  We investigate the evolution of decorrelation bandwidth of inter core
crosstalk (IC-XT) in homogeneous weakly coupled multicore fibers (WC-MCFs). The
modified mode-coupled equations (MCEs) are numerically solved by combining the
fourth order Runge-Kutta method and compound Simpson integral method. It can be
theoretically and numerically observed that the decorrelation bandwidth of
IC-XT decreases with transmission distance by fractional linear function. The
evolution rule of IC-XT's decorrelation bandwidth is further confirmed by
experiments, which can be used as an evaluation criterion for channel model.
Finally, we propose a new channel model with the coupling matrix of IC-XT
generated automatically by phase transfer function (PTF), which is in good
agreement with the above evaluation criterion. We believe the proposed channel
model can provide a good simulation platform for homogeneous WC-MCF based
communication systems.


  We generalize Rost's theory of cycle modules using Milnor-Witt K-theory
instead of the classical Milnor K-theory. We obtain a (quadratic) setting to
study general cycle complexes and their (co)homology groups. The usual
constructions are developed: proper pushfoward, (essentially) smooth pullback,
long exact sequences, (coniveau) spectral sequences and products, as well as
the homotopy invariance property; in addition, Gysin morphisms for lci maps are
constructed. We prove an adjunction theorem linking our theory to Rost's.


  We investigate the uncertainty associated with a joint quantum measurement of
two components of spin of a spin-1/2 particle and quantify this in terms of
entropy. We consider two entropic quantities: the joint entropy and the sum of
the marginal entropies, and obtain lower bounds for each of these quantities.
For the case of joint measurements where we measure each spin observable
equally well, these lower bounds are tight.


  We formulate a universal characterization of the many-particle quantum
entanglement in the ground state of a topologically ordered two-dimensional
medium with a mass gap. We consider a disk in the plane, with a smooth boundary
of length L, large compared to the correlation length. In the ground state, by
tracing out all degrees of freedom in the exterior of the disk, we obtain a
marginal density operator \rho for the degrees of freedom in the interior. The
von Neumann entropy S(\rho) of this density operator, a measure of the
entanglement of the interior and exterior variables, has the form S(\rho)=
\alpha L -\gamma + ..., where the ellipsis represents terms that vanish in the
limit L\to\infty. The coefficient \alpha, arising from short wavelength modes
localized near the boundary, is nonuniversal and ultraviolet divergent, but
-\gamma is a universal additive constant characterizing a global feature of the
entanglement in the ground state. Using topological quantum field theory
methods, we derive a formula for \gamma in terms of properties of the
superselection sectors of the medium.


  We present a novel approach for solving numerically one-dimensional
scattering problems and apply it for computing the emission probability of an
ultracold atom interacting with an arbitrary field mode of a high-$Q$ cavity.
Our method is efficient, stable and succeeds when other numerical integration
methods fail. It also replaces and improves advantageously the WKB
approximation. The cases of sinusoidal, $\mathrm{sech}^2$ and Gaussian field
modes are studied and compared. Divergences with previous works, where WKB was
used, are found.


  In this paper, several results regarding $\gamma$-translators in
$\mathbb{R}^{n+1}$ are obtained by means of maximum principle arguments. The
paper delves into characterizations of grim reaper cylinders and establishes
convexity results for translators in $\mathbb{R}^3$. Finally, it discusses the
property of bounded extrinsic geometry in terms of the function $H\gamma^{-1}$.


  As the integrated luminosity of the Run II Tevatron increases, the
sensitivity to new physics is approaching and in some cases surpassing that
previously attained in Run I. Presented below are a selection of new results
from searches for physics beyond the Standard Model at the CDF and D0
experiments.


  Modern smartphones possess hardware for audio acquisition and to perform
speech processing tasks such as speaker recognition and health assessment.
However, energy consumption remains a concern, especially for
resource-intensive DNNs. Prior work has improved the DNN energy efficiency by
utilizing a compact model or reducing the dimensions of speech features. Both
approaches reduced energy consumption during DNN inference but not during
speech acquisition. This paper proposes using a masking kernel integrated into
gradient descent during DNN training to learn the most energy-efficient speech
length and sampling rate for windowing, a common step for sample construction.
To determine the most energy-optimal parameters, a masking function with
non-zero derivatives was combined with a low-pass filter. The proposed approach
minimizes the energy consumption of both data collection and inference by 57%,
and is competitive with speaker recognition and traumatic brain injury
detection baselines.


  A distributed model predictive control scheme is developed for tracking
piecewise constant references where the terminal set is reconfigured online,
whereas the terminal controller is computed offline. Unlike many standard
existing schemes, this scheme yields large feasible regions without performing
offline centralized computations. Although the resulting optimal control
problem (OCP) is a semidefinite program (SDP), an SDP scalability method based
on diagonal dominance is used to approximate the derived SDP by a second-order
cone program. The OCPs of the proposed scheme and its approximation are
amenable to distributed optimization. Both schemes are evaluated using a power
network example and compared to a scheme where the terminal controller is
reconfigured online as well. It is found that fixing the terminal controller
results in better performance, noticeable reduction in computational cost and
similar feasible region compared to the case in which this controller is
reconfigured online.


  Most of massive stars form in binary or higher-order systems in clumpy,
sub-structured clusters. In the very first phases of their life, these stars
are expected to interact with the surrounding environment, before being
released to the field when the cluster is tidally disrupted by the host galaxy.
We present a set of N-body simulations to describe the evolution of young
stellar clusters and their binary content in the first phases of their life. To
do this, we have developed a method that generates realistic initial conditions
for binary stars in star clusters from hydrodynamical simulations. We
considered different evolutionary cases to quantify the impact of binary and
stellar evolution. Also, we compared their evolution to that of King and
fractal models with different length scales. Our results indicate that the
global expansion of the cluster from hydrodynamical simulations is initially
balanced by the sub-clump motion and accelerates when a monolithic shape is
reached, as in a post-core collapse evolution. Compared to the spherical
initial conditions, the ratio of the 50% to 10% Lagrangian radius shows a very
distinctive trend, explained by the formation of a hot core of massive stars
triggered by the high initial degree of mass segregation. As for its binary
population, each cluster shows a self-regulating behaviour by creating
interacting binaries with binding energies of the order of its energy scales.
Also, in absence of original binaries, the dynamically formed binaries present
a mass dependent binary fraction, that mimics the trend of the observed one.


  The Cherenkov Telescope Array Observatory (CTAO) is a next-generation
ground-based gamma-ray observatory that will study the universe at very high
energy using atmospheric Cherenkov light. CTAO will comprise over 67 telescopes
of three different sizes, located in the northern and southern hemispheres.
Among these, the Medium-Sized Telescope (MST) will play a crucial role in
CTAO's observations, providing excellent sensitivity and angular resolution for
gamma rays in the energy range of 100 GeV to 5 TeV. The MST is based on a
modified single-mirror Davies-Cotton design, featuring a segmented mirror with
a diameter of 12 meters, a total reflective surface of 88 square meters, and a
focal length of 16 meters. It will cover an approximately 8-degree field of
view and be equipped with two different cameras: NectarCAM and FlashCam, at the
northern and southern CTAO sites, respectively. The MST's design is optimized
for efficient observation of extended sources, including supernova remnants and
pulsar wind nebulae, as well as the study of gamma-ray bursts and active
galactic nuclei. Currently, the MST is in the midst of production and testing
stages with the aim of being installed in 2025 for the CTAO Pathfinder project.
In this project, one MST telescope will be deployed at each CTAO site to
provide on-site experience with pre-production components. This approach
facilitates cost and risk reduction before starting serial production. This
contribution provides an overview of the current status and plans of the MST's
construction at both the northern and southern CTAO sites, as well as details
on the telescope and camera designs and their expected performance.


  We study the smooth path spaces of Euclidean spaces $\mathbb{R}^N$, as
diffeological spaces. We show that the tangent spaces of the free path space
$\mathscr{P}$ are isomorphic to $\mathscr{P}$ itself, and that the tangent
spaces of the space $\mathscr{P}_{\mathbf{p}, \mathbf{q}}$ of paths with fixed
endpoints $\mathbf{p}$ and $\mathbf{q}$ are isomorphic to the smooth loop space
of $\mathbb{R}^N$ based at the origin. We also define cotangents and gradients
of smooth maps from these path spaces, and then show that, in the case of the
action functional which arises in the calculus of variations, the gradient is
precisely the path formed out of the terms of the Euler-Lagrange equations. We
show that solutions of the Euler-Lagrange equations correspond precisely to the
zeros of the gradient, and also provide analogous interpretations for the
constrained Euler-Lagrange equations. This gives an illuminating geometric
perspective on these equations. Finally, we illustrate the theory with several
concrete examples from geometry, mechanics and machine learning.


  HDR reconstruction is an important task in computer vision with many
industrial needs. The traditional approaches merge multiple exposure shots to
generate HDRs that correspond to the physical quantity of illuminance of the
scene. However, the tedious capturing process makes such multi-shot approaches
inconvenient in practice. In contrast, recent single-shot methods predict a
visually appealing HDR from a single LDR image through deep learning. But it is
not clear whether the previously mentioned physical properties would still
hold, without training the network to explicitly model them. In this paper, we
introduce the physical illuminance constraints to our single-shot HDR
reconstruction framework, with a focus on spherical panoramas. By the proposed
physical regularization, our method can generate HDRs which are not only
visually appealing but also physically plausible. For evaluation, we collect a
large dataset of LDR and HDR images with ground truth illuminance measures.
Extensive experiments show that our HDR images not only maintain high visual
quality but also top all baseline methods in illuminance prediction accuracy.


  The solution of parameter-dependent linear systems, by classical methods,
leads to an arithmetic effort that grows exponentially in the number of
parameters. This renders the multigrid method, which has a well understood
convergence theory, infeasible. A parameter-dependent representation, e.g., a
low-rank tensor format, can avoid this exponential dependence, but in these it
is unknown how to calculate the inverse directly within the representation. The
combination of these representations with the multigrid method requires a
parameter-dependent version of the classical multigrid theory and a
parameter-dependent representation of the linear system, the smoother, the
prolongation and the restriction. A derived parameter-dependent version of the
smoothing property, fulfilled by parameter-dependent versions of the Richardson
and Jacobi methods, together with the approximation property prove the
convergence of the multigrid method for arbitrary parameter-dependent
representations. For a model problem low-rank tensor formats represent the
parameter-dependent linear system, prolongation and restriction. The smoother,
a damped Jacobi method, is directly approximated in the low-rank tensor format
by using exponential sums. Proving the smoothing property for this
approximation guarantees the convergence of the parameter-dependent method.
Numerical experiments for the parameter-dependent model problem, with bounded
parameter value range, indicate a grid size independent convergence rate.


  We study the bulk flow of the local universe using Type Ia supernova data by
considering a class of cosmological model which is spatially flat,(FRW)
space-times and contains cold dark matter and $Q$ component (QCDM models) of
the fluid as a scalar field, with self interactions determined by a potential
$V(Q)=V_{0}Exp(-\lambda Q)$ evolving in Universe. We use different cumulative
redshift slices of the Union 2 catalogue. A maximum-likelihood analysis of
peculiar velocities confirms that at low redshift $0.015 <z<0.1$, bulk flow is
moving towards the $(l; b) = (302^{o}\pm20^{o}; 3^{o}\pm10^{o})$ direction with
$v _{bulk} = 240\pm 25kms^{-1} $ velocity. This direction is aligned with
direction of (SSC) and agreement with a number previous studies at
$(1-\sigma)$, however for high redshift $0.1 <z<0.2$, we get $v _{bulk} =
1000\pm 25kms^{-1} $ towards the $(l; b) = (254^{+16^{o}}_{-14^{o}};
6^{+7^{o}}_{-10^{o}})$. This indicates that for low redshift our results are
approximately consistent with the $\Lambda CDM$ model with the latest WMAP best
fit cosmological parameters however for high redshift they are in disagreement
of $\Lambda CDM$ and support the results of previous studies such as Kashlinsky
et. al, which report the large bulk flow for the Universe. We can conclude
that, in $QCDM$ model, at small scales, fluctuations of the dark energy are
damped and do not enter in the evolution equation for the perturbations in the
pressureless matter, while at very large scales $(\sim > 100 h^{-1}Mpc)$, they
leaving an imprint on the microwave background anisotropy.


  The present paper considers a homogeneous bubble inside an unbounded
polytropic compressible liquid with viscosity. The system is governed by the
Navier-Stokes equation with free boundary which is determined by the kinematic
and dynamic boundary conditions on the bubble-liquid interface. The global
existence of solution is proved, and the $\dot{H}^1$ asymptotic stability of
the spherical equilibrium in terms of viscous damping together with a explicit
decay rate is given in bare energy methods.


  The open-source community uses the GitHub platform to exchange and share
software applications and services of interest. This paper aims to identify the
open-source community's interest in gender-related projects on GitHub. Our
findings create research opportunities and identify resources by the
open-source community that promote diversity, equity, and inclusion. We use
data mining to identify GitHub projects that focus on gender-related topics. We
apply quantitative and qualitative methodologies to examine the projects'
attributes and to classify them within a gender social structure and a gender
bias taxonomy. We aim to understand the open-source community's efforts and
interests in gender topics through active projects. In this paper, we report on
a preponderance of projects focusing on specific gender topics and identify
those with a narrow focus. We examine projects focusing on gender bias and how
they address this non-inclusive behaviour. Results show a propensity of GitHub
projects focusing on recognising and detecting an individual's gender and a
dearth of projects concentrating on the cultural expectations placed on women
and men. In the gender bias domain, the projects mainly focus on occupational
biases. These findings raise opportunities to address the limited focus of
GitHub on gender-related topics through developing projects that mitigate
exclusive behaviours.


  A quantum critical point (QCP) arises at a continuous transition between
competing phases at zero temperature. Collective excitations at magnetic QCPs
give rise to metallic properties that strongly deviate from the expectations of
Landau's Fermi liquid description, the standard theory of electron correlations
in metals. Central to this theory is the notion of quasiparticles, electronic
excitations which possess the quantum numbers of the bare electrons. Here we
report measurements of thermal and electrical transport across the
field-induced magnetic QCP in the heavy-fermion compound YbRh$_2$Si$_2$. We
show that the ratio of the thermal to electrical conductivities at the
zero-temperature limit obeys the Wiedemann-Franz (WF) law above the critical
field, $B_c$. This is also expected at $B < B_c$, where weak antiferromagnetic
order and a Fermi liquid phase form below 0.07 K ($B = 0$). However, at the
critical field the low-temperature electrical conductivity suggests a
non-Fermi-liquid ground state and exceeds the thermal conductivity by about
10%. This apparent violation of the WF law provides evidence for an
unconventional type of QCP at which the fundamental concept of Landau
quasiparticles breaks down. These results imply that Landau quasiparticles
break up, and that the origin of this disintegration is inelastic scattering
associated with electronic quantum critical fluctuations. Our finding brings
new insights into understanding deviations from Fermi-liquid behaviour
frequently observed in various classes of correlated materials.


  Using the quasiclassical concept of Berry curvature we demonstrate that a
Dirac exciton - a pair of Dirac quasiparticles bound by Coulomb interactions -
inevitably possesses an intrinsic angular momentum making the exciton
effectively self-rotating. The model is applied to excitons in two-dimensional
transition metal dichalcogenides, in which the charge carriers are known to be
described by a Dirac-like Hamiltonian. We show that the topological
self-rotation strongly modifies the exciton spectrum and, as a consequence,
resolves the puzzle of the overestimated two-dimensional polarizability
employed to fit earlier spectroscopic measurements.


  The dependence of intermittent inertial properties on ultraviolet eddy
viscosity closures is examined within the framework of shell-models of
turbulent flows. Inertial intermittent exponents turn out to be fairly
independent on the way energy is dissipated at small scales.


  The HEGRA Cherenkov telescope array group recently reported a steady and
extended unidentified TeV gamma-ray source lying at the outskirts of Cygnus
OB2. This is the most massive stellar association known in the Galaxy,
estimated to contain ~2600 OB type members alone. It has been previously argued
that the large scale shocks and turbulence induced by the multiple interacting
supersonic winds from the many young stars in such associations may play a role
in accelerating Galactic cosmic rays. Indeed, Cyg OB2 also coincides with the
non-variable MeV-GeV range unidentified EGRET source, 3EG 2033+4118. We report
on the near-simultaneous follow-up observations of the extended TeV source
region with the CHANDRA X-ray Observatory and the Very Large Array (VLA) radio
telescope obtained in order to explore this possibility. Analysis of the CO,
HI, and IRAS 100 micron emissions shows that the TeV source region coincides
with an outlying sub-group of powerful OB stars which have evacuated or
destroyed much of the ambient atomic, molecular and dust material, and which
may be related to the very high-energy emissions. An interesting SNR-like
structure is also revealed near the TeV source region in the CO, HI and radio
emission maps. Applying a numerical simulation which accurately tracks the
radio to gamma-ray emission from primary hadrons as well as primary and
secondary e+/-, we find that the broadband spectrum of the TeV source region
favors a predominantly nucleonic - rather than electronic - origin of the
high-energy flux, though deeper X-ray and radio observations are needed to
confirm this. A very reasonable, ~0.1%, conversion efficiency of Cyg OB2's
extreme stellar wind mechanical luminosity to nucleonic acceleration to ~PeV
(10^15 eV) energies is sufficient to explain the multifrequency emissions.


  The microstructural evolution throughout the first order tetragonal to
orthorhombic structural transition is analyzed by powder diffraction analysis
for two different systems belonging to the class of compounds referred to as
1111 oxy-pnictides: (La1-yYy)FeAsO and SmFeAs(O1-xFx). Both systems are
characterized by a similar behaviour: on cooling microstrain along the
tetragonal hh0 direction takes place and increases as the temperature is
decreased. Just above the structural transition microstrain reaches its maximum
value and then is abruptly suppressed by symmetry breaking. No volume
discontinuity throughout the first order transition is observed and a
groupsubgroup relationship holds between the tetragonal and the orthorhombic
structures, thus suggesting that orbital ordering drives symmetry breaking.
Microstrain reflects a distribution of lattice parameters in the tetragonal
phase and explains the occurrence of anisotropic properties commonly attributed
to nematic correlations; in this scenario the nematic behaviour is induced by
the tendency towards ordering of Fe orbitals.


  Recent work by Cohen \emph{et al.} has achieved state-of-the-art results for
learning spherical images in a rotation invariant way by using ideas from group
representation theory and noncommutative harmonic analysis. In this paper we
propose a generalization of this work that generally exhibits improved
performace, but from an implementation point of view is actually simpler. An
unusual feature of the proposed architecture is that it uses the
Clebsch--Gordan transform as its only source of nonlinearity, thus avoiding
repeated forward and backward Fourier transforms. The underlying ideas of the
paper generalize to constructing neural networks that are invariant to the
action of other compact groups.


  We investigate dense coding by imposing various locality restrictions to our
decoder by employing the resource theory of asymmetry framework. In this task,
the sender Alice and the receiver Bob share an entangled state. She encodes the
classical information into it using a symmetric preserving encoder and sends
the encoded state to Bob through a noiseless quantum channel. The decoder is
limited to a measurement to satisfy a certain locality condition on the
bipartite system composed of the receiving system and the preshared
entanglement half. Our contributions are summarized as follows: First, we
derive an achievable transmission rate for this task dependently of conditions
of encoder and decoder. Surprisingly, we show that the obtained rate cannot be
improved even when the decoder is relaxed to local measurements, two-way LOCCs,
separable measurements, or partial transpose positive (PPT) measurements for
the bipartite system. Moreover, depending on the class of allowed measurements
with a locality condition, we relax the class of encoding operations to
super-quantum encoders in the framework of general probability theory (GPT).
That is, when our decoder is restricted to a separable measurement,
theoretically, a positive operation is allowed as an encoding operation.
Surprisingly, even under this type of super-quantum relaxation, the
transmission rate cannot be improved. This fact highlights the universal
validity of our analysis beyond quantum theory.


  A subminiature mesoscopic cell, consisting of an asymmetric double quantum
dot capacitively coupled to a nearby mesoscopic circuit, is proposed, which can
transform disordered noise energy to ordered electric energy. Two schemes, the
noise originating from the nearby mesoscopic circuit and from the
electromagnetic wave disturbance in external environment, are investigated. We
found that the proposed cell can manifest as a good constant current source and
the output current may not reach its largest value even if the circuit is
shorted.


  A quantum version of data centers might be significant in the quantum era. In
this paper, we introduce Quantum Data Center (QDC), a quantum version of
existing classical data centers, with a specific emphasis on combining Quantum
Random Access Memory (QRAM) and quantum networks. We argue that QDC will
provide significant benefits to customers in terms of efficiency, security, and
precision, and will be helpful for quantum computing, communication, and
sensing. We investigate potential scientific and business opportunities along
this novel research direction through hardware realization and possible
specific applications. We show the possible impacts of QDCs in business and
science, especially the machine learning and big data industries.


  In this paper a possibility of the accelerated expansion of the large scale
universe with a varying polytropic fluid of a certain type is presented. About
a special role of non-gravitational interactions between dark energy and dark
matter, in particular, about a possibility of improvement and solution of
problems arising in modern cosmology, has been discussed for a long time. This
motivates us to consider new models, where non-gravitational interactions
between varying polytropic fluid and cold dark matter are allowed. Mainly
non-linear interactions of a specific type is considered, found in recent
literature. In order to understand the behavior of suggested cosmological
models, besides cosmographic analysis, $Om$ analysis is applied. Moreover, with
different datasets, including a strong gravitational lensing dataset, the
observational constraints on the model parameters are obtained using $\chi^{2}$
analysis.


  This paper presents a RKHS, in general, of vector-valued functions intended
to be used as hypothesis space for multi-task classification. It extends
similar hypothesis spaces that have previously considered in the literature.
Assuming this space, an improved Empirical Rademacher Complexity-based
generalization bound is derived. The analysis is itself extended to an MKL
setting. The connection between the proposed hypothesis space and a Group-Lasso
type regularizer is discussed. Finally, experimental results, with some
SVM-based Multi-Task Learning problems, underline the quality of the derived
bounds and validate the paper's analysis.


  Atomically thin one dimensional (1D) van der Waals wires of transition metal
monochalocogenides (TMMs) have been anticipated as promising building blocks
for integrated nanoelectronics. While reliable production of TMM nanowires has
eluded scientists over the past few decades, we finally demonstrated a bottom
up fabrication of MoTe nanowires inside carbon nanotubes (CNTs). Still, the
current synthesis method is based on vacuum annealing of reactive MoTe2, and
limits access to a variety of TMMs. Here we report an expanded framework for
high yield synthesis of the 1D tellurides including WTe, an unprecedented
family of TMMs. Experimental and theoretical analyses revealed that the choice
of suitable metal oxides as a precursor provides useful yield for their
characterization. These TMM nanowires exhibit a significant optical absorption
in the visible light region. More important, electronic properties of CNTs can
be tuned by encapsulating different TMM nanowires.


  The pseudo--rigid body represents an example of a constrained system with a
nonunimodular gauge group. This system is treated along the guidelines of an
algebraic constraint quantization scheme which focusses on observable
quantities, translating the vanishing of the constraints into representation
conditions on the algebra of observables. The constraint which is responsible
for the nonunimodularity of the gauge group is shown not to contribute to the
observable content of the constraints, i.e., not to impose any restrictions on
the construction of the quantum theory of the system. The application of the
algebraic constraint quantization scheme yields a unique quantization of the
physical degrees of freedom, which are shown to form a realization of the
so-called CM(N) model of collective motions.


  Regulators all around the world have started identifying the portions of the
spectrum that will be used for the next generation of cellular networks. A band
in the mmWave spectrum will be exploited to increase the available capacity. In
response to the very high expected traffic demand, a sharing mechanism may make
it possible to use the spectrum more efficiently. In this work, moving within
the European and Italian regulatory conditions, we propose the use of Licensed
Spectrum Access (LSA) to coordinate sharing among cellular operators.
Additionally, we show some preliminary results on our research activities which
are focused on a dynamic spectrum sharing approach applied in simulated 5G
cellular scenarios.


  We use the illness-death model (IDM) for chronic conditions to derive a new
analytical relation between the transition rates between the states of the IDM.
The transition rates are the incidence rate (i) and the mortality rates of
people without disease (m0) and with disease (m1). For the most generic case,
the rates depend on age, calendar time and in case of m1 also on the duration
of the disease. In this work, we show that the prevalence-odds can be expressed
as a convolution-like product of the incidence rate and an exponentiated linear
combination of i, m0 and m1. The analytical expression can be used as the basis
for a maximum likelihood estimation (MLE) and associated large sample
asymptotics. In a simulation study where a cross-sectional trial about a
chronic condition is mimicked, we estimate the duration dependency of the
mortality rate m1 based on aggregated current status data using the ML
estimator. For this, the number of study participants and the number of
diseased people in eleven age groups are considered. The ML estimator provides
reasonable estimates for the parameters including their large sample confidence
bounds.


  Unconstrained partial-wave amplitudes obtained at discrete energies from fits
to complete sets of eight independent observables which are required to
uniquely reconstruct reaction amplitudes do not vary smoothly with energy, and
are in principle non-unique. We demonstrate how this behavior can be ascribed
to the continuum ambiguity. Starting from the spinless scattering case, we
demonstrate how an unknown overall phase depending on energy and angle mixes
the structures seen in the associated partial-wave amplitudes making the
partial wave decomposition non-unique, and illustrate it on a simple toy model.
We then apply these principles to pseudo-scalar meson photoproduction and show
that the non-uniqueness effect can be removed through a phase rotation
generating "up-to-a-phase" unique set of SE partial wave amplitudes. Extracting
pole positions from partial wave amplitudes is the next step. Up to now, there
was no reliable way to extract pole parameters from SE partial waves, but a new
and simple single-channel method (Laurent + Pietarinen expansion) applicable
for continuous and discrete data has been recently developed. It is based on
applying the Laurent decomposition of partial wave amplitude, and expanding the
nonresonant background into a power series of a conformal-mapping, quickly
converging power series obtaining the simplest analytic function with
well-defined partial wave analytic properties which fits the input. The
generalization of this method to multi- channel case is also developed and
presented. Unifying both methods in succession, one constructs a model
independent procedure to extract pole parameters directly from experimental
data without referring to any theoretical model.


  With the Australian Square Kilometre Array Pathfinder (ASKAP) we monitored
the black hole candidate X-ray binary MAXI J1535--571 over seven epochs from 21
September to 2 October 2017. Using ASKAP observations, we studied the HI
absorption spectrum from gas clouds along the line-of-sight and thereby
constrained the distance to the source. The maximum negative radial velocities
measured from the HI absorption spectra for MAXI J1535--571 and an
extragalactic source in the same field of view are $-69\pm4$ km s$^{-1}$ and
$-89\pm4$ km s$^{-1}$, respectively. This rules out the far kinematic distance
($9.3^{+0.5}_{-0.6}$ kpc), giving a most likely distance of $4.1^{+0.6}_{-0.5}$
kpc, with a strong upper limit of the tangent point at $6.7^{+0.1}_{-0.2}$ kpc.
At our preferred distance, the peak unabsorbed luminosity of MAXI J1535--571
was $>78$ per cent of the Eddington luminosity, and shows that the soft-to-hard
spectral state transition occurred at the very low luminosity of 1.2 -- 3.4
$\times$ 10$^{-5}$ times the Eddington luminosity. Finally, this study
highlights the capabilities of new wide-field radio telescopes to probe
Galactic transient outbursts, by allowing us to observe both a target source
and a background comparison source in a single telescope pointing.


  We study an exactly marginal deformation of N=4 SUSY Yang-Mills with gauge
group U(N) using field theory and string theory methods. The classical theory
has a Higgs branch for rational values of the deformation parameter. We argue
that the quantum theory also has an S-dual confining branch which cannot be
seen classically. The low-energy effective theory on these branches is a
six-dimensional non-commutative gauge theory with sixteen supercharges.
Confinement of magnetic and electric charges, on the Higgs and confining
branches respectively, occurs due to the formation of BPS-saturated strings in
the low energy theory. The results also suggest a new way of deconstructing
Little String Theory as a large-N limit of a confining gauge theory in four
dimensions.


  Topological quantum phases of matter have been a topic of intense interest in
contemporary condensed matter physics. Extensive efforts are devoted to
investigate various exotic properties of topological matters including
topological insulators, topological superconductors, and topological
semimetals. For topological insulators, the dissipationless transport via
gapless helical edge or surface states is supposed to play a defining role,
which unfortunately has proved difficult to realize in experiments due to
inevitable backscattering induced in the sample boundary. Motivated by the
fundamental connection between topological invariants and the Zak phase, here,
we show that the non-trivial band topologies of both two and three-dimensional
topological insulators, characterized by the Chern numbers and the
$\mathbb{Z}_2$ invariants, respectively, are directly manifested in the winding
numbers of the Wannier-Stark ladder (WSL) emerging under an electric field. We
use the Floquet Green's function formalism to show that the winding number of
the WSL is robust against interband interference as well as non-magnetic
impurity scattering.


  A graphical model is a structured representation of the data generating
process. The traditional method to reason over random variables is to perform
inference in this graphical model. However, in many cases the generating
process is only a poor approximation of the much more complex true data
generating process, leading to suboptimal estimation. The subtleties of the
generative process are however captured in the data itself and we can `learn to
infer', that is, learn a direct mapping from observations to explanatory latent
variables. In this work we propose a hybrid model that combines graphical
inference with a learned inverse model, which we structure as in a graph neural
network, while the iterative algorithm as a whole is formulated as a recurrent
neural network. By using cross-validation we can automatically balance the
amount of work performed by graphical inference versus learned inference. We
apply our ideas to the Kalman filter, a Gaussian hidden Markov model for time
sequences, and show, among other things, that our model can estimate the
trajectory of a noisy chaotic Lorenz Attractor much more accurately than either
the learned or graphical inference run in isolation.


  We prove an effective version of a result obtained recently by Kleinbock and
Weiss on equidistribution of expanding translates of orbits of horospherical
subgroups in the space of lattices.


  In this work, we consider the effects of the Lorentz-violating (LV) term $
v_{\mu}\bar{\psi}\gamma ^{\mu}\psi $ belonging to the fermion sector of the
extended standard model on the dynamics of a quantum two-level system. We
examine how its non-relativistic counterpart, ${(\mathbf{p}-e \mathbf{A})\cdot
}\mathbf{v}/{m_{e},}$ affects the Rabi oscillations of a two-level atom coupled
with a quantum cavity electromagnetic field. Taking an initial coherent field
state in a resonant cavity, it was found that the LV background increases the
Rabi frequency and the time interval between collapses and revivals of the
population inversion function. It was found that initial field states with low
mean number of photons are better probes in order to establish more stringent
upper bounds on the background magnitude. In particular, for an initial vacuum
state in the cavity the upper limit $\text{v}_{x}<10^{-10}eV$ was attained.


  Light curves for more than century optical photometric observations of the
blazar OJ 287 reveals strong flares with a quasi-period of about 12 years. For
a long time, this period has been interpreted by processes in a binary black
hole system. We propose an alternative explanation for this period, which is
based on Doppler factor periodic variations of the emitting region caused by
jet helicity. Using multi-epoch very large baseline interferometry (VLBI)
observations carried out in a framework of the MOJAVE (Monitoring Of Jets in
Active galactic nuclei with VLBA Experiments) program and other VLBA (Very Long
Baseline Array) archival experiments at the observing frequency of 15 GHz, we
derived geometrical parameters of the jet helix. To reach an agreement between
the VLBI and photometric optical observation data, the jet component motion at
a small angle to the radial direction is necessary. Such non-radial motion is
observed and, together with the jet helical shape, can be naturally explained
by the development of the Kelvin-Helmholtz instability in the parsec-scale
outflow. In this case, the true precession of the OJ 287 jet may manifest
itself in differences between the peak flux values of the 12-year optical
flares. A possibility to create this precession due to Lense-Thirring effect of
a single supermassive black hole is also discussed.


  Thickness corrections to static, axisymmetric Dirac-Nambu-Goto branes
embedded into spherically symmetric black hole spacetimes with arbitrary number
of dimensions are studied. First, by applying a perturbative approximation, it
is found that the thick solutions deviate significantly in their analytic
properties from the thin ones near the axis of the system, and perturbative
approaches around the thin configurations can not provide regular thick
solutions above a certain dimension. For the general case, a non-perturbative,
numerical approach is applied and regular solutions are obtained for arbitrary
brane and bulk dimensions. As a special case, it has been found that
2-dimensional branes are exceptional, as they share their analytic properties
with the thin branes rather than the thick solutions of all other dimensions.


  In this note, we provide some sufficient and necessary conditions for the
core inverse of the perturbed operator to have the simplest possible
expression. The results improve the recent work by H. Ma (Optimal perturbation
bounds for the core inverse, Appl. Math. Comput. 336 (2018) 176-181.).


  In pure-exploration problems, information is gathered sequentially to answer
a question on the stochastic environment. While best-arm identification for
linear bandits has been extensively studied in recent years, few works have
been dedicated to identifying one arm that is $\varepsilon$-close to the best
one (and not exactly the best one). In this problem with several correct
answers, an identification algorithm should focus on one candidate among those
answers and verify that it is correct. We demonstrate that picking the answer
with highest mean does not allow an algorithm to reach asymptotic optimality in
terms of expected sample complexity. Instead, a \textit{furthest answer} should
be identified. Using that insight to choose the candidate answer carefully, we
develop a simple procedure to adapt best-arm identification algorithms to
tackle $\varepsilon$-best-answer identification in transductive linear
stochastic bandits. Finally, we propose an asymptotically optimal algorithm for
this setting, which is shown to achieve competitive empirical performance
against existing modified best-arm identification algorithms.


  We discuss generalized global symmetries and their breaking. We extend
Goldstone's theorem to higher form symmetries by showing that a perimeter law
for an extended $p$-dimensional defect operator charged under a continuous
$p$-form generalized global symmetry necessarily results in a gapless mode in
the spectrum. We also show that a $p$-form symmetry in a conformal theory in
$2(p+1)$ dimensions has a free realization. In four dimensions this means any
1-form symmetry in a $CFT_4$ can be realized by free Maxwell electrodynamics,
i.e. the current can be photonized. The photonized theory has infinitely many
conserved 0-form charges that are constructed by integrating the symmetry
currents against suitable 1-forms. We study these charges by developing a
twistor-based formalism that is a 4d analogue of the usual holomorphic complex
analysis familiar in $CFT_2$. The charges are shown to obey an algebra with
central extension, which is an analogue of the 2d Abelian Kac-Moody algebra for
higher form symmetries.


  The use of spectral projection based methods for simulation of a stochastic
system with discontinuous solution exhibits the Gibbs phenomenon, which is
characterized by oscillations near discontinuities. This paper investigates a
dynamic bi-orthogonality based approach with appropriate post-processing for
mitigating the effects of the Gibbs phenomenon. The proposed approach uses
spectral decomposition of the spatial and stochastic fields in appropriate
orthogonal bases, while the dynamic orthogonality condition is used to derive
the resultant closed form evolution equations. The orthogonal decomposition of
the spatial field is exploited to propose a Gegenbauer reprojection based
post-processing approach, where the orthogonal bases in spatial dimension are
reprojected on the Gegenbauer polynomials in the domain of analyticity. The
resultant spectral expansion in Gegenbauer series is shown to mitigate the
Gibbs phenomenon. Efficacy of the proposed method is demonstrated for
simulation of a one-dimensional stochastic Burgers equation with uncertain
initial condition.


  With the use of object-oriented languages for HEP, many experiments have
designed their data objects to contain direct references to other objects in
the event (e.g., tracks and electromagnetic showers have references to each
other to denote matches). Unfortunately this creates tremendous dependencies
between packages which lead to brittle development systems (e.g., if the
electromagnetic code has a problem you may not be able to compile the tracking
code) and makes the storage system more complex.
  We discuss how the CLEO III experiment avoided these problems by treating an
event as an object-relational database. The discussion will include: the
constraints we placed on our objects; our use of a separate Association class
to deal with inter-object references; and our ability to use multiple sources
to supply different data items for one event.


  We give a method of constructing self-orthogonal codes from equitable
partitions of association schemes. By applying this method we construct
self-orthogonal codes from some distance-regular graphs. Some of the obtained
codes are optimal. Further, we introduce a notion of self-orthogonal subspace
codes. We show that under some conditions equitable partitions of association
schemes yield such self-orthogonal subspace codes and we give some examples
from distance-regular graphs.


  Many Big Data applications include the processing of data streams on
semi-structured data formats such as JSON. A disadvantage of such formats is
that an application may spend a significant amount of processing time just on
unselectively parsing all data. To relax this issue, the concept of raw
filtering is proposed with the idea to remove data from a stream prior to the
costly parsing stage. However, as accurate filtering of raw data is often only
possible after the data has been parsed, raw filters are designed to be
approximate in the sense of allowing false-positives in order to be implemented
efficiently.
  Contrary to previously proposed CPU-based raw filtering techniques that are
restricted to string matching, we present FPGA-based primitives for filtering
strings, numbers and also number ranges. In addition, a primitive respecting
the basic structure of JSON data is proposed that can be used to further
increase the accuracy of introduced raw filters.
  The proposed raw filter primitives are designed to allow for their
composition according to a given filter expression of a query. Thus, complex
raw filters can be created for FPGAs which enable a drastical decrease in the
amount of generated false-positives, particularly for IoT workload.
  As there exists a trade-off between accuracy and resource consumption, we
evaluate primitives as well as composed raw filters using different queries
from the RiotBench benchmark. Our results show that up to 94.3% of the raw data
can be filtered without producing any observed false-positives using only a few
hundred LUTs.


  Linear Logic was introduced by Girard as a resource-sensitive refinement of
classical logic. It turned out that full propositional Linear Logic is
undecidable (Lincoln, Mitchell, Scedrov, and Shankar) and, hence, it is more
expressive than (modalized) classical or intuitionistic logic. In this paper we
focus on the study of the simplest fragments of Linear Logic, such as the
one-literal and constant-only fragments (the latter contains no literals at
all). Here we demonstrate that all these extremely simple fragments of Linear
Logic (one-literal, $\bot$-only, and even unit-only) are exactly of the same
expressive power as the corresponding full versions. We present also a complete
computational interpretation (in terms of acyclic programs with stack) for
bottom-free Intuitionistic Linear Logic. Based on this interpretation, we prove
the fairness of our encodings and establish the foregoing complexity results.


  Exact summatory functions that count the number of prime $k$-tuples up to
some cut-off integer are presented. Related summatory $k$-tuple analogs of the
first and second Chebyshev functions are then defined. Using a gamma
distribution hypothesis for prime powers, associated average summatory
functions are conjectured. With exact and average summatory functions in hand,
pertinent $k$-tuple zeta functions can be identified, and Perron's formula
allows the formulation of $k$-tuple analogs of explicit formulae. The $k$-tuple
zeta functions are then used to make some inferences about $k$-tuple primes.


  We study the Induced $H$ Partition problem from the parameterized complexity
point of view. In the Induced $H$ Partition problem the task is to partition
vertices of a graph $G$ into sets $V_1,V_2,\dots,V_n$ such that the graph $H$
is isomorphic to the subgraph of $G$ induced by each set $V_i$ for $i =
1,2,\dots,n.$ The pattern graph $H$ is fixed.
  For the parametrization we consider three distinct structural parameters of
the graph $G$ - namely the tree-width, the neighborhood diversity, and the
modular-width. For the parametrization by the neighborhood diversity we obtain
an FPT algorithm for every graph $H.$ For the parametrization by the tree-width
we obtain an FPT algorithm for every connected graph $H.$ Finally, for the
parametrization by the modular-width we derive an FPT algorithm for every prime
graph $H.$


  Cross-modality medical image synthesis is a critical topic and has the
potential to facilitate numerous applications in the medical imaging field.
Despite recent successes in deep-learning-based generative models, most current
medical image synthesis methods rely on generative adversarial networks and
suffer from notorious mode collapse and unstable training. Moreover, the 2D
backbone-driven approaches would easily result in volumetric inconsistency,
while 3D backbones are challenging and impractical due to the tremendous memory
cost and training difficulty. In this paper, we introduce a new paradigm for
volumetric medical data synthesis by leveraging 2D backbones and present a
diffusion-based framework, Make-A-Volume, for cross-modality 3D medical image
synthesis. To learn the cross-modality slice-wise mapping, we employ a latent
diffusion model and learn a low-dimensional latent space, resulting in high
computational efficiency. To enable the 3D image synthesis and mitigate
volumetric inconsistency, we further insert a series of volumetric layers in
the 2D slice-mapping model and fine-tune them with paired 3D data. This
paradigm extends the 2D image diffusion model to a volumetric version with a
slightly increasing number of parameters and computation, offering a principled
solution for generic cross-modality 3D medical image synthesis. We showcase the
effectiveness of our Make-A-Volume framework on an in-house SWI-MRA brain MRI
dataset and a public T1-T2 brain MRI dataset. Experimental results demonstrate
that our framework achieves superior synthesis results with volumetric
consistency.


  Although pre-trained contextualized language models such as BERT achieve
significant performance on various downstream tasks, current language
representation still only focuses on linguistic objective at a specific
granularity, which may not applicable when multiple levels of linguistic units
are involved at the same time. Thus this work introduces and explores the
universal representation learning, i.e., embeddings of different levels of
linguistic unit in a uniform vector space. We present a universal
representation model, BURT (BERT-inspired Universal Representation from
learning meaningful segmenT), to encode different levels of linguistic unit
into the same vector space. Specifically, we extract and mask meaningful
segments based on point-wise mutual information (PMI) to incorporate different
granular objectives into the pre-training stage. We conduct experiments on
datasets for English and Chinese including the GLUE and CLUE benchmarks, where
our model surpasses its baselines and alternatives on a wide range of
downstream tasks. We present our approach of constructing analogy datasets in
terms of words, phrases and sentences and experiment with multiple
representation models to examine geometric properties of the learned vector
space through a task-independent evaluation. Finally, we verify the
effectiveness of our unified pre-training strategy in two real-world text
matching scenarios. As a result, our model significantly outperforms existing
information retrieval (IR) methods and yields universal representations that
can be directly applied to retrieval-based question-answering and natural
language generation tasks.


  We find equations of particle motion from the point of view of observer on a
rotating disk, and demonstrate that a particle moving along a rotating disk is
influenced by forces arising from geometry. They can be considered as analogs
of the centrifugal forces and the Coriolis forces.


  Almost all the WiFi networks today provide single band (either 2.4 GHz or 5.8
GHz) wireless communication functionality for connected mobile nodes. In a
single band network, the interference depends on number of nodes in the network
and the presence of other networks in the proximity. As the number of nodes in
a Network increases, the interference in the network also increases which
reduces the throughput of the network. If there are two single band networks,
one operating in 2.4 GHz frequency band and other in 5.8 GHz frequency band,
then nodes in network 1 will not cause any interference with nodes in network
2. This can be used as a basic idea to implement a network where the nodes in
the same network use both the frequency bands to minimize the interference
between nodes. We show that building dual band multi-hop network gives better
performance in terms of throughput compared to that of a network with single
frequency band.


  Recently, a diffusion Monte Carlo algorithm was applied to the study of spin
dependent interactions in condensed matter. Following some of the ideas
presented therein, and applied to a Hamiltonian containing a Rashba-like
interaction, a general variational Monte Carlo approach is here introduced that
treats in an efficient and very accurate way the spin degrees of freedom in
atoms when spin orbit effects are included in the Hamiltonian describing the
electronic structure. We illustrate the algorithm on the evaluation of the
spin-orbit splittings of isolated carbon and lead atoms. In the case of the
carbon atom, we investigate the differences between the inclusion of spin-orbit
in its realistic and effective spherically symmetrized forms. The method
exhibits a very good accuracy in describing the small energy splittings,
opening the way for a systematic quantum Monte Carlo studies of spin-orbit
effects in atomic systems.


  Energy disaggregation determines the energy consumption of individual
appliances from the total demand signal, which is recorded using a single
monitoring device. There are varied approaches to this problem, which are
applied to different settings. Here, we focus on small and medium enterprises
(SMEs) and explore useful applications for energy disaggregation from the
perspective of SMEs. More precisely, we use recurrence quantification analysis
(RQA) of the aggregate and the individual device signals to create a
two-dimensional map, which is an outlined region in a reduced information space
that corresponds to 'normal' energy demand. Then, this map is used to monitor
and control future energy consumption within the example business so to improve
their energy efficiency practices. In particular, our proposed method is shown
to detect when an appliance may be faulty and if an unexpected, additional
device is in use.


  The distortions in the thermal energy spectra for neutrinos produced in a
supernova when a resonant oscillation, MSW effect, occurs are determined. In
order to show this effect for some relevant and representative examples of
unified gauge models, we have chosen $SO(10)$, and $SU(5)_{SUSY}$,
$SO(10)_{SUSY}$ with a particular scheme for fermion masses (DHR model). The
analysis has been performed for two choices of neutrinos parameters, predicted
by the above models, and capable to explain the solar neutrino problem. In both
cases one observes a strong distortion in the electron neutrino energy
spectrum. This effect, computed for a wide range of $SO(10)_{SUSY}$ models has
produced the same results of the previous supersymmetric ones.


  We present a numerical model allowing to determine the electron and lattice
temperature dynamics in a gold nanoparticle under subpicosecond pulsed
excitation, as well as that of the surrounding medium. For this, we have used
the electron-phonon coupling equation in the particle with a source term linked
with the laser pulse, and the ballistic-diffusive equations for heat conduction
in the host medium. Our results show that the heat transfer rate from the
particle to the matrix is significantly smaller than the prediction of
Fourier's law. Consequently, the particle temperature rise is much larger and
its cooling dynamics is much slower than that obtained using Fourier's law,
which is attributed to the nonlocal and nonequilibrium heat conduction in the
vicinity of the nanoparticle. These results are expected to be of great
importance for interpreting pump-probe experiments performed on single
nanoparticles or nanocomposite media.


  Distinguishing between cause and effect using time series observational data
is a major challenge in many scientific fields. A new perspective has been
provided based on the principle of Independence of Causal Mechanisms (ICM),
leading to the Spectral Independence Criterion (SIC), postulating that the
power spectral density (PSD) of the cause time series is uncorrelated with the
squared modulus of the frequency response of the filter generating the effect.
Since SIC rests on methods and assumptions in stark contrast with most causal
discovery methods for time series, it raises questions regarding what
theoretical grounds justify its use. In this paper, we provide answers covering
several key aspects. After providing an information theoretic interpretation of
SIC, we present an identifiability result that sheds light on the context for
which this approach is expected to perform well. We further demonstrate the
robustness of SIC to downsampling - an obstacle that can spoil Granger-based
inference. Finally, an invariance perspective allows to explore the limitations
of the spectral independence assumption and how to generalize it. Overall,
these results support the postulate of Spectral Independence is a well grounded
leading principle for causal inference based on empirical time series.


  Assessing the aesthetics of an image is challenging, as it is influenced by
multiple factors including composition, color, style, and high-level semantics.
Existing image aesthetic assessment (IAA) methods primarily rely on
human-labeled rating scores, which oversimplify the visual aesthetic
information that humans perceive. Conversely, user comments offer more
comprehensive information and are a more natural way to express human opinions
and preferences regarding image aesthetics. In light of this, we propose
learning image aesthetics from user comments, and exploring vision-language
pretraining methods to learn multimodal aesthetic representations.
Specifically, we pretrain an image-text encoder-decoder model with
image-comment pairs, using contrastive and generative objectives to learn rich
and generic aesthetic semantics without human labels. To efficiently adapt the
pretrained model for downstream IAA tasks, we further propose a lightweight
rank-based adapter that employs text as an anchor to learn the aesthetic
ranking concept. Our results show that our pretrained aesthetic vision-language
model outperforms prior works on image aesthetic captioning over the
AVA-Captions dataset, and it has powerful zero-shot capability for aesthetic
tasks such as zero-shot style classification and zero-shot IAA, surpassing many
supervised baselines. With only minimal finetuning parameters using the
proposed adapter module, our model achieves state-of-the-art IAA performance
over the AVA dataset.


  We determine the one-loop deformation of the conformal symmetry of a general
N}=2 superconformally invariant Yang-Mills theory. The deformation is computed
for several explicit examples which have a realization as world-volume theories
on a stack of D3 branes. These include (i) N=4 SYM with gauge groups SU(N),
USp(2N) and SO(N); (ii) USp(2N) gauge theory with one hypermultiplet in the
traceless antisymmetric representation and four hypermultiplets in the
fundamental; (iii) quiver gauge theory with gauge group SU(N)xSU(N) and two
hypermultiplets in the bifundamental representations (N,\bar N) and (bar N,N).
The existence of quantum corrections to the conformal transformations imposes
restrictions on the effective action which we study on a subset of the Coulomb
branch corresponding to the separation of one brane from the stack. In the N=4
case, the one-loop corrected transformations provide a realization of the
conformal algebra; this deformation is shown to be one-loop exact. For the
other two models, higher-loop corrections are necessary to close the algebra.
Requiring closure, we infer the two-loop conformal deformation.


  A common belief in high-dimensional data analysis is that data are
concentrated on a low-dimensional manifold. This motivates simultaneous
dimension reduction and regression on manifolds. We provide an algorithm for
learning gradients on manifolds for dimension reduction for high-dimensional
data with few observations. We obtain generalization error bounds for the
gradient estimates and show that the convergence rate depends on the intrinsic
dimension of the manifold and not on the dimension of the ambient space. We
illustrate the efficacy of this approach empirically on simulated and real data
and compare the method to other dimension reduction procedures.


  The promise of multimodal models for real-world applications has inspired
research in visualizing and understanding their internal mechanics with the end
goal of empowering stakeholders to visualize model behavior, perform model
debugging, and promote trust in machine learning models. However, modern
multimodal models are typically black-box neural networks, which makes it
challenging to understand their internal mechanics. How can we visualize the
internal modeling of multimodal interactions in these models? Our paper aims to
fill this gap by proposing MultiViz, a method for analyzing the behavior of
multimodal models by scaffolding the problem of interpretability into 4 stages:
(1) unimodal importance: how each modality contributes towards downstream
modeling and prediction, (2) cross-modal interactions: how different modalities
relate with each other, (3) multimodal representations: how unimodal and
cross-modal interactions are represented in decision-level features, and (4)
multimodal prediction: how decision-level features are composed to make a
prediction. MultiViz is designed to operate on diverse modalities, models,
tasks, and research areas. Through experiments on 8 trained models across 6
real-world tasks, we show that the complementary stages in MultiViz together
enable users to (1) simulate model predictions, (2) assign interpretable
concepts to features, (3) perform error analysis on model misclassifications,
and (4) use insights from error analysis to debug models. MultiViz is publicly
available, will be regularly updated with new interpretation tools and metrics,
and welcomes inputs from the community.


  Pair-instability supernovae (PISNe) are the ultimate cosmic lighthouses,
capable of being observed at z<25 and revealing the properties of primordial
stars at cosmic dawn. But it is now understood that the spectra and light
curves of these events evolved with redshift as the universe became polluted
with heavy elements because chemically enriched stars in this mass range
typically lose most of their hydrogen envelopes and explode as bare helium
cores. The light curves of such transients can be considerably dimmer in the
near infrared (NIR) today than those of primordial PISNe of equal energy and
progenitor mass. Here, we calculate detection rates for PISNe whose progenitors
lost their outer layers to either line-driven winds or rotation at z<10, their
detection limit in redshift for the James Webb Space Telescope (JWST). We find
that JWST may be able to detect only Pop II (metal-poor) PISNe over the
redshift range of z<4, but not their Pop III (metal-free) counterparts.


  Multilevel Monte Carlo can efficiently compute statistical estimates of
discretized random variables, for a given error tolerance. Traditionally, only
a certain statistic is computed from a particular implementation of multilevel
Monte Carlo. This paper considers the multilevel case when one wants to verify
and evaluate a single ensemble that forms an empirical approximation to many
different statistics, namely an ensemble forecast. We propose a simple
algorithm that, in the univariate case, allows one to derive a statistically
consistent single ensemble forecast from the hierarchy of ensembles that are
formed during an implementation of multilevel Monte Carlo. This ensemble
forecast then allows the entire multilevel hierarchy of ensembles to be
evaluated using standard ensemble forecast verification techniques. We
demonstrate the case of evaluating the calibration of the forecast in this
paper.


  Context: the space-borne missions CoRoT and Kepler have provided photometric
observations of unprecedented quality. The study of solar-like oscillations
observed in red giant stars by these satellites allows a better understanding
of the different physical processes occurring in their interiors. In
particular, the study of the mode excitation and damping is a promising way to
improve our understanding of stellar physics that has, so far, been performed
only on a limited number of targets. Aims: the recent asteroseismic
characterization of the evolutionary status for a large number of red giants
allows us to study the physical processes acting in the interior of red giants
and how they are modify during stellar evolution. In this work, we aim to
obtain information on the excitation and damping of pressure modes through the
measurement of the stars' pressure mode widths and amplitudes and to analyze
how they are modified with stellar evolution. The objective is to bring
observational constraints on the modeling of the physical processes behind mode
excitation and damping. Methods: we fit the frequency spectra of red giants
with well defined evolutionary status using Lorentzians functions to derive the
pressure mode widths and amplitudes. To strengthen our conclusions, we used two
different fitting techniques. Results: pressure mode widths and amplitudes were
determined for more than 5000 red giants. With a stellar sample two orders of
magnitude larger than previous results, we confirmed that the mode width
depends on stellar evolution and varies with stellar effective temperature. In
addition, we discovered that the mode width depends on stellar mass. We also
confirmed observationally the influence of the stellar metallicity on the mode
amplitudes, as predicted by models.


  We investigate the importance of choosing good tetrads for the study of the
field equations of $f(T)$ gravity. It is well known that this theory is not
invariant under local Lorentz transformations, and therefore the choice of
tetrad plays a crucial role in such models. Different tetrads will lead to
different field equations which in turn have different solutions. We suggest to
speak of a good tetrad if it imposes no restrictions on the form of $f(T)$.
Employing local rotations, we construct good tetrads in the context of
homogeneity and isotropy, and spherical symmetry, where we show how to find
Schwarzschild-de Sitter solutions in vacuum. Our principal approach should be
applicable to other symmetries as well.


  We have developed an improved scheme for loading atoms into a magneto-optical
trap (MOT) from a directed alkali metal dispenser in < 10^-10 torr ultra-high
vacuum conditions. A current-driven dispenser was surrounded with a cold
absorbing "shroud" held at < 0 C, pumping rubidium atoms not directed into the
MOT. This nearly eliminates background alkali atoms and reduces the detrimental
rise in pressure normally associated with these devices. The system can be
well-described as a current-controlled, rapidly-switched, two-temperature
thermal beam, and was used to load a MOT with 3 x 10^8 atoms.


  Two common objectives for evaluating a schedule are the makespan, or schedule
length, and the average completion time. This short note gives improved bounds
on the existence of schedules that simultaneously optimize both criteria. In
particular, for any rho> 0, there exists a schedule of makespan at most 1+rho
times the minimum, with average completion time at most (1-e)^rho times the
minimum. The proof uses an infininite-dimensional linear program to generalize
and strengthen a previous analysis by Cliff Stein and Joel Wein (1997).


  We present a theoretical description of dissociative recombination of
triatomic molecular ions having large permanent dipole moments. The study has
been partly motivated by a discrepancy between experimental and theoretical
cross-sections for dissociative recombination of the HCO$^+$ ion. The HCO$^{+}$
ion has a considerable permanent dipole moment ($D\approx$4 debye), which has
not been taken explicitly into account in previous theoretical studies. In the
present study, we include explicitly the effect of the permanent electric
dipole on the dynamics of the incident electron using the generalized quantum
defect theory, and we present the resulting cross section obtained. This is the
first application of generalized quantum defect theory to the dissociative
recombination of molecular ions.


  Gravitational wave (GW) detection has enabled us to test General Relativity
in an entirely new regime. A prominent role in tests of General Relativity
takes the detection of the Quasi-normal modes (QNMs) that arise as the highly
distorted remnant formed after the merger emits GWs until it becomes a regular
Kerr BH. According to the no-hair theorem, the frequencies and damping times of
these QNMs are determined solely by the mass and spin of the remnant BH.
Therefore, detecting the QNMs offers a unique way to probe the nature of the
remnant BH and to test General Relativity. We study the detection of a merging
binary black hole (BBH) in the intermediate mass range, where the
inspiral-merger phase is detected by space-based laser interferometer detectors
TianQin and LISA while the ringdown is detected by the ground-based atom
interferometer (AI) observatory AION. The analysis of the ringdown is done
using the regular broadband mode of AI detectors as well as using the resonant
mode where the detection band is optimized to the frequencies of the QNMs
predicted from the inspiral-merger phase. We find that using the regular
broadband mode allows constraining the parameters of the BBH with relative
errors of at most $10^{-6}$ from the ringdown while the frequencies and the
damping times of the QNMs can be determined with total errors below $0.2\,{\rm
Hz}$ and $115\,{\rm \mu s}$, respectively. Furthermore, we find that using the
resonant mode can improve the parameter estimation for the BBH from the
ringdown by up to one order of magnitude. Utilizing the resonant mode
significantly limits the detection of the frequency of the QNMs but improves
the detection error of the damping times by one to four orders of magnitude.


  In the last ten years, observational evidences about a possible connection
between Type Ia Supernovae (SNe) properties and the environment where they
explode have been steadily growing. In this paper I discuss, from a theoretical
point of view but with an observer's perspective, the usage of light echoes
(LEs) to probe the CSM around SNe of Type Ia since, in principle, they give us
a unique opportunity of getting a three-dimensional description of the SN
environment. In turn, this can be used to check the often suggested association
of some Ia's with dusty/star forming regions, which would point to a young
population for the progenitors. After giving a brief introduction to the LE
phenomenon in single scattering approximation, I derive analytical and
numerical solutions for the optical light and colour curves for a few simple
dust geometries. A fully 3D multiple scattering treatment has also been
implemented in a Monte Carlo code, which I have used to investigate the effects
of multiple scattering. In particular, I have explored in detail the LE colour
dependency from time and dust distribution, since this is a promising tool to
determine the dust density and derive the effective presence of multiple
scattering from the observed properties. Finally, again by means of Monte Carlo
simulations, I have studied the effects of multiple scattering on the LE linear
polarization, analyzing the dependencies from the dust parameters and geometry.
Both the analytical formalism and MC codes described in this paper can be used
for any LE for which the light curve of the central source is known.


  Synchronization occurs ubiquitously in nature. The van der Pol oscillator has
been a favorite model to investigate synchronization. Here we study the
oscillator in the deep quantum regime, where nonclassical effects dominate the
dynamics. Our results show: (i) squeezed driving loses its effect, (ii) noise
boosts synchronization, (iii) synchronization is bounded, and (iv) the
limit-cycle is insensitive to strong driving. We propose a synchronization
measure and analytically calculate it. These results reflect intrinsic
differences between synchronization in the quantum and deep quantum regimes.


  Stable dynamical systems are a flexible tool to plan robotic motions in
real-time. In the robotic literature, dynamical system motions are typically
planned without considering possible limitations in the robot's workspace. This
work presents a novel approach to learn workspace constraints from human
demonstrations and to generate motion trajectories for the robot that lie in
the constrained workspace. Training data are incrementally clustered into
different linear subspaces and used to fit a low dimensional representation of
each subspace. By considering the learned constraint subspaces as zeroing
barrier functions, we are able to design a control input that keeps the system
trajectory within the learned bounds. This control input is effectively
combined with the original system dynamics preserving eventual asymptotic
properties of the unconstrained system. Simulations and experiments on a real
robot show the effectiveness of the proposed approach.


  We study correlation functions in two-dimensional conformal field theory
coupled to induced gravity in the light-cone gauge. Focussing on the fermion
four-point function, we display an unexpected non-perturbative singularity
structure: coupling to gravity {\it qualitatively} changes the perturbative
$(x_1-x_2)^{-1}(x_3-x_4)^{-1}$ singularity into a logarithmic one plus a
non-singular piece. We argue that this is related to the appearence of new
logarithmic operators in the gravitationally dressed operator product
expansions. We also show some evidence that non-conformal but integrable models
may remain integrable when coupled to gravity.


  Whispering gallery modes (WGMs), circulating modes near the surface of a
spheroidal material, have been known to exhibit high quality factors for both
acoustic and electromagnetic waves. Here, we report an electro-optomechanical
system, where the overlapping WGMs of acoustic and optical waves along the
equator of a dielectric sphere strongly couple to each other. The
triple-resonance phase-matching condition provides a large enhancement of the
Brillouin scattering only in a single sideband, and conversion from the input
radio-frequency signal exciting the acoustic mode to the output optical signal
is observed.


  In the framework of the MOdified Newtonian Dynamics (MOND), the internal
dynamics of a gravitating system s embedded in a larger one S is affected by
the external background field E of S even if it is constant and uniform, thus
implying a violation of the Strong Equivalence Principle: it is the so-called
External Field Effect (EFE). In the case of the solar system, E would be
A_cen\approx 10^-10 m s^-2 because of its motion through the Milky Way: it is
orders of magnitude smaller than the main Newtonian monopole terms for the
planets. We address here the following questions in a purely phenomenological
manner: are the Sun's planets affected by an EFE as large as 10^-10 m s^-2? Can
it be assumed that its effect is negligible for them because of its relatively
small size? Does $\bds E$ induce vanishing net orbital effects because of its
constancy over typical solar system's planetary orbital periods? It turns out
that a constant and uniform acceleration, treated perturbatively, does induce
non-vanishing long-period orbital effects on the longitude of the pericenter of
a test particle. In the case of the inner planets of the solar system and with
E\approx 10^-10 m s^-2, they are 4-6 orders of magnitude larger than the
present-day upper bounds on the non-standard perihelion precessions recently
obtained with by E.V. Pitjeva with the EPM ephemerides in the Solar System
Barycentric frame. The upper limits on the components of E are E_x <= 1 x
10^-15 m s^-2, E_y <= 2 x 10^-16 m s^-2, E_z <= 3 x 10^-14 m s^-2. This result
is in agreement with the violation of the Strong Equivalence Principle by MOND.


  Devinatz, Nussbaum and von Neumann established some important results on the
strong commutativity of self-adjoint and normal unbounded operators. In this
paper, we prove results in the same spirit.


  We study which integers are admissible as Fourier coefficients of even
integer weight newforms. In the specific case of the tau-function, we show that
for all odd primes $\ell < 100$ and all integers $m \geq 1$, we have $$ \tau(n)
\neq \pm \ell, \pm 5^m. $$ For general newforms $f$ with even integer weight
$2k$ and integer coefficients, we prove for most integers $j$ dividing $2k-1$
and all ordinary primes $p$ that $a_f(p^2)$ is never a $j$-th power. We prove a
similar result for $a_f(p^4)$, conditional on the Frey-Mazur Conjecture. Our
primary method involves relating questions about values of newforms to the
existence of perfect powers in certain binary recurrence sequences, and makes
use of bounds from the theory of linear forms in logarithms. The method extends
without difficulty to a large family of Lebesgue-Nagell equations with fixed
exponent. To prove results about general newforms, we also make use of the
modular method and Ribet's level-lowering theorem.


  Type-preserving (or typed) compilation uses typing derivations to certify
correctness properties of compilation. We have designed and implemented a
type-preserving compiler for a simply-typed dialect of Prolog we call T-Prolog.
The crux of our approach is a new certifying abstract machine which we call the
Typed Warren Abstract Machine (TWAM). The TWAM has a dependent type system
strong enough to specify the semantics of a logic program in the logical
framework LF. We present a soundness metatheorem which constitutes a partial
correctness guarantee: well-typed programs implement the logic program
specified by their type. This metatheorem justifies our design and
implementation of a certifying compiler from T-Prolog to TWAM.


  These are the proceedings of the Second International Workshop on Eta Meson
Physics held in May 10-11, 2007, at the resort Peniscola in Spain. The workshop
was focused on topics regarding eta and eta' -meson production and decays
physics of common interest in the EU EtaMesonNet network.


  A clump moving through the intracluster medium of a galaxy cluster can drive
a bow shock trailed by a bullet-like core. In some cases, such as in the
prototypical Bullet cluster, X-rays show a gas bullet with a protruding head
and pronounced shoulders. We point out that these features, while difficult to
explain without dark matter (DM), naturally arise as the head of the
slowed-down gas is gravitationally pulled forward toward its unhindered DM
counterpart. X-ray imaging thus provides a unique, robust probe of the offset,
collisionless DM, even without gravitational lensing or other auxiliary data.
Numerical simulations and a toy model suggest that the effect is common in
major mergers, is often associated with a small bullet-head radius of
curvature, and may lead to distinct bullet morphologies, consistent with
observations.


  A variant of the classical knapsack problem is considered in which each item
is associated with an integer weight and a qualitative level. We define a
dominance relation over the feasible subsets of the given item set and show
that this relation defines a preorder. We propose a dynamic programming
algorithm to compute the entire set of non-dominated rank cardinality vectors
and we state two greedy algorithms, which efficiently compute a single
efficient solution.


  We have been able to compare with astrometric precision AstroDrizzle
processed images of NGC 6720 (the Ring Nebula) made using two cameras on the
Hubble Space Telescope. The time difference of the observations was 12.925 yrs.
This large time-base allowed determination of tangential velocities of features
within this classic planetary nebula. Individual features were measured in [N
II] images as were the dark knots seen in silhouette against background nebular
[O III] emission. An image magnification and matching technique was also used
to test the accuracy of the usual assumption of homologous expansion. We found
that homologous expansion does apply, but the rate of expansion is greater
along the major axis of the nebula, which is intrinsically larger than the
minor axis.
  We find that the dark knots expand more slowly that the nebular gas, that the
distance to the nebula is 720 pc +/-30%, and the dynamic age of the Ring Nebula
is about 4000 yrs. The dynamic age is in agreement with the position of the
central star on theoretical curves for stars collapsing from the peak of the
Asymptotic Giant Branch to being white dwarfs.


  Every cosmology lecturer these days is confronted with teaching the modern
cosmological standard model $\Lambda$CDM, and there are many approaches to do
this. However, the danger is imminent that it is presented to students as
something set into stone, merely to be accepted as a fact based on the plenty
of evidences we have. This is even more critical, given that the standard model
of cosmology confronts us with entities not yet fully understood, namely a
cosmological constant $\Lambda$ and cold dark matter. In this article, we
report on an advanced cosmology course exercise, conducted in computer lab,
which was conceived as a means to have students experience first-hand why the
$\Lambda$CDM model has become so prevalent in the interpretation of modern
cosmological data. To this end, we focused on the cosmic microwave background
radiation (CMB) and calculated theoretical temperature and matter power
spectra, using the modern Boltzmann code CLASS. By comparing and analyzing the
outcome for $\Lambda$CDM, as well as for three other exotic cosmological
models, the students were able to grasp the impact of cosmological parameters
on CMB observables, and also to understand some of the complicated CMB physics
in a direct way. Our chosen examples are not exhaustive and can be easily
modified or expanded, so we express the hope that this article will serve as a
valuable resource for interested students and lecturers.


  We discuss integral field spectra of the compact star-forming complex that is
the brightest near-infrared (NIR) source in the central regions of the
starburst galaxy NGC 253. The spectra cover the H and K passbands and were
recorded with the Gemini NIR Spectrograph during sub-arcsec seeing conditions.
Absorption features in the spectrum of the star-forming complex are weaker than
in the surroundings. An absorption feature is found near 1.78um that coincides
with the location of a C2 bandhead. Emission lines of Brgamma, [FeII], and
HeI2.06um do not track the NIR continuum light. Pockets of star-forming
activity that do not have associated concentrations of red supergiants, and so
likely have ages < 8 Myr, are found along the western edge of the complex, and
there is evidence that one such pocket contains a rich population of Wolf-Rayet
stars. Unless the star-forming complex is significantly more metal-poor than
the surroundings, then a significant fraction of its total mass is in stars
with ages < 8 Myr. If the present-day star formation rate is maintained then
the time scale to double its stellar mass ranges from a few Myr to a few tens
of Myr, depending on the contribution made by stars older than ~ 8 Myr. If --
as suggested by some studies -- the star-forming complex is centered on the
galaxy nucleus, then the nucleus of NGC 253 is currently experiencing a phase
of rapid growth in its stellar mass.


  Our aim is to study the electron-positron vacuum pressures in presence of a
strong magnetic field $B$. To that end, we obtain a general energy-momentum
tensor, depending on external parameters, which in the zero temperature and
zero density limit leads to vacuum expressions which are
approximation-independent. Anisotropic pressures arise, and in the tree
approximation of the magnetic field case, the pressure along $B$ is positive,
whereas perpendicular to $B$ it is negative. Due to the common axial symmetry,
the formal analogy with the Casimir effect is discussed, for which in addition
to the usual negative pressure perpendicular to the plates, there is a positive
pressure along the plates. The formal correspondence between the Casimir and
black body energy-momentum tensors is analyzed. The fermion hot vacuum behavior
in a magnetic field is also briefly discussed.


  We suggest a simple modification of the usual procedures of analysis for the
high-temperature (strong-coupling or hopping-parameter) expansions of the
renormalized four-point coupling constant in the fourdimensional phi^4 lattice
scalar field theory. As a result we can more convincingly validate numerically
the triviality of the continuum limit taken from the high temperature phase.


  In this work, we investigated a Bose-Einstein condensate (BEC) inside a
Rydberg atom. We first observed the density profile of the system using the
Gross-Pitaevskii equation, and then we used the Bogoliubov theory to examine
the collective excitation spectra. We have also extended our study by taking
into account a hybrid of two BEC species. Again, for this new system, the
density profile and the collective excitation are investigated in a similar
manner. The results of the BEC for one species reveal that the Rydberg atom can
trap the BEC and that the excitation curve moves upward with increasing Rydberg
atom interaction. We have seen roton minima for two species of BEC, and the
depth of the minima shifts with the Rydberg interaction.


  Nanoparticle (NP) arrays of noble metals strongly absorb light in the visible
to infrared wavelengths through resonant interactions between the incident
electromagnetic field and the metal's free electron plasma. Such plasmonic
interfaces enhance light absorption and photocurrent in solar cells. We report
a cost effective and scalable room temperature/pressure spin-coating route to
fabricate broadband plasmonic interfaces consisting of silver NPs. The NP
interface yields photocurrent enhancement (PE) in thin film silicon devices by
up to 200% which is significantly greater than previously reported values. For
coatings produced from Ag nanoink containing particles with average diameter of
40 nm, an optimal NP surface coverage of 7% was observed. Scanning electron
microscopy of interface morphologies revealed that for low surface coverage,
particles are well-separated, resulting in broadband PE. At higher surface
coverage, formation of particle strings and clusters caused red-shifting of the
PE peak and a narrower spectral response.


  We prove an analogue of the Central Limit Theorem for operators. For every
operator $K$ defined on $\mathbb{C}[x]$ we construct a sequence of operators
$K_N$ defined on $\mathbb{C}[x_1,...,x_N]$ and demonstrate that, under certain
orthogonality conditions, this sequence converges in a weak sense to an unique
operator $\mathcal{C}$. We show that this operator $\mathcal{C}$ is a member of
a family of operators $\mathfrak{C}$ that we call {\it Centered Gaussian
Operators} and which coincides with the family of operators given by a centered
Gaussian Kernel. Inspired in the approximation method used by Beckner in [W.
Beckner, Inequalities in Fourier Analysis, Annals of Mathematics, 102 (1975),
159-182] to prove the sharp form of the Hausdorff-Young inequality, the present
article shows that Beckner's method is a special case of a general
approximation method for operators. In particular, we characterize the Hermite
semi-group as the family of Centered Gaussian Operators associated with any
semi-group of operators.


  In addition to the well-known 11-year solar cycle, the Sun's magnetic
activity also shows significant variation on shorter time scales, e.g. between
one and two years. We observe a quasi-biennial (2-year) signal in the solar
p-mode oscillation frequencies, which are sensitive probes of the solar
interior. The signal is visible in Sun-as-a-star data observed by different
instruments and here we describe the results obtained using BiSON, GOLF, and
VIRGO data. Our results imply that the 2-year signal is susceptible to the
influence of the main 11-year solar cycle. However, the source of the signal
appears to be separate from that of the 11-year cycle. We speculate as to
whether it might be the signature of a second dynamo, located in the region of
near-surface rotational shear.


  We show that there are no spurious local minima in the non-convex factorized
parametrization of low-rank matrix recovery from incoherent linear
measurements. With noisy measurements we show all local minima are very close
to a global optimum. Together with a curvature bound at saddle points, this
yields a polynomial time global convergence guarantee for stochastic gradient
descent {\em from random initialization}.


  We present an analytical model for the role of hydrogen bonding on the
spin-orbit coupling of model DNA molecule. Here we analyze in detail the
electric fields due to the polarization of the Hydrogen bond on the DNA base
pairs and derive, within tight binding analytical band folding approach, an
intrinsic Rashba coupling which should dictate the order of the spin active
effects in the Chiral-Induced Spin Selectivity (CISS) effect. The coupling
found is ten times larger than the intrinsic coupling estimated previously and
points to the predominant role of hydrogen bonding in addition to chirality in
the case of biological molecules. We expect similar dominant effects in
oligopeptides, where the chiral structure is supported by hydrogen-bonding and
bears on orbital carrying transport electrons.


  Alloy is an increasingly popular lightweight specification language based on
relational logic. Alloy models can be automatically verified within a bounded
scope using off-the-shelf SAT solvers. Since false assertions can usually be
disproved using small counter-examples, this approach suffices for most
applications. Unfortunately, it can sometimes lead to a false sense of
security, and in critical applications a more traditional unbounded proof may
be required. The automatic theorem prover Prover9 has been shown to be
particularly effective for proving theorems of relation algebras [7], a
quantifier-free (or point-free) axiomatization of a fragment of relational
logic. In this paper we propose a translation from Alloy specifications to fork
algebras (an extension of relation algebras with the same expressive power as
relational logic) which enables their unbounded verification in Prover9. This
translation covers not only logic assertions, but also the structural aspects
(namely type declarations), and was successfully implemented and applied to
several examples.


  We combine the swap Monte Carlo algorithm to long multi-CPU molecular
dynamics simulations to analyse the equilibrium relaxation dynamics of model
supercooled liquids over a time window covering ten orders of magnitude for
temperatures down to the experimental glass transition temperature $T_g$. The
analysis of \rev{several} time correlation functions coupled to spatio-temporal
resolution of particle motion allow us to elucidate the nature of the
equilibrium dynamics in deeply supercooled liquids. We find that structural
relaxation starts at early times in rare localised regions characterised by a
waiting time distribution that develops a power law near $T_g$. At longer
times, relaxation events accumulate with increasing probability in these
regions as $T_g$ is approached. This accumulation leads to a power-law growth
of the linear extension of relaxed domains with time with a large,
temperature-dependent dynamic exponent. Past the average relaxation time,
unrelaxed domains slowly shrink with time due to relaxation events happening at
their boundaries. Our results provide a complete microscopic description of the
particle motion responsible for key experimental signatures of glassy dynamics,
from the shape and temperature evolution of relaxation spectra to the core
features of dynamic heterogeneity. They also provide a microscopic basis to
understand the emergence of dynamic facilitation in deeply supercooled liquids
and allow us to critically reassess theoretical descriptions of the glass
transition.


  We generalize the Guth--Katz joints theorem from lines to varieties. A
special case says that $N$ planes (2-flats) in 6 dimensions (over any field)
have $O(N^{3/2})$ joints, where a joint is a point contained in a triple of
these planes not all lying in some hyperplane. More generally, we prove the
same bound when the set of $N$ planes is replaced by a set of 2-dimensional
algebraic varieties of total degree $N$, and a joint is a point that is regular
for three varieties whose tangent planes at that point are not all contained in
some hyperplane. Our most general result gives upper bounds, tight up to
constant factors, for joints with multiplicities for several sets of varieties
of arbitrary dimensions (known as Carbery's conjecture). Our main innovation is
a new way to extend the polynomial method to higher dimensional objects,
relating the degree of a polynomial and its orders of vanishing on a given set
of points on a variety.


  This paper derives a new class of adaptive regularization parameter choice
strategies that can be effectively and efficiently applied when regularizing
large-scale linear inverse problems by combining standard Tikhonov
regularization and projection onto Krylov subspaces of increasing dimension
(computed by the Golub-Kahan bidiagonalization algorithm). The success of this
regularization approach heavily depends on the accurate tuning of two
parameters (namely, the Tikhonov parameter and the dimension of the projection
subspace): these are simultaneously set using new strategies that can be
regarded as special instances of bilevel optimization methods, which are solved
by using a new paradigm that interlaces the iterations performed to project the
Tikhonov problem (lower-level problem) with those performed to apply a given
parameter choice rule (higher-level problem). The discrepancy principle, the
GCV, the quasi-optimality criterion, and Regi\'{n}ska criterion can all be
adapted to work in this framework. The links between Gauss quadrature and
Golub-Kahan bidiagonalization are exploited to prove convergence results for
the discrepancy principle, and to give insight into the behavior of the other
considered regularization parameter choice rules. Several numerical tests
modeling inverse problems in imaging show that the new parameter choice
strategies lead to regularization methods that are reliable, and intrinsically
simpler and cheaper than other strategies already available in the literature.


  We show that the flatness of a nonlinear discrete-time system can be checked
by computing a unique sequence of involutive distributions. The well-known test
for static feedback linearizability is included as a special case. Since the
computation of the sequence of distributions requires only the solution of
algebraic equations, it allows an efficient implementation in a computer
algebra program. In case of a positive result, a flat output can be obtained by
straightening out the involutive distributions with the Frobenius theorem.


  The common approach to crack dynamics, linear elastic fracture mechanics
(LEFM), assumes infinitesimal strains and predicts a $r^{-1/2}$ strain
divergence at a crack tip. We extend this framework by deriving a weakly
nonlinear fracture mechanics theory incorporating the leading nonlinear elastic
corrections that must occur at high strains. This yields strain contributions
"more-divergent" than $r^{-1/2}$ at a finite distance from the tip and
logarithmic corrections to the parabolic crack tip opening displacement. In
addition, a dynamic length-scale, associated with the nonlinear elastic zone,
emerges naturally. The theory provides excellent agreement with recent near-tip
measurements that can not be described in the LEFM framework.


  In this thesis a general procedure to represent the integral Bethe Ansatz
equations in the form of the Reimann-Hilbert problem is given. This allows us
to study in simple way integrable spin chains in the thermodynamic limit. Based
on the functional equations we give the procedure that allows finding the
subleading orders in the solution of various integral equations solved to the
leading order by the Wiener-Hopf technics. The integral equations are studied
in the context of the AdS/CFT correspondence, where their solution allows
verification of the integrability conjecture up to two loops of the strong
coupling expansion. In the context of the two-dimensional sigma models we
analyze the large-order behavior of the asymptotic perturbative expansion.
Obtained experience with the functional representation of the integral
equations allowed us also to solve explicitly the crossing equations that
appear in the AdS/CFT spectral problem.


  We propose a novel method to construct the Landau thermodynamic potential
directly from the fluctuations measured in heavy-ion collisions. The potential
is capable of revealing the signal of the critical end-point (CEP) and the
first order phase transition (FOPT) of QCD in the system even away from the
phase transition region. With the available experimental data, we show that the
criterion of the FOPT is negative for most of the collision energies which
indicates no signal of FOPT. The data at $\sqrt{s_\mathrm{NN}}=7.7$ GeV with
0-5% centrality shows a different behavior and the mean value of the data
satisfies the criterion. However, the uncertainty is still too large to make a
certain conclusion. The higher order fluctuations are also required for
confirming the signal. We emphasize therefore that new measurements with higher
precision for the $C_{1,...,6}$ within 0-5% centrality in the vicinity of
$\sqrt{s_\mathrm{NN}}=7.7$ GeV are in demand which may finally reveal the
signal of QCD phase transition.