  The surface structure of phosphorene crystals materials is determined using
surface sensitive dynamical micro-spot low energy electron diffraction
({\mu}LEED) analysis using a high spatial resolution low energy electron
microscopy (LEEM) system. Samples of (\textit{i}) crystalline cleaved black
phosphorus (BP) at 300 K and (\textit{ii}) exfoliated few-layer phosphorene
(FLP) of about 10 nm thicknes, which were annealed at 573 K in vacuum were
studied. In both samples, a significant surface buckling of 0.22 {\AA} and 0.30
{\AA}, respectively, is measured, which is one order of magnitude larger than
previously reported. Using first principle calculations, the presence of
surface vacancies is attributed not only to the surface buckling in BP and FLP,
but also the previously reported intrinsic hole doping of phosphorene
materials.


  The propagation of chaos is a central concept of kinetic theory that serves
to relate the equations of Boltzmann and Vlasov to the dynamics of
many-particle systems. Propagation of chaos means that molecular chaos, i.e.,
the stochastic independence of two random particles in a many-particle system,
persists in time, as the number of particles tends to infinity.
  We establish a necessary and sufficient condition for a family of general
n-particle Markov processes to propagate chaos. This condition is expressed in
terms of the Markov transition functions associated to the n-particle
processes, and it amounts to saying that chaos of random initial states
propagates if it propagates for pure initial states.
  Our proof of this result relies on the weak convergence approach to the study
of chaos due to Sznitman and Tanaka. We assume that the space in which the
particles live is homeomorphic to a complete and separable metric space so that
we may invoke Prohorov's theorem in our proof.
  We also show that, if the particles can be in only finitely many states, then
molecular chaos implies that the specific entropies in the n-particle
distributions converge to the entropy of the limiting single-particle
distribution.


  Structure of cold dense matter at subnuclear densities is investigated by
quantum molecular dynamics (QMD) simulations. We succeeded in showing that the
phases with slab-like and rod-like nuclei etc. can be formed dynamically from
hot uniform nuclear matter without any assumptions on nuclear shape. We also
observe intermediate phases, which has complicated nuclear shapes. Geometrical
structures of matter are analyzed with Minkowski functionals, and it is found
out that intermediate phases can be characterized as ones with negative Euler
characteristic. Our result suggests the existence of these kinds of phases in
addition to the simple ``pasta'' phases in neutron star crusts.


  We present new 2 cm and 6 cm maps of H2CO, radio recombination lines, and the
radio continuum in the W51 star forming complex acquired with Arecibo and the
Green Bank Telescope at ~50" resolution. We use H2CO absorption to determine
the relative line-of-sight positions of molecular and ionized gas. We measure
gas densities using the H2CO densitometer, including continuous measurements of
the dense gas mass fraction (DGMF) over the range $10^4$ cm$^{-3}$ < n(H$_2$) <
$10^6$ cm$^{-3}$- this is the first time a dense gas mass fraction has been
measured over a range of densities with a single data set. The DGMF in W51A is
high,f >~70% above $n>10^4$ cm$^{-3}$, while it is low, f<20%, in W51 B. We did
not detect any H2CO emission throughout the W51 GMC; all gas dense enough to
emit under normal conditions is in front of bright continuum sources and
therefore is seen in absorption instead. The data set has been made public at
http://dx.doi.org/10.7910/DVN/26818. Conclusions. (1) The dense gas fraction in
the W51 A and B clouds shows that W51 A will continue to form stars vigorously,
while star formation has mostly ended in W51 B. The lack of dense, star-forming
gas around W51 C indicates that collect-and-collapse is not acting or is
inefficient in W51. (2) Ongoing high-mass star formation is correlated with n ~
1x10$^5$ cm$^{-3}$ gas. Gas with n > 10$^4$ cm$^{-3}$ is weakly correlated with
low and moderate mass star formation, but does not strongly correlate with
high-mass star formation. (3) The nondetection of H$_2$CO emission implies that
the emission detected in other galaxies, e.g. Arp 220, comes from high-density
gas that is not directly affiliated with already-formed massive stars. Either
the non-star-forming ISM of these galaxies is very dense, implying the star
formation density threshold is higher, or H II regions have their emission
suppressed.


  Ultra light axion fields, motivated by the string theory, form a large
condensate (axion cloud) around rotating black holes through superradiant
instability. Several effects due to the axion cloud, such as the spin-down of
black holes and the emission of monochromatic gravitational waves, open a new
window to search for axions by astrophysical observations. When the axion
self-interaction is considered, the evolution of cloud is altered
significantly, and an explosive phenomenon called bosenova can happen. Thus, it
is necessary to understand the precise evolution of self-interacting clouds for
the detection of axions by astrophysical observations. In this paper, we
propose a new method to track the whole process of the growth of
self-interacting axion clouds employing the adiabatic approximation. We
emphasize that our method relies neither on the non-relativistic approximation
nor on perturbative treatment of the self-interaction, which is often used in
literature. Our main finding is that the evolution of cloud in the strongly
self-interacting regime depends on the strength of the gravitational coupling
between the axion and the black hole. For a large coupling, the cloud evolves
into a quasi-stationary state where the superradiant energy gain is balanced
with the energy dissipation to infinity by the self-interaction. On the other
hand, when one decreases the size of coupling, clouds become unstable at some
energy, which would be interpreted as the onset of bosenova.


  Cumulative weight enumerators of random linear codes are introduced, their
asymptotic properties are studied, and very sharp thresholds are exhibited; as
a consequence, it is shown that the asymptotic Gilbert-Varshamov bound is a
very sharp threshold point for the density of the linear codes whose relative
distance is greater than a given positive number. For arbitrary random codes,
similar settings and results are exhibited; in particular, the very sharp
threshold point for the density of the codes whose relative distance is greater
than a given positive number is located at half the asymptotic
Gilbert-Varshamov bound.


  We introduce Pixie, a novel, camera based two factor authentication solution
for mobile and wearable devices. A quick and familiar user action of snapping a
photo is sufficient for Pixie to simultaneously perform a graphical password
authentication and a physical token based authentication, yet it does not
require any expensive, uncommon hardware. Pixie establishes trust based on both
the knowledge and possession of an arbitrary physical object readily accessible
to the user, called trinket. Users choose their trinkets similar to setting a
password, and authenticate by presenting the same trinket to the camera. The
fact that the object is the trinket, is secret to the user. Pixie extracts
robust, novel features from trinket images, and leverages a supervised learning
classifier to effectively address inconsistencies between images of the same
trinket captured in different circumstances.
  Pixie achieved a false accept rate below 0.09% in a brute force attack with
14.3 million authentication attempts, generated with 40,000 trinket images that
we captured and collected from public datasets. We identify master images, that
match multiple trinkets, and study techniques to reduce their impact.
  In a user study with 42 participants over 8 days in 3 sessions we found that
Pixie outperforms text based passwords on memorability, speed, and user
preference. Furthermore, Pixie was easily discoverable by new users and
accurate under field use. Users were able to remember their trinkets 2 and 7
days after registering them, without any practice between the 3 test dates.


  X-ray properties of galaxy groups can unlock some of the most challenging
research topics in modern extragalactic astronomy: the growth of structure and
its influence on galaxy formation. Only with the advent of the Chandra and XMM
facilities have X-ray observations reached the depths required to address these
questions in a satisfactory manner. Here we present an X-ray imaging study of
two patches from the CNOC2 spectroscopic galaxy survey using combined Chandra
and XMM data. A state of the art extended source finding algorithm has been
applied, and the resultant source catalog, including redshifts from a
spectroscopic follow-up program, is presented. The total number of
spectroscopically identified groups is 25 spanning a redshift range 0.04-0.79.
Approximately 50% of CNOC2 spectroscopically selected groups in the deeper
X-ray (RA14h) field are likely X-ray detections, compared to 20% in the
shallower (RA21h) field. Statistical modeling shows that this is consistent
with expectations, assuming an expected evolution of the Lx-M relation. A
significant detection of a stacked shear signal for both spectroscopic and
X-ray groups indicates that both samples contain real groups of about the
expected mass. We conclude that the current area and depth of X-ray and
spectroscopic facilities provide a unique window of opportunity at z~0.4 to
test the X-ray appearance of galaxy groups selected in various ways. There is
at present no evidence that the correlation between X-ray luminosity and
velocity dispersion evolves significantly with redshift, which implies that
catalogs based on either method can be fairly compared and modeled.


  Applying Baxter's method of the Q-operator to the set of Sekiguchi's
commuting partial differential operators we show that Jack polynomials
P(x_1,...,x_n) are eigenfunctions of a one-parameter family of integral
operators Q_z. The operators Q_z are expressed in terms of the
Dirichlet-Liouville n-dimensional beta integral. From a composition of n
operators Q_{z_k} we construct an integral operator S_n factorising Jack
polynomials into products of hypergeometric polynomials of one variable. The
operator S_n admits a factorisation described in terms of restricted Jack
polynomials P(x_1,...,x_k,1,...,1). Using the operator Q_z for z=0 we give a
simple derivation of a previously known integral representation for Jack
polynomials.


  In this article we describe the implementation of Artificial Intelligence
models in track reconstruction software for the CLAS12 detector at Jefferson
Lab. The Artificial Intelligence based approach resulted in improved track
reconstruction efficiency in high luminosity experimental conditions. The track
reconstruction efficiency increased by $10-12\%$ for single particle, and
statistics in multi-particle physics reactions increased by $15\%-35\%$
depending on the number of particles in the reaction. The implementation of
artificial intelligence in the workflow also resulted in a speedup of the
tracking by $35\%$.


  The rate of terrestrial irradiation events by galactic gamma-ray bursts
(GRBs) is estimated using recent standard-energy results. We assume that GRBs
accelerate high-energy cosmic rays, and present results of three-dimensional
simulations of cosmic rays moving in the Galactic magnetic field and diffusing
through pitch-angle scattering. An on-axis GRB extinction event begins with a
powerful prompt gamma-ray and neutron pulse, followed by a longer-lived phase
from cosmic-ray protons and neutron-decay protons that diffuse towards Earth.
Our results force a reinterpretation of reported ~ 10^{18} eV cosmic-ray
anisotropies and offer a rigorous test of the model where high-energy cosmic
rays originate from GRBs, which will soon be tested with the Auger Observatory.


  The paper puts forward new Besov spaces of variable smoothness
$B^{\varphi_{0}}_{p,q}(G,\{t_{k}\})$ and
$\widetilde{B}^{l}_{p,q,r}(\Omega,\{t_{k}\})$ on rough domains. A~domain~$G$ is
either a~bounded Lipschitz domain in~$\mathbb{R}^{n}$ or the epigraph of
a~Lipschitz function, a~domain~$\Omega$ is an $(\varepsilon,\delta)$-domain.
These spaces are shown to be the traces of the spaces
$B^{\varphi_{0}}_{p,q}(\mathbb{R}^{n},\{t_{k}\})$ and
$\widetilde{B}^{l}_{p,q,r}(\mathbb{R}^{n},\{t_{k}\})$ on domains $G$
and~$\Omega$, respectively. The extension operator
$\operatorname{Ext}_{1}:B^{\varphi_{0}}_{p,q}(G,\{t_{k}\}) \to
B^{\varphi_{0}}_{p,q}(\mathbb{R}^{n},\{t_{k}\})$ is linear, the operator
$\operatorname{Ext}_{2}:\widetilde{B}^{l}_{p,q,r}(\Omega,\{t_{k}\}) \to
\widetilde{B}^{l}_{p,q,r}(\mathbb{R}^{n},\{t_{k}\})$ is nonlinear. As
a~corollary, an exact description of the traces of 2-microlocal Besov-type
spaces and weighted Besov-type spaces on rough domains is obtained.


  We give topological conditions to ensure that a noncollapsed almost
Ricci-flat 4-manifold admits a Ricci-flat metric. One sufficient condition is
that the manifold is spin and has a nonzero A-hat genus. Another condition is
that the fundamental group is infinite or, more generally, of sufficiently
large cardinality.


  We present a study of the propagation of three-dimensional (3D) bipolar
electromagnetic ultrashort pulses in an inhomogeneous array of semiconductor
carbon nanotubes (CNTs) in the presence of a control high-frequency (HF)
electric field. The inhomogeneity is present in the form of a layer with an
increased concentration of conduction electrons, which acts as a barrier for
the propagation of ultrashort electromagnetic pulses through the CNT array. The
dynamics of the pulse is described by a nonlinear equation for the vector
potential of the electromagnetic field (it takes the form of a 3D
generalization of the sine-Gordon equation), derived from the Maxwell's
equations and averaged over the period of the HF control field. By means of
systematic simulations, we demonstrate that, depending on the amplitude and
frequency of the HF control, the ultrashort pulse approaching the barrier layer
either passes it or bounces back. The layer's transmissivity for the incident
pulse is significantly affected by the amplitude and frequency of the HF
control field, with the reflection coefficient nearly vanishing in intervals
that make up a discrete set of transparency windows, which resembles the effect
of the electromagnetically-induced transparency. Having passed the barrier, the
ultrashort pulse continues to propagate, keeping its spatiotemporal integrity.
The results may be used for the design of soliton valves, with the
transmissivity of the soliton stream accurately controlled by the HF field.


  The uniform field assumption used to derive semi-classical cutoff energies of
$10U_p$ for electron emission and $3.17U_p$ for high harmonic generation is
applicable for ponderomotive amplitudes ($\propto E\lambda^2$) much smaller
than the field drop-off scale. For large wavelength and high field experiments
at nanoscale structures this assumption may break down by predicting energies
beyond the true classical energy limits. Here we provide generalized
calculations for these cutoff energies by taking into account the spatial field
drop-off. The modified cutoff energies vary significantly from the uniform
field results even with ponderomotive amplitudes still an order of magnitude
below the field drop-off scale. Electron emission and scattering energy as a
function of the time-of-ionization is considered for the nanotip ($\sim1/r^2$)
field profile. The cutoff energies as a function of the adiabaticity parameter
$\delta$, which may be easily calculated for given wavelength, apex field
strength, and nanostructure scale, are then determined through maximization for
nanotip, nanoblade ($\sim1/r$), and exponential field profiles. These profiles
deviate from each other in electron emission energy by up to nearly a factor of
the ponderomotive energy, indicating the importance of mid-field profile
behavior. The electron emission energy cutoff also attains an additional factor
of $U_p$ due to the smooth integrated ponderomotive force in the adiabatic
drop-off and very long pulse regime. These results also provided as
double-exponential fits for ease of use. We then compare the nanoblade electron
emission cutoffs with a quantum simulation of the electron rescattering
process. We also consider a short (few-cycle) pulsed field, focusing on a
cosine-like pulse and overviewing the general carrier-envelope phase
dependencies.


  Spin excitations of magnetic thin films are the founding element for novel
transport concepts in spintronics, magnonics, and magnetic devices in general.
While spin dynamics have been extensively studied in bulk materials, their
behaviour in mesoscopic films is less known due to experimental limitations.
Here, we employ Resonant Inelastic X-Ray Scattering to investigate the spin
excitation spectrum in mesoscopic Fe films, from bulk-like down to 3 unit cells
thick. In bulk-like samples, we find isotropic, dispersive ferromagnons
consistent with the dispersion observed by neutron scattering in bulk single
crystals. As the thickness is reduced, these ferromagnons survive and evolve
anisotropically: renormalising to lower energies along the out-of-plane
direction while retaining their dispersion in the in-plane direction. This
thickness dependence is captured by simple Heisenberg model calculations
accounting for the confinement in the out-of-plane direction through the loss
of Fe bonds. Our findings highlight the effects of mesoscopic scaling on spin
dynamics and identify thickness as a knob for fine-tuning and controlling
magnetic properties in films.


  A block graph is a graph in which every block is a complete graph. Let $G$ be
a block graph and let $A(G)$ be its (0,1)-adjacency matrix. Graph $G$ is called
nonsingular (singular) if $A(G)$ is nonsingular (singular). An interesting open
problem, proposed in 2013 by Bapat and Roy, is to characterize nonsingular
block graphs. In this article, we present some classes of nonsingular and
singular block graphs and related conjectures.


  For language model classification, would you prefer having only one workable
class or having every class working? The latter makes more practical uses.
Especially for large language models (LLMs), the fact that they achieve a fair
overall accuracy by in-context learning (ICL) obscures a large difference in
individual class accuracies. In this work, we uncover and tackle language
models' imbalance in per-class prediction accuracy by reconceptualizing it as
the Contextual Oddity Bias (COBias), and we are the first to engage nonlinear
integer programming (NIP) to debias it. Briefly, COBias refers to the
difference in accuracy by a class A compared to its ''odd'' class, which holds
the majority wrong predictions of class A. With the COBias metric, we reveal
that LLMs of varied scales and families exhibit large per-class accuracy
differences. Then we propose Debiasing as Nonlinear Integer Programming (DNIP)
to correct ICL per-class probabilities for lower bias and higher overall
accuracy. Our optimization objective is directly based on the evaluation scores
by COBias and accuracy metrics, solved by simulated annealing. Evaluations on
three LLMs across seven NLP classification tasks show that DNIP simultaneously
achieves significant COBias reduction ($-27\%$) and accuracy improvement
($+12\%$) over the conventional ICL approach, suggesting that modeling pairwise
class accuracy differences is a direction in pushing forward more accurate,
more reliable LLM predictions.


  Information flows are intrinsic properties of an multi-stage manufacturing
systems (MMS). In computer security, a basic information flow tracking
technique is dynamic taint analysis (DTA). DTA tracks taint propagation from
one data variable (e.g., a buffer holding a HTTP request) to another. Taint
propagation paths are typically determined by data flows and implicit flows in
a computer program. And the union of all the taint propagation paths forms a
taint graph. It is clear that taints graphs could significantly enhance
intrusion diagnosis. However, the existing DTA techniques cannot be directly
used in an MMS, and a main reason is as follows: Without manufacturing-specific
taint propagation rules, DTA cannot be implemented. In this work, we conduct a
case study which (a) extends the existing DTA method with
manufacturing-specific taint propagation rules, and (b) applies the extended
method to perform preliminary intrusion diagnosis with a small-scale test-bed.


  A Gelfand-Cetlin system is a completely integrable system defined on a
partial flag manifold whose image is a rational convex polytope called a
Gelfand-Cetlin polytope. Motivated by the study of Nishinou-Nohara-Ueda on the
Floer theory of Gelfand-Cetlin systems, we provide a detailed description of
topology of Gelfand-Cetlin fibers. In particular, we prove that any fiber over
an interior point of a k-dimensional face of the Gelfand-Cetlin polytope is an
isotropic submanifold and is diffeomorphic to $(S^1)^k \times N$ for some
smooth manifold $N$. We also prove that such $N$'s are exactly the vanishing
cycles shrinking to points in the associated toric variety via the toric
degeneration. We also devise an algorithm of reading off Lagrangian fibers from
the combinatorics of the ladder diagram.


  Command and control (C2) channels are an essential component of many types of
cyber attacks, as they enable attackers to remotely control their
malware-infected machines and execute harmful actions, such as propagating
malicious code across networks, exfiltrating confidential data, or initiating
distributed denial of service (DDoS) attacks. Identifying these C2 channels is
therefore crucial in helping to mitigate and prevent cyber attacks. However,
identifying C2 channels typically involves a manual process, requiring deep
knowledge and expertise in cyber operations. In this paper, we propose a
reinforcement learning (RL) based approach to automatically emulate C2 attack
campaigns using both the normal (public) and the Tor networks. In addition,
payload size and network firewalls are configured to simulate real-world attack
scenarios. Results on a typical network configuration show that the RL agent
can automatically discover resilient C2 attack paths utilizing both Tor-based
and conventional communication channels, while also bypassing network
firewalls.


  Divergences, also known as contrast functions, are distance-like quantities
defined on manifolds of non-negative or probability measures. Using the duality
in optimal transport, we introduce and study the one-parameter family of
$L^{(\pm \alpha)}$-divergences. It includes the Bregman divergence
corresponding to the Euclidean quadratic cost, and the $L$-divergence
introduced by Pal and the author in connection with portfolio theory and a
logarithmic cost function. They admit natural generalizations of exponential
family that are closely related to the $\alpha$-family and $q$-exponential
family. In particular, the $L^{(\pm \alpha)}$-divergences of the corresponding
potential functions are R\'{e}nyi divergences. Using this unified framework we
prove that the induced geometries are dually projectively flat with constant
sectional curvatures, and a generalized Pythagorean theorem holds true.
Conversely, we show that if a statistical manifold is dually projectively flat
with constant curvature $\pm \alpha$ with $\alpha > 0$, then it is locally
induced by an $L^{(\mp \alpha)}$-divergence. We define in this context a
canonical divergence which extends the one for dually flat manifolds.


  We investigate the dynamics of stellar-mass black holes (BH) in star clusters
focusing on the dynamical formation of BH-BH binaries, which are very important
sources of gravitational waves (GW). We examine the properties of these BH-BH
binaries through direct N-body computations of Plummer clusters, having
initially N(0) <= 10^5 low mass stars and a population of stellar mass BHs,
using the state-of-the-art N-body integrator "NBODY6". We find that the stellar
mass BHs segregate rapidly into the cluster core to form a central dense
sub-cluster of BHs in which BH-BH binaries form via 3-body encounters. While
most of the BH binaries finally escape from the cluster by recoils due to
super-elastic encounters with the single BHs, we find that for clusters with
N(0) >= 5 X 10^4, typically a few of them dynamically harden to the extent that
they can merge via GW emission within the cluster. Also, for each of such
clusters, there are a few escaped BH binaries that merge within a Hubble time,
most of the mergers happening within a few Gyr of cluster evolution. These
results imply that the intermediate-aged massive clusters constitute the most
important class of star clusters that can produce dynamical BH-BH mergers at
the present epoch. The BH-BH merger rates obtained from our computations imply
a significant detection rate (~ 30/yr) for the "Advanced LIGO" GW detector that
will become operative in the near future. Finally, we briefly discuss our
ongoing development on this work incorporating the formation of BHs in star
clusters from stellar evolution. In particular, we highlight the effect of
stellar metallicity on the BH sub-cluster driven expansion of a star cluster's
core.


  The rapid and massive diffusion of electric vehicles poses new challenges to
the electric system, which must be able to supply these new loads, but at the
same time opens up new opportunities thanks to the possible provision of
ancillary services. Indeed, in the so-called Vehicle-to-Grid (V2G) set-up, the
charging power can be modulated throughout the day so that a fleet of vehicles
can absorb an excess of power from the grid or provide extra power during a
shortage.To this end, many works in the literature focus on the optimization of
each vehicle daily charging profiles to offer the requested ancillary services
while guaranteeing a charged battery for each vehicle at the end of the day.
However, the size of the economic benefits related to the provision of
ancillary services varies significantly with the modeling approaches, different
assumptions, and considered scenarios. In this paper we propose a profitability
analysis with reference to a recently proposed framework for V2G optimal
operation in presence of uncertainty. We provide necessary and sufficient
conditions for profitability in a simplified case and we show via simulation
that they also hold for the general case.


  Stein's (1959) problem highlights the phenomenon called the probability
dilution in high dimensional cases, which is known as a fundamental deficiency
in probabilistic inference. The satellite conjunction problem also suffers from
probability dilution that poor-quality data can lead to a dilution of collision
probability. Though various methods have been proposed, such as generalized
fiducial distribution and the reference posterior, they could not maintain the
coverage probability of confidence intervals (CIs) in both problems. On the
other hand, the confidence distribution (CD) has a point mass at zero, which
has been interpreted paradoxical. However, we show that this point mass is an
advantage rather than a drawback, because it gives a way to maintain the
coverage probability of CIs. More recently, `false confidence theorem' was
presented as another deficiency in probabilistic inferences, called the false
confidence. It was further claimed that the use of consonant belief can
mitigate this deficiency. However, we show that the false confidence theorem
cannot be applied to the CD in both Stein's and satellite conjunction problems.
It is crucial that a confidence feature, not a consonant one, is the key to
overcome the deficiencies in probabilistic inferences. Our findings reveal that
the CD outperforms the other existing methods, including the consonant belief,
in the context of Stein's and satellite conjunction problems. Additionally, we
demonstrate the ambiguity of coverage probability in an observed CI from the
frequentist CI procedure, and show that the CD provides valuable information
regarding this ambiguity.


  We present a fault-tolerant universal quantum computing architecture based on
a code concatenation of noise-biased qubits and the parity architecture. The
parity architecture can be understood as a LDPC code tailored specifically to
obtain any desired logical connectivity from nearest neighbor physical
interactions. The code layout can be dynamically adjusted to algorithmic
requirements on-the-fly. This allows reaching arbitrary code distances and
thereby exponential suppression of errors with a universal set of
fault-tolerant gates. In addition to the previously explored tool-sets for
concatenated cat codes, our approach features parallelizable interactions
between arbitrary sets of qubits by directly addressing the parity qubits in
the code. The proposed scheme enables codes with less physical qubit overhead
compared to the repetition code with the same code distances, while requiring
only weight-3 and weight-4 stabilizers and nearest neighbor 2D square-lattice
connectivity.


  We present graph wavelet neural network (GWNN), a novel graph convolutional
neural network (CNN), leveraging graph wavelet transform to address the
shortcomings of previous spectral graph CNN methods that depend on graph
Fourier transform. Different from graph Fourier transform, graph wavelet
transform can be obtained via a fast algorithm without requiring matrix
eigendecomposition with high computational cost. Moreover, graph wavelets are
sparse and localized in vertex domain, offering high efficiency and good
interpretability for graph convolution. The proposed GWNN significantly
outperforms previous spectral graph CNNs in the task of graph-based
semi-supervised classification on three benchmark datasets: Cora, Citeseer and
Pubmed.


  We present a fully ab initio, non-perturbative description of the optical
limiting properties of a metal-free phthalocyanine, by simulating the effects
of a broadband electric field of increasing intensity. The results confirm
reverse saturable absorption as leading mechanism for optical limiting
phenomena in this system and reveal that a number of dipole-forbidden
excitations are populated by excited-state absorption, at more intense external
fields. The excellent agreement with the experimental data supports our
approach as a powerful tool to predict optical limiting, in view of
applications.


  We present the Widefield ASKAP L-band Legacy All-sky Blind surveY (WALLABY)
Pilot Phase I HI kinematic models. This first data release consists of HI
observations of three fields in the direction of the Hydra and Norma clusters,
and the NGC 4636 galaxy group. In this paper, we describe how we generate and
publicly release flat-disk tilted-ring kinematic models for 109/592 unique HI
detections in these fields. The modelling method adopted here - which we call
the WALLABY Kinematic Analysis Proto-Pipeline (WKAPP) and for which the
corresponding scripts are also publicly available - consists of combining
results from the homogeneous application of the FAT and 3DBAROLO algorithms to
the subset of 209 detections with sufficient resolution and S/N in order to
generate optimized model parameters and uncertainties. The 109 models presented
here tend to be gas rich detections resolved by at least 3-4 synthesized beams
across their major axes, but there is no obvious environmental bias in the
modelling. The data release described here is the first step towards the
derivation of similar products for thousands of spatially-resolved WALLABY
detections via a dedicated kinematic pipeline. Such a large publicly available
and homogeneously analyzed dataset will be a powerful legacy product that that
will enable a wide range of scientific studies.


  Movable antenna (MA) has emerged as a promising technology to enhance
wireless communication performance by enabling the local movement of antennas
at the transmitter (Tx) and/or receiver (Rx) for achieving more favorable
channel conditions. As the existing studies on MA-aided wireless communications
have mainly considered narrow-band transmission in flat fading channels, we
investigate in this paper the MA-aided wideband communications employing
orthogonal frequency division multiplexing (OFDM) in frequency-selective fading
channels. Under the general multi-tap field-response channel model, the
wireless channel variations in both space and frequency are characterized with
different positions of the MAs. Unlike the narrow-band transmission where the
optimal MA position at the Tx/Rx simply maximizes the single-tap channel
amplitude, the MA position in the wideband case needs to balance the amplitudes
and phases over multiple channel taps in order to maximize the OFDM
transmission rate over multiple frequency subcarriers. First, we derive an
upper bound on the OFDM achievable rate in closed form when the size of the
Tx/Rx region for antenna movement is arbitrarily large. Next, we develop a
parallel greedy ascent (PGA) algorithm to obtain locally optimal solutions to
the MAs' positions for OFDM rate maximization subject to finite-size Tx/Rx
regions. To reduce computational complexity, a simplified PGA algorithm is also
provided to optimize the MAs' positions more efficiently. Simulation results
demonstrate that the proposed PGA algorithms can approach the OFDM rate upper
bound closely with the increase of Tx/Rx region sizes and outperform
conventional systems with fixed-position antennas (FPAs) under the wideband
channel setup.


  Assuming a spatially flat universe, we study the cosmological viability of an
infrared corrected teleparallel gravity model, which accounts for late
acceleration by weakening gravity at later times on cosmological distances. The
theory does not introduce any additional free parameters into the cosmological
model, as is commonly the case with modified gravity based cosmologies. This
feature renders the cosmological model statistically comparable, on equal
footing, with $\Lambda$CDM. In this context, using recent cosmological
observations -- Pantheon supernova Type Ia, Hubble constant $H_0$, Baryon
acoustic oscillation, redshift space distortions, Big Bang nucleosynthesis and
the cosmic microwave background constraint on the decoupling acoustic scale --
we show that, although the exponential infrared-corrected gravity and
$\Lambda$CDM are physically different, they are phenomenologically and
statistically equivalent. However, the former is more adept at fitting
accurately determined observational constraints while decreasing the $H_0$
tension without worsening the $S_8$ tension. This calls for full examination of
the empirical viability of the theory at the linear perturbation level, which
is the subject of paper II.


  We prove that the defining equations of the Fermat curves of prime degree
cannot be written as the determinant of symmetric matrices with entries in
linear forms in three variables with rational coefficients. In the proof, we
use a relation between symmetric matrices with entries in linear forms and
non-effective theta characteristics on smooth plane curves. We also use some
results of Gross-Rohrlich on the rational torsion points on the Jacobian
varieties of the Fermat curves of prime degree.


  We compute the temperature profiles of accretion discs around rapidly
rotating strange stars, using constant gravitational mass equilibrium sequences
of these objects, considering the full effect of general relativity. Beyond a
certain critical value of stellar angular momentum ($J$), we observe the radius
($r_{\rm orb}$) of the innermost stable circular orbit (ISCO) to increase with
J (a property seen neither in rotating black holes nor in rotating neutron
stars). The reason for this is traced to the crucial dependence of $dr_{\rm
orb}/dJ$ on the rate of change of the radial gradient of the Keplerian angular
velocity at $r_{\rm orb}$ with respect to $J$. The structure parameters and
temperature profiles obtained are compared with those of neutron stars, as an
attempt to provide signatures for distinguishing between the two. We show that
when the full gamut of strange star equation of state models, with varying
degrees of stiffness are considered, there exists a substantial overlap in
properties of both neutron stars and strange stars. However, applying accretion
disc model constraints to rule out stiff strange star equation of state models,
we notice that neutron stars and strange stars exclusively occupy certain
parameter spaces. This result implies the possibility of distinguishing these
objects from each other by sensitive observations through future X-ray
detectors.


  Frictional interfaces are abundant in natural and manmade systems and their
dynamics still pose challenges of fundamental and technological importance. A
recent extensive compilation of multiple-source experimental data has revealed
that velocity-strengthening friction, where the steady-state frictional
resistance increases with sliding velocity over some range, is a generic
feature of such interfaces. Moreover, velocity-strengthening friction has very
recently been linked to slow laboratory earthquakes and stick-slip motion. Here
we elucidate the importance of velocity-strengthening friction by theoretically
studying three variants of a realistic rate-and-state friction model. All
variants feature identical logarithmic velocity-weakening friction at small
sliding velocities, but differ in their higher velocity behaviors. By
quantifying energy partition (e.g. radiation and dissipation), the selection of
interfacial rupture fronts and rupture arrest, we show that the presence or
absence of velocity-strengthening friction can significantly affect the global
interfacial resistance and the total energy released during frictional
instabilities ("event magnitude"). Furthermore, we show that different forms of
velocity-strengthening friction (e.g. logarithmic vs. linear) may result in
events of similar magnitude, yet with dramatically different dissipation and
radiation rates. This happens because the events are mediated by interfacial
rupture fronts with vastly different propagation velocities, where stronger
velocity-strengthening friction promotes slower rupture. These theoretical
results may have significant implications on our understanding of frictional
dynamics.


  A concept of a 650 MHz CW magnetron transmitter with fast control in phase
and power, based on two-stage injection-locked CW magnetrons, has been proposed
to drive Superconducting Cavities (SC) for intensity-frontier accelerators. The
concept is based on a theoretical model considering a magnetron as a forced
oscillator and experimentally verified with a 2.5 MW pulsed magnetron. To
fulfill fast control of phase and output power requirements of SC accelerators,
both two-stage injection-locked CW magnetrons are combined with a 3-dB hybrid.
Fast control in output power is achieved by varying the input phase of one of
the magnetrons. For output power up to 250 kW we expect the output/input power
ratio to be about 35 to 40 dB in CW or quasi-CW mode with long pulse duration.
All magnetrons of the transmitter should be based on commercially available
models to decrease the cost of the system. An experimental model using 1 kW,
CW, S-band, injection-locked magnetrons with a 3-dB hybrid combiner has been
developed and built for study. A description of the model, simulations, and
experimental results are presented and discussed in this work.


  The dependence of the sixth equation of Painleve' on its four parameters $(2
\alpha,-2 \beta,2 \gamma,1-2 \delta)
=(\theta_{\infty}^2,\theta_{0}^2,\theta_{1}^2,\theta_{x}^2)$ is holomorphic,
therefore one expects all its Lax pairs to display such a dependence. This is
indeed the case of the second order scalar ``Lax'' pair of Fuchs, but the
second order matrix Lax pair of Jimbo and Miwa presents a meromorphic
dependence on $\theta_\infty$ (and a holomorphic dependence on the three other
$\theta_j$). We analyze the reason for this feature and make suggestions to
suppress it.


  Schmidt, Jones, and Kennedy's (SJK) (2023,
https://doi.org/10.1029/2022GL102530) critique of Scafetta (2022,
https://doi.org/10.1029/2022GL097716) is flawed. Their assessment of the error
of the ERA-T2m 2011-2021 mean (about 0.10 {\deg}C) is 5-10 times overestimated
and contradicts published literature. SJK confused natural variability with
random noise and mistook the error of the mean of a temperature chronology for
the stochastic error of the regression parameter M of a nonphysical isothermal
climate model (T(t) = M). SJK's allegations regarding the internal variability
of the models, the role of the global climate model ensemble members, and other
issues were partially addressed in Scafetta (2022,
https://doi.org/10.1029/2022GL097716) and, later, more extensively in Scafetta
(2023a, https://doi.org/10.1007/s00382-022-06493-w) where Scafetta's (2022,
https://doi.org/10.1029/2022GL097716) conclusions were confirmed.


  In this article we have shown that the atomic states can be engineered by
tunning the coupling Rabi frequency for a system with $\mathcal{N}$-type
configuration. Electromagnetically induced transparency (EIT),
Electromagnetically induced absorption (EIA) and Autler-Townes (AT) splitting
has been observed experimentally in a four level $\mathcal{N}$-type atomic
vapor of $^{85}Rb$ atoms in the hyperfine levels of $D_2$ transition. It has
been shown that the response of the atomic medium can be tunned from highly
transparent to highly absorptive in our case. The evolution of the atomic
states from the dark state |D> to the non-coupled state |NC> has been studied
with the partial dressed state approach which makes the backbone of the
modification of the atomic response. In addition, transient solutions in the
time domain and steady state solution in the frequency domain has been studied.
The population dynamics and the coherence contribution in each case has been
analyzed by the time dependent solutions. The experimentally observed steady
line-shape profiles has been supported by the steady state solution of
optical-Bloch equations considering the Maxwell Boltzmann velocity
distributions of the atoms. It has been observed that the crossover between the
EIT and the AT splitting has been replaced by the interference contribution of
the EIA in this $\mathcal{N}$-type system.


  Most of previous work on learning diacritization of the Arabic language
relied on training models from scratch. In this paper, we investigate how to
leverage pre-trained language models to learn diacritization. We finetune
token-free pre-trained multilingual models (ByT5) to learn to predict and
insert missing diacritics in Arabic text, a complex task that requires
understanding the sentence semantics and the morphological structure of the
tokens. We show that we can achieve state-of-the-art on the diacritization task
with minimal amount of training and no feature engineering, reducing WER by
40%. We release our finetuned models for the greater benefit of the researchers
in the community.


  This paper presents the Coded Packet Transport (CPT) scheme, a novel
transport mechanism for Optical Packet/Burst Switched (OPS/OBS) networks. The
CPT scheme exploits the combined benefits of source coding by erasure codes and
path diversity to provide efficient means for recovering from packet loss due
to contentions and path failures, and to provide non-cryptographic secrecy. In
the CPT scheme, erasure coding is employed at the OPS/OBS ingress node to form
coded packets, which are transmitted on disjoint paths from the ingress node to
an egress node in the network. The CPT scheme allows for a unified view of
Quality of Service (QoS) in OPS/OBS networks by linking the interactions
between survivability, performance and secrecy. We provide analytical models
that illustrate how QoS aspects of CPT are affected by the number of disjoint
paths, packet overhead and processing delay.


  A graph $G$ is well-covered if all maximal independent sets of $G$ have the
same cardinality. In 1992 Topp and Volkmann investigated the structure of
well-covered graphs that have nontrivial factorizations with respect to some of
the standard graph products. In particular, they showed that both factors of a
well-covered direct product are also well-covered and proved that the direct
product of two complete graphs (respectively, two cycles) is well-covered
precisely when they have the same order (respectively, both have order 3 or 4).
Furthermore, they proved that the direct product of two well-covered graphs
with independence number one-half their order is well-covered. We initiate a
characterization of nontrivial, connected well-covered graphs $G$ and $H$,
whose independence numbers are strictly less than one-half their orders, such
that their direct product $G \times H$ is well-covered. In particular, we show
that in this case both $G$ and $H$ have girth 3 and we present several infinite
families of such well-covered direct products. Moreover, we show that if $G$ is
a factor of any well-covered direct product, then $G$ is a complete graph
unless it is possible to create an isolated vertex by removing the closed
neighborhood of some independent set of vertices in $G$.


  The stability of Yang-Mills bundles over the usual $S^4$ space-time manifold
is investigated according to the topological methods. The necessary gauge- and
topological invaraint criterion for the exsitence of the related critical
points is defined. It is shown that according to this criterion there exists no
critical point even for the action functional of the standard U(1) gauge theory
of electrodynamics on a $S^4$ manifold in view of its topological structure and
therefore such a theory can not be stable. We will discuss also a general
consequence of this result according to which for a stable U(1) Yang-Mills
theory over a compact 4-manifold, this manifold should possess some self
consistent compact 2-manifold substructure. These results are also in agreement
with the known very general result for the {\it structural stability} of
dynamical systems.


  I provide an alternate and self-contained proof of Botha's theorem on
products of idempotent and square-zero matrices where the product contains two
square-zero factors, and provide a conclusive characterisation of products of
singular quadratic matrices based on previous results.


  We study the constraints on HST models of AdS space-time. The causal diamonds
of HST along time-like geodesics of AdS space-time, fit nicely into the FRW
patch of AdS space. The coordinate singularity of the FRW patch is identified
with the proper time at which the Hilbert space of the causal diamond becomes
infinite dimensional. For diamonds much smaller than the AdS radius, RAdS, the
time dependent Hamiltonians of HST are the same as those used to describe
similar diamonds in Minkowski space. In particular, they are invariant under
the fuzzy analog of volume preserving diffeomorphisms of the holographic
screen, which leads to fast scrambling of perturbations on the horizon of a
black hole of size smaller than RAdS. We argue that, in order to take a limit
of this system which converges to a CFT, one must choose Hamiltonians, in a
range of proper times of order RAdS, which break this invariance, and become
local in a particular choice of basis for the variables. We show that,
beginning with flat, sub-RAdS, patches of dimension D, the resulting CFT,
constructed from the variables of HST, is inconsistent with the entropy of
large black holes, unless one has at least two compact dimensions, whose size
is of order RAdS. The argument is connected to a new observation about the
scrambling rate of information localized on the compact dimensions. Our
construction explains why large AdS black holes do not have the fast scrambling
property. Our present approach cannot deal with models where string theory is
weakly coupled and RAdS is of order the string scale, because the relationship
between area and entropy is non-universal in such models. On spatial length
scales longer than RAdS, our mapping of HST variables into CFT shares much with
the Tensor Network Renormalization Group (TNRG)[1] and is a sort of evolving
error correcting code[2].


  Realizations of scale invariance are studied in the context of a
gravitational theory where the action (in the first order formalism) is of the
form $S = \int L_{1} \Phi d^{4}x$ + $\int L_{2}\sqrt{-g}d^{4}x$ where $\Phi$ is
a density built out of degrees of freedom, the "measure fields" independent of
$g_{\mu\nu}$ and matter fields appearing in $L_{1}$, $L_{2}$. If $L_{1}$
contains the curvature, scalar potential $V(\phi)$ and kinetic term for $\phi$,
$L_{2}$ another potential for $\phi$, $U(\phi)$, then the true vacuum state has
zero energy density, when theory is analyzed in the conformal Einstein frame
(CEF), where the equations assume the Einstein form. Global Scale invariance is
realized when $V(\phi)$ = $f_{1}e^{\alpha\phi}$ and $U(\phi)$ =
$f_{2}e^{2\alpha\phi}$. In the CEF the scalar field potential energy
$V_{eff}(\phi)$ has in, addition to a minimum at zero, a flat region for
$\alpha\phi \to\infty$, with non zero vacuum energy, which is suitable for
either a New Inflationary scenario for the Early Universe or for a slowly
rolling decaying $\Lambda$-scenario for the late universe, where the smallness
of the vacuum energy can be understood as a kind of see-saw mechanism.


  We undertake an optical and ultraviolet spectroscopic analysis of a sample of
20 Galactic B0 - B5 supergiants of luminosity classes Ia, Ib, Iab and II.
Fundamental stellar parameters are obtained from optical diagnostics and a
critical comparison of the model predictions to observed UV spectral features
is made. These parameters are derived for individual stars using CMFGEN, the
nLTE, line-blanketed model atmosphere code of Hillier et al., 1998. The B
supergiant temperature scale derived here shows a reduction of 1000 - 3000 K
compared to previous results obtained using unblanketed codes. Mass loss rate
estimates are in good agreement with predicted theoretical values and all of
the 20 B0 - B5 supergiants analysed show evidence for CNO processing. The
observed WLR values calculated for B0 - B0.7 supergiants are larger than
predicted values, whereas the reverse is true for B1 - B5 supergiants. This
means that the discrepancy between observed and theoretical values cannot be
resolved by adopting clumped (i.e., lower) mass loss rates, as for O stars. The
most surprising result is that, although CMFGEN succeeds in reproducing the
optical spectrum accurately, it fails to reproduce key UV diagnostics, such as
NV and CIV P Cygni profiles, precisely. This problem arises because the models
are not ionised enough and fail to reproduce the full extent of the observed
absorption trough of the P Cygni profiles. These findings add further support
to the need to revise the standard model of massive star winds.


  The Stochastic Series Expansion (SSE) technique is a quantum Monte Carlo
method that is especially efficient for many quantum spin systems and boson
models. It was the first generic method free from the discretization errors
affecting previous path integral based approaches. These lecture notes give a
brief overview of the SSE method and its applications. In the introductory
section, the representation of quantum statistical mechanics by the power
series expansion of ${\rm e}^{-\beta H}$ will be compared with path integrals
in discrete and continuous imaginary time. Extensions of the SSE approach to
ground state projection and quantum annealing in imaginary time will also be
briefly discussed. The later sections introduce efficient sampling schemes
(loop and cluster updates) that have been developed for many classes of models.
A summary of generic forms of estimators for important observables are also
given. Applications are discussed in the last section.


  We reinvestigated the neutron multiplicity yields of Ba-Mo, Ce-Zr, Te-Pd, and
Nd-Sr from the spontaneous fission of $^{252}$Cf; by (i) using both
$\gamma$-$\gamma$-$\gamma$-$\gamma$ and $\gamma$-$\gamma$-$\gamma$ coincidence
data, (ii) using up to date level scheme structures, and (iii) cross-checking
analogous energy transitions in multiple isotopes, we have achieved higher
precision than previous analyses. Particular attention was given to the Ba-Mo
pairs where our results clearly confirm that the Ba-Mo yield data have a second
hot fission mode where 8, 9, 10, and now 11 neutron evaporation channels are
observed. These are the first observations of the 11 neutron channel. These
8-11 neutron channels are observed for the first time in the Ce-Zr pairs, but
are not observed in other fission pairs. The measured intensities of the second
mode in Ba-Mo and Ce-Zr pairs are $\sim$1.5(4)$\%$ and $\sim$1.0(3)$\%$,
respectively. These high neutron number evaporation modes can be an indication
of hyperdeformation and/or octupole deformation in $^{143-145}$Ba and in
$^{146,148}$Ce at scission to give rise to such high neutron multiplicities.


  We study the reaction $\pi^\pm p \to \pi^\pm \pi^+ n$ and $\pi^- p \to \pi^0
\pi^0 n$ in heavy-baryon chiral perturbation theory of chiral order three from
threshold up to pion laboratory kinetic energies of 400 MeV. We find that the
contributions from amplitudes of chiral order three are large and play an
essential role in reproducing the experimental data.


  The two- and three-point functions and the four-gluon vertex of
three-dimensional Yang-Mills theory are calculated from their Dyson-Schwinger
equations and the 3PI effective action. Within a self-contained truncation
various effects of truncating Dyson-Schwinger equations are studied. Estimates
for the errors induced by truncations are derived from comparisons between
results from different equations, comparisons with lattice results, and varying
higher Green functions. The results indicate that the two-loop diagrams are
important in the gluon propagator, where they are explicitly calculated, but
not for the vertices. Furthermore, the influence of the four-gluon vertex on
lower Green functions is found to be small.


  We discuss the question of the existence of quantum one-way permutations.
First, we prove the equivalence between inverting a permutation and that of
constructing a polynomial size network for reflecting about a given quantum
state. Next, we consider the question: if a state is difficult to prepare, is
the operator reflecting about that state difficult to construct? By revisiting
Grover's algorithm, we present the relationship between this question and the
existence of one-way permutations. Moreover, we compare our method to Grover's
algorithm and discuss possible applications of our results.


  Several examples of similarity transformations connecting two string theories
with different backgrounds are reviewed. We also discuss general structure
behind the similarity transformations from the point of view of the topological
conformal algebra and of the non-linear realization of gauge symmetry.


  This article addresses the intersection of various educational theories and
their relationship with the education of computer science students, with a
focus on the importance of understanding computational thinking and its
application in education. The historical context and fundamental concepts of
Cognitive Load Theory, Multimedia Learning, and Constructivism are explored,
highlighting their underlying biological assumptions about human learning. It
also examines how these theories can be integrated with the use of Artificial
Intelligence (AI) in education, with a particular emphasis on the attention
mechanisms and abstract learning present in AI models like Transformers.
Lastly, the relevance of these theories and practices for computer education
student training is discussed, emphasizing how the development of computational
thinking can contribute to a more effective approach in teaching and learning.


  High-gain antennas are essential hardware devices, powering numerous daily
applications, including distant point-to-point communications, safety radars,
and many others. While a common approach to elevate gain is to enlarge an
antenna aperture, highly resonant subwavelength structures can potentially
grant high gain performances. The Chu-Harrington limit is a standard criterion
to assess electrically small structures and those surpassing it are called
superdirective. Supergain is obtained in a case when internal losses are
mitigated, and an antenna is matched to radiation, though typically in a very
narrow frequency band. Here we develop a concept of a spectrally overlapping
resonant cascading, where tailored multipole hierarchy grants both high gain
and sufficient operational bandwidth. Our architecture is based on a near-field
coupled wire bundle. Genetic optimization, constraining both gain and
bandwidth, is applied on a 24-dimensional space and predicts 8.81 dBi realized
gain within a half-wavelength in a cube volume. The experimental gain is 6.15
with 13% fractional bandwidth. Small wire bundle structures are rather
attractive for designing superscattering and superdirective structures, as they
have a sufficient number of degrees of freedom to perform an optimization, and,
at the same time rely on simple fabrication-tolerant layouts, based on low-loss
materials. The developed approach can be applied to low-frequency (e.g.,
kHz-MHz) applications, where miniaturization of wireless devices is highly
demanded.


  A bilayer graphene based electrostatically doped tunnel field-effect
transistor (BED-TFET) is proposed in this work. Unlike graphene nanoribbon
TFETs in which the edge states deteriorate the OFF-state performance, BED-TFETs
operate based on different bandgaps induced by vertical electric fields in the
source, channel, and drain regions without any chemical doping. The performance
of the transistor is evaluated by self-consistent quantum transport
simulations. This device has several advantages: 1) ultra-low power (VDD=0.1V),
2) high performance (ION/IOFF>104), 3) steep subthreshold swing (SS<10mv/dec),
and 4) electrically configurable between N-TFET and P-TFET post fabrication.
Here, the operation principle of the BED-TFET and its performance sensitivity
to the device design parameters are studied.


  There are several exotic tunneling processes that can be realized only by
incorporating the effect of gravity. Here, we point out that we encounter
difficulties in constructing the WKB wave function, once we try to describe
quantum fluctuations around the semi-classical tunneling path. We present
examples of pathology in the true vacuum decay/upward tunneling, the false
vacuum decay catalyzed by a black hole and the tunneling with black
hole/wormhole production.


  The second layer of He-4 adsorbed on a graphite substrate is studied by
Quantum Monte Carlo simulations. We make use of a microscopic model of the
substrate fully accounting for its corrugation, and compare the results to
those obtained with a smooth substrate. The only effect of corrugation is a
~20% reduction of the value of the superfluid fraction of the top layer, in the
limit of zero temperature. No evidence of any commensurate (7/12) crystalline
and/or "supersolid" phase is found; the superfluid transition temperature is
estimated to be ~ 0.75 K. We discuss the implication of these findings on the
interpretation of recent experiments.


  In this paper, we continue to study random convex analysis. First, we
introduce the notion of an $L^0$--pre--barreled module. Then, we develop the
theory of random duality under the framework of a random locally convex module
endowed with the locally $L^0$--convex topology in order to establish a
characterization for a random locally convex module to be $L^0$--pre--barreled,
in particular we prove that the model space $L^{p}_{\mathcal{F}}(\mathcal{E})$
employed in the module approach to conditional risk measures is
$L^0$--pre--barreled, which forms the most difficult part of this paper.
Finally, we prove the continuity and subdifferentiability theorems for a proper
lower semicontinuous $L^0$--convex function on an $L^{0}$--pre--barreled random
locally convex module. So the principal results of this paper may be well
suited to the study of continuity and subdifferentiability for $L^0$--convex
conditional risk measures.


  Time series forecasting is an important problem across many domains,
including predictions of solar plant energy output, electricity consumption,
and traffic jam situation. In this paper, we propose to tackle such forecasting
problem with Transformer [1]. Although impressed by its performance in our
preliminary study, we found its two major weaknesses: (1) locality-agnostics:
the point-wise dot-product self-attention in canonical Transformer architecture
is insensitive to local context, which can make the model prone to anomalies in
time series; (2) memory bottleneck: space complexity of canonical Transformer
grows quadratically with sequence length $L$, making directly modeling long
time series infeasible. In order to solve these two issues, we first propose
convolutional self-attention by producing queries and keys with causal
convolution so that local context can be better incorporated into attention
mechanism. Then, we propose LogSparse Transformer with only $O(L(\log L)^{2})$
memory cost, improving forecasting accuracy for time series with fine
granularity and strong long-term dependencies under constrained memory budget.
Our experiments on both synthetic data and real-world datasets show that it
compares favorably to the state-of-the-art.


  For practical applications, any neighborhood concept imposed on a finite
point set P is not of any use if it cannot be computed efficiently. Thus, in
this paper, we give an introduction to the data structure of k-d trees, first
presented by Friedman, Bentley, and Finkel in 1977. After a short introduction
to the data structure (Section 1), we turn to the proof of efficiency by
Friedman and his colleagues (Section 2). The main contribution of this paper is
the translation of the proof of Freedman, Bentley, and Finkel into modern terms
and the elaboration of the proof.


  The origin of many elements of the periodic table remains an unsolved
problem. While many nucleosynthetic channels are broadly understood,
significant uncertainties remain regarding certain groups of elements such as
the intermediate and rapid neutron-capture processes, the p-process, or the
origin of odd-Z elements in the most metal-poor stars. Canada has a long
tradition of leadership in nuclear astrophysics, dating back to the work of
Alastair Cameron in the 1950s. Recent faculty hires have further boosted
activity in the field, including transient observation and theory, survey
science on galactic nucleosynthesis, and nuclear experiments. This white paper
contains a brief overview of recent activity in the community, highlighting
strengths in each sub-field, and provides recommendations to improve
interdisciplinary collaboration. Sustaining Canadian leadership in the next
decade will require, on the observational side, access to transient and
non-transient surveys like LSST, SKA, or MSE, support for target-of-opportunity
observing in current and future Canadian telescopes, and participation in
next-generation X-ray telescopes such as ATHENA. State-of-the-art theoretical
predictions will require an ambitious succession plan for the Niagara
supercomputer to support large parallel jobs. We propose a funding instrument
for postdoctoral training that reflects the interdisciplinary nature of nuclear
astrophysics research, and the creation of a national collaborative funding
program that allows for joint projects and workshop organization.


  This paper presents a fast and powerful method for the computation of
eigenvalue bounds for Hessian matrices $\nabla^2 \varphi(x) $ of nonlinear
functions $\varphi: U \subseteq R^n\rightarrow R$ on hyperrectangles $B \subset
U$. The method is based on a recently proposed procedure for an efficient
computation of spectral bounds using extended codelists. Both the previous
approach and the one presented here substantially differ from established
methods in that they do deliberately not use any interval matrices and thus
result in a favorable numerical complexity of order $O(n)\,N(\varphi)$, where
$N(\varphi)$ denotes the number of operations needed to evaluate $\varphi$ at a
point in its domain. We improve the previous method by exploiting sparsity,
which naturally arises in the underlying codelists.


  We consider a measurable stationary Gaussian stochastic process. A criterion
for testing hypotheses about the covariance function of such a process using
estimates for its norm in the space $L_p(\mathbb {T}),\,p\geq1$, is
constructed.


  We study the quantum Fisher information (QFI) and, thus, the multipartite
entanglement structure of thermal pure states in the context of the Eigenstate
Thermalization Hypothesis (ETH). In both the canonical ensemble and the ETH,
the quantum Fisher information may be explicitly calculated from the response
functions. In the case of ETH, we find that the expression of the QFI bounds
the corresponding canonical expression from above. This implies that although
average values and fluctuations of local observables are indistinguishable from
their canonical counterpart, the entanglement structure of the state is starkly
different; with the difference amplified, e.g., in the proximity of a thermal
phase transition. We also provide a state-of-the-art numerical example of a
situation where the quantum Fisher information in a quantum many-body system is
extensive while the corresponding quantity in the canonical ensemble vanishes.
Our findings have direct relevance for the entanglement structure in the
asymptotic states of quenched many-body dynamics.


  We present the results of population syntheses for binary stars carried out
using the ``Scenario Machine'' code with the aim of analyzing events that may
result in long gamma-ray bursts. We show that the observed distribution of
morphological types of the host galaxies of long gamma-ray bursts can be
explained in a model in which long gamma-ray bursts result from the core
collapse of massive Wolf-Rayet stars in close binaries. The dependence of the
burst rate on galaxy type is associated with an increase in the rate of
stellar-wind mass-loss with increasing stellar metallicity. The separation of
binary components at the end of their evolution increases with the stellar-wind
rate, resulting in a reduction of the number of binaries that produce
gamma-bursts.


  We study two important SVM variants: hard-margin SVM (for linearly separable
cases) and $\nu$-SVM (for linearly non-separable cases). We propose new
algorithms from the perspective of saddle point optimization. Our algorithms
achieve $(1-\epsilon)$-approximations with running time $\tilde{O}(nd+n\sqrt{d
/ \epsilon})$ for both variants, where $n$ is the number of points and $d$ is
the dimensionality. To the best of our knowledge, the current best algorithm
for $\nu$-SVM is based on quadratic programming approach which requires
$\Omega(n^2 d)$ time in worst case~\cite{joachims1998making,platt199912}. In
the paper, we provide the first nearly linear time algorithm for $\nu$-SVM. The
current best algorithm for hard margin SVM achieved by Gilbert
algorithm~\cite{gartner2009coresets} requires $O(nd / \epsilon )$ time. Our
algorithm improves the running time by a factor of $\sqrt{d}/\sqrt{\epsilon}$.
Moreover, our algorithms can be implemented in the distributed settings
naturally. We prove that our algorithms require $\tilde{O}(k(d
+\sqrt{d/\epsilon}))$ communication cost, where $k$ is the number of clients,
which almost matches the theoretical lower bound. Numerical experiments support
our theory and show that our algorithms converge faster on high dimensional,
large and dense data sets, as compared to previous methods.


  It is shown that single crystals are sensitive to the initial circular
polarization of gamma-quanta with energies in tens GeV and more. The
possibility of measurement of gamma-beam polarization is discussed. The
obtained results may be useful for creation of polarimeters for high energy
beams of gamma-quanta.


  We present a deep XMM-Newton observation of the extremely massive, rapidly
rotating, relativistic-jet-launching spiral galaxy 2MASX J23453268-0449256.
Diffuse X-ray emission from the hot gaseous halo around the galaxy is robustly
detected out to a radius of 160 kpc, corresponding roughly to 35 per cent of
the virial radius ($\approx 450$ kpc). We fit the X-ray emission with the
standard isothermal $\beta$ model, and it is found that the enclosed gas mass
within 160 kpc is $1.15_{-0.24}^{+0.22} \times 10^{11} \, \rm{M}_{\odot}$.
Extrapolating the gas mass profile out to the virial radius, the estimated gas
mass is $8.25_{-1.77}^{+1.62} \times 10^{11} \, \rm{M}_{\odot}$, which makes up
roughly 65 per cent of the total baryon mass content of the galaxy. When the
stellar mass is considered and accounting for the statistical and systematic
uncertainties, the baryon mass fraction within the virial radius is
$0.121_{-0.043}^{+0.043}$, in agreement with the universal baryon fraction. The
baryon mass fraction is consistent with all baryons falling within $r_{200}$,
or with only half of the baryons falling within $r_{200}$. Similar to the
massive spiral galaxies NGC 1961 and NGC 6753, we find a low value for the
metal abundance of $\approx 0.1 {\rm{Z}}_{\odot}$, which appears uniform with
radius. We also detect diffuse X-ray emission associated with the northern and
southern lobes, possibly attributed to inverse Compton scattering of cosmic
microwave background photons. The estimated energy densities of the electrons
and magnetic field in these radio lobes suggest that they are
electron-dominated by a factor of 10$-$200, depending on the choice of the
lower cut-off energy of the electron spectrum.


  In this paper we study the possibility of probing for the absolute neutrino
mass and its variation with short Gamma Ray Burst (GRB). We have calculated the
flight time difference between a massive neutrino and a photon in two different
approaches to mass varying neutrinos. Firstly we parametrize the neutrino mass
as a function of redshift in a model independent way, then we consider two
specific models where the neutrino mass varies during the evolution of the
Quintessence fields. Our calculations show in general the value of the time
delay is changed substantially relative to a constant neutrino mass.
Furthermore our numerical results show that the flight time delay in these
models is expected to be larger than the duration time of the short GRB, which
opens a possibility of testing the scenario of mass varying neutrino with the
short GRB.


  Different AdS-Rindler wedges can be mapped to each other using bulk
isometries. In this paper we address how the boundary representations
corresponding to the AdS-Rindler wedges transform under such isometries. We
show that when a bulk wedge is mapped to another using a bulk isometry, their
boundary representations are mapped by the conformal transformation
corresponding to the isometry. We comment on the import of this result on the
relation between AdS/CFT and quantum error correction.


  The discourse surrounding the structural organization of mutualistic
interactions mostly revolves around modularity and nestedness. The former is
known to enhance the stability of communities, while the latter is related to
their feasibility, albeit compromising the stability. However, it has recently
been shown that the joint emergence of these structures poses challenges that
can eventually lead to limitations in the dynamic properties of mutualistic
communities. We hypothesize that considering compound arrangements -- modules
with internal nested organization -- can offer valuable insights in this
debate. We analyze the temporal structural dynamics of 20 plant-pollinator
interaction networks and observe large structural variability throughout the
year. Compound structures are particularly prevalent during the peak of the
pollination season, often coexisting with nested and modular arrangements in
varying degrees. Motivated by these empirical findings, we synthetically
investigate the dynamics of the structural patterns across two control
parameters -- community size and connectance levels -- mimicking the
progression of the pollination season. Our analysis reveals contrasting impacts
on the stability and feasibility of these mutualistic communities. We
characterize the consistent relationship between network structure and
stability, which follows a monotonic pattern. But, in terms of feasibility, we
observe non-linear relationships. Compound structures exhibit a favorable
balance between stability and feasibility, particularly in mid-sized ecological
communities, suggesting they may effectively navigate the simultaneous
requirements of stability and feasibility. These findings may indicate that the
assembly process of mutualistic communities is driven by a delicate balance
among multiple properties, rather than the dominance of a single one.


  We show that the simultaneous modulation of the propagation constant and of
the gain/loss coefficient along the multimode fibers results in unidirectional
coupling among the modes, which, depending on the modulation parameters, leads
to the enhancement or reduction of the excitation of higher order transverse
modes. In the latter case, effective mode-cleaning is predicted, in ideal case
resulting in single-mode spatially coherent output. The effect is
semi-analytically predicted on a simplified Gaussian beam approximation and
numerically proven by solving the wave propagation equation introducing the
modulated potential.


  The policy objective of safeguarding financial stability has stimulated a
wave of research on systemic risk analytics, yet it still faces challenges in
measurability. This paper models systemic risk by tapping into expert knowledge
of financial supervisors. We decompose systemic risk into a number of
interconnected segments, for which the level of vulnerability is measured. The
system is modeled in the form of a Fuzzy Cognitive Map (FCM), in which nodes
represent vulnerability in segments and links their interconnectedness. A main
problem tackled in this paper is the aggregation of values in different
interrelated nodes of the network to obtain an estimate systemic risk. To this
end, the Choquet integral is employed for aggregating expert evaluations of
measures, as it allows for the integration of interrelations among factors in
the aggregation process. The approach is illustrated through two applications
in a European setting. First, we provide an estimation of systemic risk with a
of pan-European set-up. Second, we estimate country-level risks, allowing for a
more granular decomposition. This sets a starting point for the use of the
rich, oftentimes tacit, knowledge in policy organizations.


  Relation of genome sizes to organisms complexity is still described rather
equivocally. Neither the number of genes (G-value), nor the total amount of DNA
(C-value) correlates consistently with phenotype complexity. Using information
theory considerations we developed a model that allows a quantative estimate
for the amount of functional information in a genomic sequence. This model
easily answers the long-standing question of why GC content is increased in
functional regions. The model allows consistent estimate of genome
complexities, resolving the major discrepancies of G- and C-values. For related
organisms with similarly complex phenotypes, this estimate provides biological
insights into their niches complexities. This theoretical framework suggests
that biological information can rapidly evolve on demand from environment,
mainly in non-coding genomic sequence and explains the role of duplications in
the evolution of biological information. Knowing the approximate amount of
functionality in a genomic sequence is useful for many applications such as
phylogenetics analyses, in-silico functional elements discovery or prioritising
targets for genotyping and sequencing.


  How can we detect fraudulent lockstep behavior in large-scale multi-aspect
data (i.e., tensors)? Can we detect it when data are too large to fit in memory
or even on a disk? Past studies have shown that dense subtensors in real-world
tensors (e.g., social media, Wikipedia, TCP dumps, etc.) signal anomalous or
fraudulent behavior such as retweet boosting, bot activities, and network
attacks. Thus, various approaches, including tensor decomposition and search,
have been proposed for detecting dense subtensors rapidly and accurately.
However, existing methods have low accuracy, or they assume that tensors are
small enough to fit in main memory, which is unrealistic in many real-world
applications such as social media and web. To overcome these limitations, we
propose D-CUBE, a disk-based dense-subtensor detection method, which also can
run in a distributed manner across multiple machines. Compared to
state-of-the-art methods, D-CUBE is (1) Memory Efficient: requires up to 1,561X
less memory and handles 1,000X larger data (2.6TB), (2) Fast: up to 7X faster
due to its near-linear scalability, (3) Provably Accurate: gives a guarantee on
the densities of the detected subtensors, and (4) Effective: spotted network
attacks from TCP dumps and synchronized behavior in rating data most
accurately.


  In this note, we prove two Kazdan-Warner type identities involving
$v^{(2k)}$, the renormalized volume coefficients of a Riemannian manifold
$(M^n,g)$, and $G_{2r}$, the so-called Gauss-Bonnet curvature, and a conformal
Killing vector field on $(M^n,g)$. In the case when the Riemannian manifold is
locally conformally flat, $v^{(2k)}=(-2)^{-k}\sigma_k$,
$G_{2r}(g)=\frac{4^r(n-r)!r!}{(n-2r)!}\sigma_r$, and our results reduce to
earlier ones established by Viaclovsky and by the second author.


  Biologically Inspired Design (BID), or Biomimicry, is a problem-solving
methodology that applies analogies from nature to solve engineering challenges.
For example, Speedo engineers designed swimsuits based on shark skin. Finding
relevant biological solutions for real-world problems poses significant
challenges, both due to the limited biological knowledge engineers and
designers typically possess and to the limited BID resources. Existing BID
datasets are hand-curated and small, and scaling them up requires costly human
annotations.
  In this paper, we introduce BARcode (Biological Analogy Retriever), a search
engine for automatically mining bio-inspirations from the web at scale. Using
advances in natural language understanding and data programming, BARcode
identifies potential inspirations for engineering challenges. Our experiments
demonstrate that BARcode can retrieve inspirations that are valuable to
engineers and designers tackling real-world problems, as well as recover famous
historical BID examples. We release data and code; we view BARcode as a step
towards addressing the challenges that have historically hindered the practical
application of BID to engineering innovation.


  Human communication relies on common ground (CG), the mutual knowledge and
beliefs shared by participants, to produce coherent and interesting
conversations. In this paper, we demonstrate that current response generation
(RG) models produce generic and dull responses in dialogues because they act
reflexively, failing to explicitly model CG, both due to the lack of CG in
training data and the standard RG training procedure. We introduce Reflect, a
dataset that annotates dialogues with explicit CG (materialized as inferences
approximating shared knowledge and beliefs) and solicits 9k diverse
human-generated responses each following one common ground. Using Reflect, we
showcase the limitations of current dialogue data and RG models: less than half
of the responses in current data are rated as high quality (sensible, specific,
and interesting) and models trained using this data have even lower quality,
while most Reflect responses are judged high quality. Next, we analyze whether
CG can help models produce better-quality responses by using Reflect CG to
guide RG models. Surprisingly, we find that simply prompting GPT3 to "think"
about CG generates 30% more quality responses, showing promising benefits to
integrating CG into the RG process.


  We reveal a relation between the behaviour of localizing invariants $E$ on
pushouts and on pullbacks of ring spectra. More concretely, we show that the
failure of $E$ sending a pushout of ring spectra to a pushout is controlled by
the value of $E$ on a pullback of ring spectra. Vice versa, in many situations,
we show that the failure $E$ of sending a pullback square to a pullback is
controlled by the value of $E$ on a pushout of ring spectra.
  The latter can be interpreted as identifying the $\odot$-ring, introduced in
earlier work of ours, as a pushout which turns out to be explicitly computable
in many cases. This opens up new possibilities for direct computations. As
further applications, we give new proofs of (generalizations) of Waldhausen's
seminal results on the $K$-theory of generalized free products and obtain a
general relation between the value of a localizing invariant on trivial square
zero extensions and on tensor algebras.


  Recent studies have exploited advanced generative language models to generate
Natural Language Explanations (NLE) for why a certain text could be hateful. We
propose the Chain of Explanation (CoE) Prompting method, using the heuristic
words and target group, to generate high-quality NLE for implicit hate speech.
We improved the BLUE score from 44.0 to 62.3 for NLE generation by providing
accurate target information. We then evaluate the quality of generated NLE
using various automatic metrics and human annotations of informativeness and
clarity scores.


  In this article, we propose measurement-induced nonlocality (MIN) quantified
by Hellinger distance using von Neumann projective measurement. The proposed
MIN is a bonafide measure of nonlocal correlation and is resistant to local
ancilla problem. We obtain an analytical expression of the Hellinger distance
MIN for general pure and $2 \otimes n$ mixed states. In addition to comparing
with similar measures, we explore the role of weak measurement in capturing
nonlocal correlation.


  In this paper we study some basic properties of strong A-statistical
convergence and strong A-statistical Cauchyness of sequences in probabilistic
metric spaces not done earlier. We also study some basic properties of strong
A-statistical limit points and strong A-statistical cluster points of a
sequence in a probabilistic metric space. Further we also introduce the notion
of strong statistically A-summable sequence in a probabilistic metric space and
study its relationship with strong A-statistical convergence.


  We study distribution-free property testing and learning problems where the
unknown probability distribution is a product distribution over $\mathbb{R}^d$.
For many important classes of functions, such as intersections of halfspaces,
polynomial threshold functions, convex sets, and $k$-alternating functions, the
known algorithms either have complexity that depends on the support size of the
distribution, or are proven to work only for specific examples of product
distributions. We introduce a general method, which we call downsampling, that
resolves these issues. Downsampling uses a notion of "rectilinear isoperimetry"
for product distributions, which further strengthens the connection between
isoperimetry, testing, and learning. Using this technique, we attain new
efficient distribution-free algorithms under product distributions on
$\mathbb{R}^d$:
  1. A simpler proof for non-adaptive, one-sided monotonicity testing of
functions $[n]^d \to \{0,1\}$, and improved sample complexity for testing
monotonicity over unknown product distributions, from $O(d^7)$ [Black,
Chakrabarty, & Seshadhri, SODA 2020] to $\widetilde O(d^3)$.
  2. Polynomial-time agnostic learning algorithms for functions of a constant
number of halfspaces, and constant-degree polynomial threshold functions.
  3. An $\exp(O(d \log(dk)))$-time agnostic learning algorithm, and an
$\exp(O(d \log(dk)))$-sample tolerant tester, for functions of $k$ convex sets;
and a $2^{\widetilde O(d)}$ sample-based one-sided tester for convex sets.
  4. An $\exp(\widetilde O(k \sqrt d))$-time agnostic learning algorithm for
$k$-alternating functions, and a sample-based tolerant tester with the same
complexity.


  Infrared (IR) absorption in the 1000-3700 cm-1 range and 1H NMR spectroscopy
reveal the existence of an asymmetric protonated water trimer, H7+O3, in
acetonitrile. The core H7+O3 motif persists in larger protonated water clusters
in acetonitrile up to at least 8 water molecules. Quantum mechanics/molecular
mechanics (QM/MM) molecular dynamics (MD) simulations reveal irreversible
proton transport promoted by propagating the asymmetric H7+O3 structure in
solution. The QM/MM calculations allow for the successful simulation of the
measured IR absorption spectra of H7+O3 in the OH stretch region, which
reaffirms the assignment of the H7+O3 spectra to a hybrid-complex structure: a
protonated water dimer strongly hydrogen-bonded to a third water molecule with
the proton exchanging between the two possible shared-proton Zundel-like
centers. The H7+O3 structure lends itself to promoting irreversible proton
transport in presence of even one additional water molecule. We demonstrate how
continuously evolving H7+O3 structures may support proton transport within
larger water solvates.


  We demonstrate a femtosecond pump-probe spectrometer which utilizes a white
light supercontinuum as input, and relies on mutual synchronization of
acousto-optical chopper, pump-probe delay stage and the CCD camera to record
shot-to-shot pump-probe spectra while the pump-probe delay is scanned
synchronously with the laser repetition rate. The unique combination of
technologies implemented here allows for electronically controllable and
repetition-rate scalable detection throughput that is only limited by the
camera frame rate. Despite RMS white-light probe fluctuations of ~5.5%, fully
leveraging the temporal correlations in white light and fine sampling of
pump-probe delay along with 30x reduction in equivalent data collection time
compared to stepwise scanning leads to reduction of RMS noise without
multichannel referencing down to ~0.33 mOD for a scattering nanotube sample.
This demonstration opens door for impulsive pump-probe micro-spectroscopy of
scattering samples with broadband spectral coverage and minimized sample
exposure.


  Above-light-line surface plasmon polaritons can arise at the interface
between a metal and epsilon-near-zero metamaterial. This unique feature induces
unusual fast-wave non-radiative modes in a epsilon-near-zero material/metal
bilayer. Excitation of this peculiar mode leads to wide-angle perfect
absorption in low-loss ultrathin metamaterials. The ratio of the perfect
absorption wavelength to the thickness of the epsilon-near-zero metamaterial
can be as high as 10^4; the electromagnetic energy can be confined in a layer
as thin as {\lambda}/10000. Unlike conventional fast-wave leaky modes, these
fast-wave non-radiative modes have quasi-static capacitive features that
naturally match with the space-wave field, and thus are easily accessible from
free space. The perfect absorption wavelength can be tuned from mid- to
far-infrared by tuning the epsilon = 0 wavelength while keeping the thickness
of the structure unchanged.


  The right key of a semistandard Young tableau is a tool used to find Demazure
characters for $sl_n(\mathbb{C})$. This thesis gives methods to obtain the
right and left keys by inspection of the semistandard Young tableau. Given a
partition $\lambda$ and a Weyl group element $w$, there is a semistandard Young
tableau $Y_\lambda(w)$ of shape $\lambda$ that corresponds to $w$. The Demazure
character for $\lambda$ and $w$ is known to be the sum of the weights of all
tableaux whose right key is dominated by $Y_\lambda(w)$. The set of all such
tableaux is denoted $\mathcal{D}_\lambda(w)$. Exploiting the method mentioned
above for obtaining right keys, this thesis describes the entry at each
location in any $T \in \mathcal{D}_\lambda(w)$. Lastly, we will consider
$\mathcal{D}_\lambda(w)$ as an integral subset of Euclidean space. The final
results present a condition that is both necessary and sufficient for this
subset to be convex.


  The radiative decays $ B^{*} (D^{*})\rightarrow B(D) \gamma$ are investigated
in the framework of light cone QCD sum rules. The transition amplitude and
decay rates are estimated.It is shown that our results on branching ratios of D
meson decays are in good agreement with the existing experimental data.


  Errors in the kinematic distances, under the assumption of circular gas
orbits, were estimated by performing synthetic observations of a model disk
galaxy. It was found that the error is < 0.5 kpc for most of the disk when the
measured rotation curve was used, but larger if the real rotation curve is
applied. In both cases, the error is significantly larger at the positions of
the spiral arms. The error structure is such that, when kinematic distances are
used to develope a picture of the large scale density distribution, the most
significant features of the numerical model are significantly distorted or
absent, while spurious structure appears. By considering the full velocity
field in the calculation of the kinematic distances, most of the original
density structures can be recovered.


  Some analysis on the Lorentzian distance in a spacetime with controlled
sectional (or Ricci) curvatures is done. In particular, we focus on the study
of the restriction of such distance to a spacelike hypersurface satisfying the
Omori-Yau maximum principle. As a consequence, and under appropriate hypotheses
on the (sectional or Ricci) curvatures of the ambient spacetime, we obtain
sharp estimates for the mean curvature of those hypersurfaces. Moreover, we
also give a suficient condition for its hyperbolicity.


  Recent progress in optically trapped ultracold atomic gases is now making it
possible to access microscopic observables in doped Mott insulators, which are
the parent states of high-temperature superconductors. This makes it possible
to address longstanding questions about the temperature scales at which
attraction between charge carriers are present, and their mechanism.
Controllable theoretical results for this problem are not available at low
temperature due to the sign problem. In this work, we employ worm-algorithm
Monte Carlo to obtain completely unbiased results for two charge carriers in a
Mott insulator. Our method gives access to lower temperatures than what is
currently possible in experiments, and provides evidence for attraction between
dopants at a temperature scale that is now feasible in ultracold atomic
systems. We also report on spin-correlations in the presence of charge
carriers, which are directly comparable to experiments.


  We survey some aspects of the theory of elliptic surfaces and give some
results aimed at determining the Picard number of such a surface. For the
surfaces considered, this will be equivalent to determining the Mordell-Weil
rank of an elliptic curve defined over a function field in one variable. An
interesting conjecture concerning Galois actions on the relative de~Rham
cohomology of these surfaces is discussed.


  The usual spinor construction from one fermion yields four irreducible
representations of the Virasoro algebra with central charge $c = 1/2$. The
Neveu-Schwarz (NS) sector is the direct sum of an $h = 0$ and an $h = 1/2$
module, and the Ramond (R) sector is the direct sum of two copies of an $h =
1/16$ module. In addition to the fundamental fermions, which represent a
Clifford algebra, and the Virasoro operators, there are infinitely many other
vertex operators, in one-to-one correspondence with the vectors (states) in the
NS sector. These give the NS sector the structure of a Vertex Operator
SuperAlgebra, and the R sector the structure of a ${\bold Z}_2$-twisted module
for that VOSA. Keeping both copies of the $h = 1/16$ modules in the R sector,
we can define intertwining operators in one-to-one correspondence with the
states in the R sector such that the usual Ising fusion rules for just three
modules are replaced by a rule given by the group ${\bold Z}_4$. The main
objective is to find a generalization of the VOSA Jacobi-Cauchy identity which
is satisfied by these intertwining operators. There are several novel features
of this new ``Matrix'' Jacobi-Cauchy Identity (MJCI), most of which come from
the fact that correlation functions made from two intertwiners are
hypergeometric functions. In order to relate and rationalize the correlation
functions we use the Kummer quadratic transformation formulas, lifting the
functions to a four-sheeted covering, branched over the usual three poles,
where the Cauchy residue theorem can be applied. The six possible poles on the
cover give six terms in the MJCI. Furthermore, we organize those functions into
$2\times 4$ matrices and find the $2\times 2$ (fusion and braiding) matrices
which relate them at the six poles. These results for intertwiners


  Steven Jones et al. reported to have observed nuclear fusion at room
temperature. They observed this "cold fusion" by electrolyzing heavy water.
Later experiments confirmed these observations. These experiments confirmed the
generation of strong electric fields within the deuterided metals. These
electric fields accelerate the deuterons to keV energies and allow the observed
nuclear fusion. Roman Sioda and I suggested a theoretical description of this
nuclear fusion. Our "extended micro hot fusion" scenario explains how nuclear
fusion can be generated over a long time within deuterided metals. Moreover we
predicted the explosion of large pieces of deuterided metals. This article
reviews the "cold fusion" work of Steven Jones et al. and discusses the
fracto-fusion scenario. I show that the extended micro hot fusion scenario can
explain the observed neutron emissions, neutron bursts, and heat bursts.


  We study stochastic evolution equations describing the dynamics of open
quantum systems. First, using resolvent approximations, we obtain a sufficient
condition for regularity of solutions to linear stochastic Schroedinger
equations driven by cylindrical Brownian motions applying to many physical
systems. Then, we establish well-posedness and norm conservation property of a
wide class of open quantum systems described in position representation.
Moreover, we prove Ehrenfest-type theorems that describe the evolution of the
mean value of quantum observables in open systems. Finally, we give a new
criterion for existence and uniqueness of weak solutions to non-linear
stochastic Schroedinger equations. We apply our results to physical systems
such as fluctuating ion traps and quantum measurement processes of position.


  We demonstrate the existence of Giant proximity magnetoresistance (PMR)
effect in a graphene spin valve where spin polarization is induced by a nearby
magnetic insulator. PMR calculations were performed for yttrium iron garnet
(YIG), cobalt ferrite (CFO), and two europium chalcogenides EuO and EuS. We
find a significant PMR (up to 100%) values defined as a relative change of
graphene conductance with respect to parallel and antiparallel alignment of two
proximity induced magnetic regions within graphene. Namely, for high Curie
temperature (Tc) CFO and YIG insulators which are particularly important for
applications, we obtain 22% and 77% at room temperature, respectively. For low
Tc chalcogenides, EuO and EuS, the PMR is 100% in both cases. Furthermore, the
PMR is robust with respect to system dimensions and edge type termination. Our
findings show that it is possible to induce spin polarized currents in graphene
with no direct injection through magnetic materials.


  Semantic segmentation usually benefits from global contexts, fine
localisation information, multi-scale features, etc. To advance
Transformer-based segmenters with these aspects, we present a simple yet
powerful semantic segmentation architecture, termed as IncepFormer. IncepFormer
has two critical contributions as following. First, it introduces a novel
pyramid structured Transformer encoder which harvests global context and fine
localisation features simultaneously. These features are concatenated and fed
into a convolution layer for final per-pixel prediction. Second, IncepFormer
integrates an Inception-like architecture with depth-wise convolutions, and a
light-weight feed-forward module in each self-attention layer, efficiently
obtaining rich local multi-scale object features. Extensive experiments on five
benchmarks show that our IncepFormer is superior to state-of-the-art methods in
both accuracy and speed, e.g., 1) our IncepFormer-S achieves 47.7% mIoU on
ADE20K which outperforms the existing best method by 1% while only costs half
parameters and fewer FLOPs. 2) Our IncepFormer-B finally achieves 82.0% mIoU on
Cityscapes dataset with 39.6M parameters. Code is
available:github.com/shendu0321/IncepFormer.


  We study classical dynamics of an open string tachyon $T$ of unstable
D$p$-brane coupled to the gauge field $A_\mu$. In the vacuum with vanishing
potential, V=0, two fluid-like degrees of freedom, string fluid and tachyon
matter, survive the tachyon condensation. We offer general analysis of the
associated Hamiltonian dynamics in arbitrary background. The canonical field
equations are organized into two sets, fluid equations of motion augmented by
an integrability condition. We show that a large class of motionless and
degenerate family of classical solutions exist and represent arbitrary
transverse distribution of tachyon matter and flux lines. We further test their
stability by perturbing the fluid equation up to the second order.
  Second half of this note considers possibility of $V \neq 0$ in the dynamics.
We incorporate $V$ in the Hamiltonian equation of motion and consider
interaction between domain walls and string fluid. During initial phase of
tachyon condensation, topological defect at T=0 is shown to attract nearby and
parallel flux lines. The final state is fundamental strings absorbed and spread
in some singular D$(p-1)$ brane soliton. When string fluid is transverse to the
domain wall, the latter is known to turn into a smooth solution. We point out
that a minimal solution of this sort exists and saturates a BPS energy bound of
fundamental string ending on a D$(p-1)$ brane.