a stationary point are proved. The Hessian matrix of the
Hamiltonian at the stationary point can be singular. However, it is assumed
that the local topological degree of the gradient of the Hamiltonian at the
stationary point is nonzero. It is shown that (global) bifurcation points of
solutions with given periods can be identified with zeros of appropriate
continuous functions on the space of parameters. Explicit formulae for such
functions are given in the case when the Hessian matrix of the Hamiltonian at
the stationary point is block-diagonal. Symmetry breaking results concerning
bifurcation of solutions with different minimal periods are obtained. A
geometric description of the set of bifurcation points is given. Examples of
constructive application of the theorems proved to analytical and numerical
investigation and visualization of the set of all bifurcation points in given
domain are provided.
  This paper is based on a part of the author's thesis [W. Radzki, ``Branching
points of periodic solutions of autonomous Hamiltonian systems'' (Polish), PhD
thesis, Nicolaus Copernicus University, Faculty of Mathematics and Computer
Science, Toru\'{n}, 2005].


  The next-next-to-leading order QCD corrections to the e+e- annihilation into
hadrons are considered. The stability of the predictions with respect to change
of the renormalization scheme is discussed in detail for the case of five, four
and three active quark flavors. The analysis is based on the recently proposed
condition for selecting renormalization schemes according to the degree of
cancellation that they introduce in the expression for the scheme invariant
combination of the expansion coefficients. It is demonstrated that the scheme
dependence ambiguity in the predictions obtained with the conventional
expansion is substantial, particularly at lower energies. It is shown however,
that the stability of the predictions is greatly improved when QCD corrections
are evaluated in a more precise way, by utilizing the contour integral
representation and calculating numerically the contour integral.


  We give an overview of five rationalization theories for spaces
(Bousfield-Kan's $\mathbb Q$-completion; Sullivan's rationalization;
Bousfield's homology rationalization; Casacuberta-Peschke's
$\Omega$-rationalization; G\'{o}mez-Tato-Halperin-Tanr\'{e}'s $\pi_1$-fiberwise
rationalization) that extend the classical rationalization of simply connected
spaces. We also give an overview of the corresponding rationalization theories
for groups ($\mathbb Q$-completion; $H\mathbb Q$-localization; Baumslag
rationalization) that extend the classical Malcev completion.


  The virtual knot theory is a new interesting subject in the recent study of
low dimensional topology. In this paper, we explore the algebraic structure
underlying the virtual braid group and call it the virtual Temperley--Lieb
algebra which is an extension of the Temperley--Lieb algebra by adding the
group algebra of the symmetrical group. We make a connection clear between the
Brauer algebra and virtual Temperley--Lieb algebra, and show the algebra
generated by permutation and its partial transpose to be an example for the
virtual Temperley--Lieb algebra and its important quotients.


  We prove that, for functions in the Orlicz class LloglogLloglogloglogL,
lacunary subsequences of the Fourier and the Walsh-Fourier series converge
almost everywhere. Our integrability condition is less stringent than the
homologous assumption in the almost everywhere convergence theorems of Lie
(Fourier case) and Do-Lacey (Walsh-Fourier case), where the quadruple
logarithmic term is replaced by a triple logarithm. Our proof of the
Walsh-Fourier case is self-contained and, in antithesis to Do and Lacey's
argument, avoids the use of Antonov's lemma, arguing directly via novel
weak-L^p bounds for the Walsh-Carleson operator.


  A recent study by Ramirez et al. (2014) demonstrated that an atmosphere with
1.3-4 bar of CO2 and H2O, in addition to 5-20% H2, could have raised the mean
annual and global surface temperature of early Mars above the freezing point of
water. Such warm temperatures appear necessary to generate the rainfall (or
snowfall) amounts required to carve the ancient martian valleys. Here, we use
our best estimates for early martian outgassing rates, along with a 1-D
photochemical model, to assess the conversion efficiency of CO, CH4, and H2S to
CO2, SO2, and H2. Our outgassing estimates assume that Mars was actively
recycling volatiles between its crust and interior, as Earth does today. H2
production from serpentinization and deposition of banded iron-formations is
also considered. Under these assumptions, maintaining an H2 concentration of
~1-2% by volume is achievable, but reaching 5% H2 requires additional H2
sources or a slowing of the hydrogen escape rate below the diffusion limit. If
the early martian atmosphere was indeed H2-rich, we might be able to see
evidence of this in the rock record. The hypothesis proposed here is consistent
with new data from the Curiosity Rover, which show evidence for a long-lived
lake in Gale Crater near Mt. Sharp. It is also consistent with measured oxygen
fugacities of martian meteorites, which show evidence for progressive mantle
oxidation over time.


  Let $G$ be a connected reductive group over a perfect field $k$. We study a
certain normal reductive monoid $\overline M$ associated to a parabolic
$k$-subgroup $P$ of $G$. The group of units of $\overline M$ is the Levi factor
$M$ of $P$. We show that $\overline M$ is a retract of the affine closure of
the quasi-affine variety $G/U(P)$. Fixing a parabolic $P^-$ opposite to $P$, we
prove that the affine closure of $G/U(P)$ is a retract of the affine closure of
the boundary degeneration $(G \times G)/(P \times_M P^-)$. Using idempotents,
we relate $\overline M$ to the Vinberg semigroup of $G$. The monoid $\overline
M$ is used implicitly in the study of stratifications of Drinfeld's
compactifications of the moduli stacks $\mathrm{Bun}_P$ and $\mathrm{Bun}_G$.


  We present a new method for measuring the CMB temperature quadrupole, using
large scale CMB polarization. The method exploits the fact that CMB
polarization is partially sourced by the local temperature quadrupole. We link
the temperature with the polarization spectrum directly by relating the local
quadrupole at the onset of reionization to both of them. The dominant
contribution is at l<30 and since we use many l values, we can reduce the error
significantly below cosmic variance. In particular, for our fiducial model, the
error on the temperature quadrupole is reduced to 24%. This has the potential
of reducing the probability of a low quadrupole by two orders of magnitude.


  We present a new family of hook-length formulas for the number of standard
increasing tableaux which arise in the study of factorial Grothendieck
polynomials. In the case of straight shapes our formulas generalize the
classical hook-length formula and Stanley's formula. For skew shapes, our
formulas generalize the Naruse hook-length formula and its $q$-analogues, which
were studied in previous papers of the series.


  We investigate the injection spectrum of ultra-high-energy (>10^{15} eV)
cosmic rays under the hypotheses that (1) these cosmic rays are protons and (2)
the sources of these cosmic rays are extra-galactic and are homogeneously
distributed in space. The most puzzling aspect of the observed
ultra-high-energy cosmic ray spectrum is the apparent nonexistence of a
``Greisen cut-off'' at about 10^{19.8} eV. We show that this fact could be
naturally explained if most (or all) of the cosmic rays presently observed
above about 10^{19.6} eV were initially injected with energy above the Greisen
cut-off. However, we find that the injection of cosmic rays above the Greisen
cut-off cannot account for the observed flux below about 10^{19.6} eV unless
the injection rate of these particles was enormously higher in the past, as
would be the case if the injection resulted from the decay of an ultra-massive
particle with lifetime of order 10^{9} yr. Even with such a rapid source
evolution, the observed cosmic ray spectrum below about 10^{18.5} eV cannot be
explained in this manner. However, we show that a 1/E^3 injection spectrum can
account for the observed spectrum below 10^{18.5} eV}, with the steepening
observed by the Fly's Eye group between 10^{17.6} eV and 10^{18.5} eV being
very naturally explained by e+ - e- production effects. This latter fact lends
support to the hypothesis that the cosmic rays in this energy regime are
protons. However, due to e+ - e- production effects, a 1/E^3 injection spectrum
cannot account for the observed flux above about 10^{18.5} eV.


  We propose the ternary generalization of the classical anti-commutativity and
study the algebras whose generators are ternary anti-commutative. The integral
over an algebra with an arbitrary number of generators N is defined and the
formula of a change of variables is proved. In analogy with the fermion
integral we define an analogue of the Pfaffian for a cubic matrix by means of
Gaussian type integral and calculate its explicit form in the case of N=3.


  LIGO/Virgo Collaboration reported the detection of the most massive black
hole - black hole (BH-BH) merger up to date with component masses of 85 Msun
and 66 Msun (GW190521). Motivated by recent observations of massive stars in
the 30 Doradus cluster in the Large Magellanic Cloud (>200 Msun; e.g. R136a)
and employing newly estimated uncertainties on pulsational pair-instability
mass-loss (that allow for possibility of forming BHs with mass up to 90Msun) we
show that it is trivial to form such massive BH-BH mergers through the
classical isolated binary evolution (with no assistance from either dynamical
interactions or exotica). A binary consisting of two massive (180+150 Msun)
Population II stars (Z=0.0001) evolves through a stable Roche lobe overflow and
common envelope episode. Both exposed stellar cores undergo direct
core-collapse and form massive BHs while avoiding pair-instability pulsation
mass-loss or total disruption. LIGO/Virgo observations show that the merger
rate density of light BH-BH mergers (both components: <50 Msun) is of the order
of 10-100 Gpc^-3 yr^-1, while GW190521 indicates that the rate of heavier
mergers is 0.02-0.43 Gpc^-3 yr^-1. Our model (with standard assumptions about
input physics) but extended to include 200 Msun stars and allowing for the
possibility of stellar cores collapsing to 90 Msun BHs produces the following
rates: 63 Gpc^-3 yr^-1 for light BH-BH mergers and 0.04 Gpc^-3 yr^-1 for heavy
BH-BH mergers. We do not claim that GW190521 was formed by an isolated binary,
but it appears that such a possibility can not be excluded.


  Linear complementarity problems provide a powerful framework to model
nonsmooth phenomena in a variety of real-world applications. In dynamical
control systems, they appear coupled to a linear input-output system in the
form of linear complementarity systems. Mimicking the program that led to the
foundation of bifurcation theory in smooth maps, we introduce a novel notion of
equivalence between linear complementarity problems that sets the basis for a
theory of bifurcations in a large class of nonsmooth maps, including, but not
restricted to, steadystate bifurcations in linear complementarity systems. Our
definition exploits the rich geometry of linear complementarity problems and
leads to constructive algebraic conditions for identifying and classifying the
nonsmooth singularities associated with nonsmooth bifurcations. We thoroughly
illustrate our theory on an extended applied example, the design of bistability
in an electrical network, and a more theoretical one, the identification and
classification of all possible equivalence classes in two-dimensional linear
complementarity problems.


  Open quantum systems are inherently coupled to their environments, which in
turn also obey quantum dynamical rules. By restricting to dissipative dynamics,
here we propose a measure that quantifies how far the environment action on a
system departs from the influence of classical noise fluctuations. It relies on
the lack of commutativity between the initial reservoir state and the
system-environment total Hamiltonian. Independently of the nature of the
dissipative system evolution, Markovian or non-Markovian, the measure can be
written in terms of the dual propagator that defines the evolution of system
operators. The physical meaning and properties of the proposed definition are
discussed in detail and also characterized through different paradigmatic
dissipative Markovian and non-Markovian open quantum dynamics.


  In this contribution we discuss the properties of the jacobian asymmetry, the
new observable introduced in hep-ph/2301.04059 for a robust determination of
the value and uncertainty of the $W$-boson mass at hadron colliders.


  Vladimir Shpilrain and Jie-Tai Yu have asked for an effective algorithm to
decide if two elements of C[x,y] are related by an automorphism of C[x,y]. We
describe here an efficient algorithm that decides this question and finds the
automorphism if it exists. The algorithm is due to the second author, who
described it in terms of Newton polygons, with C replaceable by a field of any
characteristic. Here we describe it in terms of splice diagrams, which gains
some efficiency at cost of generality (it currently applies only to
characteristic zero). Part of the purpose of this paper is to give an
exposition of the use of splice diagrams in studying C[x,y].


  We investigate properties below T_c of odd-frequency pairing which is
realized by antiferromagnetic critical spin fluctuations or spin wave modes. It
is shown that \Delta(\epsilon_n) becomes maximum at finite \epsilon_n, and
\Delta(\pi T) becomes maximum at finite T. Implications of the present results
to the experimental results of CeCu_2Si_2 and CeRhIn_5 are given.


  Fresnel zone plates are diffractive elements that are essential to form
images in many scientific and technological areas, especially where refractive
optics is not available. One of the main shortcomings of Fresnel zone plates,
which limit their utility with broadband sources, is their high chromatic
aberration. Recently presented, Fractal Zone Plates (FZPs) are diffractive
lenses characterized by an extended focal depth with a fractal structure. This
behaviour predicts an improved performance of FZPs as image forming devices
with an extended depth of field and a reduced chromatic aberration. Here we
report the achievement of the first polychromatic images obtained with a FZP
that confirm these predictions. We show that the polychromatic modulation
transfer function (MTF) of a FZP affected by defocus is about two times better
than one corresponding to a Fresnel zone plate. This result opens the
possibility to improve imaging techniques that use conventional Fresnel zone
plates over a wide range of the electromagnetic spectrum, ranging from x-rays
to THz.


  This paper investigates cylindrically symmetric distribution of an-isotropic
fluid under the expansion-free condition, which requires the existence of
vacuum cavity within the fluid distribution. We have discussed two family of
solutions which further provide two exact models in each family. Some of these
solutions satisfy Darmois junction condition while some show the presence of
thin shell on both boundary surfaces. We also formulate a relation between the
Weyl tensor and energy density.


  Complex Fe-K emission/absorption line features are commonly observed in the
6--11 keV band from Active Galactic Nuclei (AGN). These features are formed in
various physical components surrounding the black holes. The Narrow-Line
Seyfert 1 (NLS1) galaxy Mrk 766, in particular, exhibits characteristic
blue-shifted Fe-K absorption lines caused by the ultra-fast outflow (UFO), and
a broad Fe-K emission line, as well as variable absorbers partially covering
the X-ray emitting region. We re-analyze the Mrk 766 archival data of
XMM-Newton, NuSTAR, and Swift to investigate the origin of the Fe-K line
feature and the 0.3--79 keV energy spectral variation. We have found that the
spectral variation in $\lesssim$10 keV is primarily explained by the variable
partial covering of the central X-ray source by multi-layer absorbing clouds.
The Fe-K line feature consists of the blue-shifted absorption lines due to the
UFO, a narrow emission line from the distant material, a broad emission line
from the inner-disk reflection, and a slightly broadened weak emission line at
around 6.4--6.7 keV whose equivalent width is $\sim$0.05 keV. The last one is
presumably due to the resonance scattering in the UFO out of the line-of-sight,
as predicted by a Monte Carlo simulation based on the hydrodynamical UFO
modeling. We suggest that the seemingly complex Fe-K line features and the
X-ray energy spectra of Mrk 766 are explained by a moderately extended central
X-ray source around a Schwarzschild black hole, an optically thick accretion
disk with a truncated inner-radius, the UFO, multi-layer partial covering
clouds, and a torus.


  In large scale dynamic wireless networks, the amount of overhead caused by
channel estimation (CE) is becoming one of the main performance bottlenecks.
This is due to the large number users whose channels should be estimated, the
user mobility, and the rapid channel change caused by the usage of the
high-frequency spectrum (e.g. millimeter wave). In this work, we propose a new
hybrid channel estimation/prediction (CEP) scheme to reduce overhead in
time-division duplex (TDD) wireless cell-free massive
multiple-input-multiple-output (mMIMO) systems. The scheme proposes sending a
pilot signal from each user only once in a given number (window) of coherence
intervals (CIs). Then minimum mean-square error (MMSE) estimation is used to
estimate the channel of this CI, while a deep neural network (DNN) is used to
predict the channels of the remaining CIs in the window. The DNN exploits the
temporal correlation between the consecutive CIs and the received pilot signals
to improve the channel prediction accuracy. By doing so, CE overhead is reduced
by at least 50 percent at the expense of negligible CE error for practical user
mobility settings. Consequently, the proposed CEP scheme improves the spectral
efficiency compared to the conventional MMSE CE approach, especially when the
number of users is large, which is demonstrated numerically.


  Let $F_{p,q}$ be the generalized friendship graph $K_1\bigvee (pK_q)$ on
$pq+1$ vertices obtained by joining a vertex to all vertices of $p$ disjoint
copies of the complete graph $K_q$ on $q$ vertices. In this paper, we prove
that $F_{p,q}$ is determined by its normalized Laplacian spectrum if and only
if $q\ge 2$, or $q=1$ and $p\le 2$.


  We investigate the possibility that dark matter is a mixture of two
non-interacting perfect fluids, with different four-velocities and
thermodynamic parameters. The two-fluid model can be described as an effective
single anisotropic fluid, with distinct radial and tangential pressures. The
basic equations describing the equilibrium structure of the two-fluid dark
matter model, and of the tangential velocity of test particles in stable
circular orbits, are obtained for the case of a spherically symmetric static
geometry. By assuming a non-relativistic kinetic model for the dark matter
particles, the density profile and the tangential velocity of the dark matter
mixture are obtained by numerically integrating the gravitational field
equations. The cosmological implications of the model are also briefly
considered, and it is shown that the anisotropic two-fluid model isotropizes in
the large time limit.


  We investigate the spherical photon orbits in near-extremal Kerr spacetimes.
We show that the spherical photon orbits with impact parameters in a finite
range converge on the event horizon. Furthermore, we demonstrate that the Weyl
curvature near the horizon does not generate the shear of a congruence of such
light rays. Because of this property, a series of images produced by the light
orbiting around a near-extremal Kerr black hole several times can be
observable.


  Robustness of the Luttinger theorem for fermionic liquids is examined in
holography. The statement of the Luttinger theorem, the equality between the
fermion charge density and the volume enclosed by the Fermi surface, can be
mapped to a Gauss's law in the gravity dual, a la Sachdev. We show that various
deformations in the gravity dual, such as inclusion of magnetic fields, a
parity-violating theta-term, dilatonic deformations, and higher-derivative
corrections, do not violate the holographic derivation of the Luttinger
theorem, as long as the theory is in a confining phase. Therefore a robustness
of the theorem is found for strongly correlated fermions coupled with strongly
coupled sectors which admit gravity duals. On the other hand, in the deconfined
phase, we also show that the deficit appearing in the Luttinger theorem is
again universal. It measures a total deficit which measures the charge of the
deconfined ("fractionalized") fermions, independent of the deformation
parameters.


  Distributing the inference of convolutional neural network (CNN) to multiple
mobile devices has been studied in recent years to achieve real-time inference
without losing accuracy. However, how to map CNN to devices remains a
challenge. On the one hand, scheduling the workload of state-of-the-art CNNs
with multiple devices is NP-Hard because the structures of CNNs are directed
acyclic graphs (DAG) rather than simple chains. On the other hand, distributing
the inference workload suffers from expensive communication and unbalanced
computation due to the wireless environment and heterogeneous devices. This
paper presents PICO, a pipeline cooperation framework to accelerate the
inference of versatile CNNs on diverse mobile devices. At its core, PICO
features: (1) a generic graph partition algorithm that considers the
characteristics of any given CNN and orchestrates it into a list of model
pieces with suitable granularity, and (2) a many-to-many mapping algorithm that
produces the best pipeline configuration for heterogeneous devices. In our
experiment with 2 ~ 8 Raspberry-Pi devices, the throughput can be improved by
1.8 ~ 6.8x under different CPU frequencies.


  The annihilation process p bar(p) -> p D0 bar(Lambda)_c(2286) is studied
taking into account t-channel D0, D*0 meson exchange and the resonance
contribution of Lambda_c(2286) and Lambda_c(2940) baryons. We assume that the
Lambda_c(2940) baryon is a pD*0 molecular state with spin-parity (1/2)+ and
(1/2)-. Our results show that near the threshold of p bar(p) -> Lambda_c(2286)
bar(Lambda)_c(2286) the contribution from the intermediate state Lambda_c(2940)
is also sizeable and can be observed at the PANDA experiment. Another
conclusion is that the spin-parity assignment (1/2)- for Lambda_c(2940) gives
enhancement for the cross section in comparison with a choice (1/2)+.


  We point out and explicitly demonstrate a close connection that exists
between featureless Mott insulators and fractional quantum Hall liquids. Using
magnetic Wannier states as the single-particle basis in the lowest Landau level
(LLL), we demonstrate that the Hamiltonian of interacting bosons in the LLL
maps onto a Hamiltonian of a featureless Mott insulator on triangular lattice,
formed by the magnetic Wannier states. The Hamiltonian is remarkably simple and
consists only of short-range repulsion and ring-exchange terms.


  Background: Widespread adoption of electronic health records (EHRs) has
enabled secondary use of EHR data for clinical research and healthcare
delivery. Natural language processing (NLP) techniques have shown promise in
their capability to extract the embedded information in unstructured clinical
data, and information retrieval (IR) techniques provide flexible and scalable
solutions that can augment the NLP systems for retrieving and ranking relevant
records. Methods: In this paper, we present the implementation of Cohort
Retrieval Enhanced by Analysis of Text from EHRs (CREATE), a cohort retrieval
system that can execute textual cohort selection queries on both structured and
unstructured EHR data. CREATE is a proof-of-concept system that leverages a
combination of structured queries and IR techniques on NLP results to improve
cohort retrieval performance while adopting the Observational Medical Outcomes
Partnership (OMOP) Common Data Model (CDM) to enhance model portability. The
NLP component empowered by cTAKES is used to extract CDM concepts from textual
queries. We design a hierarchical index in Elasticsearch to support CDM concept
search utilizing IR techniques and frameworks. Results: Our case study on 5
cohort identification queries evaluated using the IR metric, P@5 (Precision at
5) at both the patient-level and document-level, demonstrates that CREATE
achieves an average P@5 of 0.90, which outperforms systems using only
structured data or only unstructured data with average P@5s of 0.54 and 0.74,
respectively.


  De Bruijn graphs are essential for sequencing data analysis and must be
efficiently constructed and stored for large-scale population studies. They
also need to be dynamic to allow updates such as adding or removing edges and
nodes. Existing dynamic implementations include DynamicBOSS and dynamicDBG. In
2018, a new family of data structures called learned indexes was introduced by
Tim Kraska and Alex Beutel, with a particularly efficient implementation
proposed by Paolo Ferragina and Giorgio Vinciguerra in 2020. This paper
presents a new method for implementing De Bruijn graphs using learned indexes
and compares its performance with current implementations. The new method shows
improved time and memory efficiency for edge and node insertions, particularly
with large datasets (over 110 million k-mers).


  Mott noted a one-to-one correspondence between saturated multiplicatively
closed subsets of a domain D and directed convex subgroups of the group of
divisibility D. With this, we construct a functor between inclusions into
saturated localizations of D and projections onto partially ordered quotient
groups of G(D). We use this functor to construct many cochain complexes of
o-homomorphisms of po-groups. These complexes naturally lead to some
fundamental structure theorems and some natural homology theory that provide
insight into the factorization behavior of D.


  The chiral Abelian Higgs model is studied at finite temperature. By
integrating out the heavy modes, we make a three-dimensional effective theory
for the static modes. It is demonstrated that the plasma masses are correctly
reproduced to leading order in $m^{2}/T^{2}$. The effective potential for the
composite operator $\phi^{\dagger}\phi$ is calculated at one loop for the
resulting three-dimensional theory and it is shown that the result is gauge
parameter invariant. The numerical investigation of the potential reveals that
the symmetry is restored via a first order phase transition. Comparison with
the ordinary ring improved potential is made and it is found that the barrier
height at $T_{c}$ is somewhat higher.


  The paper is concerned with distributed learning and optimization in
large-scale settings. The well-known Fictitious Play (FP) algorithm has been
shown to achieve Nash equilibrium learning in certain classes of multi-agent
games. However, FP can be computationally difficult to implement when the
number of players is large. Sampled FP is a variant of FP that mitigates the
computational difficulties arising in FP by using a Monte-Carlo (i.e.,
sampling-based) approach. The Sampled FP algorithm has been studied both as a
tool for distributed learning and as an optimization heuristic for large-scale
problems. Despite its computational advantages, a shortcoming of Sampled FP is
that the number of samples that must be drawn in each round of the algorithm
grows without bound (on the order of $\sqrt{t}$, where $t$ is the round of the
repeated play). In this paper we propose Computationally Efficient Sampled FP
(CESFP)---a variant of Sampled FP in which only one sample need be drawn each
round of the algorithm (a substantial reduction from $O(\sqrt{t})$ samples per
round, as required in Sampled FP). CESFP operates using a
stochastic-approximation type rule to estimate the expected utility from round
to round. It is proven that the CESFP algorithm achieves Nash equilibrium
learning in the same sense as classical FP and Sampled FP. Simulation results
suggest that the convergence rate of CESFP (in terms of repeated-play
iterations) is similar to that of Sampled FP.


  Generative adversarial networks (GANs) nowadays are capable of producing
images of incredible realism. One concern raised is whether the
state-of-the-art GAN's learned distribution still suffers from mode collapse,
and what to do if so. Existing diversity tests of samples from GANs are usually
conducted qualitatively on a small scale, and/or depends on the access to
original training data as well as the trained model parameters. This paper
explores to diagnose GAN intra-mode collapse and calibrate that, in a novel
black-box setting: no access to training data, nor the trained model
parameters, is assumed. The new setting is practically demanded, yet rarely
explored and significantly more challenging. As a first stab, we devise a set
of statistical tools based on sampling, that can visualize, quantify, and
rectify intra-mode collapse. We demonstrate the effectiveness of our proposed
diagnosis and calibration techniques, via extensive simulations and
experiments, on unconditional GAN image generation (e.g., face and vehicle).
Our study reveals that the intra-mode collapse is still a prevailing problem in
state-of-the-art GANs and the mode collapse is diagnosable and calibratable in
black-box settings. Our codes are available at:
https://github.com/VITA-Group/BlackBoxGANCollapse.


  The electronic transport properties and switching mechanism of single
photochromic diarylethene derivatives sandwiched between two gold surfaces with
closed and open configurations are investigated by a fully self-consistent
nonequilibrium Green's function method combined with density functional theory.
The calculated transmission spectra of two configurations are strikingly
distinctive. The open form lacks any significant transmission peak within a
wide energy window, while the closed structure has two significant transmission
peaks on the both sides of the Fermi level. The electronic transport properties
of the molecular junction with closed structure under a small bias voltage are
mainly determined by the tail of the transmission peak contributed unusually by
the perturbed lowest perturbed unoccupied molecular orbital. The calculated
on-off ratio of currents between the closed and open configurations is about
two orders of magnitude, which reproduces the essential features of the
experimental measured results. Moreover, we find that the switching behavior
within a wide bias voltage window is extremely robust to both substituting F or
S for H or O and varying end anchoring atoms from S to Se and Te.


  $O(n) \times O(m)$ symmetric Landau-Ginzburg models in $d=3$ dimension
possess a rich structure of the renormalization group and its understanding
offers a theoretical prediction of the phase diagram in frustrated spin models
with non-collinear order. Depending on $n$ and $m$, they may show
chiral/anti-chiral/Heisenberg/Gaussian fixed points within the same
universality class. We approach all the fixed points in the conformal bootstrap
program by examining the bound on the conformal dimensions for scalar operators
as well as non-conserved current operators with consistency crosschecks. For
large $n/m$, we show strong evidence for the existence of four fixed points by
comparing the operator spectrum obtained from the conformal bootstrap program
with that from the large $n/m$ analysis. We propose a novel non-perturbative
approach to the determination of the conformal window in these models based on
the conformal bootstrap program. From our numerical results, we predict that
for $m=3$, $n=7\sim 8$ is the edge of the conformal window for the anti-chiral
fixed points.


  In symmetric Macdonald polynomial theory the Pieri formula gives the
branching coefficients for the product of the rth elementary symmetric function
and the Macdonald polynomial. In this paper we give the nonsymmetric analogues
for the cases r=1 and r=n-1. We do this by first deducing the the decomposition
for the product of any nonsymmetric Macdonald polynomial with a linear function
in terms of nonsymmetric Macdonald polynomials. As a corollary of finding the
branching coefficients of the product of the first elementary function with a
nonsymmetric Macdonald polynomial we evaluate the generalised binomial
coefficients associated with the nonsymmetric Macdonald polynomials for
|u|=|v|+1.


  The theory of abstract kernels in non-trivial extensions for many kinds of
algebraical objects, such as groups, rings and graded rings, associative
algebras, Lie algebras, restricted Lie algebras, DG-algebras and DG-Lie
algebras, has been widely studied since 1940's. Gerhard Hochschild firstly
treats associative algebra as an generic type in the series of kernel problems.
He proves the theorem of constructing kernel by presenting many tedious
relations that may lost the readers today. In this paper, we shall illustrate
the formulation and recast it for Lie algebra(-oid) kernels. We also prove the
independence of 3-cocycle in the case of associative algebra. Finally, we use
the universal enveloping algebra of Lie algebra to reduce the difficulty of a
direct construction for the derivation algebras.


  Accurate measurements of the cross-plane thermal conductivity {\Lambda}_cross
of a high-thermal-conductivity thin film on a low-thermal-conductivity
({\Lambda}_s) substrate (e.g., {\Lambda}_cross/{\Lambda}_s>20) are challenging,
due to the low thermal resistance of the thin film compared to that of the
substrate. In principle, {\Lambda}_cross could be measured by time-domain
thermoreflectance (TDTR), using a high modulation frequency f_h and a large
laser spot size. However, with one TDTR measurement at f_h, the uncertainty of
the TDTR measurement is usually high due to low sensitivity of TDTR signals to
{\Lambda}_cross and high sensitivity to the thickness h_Al of Al transducer
deposited on the sample for TDTR measurements. We observe that in most TDTR
measurements, the sensitivity to h_Al only depends weakly on the modulation
frequency f. Thus, we performed an additional TDTR measurement at a low
modulation frequency f_0, such that the sensitivity to h_Al is comparable but
the sensitivity to {\Lambda}cross is near zero. We then analyze the ratio of
the TDTR signals at f_h to that at f_0, and thus significantly improve the
accuracy of our {\Lambda}cross measurements. As a demonstration of the
dual-frequency approach, we measured the cross-plane thermal conductivity of a
400-nm-thick nickel-iron alloy film and a 3-{\mu}m-thick Cu film, both with an
accuracy of ~10%. The dual-frequency TDTR approach is useful for future studies
of thin films.


  The alternating direction method of multipliers (ADMM) is a powerful
optimization solver in machine learning. Recently, stochastic ADMM has been
integrated with variance reduction methods for stochastic gradient, leading to
SAG-ADMM and SDCA-ADMM that have fast convergence rates and low iteration
complexities. However, their space requirements can still be high. In this
paper, we propose an integration of ADMM with the method of stochastic variance
reduced gradient (SVRG). Unlike another recent integration attempt called
SCAS-ADMM, the proposed algorithm retains the fast convergence benefits of
SAG-ADMM and SDCA-ADMM, but is more advantageous in that its storage
requirement is very low, even independent of the sample size $n$. We also
extend the proposed method for nonconvex problems, and obtain a convergence
rate of $O(1/T)$. Experimental results demonstrate that it is as fast as
SAG-ADMM and SDCA-ADMM, much faster than SCAS-ADMM, and can be used on much
bigger data sets.


  Finite cellular automata (FCA) are widely used in simulating nonlinear
complex systems, and their reversibility is closely related to information loss
during the evolution. However, only a relatively small portion of their
reversibility problems has been solved. In this paper, we perform calculations
on two graphs and discover that the reversibility of any one-dimensional FCA
exhibits periodicity as the number of cells increases. We also successfully
provide a method to compute the reversibility sequence that encompasses the
reversibility of one-dimensional FCA with any number of cells. Additionally,
the calculations in this paper are applicable to FCA with various types of
boundaries. This means that we will have an efficient method to determine the
reversibility of almost all one-dimensional FCA, with a complexity independent
of cell number.


  Currently the only technique sensitive to Earth mass planets around nearby
stars (that are too close for microlensing) is the monitoring of the transit
time variations of the transiting extrasolar planets. We search for additional
planets in the systems of the hot Neptune GJ 436b, and the hot-Jupiter XO-1b,
using high cadence observations in the J and Ks bands. New high-precision
transit timing measurements are reported: GJ 436b Tc = 2454238.47898 \pm
0.00046 HJD; XO-1b Tc(A) = 2454218.83331 \pm 0.00114 HJD, Tc(B) = 2454222.77539
\pm 0.00036 HJD, Tc(C) = 2454222.77597 \pm 0.00039 HJD, Tc(D) = 2454226.71769
\pm 0.00034 HJD, and they were used to derive new ephemeris. We also determined
depths for these transits. No statistically significant timing deviations were
detected. We demonstrate that the high cadence ground based near-infrared
observations are successful in constraining the mean transit time to ~30 sec.,
and are a viable alternative to space missions.


  The growth of large, programatically accessible bibliometrics databases
presents new opportunities for complex analyses of publication metadata. In
addition to providing a wealth of information about authors and institutions,
databases such as those provided by Dimensions also provide conceptual
information and links to entities such as grants, funders and patents. However,
data is not the only challenge in evaluating patterns in scholarly work: These
large datasets can be challenging to integrate, particularly for those
unfamiliar with the complex schemas necessary for accommodating such
heterogeneous information, and those most comfortable with data mining may not
be as experienced in data visualisation. Here, we present an open-source Python
library that streamlines the process accessing and diagramming subsets of the
Dimensions on Google BigQuery database and demonstrate its use on the freely
available Dimensions COVID-19 dataset. We are optimistic that this tool will
expand access to this valuable information by streamlining what would otherwise
be multiple complex technical tasks, enabling more researchers to examine
patterns in research focus and collaboration over time.


  Robotics systems are complex, often consisted of basic services including
SLAM for localization and mapping, Convolution Neural Networks for scene
understanding, and Speech Recognition for user interaction, etc. Meanwhile,
robots are mobile and usually have tight energy constraints, integrating these
services onto an embedded platform with around 10 W of power consumption is
critical to the proliferation of mobile robots. In this paper, we present a
case study on integrating real-time localization, vision, and speech
recognition services on a mobile SoC, Nvidia Jetson TX1, within about 10 W of
power envelope. In addition, we explore whether offloading some of the services
to cloud platform can lead to further energy efficiency while meeting the
real-time requirements


  In many research fields in artificial intelligence, it has been shown that
deep neural networks are useful to estimate unknown functions on high
dimensional input spaces. However, their generalization performance is not yet
completely clarified from the theoretical point of view because they are
nonidentifiable and singular learning machines. Moreover, a ReLU function is
not differentiable, to which algebraic or analytic methods in singular learning
theory cannot be applied. In this paper, we study a deep ReLU neural network in
overparametrized cases and prove that the Bayesian free energy, which is equal
to the minus log marginal likelihoodor the Bayesian stochastic complexity, is
bounded even if the number of layers are larger than necessary to estimate an
unknown data-generating function. Since the Bayesian generalization error is
equal to the increase of the free energy as a function of a sample size, our
result also shows that the Bayesian generalization error does not increase even
if a deep ReLU neural network is designed to be sufficiently large or in an
opeverparametrized state.


  A many body Hamiltonian involving the mean field for a projected spherical
single particle basis, the pairing interactions for alike nucleons and the
dipole-dipole proton-neutron interactions in the particle-hole ($ph$) and
particle-particle ($pp$) channels is treated by the projected gauge fully
renormalized proton-neutron quasiparticle random phase approximation
(PGFRpnQRPA) approach. The resulting wave functions and energies for the mother
and the daughter nuclei are used to calculate the $2\nu\beta\beta$ decay rate
and the process half life. For illustration, the formalism is applied for the
decay $^{100}$Mo$ \to$ $^{100}$Ru. The results are in good agreement with the
corresponding experimental data. The Ikeda sum rule ($ISR$) is obeyed. The
gauge projection makes the $pp$ interaction inefficient.


  We investigate the role of partonic degrees of freedom in high multiplicity
p-Pb collisions at $\sqrt{s_{NN}}=$ 5.02 TeV carried out at the Large Hadron
Collider (LHC) by studying the production and collective flow of identified
hadrons at intermediate $p_T$ via the coalescence of soft and hard partons
generated from viscous hydrodynamics (VISH2+1) and the energy loss model (LBT),
respectively. We find that combining the intermediate $p_T$ hadrons from the
coalescence with the low $p_T$ hadrons from hydrodynamics and high $p_T$
hadrons from the jet fragmentation, our Hydro-Coal-Frag model provides a nice
description of the measured $p_T$-spectra and the differential elliptic flow
$v_2(p_T)$ of pions, kaons and protons over the $p_T$ range from 0 to 6 GeV. We
further demonstrate the necessity of including the quark coalescence
contribution to reproduce the experimentally observed approximate number of
constituent quark scaling of hadron $v_2$ at intermediate $p_T$. Our results
thus indicate the importance of partonic degrees of freedom and also hint at
the possible formation of quark-gluon plasma in high multiplicity p+Pb
collisions at the LHC.


  The current global pandemic occasioned by the SARS-CoV-2 virus has been
attributed, partially, to the growing range of cyber vises within the cyber
ecosystem. One area of such impact is the increasing tendencies of
cyber-bullying among students. Cyberbullying -- the act of subjugating others
using a cyber platform -- is a growing concern among educators, especially in
High-S chools. Whilst studies have been carried out towards understanding this
menace, the approach towards id entifying indicators of cyberbullying is
largely missing in the literature. To address this research gap, this study
proposed a cyberbullying framework based on the identification of some
observable behavioral indicators. Using a self-administered measurement
instrument from 30-respondents, the study observed the probability of a
cyberbully construct, as a potential measure of the presence of cyberbullying;
a probability that has been largely ignored in extant literature. This
observation presents a veritable tool for the development of an active and
integrated learning platform void of abuse among students. Furthermore, within
the cyber education ecosystem, a cyberbullying construct would provide a
mechanism for the development of an appropriate online learning platform, which
would be useful to the information system and cyber education research
communities.


  In minimally invasive endovascular procedures, contrast-enhanced angiography
remains the most robust imaging technique. However, it is at the expense of the
patient and clinician's health due to prolonged radiation exposure. As an
alternative, interventional ultrasound has notable benefits such as being
radiation-free, fast to deploy, and having a small footprint in the operating
room. Yet, ultrasound is hard to interpret, and highly prone to artifacts and
noise. Additionally, interventional radiologists must undergo extensive
training before they become qualified to diagnose and treat patients
effectively, leading to a shortage of staff, and a lack of open-source
datasets. In this work, we seek to address both problems by introducing a
self-supervised deep learning architecture to segment catheters in longitudinal
ultrasound images, without demanding any labeled data. The network architecture
builds upon AiAReSeg, a segmentation transformer built with the Attention in
Attention mechanism, and is capable of learning feature changes across time and
space. To facilitate training, we used synthetic ultrasound data based on
physics-driven catheter insertion simulations, and translated the data into a
unique CT-Ultrasound common domain, CACTUSS, to improve the segmentation
performance. We generated ground truth segmentation masks by computing the
optical flow between adjacent frames using FlowNet2, and performed thresholding
to obtain a binary map estimate. Finally, we validated our model on a test
dataset, consisting of unseen synthetic data and images collected from silicon
aorta phantoms, thus demonstrating its potential for applications to clinical
data in the future.