  We investigate the baseline range in which the $\theta_{23}$ degeneracy in
neutrino oscillation probabilities is absent for fixed values of $\theta_{13}$
and CP violation phase $\delta_{\rm CP}$. We begin by studying sensitivities of
neutrino oscillation probabilities to $\theta_{13}$, $\theta_{23}$ and
$\delta_{\rm CP}$ for very-long-baseline neutrino oscillations. We show contour
graphs of the muon-neutrino survival probability $P(\nu_{\mu}\to \nu_{\mu})$
and the appearance probability $P(\nu_e\to \nu_{\mu})$ on the $\cos
2\theta_{23}-\sin 2\theta_{13}$ plane for baseline lengths $L=1000, 5000, \
10000$, and 12000 km. For each baseline length, it is found that
$P(\nu_{\mu}\to \nu_{\mu})$ is more sensitive to $\sin 2\theta_{13}$ at
energies around its local maximum while it is more sensitive to $\cos
2\theta_{23}$ at energies around its local minimum. On the other hand, the
appearance probability $P(\nu_e\to \nu_{\mu})$ is sensitive to
$\sin2\theta_{13}$ and $\cos2\theta_{23}$ only near its local maximum. We
observe that the $\theta_{23}$ degeneracy in $P(\nu_{\mu}\to \nu_{\mu})$ is
absent at energies around the local maximum of this probability, provided
$\theta_{13}$ is sufficiently large. The $\theta_{23}$ degeneracy is also
absent in general near the local maximum of $P(\nu_e\to \nu_{\mu})$. Using
analytic approximations for neutrino oscillation probabilities, we demonstrate
that the above observations for $L=1000, 5000, 10000, {\rm and} 12000$ km are
in fact valid for all distances. The implications of these results on probing
the octant of $\theta_{23}$ are discussed in details.


  Recently High Electron Mobility Transistor (HEMT) inspired III-V
electro-optic modulator topologies were proposed for realizing high speed
electro-optic modulators leveraging plasma dispersion effect due to the 2D
Electron Gas (2DEG) present at the III-V heterostructure interface. The 2DEG is
highly confined at the interface, extending to very low depths in the bulk
($\approx$10nm) and therefore has limited spatial overlap with the optical
mode. In this paper, we propose a novel modulator design to boost the
2DEG-light interaction, wherein the HEMT is embedded within a high contrast
grating (HCG) mirror. We present an analytical model extending the conventional
HCG model to multi-layer structures and observe good agreement with rigorous
coupled-wave analysis (RCWA). We explore the design space for identifying
optimal device topology and present geometries that produce a change in
reflectivity as large as 70% for C- and L-band wavelengths. We also present
results of sensitivity analysis and observe low variation in device performance
due to geometry variation arising from device fabrication imperfections. The
device platforms presented here are suitable for designing high efficiency
electro-optic modulators by incorporating the HEMT HCG into a Fabry-Perot
cavity.


  Object rearrangement is a challenge for embodied agents because solving these
tasks requires generalizing across a combinatorially large set of
configurations of entities and their locations. Worse, the representations of
these entities are unknown and must be inferred from sensory percepts. We
present a hierarchical abstraction approach to uncover these underlying
entities and achieve combinatorial generalization from unstructured visual
inputs. By constructing a factorized transition graph over clusters of entity
representations inferred from pixels, we show how to learn a correspondence
between intervening on states of entities in the agent's model and acting on
objects in the environment. We use this correspondence to develop a method for
control that generalizes to different numbers and configurations of objects,
which outperforms current offline deep RL methods when evaluated on simulated
rearrangement tasks.


  In this thesis, we consider the properties of measurements in quantum theory
and other operational theories. After having introduced the framework of
operational theories, we consider a communication scheme based on an
experimental prepare-and-measure scenario and demonstrate this with different
communication tasks. This gives us context for how the different communication
tasks can be implemented in different theories, in doing so establishing
quantum theory intuitively as an operational theory among other theories. The
main property of measurements we focus on in this work is the simulation of
measurements, which consists of manipulating the inputs and outputs of the
measurement devices. We study how using this process on existing measurement
devices can be used to operationally imitate new devices, and what kind of
structure the simulation process induces on measurements. We also consider
applications of simulability. Firstly, we consider operational restrictions
imposed upon measurements. We argue that the restricted set of physical
measurements must be closed with respect to the simulation process since the
simulation of physical devices must lead to other physically feasible devices.
We demonstrate different types of restrictions by classifying them. As a second
application we see how the simulation of measurements relates to compatibility
of measurements and how it can be viewed as a generalisation of it. This allows
us to present an operational principle previously known to quantum theory, the
no-free-information principle, according to which any measurement that is
compatible with all other measurement must not provide any useful, and
therefore free, information about the system. Whilst this principle holds in
quantum theory, there are non-classical theories for which it is violated, and
so enforcing this principle may be considered a way to exclude some unphysical
theories.


  We present our extension of ACL2 with Satisfiability Modulo Theories (SMT)
solvers using ACL2's trusted clause processor mechanism. We are particularly
interested in the verification of physical systems including Analog and
Mixed-Signal (AMS) designs. ACL2 offers strong induction abilities for
reasoning about sequences and SMT complements deduction methods like ACL2 with
fast nonlinear arithmetic solving procedures. While SAT solvers have been
integrated into ACL2 in previous work, SMT methods raise new issues because of
their support for a broader range of domains including real numbers and
uninterpreted functions. This paper presents Smtlink, our clause processor for
integrating SMT solvers into ACL2. We describe key design and implementation
issues and describe our experience with its use.


  Different approaches to the problem of a gauge-invariant operator definition
of transverse-momentum dependent parton densities (TMDs) are reviewed and
compared from the point of view of their compatibility with the operator
definition of collinear (integrated) parton distribution functions. In
particular, geometry of the longitudinal and transverse gauge links (Wilson
lines) both in unsubtracted quark TMDs and in the associate soft factors is
addressed. A possible connection between different operator definitions is also
discussed.


  This paper is a sequel to math.AG/0203287. A generalization of the Mukai flop
has been studied by E. Markman. Here we call it a stratified Mukai flop. In
this paper, we observe that, for a stratified Mukai flop: $X \to \bar{X}
\leftarrow X^+$, the fiber product $X \times_{\bar{X}}X^+$ defines an
isomorphism of Grothendieck groups $K(X) \to K(X^+)$, but, at the level of
derived categories, the fiber product does not generally give an equivalence.


  We study dynamical phase transitions in a model supercooled liquid. These
transitions occur in ensembles of trajectories that are biased towards low (or
high) dynamical activity. We compare two different measures of activity that
were introduced in recent papers and we find that they are anti-correlated with
each other. To interpret this result, we show that the two measures couple to
motion on different length and time scales. We find that inactive states with
very slow structural relaxation nevertheless have increased molecular motion on
short scales. We discuss these results in terms of the potential energy
landscape of the system and in terms of the liquid structure in active/inactive
states.


  We consider the problem of in-network compressed sensing from distributed
measurements. Every agent has a set of measurements of a signal $x$, and the
objective is for the agents to recover $x$ from their collective measurements
using only communication with neighbors in the network. Our distributed
approach to this problem is based on the centralized Iterative Hard
Thresholding algorithm (IHT). We first present a distributed IHT algorithm for
static networks that leverages standard tools from distributed computing to
execute in-network computations with minimized bandwidth consumption. Next, we
address distributed signal recovery in networks with time-varying topologies.
The network dynamics necessarily introduce inaccuracies to our in-network
computations. To accommodate these inaccuracies, we show how centralized IHT
can be extended to include inexact computations while still providing the same
recovery guarantees as the original IHT algorithm. We then leverage these new
theoretical results to develop a distributed version of IHT for time-varying
networks. Evaluations show that our distributed algorithms for both static and
time-varying networks outperform previously proposed solutions in time and
bandwidth by several orders of magnitude.


  In this paper, we establish the stability of the quasineutral limit for the
ionic Vlasov-Poisson system under perturbations exponentially small in
Wasserstein sense. Notably, we emphasize that exponential smallness is a
necessary condition in the electron case, as the presence of instabilities
makes polynomial smallness insufficient.
  The study's quantitative nature introduces unique challenges, primarily
arising from the exponential Poisson coupling. These challenges necessitate
careful optimization at every step of the proof, whether it be in refining
estimates or in the overall approach.
  Within this paper, we introduce novel tools and approaches to address these
challenges. Specifically, we enhance the existing theory concerning the growth
of characteristics in Vlasov systems featuring nonlinear couplings.
Additionally, we combine stability estimates using kinetic-Wasserstein
distances with improved regularity bounds on the elliptic coupling.
  In the course of demonstrating our central result, we also enhance the moment
assumptions associated with the well-posedness of the ionic Vlasov-Poisson
system.


  Graphs of the most probable transitions for a transition probability matrix,
$e^{\tau K}$, i.e., the time evolution matrix of the transition rate matrix $K$
over a finite time interval $\tau$, are considered. We study how the graph
structures of the most probable transitions change as functions of $\tau$,
thereby elucidating that a kinetic threshold $\tau_g$ for the graph structures
exists. Namely, for $\tau<\tau_g$, the number of connected graph components are
constant. In contrast, for $\tau\geq \tau_g$, recombinations of most probable
transitions over the connected graph components occur multiple times, which
introduce drastic changes into the graph structures. Using an illustrative
multi-funnel model, we show that the recombination patterns indicate the
existence of the eigenvalues and eigenvectors of slowest relaxation modes quite
precisely. We also devise an evaluation formula that enables us to correct the
values of eigenvalues with high accuracy from the data of merging processes. We
show that the graph-based method is valid for a wide range of kinetic systems
with degenerate, as well as non-degenerate, relaxation rates.


  We propose a novel framework that unifies and extends existing methods of
transfer learning (TL) for regression. To bridge a pretrained source model to
the model on a target task, we introduce a density-ratio reweighting function,
which is estimated through the Bayesian framework with a specific prior
distribution. By changing two intrinsic hyperparameters and the choice of the
density-ratio model, the proposed method can integrate three popular methods of
TL: TL based on cross-domain similarity regularization, a probabilistic TL
using the density-ratio estimation, and fine-tuning of pretrained neural
networks. Moreover, the proposed method can benefit from its simple
implementation without any additional cost; the regression model can be fully
trained using off-the-shelf libraries for supervised learning in which the
original output variable is simply transformed to a new output variable. We
demonstrate its simplicity, generality, and applicability using various real
data applications.


  Panoptic segmentation is a scene parsing task which unifies semantic
segmentation and instance segmentation into one single task. However, the
current state-of-the-art studies did not take too much concern on inference
time. In this work, we propose an Efficient Panoptic Segmentation Network
(EPSNet) to tackle the panoptic segmentation tasks with fast inference speed.
Basically, EPSNet generates masks based on simple linear combination of
prototype masks and mask coefficients. The light-weight network branches for
instance segmentation and semantic segmentation only need to predict mask
coefficients and produce masks with the shared prototypes predicted by
prototype network branch. Furthermore, to enhance the quality of shared
prototypes, we adopt a module called "cross-layer attention fusion module",
which aggregates the multi-scale features with attention mechanism helping them
capture the long-range dependencies between each other. To validate the
proposed work, we have conducted various experiments on the challenging COCO
panoptic dataset, which achieve highly promising performance with significantly
faster inference speed (53ms on GPU).


  Distant supernovae can now be detected routinely. To date 34 supernovae at $z
> 0.1$ have been discovered. Among them are 12 Type~Ia supernovae confirmed
spectroscopically and suited to measure the cosmic deceleration when
appropriately employed as standard candles. However, peak magnitudes have been
determined for only two objects so far and a determination of $q_0$ is not yet
possible. We describe the current status of the searches and possible pitfalls
of the method which rests on few basic assumptions. The importance of
sufficient information on the distant events is stressed and the observations
of SN~1995K are used as an example of the detailed procedures employed in the
analysis. Only spectroscopic classification and light curves in at least two
filter bands provide the basis to use correction schemes for the luminosity
which have successfully been established in nearby samples. Time dilation has
been detected acting on the light curve of SN~1995K at a redshift of 0.478,
providing clear evidence of universal expansion. The observations are fully
consistent with local Type Ia supernovae in an expanding universe but
incompatible with the expectations from a static universe. The contributions of
the new, large telescopes to this research area are described. The extension of
the observations to even more distant objects will provide a better leverage to
distinguish between the possible decelerations and the inclusion of Type II
supernovae into the sample add an independent check on the cosmological
distances.


  I present a generalization of the Ehrenfest urn model that is aimed at
simulating the approach to equilibrium in a dilute gas. The present model
differs from the original one in two respects: 1) the two boxes have different
volumes and are divided into identical cells with either multiple or single
occupancy; 2) particles, which carry also a velocity vector, are subjected to
random, but elastic, collisions, both mutual and against the container walls. I
show, both analytically and numerically, that the number and energy of
particles in a given urn evolve eventually to an equilibrium probability
density $W$ which, depending on cell occupancy, is binomial or hypergeometric
in the particle number and beta-like in the energy. Moreover, the Boltzmann
entropy $\ln W$ takes precisely the same form as the thermodynamic entropy of
an ideal gas. This exercise can be useful for pedagogical purposes in that it
provides, although in an extremely simplified case, a probabilistic
justification for the maximum-entropy principle.


  In 1970, Erd\H{o}s and S\'ark\"ozy wrote a joint paper studying sequences of
integers $a_1<a_2<\dots$ having what they called property P, meaning that no
$a_i$ divides the sum of two larger $a_j,a_k$. In the paper, it was stated that
the authors believed, but could not prove, that a subset $A\subset[n]$ with
property P has cardinality at most $|A|\leqslant \left\lfloor
\frac{n}{3}\right\rfloor+1$. In 1997, Erd\H{o}s offered \$100 for a proof or
disproof of the claim that $|A|\leqslant \frac{n}{3}+C$, for some absolute
constant $C$. We resolve this problem, and in fact prove that
$|A|\leqslant\left\lfloor \frac{n}{3}\right\rfloor+1$ for $n$ sufficiently
large.


  What is the shape of a uniformly massive object that generates a
gravitational potential equivalent to that of two equal point-masses? If the
weight of each point-mass is sufficiently small compared to the distance
between the points then the answer is a pair of balls of equal radius, one
centered at each of the two points, but otherwise it is a certain domain of
revolution about the axis passing through the two points. The existence and
uniqueness of such a domain is known, but an explicit parameterization is known
only in the plane where the region is referred to as a Neumann oval. We
construct a four-dimensional "Neumann ovaloid", solving explicitly this inverse
potential problem.


  In this paper the experimental results of the recent dynamic aperture at top
energy for the CERN Large Hadron Collider are analysed by means of a diffusion
model whose novelty consists of deriving the functional form of the diffusion
coefficient from Nekhoroshev theorem. This theorem provides an optimal estimate
of the remainder of perturbative series for Hamiltonian systems. As a
consequence, a three-parameter diffusion model is built that reproduces the
experimental results with a high level of accuracy. A detailed discussion of
the physical interpretation of the proposed model is also presented.


  Two-dimensional ($2D$) Lifshitz-like black holes in special $F(R)$ gravity
cases are extracted. We indicate an essential singularity at $r=0$, covered
with an event horizon. Then conserved and thermodynamic quantities such as
temperature, mass, entropy, and the heat capacity of $2D$ Lifshitz-like black
holes in $F(R)$ gravity are evaluated. Our analysis shows that $2D$
Lifshitz-like black hole solutions can be physical solutions, provided that the
cosmological constant is negative ($\Lambda<0$). Indeed, there is a phase
transition between stable and unstable cases by increasing the radius of AdS
black holes. In other words, the $2D$ Lifshitz-like AdS black holes with large
radii are physical and enjoy thermal stability. The obtained $2D$ Lifshitz-like
AdS-black holes in $F(R)$ gravity turn to the well-known $2D$ Schwarzschild
AdS-black holes when the Lifshitz-like parameter is zero ($s=0$). Also,
correspondence between these black hole solutions and the $2D$ rotating black
hole solutions is found by adjusting the Lifshitz-like parameter.


  We show that the Schnakenberg's entropy production rate in a master equation
is lower bounded by a function of the weight of the Markov graph, here defined
as the sum of the absolute values of probability currents over the edges. The
result is valid for time-dependent nonequilibrium entropy production rates.
Moreover, in a general framework, we prove a theorem showing that the
Kullback-Leibler divergence between distributions $P(s)$ and $P'(s):=P(m(s))$,
where $m$ is an involution, $m(m(s))=s$, is lower bounded by a function of the
total variation of $P$ and $P'$, for any $m$. The bound is tight and it
improves on Pinsker's inequality for this setup. This result illustrates a
connection between nonequilibrium thermodynamics and graph theory with
interesting applications.


  The radiation produced by a classical charged current coupled to a quantized
$A_{\mu}$ is first computed. To each order in $\alpha$, all infrared
divergences cancel between the virtual $\gamma$'s and the real $\gamma$'s that
are absorbed from or emitted into the plasma. When all orders of perturbation
theory are summed, the finite answer predicts a suppression of radiation with
$\omega< \alpha T$. The analysis of QED then consists of two steps. First, a
general probability at $T\neq 0$ is organized so that all the virtual
$e^{\pm},\gamma$ are in the amplitudes and all the real $e^{\pm},\gamma$ are in
the phase space integrations. Next, the cancellations of IR divergences between
virtual and real are demonstrated.


  Let K be a non-trivial knot in the 3-sphere and let Y be the 3-manifold
obtained by surgery on K with surgery-coefficient 1. Using tools from gauge
theory and symplectic topology, it is shown that the fundamental group of Y
admits a non-trivial homomorphism to the group SO(3). In particular, Y cannot
be a homotopy-sphere.


  We discuss two concepts of metric and linear connections in noncommutative
geometry, applying them to the case of the product of continuous and discrete
(two-point) geometry.


  We study the asymptotic performance of two multi-hop overlaid ad-hoc networks
that utilize the same temporal, spectral, and spatial resources based on random
access schemes. The primary network consists of Poisson distributed legacy
users with density \lambda^{(p)} and the secondary network consists of Poisson
distributed cognitive radio users with density \lambda^{(s)} =
(\lambda^{(p)})^{\beta} (\beta>0, \beta \neq 1) that utilize the spectrum
opportunistically. Both networks are decentralized and employ ALOHA medium
access protocols where the secondary nodes are additionally equipped with
range-limited perfect spectrum sensors to monitor and protect primary
transmissions. We study the problem in two distinct regimes, namely \beta>1 and
0<\beta<1. We show that in both cases, the two networks can achieve their
corresponding stand-alone throughput scaling even without secondary spectrum
sensing (i.e., the sensing range set to zero); this implies the need for a more
comprehensive performance metric than just throughput scaling to evaluate the
influence of the overlaid interactions. We thus introduce a new criterion,
termed the asymptotic multiplexing gain, which captures the effect of
inter-network interferences with different spectrum sensing setups. With this
metric, we clearly demonstrate that spectrum sensing can substantially improve
primary network performance when \beta>1. On the contrary, spectrum sensing
turns out to be unnecessary when \beta<1 and setting the secondary network's
ALOHA parameter appropriately can substantially improve primary network
performance.


  The proliferation of early diagnostic technologies, including self-monitoring
systems and wearables, coupled with the application of these technologies on
large segments of healthy populations may significantly aggravate the problem
of overdiagnosis. This can lead to unwanted consequences such as overloading
health care systems and overtreatment, with potential harms to healthy
individuals. The advent of machine-learning tools to assist diagnosis -- while
promising rapid and more personalised patient management and screening -- might
contribute to this issue. The identification of overdiagnosis is usually post
hoc and demonstrated after long periods (from years to decades) and costly
randomised control trials. In this paper, we present an innovative approach
that allows us to preemptively detect potential cases of overdiagnosis during
predictive model development. This approach is based on the combination of
labels obtained from a prediction model and clustered medical trajectories,
using sepsis in adults as a test case. This is one of the first attempts to
quantify machine-learning induced overdiagnosis and we believe will serves as a
platform for further development, leading to guidelines for safe deployment of
computational diagnostic tools.


  We discuss the effects of lepton number violating interactions namely,
R-parity violation and leptoquarks on top quark pair production at the upcoming
$e^+ e^-$ linear colliders. Effects of SU(2) singlet, doublet and triplet
leptoquark interactions are investigated. R-parity violating minimal
supersymmetric standard model also allows certain kinds of lepton number
violating interactions which are same as singlet leptoquarks with left-handed
interactions. We have calculated the cross-section of $e^+ e^- \to t \bar t$ in
presence of the above interactions. With conservative values of lepton number
violating coupling strengths we got enhancement of top-pair production
cross-section in all of the above cases.


  We investigate the effects of strong magnetic fields on the QCD phase
structure at vanishing density by solving the gluon and quark gap equations,
and by studying the dynamics of the quark scattering with the four-fermi
coupling. The chiral crossover temperature as well as the chiral condensate are
computed. For asymptotically large magnetic fields we find magnetic catalysis,
while we find inverse magnetic catalysis for intermediate magnetic fields.
Moreover, for large magnetic fields the chiral phase transition for massless
quarks turns into a crossover. The underlying mechanisms are then investigated
analytically within a few simplifications of the full numerical analysis. We
find that a combination of gluon screening effects and the weakening of the
strong coupling is responsible for the phenomenon of inverse catalysis. In
turn, the magnetic catalysis at large magnetic field is already indicated by
simple arguments based on dimensionality.


  This paper presents an approach for automatic detection of Munro's
Microabscess in stratum corneum (SC) of human skin biopsy in order to realize a
machine assisted diagnosis of Psoriasis. The challenge of detecting neutrophils
in presence of nucleated cells is solved using the recent advances of deep
learning algorithms. Separation of SC layer, extraction of patches from the
layer followed by classification of patches with respect to presence or absence
of neutrophils form the basis of the overall approach which is effected through
an integration of a U-Net based segmentation network and a capsule network for
classification. The novel design of the present capsule net leads to a drastic
reduction in the number of parameters without any noticeable compromise in the
overall performance. The research further addresses the challenge of dealing
with Mega-pixel images (in 10X) vis-a-vis Giga-pixel ones (in 40X). The
promising result coming out of an experiment on a dataset consisting of 273
real-life images shows that a practical system is possible based on the present
research. The implementation of our system is available at
https://github.com/Anabik/CapsDeMM.


  PySAD is an open-source python framework for anomaly detection on streaming
data. PySAD serves various state-of-the-art methods for streaming anomaly
detection. The framework provides a complete set of tools to design anomaly
detection experiments ranging from projectors to probability calibrators. PySAD
builds upon popular open-source frameworks such as PyOD and scikit-learn. We
enforce software quality by enforcing compliance with PEP8 guidelines,
functional testing and using continuous integration. The source code is
publicly available on https://github.com/selimfirat/pysad.


  A quantum characteristic exponent may be defined, with the same operational
meaning as the classical Lyapunov exponent when the latter is expressed as a
functional of densities. Existence conditions and supporting measure properties
are discussed as well as the problems encountered in the numerical computation
of the quantum exponents. Although an example of true quantum chaos may be
exhibited, the taming effect of quantum mechanics on chaos is quite apparent in
the computation of the quantum exponents. However, even when the exponents
vanish, the functionals used for their definition may still provide a
characterization of distinct complexity classes for quantum behavior.


  Optical frequency combs emit narrow pulses of light with a stable repetition
rate. Equivalently, the generated light spectrum consists of many discrete
frequencies spaced by this same repetition rate. These precision light sources
have become ubiquitous in applications of photonic technologies because they
allow coherent sampling over a broad part of the optical spectrum. The addition
of another comb, with a slightly different line spacing, results in a dual
comb. Widely used in spectroscopy, dual combs allow one to read out the broad
frequency response of a sample in a simple electronic measurement. Many dual
comb applications require a high level of mutual coherence between the combs,
but achieving this stability can be demanding. Here, by exploiting the rich
structure of the nonlinear electro-optic tensor in lithium niobate, we generate
ultra-stable dual combs with the two combs naturally having orthogonal
polarizations. Our combs have relative linewidths down to 400 microhertz, and
require no stabilization or post-processing methods. The ultra-high stability
of the spectrum emitted by our device, along with its simplicity of operation
and energy efficiency, offer a route to the deployment of robust and versatile
dual comb sources.


  Recent years have witnessed the rapid deployment of smart homes; most of them
are controlled by remote servers in the cloud. Such designs raise security and
privacy concerns for end users. In this paper, we describe the design of
Sovereign, a home IoT system framework that provides end users complete control
of their home IoT systems. Sovereign lets home IoT devices and applications
communicate via application-named data and secures data directly. This enables
direct, secure, one-to-one and one-to-many device-to-device communication over
wireless broadcast media. Sovereign utilizes semantic names to construct usable
security solutions. We implement Sovereign as a publish-subscribe-based
development platform together with a prototype home IoT controller. Our
preliminary evaluation shows that Sovereign provides a systematic, easy-to-use
solution to user-controlled, self-contained smart homes running on existing IoT
hardware without imposing noticeable overhead.


  In this paper we study the problem of constructing bootstrap confidence
intervals for the L\'evy density of the driving L\'evy process based on
high-frequency observations of a L\'evy-driven moving average processes. Using
a spectral estimator of the L\'evy density, we propose a novel implementations
of multiplier and empirical bootstraps to construct confidence bands on a
compact set away from the origin. We also provide conditions under which the
confidence bands are asymptotically valid.


  Abell 2146 ($z$ = 0.232) consists of two galaxy clusters undergoing a major
merger. The system was discovered in previous work, where two large shock
fronts were detected using the $\textit{Chandra X-ray Observatory}$, consistent
with a merger close to the plane of the sky, caught soon after first core
passage. A weak gravitational lensing analysis of the total gravitating mass in
the system, using the distorted shapes of distant galaxies seen with ACS-WFC on
$\textit{Hubble Space Telescope}$, is presented. The highest peak in the
reconstruction of the projected mass is centred on the Brightest Cluster Galaxy
(BCG) in Abell 2146-A. The mass associated with Abell 2146-B is more extended.
Bootstrapped noise mass reconstructions show the mass peak in Abell 2146-A to
be consistently centred on the BCG. Previous work showed that BCG-A appears to
lag behind an X-ray cool core; although the peak of the mass reconstruction is
centred on the BCG, it is also consistent with the X-ray peak given the
resolution of the weak lensing mass map. The best-fit mass model with two
components centred on the BCGs yields $M_{200}$ =
1.1$^{+0.3}_{-0.4}$$\times$10$^{15}$M$_{\odot}$ and
3$^{+1}_{-2}$$\times$10$^{14}$M$_{\odot}$ for Abell 2146-A and Abell 2146-B
respectively, assuming a mass concentration parameter of $c=3.5$ for each
cluster. From the weak lensing analysis, Abell 2146-A is the primary halo
component, and the origin of the apparent discrepancy with the X-ray analysis
where Abell 2146-B is the primary halo is being assessed using simulations of
the merger.


  Models of self-gravitating gas in the early stages of pressure-free collapse
are compared for initial states which are equilibrium layers, cylinders, and
Bonnor-Ebert spheres. For each geometrical case the density profile has an
inner region of shallow slope surrounded by an outer region of steep slope, and
the profile shape during early collapse remains similar to the profile shape of
the initial equilibrium. The two-slope density structure divides the spherical
collapse history into a starless infall phase and a protostellar accretion
phase. The similarity of density profiles implies that Bonnor-Ebert fits to
observed column density maps may not distinguish spherical cores from oblate or
prolate cores, and may not distinguish static cores from collapsing cores. The
velocity profiles discriminate better than the density profiles between initial
geometries and between collapse ages. The infall velocity generally has a
subsonic maximum value, which is approximately equal to the initial velocity
dispersion times the ratio of collapse age to central free-fall time.
  Observations of starless core line profiles constrain collapse models.
Collapse from initial states which are strongly condensed and slightly prolate
is consistent with infall asymmetry observed around starless cores, and is more
consistent than collapse from initial states which are weakly condensed, and/or
oblate. Spherical models match observed inward speeds 0.05-0.09 km/s over
0.1-0.2 pc, if the collapse has a typical age 0.3-0.5 free fall times, and if
it began from a centrally condensed state which was not in stable equilibrium.
In a collapsing core, optically thin line profiles should broaden and develop
two-peak structure as seen in L1544.


  The notion of mutation plays crucial roles in representation theory of
algebras. Two kinds of mutation are well-known: tilting/silting mutation and
quiver-mutation. In this paper, we focus on tilting mutation for symmetric
algebras. Introducing mutation of SB quivers, we explicitly give a
combinatorial description of tilting mutation of symmetric special biserial
algebras. As an application, we generalize Rickard's star theorem. We also
introduce flip of Brauer graphs and apply our results to Brauer graph algebras.


  We prove singularity of some distributions of random continued fractions that
correspond to iterated function systems with overlap and a parabolic point.
These arose while studying the conductance of Galton-Watson trees.


  Computational tools in numerical algebraic geometry can be used to
numerically approximate solutions to a system of polynomial equations. If the
system is well-constrained (i.e., square), Newton's method is locally
quadratically convergent near each nonsingular solution. In such cases, Smale's
alpha theory can be used to certify that a given point is in the quadratic
convergence basin of some solution. This was extended to certifiably determine
the reality of the corresponding solution when the polynomial system is real.
Using the theory of Newton-invariant sets, we certifiably decide the reality of
projections of solutions. We apply this method to certifiably count the number
of real and totally real tritangent planes for instances of curves of genus 4.


  We construct useful sets of one-particle states in the quantum Hall system
based on the von Neumann lattice. Using the set of momentum states, we develop
a field-theoretical formalism and apply the formalism to the system subjected
to a periodic potential. The topological formula of the Hall conductance
written by the winding number of propagator is generalized to Bloch electrons.
The relation between the winding number and the Chern number is clarified.


  Observations are reported on isotactic polypropylene (i) in a series of
tensile tests with a constant strain rate on specimens annealed for 24 h at
various temperatures in the range from 110 to 150 C and (ii) in two series of
creep tests in the sub-yield region of deformation on samples not subjected to
thermal treatment and on specimens annealed at 140 C. A model is developed for
the elastoplastic and nonlinear viscoelastic responses of semicrystalline
polymers. A polymer is treated an equivalent transient network of
macromolecules bridged by junctions (physical cross-links, entanglements and
lamellar blocks). The network is assumed to be highly heterogeneous, and it is
thought of as an ensemble of meso-regions with different activation energies
for separation of strands from temporary nodes. The elastoplastic behavior is
modelled as sliding of meso-domains with respect to each other driven by
mechanical factors. The viscoelastic response is attributed to detachment of
active strands from temporary junctions and attachment of dangling chains to
the network. Constitutive equations for isothermal uniaxial deformation are
derived by using the laws of thermodynamics. Adjustable parameters in the
stress-strain relations are found by fitting the experimental data.


  Using the potentials derived from vector-meson-exchanges, the $K\bar K$,
$DK$, $B\bar K$, $D\bar D$, $B\bar B$, $BD$, $\bar D K$, $BK$ and $B\bar D$
systems are studied. Possible S-wave bound-states of two pseudoscalar mesons
are discussed. We find that systems of $DB$, $D\bar D$, $B\bar B$ and $DK$ with
isospin 0 are likely to form S-wave bound states via strong interactions while
the others are unlikely to be bound by the strong interaction sector alone.
With the Coulomb potential, the $K^+K^-$ system can form an atomic bound state
- the kaonium. The influence of the one-meson-exchange potential on the ground
state energy of the kaonium and its decay widths to $\pi\pi$ and $\pi\eta$ are
evaluated.


  Wind energy has gained a huge interest in the recent years in various
countries due to the high demand of energy and the shortage of traditional
electricity sources. This is because it is cost effective and environmentally
friendly source that could contribute significantly to the reduction of the
ever-increasing carbon emissions. Wind energy is one of the fastest growing
green technology worldwide with a total generation share of 564 GW as the end
of 2018. In Malaysia, wind energy has been a topic of interest in both academia
and green energy industry. In this paper, the current status of wind energy
research in Malaysia is reviewed. Different contributing factors such as
potentiality and assessments, wind speed and direction modelling, wind
prediction and spatial mapping, and optimal sizing of wind farms are
extensively discussed. This paper discusses the progress of all wind studies
and presents conclusions and recommendations to improve wind research in
Malaysia.


  We investigate the interplay between ferromagnetic and superconducting order
at the edge of a quantum spin Hall insulator. Using complementary analytical
and self-consistent numerical approaches, we study a ferromagnetic Josephson
junction and show how the direct coupling between magnetism and the
superconducting U(1) phase gives rise to several unusual phenomena which
distinguishes the present system from its non-topological equivalent. In
particular, we demonstrate how the anomalous current-phase relation triggers
supercurrent-induced magnetization dynamics and also study the spatial
localization of the Majorana fermions appearing in the junction.


  We show the vanishing viscosity limit to entropy shocks for the fractal
Burgers equation in one space dimension. More precisely, we quantify the rate
of convergence of the inviscid limit in $L^2$ for large initial perturbations
around the entropy shock on any bounded time interval. This is the first result
on the inviscid limit to entropy shock for the fractal Burgers equation with
the quantified convergence, for large initial perturbations.


  An upgraded version of the OGRAN -- combined optical-acoustic gravitational
wave detector -- has been investigated in a long-term operation mode. This
installation, located at the Baksan Neutrino Observatory (BNO) INR RAS, is
designed to work under the program for detecting collapsing stars in parallel
with the neutrino detector: Baksan Underground Scintillation Telescope (BUST).
Such joint search corresponds to the modern trend for a development of
"multi-messenger astronomy". In this work the effects of thermal relaxation
OGRAN are experimentally investigated using passive and active thermal
stabilization systems in the underground laboratory BNO PK-14.


  We use extensive first principle simulations to show the major role played by
interfaces in the mechanism of phase separation observed in semiconductor
multifunctional materials. We make an analogy with the precipitation sequence
observed in over-saturated AlCu alloys, and replace the Guinier-Preston zones
in this new context. A new class of materials, the $\alpha$ phases, is proposed
to understand the formation of the coherent precipitates observed in the GeMn
system. The interplay between formation and interface energies is analyzed for
these phases and for the structures usually considered in the literature. The
existence of the alpha phases is assessed with both theoretical and
experimental arguments.


  We investigate Robinson-Schensted-Knuth algorithm (RSK) and
Sch\"utzenberger's jeu de taquin in the infinite setup. We show that the
recording tableau in RSK defines an isomorphism of the following two dynamical
systems: (i) a sequence of i.i.d. random letters equipped with Bernoulli shift,
and (ii) a random infinite Young tableau (with the distribution given by
Vershik-Kerov measure, corresponding to some Thoma character of the infinite
symmetric group) equipped with jeu de taquin transformation. As a special case
we recover the results on non-colliding random walks and multidimensional
Pitman transform.


  One main theme in current condensed matter physics is the search of quantum
spin liquid (QSL), an exotic magnetic state with strongly-fluctuating and
highly-entangled spins down to zero temperature without static order. However,
there is no consensus on the existence of a QSL ground state in any real
material so far. The disorders and competing exchange interactions may prevent
the formation of an ideal QSL state on frustrated spin lattices. Here we report
systematic heat transport measurements on a honeycomb-lattice compound
BaCo2(AsO4)2, which manifests magnetic order in zero field. In a narrow field
range after the magnetic order is nearly suppressed by an in-plane field, in
both perpendicular and parallel to the zigzag direction, a finite residual
linear term of thermal conductivity is clearly observed, which is attributed to
the mobile fractionalized spinon excitations. This provides smoking-gun
evidence for a gapless QSL state in BaCo2(AsO4)2. We discuss the underlying
physics to form this exotic gapless QSL state in Co2+ honeycomb lattice.


  Transfer learning aims to improve the performance of target tasks by
transferring knowledge acquired in source tasks. The standard approach is
pre-training followed by fine-tuning or linear probing. Especially, selecting a
proper source domain for a specific target domain under predefined tasks is
crucial for improving efficiency and effectiveness. It is conventional to solve
this problem via estimating transferability. However, existing methods can not
reach a trade-off between performance and cost. To comprehensively evaluate
estimation methods, we summarize three properties: stability, reliability and
efficiency. Building upon them, we propose Principal Gradient Expectation(PGE),
a simple yet effective method for assessing transferability. Specifically, we
calculate the gradient over each weight unit multiple times with a restart
scheme, and then we compute the expectation of all gradients. Finally, the
transferability between the source and target is estimated by computing the gap
of normalized principal gradients. Extensive experiments show that the proposed
metric is superior to state-of-the-art methods on all properties.


  In this paper, we propose an extended version of the memristive STDP model,
which is one of the most important and exciting recent discoveries in
neuromorphic engineering. The proposed model aims to claim compatibility with
another importent STDP rule beyond the pair-based rule, known as the triplet
STDP rule. This is an extension of the asynchronous memristive model of
Linares-Barranco, et al., capable of explaining the pair-based rule based on
the analogy of the synapse to the memristor. The proposed new model is
compatible with both the pair-baed and triplet-based rule, by assuming a
mechanism of variable thresholds adapting to synaptic potentiation and
depression. The dynamical process is governed by ordinary differential
equations. The model is an expression of Froemke's principle of suppression for
triplet rules and reveals a similar time dependence with that in the
suppression STDP model.


  We establish the equivalence between the refined topological vertex of
Iqbal-Kozcaz-Vafa and a certain representation theory of the quantum algebra of
type W_{1+infty} introduced by Miki. Our construction involves trivalent
intertwining operators Phi and Phi^* associated with triples of the bosonic
Fock modules. Resembling the topological vertex, a triple of vectors in Z^2 is
attached to each intertwining operator, which satisfy the Calabi-Yau and
smoothness conditions. It is shown that certain matrix elements of Phi and
Phi^* give the refined topological vertex C_{lambda mu nu}(t,q) of
Iqbal-Kozcaz-Vafa. With another choice of basis, we recover the refined
topological vertex C_{lambda mu}^nu(q,t) of Awata-Kanno. The gluing factors
appears correctly when we consider any compositions of Phi and Phi^*. The
spectral parameters attached to Fock spaces play the role of the K"ahler
parameters.


  (Abridged) We present a Chandra observation of the supernova remnant (SNR) 3C
397 (G41.1-0.3) obtained with ACIS-S. Previous studies of this SNR have shown
that it harbors a central X-ray `hot spot' suggestive of a compact object
associated with 3C 397. With the Chandra data, we can rule out the nature of
the hot spot as a pulsar or a pulsar wind nebula, and put an upper limit on the
flux of a hidden compact object of F (0.5--10 keV)~6E-13 erg/cm2/s. We found
two point sources in the Chandra field. We argue that none of them is
associated with 3C 397; and that the hard source, CXO J190741.2+070650, is a
newly discovered AGN. The Chandra image reveals arcseconds-scale clumps and
knots which are strongly correlated with the radio VLA image, except for the
X-ray hot spot. Our Chandra spatially resolved spectroscopic study shows that
one-component models are inadequate, and that at least two non-equilibrium
ionization thermal components are needed to fit the spectra of each selected
region. The derived average spectral parameters are consistent with the
previous global ASCA fits performed by Safi-Harb et al. (2000). However, the
hard component requires a high abundance of Fe indicating the presence of hot
Fe ejecta. When comparing the eastern with the western lobe, we find that the
column density, the brightness, and the ionization timescales are generally
higher for the western side. This result, combined with our study of the 3C397
environs at millimeter wavelengths, indicate a denser medium to the west of the
SNR. Our multi-wavelength imaging and spectral study favors the scenario where
3C 397 is a ~5,300-year old SNR expanding in a medium with a marked density
gradient, and which is likely to be encountering a molecular cloud on the
western side. We propose that 3C 397 will evolve into a mixed-morphology SNR.


  Characterizing interactions between drugs is important to avoid potentially
harmful combinations, to reduce off-target effects of treatments and to fight
antibiotic resistant pathogens, among others. Here we present a network
inference algorithm to predict uncharacterized drug-drug interactions. Our
algorithm takes, as its only input, sets of previously reported interactions,
and does not require any pharmacological or biochemical information about the
drugs, their targets or their mechanisms of action. Because the models we use
are abstract, our approach can deal with adverse interactions,
synergistic/antagonistic/suppressing interactions, or any other type of drug
interaction. We show that our method is able to accurately predict
interactions, both in exhaustive pairwise interaction data between small sets
of drugs, and in large-scale databases. We also demonstrate that our algorithm
can be used efficiently to discover interactions of new drugs as part of the
drug discovery process.


  We consider the quasi-commutative approximation to a noncommutative geometry
defined as a generalization of the moving frame formalism. The relation which
exists between noncommutativity and geometry is used to study the properties of
the high-frequency waves on the flat background.


  We consider one-dimensional and two-dimensional models of the stochastic
resin transfer molding process, which are formulated as random moving boundary
problems. We study their properties, analytically in the one-dimensional case
and numerically in the two-dimensional case. We show how variability of time to
fill depends on correlation lengths and smoothness of a random permeability
field.


  We consider the non-eikonal corrections to particle production in the Color
Glass Condensate stemming from the relaxation of the shockwave approximation
for the target that acquires a finite longitudinal dimension. We derive a
modified expression of the Lipatov vertex which takes into account this finite
target width. This expression is employed to compute single, double and triple
gluon production in the Glasma graph limit valid for the scattering of two
dilute objects, at all orders in the expansion in the number of colors. We
justify and generalize previous results, and discuss the possible implications
on two particle correlations of these non-eikonal corrections that induce
differences between the away- and near-side peaks.


  We consider the problem of randomly distributed positive delta-function
scatterers in a strong magnetic field and study the behavior of density of
states close to the spectral boundary at $E=\hbar\omega_{c}/2$ in both two and
three dimensions. Starting from dimensionally reduced expression of Brezin et
al. and using the semiclassical approximation we show that the density of
states in the Lifshitz tail at small energies is proportio- nal to $e^{f-2}$ in
two dimensions and to $\exp(-3.14f\ln(3.14f/\pi e)/ \sqrt(2me))$ in three
dimensions, where $e$ is the energy and $f$ is the density of scatterers in
natural units.


  We present and interpret simulation results showing how a fluid moves on a
hydrophilic substrate patterned by a square array of triangular posts. We
demonstrate that the shape of the posts leads to anisotropic spreading, and
discuss how this is influenced by the different ways in which the posts can pin
the advancing front.


  We suggest that the recently observed charmed scalar mesons $D_0^{0}(2308)$
(BELLE) and $D_0^{0,+}(2405)$ (FOCUS) are considered as different resonances.
Using the QCD sum rule approach we investigate the possible four-quark
structure of these mesons and also of the very narrow $D_{sJ}^{+}(2317)$,
firstly observed by BABAR. We use diquak-antidiquark currents and work to the
order of $m_s$ in full QCD, without relying on $1/m_c$ expansion. Our results
indicate that a four-quark structure is acceptable for the resonances observed
by BELLE and BABAR: $D_0^{0}(2308)$ and $D_{sJ}^{+}(2317)$ respectively, but
not for the resonances observed by FOCUS: $D_0^{0,+}(2405)$.


  The global decline in bee populations poses significant risks to agriculture,
biodiversity, and environmental stability. To bridge the gap in existing data,
we introduce ApisTox, a comprehensive dataset focusing on the toxicity of
pesticides to honey bees (Apis mellifera). This dataset combines and leverages
data from existing sources such as ECOTOX and PPDB, providing an extensive,
consistent, and curated collection that surpasses the previous datasets.
ApisTox incorporates a wide array of data, including toxicity levels for
chemicals, details such as time of their publication in literature, and
identifiers linking them to external chemical databases. This dataset may serve
as an important tool for environmental and agricultural research, but also can
support the development of policies and practices aimed at minimizing harm to
bee populations. Finally, ApisTox offers a unique resource for benchmarking
molecular property prediction methods on agrochemical compounds, facilitating
advancements in both environmental science and cheminformatics. This makes it a
valuable tool for both academic research and practical applications in bee
conservation.


  In this note we analyze how perturbations of a ball $\mathfrak{B}_r \subset
\mathbb{R}^n$ behaves in terms of their first (non-trivial) Neumann and
Dirichlet $\infty-$eigenvalues when a volume constraint $\\mathscr{L}^n(\Omega)
= \mathscr{L}^n(\mathfrak{B}_r)$ is imposed. Our main result states that
$\Omega$ is uniformly close to a ball when it has first Neumann and Dirichlet
eigenvalues close to the ones for the ball of the same volume $\mathfrak{B}_r$.
In fact, we show that, if $$
  |\lambda_{1,\infty}^D(\Omega) - \lambda_{1,\infty}^D(\mathfrak{B}_r)| =
\delta_1 \quad \text{and} \quad |\lambda_{1,\infty}^N(\Omega) -
\lambda_{1,\infty}^N(\mathfrak{B}_r)| = \delta_2, $$ then there are two balls
such that $$\mathfrak{B}_{\frac{r}{\delta_1 r+1}} \subset \Omega \subset
\mathfrak{B}_{\frac{r+\delta_2 r}{1-\delta_2 r}}.$$ In addition, we also obtain
a result concerning stability of the Dirichlet $\infty-$eigen-functions.


  We investigate the dynamics of a two dimensional axial next nearest neighbour
Ising (ANNNI) model following a quench to zero temperature. The Hamiltonian is
given by $H = -J_0\sum_{i,j=1}^L S_{i,j}S_{i+1,j} - J_1\sum_{i,j=1} [S_{i,j}
S_{i,j+1} -\kappa S_{i,j} S_{i,j+2}]$. For $\kappa <1$, the system does not
reach the equilibrium ground state but slowly evolves to a metastable state.
For $\kappa > 1$, the system shows a behaviour similar to the two dimensional
ferromagnetic Ising model in the sense that it freezes to a striped state with
a finite probability. The persistence probability shows algebraic decay here
with an exponent $\theta = 0.235 \pm 0.001$ while the dynamical exponent of
growth $z=2.08\pm 0.01$. For $\kappa =1$, the system belongs to a completely
different dynamical class; it always evolves to the true ground state with the
persistence and dynamical exponent having unique values. Much of the dynamical
phenomena can be understood by studying the dynamics and distribution of the
number of domains walls. We also compare the dynamical behaviour to that of a
Ising model in which both the nearest and next nearest neighbour interactions
are ferromagnetic.


  Fog computing promises to enable machine learning tasks to scale to large
amounts of data by distributing processing across connected devices. Two key
challenges to achieving this goal are heterogeneity in devices compute
resources and topology constraints on which devices can communicate with each
other. We address these challenges by developing the first network-aware
distributed learning optimization methodology where devices optimally share
local data processing and send their learnt parameters to a server for
aggregation at certain time intervals. Unlike traditional federated learning
frameworks, our method enables devices to offload their data processing tasks
to each other, with these decisions determined through a convex data transfer
optimization problem that trades off costs associated with devices processing,
offloading, and discarding data points. We analytically characterize the
optimal data transfer solution for different fog network topologies, showing
for example that the value of offloading is approximately linear in the range
of computing costs in the network. Our subsequent experiments on testbed
datasets we collect confirm that our algorithms are able to improve network
resource utilization substantially without sacrificing the accuracy of the
learned model. In these experiments, we also study the effect of network
dynamics, quantifying the impact of nodes entering or exiting the network on
model learning and resource costs.


  Inspired by recent advances in diffusion models, which are reminiscent of
denoising autoencoders, we investigate whether they can acquire discriminative
representations for classification via generative pre-training. This paper
shows that the networks in diffusion models, namely denoising diffusion
autoencoders (DDAE), are unified self-supervised learners: by pre-training on
unconditional image generation, DDAE has already learned strongly
linear-separable representations within its intermediate layers without
auxiliary encoders, thus making diffusion pre-training emerge as a general
approach for generative-and-discriminative dual learning. To validate this, we
conduct linear probe and fine-tuning evaluations. Our diffusion-based approach
achieves 95.9% and 50.0% linear evaluation accuracies on CIFAR-10 and
Tiny-ImageNet, respectively, and is comparable to contrastive learning and
masked autoencoders for the first time. Transfer learning from ImageNet also
confirms the suitability of DDAE for Vision Transformers, suggesting the
potential to scale DDAEs as unified foundation models. Code is available at
github.com/FutureXiang/ddae.


  We consider the dielectric breakdown model in the limit $\eta\to 0^+$. A
differential equation describing the surface growth is derived; this equation
is KPZ plus a term causing linear instability, and includes a short-distance
regularization similar to a viscosity. The equation exhibits an interesting
dynamics in terms of poles, permitting us to derive a large family of solutions
to the equation of motion. In terms of poles, we find all stationary
configurations of the surface, and analytically calculate their stability. For
each value of the viscosity, only one stable configuration is found, but this
configuration is nonlinearly unstable in the presence of an exponentially small
amount of noise. The present approach may be useful in understanding the
dynamics for finite $\eta$, in particular the DLA model, in terms of
perturbations to the infinitesimal $\eta$ problem.


  Starting from an {\it ab initio}-derived two-site dimer Hubbard hamiltonian
on a triangular lattice, we calculate the superconducting gap functions and
critical temperatures for representative $\kappa$-(BEDT-TTF)$_2$X
superconductors by solving the linearized Eliashberg equation using the
Two-Particle Self-Consistent approach (TPSC) extended to multi-site problems.
Such an extension allows for the inclusion of molecule degrees of freedom in
the description of these systems. We present both, benchmarking results for the
half-filled dimer model as well as detailed investigations for the 3/4-filled
molecule model. Remarkably, we find in the latter model that the phase boundary
between the two most competing gap symmetries discussed in the context of these
materials -d$_{xy}$ and the recently proposed eight-node gap s+d$_{x^2-y^2}$
symmetry- is located within the regime of realistic model parameters and is
especially sensitive to the degree of in-plane anisotropy in the materials as
well as to the value of the on-site Hubbard repulsion. We show that these
results provide a more complete and accurate description of the superconducting
properties of $\kappa$-(BEDT-TTF)$_2$X than previous Random Phase Approximation
(RPA) calculations and, in particular, we discuss predicted critical
temperatures in comparison to experiments. Finally, our findings suggest that
it may be even easier to experimentally switch between the two pairing
symmetries as previously anticipated by invoking pressure, chemical doping or
disorder effects.


  A 3-dimensional Catalan word is a word on three letters so that the subword
on any two letters is a Dyck path. For a given Dyck path $D$, a recently
defined statistic counts the number of Catalan words with the property that any
subword on two letters is exactly $D$. In this paper, we enumerate Dyck paths
with this statistic equal to certain values, including all primes. The formulas
obtained are in terms of Motzkin numbers and Motzkin ballot numbers.


  We obtain the quite exact exponential bounds for tails of distributions of
sums of Banach space valued random variables uniformly over the number of
summands under natural for the Law of Iterated Logarithm (LIL) norming.
  We study especially the case of the so-called mixed (anisotropic)
Lebesgue-Riesz spaces, on the other words, Bochner's spaces, for instance,
continuous-Lebesgue spaces, which appear for example in the investigation of
non-linear Partial Differential Equations of evolutionary type.
  We give also some examples in order to show the exactness of our estimates.


  We show that any complete $k$-partite graph $G$ on $n$ vertices, with $k \ge
3$, whose edges are two-coloured, can be covered with two vertex-disjoint
monochromatic paths of distinct colours. We prove this under the necessary
assumption that the largest partition class of $G$ contains at most $n/2$
vertices. This extends known results for complete and complete bipartite
graphs.
  Secondly, we show that in the same situation, all but $o(n)$ vertices of the
graph can be covered with two vertex-disjoint monochromatic cycles of distinct
colours, if colourings close to a split colouring are excluded. From this we
derive that the whole graph, if large enough, may be covered with 14
vertex-disjoint monochromatic cycles.


  The performance of peer-to-peer file replication comes from its piece and
peer selection strategies. Two such strategies have been introduced by the
BitTorrent protocol: the rarest first and choke algorithms. Whereas it is
commonly admitted that BitTorrent performs well, recent studies have proposed
the replacement of the rarest first and choke algorithms in order to improve
efficiency and fairness. In this paper, we use results from real experiments to
advocate that the replacement of the rarest first and choke algorithms cannot
be justified in the context of peer-to-peer file replication in the Internet.
We instrumented a BitTorrent client and ran experiments on real torrents with
different characteristics. Our experimental evaluation is peer oriented,
instead of tracker oriented, which allows us to get detailed information on all
exchanged messages and protocol events. We go beyond the mere observation of
the good efficiency of both algorithms. We show that the rarest first algorithm
guarantees close to ideal diversity of the pieces among peers. In particular,
on our experiments, replacing the rarest first algorithm with source or network
coding solutions cannot be justified. We also show that the choke algorithm in
its latest version fosters reciprocation and is robust to free riders. In
particular, the choke algorithm is fair and its replacement with a bit level
tit-for-tat solution is not appropriate. Finally, we identify new areas of
improvements for efficient peer-to-peer file replication protocols.


  In this paper, a matrix is said to be prime if the row and column of this
matrix are both prime numbers. We establish various necessary and sufficient
conditions for developing matrices into the sum of tensor products of prime
matrices. For example, if the diagonal of a matrix blocked evenly are pairwise
commutative, it yields such a decomposition. The computational complexity of
multiplication of these algorithms is shown to be $O(n^{5/2})$. In the section
5, a decomposition is proved to hold if and only if every even natural number
greater than 2 is the sum of two prime numbers.


  We present 32 epochs of optical (3300-9700 \AA) spectrophotometric
observations of the nearby quintessential "normal" type Ia supernova (SN Ia) SN
2011fe in the galaxy M101, extending from -15 to +97 d with respect to B-band
maximum, obtained by the Nearby Supernova Factory collaboration. SN 2011fe is
the closest (\mu = 29.04) and brightest (Bmax = 9.94 mag) SN Ia observed since
the advent of modern large scale programs for the intensive periodic followup
of supernovae. Both synthetic light curve measurements and spectral feature
analysis attest to the normality of SN 2011fe. There is very little evidence
for reddening in its host galaxy. The homogeneous calibration, intensive time
sampling, and high signal-to-noise ratio of the data set make it unique. Thus
it is ideal for studying the physics of SN Ia explosions in detail, and for
furthering the use of SNe Ia as standardizable candles for cosmology. Several
such applications are shown, from the creation of a bolometric light curve and
measurement of the 56Ni mass, to the simulation of detection thresholds for
unburned carbon, direct comparisons with other SNe Ia, and existing spectral
templates.


  The spreading of a pure, volatile liquid on a wettable substrate has been
studied in extensive detail. Here we show that the addition of a miscible,
non-volatile liquid can strongly alter the contact line dynamics and the final
liquid deposition pattern. We observe two distinct regimes of behavior
depending on the relative strength of solutal Marangoni forces and surface
wetting. Finger-like instabilities precede the deposition of a sub-micron thick
film for large Marangoni forces and small solute contact angles, whereas
isolated, pearl-like drops emerge and are deposited in quasi-crystalline
patterns for small Marangoni forces and large solute contact angles. This
behavior can be tuned by directly varying the contact angle of the solute
liquid on the solid substrate.


  Measuring the tau-lepton ($\tau$) anomalous magnetic moment
$a_\tau=(g_\tau-2)/2$ in photon fusion production ($\gamma\gamma\to\tau\tau$)
tests foundational Standard Model principles. However,
$\gamma\gamma\to\tau\tau$ eludes observation in LHC proton collisions (pp)
despite enhanced new physics sensitivity from higher-mass reach than existing
probes. We propose a novel strategy to measure
$\text{pp}\to\text{p}(\gamma\gamma\to\tau\tau)\text{p}$ by introducing the
overlooked electron-muon signature with vertex isolation for signal extraction.
Applying the effective field theory of dipole moments, we estimate 95% CL
sensitivity of $-0.0092<a_{\tau}<0.011$ assuming 300 fb$^{-1}$ luminosity and
5% systematics. This fourfold improvement beyond existing constraints opens a
crucial path to unveiling new physics imprinted in tau-lepton dipoles.


  We discuss the target and beam normal spin asymmetries in elastic
electron-nucleon scattering which depend on the imaginary part of two-photon
exchange processes between electron and nucleon. We express this imaginary part
as a phase space integral over the doubly virtual Compton scattering tensor on
the nucleon. We use unitarity to model the doubly virtual Compton scattering
tensor in the resonance region in terms of $\gamma^* N \to \pi N$
electroabsorption amplitudes. Taking those amplitudes from a phenomenological
analysis of pion electroproduction observables, we present results for beam and
target normal single spin asymmetries for elastic electron-nucleon scattering
for beam energies below 1 GeV and in the 1-3 GeV region, where several
experiments are performed or are in progress.


  It is believed that there exists a rich phase structure of quantum
chromodynamics (QCD) at finite temperature and baryon density, namely, the
deconfinement process from hadron gas to quark-gluon plasma, the transition
from chiral symmetry breaking phase to the symmetry restoration phase, and the
color superconductivity at low temperature and high baryon density. In the
present work we study the hadron-quark phase transition by investigating the
binodal surface and extending it to finite temperature in order to mimic the
QCD phase diagram. In order to obtain these conditions we use different models
for the two possible phases, namely the quark and hadron phases. The phase
separation boundary (binodal) is determined by the Gibbs criteria for phase
equilibrium. The boundaries of the mixed phase and the related critical points
for symmetric and asymmetric matter are obtained. Isospin effects appear to be
rather significant. The critical endpoint (CEP) and the phase structure are
also studied in the Polyakov-loop extended Nambu-Jona-Lasinio model.


  The present article deals with a formulation of the so called (vacuum)
Palatini gravity as a general variational principle. In order to accomplish
this goal, some geometrical tools related to the geometry of the bundle of
connections of the frame bundle $LM$ are used. A generalization of
Lagrange-Poincar\'e reduction scheme to these types of variational problems
allows us to relate it with the Einstein-Hilbert variational problem. Relations
with some other variational problems for gravity found in the literature are
discussed.


  In this paper we perform canonical quantization of the product of the gauged
WZW models on a strip with boundary conditions specified by permutation branes.
We show that the phase space of the $N$-fold product of the gauged WZW model
$G/H$ on a strip with boundary conditions given by permutation branes is
symplectomorphic to the phase space of the double Chern-Simons theory on a
sphere with $N$ holes times the time-line with $G$ and $H$ gauge fields both
coupled to two Wilson lines. For the special case of the topological coset
$G/G$ we arrive at the conclusion that the phase space of the $N$-fold product
of the topological coset $G/G$ on a strip with boundary conditions given by
permutation branes is symplectomorphic to the phase space of Chern-Simons
theory on a Riemann surface of the genus $N-1$ times the time-line with four
Wilson lines.


  Cosmological models that invoke warm or cold dark matter can not explain
observed regularities in the properties of dwarf galaxies, their highly
anisotropic spatial distributions, nor the correlation between observed mass
discrepancies and acceleration. These problems with the standard model of
cosmology have deep implications, in particular in combination with the
observation that the data are excellently described by Modified Newtonian
Dynamics (MOND). MOND is a classical dynamics theory which explains the mass
discrepancies in galactic systems, and in the universe at large, without
invoking dark entities. MOND introduces a new universal constant of nature with
the dimensions of acceleration, a0, such that the pre-MONDian dynamics is valid
for accelerations a >> a0, and the deep MONDian regime is obtained for a << a0,
where space-time scale invariance is invoked. Remaining challenges for MOND are
(i) explaining fully the observed mass discrepancies in galaxy clusters, and
(ii) the development of a relativistic theory of MOND that will satisfactorily
account for cosmology. The universal constant a0 turns out to have an
intriguing connection with cosmology: \bar a0 == 2 pi a0 \approx c H_0 \approx
c^2(Lambda/3)^{1/2}. This may point to a deep connection between cosmology and
internal dynamics of local systems.


  The algebra of strongly regular functions F[G_m] on a symmetrizable minimal
Kac-Moody group G_m over a field F of characteristic zero has been introduced
by V. Kac and D. Peterson as a coordinate ring of the minimal Kac-Moody group.
We determine its F-valued points. The product (G_f) x (G_f) of two formal
Kac-Moody groups G_f acts on the F-valued points by morphisms. We describe the
partition in (G_f) x (G_f)-orbits, and the closure relation of the orbits. We
give stratified transversal slices to the orbits. We define and describe big
cells of each orbit. We describe the partition in (B_f) x (B_f)-orbits, B_f the
standard formal Borel subgroup of G_f.


  Several coronagraph designs have been proposed over the last two decades to
directly image exoplanets. Among these designs, the vector vortex coronagraphs
provide theoretically perfect starlight cancellation along with small inner
working angles when deployed on telescopes with unobstructed pupils. However,
current and planned space missions and ground-based extremely large telescopes
present complex pupil geometries, including secondary mirror central
obscurations, that prevent vortex coronagraphs from rejecting on-axis sources
entirely. Recent solutions combining the vortex phase mask with a ring-apodized
pupil have been proposed to circumvent this issue, but provide a limited
throughput for vortex charges $>2$. We present a family of pupil plane
apodizations that compensate for pupil geometries with circularly symmetric
central obstructions caused by on-axis secondary mirrors for charge 2, 4, and 6
vector vortex coronagraphs. These apodizations are derived analytically and
allow the vortex coronagraph to retain theoretically perfect nulling in the
presence of central obscurations. For a charge 4 vortex, we design polynomial
apodization functions assuming a greyscale apodizing filter that represent a
substantial gain in throughput over the ring-apodized vortex coronagraph
design, while for a charge 6 vortex, we design polynomial apodized vortex
coronagraphs that have $\gtrsim 70\%$ total energy throughput for the entire
range of central obscuration sizes studied. We propose methods for optimizing
apodizations produced with either greyscale apodizing filters or shaped
mirrors. We conclude by demonstrating how this design may be combined with
apodizations numerically optimized for struts and segment gaps in telescope
pupils to design terrestrial exoplanet imagers for complex pupils.


  In this work, we present a time-dependent (TD) selected configuration
interaction method based on our recently-introduced adaptive configuration
interaction (ACI). We show that ACI, in either its ground or excited state
formalisms, is capable of building a compact basis for use in real-time
propagation of wave functions for computing electron dynamics. TD-ACI uses an
iteratively selected basis of determinants in real-time propagation capable of
capturing strong correlation effects in both ground and excited states, all
with an accuracy---and associated cost---tunable by the user. We apply TD-ACI
to study attosecond-scale migration of charge following ionization in small
molecules. We first compute attosecond charge dynamics in a benzene model to
benchmark and understand the utility of TD-ACI with respect to an exact
solution. Finally, we use TD-ACI to reproduce experimentally determined
ultrafast charge migration dynamics in iodoacetylene. TD-ACI is shown to be a
valuable benchmark theory for electron dynamics, and it represents an important
step towards accurate and affordable time-dependent multireference methods.


  Gravitational waves from oscillating neutron stars in axial symmetry are
studied performing numerical simulations in full general relativity. Neutron
stars are modeled by a polytropic equation of state for simplicity. A
gauge-invariant wave extraction method as well as a quadrupole formula are
adopted for computation of gravitational waves. It is found that the
gauge-invariant variables systematically contain numerical errors generated
near the outer boundaries in the present axisymmetric computation. We clarify
their origin, and illustrate it possible to eliminate the dominant part of the
systematic errors. The best corrected waveforms for oscillating and rotating
stars currently contain errors of magnitude $\sim 10^{-3}$ in the local wave
zone. Comparing the waveforms obtained by the gauge-invariant technique with
those by the quadrupole formula, it is shown that the quadrupole formula yields
approximate gravitational waveforms besides a systematic underestimation of the
amplitude of $O(M/R)$ where $M$ and $R$ denote the mass and the radius of
neutron stars. However, the wave phase and modulation of the amplitude can be
computed accurately. This indicates that the quadrupole formula is a useful
tool for studying gravitational waves from rotating stellar core collapse to a
neutron star in fully general relativistic simulations. Properties of the
gravitational waveforms from the oscillating and rigidly rotating neutron stars
are also addressed paying attention to the oscillation associated with
fundamental modes.


  We study in $\mathbb{R}^{3+1}$ a system of nonlinearly coupled Klein-Gordon
equations under null condition, with (possibly vanishing) mass varying in the
interval $[0, 1]$. Our goal is three folds: 1) we want to establish the global
well-posedness result to the system which is uniform in terms of the mass
parameter; 2) we want to obtain unified pointwise decay result for the solution
to the system, in the sense that the solution decays more like a wave component
(independent of the mass parameter) in certain range of time, while the
solution decays as a Klein-Gordon component with a factor depending on the mass
parameter in the other part of the time range; 3) the solution to the
Klein-Gordon system converges to the solution to the corresponding wave system
in certain sense when the mass parameter goes to 0. In order to achieve these
goals, we will rely on both the flat and the hyperboloidal foliation of the
spacetime.


  We report for the first time a relationship between galaxy kinematics and net
Lyman-alpha equivalent width (net Lya EW) in star forming galaxies during the
epoch of peak cosmic star formation. Building on the previously reported
broadband imaging segregation of Lya-emitting and Lya-absorbing Lyman break
galaxies (LBGs) at z~2 (Paper I in this series) and previously at z~3, we use
the Lya spectral type classification method to study the relationship between
net Lya EW and nebular emission-line kinematics determined from IFU
spectroscopy. We show that z~2 and z~3 LBGs segregate in colour-magnitude space
according to their kinematic properties and Lyman-alpha spectral type, and
conclude that LBGs with Lya dominant in absorption are almost exclusively
rotation-dominated (presumably disc-like) systems, and LBGs with Lya dominant
in emission characteristically have dispersion-dominated kinematics. We
quantify the relationship between the strength of rotational dynamic support
and net Lya EW, and demonstrate the consistency of our result with other
properties that scale with net Lya EW and kinematics. Based on these findings,
we suggest a method by which large samples of rotation- and
dispersion-dominated galaxies might be selected using broadband imaging in as
few as three filters and/or net Lya EW alone. Application of this method will
enable an understanding of galaxy kinematic behaviour over large scales in
datasets from current and future large-area and all-sky photometric surveys
that will select hundreds of millions of LBGs in redshift ranges from z~2-6
across many hundreds to thousands of Mpc. Finally, we speculate that the
combination of our result linking net Lya EW and nebular emission-line
kinematics with the known large-scale clustering behaviour of Lya-absorbing and
Lya-emitting LBGs is evocative of a nascent morphology-density relation at
z~2-3.


  The survival of unbound density substructure against orbital mixing imposes
strong constraints on the slope of the underlying gravitational potential and
provides a new test on modified gravities. Here we investigate whether the
interpretation that the stellar clump in Ursa Minor (UMi) dwarf spheroidal
galaxy is a `dynamical fossil' is consistent with Modified Newtonian dynamics
(MOND). For UMi mass models inferred by fitting the velocity dispersion
profile, the stellar clump around the second peak of UMi is erased very
rapidly, within 1.25 Gyr (6.5 orbits), even with the inclusion of self-gravity.
We find that the clump can hardly survive for more than 2 Gyr even under more
generous conditions. Alternative scenarios which could lead to a kinematically
cold clump are discussed but, so far, none of them were found to be fully
satisfactory. Our conclusion is that the cold clump in UMi poses a challenge
for both LambdaCDM and MOND.


  The advancement of socially-aware autonomous vehicles hinges on precise
modeling of human behavior. Within this broad paradigm, the specific challenge
lies in accurately predicting pedestrian's trajectory and intention.
Traditional methodologies have leaned heavily on historical trajectory data,
frequently overlooking vital contextual cues such as pedestrian-specific traits
and environmental factors. Furthermore, there's a notable knowledge gap as
trajectory and intention prediction have largely been approached as separate
problems, despite their mutual dependence. To bridge this gap, we introduce
PTINet (Pedestrian Trajectory and Intention Prediction Network), which jointly
learns the trajectory and intention prediction by combining past trajectory
observations, local contextual features (individual pedestrian behaviors), and
global features (signs, markings etc.). The efficacy of our approach is
evaluated on widely used public datasets: JAAD and PIE, where it has
demonstrated superior performance over existing state-of-the-art models in
trajectory and intention prediction. The results from our experiments and
ablation studies robustly validate PTINet's effectiveness in jointly exploring
intention and trajectory prediction for pedestrian behaviour modelling. The
experimental evaluation indicates the advantage of using global and local
contextual features for pedestrian trajectory and intention prediction. The
effectiveness of PTINet in predicting pedestrian behavior paves the way for the
development of automated systems capable of seamlessly interacting with
pedestrians in urban settings.


  A classical problem in statistics is estimating the expected coverage of a
sample, which has had applications in gene expression, microbial ecology,
optimization, and even numismatics. Here we consider a related extension of
this problem to random samples of two discrete distributions. Specifically, we
estimate what we call the dissimilarity probability of a sample, i.e., the
probability of a draw from one distribution not being observed in k draws from
another distribution. We show our estimator of dissimilarity to be a
U-statistic and a uniformly minimum variance unbiased estimator of
dissimilarity over the largest appropriate range of k. Furthermore, despite the
non-Markovian nature of our estimator when applied sequentially over k, we show
it converges uniformly in probability to the dissimilarity parameter, and we
present criteria when it is approximately normally distributed and admits a
consistent jackknife estimator of its variance. As proof of concept, we analyze
V35 16S rRNA data to discern between various microbial environments. Other
potential applications concern any situation where dissimilarity of two
discrete distributions may be of interest. For instance, in SELEX experiments,
each urn could represent a random RNA pool and each draw a possible solution to
a particular binding site problem over that pool. The dissimilarity of these
pools is then related to the probability of finding binding site solutions in
one pool that are absent in the other.


  A "two-dimensional ballistic deposition" (2D-BD) code has been developed to
study the geometric effects in ballistic deposition of thin-film growth.
Circular discs are used as depositing specie to understand the shadowing
effects during the evolution of a thin-film. We carried out the 2D-BD
simulations for the angles of deposition $20^0$-$80^0$ in steps of $10^0$.
Standard deviations $1^0$, $2^0$, $4^0$, $6^0$ and $10^0$ are used for each
angle of deposition with disc size of $1.5 \overset{\circ}{A}$ to understand
its effect on the microstructure of the thin-films. Angle of growth, porosity
and surface roughness properties have been studied for the afore-mentioned
angles of deposition and their standard deviations. Ballistic deposition
simulations with the discs of different sizes have been carried out to
understand the effect of size in ballistic deposition. The results from this
code are compared with the available theoretical and experimental results. The
code is used to simulate a collimated glancing angle deposition (C-GLAD)
experiment. We obtain a good qualitative match for various features of the
deposits.


  We consider a somehow peculiar Token/Bucket problem which at first sight
looks confusing and difficult to solve. The winning approach to solve the
problem consists in going back to the simple and traditional methods to solve
computer science problems like the one taught to us by Knuth. Somehow the main
trick is to be able to specify clearly what needs to be achieved, and then the
solution, even if complex, appears almost by itself.


  The dispersive spreading of microscopic particles in shear flows is
influenced both by advection and thermal motion. At the nanoscale, interactions
between such particles and their confining boundaries become unavoidable. We
address the roles of electrostatic repulsion and absorption on the spatial
distribution and dispersion of charged nanoparticles in near-surface shear
flows, observed under evanescent illumination. The electrostatic repulsion
between particles and the lower charged surface is tuned by varying electrolyte
concentrations. Particles leaving the field of vision can be neglected from
further analysis, such that the experimental ensemble is equivalent to that of
Taylor dispersion with absorption. These two ingredients modify the particle
distribution, deviating strongly from the Gibbs-Boltzmann one at the nanoscale
studied here. The overall effect is to restrain the accessible space available
to particles, leading to a striking, ten-fold reduction in the spreading
dynamics as compared to the non-interacting case.


  A numerical method to build an orthonormal basis of properly symmetrized
hyperspherical harmonic functions is developed. As a part of it, refined
algorithms for calculating the transformation coefficients between
hyperspherical harmonics constructed from different sets of Jacobi vectors are
derived and discussed. Moreover, an algorithm to directly determine the numbers
of independent symmetric hyperspherical states (in case of bosonic systems) and
antisymmetric hyperspherical-spinisospin states (in case of fermionic systems)
entering the expansion of the A-body wave functions is presented. Numerical
implementations for systems made with up to five bodies are reported.


  This paper proposes a blockchain-based Federated Learning (FL) framework with
Intel Software Guard Extension (SGX)-based Trusted Execution Environment (TEE)
to securely aggregate local models in Industrial Internet-of-Things (IIoTs). In
FL, local models can be tampered with by attackers. Hence, a global model
generated from the tampered local models can be erroneous. Therefore, the
proposed framework leverages a blockchain network for secure model aggregation.
Each blockchain node hosts an SGX-enabled processor that securely performs the
FL-based aggregation tasks to generate a global model. Blockchain nodes can
verify the authenticity of the aggregated model, run a blockchain consensus
mechanism to ensure the integrity of the model, and add it to the distributed
ledger for tamper-proof storage. Each cluster can obtain the aggregated model
from the blockchain and verify its integrity before using it. We conducted
several experiments with different CNN models and datasets to evaluate the
performance of the proposed framework.


  We investigate the renormalization-group scale and scheme dependence of the
$H \rightarrow gg$ decay rate at the order N$^4$LO in the renormalization-group
summed perturbative theory, which employs the summation of all
renormalization-group accessible logarithms including the leading and
subsequent four sub-leading logarithmic contributions to the full perturbative
series expansion. Moreover, we study the higher-order behaviour of the $H
\rightarrow gg$ decay width using the asymptotic Pad\'e approximant method in
four different renormalization schemes. Furthermore, the higher-order behaviour
is independently investigated in the framework of the asymptotic Pad\'e-Borel
approximant method where generalized Borel-transform is used as an analytic
continuation of the original perturbative expansion. The predictions of the
asymptotic Pad\'e-Borel approximant method are found to be in agreement with
that of the asymptotic Pad\'e approximant method. Finally, we provide the $H
\rightarrow gg$ decay rate at the order N$^5$LO in the fixed-order $
\Gamma_{\rm N^5LO} \,=\, \Gamma_0 (1.8375 \pm 0.047 _{\alpha_s(M_Z),1\%}\pm
0.0004_{M_t} \pm 0.0066_{M_H}
  \pm 0.0036_{\rm P} \pm 0.007_{\text{s}} \pm 0.0005_{sc} ),$ and $\Gamma_{\rm
RGSN^5LO} \,=\, \Gamma_0 (1.841 \pm 0.047 _{\alpha_s(M_Z),1\%} \pm
0.0005_{M_t}\pm 0.0066_{M_H} \pm 0.0002_{\mu} \pm 0.0027_{\rm P} \pm 0.001_{sc}
)$ in the renormalization-group summed perturbative theories.


  Magnetic monopoles have long been predicted in theory and could exist as a
stable object in our universe. As they move around in galaxies, magnetic
monopoles could be captured by astrophysical objects like stars and planets.
Here, we provide a novel method to search for magnetic monopoles by detecting
the monopole moment of the Earth's magnetic field. Using over six years of
public geomagnetic field data obtained by the Swarm satellites, we apply
Gauss's law to measure the total magnetic flux, which is proportional to the
total magnetic charge inside the Earth. To account for the secular variation of
satellite altitudes, we define an altitude-rescaled magnetic flux to reduce the
dominant magnetic dipole contribution. The measured magnetic flux is consistent
with the existing magnetic field model that does not contain a monopole moment
term. We therefore set an upper limit on the magnetic field strength at Earth's
surface from magnetic monopoles to be $|B_{\rm m}| < 0.13$ nT at 95% confidence
level, which is less than $2\times 10^{-6}$ of Earth's magnetic field strength.
This constrains the abundance of magnetically-charged objects, including
magnetic black holes with large magnetic charges.


  This work is devoted to study the global behavior of viscous flows contained
in a symmetric domain with complete slip boundary. In such scenario the
boundary no longer provides friction and therefore the perturbation of angular
velocity lacks decaying structure. In fact, we show the existence of uniformly
rotating solutions as steady states for the compressible Navier-Stokes
equations. By manipulating the conservation law of angular momentum, we
establish a suitable Korn's type inequality to control the perturbation and
show the asymptotic stability of the uniformly rotating solutions with small
angular velocity. In particular, the initial perturbation which preserves the
angular momentum would decay exponentially in time and the solution to the
Navier-Stokes equations converges to the steady state as time grows up.


  We study instanton solutions and superpotentials for the large number of
vacua of the plane-wave matrix model and a 2+1 dimensional Super Yang-Mills
theory on $R\times S^2$ with sixteen supercharges. We get the superpotential in
the weak coupling limit from the gauge theory description. We study the gravity
description of these instantons. Perturbatively with respect to a background,
they are Euclidean branes wrapping cycles in the dual gravity background.
Moreover, the superpotential can be given by the energy of the electric charge
system characterizing each vacuum. These charges are interpreted as the
eigenvalues of matrices from a reduction for the 1/8 BPS sector of the gauge
theories. We also discuss qualitatively the emergence of the extra spatial
dimensions appeared on the gravity side.


  Hydrogenation of amorphous silicon (a-Si:H) is critical for reducing defect
densities, passivating mid-gap states and surfaces, and improving
photoconductivity in silicon-based electro-optical devices. Modelling the
atomic scale structure of this material is critical to understanding these
processes, which in turn is needed to describe c-Si/a-Si:H heterjunctions that
are at the heart of the modern solar cells with world record efficiency.
Density functional theory (DFT) studies achieve the required high accuracy but
are limited to moderate system sizes a hundred atoms or so by their high
computational cost. Simulations of amorphous materials in particular have been
hindered by this high cost because large structural models are required to
capture the medium range order that is characteristic of such materials.
Empirical potential models are much faster, but their accuracy is not
sufficient to correctly describe the frustrated local structure. Data driven,
"machine learned" interatomic potentials have broken this impasse, and have
been highly successful in describing a variety of amorphous materials in their
elemental phase. Here we extend the Gaussian approximation potential (GAP) for
silicon by incorporating the interaction with hydrogen, thereby significantly
improving the degree of realism with which amorphous silicon can be modelled.
We show that our Si:H GAP enables the simulation of hydrogenated silicon with
an accuracy very close to DFT, but with computational expense and run times
reduced by several orders of magnitude for large structures. We demonstrate the
capabilities of the Si:H GAP by creating models of hydrogenated liquid and
amorphous silicon, and showing that their energies, forces and stresses are in
excellent agreement with DFT results, and their structure as captured by bond
and angle distributions, with both DFT and experiments.


  For a graph $G=(V,E)$, a set $D \subseteq V$ is called a semitotal dominating
set of $G$ if $D$ is a dominating set of $G$, and every vertex in $D$ is within
distance~$2$ of another vertex of~$D$. The \textsc{Minimum Semitotal
Domination} problem is to find a semitotal dominating set of minimum
cardinality. Given a graph $G$ and a positive integer $k$, the
\textsc{Semitotal Domination Decision} problem is to decide whether $G$ has a
semitotal dominating set of cardinality at most $k$. The \textsc{Semitotal
Domination Decision} problem is known to be NP-complete for general graphs. In
this paper, we show that the \textsc{Semitotal Domination Decision} problem
remains NP-complete for planar graphs, split graphs and chordal bipartite
graphs. We give a polynomial time algorithm to solve the \textsc{Minimum
Semitotal Domination} problem in interval graphs. We show that the
\textsc{Minimum Semitotal Domination} problem in a graph with maximum
degree~$\Delta$ admits an approximation algorithm that achieves the
approximation ratio of $2+3\ln(\Delta+1)$, showing that the problem is in the
class log-APX. We also show that the \textsc{Minimum Semitotal Domination}
problem cannot be approximated within $(1 - \epsilon)\ln |V| $ for any
$\epsilon > 0$ unless NP $\subseteq$ DTIME $(|V|^{O(\log \log |V|)})$. Finally,
we prove that the \textsc{Minimum Semitotal Domination} problem is APX-complete
for bipartite graphs with maximum degree $4$.


  Local community detection consists of finding a group of nodes closely
related to the seeds, a small set of nodes of interest. Such group of nodes are
densely connected or have a high probability of being connected internally than
their connections to other clusters in the network. Existing local community
detection methods focus on finding either one local community that all seeds
are most likely to be in or finding a single community for each of the seeds.
However, a seed member usually belongs to multiple local overlapping
communities. In this work, we present a novel method of detecting multiple
local communities to which a single seed member belongs. The proposed method
consists of three key steps: (1) local sampling with Personalized PageRank
(PPR); (2) using the sparseness generated by a sparse nonnegative matrix
factorization (SNMF) to estimate the number of communities in the sampled
subgraph; (3) using SNMF soft community membership vectors to assign nodes to
communities. The proposed method shows favorable accuracy performance and a
good conductance when compared to state-of-the-art community detection methods
by experiments using a combination of artificial and real-world networks.


  Population Monte Carlo has been introduced as a sequential importance
sampling technique to overcome poor fit of the importance function. In this
paper, we compare the performances of the original Population Monte Carlo
algorithm with a modified version that eliminates the influence of the
transition particle via a double Rao-Blackwellisation. This modification is
shown to improve the exploration of the modes through an large simulation
experiment on posterior distributions of mean mixtures of distributions.


  We prove that for all natural numbers $m$ and $k$ where $k$ is odd, there
exists a natural number $N(k)$ such that any 3-connected cubic graph with at
least $N(k)$ vertices contains a cycle of length $m$ modulo $k$. We also
construct a family of graphs showing that this is not true for 2-connected
cubic graphs if $m$ and $k$ are divisible by 3 and $k\geq 12$.


  We present a non-perturbative determination of the renormalization factor Z_S
of the scalar density in quenched QCD with overlap fermions. Results are
obtained at four values of the lattice spacing. By combining Z_S with results
for the low-energy constant Sigma we are able to compute the renormalization
group invariant scalar condensate in the continuum limit with a total accuracy
of 7%, excluding dynamical quark effects. Our result translates to
Sigma_msbar(2 GeV)=(285+/-9 MeV)^3 if the scale is set by the kaon decay
constant. We have also performed scaling studies of the pseudoscalar decay
constant and the vector mass. Our results indicate that quantities computed
using overlap quarks exhibit excellent scaling behaviour, with small residual
lattice artifacts.