  This paper investigates Cell-Free massive MIMO networks, where each access
point (AP) is equipped with a hybrid transceiver, reducing the complexity and
cost compared to a fully digital transceiver. Asymptotic approximations for the
spectral efficiency are derived for uplink and downlink. Capitalizing on these
expressions, a max-min problem is formulated to optimize the (i) analog
beamformer at the APs and (ii) pilot assignment. Simulations show that the
optimization of these variables substantially increases the network
performance.


  Accreting millisecond X-ray pulsars are known to provide a wealth of physical
information during their successive states of outburst and quiescence. Based on
the observed spin-up and spin-down rates of these objects it is possible, among
other things, to infer the stellar magnetic field strength and test models of
accretion disc flow. In this paper we consider the three accreting X-ray
pulsars (XTE J1751-305, IGR J00291+5934, and SAX J1808.4-3658) with the best
available timing data, and model their observed spin-up rates with the help of
a collection of standard torque models that describe a magnetically-threaded
accretion disc truncated at the magnetospheric radius. Whilst none of these
models are able to explain the observational data, we find that the inclusion
of the physically motivated phenomenological parameter $\xi$, which controls
the uncertainty in the location of the magnetospheric radius, leads to an
enhanced disc-integrated accretion torque. These 'new' torque models are
compatible with the observed spin-up rates as well as the inferred magnetic
fields of these objects provided that $\xi \approx 0.1-0.5$. Our results are
supplemented with a discussion of the relevance of additional physics effects
that include the presence of a multipolar magnetic field and
general-relativistic gravity.


  We propose a novel recursive utility for controlling stochastic processes
under risk and uncertainty. Our formulation uses a robustified Orlicz risk that
can evaluate risk and uncertainty simultaneously. We focus on a control problem
of a photovoltaic power generation system that supplies excess electricity to a
secondary purpose for generating green hydrogen. The corresponding
Hamilton-Jacobi-Bellman equation having a novel nonlinear term is then derived.
Computational examples with the available data are finally presented,
demonstrating that our methodology can be used for the photovoltaic power
generation under different meteorological and operational conditions.


  A multi-component formalism is developed to describe three-body systems with
nonstatic pairwise interactions and non-nucleonic degrees of freedom. The
dressed-bag model for $NN$ interaction based on the formation of an
intermediate six-quark bag dressed by a $\sigma$-field is applied to the $3N$
system, where it results in a new three-body force between the six-quark bag
and a third nucleon. Concise variational calculations of $3N$ bound states are
carried out in the dressed-bag model including the new three-body force. It is
shown that this three-body force gives at least half the $3N$ total binding
energy, while the weight of non-nucleonic components in the $^3$H and $^3$He
wavefunctions can exceed 10%. The new force model provides a very good
description of $3N$ bound states with a reasonable magnitude of the $\sigma NN$
coupling constant. The model can serve as a natural bridge between dynamical
description of few-nucleon systems and the very successful Walecka approach to
heavy nuclei and nuclear matter.


  In a world driven by data visualization, ensuring the inclusive accessibility
of charts for Blind and Visually Impaired (BVI) individuals remains a
significant challenge. Charts are usually presented as raster graphics without
textual and visual metadata needed for an equivalent exploration experience for
BVI people. Additionally, converting these charts into accessible formats
requires considerable effort from sighted individuals. Digitizing charts with
metadata extraction is just one aspect of the issue; transforming it into
accessible modalities, such as tactile graphics, presents another difficulty.
To address these disparities, we propose Chart4Blind, an intelligent user
interface that converts bitmap image representations of line charts into
universally accessible formats. Chart4Blind achieves this transformation by
generating Scalable Vector Graphics (SVG), Comma-Separated Values (CSV), and
alternative text exports, all comply with established accessibility standards.
Through interviews and a formal user study, we demonstrate that even
inexperienced sighted users can make charts accessible in an average of 4
minutes using Chart4Blind, achieving a System Usability Scale rating of 90%. In
comparison to existing approaches, Chart4Blind provides a comprehensive
solution, generating end-to-end accessible SVGs suitable for assistive
technologies such as embossed prints (papers and laser cut), 2D tactile
displays, and screen readers. For additional information, including open-source
codes and demos, please visit our project page
https://moured.github.io/chart4blind/.


  If the constitutive law linking the second Piola-Kirchhoff stress tensor and
the right Cauchy-Green strain tensor derives from a potential, then the Cauchy
stress tensor and the logarithm of the left Cauchy-Green strain tensor are
linked by a related potential. We give a new and concise proof which is based
on an explicit formula expressing the derivative of the exponential of a
tensor.


  We discuss an extension of the standard logical rules (functional application
and abstraction) in Categorial Grammar (CG), in order to deal with some
specific cases of polysemy. We borrow from Generative Lexicon theory which
proposes the mechanism of {\em coercion}, next to a rich nominal lexical
semantic structure called {\em qualia structure}.
  In a previous paper we introduced coercion into the framework of {\em
sign-based} Categorial Grammar and investigated its impact on traditional
Fregean compositionality. In this paper we will elaborate on this idea, mostly
working towards the introduction of a new semantic dimension. Where in current
versions of sign-based Categorial Grammar only two representations are derived:
a prosodic one (form) and a logical one (modelling), here we introduce also a
more detaled representation of the lexical semantics. This extra knowledge will
serve to account for linguistic phenomena like {\em metonymy\/}.


  We design a new sparse projection method for a set of vectors that guarantees
a desired average sparsity level measured leveraging the popular Hoyer measure
(an affine function of the ratio of the $\ell_1$ and $\ell_2$ norms). Existing
approaches either project each vector individually or require the use of a
regularization parameter which implicitly maps to the average $\ell_0$-measure
of sparsity. Instead, in our approach we set the sparsity level for the whole
set explicitly and simultaneously project a group of vectors with the sparsity
level of each vector tuned automatically. We show that the computational
complexity of our projection operator is linear in the size of the problem.
Additionally, we propose a generalization of this projection by replacing the
$\ell_1$ norm by its weighted version. We showcase the efficacy of our approach
in both supervised and unsupervised learning tasks on image datasets including
CIFAR10 and ImageNet. In deep neural network pruning, the sparse models
produced by our method on ResNet50 have significantly higher accuracies at
corresponding sparsity values compared to existing competitors. In nonnegative
matrix factorization, our approach yields competitive reconstruction errors
against state-of-the-art algorithms.


  Classical radiation power from an accelerated massive charge diverges in the
zero-mass limit, while some general arguments suggest that strictly massless
charge does not not radiate at all. On the other hand, the regularized
classical radiation reaction force, though looking odd, is non-zero and finite.
To clarify this controversy, we consider radiation problem in massless scalar
quantum electrodynamics in the external magnetic field. In this framework,
synchrotron radiation is found to be non-zero, finite, and essentially quantum.
Its spectral distribution is calculated using Schwinger's proper time technique
for {\em ab initio} massless particle of zero spin. Provided $E^2\gg eH$, the
maximum in the spectrum is shown to be at $\hbar \omega=E/3$, and the average
photon energy is $4E/9$. The normalized spectrum is universal, depending
neither on $E$ nor on $H$. Quantum nature of radiation makes classical
radiation reaction equation meaningless for massless charge. Our results are
consistent with the view (supported by the renormalization group argument) that
the correct classical limit of massless quantum electrodynamics is free theory.


  Low-lying energy levels of two interacting electrons confined in a
two-dimensional parabolic quantum dot in the presence of an external magnetic
field have been revised within the frame of a novel model. The present
formalism, which gives closed algebraic solutions for the specific values of
magnetic field and spatial confinement length, enables us to see explicitly
individual effects of the electron correlation.


  We establish special value results of convolutions of Goss and Pellarin
$L$-series attached to Drinfeld modules that take values in Tate algebras.
Applying the class module formula of Demeslay to certain rigid analytic twists
of one Drinfeld module by another, we extend the special value formula for the
Pellarin $L$-function associated to the Carlitz module and the Anderson-Thakur
function to Drinfeld modules of arbitrary rank and their rigid analytic
trivializations. By way of the theory of Schur polynomials these identities
take the form of specializations of convolutions of Rankin-Selberg type.


  Following an original idea of F. Guerra, in this notes we analyze the
Sherrington-Kirkpatrick model from different perspectives, all sharing the
underlying approach which consists in linking the resolution of the statistical
mechanics of the model (e.g. solving for the free energy) to well-known partial
differential equation (PDE) problems (in suitable spaces). The plan is then to
solve the related PDE using techniques involved in their native field and
lastly bringing back the solution in the proper statistical mechanics
framework. Within this strand, after a streamlined test-case on the Curie-Weiss
model to highlight the methods more than the physics behind, we solve the SK
both at the replica symmetric and at the 1-RSB level, obtaining the correct
expression for the free energy via an analogy to a Fourier equation and for the
self-consistencies with an analogy to a Burger equation, whose shock wave
develops exactly at critical noise level (triggering the phase transition). Our
approach, beyond acting as a new alternative method (with respect to the
standard routes) for tackling the complexity of spin glasses, links symmetries
in PDE theory with constraints in statistical mechanics and, as a novel result
from the theoretical physics perspective, we obtain a new class of polynomial
identities (namely of Aizenman-Contucci type but merged within the Guerra's
broken replica measures), whose interest lies in understanding, via the recent
Panchenko breakthroughs, how to force the overlap organization to the
ultrametric tree predicted by Parisi.


  Since 2011, the SOPHIE spectrograph has been used to search for Neptunes and
super-Earths in the Northern Hemisphere. As part of this observational program,
290 radial velocity measurements of the 6.4 V magnitude star HD 158259 were
obtained. Additionally, TESS photometric measurements of this target are
available. We present an analysis of the SOPHIE data and compare our results
with the output of the TESS pipeline. The radial velocity data, ancillary
spectroscopic indices, and ground-based photometric measurements were analyzed
with classical and $\ell_1$ periodograms. The stellar activity was modeled as a
correlated Gaussian noise and its impact on the planet detection was measured
with a new technique. The SOPHIE data support the detection of five planets,
each with $m \sin i \approx 6 M_\oplus$, orbiting HD 158259 in 3.4, 5.2, 7.9,
12, and 17.4 days. Though a planetary origin is strongly favored, the 17.4 d
signal is classified as a planet candidate due to a slightly lower statistical
significance and to its proximity to the expected stellar rotation period. The
data also present low frequency variations, most likely originating from a
magnetic cycle and instrument systematics. Furthermore, the TESS pipeline
reports a significant signal at 2.17 days corresponding to a planet of radius
$\approx 1.2 R_\oplus$. A compatible signal is seen in the radial velocities,
which confirms the detection of an additional planet and yields a $\approx 2
M_\oplus$ mass estimate. We find a system of five planets and a strong
candidate near a 3:2 mean motion resonance chain orbiting HD 158259. The
planets are found to be outside of the two and three body resonances.


  It is shown that if T is a connected nontrivial graph and X is an arbitrary
finite simplicial complex, then there is a graph G such that the complex
Hom(T,G) is homotopy equivalent to X. The proof is constructive, and uses a
nerve lemma. Along the way several results regarding Hom complexes,
exponentials, and subdivision are established that may be of independent
interest.


  This work presents the results of a theoretical study that analyzed the
possibility of nucleobases to form in the interstellar medium, in the Horsehead
nebula, which is a region considered an archetype of molecular cloud.
Performing the Meudon PDR code, the reactions of the nitrogen bases formation
from formamide, which is a precursor compound identified in several
interstellar environment, where simulated. The model showed that at least
cytosine and uracil presented significant abundances. Finally, from
thermochemical and quantum calculations, a investigation was carried out on the
formation reactions considered for the nucleobases and no insurmountable energy
barrier which would prevent the reactions was found.


  In this paper we propose a distributed dual gradient algorithm for minimizing
linearly constrained separable convex problems and analyze its rate of
convergence. In particular, we prove that under the assumption of strong
convexity and Lipshitz continuity of the gradient of the primal objective
function we have a global error bound type property for the dual problem. Using
this error bound property we devise a fully distributed dual gradient scheme,
i.e. a gradient scheme based on a weighted step size, for which we derive
global linear rate of convergence for both dual and primal suboptimality and
for primal feasibility violation. Many real applications, e.g. distributed
model predictive control, network utility maximization or optimal power flow,
can be posed as linearly constrained separable convex problems for which dual
gradient type methods from literature have sublinear convergence rate. In the
present paper we prove for the first time that in fact we can achieve linear
convergence rate for such algorithms when they are used for solving these
applications. Numerical simulations are also provided to confirm our theory.


  Optimal power flow (OPF) is a fundamental tool for analyzing the
characteristics of bipolar DC distribution network (DCDN). However, existing
OPF models face challenges in reflecting the power distribution and exchange of
bipolar DCDN directly since its decision variables are voltage and current.
This paper addresses this issue by establishing a convex OPF model that can be
used for the planning and operation of bipolar DCDN. First, the power flow
characteristics of bipolar DCDN are revealed through power injection-based
equations, upon which the original OPF model is established. Next, the original
OPF model undergoes a transformation into a convex OPF model based on
second-order cone programming (SOCP) through variable substitution, secondorder
cone relaxation, McCormick relaxation, and first-order Taylor expansion,
respectively. Finally, the sequence bound tightening algorithm (STBA) is
employed to tighten the boundaries of McCormick envelopes in each iteration to
ensure the exactness of the convex OPF model. The effectiveness of this novel
OPF model for bipolar DCDN is verified through two case studies, i.e., capacity
configuration of distributed generation (DG) and operation optimization of
bipolar DCDN.


  We have investigated the many-body equations of $D$ and $\bar{B}$ mesons in a
thermal medium by applying an effective field theory based on chiral and
heavy-quark symmetries. Exploiting these symmetries within kinetic theory, we
have derived an off-shell Fokker-Planck equation which incorporates information
of the full spectral functions of these states. In this contribution we present
our latest results on heavy-flavor transport coefficients below the chiral
restoration temperature, in both charm and bottom sectors. The calculation
incorporating temperature-dependent spectral functions and interactions,
together with off-shell effects, allows for an improved matching to the
state-of-the-art calculations above the chiral transition temperature.


  The structure of social networks is a key determinant in fostering
cooperation and other altruistic behavior among naturally selfish individuals.
However, most real social interactions are temporal, being both finite in
duration and spread out over time. This raises the question of whether stable
cooperation can form despite an intrinsically fragmented social fabric. Here we
develop a framework to study the evolution of cooperation on temporal networks
in the setting of the classic Prisoner's Dilemma. By analyzing both real and
synthetic datasets, we find that temporal networks generally facilitate the
evolution of cooperation compared to their static counterparts. More
interestingly, we find that the intrinsic human interactive pattern like bursty
behavior impedes the evolution of cooperation. Finally, we introduce a measure
to quantify the temporality present in networks and demonstrate that there is
an intermediate level of temporality that boosts cooperation most. Our results
open a new avenue for investigating the evolution of cooperation in more
realistic structured populations.


  Autotuning is an established technique for optimizing the performance of
parallel applications. However, programmers must prepare applications for
autotuning, which is tedious and error prone coding work. We demonstrate how
applications become ready for autotuning with few or no modifications by
extending Threading Building Blocks (TBB), a library for parallel programming,
with autotuning. The extended TBB library optimizes all application-independent
tuning parameters fully automatically. We compare manual effort, autotuning
overhead and performance gains on 17 examples. While some examples benefit only
slightly, others speed up by 28% over standard TBB.


  We investigate molecular evolution in a star-forming core that is initially a
hydrostatic starless core and collapses to form a low-mass protostar. The
results of a one-dimensional radiation-hydrodynamics calculation are adopted as
a physical model of the core. We first derive radii at which CO and large
organic species sublimate. CO sublimation in the central region starts shortly
before the formation of the first hydrostatic core. When the protostar is born,
the CO sublimation radius extends to 100 AU, and the region inside $\lesssim
10$ AU is hotter than 100 K, at which some large organic species evaporate. We
calculate the temporal variation of physical parameters in infalling shells, in
which the molecular evolution is solved using an updated gas-grain chemical
model to derive the spatial distribution of molecules in a protostellar core.
The shells pass through the warm region of $10 -100$ K in several $\times$
$10^4$ yr, and fall into the central star $\sim 100$ yr after they enter the
region where $T \gtrsim 100$ K. We find that large organic species are formed
mainly via grain-surface reactions at temperatures of $20 -40$ K and then
desorbed into the gas-phase at their sublimation temperatures. Carbon-chain
species can be formed by a combination of gas-phase reactions and grain-surface
reactions following the sublimation of CH$_4$. Our model also predicts that
CO$_2$ is more abundant in isolated cores, while gas-phase large organic
species are more abundant in cores embedded in ambient clouds.


  The short-time linear canonical transform (STLCT) can be identified as a
generalization of the short-time Fourier transform (STFT). It is a novel
time-frequency analysis tool. In this paper, we generalize some different
uncertainty principles for the STLCT of complex signals. Firstly, one
uncertainty principle for the STLCT of complex signals in time and frequency
domains is derived. Secondly, the uncertainty principle for the STLCT of
complex signals in two STLCT domains is obtained. Finally, the uncertainty
principle for the two conditional standard deviations of the spectrogram
associated with the STLCT is discussed.


  In this work, Laser-induced magnetization dynamics of nanostructured nickel
films is investigated. The influence of the nanosize is discussed considering
the time-scale of hundreds of femtoseconds as well as the GHz regime. While no
nanosize effect is observed on the short time-scale, the excited magnetic mode
in the GHz regime can be identified by comparison with micromagnetic
simulations. The thickness dependence reveals insight on the dipole interaction
between single nickel structures. Also, transient reflectivity changes are
discussed.


  The present status of our knowledge of the magnitude of the quark mixing
parameter Vcb is reviewed, with particular emphasis on the factors affecting
experimental and theoretical errors and on prospects for a more precise
determination.


  For the first time it is shown that for thin metallic films thickness of
which does not exceed thickness of skin - layer, the problem of description of
surface plasma oscillations allows analytical solution under arbitrary ratio of
length of electrons free path and thickness of a film. The dependance of
frequency of surface plasma oscillations on wave number is carried out. We
consider a case of specularity - diffusive boundary value problems.


  This review investigates the landscapes of prevalent hybrid quantum-classical
optimization algorithms in many rapidly developing quantum technologies, where
the objective function is either computed by a natural quantum system or a
quantum ansatz that is engineered, but the optimizer is classical. In any
particular case, the nature of the underlying control landscape is
fundamentally important for systematic optimization of the objective. In early
studies on the optimal control of few-body dynamics, the optimizer could take
full control of the quantum systems to be manipulated whose Hilbert space
dimension is relatively small. Stepping into the noisy intermediate-scale
quantum (NISQ) era, the experimentally growing computational power of the
ansatz expressed as quantum hardware may bring quantum advantage over classical
computers, but the classical optimizer is often limited by the available
control resources. Across these different scales, we will show that the
landscape's geometry experiences morphological changes from favorable trap-free
landscapes to easily trapping rugged landscapes, and eventually to
barren-plateau landscapes on which the optimizer can hardly move. This unified
view provides the basis for understanding classes of systems that may be
readily controlled out to those with special consideration, including the
difficulties and potential advantages of NISQ technologies, as well as seeking
possible ways to escape traps or plateaus, in particular circumstances.


  The ground state phase diagram of the half-filled one-dimensional
Holstein-Hubbard model contains a charge-density-wave (CDW) phase, driven by
the electron-phonon (e-ph) coupling, and a spin-density-wave (SDW) phase,
driven by the on-site electron-electron (e-e) repulsion. Recently, the
existence of a third phase, which is metallic and lies in a finite region of
parameter space between these two gapped phases, has been claimed. We study
this claim using a renormalization-group method for interacting electrons that
has been extended to include also e-ph couplings. Our method treats e-e and
e-ph interactions on an equal footing and takes retardation effects fully into
account. We find a direct transition between the spin- and charge-density wave
states. We study the effects of retardation, which are particularly important
near the transition, and find that Umklapp processes at finite frequencies
drive the CDW instability close to the transition. We also perform
determinantal quantum Monte Carlo calculations of correlation functions to
confirm our results for the phase diagram.


  It is shown that extremely strong electric fields may be generated at the
surface of strange quark matter in the color-flavor locked phase because of the
surface effects. Some properties of strange stars made of this matter are
briefly discussed.


  For many people, Wikipedia represents one of the primary sources of knowledge
about foreign cultures. Yet, different Wikipedia language editions offer
different descriptions of cultural practices. Unveiling diverging
representations of cultures provides an important insight, since they may
foster the formation of cross-cultural stereotypes, misunderstandings and
potentially even conflict. In this work, we explore to what extent the
descriptions of cultural practices in various European language editions of
Wikipedia differ on the example of culinary practices and propose an approach
to mine cultural relations between different language communities trough their
description of and interest in their own and other communities' food culture.
We assess the validity of the extracted relations using 1) various external
reference data sources (i.e., the European Social Survey, migration
statistics), 2) crowdsourcing methods and 3) simulations.


  We study isometric actions on Riemannian symmetric spaces of noncompact type
which are induced by reductive algebraic subgroups of the isometry group. We
show that for such an action there exists a corresponding isometric action on a
dual compact symmetric space, which reflects many properties of the original
action. For example, the principal isotropy subgroups of both actions are
locally isomorphic and the dual action is (hyper)polar if and only if the
original action is (hyper)polar. This fact provides many new examples for polar
actions on symmetric spaces of noncompact type and we use duality as a method
to study polar actions by reductive algebraic subgroups in the isometry group
of an irreducible symmetric space. Among other applications, we show that they
are hyperpolar if the space is of type III and of higher rank; we prove that
such actions are orbit equivalent to Hermann actions if they are hyperpolar and
of cohomogeneity greater than one. Furthermore, we classify polar actions by
reductive algebraic subgroups of the isometry group on noncompact symmetric
spaces of rank one.


  We study a $U(1)\times U(1)$ system in (2+1)-dimensions with long-range
interactions and mutual statistics. The model has the same form after the
application of operations from the modular group, a property which we call
modular invariance. Using the modular invariance of the model, we propose a
possible phase diagram. We obtain a sign-free reformulation of the model and
study it in Monte Carlo. This study confirms our proposed phase diagram. We use
the modular invariance to analytically determine the current-current
correlation functions and conductivities in all the phases in the diagram, as
well as at special "fixed" points which are unchanged by an operation from the
modular group. We numerically determine the order of the phase transitions, and
find segments of second-order transitions. For the statistical interaction
parameter $\theta=\pi$, these second-order transitions are evidence of a
critical loop phase obtained when both loops are trying to condense
simulataneously. We also measure the critical exponents of the second-order
transitions.


  The aim of this review is to develop the kinetic theory of phonons in
classical particle chains to a point which allows comparing the kinetic theory
of normally conducting chains, with an anharmonic pinning potential, to the
kinetic theory of the anomalously conducting FPU chains. In addition to
reviewing existing results from the literature, we present a streamlined
derivation of the phonon Boltzmann collision operators using Wick polynomials,
as well as details about the estimates which are needed to study the effect of
the collision operator. This includes explicit solutions of the collisional
constraints, both with and without harmonic pinning. We also recall in detail
the derivation of the Green-Kubo formula for thermal conductivity in these
systems, and the relation between entropy and the Boltzmann H-theorem for the
phonon Boltzmann equations. The focus is in systems which are spatially
translation invariant perturbations of thermal equilibrium states. We apply the
results to obtain detailed predictions from kinetic theory for the Green-Kubo
correlation functions, and hence the thermal conductivities, of the chain with
a quartic pinning potential as well as the standard FPU-beta chain.


  The conversion between amplitude modulation and phase modulation as a
modulated signal goes thrugh a filter is analyzed. The difference in how the
modulated sideband ampitude experience the filter, and how AM and PM has
opposite signs for one of their sidebands interact. The conversion between AM
and PM is modelled, providing a scatter model and evaluation of two functions
based on the linear filters transfer function. The system bandwidth effects is
analyzed and rule of thumb developed to ensure AM and PM isolation.


  We give defining equations for function fields over finite fields with many
rational places. They are obtained from composita of quadratic extensions of
the rational function field.


  We prove the convergence of K\"ahler-Ricci flow with some small initial
curvature conditions. As applications, we discuss the convergence of
K\"ahler-Ricci flow when the complex structure varies on a K\"ahler-Einstein
manifold.


  We discuss in depth the application of the classical concepts for
interpreting the quantal results from the triaxial rotor core without and with
odd-particle. The corresponding limitations caused by the discreteness and
finiteness of the angular momentum Hilbert space and the extraction of the
relevant features from the complex wave function and distributions of various
angular momentum components are discussed in detail. New methods based on spin
coherent states and spin squeezed states are introduced. It is demonstrated
that the spin coherent state map is a powerful tool to visualize the angular
momentum geometry of rotating nuclei. The topological nature of the concepts of
transverse and longitudinal wobbling is clarified and the transitional
axis-flipregime is analysed for the first time.


  Following the Renormalization Group scheme recently developed by Pietronero
{\it et al}, we introduce a simplifying strategy for the renormalization of the
relaxation dynamics of sandpile models. In our scheme, five sub-cells at a
generic scale $b$ form the renormalized cell at the next larger scale. Now the
fixed point has a unique nonzero dynamical component that allows for a great
simplification in the computation of the critical exponent $z$. The values
obtained are in good agreement with both numerical and theoretical results
previously reported.


  Within supersymmetric SU(5) Grand Unified Theory, we present several new
scenarios with anomaly free flavor symmetry U(1)_F. Within each scenario, a
variety of cases offer many possibilities for phenomenologically interesting
model building. We present three concrete and economical models with anomaly
free U(1)_F leading to natural understanding of observed hierarchies between
charged fermion masses and CKM mixing angles.


  We present the analysis of the first circumbinary planet microlensing event,
OGLE-2007-BLG-349. This event has a strong planetary signal that is best fit
with a mass ratio of $q \approx 3.4\times10^{-4}$, but there is an additional
signal due to an additional lens mass, either another planet or another star.
We find acceptable light curve fits with two classes of models: 2-planet models
(with a single host star) and circumbinary planet models. The light curve also
reveals a significant microlensing parallax effect, which constrains the mass
of the lens system to be $M_L \approx 0.7 M_\odot$. Hubble Space Telescope
images resolve the lens and source stars from their neighbors and indicate
excess flux due to the star(s) in the lens system. This is consistent with the
predicted flux from the circumbinary models, where the lens mass is shared
between two stars, but there is not enough flux to be consistent with the
2-planet, 1-star models. So, only the circumbinary models are consistent with
the HST data. They indicate a planet of mass $m_c = 80\pm 13\,M_\oplus$,
orbiting a pair of M-dwarfs with masses of $M_A = 0.41\pm 0.07 M_\odot$ and
$M_B = 0.30\pm 0.07 M_\oplus$, which makes this the lowest mass circumbinary
planet system known. The ratio of the separation between the planet and the
center-of-mass to the separations of the two stars is $\sim 40$, so unlike most
of the circumbinary planets found by Kepler, the planet does not orbit near the
stability limit.


  We introduce higher order polynomial deformations of $A_1$ Lie algebra. We
construct their unitary representations and the corresponding single-variable
differential operator realizations. We then use the results to obtain exact
(Bethe ansatz) solutions to a class of 2-mode boson systems, including the
Boson-Einstein Condensate models as special cases. Up to an overall factor, the
eigenfunctions of the 2-mode boson systems are given by polynomials whose roots
are solutions of the associated Bethe ansatz equations. The corresponding
eigenvalues are expressed in terms of these roots. We also establish the
spectral equivalence between the BEC models and certain quasi-exactly solvable
Sch\"ordinger potentials.


  In this paper, a turbulence model based on deep neural network is developed
for turbulent flow around airfoil at high Reynolds numbers. According to the
data got from the Spalart-Allmaras (SA) turbulence model, we build a neural
network model that maps flow features to eddy viscosity. The model is then used
to replace the SA turbulence model to mutually couple with the CFD solver. We
build this suitable data-driven turbulence model mainly from the inputs,
outputs features and loss function of the model. A feature selection method
based on feature importance is also implemented. The results show that this
feature selection method can effectively remove redundant features. The model
based on the new input features has better accuracy and stability in mutual
coupling with the CFD solver. The force coefficient obtained from solution can
match the sample data well. The developed model also shows strong
generalization at different inflow condition (angle of attack, Mach number,
Reynolds number and airfoil).


  An overview is provided of the singularity theorems in cosmological contexts
at a level suitable for advanced graduate students. The necessary background
from tensor and causal geometry to understand the theorems is supplied, the
mathematical notion of a cosmology is described in some detail and issues
related to the range of validity of general relativity are also discussed.


  We study the statistical distributions of the spins of generic black-hole
binaries during the inspiral and merger, as well as the distributions of the
remnant mass, spin, and recoil velocity. For the inspiral regime, we start with
a random uniform distribution of spin directions S1 and S2 and magnitudes
S1=S2=0.97 for different mass ratios. Starting from a fiducial initial
separation of ri=50m, we perform 3.5PN evolutions down to rf=5m. At this final
fiducial separation, we compute the angular distribution of the spins with
respect to the final orbital angular momentum, L. We perform 16^4 simulations
for six mass ratios between q=1 and q=1/16 and compute the distribution of the
angles between L and Delta and L and S, directly related to recoil velocities
and total angular momentum. We find a small but statistically significant bias
of the distribution towards counter-alignment of both scalar products. To study
the merger of black-hole binaries, we turn to full numerical techniques. We
introduce empirical formulae to describe the final remnant black hole mass,
spin, and recoil velocity for merging black-hole binaries with arbitrary mass
ratios and spins. We then evaluate those formulae for randomly chosen
directions of the individual spins and magnitudes as well as the binary's mass
ratio. We found that the magnitude of the recoil velocity distribution decays
as P(v) \exp(-v/2500km/s), <v>=630km/s, and sqrt{<v^2> - <v>^2}= 534km/s,
leading to a 23% probability of recoils larger than 1000km/s, and a highly
peaked angular distribution along the final orbital axis. The final black-hole
spin magnitude show a universal distribution highly peaked at Sf/mf^2=0.73 and
a 25 degrees misalignment with respect to the final orbital angular momentum.


  Recent observational evidence seems to allow the possibility that our
universe may currently be under a dark energy effect of a phantom nature. A
suitable effective phantom fluid behaviour can emerge in brane cosmology; In
particular, within the normal non self-accelerating DGP branch, without any
exotic matter and due to curvature effects from induced gravity. The
phantom-like behaviour is based in defining an effective energy density that
grows as the brane expands. This effective description breaks down at some
point in the past when the effective energy density becomes negative and the
effective equation of state parameter blows up. In this paper we investigate if
the phantom-like regime can be enlarged by the inclusion of a Gauss-Bonnet (GB)
term into the bulk. The motivation is that such a GB component would model
additional curvature effects on the brane setting. More precisely, our aim is
to determine if the GB term, dominating and modifying the early behaviour of
the brane universe, may eventually extend the regime of validity of the phantom
mimicry on the brane. However, we show that the opposite occurs: the GB effect
seems instead to induce a breakdown of the phantom-like behaviour at an even
smaller redshift.


  In this paper we address the numerical solution of nonlinear ill-posed
systems by iterative regularization methods in the classes of
Levenberg-Marquardt, trust-region and adaptive quadratic regularization
procedures. Both with exact and noisy data, our focus is on the potential to
approach a solution of the unperturbed systems without assumptions on its
vicinity to the initial guess. Regularizing properties of the methods proposed
are shown theoretically and validated numerically along with enhanced
convergence.


  In 1927, at the Solvay conference, Einstein posed a thought experiment with
the primary intention of showing the incompleteness of quantum mechanics; to
prove it, he uses the instantaneous nonlocal effects caused by the collapse of
the wave function of a single particle -the spooky action at a distance-, when
a measurement is done. This historical event precede the well-know
Einstein-Podolsk-Rosen criticism over the incompleteness of quantum mechanics.
Here, by using the Stern-Gerlach experiment (SGE), we demonstrate how the
instantaneous nonlocal feature of the collapse of the wave function together
with the single-particle entanglement can be used to produce the nonlocal
effect of steering. In the steering process Bob gets a quantum state depending
on which observable Alice decides to measure. To accomplish this, we fully
exploit the spreading (over large distances) of the entangled wave function of
the single-particle. In particular, we demonstrate that the nonlocality of the
single-particle entanglement allows the particle to know which detector Alice
is using to steer Bob's state. Therefore, notwithstanding strong
counterarguments, we prove that the single-particle entanglement gives rise to
truly nonlocal effects at two far a away places. This open the possibility of
using the single-particle entanglement for implementing truly nonlocal task.


  We study the effects of quasidisorder and Anderson disorder on a two
dimensional topological superconductor with an applied external magnetic field.
The cases of a $p$-wave superconductor and a noncentrosymmetric superconductor
with mixed $p$ and $s$-wave pairings and Rashba spin-orbit coupling are
studied. We show that, for a perpendicular magnetic field, the introduction of
quasidisorder leads to the appearance of topological phases in new regions,
characterised by an integer value of the Chern number. For a parallel magnetic
field, we identify regimes with the appearance of new Majorana flat bands and
also new unidirectional Majorana edge states, as quasidisorder is introduced.
We show that the Majorana flat bands have a quantized Berry phase of $\pi$ and
identify it as a topological invariant. Two topological transitions are
identified and the values of the critical exponents $z$ and $\nu$ are obtained.
The fractal nature of the eigenstates is discussed both for Anderson disorder
and Aubry-Andr\'e disorder.


  The mean-field approximation based on effective interactions or density
functionals plays a pivotal role in the description of finite quantum many-body
systems that are too large to be treated by ab initio methods. Some examples
are strongly interacting medium and heavy mass atomic nuclei and mesoscopic
condensed matter systems. In this approach, the linear Schrodinger equation for
the exact many-body wave function is mapped onto a non-linear density-dependent
one-body potential problem. This approximation, not only provides
computationally very simple solutions even for systems with many particles, but
due to the non-linearity, it also allows for obtaining solutions that break
essential symmetries of the system, often connected with phase transitions. In
this way, additional correlations are subsumed in the system. However, the
mean-field approach suffers from the drawback that the corresponding wave
functions do not have sharp quantum numbers and, therefore, many results cannot
be compared directly with experimental data. In this article, we discuss
general group-theory techniques to restore the broken symmetries, and provide
detailed expressions on the restoration of translational, rotational, spin,
isospin, parity and gauge symmetries, where the latter corresponds to the
restoration of the particle number. In order to avoid the numerical complexity
of exact projection techniques, various approximation methods available in the
literature are examined. Applications of the projection methods are presented
for simple nuclear models, realistic calculations in relatively small
configuration spaces, nuclear energy density functional theory, as well as in
other mesoscopic systems. Further, unresolved problems in the application of
the symmetry restoration methods to the energy density functional theories are
highlighted in the present work.


  In clinical practice, one often needs to identify whether a patient is at
high risk of adverse outcomes after some key medical event. For example,
quantifying the risk of adverse outcomes after an acute cardiovascular event
helps healthcare providers identify those patients at the highest risk of poor
outcomes; i.e., patients who benefit from invasive therapies that can lower
their risk. Assessing the risk of adverse outcomes, however, is challenging due
to the complexity, variability, and heterogeneity of longitudinal medical data,
especially for individuals suffering from chronic diseases like heart failure.
In this paper, we introduce Event-Based Contrastive Learning (EBCL) - a method
for learning embeddings of heterogeneous patient data that preserves temporal
information before and after key index events. We demonstrate that EBCL can be
used to construct models that yield improved performance on important
downstream tasks relative to other pretraining methods. We develop and test the
method using a cohort of heart failure patients obtained from a large hospital
network and the publicly available MIMIC-IV dataset consisting of patients in
an intensive care unit at a large tertiary care center. On both cohorts, EBCL
pretraining yields models that are performant with respect to a number of
downstream tasks, including mortality, hospital readmission, and length of
stay. In addition, unsupervised EBCL embeddings effectively cluster heart
failure patients into subgroups with distinct outcomes, thereby providing
information that helps identify new heart failure phenotypes. The contrastive
framework around the index event can be adapted to a wide array of time-series
datasets and provides information that can be used to guide personalized care.


  We construct and analyze an $SU(6)\times SU(2)$ GUT. The model is k=1 string
embedable in the sense that we employ only chiral representations allowed at
the k=1 level of the associated Ka\v{c}-Moody Algebra. Both cases $SU(6)\times
SU(2)_{L}$ and $SU(6)\times SU(2)_{R}$ are realized. The model is characterized
by the $SU(6)\times SU(2) \to SU(4)\times SU(2)\times SU(2)$ breaking scale
$M_X$, and the $SU(4)\times SU(2)\times SU(2) \to SU(3)_{C}\times
SU(2)_{L}\times U(1)_{Y}$ breaking scale $M_{R}$ . The spectrum bellow $M_R$
includes an extra pair of charge-1/3 colour-triplets of mass $M_{I}\leq M_{R}$
that does not couple to matter fields and, possibly, an extra pair of
isodoublets. Above $M_{X}$ the SU(6) and SU(2) gauge couplings always unify at
a scale which can be taken to be the string unification scale $M_{s}\sim
5\times 10^{17} GeV$. The model has Yukawa coupling unification since quarks
and leptons obtain their masses from a single Yukawa coupling. Neutrinos obtain
acceptably small masses through a see-saw mechanism. Coloured triplets that
couple to matter fields are naturally split from the coexisting isodoublets
without the need of any numerical fine tuning.


  We considered the wave propagation between two medias. For description of
physical model choose nonlinear Schredinger equation with saturation parameter.
The solutions of respectively equation are found and analyzed.


  Volborthite offers an interesting example of a highly frustrated quantum
magnet in which ferromagnetic and antiferromagnetic interactions compete on
anisotropic kagome lattices. A recent density functional theory calculation has
provided a magnetic model based on coupled trimers, which is consistent with a
broad 1/3-magnetization plateau observed experimentally. Here we study the
effects of Dzyaloshinskii-Moriya (DM) interactions in volborthite. We derive an
effective model in which pseudospin-1/2 moments emerging on trimers form a
network of an anisotropic triangular lattice. Using the effective model, we
show that for a magnetic field perpendicular to the kagome layer, magnon
excitations from the 1/3-plateau feel a Berry curvature due to the DM
interactions, giving rise to a thermal Hall effect. Our magnon Bose gas theory
can explain qualitative features of the magnetization and the thermal Hall
conductivity measured experimentally. A further quantitative comparison with
experiment poses constraints on the coupling constants in the effective model,
promoting a quasi-one-dimensional picture. Based on this picture, we analyze
low-temperature magnetic phase diagrams using effective field theory, and point
out their crucial dependence on the field direction.


  We systematically investigate effect of oxygen isotope in
$(Pr_{1-x}Sm_x)_{0.7}Ca_{0.3}CoO_3$ which shows a crossover with x from
ferromagnetic metal to the insulator with spin-state transition. A striking
feature is that effect of oxygen isotope on the ferromagnetic transition is
negligible in the metallic phase, while replacing $^{16}O$ with $^{18}O$ leads
to a giant up-shift of the spin-state transition temperature ($T_s$) in the
insulating phase, especially $T_s$ shifts from 36 to 54 K with isotope
component $\alpha_S=-4.7$ for the sample with x=0.175. A metal-insulator
transition is induced by oxygen isotope exchange in the sample x=0.172 being
close to the insulating phase. The contrasting behaviors observed in the two
phases can be well explained by occurrence of static Jahn-Teller distortions in
the insulating phase, while absence of them in the metallic phase.


  The spectral energy distribution of the dark cloud LDN1622, as measured by
Finkbeiner using WMAP data, drops above 30GHz and is suggestive of a Boltzmann
cutoff in grain rotation frequencies, characteristic of spinning dust emission.
  LDN1622 is conspicuous in the 31 GHz image we obtained with the Cosmic
Background Imager, which is the first cm-wave resolved image of a dark cloud.
The 31GHz emission follows the emission traced by the four IRAS bands. The
normalised cross-correlation of the 31 GHz image with the IRAS images is higher
by 6.6sigma for the 12um and 25um bands than for the 60um and 100um bands:
C(12+25) = 0.76+/-0.02 and C(60+100) = 0.64+/-0.01.
  The mid-IR -- cm-wave correlation in LDN 1622 is evidence for very small
grain (VSG) or continuum emission at 26-36GHz from a hot molecular phase. In
dark clouds and their photon-dominated regions (PDRs) the 12um and 25um
emission is attributed to stochastic heating of the VSGs. The mid-IR and
cm-wave dust emissions arise in a limb-brightened shell coincident with the PDR
of LDN1622, where the incident UV radiation from the Ori OB1b association heats
and charges the grains, as required for spinning dust.


  We extend two well-known results in Ramsey theory from from $K_n$ to
arbitrary $n$-chromatic graphs. The first is a note of Erd\H os and Rado
stating that in every 2-coloring of the edges of $K_n$ there is a monochromatic
tree on $n$ vertices. The second is the theorem of Cockayne and Lorimer stating
that for positive integers satisfying $n_1=\max\{n_1,n_2,\dots,n_t\}$ and with
$n=n_1+1+\sum_{i=1}^t (n_i-1)$, the following holds. In every coloring of the
edges of $K_n$ with colors $1,2\dots,t$ there is a monochromatic matching of
size $n_i$ for some $i\in \{1,2,\dots,t\}$.


  This work proposes convolutional-sparse-coded dynamic mode decomposition
(CSC-DMD) by unifying extended dynamic mode decomposition (EDMD) and
convolutional sparse coding. EDMD is a data driven analysis method for
describing a nonlinear dynamical system with a linear time-evolution equation.
Compared with existing EDMD methods, CSC-DMD has an advantage of reflecting
spatial structure of the target. As an example, the proposed method is applied
to river bed shape estimation from the water surface observation. The
estimation problem is reduced to sparsity-aware restoration with a hard
constraint, which is given by the CSC-DMD prediction, where the algorithm is
derived by the primal-dual splitting method. A time series set of water surface
and bed shape measured through an experimental river setup is used to train and
test the system. From the result, the significance of the proposed method is
verified.


  We consider an interesting and practically important case of elastic domain
structure, which is the analogue of c/a domain pattern with 90$^\circ$ walls in
perovskites, and is solvable analytically for arbitrary misfit strain. There is
no critical thickness, below which the domain structure cannot exist, when the
"extrinsic" misfit is zero and the domains are of equal width. At the boundary
of polydomain-monodomain transition the period of the pattern diverges, as does
the dynamic stiffness of the domain structure. It is unlikely, therefore, that
one can achieve a softness of the dielectric response of the c/a elastic
domains in ferroelectric-ferroelastic thin films.


  We present the study of accessing unpolarized and linearly polarized gluon
TMDs in J/{\psi} and {\Upsilon}(1S) production in unpolarized proton-proton
collision at LHC, RHIC and AFTER energies. Non- relativistic QCD based color
octet model (COM) is used for estimating quarkonium production rates within
transverse momentum dependent factorization formalism. A comparison is drawn
between the experimental data and the transverse momentum distribution of
quarkonium obtained in COM and color evaporation model.


  High-throughput shotgun sequence data makes it possible in principle to
accurately estimate population genetic parameters without confounding by SNP
ascertainment bias. One such statistic of interest is the proportion of
heterozygous sites within an individual's genome, which is informative about
inbreeding and effective population size. However, in many cases, the available
sequence data of an individual is limited to low coverage, preventing the
confident calling of genotypes necessary to directly count the proportion of
heterozygous sites. Here, we present a method for estimating an individual's
genome-wide rate of heterozygosity from low-coverage sequence data, without an
intermediate step calling genotypes. Our method jointly learns the shared
allele distribution between the individual and a panel of other individuals,
together with the sequencing error distributions and the reference bias. We
show our method works well, first by its performance on simulated sequence
data, and secondly on real sequence data where we obtain estimates using low
coverage data consistent with those from higher coverage. We apply our method
to obtain estimates of the rate of heterozygosity for 11 humans from diverse
world-wide populations, and through this analysis reveal the complex dependency
of local sequencing coverage on the true underlying heterozygosity, which
complicates the estimation of heterozygosity from sequence data. We show
filters can correct for the confounding by sequencing depth. We find in
practice that ratios of heterozygosity are more interpretable than absolute
estimates, and show that we obtain excellent conformity of ratios of
heterozygosity with previous estimates from higher coverage data.


  We find analogues of the Willmore functional for each of the Thurston
geometries with 4-dimensional isometry group such that the CMC-spheres in these
geometries are critical points of these functionals.


  The Na-O anticorrelation seen in almost all globular clusters ever studied
using high-resolution spectroscopy is now generally explained by the primordial
pollution from the first generation of the intermediate-mass asymptotic giant
branch stars to the proto-stellar clouds of the second generation of stars.
However, the primordial pollution scenario may not tell the whole story for the
observed Na-O anticorrelations in globular clusters. Using the recent data by
Carretta and his collaborators, the different shapes of the Na-O
anticorrelations for red giant branch stars brighter than and fainter than the
red giant branch bump can be clearly seen. If the elemental abundance
measurements by Carretta and his collaborators are not greatly in error, this
variation in the Na-O anticorrelation against luminosity indicates an internal
deep mixing episode during the ascent of the low-mass red giant branch in
globular clusters. Our result implies that the multiple stellar population
division scheme solely based on [O/Fe] and [Na/Fe] ratios of a globular
cluster, which is becoming popular, is not reliable for stars brighter than the
red giant branch bump. Our result also suggests that sodium supplied by the
deep mixing may alleviate the sodium under-production problem within the
primordial asymptotic giant branch pollution scenario.


  We calculate high-order quasinormal modes with large imaginary frequencies
for electromagnetic and gravitational perturbations in nearly extremal
Schwarzschild-de Sitter spacetimes. Our results show that for low-order
quasinormal modes, the analytical approximation formula in the extremal limit
derived by Cardoso and Lemos is a quite good approximation for the quasinormal
frequencies as long as the model parameter $r_1\kappa_1$ is small enough, where
$r_1$ and $\kappa_1$ are the black hole horizon radius and the surface gravity,
respectively. For high-order quasinormal modes, to which corresponds
quasinormal frequencies with large imaginary parts, on the other hand, this
formula becomes inaccurate even for small values of $r_1\kappa_1$. We also find
that the real parts of the quasinormal frequencies have oscillating behaviors
in the limit of highly damped modes, which are similar to those observed in the
case of a Reissner-Nordstr{\" o}m black hole. The amplitude of oscillating
${\rm Re(\omega)}$ as a function of ${\rm Im}(\omega)$ approaches a non-zero
constant value for gravitational perturbations and zero for electromagnetic
perturbations in the limit of highly damped modes, where $\omega$ denotes the
quasinormal frequency. This means that for gravitational perturbations, the
real part of quasinormal modes of the nearly extremal Schwarzschild-de Sitter
spacetime appears not to approach any constant value in the limit of highly
damped modes. On the other hand, for electromagnetic perturbations, the real
part of frequency seems to go to zero in the limit.


  Immersive video, such as virtual reality (VR) and multi-view videos, is
growing in popularity. Its wireless streaming is an instance of general
multicast, extending conventional unicast and multicast, whose effective design
is still open. This paper investigates general rate splitting for general
multicast. Specifically, we consider a multi-carrier single-cell wireless
network where a multi-antenna base station (BS) communicates to multiple
single-antenna users via general multicast. We consider linear beamforming at
the BS and joint decoding at each user in the slow fading and fast fading
scenarios. In the slow fading scenario, we consider the maximization of the
weighted sum average rate, which is a challenging nonconvex stochastic problem
with numerous variables. To reduce computational complexity, we decouple the
original nonconvex stochastic problem into multiple nonconvex deterministic
problems, one for each system channel state. Then, we propose an iterative
algorithm for each deterministic problem to obtain a Karush-Kuhn-Tucker (KKT)
point using the concave-convex procedure (CCCP). In the fast fading scenario,
we consider the maximization of the weighted sum ergodic rate. This problem is
more challenging than the one for the slow fading scenario, as it is not
separable. First, we propose a stochastic iterative algorithm to obtain a KKT
point using stochastic successive convex approximation (SSCA) and the exact
penalty method. Then, we propose two low-complexity iterative algorithms to
obtain feasible points with promising performance for two cases of channel
distributions using approximation and CCCP. The proposed optimization framework
generalizes the existing ones for rate splitting for various types of services.
Finally, we numerically show substantial gains of the proposed solutions over
existing schemes in both scenarios.


  Collateralized debt obligation (CDO) has been one of the most commonly used
structured financial products and is intensively studied in quantitative
finance. By setting the asset pool into different tranches, it effectively
works out and redistributes credit risks and returns to meet the risk
preferences for different tranche investors. The copula models of various kinds
are normally used for pricing CDOs, and the Monte Carlo simulations are
required to get their numerical solution. Here we implement two typical CDO
models, the single-factor Gaussian copula model and Normal Inverse Gaussian
copula model, and by applying the conditional independence approach, we manage
to load each model of distribution in quantum circuits. We then apply quantum
amplitude estimation as an alternative to Monte Carlo simulation for CDO
pricing. We demonstrate the quantum computation results using IBM Qiskit. Our
work addresses a useful task in finance instrument pricing, significantly
broadening the application scope for quantum computing in finance.


  We present a convergence analysis of the penalty method applied to unilateral
contact problems in two and three space dimensions. We first consider, under
various regularity assumptions on the exact solution to the unilateral contact
problem, the convergence of the continuous penalty solution as the penalty
parameter $\varepsilon$ vanishes. Then, the analysis of the finite element
discretized penalty method is carried out. Denoting by $h$ the discretization
parameter, we show that the error terms we consider give the same estimates as
in the case of the constrained problem when the penalty parameter is such that
$\varepsilon = h$.


  We bring forth a consistent theory for the electron-mediated vibrational
intermode coupling that clarifies the microscopic mechanism behind the
vibrational relaxation of adsorbates on metal surfaces. Our analysis points out
the inability of state-of-the-art nonadiabatic theories to quantitatively
reproduce the experimental linewidth of the CO internal stretch mode on Cu(100)
and it emphasizes the crucial role of the electron-mediated phonon-phonon
coupling in this regard. The results demonstrate a strong electron-mediated
coupling between the internal stretch and low-energy CO modes, but also a
significant role of surface motion. Our nonadiabatic theory is also able to
explain the temperature dependence of the internal stretch phonon linewidth,
thus far considered a sign of the direct anharmonic coupling.


  In a quantum computer, creating superpositions of quantum bits (qubits) in
different states can lead to a speed-up over classical computers [1], but
quantum mechanics also allows for the superposition of quantum circuits [2]. In
fact, it has recently been theoretically predicted that superimposing quantum
circuits, each with a different gate order, could provide quantum computers
with an even further computational advantage [3-5]. Here, we experimentally
demonstrate this enhancement by applying two quantum gates in a superposition
of both possible orders to determine whether the two gates commute or
anti-commute. We are able to make this determination with only a single use (or
query) of each gate, while all quantum circuits with a fixed order of gates
would require at least two uses of one of the gates [3]. Remarkably, when the
problem is scaled to N gates, creating a superposition of quantum circuits is
likely to provide an exponential advantage over classical algorithms, and a
linear advantage over quantum algorithms with fixed gate order [4]. The new
resource that we exploit in our experiment can be interpreted as a
"superposition of causal orders". We demonstrate such a superposition could
allow some quantum algorithms to be implemented with an efficiency that is
unlikely to be achieved on a quantum computer with a fixed gate order.


  Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett.
\textbf{88}, 017901 (2001)], is a measure of the discrepancy between quantum
versions of two classically equivalent expressions for mutual information and
is found to be useful in quantification and application of quantum correlations
in mixed states. It is viewed as a key resource present in certain quantum
communication tasks and quantum computational models without containing much
entanglement. An early step toward the quantification of quantum discord in a
quantum state was by Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105,190502
(2010)] who introduced a geometric measure of quantum discord and derived an
explicit formula for any two-qubit state. Recently, Luo and Fu [Phys. Rev. A
\textbf{82}, 034302 (2010)] introduced a generic form of the geometric measure
of quantum discord for a bipartite quantum state. We extend these results and
find generic forms of the geometric measure of quantum discord and total
quantum correlations in a general N-partite quantum state. Further, we obtain
computable exact formulas for the geometric measure of quantum discord and
total quantum correlations in a N-qubit quantum state. The exact formulas for
the $N$-qubit quantum state are experimentally implementable.


  A fundamental theorem of linear algebra asserts that every basis for the
vector space $\mathbb{R}^n$ has $n$ elements. In this expository note we
present a theorem of W. G. Leavitt describing one way in which this invariant
basis number property can fail when one does linear algebra over rings, rather
than over fields. We give a proof of Leavitt's theorem that combines ideas of
P. M. Cohn and A. L. S. Corner into an elementary form requiring only a nodding
acquaintance with matrices and modular arithmetic.


  The aim of this note consists of the introduction of unfolding operator in
the Orlicz setting.


  In the realm of Tiny AI, we introduce ``You Only Look at Interested Cells"
(YOLIC), an efficient method for object localization and classification on edge
devices. Through seamlessly blending the strengths of semantic segmentation and
object detection, YOLIC offers superior computational efficiency and precision.
By adopting Cells of Interest for classification instead of individual pixels,
YOLIC encapsulates relevant information, reduces computational load, and
enables rough object shape inference. Importantly, the need for bounding box
regression is obviated, as YOLIC capitalizes on the predetermined cell
configuration that provides information about potential object location, size,
and shape. To tackle the issue of single-label classification limitations, a
multi-label classification approach is applied to each cell for effectively
recognizing overlapping or closely situated objects. This paper presents
extensive experiments on multiple datasets to demonstrate that YOLIC achieves
detection performance comparable to the state-of-the-art YOLO algorithms while
surpassing in speed, exceeding 30fps on a Raspberry Pi 4B CPU. All resources
related to this study, including datasets, cell designer, image annotation
tool, and source code, have been made publicly available on our project website
at https://kai3316.github.io/yolic.github.io


  Lutwak, Yang and Zhang [23] introduced the concept of Lp dual curvature
measure for convex bodies and star bodies, and studied the Minkowski problem.
We in this paper establish a new unified concept, in briefly, the (p,q)-mixed
quermassintegrals, via (p,q)-dual mixed curvature measure, and further have a
deep discussion on Minkowski problem with respect to the (p,q)-dual mixed
curvature measure. By the way, we derive at some important properties and
geometric inequalities for (p,q)-mixed quermassintegrals.


  The cobordism group $N(M^n)$ of codimension-one immersions in the
$n$-manifold $M^n$ has a natural filtration induced by any cellular
decomposition. The problem addressed in this paper is the explicit computation
of the graded group $gr^*N(M^n)$. We introduce some new invariants for
immersions enlightening the Atiyah-Hirzebruch spectral sequence associated to
$N(M)$, which are of combinatorial-geometric nature. Explicit computations are
developed for $n\leq7$, and the group structure is also investigated for
orientable 4-manifolds.


  The productivity of a magnitude $m$ event can be characterized in term of
triggered events of magnitude above $m-\Delta$: it is the number of direct
"descendants" $\nu_\Delta$ and the number of all "descendants" $V_\Delta$.
There is evidence in favour of the discrete exponential distribution for both
$\nu_\Delta$ and $V_\Delta$ with a dominant magnitude $m$ (the case of
aftershock cluster). We consider the general Epidemic Type Aftershock Sequence
(ETAS) model adapted to any distribution of $\nu_\Delta$. It turns out that the
branching structure of the model excludes the possibility of having exponential
distributions for both productivity characteristics at once. We have
analytically investigated the features of the $V_\Delta$ distribution within a
wide class of ETAS models. We show the fundamental difference in tail behavior
of the $V_\Delta$-distributions for general-type clusters and clusters with a
dominant initial magnitude: the tail is heavy in the former case and light in
the latter. The real data demonstrate the possibilities of this kind. This
result provides theoretical and practical constraints for distributional
analysis of $V_\Delta$.


  Linear codes with few weights have applications in data storage systems,
secret
  sharing schemes, and authentication codes. In this paper, some kinds of p-ary
linear codes
  with few weights are constructed by use of the given de ning set, where p is
a prime.
  Their weight distributions are determined based on Kloosterman sums over nite
elds. In
  addition, some linear codes we given is minimal.


  [abridged abstract]
  Low amplitude (~=0.5%) 29-s oscillations have been detected in HST/FOS
eclipse observations of the nova-like cataclysmic variable UX UMa. These are
the same dwarf nova-type oscillations that were originally discovered in this
system by Warner & Nather in 1972. The oscillations are sinusoidal to within
the small observational errors and undergo an approximately -360 degree phase
shift during eclipses. Their amplitudes are highest at pre-eclipse orbital
phases and exhibit a rather gradual eclipse whose shape is roughly similar to
UX~UMa's overall light curve. Oscillation spectra derived from pre-eclipse data
segments are extremely blue, whereas mid-eclipse oscillation spectra are much
redder.
  We suggest that the ultimate source of the oscillations is a hot, compact
region near disk center, but that a significant fraction of the observed,
modulated flux is due to reprocessing of the light emitted by this source in
the accretion disk atmosphere. The compact source is occulted at orbital phases
near mid-eclipse, leaving only part of the more extended reprocessing region(s)
to produce the weak oscillations that persist even at conjunction.
  The highly sinusoidal oscillation pulse shape does not permit the
identification of the compact component in this model with emission produced by
a rotating disturbance in the inner disk or in an equatorial boundary layer,
and a standard intermediate polar model can also be ruled out. A model invoking
magnetically controlled accretion onto differentially rotating WD surface
layers may be viable, but needs more theoretical work.


  The Bandwidth theorem of B\"ottcher, Schacht and Taraz gives a condition on
the minimum degree of an $n$-vertex graph $G$ that ensures $G$ contains every
$r$-chromatic graph $H$ on $n$ vertices of bounded degree and of bandwidth
$o(n)$, thereby proving a conjecture of Bollob\'as and Koml\'os. In this paper
we prove a version of the Bandwidth theorem for locally dense graphs. Indeed,
we prove that every locally dense $n$-vertex graph $G$ with $\delta (G) >
(1/2+o(1))n$ contains as a subgraph any given (spanning) $H$ with bounded
maximum degree and sublinear bandwidth.


  We present a classical enhancement to improve the accuracy of the Hybrid
variant (Hybrid HHL) of the quantum algorithm for solving liner systems of
equations proposed by Harrow, Hassidim, and Lloyd (HHL). We achieve this by
using higher precision quantum estimates of the eigenvalues relevant to the
linear system, and an enhanced classical processing step to guide the
eigenvalue inversion part of Hybrid HHL. We show that eigenvalue estimates with
just two extra bits of precision results in tighter error bounds for our
Enhanced Hybrid HHL compared to HHL. We also show that our enhancement reduces
the error of Hybrid HHL by an average of 57 percent on an ideal quantum
processor for a representative sample of 2x2 systems. On IBM Hanoi and IonQ
Aria-1 hardware, we see that the error of Enhanced Hybrid HHL algorithm is on
average 13 percent and 20 percent (respecitvely) less than that of HHL for a
similar set of 2x2 systems. Finally, we use simulated eigenvalue estimates to
perform an inversion of a 4x4 matrix on IonQ Aria-1 with a fidelity of 0.61. To
our knowledge this is the largest HHL implementation with a fidelity greater
than 0.5.


  We study two types of models for the superconducting layered nitride
$\beta$-MNCl(M=Hf,Zr); a single band model on a triangular lattice, and a two
band model on a honeycomb lattice. We find that the former model does not
suffice as an effecitive model, while the latter one can be a good candidate.
We propose from the study on the two band model a possibility of spin
fluctuation mediated $d+id'$-wave superconductivity in the doped $\beta$-MNCl.
We show that the relatively high $T_c$ obtained in the doped band insulator is
a characteristic feature of the spin fluctuation mediated superconductivity on
a honeycomb lattice. We also find that the gap anisotropy on the Fermi surface
strongly increases upon increasing the doping concentration, and the inter
layer hopping suppresses superconductivity. These results are in qualitative
agreement with the experimental findings.


  The statistical supervised learning framework assumes an input-output set
with a joint probability distribution that is reliably represented by the
training dataset. The learner is then required to output a prediction rule
learned from the training dataset's input-output pairs. In this work, we
provide meaningful insights into the asymptotic equipartition property (AEP)
\citep{Shannon:1948} in the context of machine learning, and illuminate some of
its potential ramifications for few-shot learning. We provide theoretical
guarantees for reliable learning under the information-theoretic AEP, and for
the generalization error with respect to the sample size. We then focus on a
highly efficient recurrent neural net (RNN) framework and propose a
reduced-entropy algorithm for few-shot learning. We also propose a mathematical
intuition for the RNN as an approximation of a sparse coding solver. We verify
the applicability, robustness, and computational efficiency of the proposed
approach with image deblurring and optical coherence tomography (OCT) speckle
suppression. Our experimental results demonstrate significant potential for
improving learning models' sample efficiency, generalization, and time
complexity, that can therefore be leveraged for practical real-time
applications.


  We investigate a network of coupled superconducting transmission line
resonators, each of them made nonlinear with a capacitively shunted Josephson
junction coupling to the odd flux modes of the resonator. The resulting
eigenmode spectrum shows anticrossings between the plasma mode of the shunted
junction and the odd resonator modes. Notably, we find that the combined device
can inherit the complete nonlinearity of the junction, allowing for a
description as a harmonic oscillator with a Kerr nonlinearity. Using a dc SQUID
instead of a single junction, the nonlinearity can be tuned between 10 kHz and
4 MHz while maintaining resonance frequencies of a few gigahertz for realistic
device parameters. An array of such nonlinear resonators can be considered a
scalable superconducting quantum simulator for a Bose-Hubbard Hamiltonian. The
device would be capable of accessing the strongly correlated regime and be
particularly well suited for investigating quantum many-body dynamics of
interacting particles under the influence of drive and dissipation.


  K. Borsuk in 1979, in the Topological Conference in Moscow, introduced the
concept of the capacity of a compactum. In this paper, we compute the capacity
of the product of two spheres of the same or different dimensions and the
capacity of lense spaces. Also, we present an upper bound for the capacity of a
$\mathbb{Z}_n$-complex, i.e., a connected finite 2-dimensional CW-complex with
finite cyclic fundamental group $\mathbb{Z}_n$.


  The paper studies the problem of constructing nonparametric simultaneous
confidence bands with nonasymptotic and distribition-free guarantees. The
target function is assumed to be band-limited and the approach is based on the
theory of Paley-Wiener reproducing kernel Hilbert spaces. The starting point of
the paper is a recently developed algorithm to which we propose three types of
improvements. First, we relax the assumptions on the noises by replacing the
symmetricity assumption with a weaker distributional invariance principle.
Then, we propose a more efficient way to estimate the norm of the target
function, and finally we enhance the construction of the confidence bands by
tightening the constraints of the underlying convex optimization problems. The
refinements are also illustrated through numerical experiments.


  We describe a dynamically polarized target that has been utilized for two
electron scattering experiments in Hall A at Jefferson Lab. The primary
components of the target are a new, high cooling power 4He evaporation
refrigerator, and a re-purposed, superconducting split-coil magnet. It has been
used to polarize protons in irradiated NH3 at a temperature of 1 K and at
fields of 2.5 and 5.0 Tesla. The performance of the target material in the
electron beam under these conditions will be discussed. Maximum polarizations
of 28% and 95% were obtained at those fields, respectively. To satisfy the
requirements of both experiments, the magnet had to be routinely rotated
between angles of 0, 6, and 90 degrees with respect to the incident electron
beam. This was accomplished using a new rotating vacuum seal which permits
rotations to be performed in only a few minutes.


  Let $\pi$ be a Speh module of $\mathbf{GL}(2n,\mathbb{R})$ based on a
discrete series of $\textbf{GL}(2,\mathbb{R})$. The aim of this paper is to
build a chain complex of $\pi$ by direct sum of auto-duals standard modules,
\begin{align}\label{eq:abstract} 0\rightarrow \pi\rightarrow X_{0}\rightarrow
\cdots\rightarrow X_{i}\xrightarrow{\phi_{i}}
X_{i+1}\rightarrow\cdots\rightarrow 0. \end{align} The standard modules in the
previous chain are the auto-duals standard modules which occurs in the
Johnson's resolution of $\pi$, they are parameterized by the set of involutions
$\mathfrak{I}_{n}$ of the symmetric group $\mathfrak{S}_{n}$. Under this
parametrization one can show that the inversion of the Bruhat order in
$\mathfrak{I}_{n}$ coincide with the Vogan order defined over the set of
irreducible representations of $\mathbf{GL}(\mathbb{R})$. This allows us to
reduce the construction of the chain complex to the study of combinatorial
properties of the Bruhat order on $\mathfrak{I}_{n}$. In the last chapter we
show that the chain complex of $\pi$, for $n\leq 4$, is $\theta$-exact i.e. the
twisted trace of $\ker\phi_{i+1}/\text{im}\phi_{i}$ is trivial. This allows us
to write the twisted trace of $\pi$ as a linear combination of twisted traces
of standard modules, wich implies for $\pi$ one of the the main results of the
paper, $\textit{Paquets d'Arthur des Groupes classiques et unitaires}$.


  We point out a redundancy in the operator structure of the pionless effective
field theory which dramatically simplifies computations. This redundancy is
best exploited by using dibaryon fields as fundamental degrees of freedom. In
turn, this suggests a new power counting scheme which sums range corrections to
all orders. We explore this method with a few simple observables: the deuteron
charge form factor, n p -> d gamma, and Compton scattering from the deuteron.
Higher dimension operators involving electroweak gauge fields are not
renormalized by the s-wave strong interactions, and therefore do not scale with
inverse powers of the renormalization scale. Thus, naive dimensional analysis
of these operators is sufficient to estimate their contribution to a given
process.


  We discuss how the Schrodinger equation can predict Born statistics for
evolution to eigenstates when a potential energy causes the quantum system to
undergo a random walk. Specifically, we show how the random walk results in a
quantum state during a measurement evolving arbitrarily close to eigenstates
with the expected Born probabilities. The random walk is described in terms of
the time-dependent unitary matrix U(t) that has a one-to-one equivalence to the
external potential in Schrodinger's equation. Assuming the analysis is correct,
some interesting questions arise. Are any measurements described by such
physics? Can a measurement apparatus be designed that results in measurement
statistics that deviate from Born statistics while still being a reliable
measurement? For quantum information systems, are there implications for qubit
noise and algorithm design? This is a draft of a work in progress, and
respectful questions, comments, suggestions, or interest in informal or formal
collaboration are welcome.


  This Letter describes a model-independent search for production of new
resonant states in photon-jet events in 2.11 fb^-1 of proton-proton collisions
at sqrt(s) = 7 TeV. We compare the photon-jet mass distribution to a
data-driven background estimate and find consistency with the background
hypothesis. Given the lack of evidence for a signal, we set 95% CL limits on
generic Gaussian-shape signals and on a benchmark excited-quark (q*) model,
excluding 2 TeV Gaussian resonances with cross section times branching ratio
times acceptance times efficiency near 5 fb and excluding q* masses below 2.46
TeV, respectively.


  We derive a combinatorial equilibrium for bounded juggling patterns with a
random, $q$-geometric throw distribution. The dynamics are analyzed via rook
placements on staircase Ferrers boards, which leads to a steady-state
distribution containing $q$-rook polynomial coefficients and $q$-Stirling
numbers of the second kind. We show that the equilibrium probabilities of the
bounded model can be uniformly approximated with the equilibrium probabilities
of a corresponding unbounded model. This observation leads to new limit
formulae for $q$-analogues.
  Keywords: juggling pattern; $q$-Stirling number of the second kind; Ferrers
board; Markov process; combinatorial equilibrium


  There is a persistent $H_0$-tension, now at more than $\gtrsim 4\sigma$
level, between the local distance ladder value and the \emph{Planck} cosmic
microwave background measurement, in the context of flat $\Lambda$CDM model. We
reconstruct $H(z)$ in a cosmological-model-independent way using three
low-redshift distance probes including the latest data from baryon acoustic
oscillation, Type Ia supernova and four gravitational lensing Time-Delay
observations. We adopt general parametric models of $H(z)$ and assume a
Gaussian prior on the sound horizon at drag epoch, $r_{\mathrm s}$, from
\emph{Planck} measurement. The reconstructed $H_0$ using Pantheon SN Ia and BAO
data are consistent with the \emph{Planck} flat $\Lambda$CDM value. When
including the GLTD data, $H_0$ increases mildly, yet remaining discrepant with
the local measurement at $\sim 2.5\sigma$ level. Our reconstructions being
blind to the dark sectors at low redshift, we reaffirm the earlier claims that
the Hubble tension is not likely to be solved by modifying the energy budget of
the low-redshift universe. We further forecast the constraining ability of
future realistic mock BAO data from DESI and GLTD data from LSST, combining
which, we anticipate that the uncertainty of the inferred $H_0$ would be
improved by $\sim 38\%$, reaching $\sigma_{H_0} \approx 0.56$ uncertainty
level.


This paper is superseded by arXiv:1106.3363.


  Q-ball is a non-topological soliton whose stability is ensured by global U(1)
symmetry. We study a Q-ball which arises in the Affleck-Dine mechanism for
baryogenesis and consider its possible instability due to U(1) breaking term
($A$-term) indispensable for successful baryogenesis. It is found that the
instability destroys the Q-ball if its growth rate exceeds inverse of the
typical relaxation time scale of the Q-ball. However, the instability is not so
strong as it obstructs the cosmological formation of the Q-balls.


  The KATRIN experiment is going to search for the mass of the electron
antineutrino down to 0.2 eV/c^2. In order to reach this sensitivity the
background rate has to be understood and minimised to 0.01 counts per second.
One of the background sources is the unavoidable Penning trap for electrons due
to the combination of the electric and magnetic fields between the pre- and the
main spectrometer at KATRIN. In this article we will show that by sweeping a
conducting wire periodically through such a particle trap stored particles can
be removed, an ongoing discharge in the trap can be stopped, and the count rate
measured with a detector looking at the trap is reduced.


  The quantum dynamics of quarks, gluons and the scalar degrees of freedom
associated with the non-linear regime of the non-linear gauge is derived. We
discuss the subtleties in quantizing in a stochastic background. Then we show
in detail that the stochastic average of the Yang-Mills action is only
dependent on the gluon and not on the scalars thus proving that the scalars are
non-propagating. Integrating out the scalars from the stochastically averaged
fermion action leads to fermions that decline exponentially. Finally, we derive
the effective action of the gluons and fermions resulting from stochastic
averaging. We show that it leads to a confining four-fermi interaction.


  The classical motion of gliding dislocation lines in slip planes of
crystalline solid helium leads to plastic deformation even at temperatures far
below the Debye temperature and can affect elastic properties. In this work we
argue that the gliding of dislocations and plasticity may be the origin of many
observed elastic anomalies in solid He-4, which have been argued to be
connected to supersolidity. We present a dislocation motion model that
describes the stress-strain $\tau$-$\epsilon$ curves and work hardening rate
$d\tau/d\epsilon$ of a shear experiment performed at constant strain rate
$\dot{\epsilon}$ in solid helium. The calculated $d\tau/d\epsilon$ exhibits
strong softening with increasing temperature due to the motion of dislocations,
which mimics anomalous softening of the elastic shear modulus $\mu$. In the
same temperature region the motion of dislocations causes dissipation with a
prominent peak.


  The reconstruction of a smooth field onto a fixed grid is a necessary step
for direct comparisons to various real-world observations. Projecting SPH data
onto a fixed grid becomes challenging in adaptive environments, where some
particles may have smoothing lengths far below the grid size, whilst others are
resolved by thousands of pixels. In this paper we show how the common approach
of treating particles below the grid size as Monte Carlo tracers of the field
leads to significant reconstruction errors, and despite good convergence
properties is unacceptable for use in synthetic observations in astrophysics.
We propose a new method, where particles smaller than the grid size are
`blitted' onto the grid using a high-resolution pre-calculated kernel, and
those close to the grid size are subsampled, that allows for converged
predictions for projected quantities at all grid sizes.


  Recent work demonstrates that, after instruction tuning, Code Large Language
Models (Code LLMs) can obtain impressive capabilities to address a wide range
of code-related tasks. However, current instruction tuning methods for Code
LLMs mainly focus on the traditional code generation task, resulting in poor
performance in complex multi-task scenarios. In this paper, we concentrate on
multiple code-related tasks and present WaveCoder, a series of Code LLMs
trained with Widespread And Versatile Enhanced instruction data. To enable the
models to tackle complex code-related tasks, we propose a method to stably
generate diverse, high-quality instruction data from open source code dataset
in multi-task scenarios and obtain CodeSeaXDataset, a dataset comprising 19,915
instruction instances across 4 code-related tasks, which is aimed at improving
the generalization ability of Code LLM. Our experiments demonstrate that
WaveCoder models significantly outperform other open-source models in terms of
the generalization ability across different code-related tasks. Moreover,
WaveCoder-Ultra-6.7B presents the state-of-the-art generalization abilities on
a wide range of code-related tasks.


  We show how the Fuss-Catalan numbers $ \frac{1}{p n+1}\binom{pn+1}{n}$ enter
different problems of counting simple and multiple planar partitions.


  Three-level quantum systems have formed a cornerstone of quantum optics since
the discovery of coherent population trapping (CPT) and electromagnetically
induced transparency. Key to these phenomena is quantum interference, which
arises if two of the three available transitions are coherently driven at
well-controlled amplitudes and phases. The additional coherent driving of the
third available transition would form a closed-contour interaction (CCI) from
which fundamentally new phenomena would emerge, including phase-controlled CPT
and one atom interferometry. However, due to the difficulty in experimentally
realising a fully coherent CCI, such aspects of three-level systems remain
unexplored as of now. Here, we exploit recently developed methods for coherent
driving of single Nitrogen-Vacancy (NV) electronic spins to implement highly
coherent CCI driving. Our experiments reveal phase-controlled, single spin
quantum interference fringes, reminiscent of electron dynamics on a triangular
lattice, with the driving field phases playing the role of a synthetic magnetic
flux. We find that for suitable values of this phase, CCI driving leads to
efficient coherence protection of the NV spin, yielding a nearly two orders of
magnitude improvement of the coherence time, even for moderate drive strengths
<~1MHz. Our results establish CCI driving as a novel paradigm in coherent
control of few-level systems that offers attractive perspectives for
applications in quantum sensing or quantum information processing.


  In vertebrates, insufficient availability of calcium and phosphate ions in
extracellular fluids leads to loss of bone density and neuronal
hyper-excitability. To counteract this problem, calcium ions are present at
high concentrations throughout body fluids -- at concentrations exceeding the
saturation point. This condition leads to the opposite situation where unwanted
mineral sedimentation may occur. Remarkably, ectopic or out-of-place
sedimentation into soft tissues is rare, in spite of the thermodynamic driving
factors. This fortunate fact is due to the presence of auto-regulatory proteins
that are found in abundance in bodily fluids. Yet, many important inflammatory
disorders such as atherosclerosis and osteoarthritis are associated with this
undesired calcification. Hence, it is important to gain an understanding of the
regulatory process and the conditions under which it can go awry. In this
manuscript, we adapt mean-field classical nucleation theory to the case of
surface-shielding in order to study the regulation of sedimentation of calcium
phosphate salts in biological tissues through the mechanism of post-nuclear
shielding of nascent mineral particles by binding proteins. We develop a
mathematical description of this phenomenon using a countable system of
hyperbolic partial differential equations. A critical concentration of
regulatory protein is identified as a function of the physical parameters that
describe the system.


  Self-testing is a method to infer the underlying physics of a quantum
experiment in a black box scenario. As such it represents the strongest form of
certification for quantum systems. In recent years a considerable self-testing
literature has been developed, leading to progress in related
device-independent quantum information protocols and deepening our
understanding of quantum correlations. In this work we give a thorough and
self-contained introduction and review of self-testing and its application to
other areas of quantum information.


  We propose an analytic method to calculate the matter field K\"ahler metric
in heterotic compactifications on smooth Calabi-Yau three-folds with Abelian
internal gauge fields. The matter field K\"ahler metric determines the
normalisations of the ${\cal N}=1$ chiral superfields, which enter the
computation of the physical Yukawa couplings. We first derive the general
formula for this K\"ahler metric by a dimensional reduction of the relevant
supergravity theory and find that its T-moduli dependence can be determined in
general. It turns out that, due to large internal gauge flux, the remaining
integrals localise around certain points on the compactification manifold and
can, hence, be calculated approximately without precise knowledge of the
Ricci-flat Calabi-Yau metric. In a final step, we show how this local result
can be expressed in terms of the global moduli of the Calabi-Yau manifold. The
method is illustrated for the family of Calabi-Yau hypersurfaces embedded in
$\mathbb{P}^1\times\mathbb{P}^3$ and we obtain an explicit result for the
matter field K\"ahler metric in this case.


  We present the result of a photometric and Keck-LRIS spectroscopic study of
dwarf galaxies in the core of the Perseus Cluster, down to a magnitude of M_B =
-12.5. Spectra were obtained for twenty-three dwarf-galaxy candidates, from
which we measure radial velocities and stellar population characteristics from
absorption line indices. From radial velocities obtained using these spectra we
confirm twelve systems as cluster members, with the remaining eleven as
non-members. Using these newly confirmed cluster members, we are able to extend
the confirmed colour-magnitude relation for the Perseus Cluster down to M_B =
-12.5. We confirm an increase in the scatter about the colour magnitude
relationship below M_B = -15.5, but reject the hypothesis that very red dwarfs
are cluster members. We measure the faint-end slope of the luminosity function
between M_B = -18 and M_B = -12.5, finding alpha = -1.26 \pm 0.06, which is
similar to that of the field. This implies that an overabundance of dwarf
galaxies does not exist in the core of the Perseus Cluster. By comparing metal
and Balmer absorption line indices with alpha-enhanced single stellar
population models, we derive ages and metallicities for these newly confirmed
cluster members. We find two distinct dwarf elliptical populations: an old,
metal poor population with ages ~ 8 Gyr and metallicities [Fe/H] < -0.33, and a
young, metal rich population with ages < 5 Gyr and metallicities [Fe/H] >
-0.33. Dwarf galaxies in the Perseus Cluster are therefore not a simple
homogeneous population, but rather exhibit a range in age and metallicity.


  A primary challenge in abstractive summarization is hallucination -- the
phenomenon where a model generates plausible text that is absent in the source
text. We hypothesize that the domain (or topic) of the source text triggers the
model to generate text that is highly probable in the domain, neglecting the
details of the source text. To alleviate this model bias, we introduce a
decoding strategy based on domain-conditional pointwise mutual information.
This strategy adjusts the generation probability of each token by comparing it
with the token's marginal probability within the domain of the source text.
According to evaluation on the XSUM dataset, our method demonstrates
improvement in terms of faithfulness and source relevance. The code is publicly
available at \url{https://github.com/qqplot/dcpmi}.


  Sequences of Genocchi numbers of the first and second kind are considered.
For these numbers, an approach based on their representation using sequences of
polynomials is developed. Based on this approach, for these numbers some
identities generalizing the known identities are constructed.


  Poor air quality can have a significant impact on human health. The National
Oceanic and Atmospheric Administration (NOAA) air quality forecasting guidance
is challenged by the increasing presence of extreme air quality events due to
extreme weather events such as wild fires and heatwaves. These extreme air
quality events further affect human health. Traditional methods used to correct
model bias make assumptions about linearity and the underlying distribution.
Extreme air quality events tend to occur without a strong signal leading up to
the event and this behavior tends to cause existing methods to either under or
over compensate for the bias. Deep learning holds promise for air quality
forecasting in the presence of extreme air quality events due to its ability to
generalize and learn nonlinear problems. However, in the presence of these
anomalous air quality events, standard deep network approaches that use a
single network for generalizing to future forecasts, may not always provide the
best performance even with a full feature-set including geography and
meteorology. In this work we describe a method that combines unsupervised
learning and a forecast-aware bi-directional LSTM network to perform bias
correction for operational air quality forecasting using AirNow station data
for ozone and PM2.5 in the continental US. Using an unsupervised clustering
method trained on station geographical features such as latitude and longitude,
urbanization, and elevation, the learned clusters direct training by
partitioning the training data for the LSTM networks. LSTMs are forecast-aware
and implemented using a unique way to perform learning forward and backwards in
time across forecasting days. When comparing the RMSE of the forecast model to
the RMSE of the bias corrected model, the bias corrected model shows
significant improvement (27\% lower RMSE for ozone) over the base forecast.


  Recently, generated images could reach very high quality, even human eyes
could not tell them apart from real images. Although there are already some
methods for detecting generated images in current forensic community, most of
these methods are used to detect a single type of generated images. The new
types of generated images are emerging one after another, and the existing
detection methods cannot cope well. These problems prompted us to propose a
scalable framework for multi-class classification based on deep metric
learning, which aims to classify the generated images finer. In addition, we
have increased the scalability of our framework to cope with the constant
emergence of new types of generated images, and through fine-tuning to make the
model obtain better detection performance on the new type of generated data.