  NASA's Solar Dynamics Observatory (SDO) was launched 11 February 2010 with 3
instruments on board, including the Helioseismic and Magnetic Imager (HMI).
Since beginning normal operations on 1 May 2010, HMI has observed the Sun's
entire visible disk almost continuously. HMI collects sequences of polarized
filtergrams taken at a fixed cadence with two 4096 x 4096 cameras from which
are computed arcsecond-resolution maps of photospheric observables: the
line-of-sight (LoS) velocity and magnetic field, continuum intensity, line
width, line depth, and the Stokes polarization parameters, I Q U V, at 6
wavelengths. Two processing pipelines implemented at the SDO Joint Science
Operations Center (JSOC) at Stanford University compute observables from
calibrated Level-1 filtergrams. One generates LoS quantities every 45s, and the
other, primarily for the vector magnetic field, computes averages on a 720s
cadence. Corrections are made for static and temporally changing CCD
characteristics, bad pixels, image alignment and distortion, polarization
irregularities, filter-element uncertainty and non-uniformity, as well as
Sun-spacecraft velocity. This report explains issues affecting the resulting
physical quantities, describes the impact of regular updates to the instrument
calibration, and shows how the computations are optimized for actual HMI
observations. During the 5 years of the SDO prime mission, regular calibration
sequences have been used to regularly improve and update the instrument
calibration and to monitor instrument changes. The instrument more than
satisfies the original specifications for data quality and continuity. The
procedures described here still have significant room for improvement. The most
significant remaining systematic errors are associated with the spacecraft
orbital velocity.


  We show that the more energetic superluminal neutrinos with quadratically
dispersed superluminalities \delta=\beta^2-1, for \beta=v/c where v is the
neutrino velocity, also lose significant energy to radiation to the \nu+e^-+e^+
final state in travelling from CERN to Gran Sasso as has been shown to occur
for those with constant superluminality by Cohen and Glashow if indeed \delta
\simeq 5\times 10^{-5}. In addition, we clarify the dependence of such
radiative processes on the size of the superluminality.


  In recent years, two-dimensional boron sheets (borophene) have been
experimentally synthesized and theoretically observed as promising conductor or
transistor with novel thermal and electronic properties. We first give a
general survey of some notable electronic properties of borophene, including
the superconductivity and topological characters. We then mainly review the
basic approaches, thermal transport, as well as the mechanical properties of
borophene with different configurations. This review gives a general
understanding of some of the crucial thermal transport and electronic
properties of borophene, and also calls for further experimental investigations
and applications on certain scientific community.


  The Wilkinson Microwave Anisotropy Probe (WMAP) has measured lower amplitudes
for the temperature quadrupole and octopole anisotropies than expected in the
best fitting (concordance) Lambda-dominated cold dark matter cosmology. Some
authors have argued that this discrepancy may require new physics. Yet the
statistical significance of this result is not clear. Some authors have applied
frequentist arguments and claim that the discrepancy would occur by chance
about 1 time in 700 if the concordance model is correct. Other authors have
used Bayesian arguments to claim that the data show marginal evidence for new
physics. I investigate these confusing and apparently conflicting claims using
a frequentist analysis and a simplified Bayesian analysis. I conclude that the
WMAP results are consistent with the concordance Lambda CDM model.


  Relaxometry studies in preterm and at-term newborns have provided insight
into brain microstructure, thus opening new avenues for studying normal brain
development and supporting diagnosis in equivocal neurological situations.
However, such quantitative techniques require long acquisition times and
therefore cannot be straightforwardly translated to in utero brain
developmental studies. In clinical fetal brain magnetic resonance imaging
routine, 2D low-resolution T2-weighted fast spin echo sequences are used to
minimize the effects of unpredictable fetal motion during acquisition. As
super-resolution techniques make it possible to reconstruct a 3D
high-resolution volume of the fetal brain from clinical low-resolution images,
their combination with quantitative acquisition schemes could provide fast and
accurate T2 measurements. In this context, the present work demonstrates the
feasibility of using super-resolution reconstruction from conventional
T2-weighted fast spin echo sequences for 3D isotropic T2 mapping. A
quantitative magnetic resonance phantom was imaged using a clinical T2-weighted
fast spin echo sequence at variable echo time to allow for super-resolution
reconstruction at every echo time and subsequent T2 mapping of samples whose
relaxometric properties are close to those of fetal brain tissue. We
demonstrate that this approach is highly repeatable, accurate and robust when
using six echo times (total acquisition time under 9 minutes) as compared to
gold-standard single-echo spin echo sequences (several hours for one single 2D
slice).


  This article is concerned with a regularity analysis of parametric operator
equations with a perspective on uncertainty quantification. We study the
regularity of mappings between Banach spaces near branches of isolated
solutions that are implicitly defined by a residual equation. Under $s$-Gevrey
assumptions on on the residual equation, we establish $s$-Gevrey bounds on the
Fr\'echet derivatives of the local data-to-solution mapping. This abstract
framework is illustrated in a proof of regularity bounds for a semilinear
elliptic partial differential equation with parametric and random field input.


  $\newcommand{\eps}{\varepsilon}$ In this paper, we consider two important
problems defined on finite metric spaces, and provide efficient new algorithms
and approximation schemes for these problems on inputs given as graph shortest
path metrics or high-dimensional Euclidean metrics. The first of these problems
is the greedy permutation (or farthest-first traversal) of a finite metric
space: a permutation of the points of the space in which each point is as far
as possible from all previous points. We describe randomized algorithms to find
$(1+\eps)$-approximate greedy permutations of any graph with $n$ vertices and
$m$ edges in expected time $O(\eps^{-1}(m+n)\log n\log(n/\eps))$, and to find
$(1+\eps)$-approximate greedy permutations of points in high-dimensional
Euclidean spaces in expected time $O(\eps^{-2} n^{1+1/(1+\eps)^2 + o(1)})$.
Additionally we describe a deterministic algorithm to find exact greedy
permutations of any graph with $n$ vertices and treewidth $O(1)$ in worst-case
time $O(n^{3/2}\log^{O(1)} n)$. The second of the two problems we consider is
distance selection: given $k \in [ \binom{n}{2} ]$, we are interested in
computing the $k$th smallest distance in the given metric space. We show that
for planar graph metrics one can approximate this distance, up to a constant
factor, in near linear time.


  It is well established that the occurrence of superconductivity in iron
pnictides is closely related to the tetragonal to orthorhombic structural and
antiferromagnetic (AFM) phase transitions. It, however, has not been clear
whether the same scenario is appropriate for iron chalcogenide counterparts due
to the absence of parent compounds for the latter family of superconductors.
Here, we report the synthesis and structure determination of two novel phases
in ethylenediamine intercalated FeSe, one is tetragonal and the other
orthorhombic in room temperature, which can be stabilized with neutral spacer
layers. Both phases can be regarded as the parent compounds for
superconductivity as they are non-superconducting (non-SC) in pristine form and
superconducting (SC) with Tc up to 38K and 46K, respectively after Na doping,
and the switch between SC and no-SC is reversible. Moreover, the two non-SC
parent compounds show no evidence of long-range magnetic ordering down to 2K,
only with dynamic spin fluctuations at low temperatures, suggesting that no
competition between SC and AFM ordering. Our results reveal that undoped iron
selenides are quantum paramagnetic in ground state, implying that they are
distinct from their pnictide counterparts in pairing mechanism.


  In this work we compute the rates and numbers of different types of stars and
phenomena (SNe, novae, white dwarfs, merging neutron stars, black holes) that
contributed to the chemical composition of the Solar System. Stars die and
restore the newly formed elements into the interstellar gas. This process is
called "chemical evolution". In particular, we analyse the death rates of stars
of all masses, dying either quiescently or explosively. These rates and total
star numbers are computed in the context of a revised version of the two-infall
model for the chemical evolution of the Milky Way, which reproduces fairly well
the observed abundance patterns of several chemical species, as well as the
global solar metallicity. We compute also the total number of stars ever born
and still alive as well as the number of stars born up to the formation of the
Solar System and with a mass and metallicity like the Sun. This latter number
will account for all the possible existing Solar Systems which can host life in
the solar vicinity. Among all the stars (from 0.8 to 100 M$_{\odot}$) born and
died from the beginning up to the Solar System formation epoch, which
contributed to its chemical composition, 93.00$\%$ are represented by stars
dying as single white dwarfs (without interacting significantly with a
companion star) and originating in the mass range 0.8-8 M$_{\odot}$, while
5.24$\%$ are neutron stars and 0.73$\%$ are black holes, both originating from
SNe core-collapse (M>8 M$_{\odot}$); 0.64$\%$ are Type Ia SNe and 0.40$\%$ are
nova systems, both originating from the same mass range as the white dwarfs.
The number of stars similar to the Sun born from the beginning up to the Solar
System formation, with metallicity in the range 12+log(Fe/H)= 7.50 $\pm$ 0.04
dex is 3.1732$\cdot$ 10$^{7}$, and in particular our Sun is the 2.6092$\cdot$
10$^7$-th star of this kind, born in the solar vicinity.


  Solar Energetic Particles (SEPs) possess a high destructive potential as they
pose multiple radiation hazards on Earth and onboard spacecrafts. The present
work continues a series started with the paper by Borovikov et al.(2018)
describing a computational tool to simulate and, potentially, predict the SEP
threat based on the observations of the Sun. Here we present the kinetic model
coupled with the globalMHD model for the Solar Corona (SC) and Inner
Heliosphere (IH), which was described in the first paper in the series. At the
heart of the coupled model is a self-consistent treatment of the Alfven wave
turbulence. The turbulence not only heats corona, powers and accelerates the
solar wind, but also serves as the main agent to scatter the SEPs and thus
controls their acceleration and transport. The universal character of the
turbulence in the coupled model provides a realistic description of the SEP
transport by using the level of turbulence as validated with the solar wind and
coronal plasma observations. At the same time, the SEP observations at 1 AU can
be used to validate the model for turbulence in the IH, since the observed SEPs
have witnessed this turbulence on their way through the IH.


  Residuated lattices play an important role in the study of fuzzy logic based
of t-norm. In this paper, we introduced the notions of n-fold implicative
filters, n-fold positive implicative filters, n-fold boolean filters, n-fold
fantastic filters, n-fold normal filters and n-fold obstinate filters in
residuated lattices and study the relations among them. This generalized the
similar existing results in BL-algebra with the connection of the work of Kerre
and all in [14], Kondo and all in [7], [11] and Motamed and all in [9]. At the
end of this paper, we draw two diagrams; the first one describe the relations
between some type of n-fold filters in residuated lattices and the second one
describe the relations between some type of n-fold residuated lattices.


  Achieving accurate numerical results of hydrodynamic loads based on the
potential-flow theory is very challenging for structures with sharp edges, due
to the singular behavior of the local-flow velocities. In this paper, we
introduce the Extended Finite Element Method (XFEM) to solve fluid-structure
interaction problems involving sharp edges on structures. Four different FEM
solvers, including conventional linear and quadratic FEMs as well as their
corresponding XFEM versions with local enrichment by singular basis functions
at sharp edges, are implemented and compared. To demonstrate the accuracy and
efficiency of the XFEMs, a thin flat plate in an infinite fluid domain and a
forced heaving rectangle at the free surface, both in two dimensions, will be
studied. For the flat plate, the mesh convergence studies are carried out for
both the velocity potential in the fluid domain and the added mass, and the
XFEMs show apparent advantages thanks to their local enhancement at the sharp
edges. Three different enrichment strategies are also compared, and suggestions
will be made for the practical implementation of the XFEM. For the forced
heaving rectangle, the linear and 2nd order mean wave loads are studied. Our
results confirm the previous conclusion in the literature that it is not
difficult for a conventional numerical model to obtain convergent results for
added mass and damping coefficients. However, when the 2nd order mean wave
loads requiring the computation of velocity components are calculated via
direct pressure integration, it takes a tremendously large number of elements
for the conventional FEMs to get convergent results. On the contrary, the
numerical results of XFEMs converge rapidly even with very coarse meshes,
especially for the quadratic XFEM.


  We provide uniqueness results for compact minimal submanifolds in a large
class of Riemannian manifolds of arbitrary dimension. In the case compact and
Cartan-Hadamard manifolds we obtain general results for these submanifolds.
Several applications to Geometric Analysis are also showed.


  The decay $\eta'\rightarrow\pi^0\gamma\gamma$ is studied theoretically in the
framework of the Vector Meson Dominance model (VMD). We find theoretically a
significant contribution of the interference of $\omega-\rho$ and provide
theoretical Dalitz-plots. Comparison with the experimental results of BES-III
\cite{BES-III} is done. We find some tension between our predicted value and
the observed result. Our calculations can be also checked using the data of
GAMS-$4\pi$.


  Multiple Reflection Expansion (MRE) formalism has been applied to hadron
resonance gas (HRG) model to study the finite-size effect on thermodynamics of
small systems of hadron gas at the chemical freeze-out temperature in
high-multiplicity events of proton-proton (pp) colisions at the LHC. Comparison
with larger systems of heavy-ion (AA) collisions helps in undersanding the
usefulness of the effect on small systems. Thermodynamic properties of these
systems at the chemical freeze-out, with and without system-size effect, are
contrasted with those for infinite hadronic phase of strongly interacting
matter at ideal thermodynamic limit, as provided by LQCD calculations. On
introduction of finite size effect, the small hadronic systems produced in
high-multiplicity pp events, unlike those in AA collisions, remain away from
ideal thermodynamic limit. Knudsen number estimations validate the findings.


  Fine-tuning pre-trained large language models in a parameter-efficient manner
is widely studied for its effectiveness and efficiency. The popular method of
low-rank adaptation (LoRA) offers a notable approach, hypothesizing that the
adaptation process is intrinsically low-dimensional. Although LoRA has
demonstrated commendable performance, it is implemented with a fixed and
unalterable intrinsic rank that might not always be the ideal choice.
Recognizing the need for more flexible adaptation, we extend the methodology of
LoRA to an innovative approach we call sparse low-rank adaptation (SoRA) that
enables dynamic adjustments to the intrinsic rank during the adaptation
process. We achieve this through the incorporation of a gate unit optimized
with proximal gradient method in the training stage, controlling the
cardinality of rank under the sparsity of the gate. In the subsequent inference
stage, we eliminate the parameter blocks corresponding to the zeroed-out ranks,
to reduce each SoRA module back to a concise yet rank-optimal LoRA. Our
approach strengthens the representation power of LoRA by initializing it with a
higher rank, while efficiently taming a temporarily increased number of
parameters via updating in a sparse way. We further introduce a sparsifying
scheduler for SoRA, aiming to examine the impact of the number of non-zero
parameters on the model's memorization and generalization. Our experimental
results demonstrate that SoRA can outperform other baselines even with 70%
retained parameters and 70% training time.


  We simulate a two-dimensional array of droplets being compressed between two
walls. The droplets are adhesive due to an attractive depletion force. As one
wall moves toward the other, the droplet array is compressed and eventually
induced to rearrange. The rearrangement occurs via a fracture, where depletion
bonds are quickly broken between a subset of droplets. For monodisperse,
hexagonally ordered droplet arrays, this fracture is preceded by a maximum
force exerted on the walls, which drops rapidly after the fracture occurs. In
small droplet arrays a fracture is a single well-defined event, but for larger
droplet arrays, competing fractures can be observed. These are fractures
nucleated nearly simultaneously in different locations. Finally, we also study
the compression of bidisperse droplet arrays. The addition of a second droplet
size further disrupts fracture events, showing differences between ideal
crystalline arrays, crystalline arrays with a small number of defects, and
fully amorphous arrays. These results are in good agreement with previously
published experiments.


  Digital cameras that use Color Filter Arrays (CFA) entail a demosaicking
procedure to form full RGB images. As today's camera users generally require
images to be viewed instantly, demosaicking algorithms for real applications
must be fast. Moreover, the associated cost should be lower than the cost saved
by using CFA. For this purpose, we revisit the classical Hamilton-Adams (HA)
algorithm, which outperforms many sophisticated techniques in both speed and
accuracy. Inspired by HA's strength and weakness, we design a very low cost
edge sensing scheme. Briefly, it guides demosaicking by a logistic functional
of the difference between directional variations. We extensively compare our
algorithm with 28 demosaicking algorithms by running their open source codes on
benchmark datasets. Compared to methods of similar computational cost, our
method achieves substantially higher accuracy, Whereas compared to methods of
similar accuracy, our method has significantly lower cost. Moreover, on test
images of currently popular resolution, the quality of our algorithm is
comparable to top performers, whereas its speed is tens of times faster.


  We evaluate the dipolar oscillations of a harmonically trapped fermion gas
containing thermal bosonic impurities as a function of the anisotropy of the
trap, from the numerical solution of the Vlasov-Landau equations for the
one-body phase-space distribution functions. Starting from a situation in which
the two components of the gaseous mixture perform almost independent
oscillations inside a spherical trap, we demonstrate that different collision
behaviors arise for oscillations in different directions as the trap is
deformed into an elongated cigar-like shape. An increase in the anisotropy of
the confinement thus suffices to drive a transition of dipolar modes from a
collisionless to a collisional regime.


  We develop a general strategy in order to implement (approximate) discrete
transparent boundary conditions for finite difference approximations of the
two-dimensional transport equation. The computational domain is a rectangle
equipped with a Cartesian grid. For the two-dimensional leapfrog scheme, we
explain why our strategy provides with explicit numerical boundary conditions
on the four sides of the rectangle and why it does not require prescribing any
condition at the four corners of the computational domain. The stability of the
numerical boundary condition on each side of the rectangle is analyzed by means
of the so-called normal mode analysis. Numerical investigations for the full
problem on the rectangle show that strong instabilities may occur when coupling
stable strategies on each side of the rectangle. Other coupling strategies
yield promising results.


  In this study, we explore the application of game theory, in particular
Stackelberg games, to address the issue of effective coordination strategy
generation for heterogeneous robots with one-way communication. To that end,
focusing on the task of multi-object rearrangement, we develop a theoretical
and algorithmic framework that provides strategic guidance for a pair of robot
arms, a leader and a follower where the leader has a model of the follower's
decision-making process, through the computation of a feedback Stackelberg
equilibrium. With built-in tolerance of model uncertainty, the strategic
guidance generated by our planning algorithm not only improves the overall
efficiency in solving the rearrangement tasks, but is also robust to common
pitfalls in collaboration, e.g., chattering.


  Let $A_K$ be an abelian variety with semistable reduction over a strictly
henselian field of positive characteristic with perfect residue class field. We
show that there is a close connection between the pairings of Grothendieck,
Bester/Bertapelle and Shafarevic. In particular, we show that the pairing of
Bester/Bertapelle can be used to describe the $p$-part of Grothendieck's
pairing in the semistable reduction case, thus proving a conjecture of
Bertapelle.


  We have analyzed the properties of the star formation episodes taking place
in a sample of Blue Compact and Irregular galaxies by comparing their
multiwavelength observational properties with the predictions of evolutionary
population synthesis models. This method has allowed us to constrain the age,
star formation regime (instantaneous or extended) and Initial Mass Function
slope, as well as the shape and strentgh of the interstellar extinction in
these regions.


  We find an infinite dimensional free algebra which lives at large N in any
SU(N)-invariant action or Hamiltonian theory of bosonic matrices. The natural
basis of this algebra is a free-algebraic generalization of Chebyshev
polynomials and the dual basis is closely related to the planar connected
parts. This leads to a number of free-algebraic forms of the master field
including an algebraic derivation of the Gopakumar-Gross form. For action
theories, these forms of the master field immediately give a number of new
free-algebraic packagings of the planar Schwinger-Dyson equations.


  The paper explores the prospects of observing the phenomenon of dynamical
Anderson localisation via non-resonant Raman-type rotational excitation of
molecules by periodic trains of short laser pulses. We define conditions for
such an experiment, and show that current femtosecond technology used for
non-adiabatic laser alignment of linear molecules is sufficient for this task.
Several observables which can serve as indicator for Anderson localisation are
suggested for measurement, and the influence of experimental limitations
imposed by laser intensity noise, finite pulse duration, limited number of
pulses in a train, and thermal effects is analysed.


  We apply the mathematical technique of factorization of differential
operators to two different problems. First we review our results related to the
supersymmetry of the Montroll kinks moving onto the microtubule walls as well
as mentioning the sine-Gordon model for the microtubule nonlinear excitations.
Second, we find analytic expressions for a class of one-parameter solutions of
a sort of diffusion equation of Bessel type that is obtained by supersymmetry
from the homogeneous form of a simple damped wave equations derived in the
works of P.A. Robinson and collaborators for the corticothalamic system. We
also present a possible interpretation of the diffusion equation in the brain
context


  Training or finetuning large-scale language models (LLMs) such as GPT-3
requires substantial computation resources, motivating recent efforts to
explore parameter-efficient adaptation to downstream tasks. One practical area
of research is to treat these models as black boxes and interact with them
through their inference APIs. In this paper, we investigate how to optimize
few-shot text classification without accessing the gradients of the LLMs. To
achieve this, we treat the black-box model as a feature extractor and train a
classifier with the augmented text data. Data augmentation is performed using
prompt-based finetuning on an auxiliary language model with a much smaller
parameter size than the black-box model. Through extensive experiments on eight
text classification datasets, we show that our approach, dubbed BT-Classifier,
significantly outperforms state-of-the-art black-box few-shot learners and
performs on par with methods that rely on full-model tuning.


  Neutron $2p$ and $1f$ spin--orbit splittings were recently measured in the
isotones $^{37}$S and $^{35}$Si by $(d,p)$ transfer reactions. Values were
reported by using the major fragments of the states. An important reduction of
the $p$ splitting was observed, from $^{37}$S to $^{35}$Si, associated to a
strong modification of the spin--orbit potential in the central region of the
nucleus $^{35}$Si. We analyze $2p$ and $1f$ neutron spin--orbit splittings in
the $N=20$ isotones $^{40}$Ca, $^{36}$S, and $^{34}$Si. We employ several
Skyrme and Gogny interactions, to reliably isolate pure spin--orbit and
tensor--induced contributions, within the mean--field approximation. We use
interactions (i) without the tensor force; (ii) with the tensor force and with
tensor parameters adjusted on top of existing parametrizations; (iii) with the
tensor force and with tensor and spin--orbit parameters adjusted simultaneously
on top of existing parametrizations. We predict in cases (ii) and (iii) a non
negligible reduction of both $p$ and $f$ splittings, associated to
neutron--proton tensor effects, from $^{40}$Ca to $^{36}$S. The two splittings
are further decreased for the three types of interactions, going from $^{36}$S
to $^{34}$Si. This reduction is produced by the spin--orbit force and is not
affected by tensor--induced contributions. For both reductions, from $^{40}$Ca
to $^{36}$S and from $^{36}$S to $^{34}$Si, we predict in all cases that the
modification is more pronounced for $p$ than for $f$ splittings. The
measurement of the centroids for neutron $2p$ and $1f$ states in the nuclei
$^{36}$S and $^{34}$Si would be interesting to validate this prediction
experimentally. We show the importance of using interactions of type (iii),
because they provide $p$ and $f$ splittings in the nucleus $^{40}$Ca which are
in agreement with the corresponding experimental values.


  It is conjectured that in the geometric formulation of quantum computing, one
can study quantum complexity through classical entropy of statistical ensembles
established non-relativistically in the group manifold of unitary operators.
The kinetic and positional decompositions of statistical entropy are
conjectured to correspond to the Kolmogorov complexity and computational
complexity, respectively, of corresponding quantum circuits. In this paper, we
claim that by applying the virial theorem to the group manifold, one can derive
a generic relation between Kolmogorov complexity and computational complexity
in the thermal equilibrium.


  We explore various models for the pattern forming instability in a
laser-driven cloud of cold two-level atoms with a plane feedback mirror. Focus
is on the combined treatment of nonlinear propagation in a diffractively thick
medium and the boundary condition given by feedback. The combined presence of
purely transverse transmission gratings and reflection gratings on wavelength
scale is addressed. Different truncation levels of the Fourier expansion of the
dielectric susceptibility in terms of these gratings are discussed and compared
to literature. A formalism to calculate the exact solution for the homogenous
state in presence of absorption is presented. The relationship between the
counterpropagating beam instability and the feedback instability is discussed.
Feedback reduces the threshold by a factor of two under optimal conditions.
Envelope curves which bound all possible threshold curves for varying mirror
distances are calculated. The results are comparing well to experimental
results regarding the observed length scales and threshold conditions. It is
clarified where the assumption of a diffractively thin medium is justified.


  We consider the fist order, gradient-flow, description of the scalar fields
coupled to spherically symmetric, asymptotically flat black holes in extended
supergravities. Using the identification of the fake superpotential with
Hamilton's characteristic function we clarify some of its general properties,
showing in particular (besides reviewing the issue of its duality invariance)
that W has the properties of a Liapunov's function, which implies that its
extrema (associated with the horizon of extremal black holes) are
asymptotically stable equilibrium points of the corresponding first order
dynamical system (in the sense of Liapunov). Moreover, we show that the fake
superpotential W has, along the entire radial flow, the same flat directions
which exist at the attractor point. This allows to study properties of the ADM
mass also for small black holes where in fact W has no critical points at
finite distance in moduli space. In particular the W function for small non-BPS
black holes can always be computed analytically, unlike for the large
black-hole case.


  We present the first results from the KMOS AGN Survey at High redshift
(KASHz), a VLT/KMOS integral-field spectroscopic survey of z>0.6 AGN. We
present galaxy-integrated spectra of 89 X-ray AGN (Lx=10^42-10^45 erg/s), for
which we observed [O III] (z=1.1-1.7) or Halpha emission (z=0.6-1.1). The
targets have X-ray luminosities representative of the parent AGN population and
we explore the emission-line luminosities as a function of X-ray luminosity.
For the [O III] targets, ~50 per cent have ionised gas velocities indicative of
gas that is dominated by outflows and/or highly turbulent material (i.e.,
overall line-widths >~600 km/s). The most luminous half (i.e., Lx>6x10^43
erg/s) have a >~2 times higher incidence of such velocities. On the basis of
our results, we find no evidence that X-ray obscured AGN are more likely to
host extreme kinematics than unobscured AGN. Our KASHz sample has a
distribution of gas velocities that is consistent with a luminosity-matched
sample of z<0.4 AGN. This implies little evolution in the prevalence of ionised
outflows, for a fixed AGN luminosity, despite an order-of-magnitude decrease in
average star-formation rates over this redshift range. Furthermore, we compare
our Halpha targets to a redshift-matched sample of star-forming galaxies and
despite a similar distribution of Halpha luminosities and likely star-formation
rates, we find extreme ionised gas velocities are up to ~10x more prevalent in
the AGN-host galaxies. Our results reveal a high prevalence of extreme ionised
gas velocities in high-luminosity X-ray AGN and imply that the most powerful
ionised outflows in high-redshift galaxies are driven by AGN activity.


  Quantification of sputter depth profiles is frequently done by fitting the
convolution integral over concentration and depth resolution function. For a
thin delta layer, there exist analytical solutions. The analytical depth
resolution functions of two popular approaches, that of the MRI model and that
of Dowsett and coworkers are compared. It is concluded that the analytical
depth resolution function of the MRI model gives the correct location of a
buried delta layer with respect to the measured profile, and a clear
description of the information depth in AES, XPS and SIMS. Both analytical
solutions can be extended to larger layer thickness. But they are less flexible
with respect to physical parameters which are not constant with concentration
or sputtered depth, such as detection sensitivity, atomic mixing, roughness or
preferential sputtering. For these cases, numerical solutions have to be used.


  Self-imitation learning motivated by lower-bound Q-learning is a novel and
effective approach for off-policy learning. In this work, we propose a n-step
lower bound which generalizes the original return-based lower-bound Q-learning,
and introduce a new family of self-imitation learning algorithms. To provide a
formal motivation for the potential performance gains provided by
self-imitation learning, we show that n-step lower bound Q-learning achieves a
trade-off between fixed point bias and contraction rate, drawing close
connections to the popular uncorrected n-step Q-learning. We finally show that
n-step lower bound Q-learning is a more robust alternative to return-based
self-imitation learning and uncorrected n-step, over a wide range of continuous
control benchmark tasks.


  This is a manuscript containing the full proofs of results announced in [KW],
together with some recent updates. We prove that the Nazarov-Sodin constant,
which up to a natural scaling gives the leading order growth for the expected
number of nodal components of a random Gaussian field, genuinely depends on the
field. We then infer the same for "arithmetic random waves", i.e. random toral
Laplace eigenfunctions.


  This study presents miscellaneous properties of pseudo-factorials, which are
numbers whose recurrence relation is a twisted form of that of usual
factorials. These numbers are associated with special elliptic functions, most
notably, a Dixonian and a Weierstrass function, which parametrize the Fermat
cubic curve and are relative to a hexagonal lattice. A continued fraction
expansion of the ordinary generating function of pseudo-factorials, first
discovered empirically, is established here. This article also provides a
characterization of the associated orthogonal polynomials, which appear to form
a new family of "elliptic polynomials", as well as various other properties of
pseudo-factorials, including a hexagonal lattice sum expression and elementary
congruences.


  Pulsars spin-down due to magnetic torque reducing its radius and increasing
the central energy density. Some pulsar which are born with central densities
close to the critical value of quark deconfinement may undergo a phase
transition and structural re-arrengement. This process may excite oscillation
modes and emmit gravitational waves. We determine the rate of quark core
formation in neutron stars using a realistic population synthesis code.


  Despite significant advances, continual learning models still suffer from
catastrophic forgetting when exposed to incrementally available data from
non-stationary distributions. Rehearsal approaches alleviate the problem by
maintaining and replaying a small episodic memory of previous samples, often
implemented as an array of independent memory slots. In this work, we propose
to augment such an array with a learnable random graph that captures pairwise
similarities between its samples, and use it not only to learn new tasks but
also to guard against forgetting. Empirical results on several benchmark
datasets show that our model consistently outperforms recently proposed
baselines for task-free continual learning.


  This article introduces a Tensor Network Kalman filter, which can estimate
state vectors that are exponentially large without ever having to explicitly
construct them. The Tensor Network Kalman filter also easily accommodates the
case where several different state vectors need to be estimated simultaneously.
The key lies in rewriting the standard Kalman equations as tensor equations and
then implementing them using Tensor Networks, which effectively transforms the
exponential storage cost and computational complexity into a linear one. We
showcase the power of the proposed framework through an application in
recursive nonlinear system identification of high-order discrete-time
multiple-input multiple-output (MIMO) Volterra systems. The identification
problem is transformed into a linear state estimation problem wherein the state
vector contains all Volterra kernel coefficients and is estimated using the
Tensor Network Kalman filter. The accuracy and robustness of the scheme are
demonstrated via numerical experiments, which show that updating the Kalman
filter estimate of a state vector of length $10^9$ and its covariance matrix
takes about 0.007s on a standard desktop computer in Matlab.


  We incorporate elements of the recently discovered exact solutions of the
quantum constraints of loop quantum gravity for vacuum spherically symmetric
space-times into the paradigm of black hole evaporation due to Ashtekar and
Bojowald. The quantization of the area of the surfaces of symmetry of the
solutions implies that the number of nice slices that can be fit inside the
black hole is finite. The foliation eventually moves through the region where
the singularity in the classical theory used to be and all the particles that
fell into the black hole due to Hawking radiation emerge finally as a white
hole. This yields a variant of a scenario advocated by Arkani-Hamed {\em et
al.} Fluctuations in the horizon that naturally arise in the quantum space time
allow radiation to emerge during the evaporation process due to stimulated
emission allowing evaporation to proceed beyond Page time without reaching the
maximum entanglement limit until the formation of the white hole. No firewalls
nor remnants arise in this scenario.


  We consider Majorana fermions tunneling among an array of vortices in a 2D
chiral p-wave superconductor or equivalent material. The amplitude for Majorana
fermions to tunnel between a pair of vortices is found to necessarily depend on
the background superconducting phase profile; it is found to be proportional to
the sine of half the difference between the phases at the two vortices. Using
this result we study tight-binding models of Majorana fermions in vortices
arranged in triangular or square lattices. In both cases we find that the
aforementioned phase-tunneling relationship leads to the creation of
superlattices where the Majorana fermions form macroscopically degenerate
localizable flat bands at zero energy, in addition to other dispersive bands.
This finding suggests that tunneling processes in these vortex arrays do not
change the energies of a finite fraction of Majorana fermions, contrary to
previous expectation. The presence of flat Majorana bands, and hence
less-than-expected decoherence in these vortex arrays, bodes well for the
prospects of topological quantum computation with large numbers of Majorana
states.


  The strange quark mass is determined from a new QCD Finite Energy Sum Rule
(FESR) optimized to reduce considerably the systematic uncertainties arising
from the hadronic resonance sector. As a result, the main uncertainty in this
determination is due to the value of $\Lambda_{QCD}$. The correlator of
axial-vector divergences is used in perturbative QCD to five-loop order,
including quark and gluon condensate contributions, in the framework of both
Fixed Order (FOPT), and Contour Improved Perturbation Theory (CIPT). The latter
exhibits very good convergence, leading to a remarkably stable result in the
very wide range $s_0 = 1.0 - 4.0 {GeV}^2$, where $s_0$ is the radius of the
integration contour in the complex energy (squared) plane. The value of the
strange quark mass in this framework at a scale of 2 GeV is $m_s(2 {GeV}) = 95
\pm 5 (111 \pm 6) {MeV}$ for $\Lambda_{QCD} = 420
  (330) {MeV}$, respectively.


  We consider the combined influence of disorder, electron-electron
interactions and quantum hopping on the properties of electronic systems in a
localized phase, approaching an insulator-metal transition. The generic models
in this regime are the quantum Coulomb glass and its generalization to
electrons with spin. After introducing these models we explain our
computational method, the Hartree-Fock based diagonalization. We then discuss
the conductance and compare spinless fermions and electrons. It turns out that
spin degrees of freedom do not play an essential role in the systems
considered. Finally, we analyze localization and decay of single-particle
excitations. We find that interactions generically tend to localize these
excitations which is a result of the Coulomb gap in the single-particle density
of states.


  The propagation of electromagnetic plane waves with negative phase velocity
(NPV) is considered in Schwarzschild-(anti-)de Sitter spacetime. It is
demonstrated that NPV propagation occurs in Schwarzschild-de Sitter spacetime
at lower values of the cosmological constant than is the case for de Sitter
spacetime. Furthermore, we report that neither is NPV propagation observed in
Schwarzschild-anti-de Sitter spacetime, nor is it possible outside the event
horizon of a Schwarzschild blackhole.


  Classical field theory is considered as a theory of unparametrized surfaces
embedded in a configuration space, which accommodates, in a symmetric way,
spacetime positions and field values. Dynamics is defined by a (Hamiltonian)
constraint between multivector-valued generalized momenta, and points in the
configuration space. Starting from a variational principle, we derive local
equations of motion, that is, differential equations that determine classical
surfaces and momenta. A local Hamilton-Jacobi equation applicable in the field
theory then follows readily. The general method is illustrated with three
examples: non-relativistic Hamiltonian mechanics, De Donder-Weyl scalar field
theory, and string theory.
  Throughout, we use the mathematical formalism of geometric algebra and
geometric calculus, which allows to perform completely coordinate-free
manipulations.


  We propose a new way of understanding how chiral symmetry is realized in the
high temperature phase of QCD. Based on the finding that a simple free
instanton gas precisely describes the details of the lowest part of the
spectrum of the lattice overlap Dirac operator, we propose an instanton-based
random matrix model of QCD with dynamical quarks. Simulations of this model
reveal that even for small quark mass the Dirac spectral density has a
singularity at the origin, caused by a dilute gas of free instantons. Even
though the interaction, mediated by light dynamical quarks creates small
instanton-antiinstanton molecules, those do not influence the singular part of
the spectrum, and this singular part is shown to dominate Banks-Casher type
sums in the chiral limit. By generalizing the Banks-Casher formula for the
singular spectrum, we show that in the chiral limit the chiral condensate
vanishes if there are at least two massless flavors. Our model also indicates a
possible way of resolving a long-standing debate, as it suggests that for two
massless quark flavors the $U(1)_{A}$ symmetry is likely to remain broken up to
arbitrarily high finite temperatures.


  In this work, we study the hypothesis that speaker identity embeddings
extracted from speech samples may be used for detection and classification of
emotion. In particular, we show that emotions can be effectively identified by
learning speaker identities by use of a 1-D Triplet Convolutional Neural
Network (CNN) & Global Style Token (GST) scheme (e.g., DeepTalk Network) and
reusing the trained speaker recognition model weights to generate features in
the emotion classification domain. The automatic speaker recognition (ASR)
network is trained with VoxCeleb1, VoxCeleb2, and Librispeech datasets with a
triplet training loss function using speaker identity labels. Using an Support
Vector Machine (SVM) classifier, we map speaker identity embeddings into
discrete emotion categories from the CREMA-D, IEMOCAP, and MSP-Podcast
datasets. On the task of speech emotion detection, we obtain 80.8% ACC with
acted emotion samples from CREMA-D, 81.2% ACC with semi-natural emotion samples
in IEMOCAP, and 66.9% ACC with natural emotion samples in MSP-Podcast. We also
propose a novel two-stage hierarchical classifier (HC) approach which
demonstrates +2% ACC improvement on CREMA-D emotion samples. Through this work,
we seek to convey the importance of holistically modeling intra-user variation
within audio samples


  Knowledge graphs (KGs) have become important auxiliary information for
helping recommender systems obtain a good understanding of user preferences.
Despite recent advances in KG-based recommender systems, existing methods are
prone to suboptimal performance due to the following two drawbacks: 1) current
KG-based methods over-emphasize the heterogeneous structural information within
a KG and overlook the underlying semantics of its connections, hindering the
recommender from distilling the explicit user preferences; and 2) the inherent
incompleteness of a KG (i.e., missing facts, relations and entities) will
deteriorate the information extracted from KG and weaken the representation
learning of recommender systems.
  To tackle the aforementioned problems, we investigate the potential of
jointly incorporating the structural and semantic information within a KG to
model user preferences in finer granularity. A new framework for KG-based
recommender systems, namely \textit{K}nowledge \textit{I}nfomax
\textit{R}ecommender \textit{S}ystem with \textit{C}ontrastive
\textit{L}earning (KIRS-CL) is proposed in this paper. Distinct from previous
KG-based approaches, KIRS-CL utilizes structural and connectivity information
with high-quality item embeddings learned by encoding KG triples with a
pre-trained language model. These well-trained entity representations enable
KIRS-CL to find the item to recommend via the preference connection between the
user and the item. Additionally, to improve the generalizability of our
framework, we introduce a contrastive warm-up learning strategy, making it
capable of dealing with both warm- and cold-start recommendation scenarios.
Extensive experiments on two real-world datasets demonstrate remarkable
improvements over state-of-the-art baselines.


  Chi-square processes with trend appear naturally as limiting processes in
various statistical models. In this paper we are concerned with the exact tail
asymptotics of the supremum taken over (0; 1) of a class of locally stationary
chi-square processes with particular admissible trends. An important tool for
establishing our results is a weak version of Slepian's lemma for chi-square
processes. Some special cases including squared Brownian bridge and Bessel
process are discussed.


  We investigate the tensor form factors of the baryon octet within the
framework of the chiral quark-soliton model, emphasizing those of the nucleon,
taking linear 1/N_c rotational as well as linear m_s corrections into account,
and applying the symmetry-conserving quantization. We explicitly calculate the
tensor form factors H_{T}^{q}(Q^{2}) corresponding to the generalized parton
distributions H_{T}(x,\xi,t). The tensor form factors are obtained for the
momentum transfer up to Q^{2}\leq1\,\mathrm{GeV}^{2} and at a renormalization
scale of 0.36\,\mathrm{GeV}^{2}. We find for the tensor charges \delta u=1.08,
\delta d=-0.32, \delta s=-0.01 and discuss their physical consequences,
comparing them with those from other models. Results for tensor charges for the
baryon octet are also given.


  Two-dimensional (2D) half-metallic materials are highly desirable for
nanoscale spintronic applications. Here, we propose a new mechanism that can
achieve half-metallicity in 2D ferromagnetic (FM) material with two-layer
magnetic atoms by electric field tuning. We use a concrete example of
experimentally synthesized CrSBr monolayer to illustrate our proposal through
the first-principle calculations. It is found that the half-metal can be
achieved in CrSBr within appropriate electric field range, and the
corresponding amplitude of electric field intensity is available in experiment.
Janus monolayer $\mathrm{Cr_2S_2BrI}$ is constructed, which possesses built-in
electric field due to broken horizontal mirror symmetry. However,
$\mathrm{Cr_2S_2BrI}$ without and with applied external electric field is
always a FM semiconductor. A possible memory device is also proposed based on
CrSBr monolayer. Our works will stimulate the application of 2D FM CrSBr in
future spintronic nanodevices.


  Homophily and heterophobia, the tendency for people with similar
characteristics to preferentially interact with (or avoid) each other are
pervasive in human social networks. Here, we develop an extension of the
mathematical theory of urban scaling which describes the effects of homophily
and heterophobia on social interactions and resulting economic outputs of
cities. Empirical tests of our model show that increased residential racial
heterophobia and segregation in U.S. cities are associated with reduced
economic outputs and that the strength of this relationship increased
throughout the 2010s. Our findings provide the means for the formal
incorporation of general homophilic and heterophobic effects into theories of
modern urban science and suggest that racial segregation is increasingly and
adversely impacting the economic performance and connectivity of urban
societies in the U.S.


  Top-k keyword and top-k document extraction are very popular text analysis
techniques. Top-k keywords and documents are often computed on-the-fly, but
they exploit weighted vocabularies that are costly to build. To compare
competing weighting schemes and database implementations, benchmarking is
customary. To the best of our knowledge, no benchmark currently addresses these
problems. Hence, in this paper, we present T${}^2$K${}^2$, a top-k keywords and
documents benchmark, and its decision support-oriented evolution
T${}^2$K${}^2$D${}^2$. Both benchmarks feature a real tweet dataset and queries
with various complexities and selectivities. They help evaluate weighting
schemes and database implementations in terms of computing performance. To
illustrate our bench-marks' relevance and genericity, we successfully ran
performance tests on the TF-IDF and Okapi BM25 weighting schemes, on one hand,
and on different relational (Oracle, PostgreSQL) and document-oriented
(MongoDB) database implementations, on the other hand.


  We have calculated the physical parameters of the RR Lyrae stars in the
globular cluster NGC~4147 via the Fourier decomposition of their light curves,
using new data and well-established semi-empirical calibrations and zero
points. The mean metallicity and distance estimated using the RRc stars are
[Fe/H]$_{ZW}=-1.72\pm0.15$ and $19.05\pm0.46$ kpc respectively. The star V18,
whose variability has been previously in dispute, is confirmed to be a variable
of the SR type with a period of about 24.8d, and it has been used to get and
independent distance estimate of the cluster. It is observed that the RRab and
RRc stars do not share the inter-mode region in the horizontal branch. The
cluster can be classified as of intermediate Oosterhoff type. Its horizontal
branch structure and metallicity make a good case for extragalactic origin. It
follows the distribution of Oo~I type globular clusters in the $M_V-$[Fe/H]
plane, as depicted from the RRc stars.


  We study the evolution of heavy quarkonium states with temperature in a
Quark-Gluon Plasma by evaluating an in-medium Q\bar{Q} T-matrix within a
reduced Bethe-Salpeter equation in S- and P-wave channels. The interaction
kernel is extracted from finite-temperature QCD lattice calculations of the
singlet free energy of a Q\bar{Q} pair. Quarkonium bound states are found to
gradually move across the Q\bar{Q} threshold after which they rapidly dissolve
in the hot system. We calculate Euclidean-time correlation functions and
compare to results from lattice QCD. We also study finite-width effects in the
heavy-quark propagators.


  Although many anti-theft technologies are implemented, auto-theft is still
increasing. Also, security vulnerabilities of cars can be used for auto-theft
by neutralizing anti-theft system. This keyless auto-theft attack will be
increased as cars adopt computerized electronic devices more. To detect
auto-theft efficiently, we propose the driver verification method that analyzes
driving patterns using measurements from the sensor in the vehicle. In our
model, we add mechanical features of automotive parts that are excluded in
previous works, but can be differentiated by drivers' driving behaviors. We
design the model that uses significant features through feature selection to
reduce the time cost of feature processing and improve the detection
performance. Further, we enrich the feature set by deriving statistical
features such as mean, median, and standard deviation. This minimizes the
effect of fluctuation of feature values per driver and finally generates the
reliable model. We also analyze the effect of the size of sliding window on
performance to detect the time point when the detection becomes reliable and to
inform owners the theft event as soon as possible. We apply our model with real
driving and show the contribution of our work to the literature of driver
identification.


  Societal rules, as exemplified by norms, aim to provide a degree of
behavioural stability to multi-agent societies. Norms regulate a society using
the deontic concepts of permissions, obligations and prohibitions to specify
what can, must and must not occur in a society. Many implementations of
normative systems assume various combinations of the following assumptions:
that the set of norms is static and defined at design time; that agents joining
a society are instantly informed of the complete set of norms; that the set of
agents within a society does not change; and that all agents are aware of the
existing norms. When any one of these assumptions is dropped, agents need a
mechanism to identify the set of norms currently present within a society, or
risk unwittingly violating the norms. In this paper, we develop a norm
identification mechanism that uses a combination of parsing-based plan
recognition and Hierarchical Task Network (HTN) planning mechanisms, which
operates by analysing the actions performed by other agents. While our basic
mechanism cannot learn in situations where norm violations take place, we
describe an extension which is able to operate in the presence of violations.


  It is shown that one can fit the available data on the a0(980), f0(980),
f0(1300) and K*0(1430) mesons as a distorted 0++ qq bar nonet using very few
(5-6) parameters and an improved version of the unitarized quark model. This
includes all light two-pseudoscalar thresholds, constraints from Adler zeroes,
flavour symmetric couplings, unitarity and physically acceptable analyticity.
The parameters include a bare uu bar or dd bar mass, an over-all coupling
constant, a cutoff and a strange quark mass of 100 MeV, which is in accord with
expectations from the quark model.
  It is found that in particular for the a0(980) and f0(980) the KK bar
component in the wave function is large, i.e., for a large fraction of the time
the qq bar state is transformed into a virtual KK bar pair. This KK bar
component, together with a similar component of eta' pi for the a0(980) , and
eta eta, eta eta' and eta' eta' components for the f0(980), causes the
substantial shift to a lower mass than what is naively expected from the qq bar
component alone.
  Mass, width and mixing parameters, including sheet and pole positions, of the
four resonances are given, with a detailed pedagogical discussion of their
meaning.


  The measurement of direct photons from Au$+$Au collisions at
$\sqrt{s_{_{NN}}}=39$ and 62.4 GeV in the transverse-momentum range $0.4<p_T<3$
Gev/$c$ is presented by the PHENIX collaboration at the Relativistic Heavy Ion
Collider. A significant direct-photon yield is observed in both collision
systems. A universal scaling is observed when the direct-photon $p_T$ spectra
for different center-of-mass energies and for different centrality selections
at $\sqrt{s_{_{NN}}}=62.4$ GeV is scaled with $(dN_{\rm ch}/d\eta)^{\alpha}$
for $\alpha=1.21{\pm}0.04$. This scaling also holds true for direct-photon
spectra from Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV measured earlier
by PHENIX, as well as the spectra from Pb$+$Pb at $\sqrt{s_{_{NN}}}=2760$ GeV
published by ALICE. The scaling power $\alpha$ seems to be independent of
$p_T$, center of mass energy, and collision centrality. The spectra from
different collision energies have a similar shape up to $p_T$ of 2 GeV/$c$. The
spectra have a local inverse slope $T_{\rm eff}$ increasing with $p_T$ of
$0.174\pm0.018$ GeV/$c$ in the range $0.4<p_T<1.3$ GeV/$c$ and increasing to
$0.289\pm0.024$ GeV/$c$ for $0.9<p_T<2.1$ GeV/$c$. The observed similarity of
low-$p_T$ direct-photon production from $\sqrt{s_{_{NN}}}= 39$ to 2760 GeV
suggests a common source of direct photons for the different collision energies
and event centrality selections, and suggests a comparable space-time evolution
of direct-photon emission.


  Supernova (SN) explosions are crucial engines driving the evolution of
galaxies by shock heating gas, increasing the metallicity, creating dust, and
accelerating energetic particles. In 2012 we used the Atacama Large
Millimeter/Submillimeter Array to observe SN 1987A, one of the best-observed
supernovae since the invention of the telescope. We present spatially resolved
images at 450um, 870um, 1.4mm, and 2.8mm, an important transition wavelength
range. Longer wavelength emission is dominated by synchrotron radiation from
shock-accelerated particles, shorter wavelengths by emission from the largest
mass of dust measured in a supernova remnant (>0.2Msun). For the first time we
show unambiguously that this dust has formed in the inner ejecta (the cold
remnants of the exploded star's core). The dust emission is concentrated to the
center of the remnant, so the dust has not yet been affected by the shocks. If
a significant fraction survives, and if SN 1987A is typical, supernovae are
important cosmological dust producers.


  We compute chiral logarithms in the presence of "taste" symmetry breaking of
staggered fermions. The lagrangian of Lee and Sharpe is generalized and then
used to calculate the logs in $\pi$ and $K$ masses. We correct an error in Ref.
[1] [C. Bernard, hep-lat/0111051]; the issue turns out to have implications for
the comparison with simulations, even at tree level. MILC data with three light
dynamical flavors can be well fit by our formulas. However, two new chiral
parameters, which describe order $a^2$ hairpin diagrams for taste-nonsinglet
mesons, enter in the fits. To obtain precise results for the physical
coefficients at order $p^4$, these new parameters will need to be bounded, at
least roughly.


  We construct a number of explicit examples of hyperbolic monopoles, with
various charges and often with some platonic symmetry. The fields are obtained
from instanton data in four-dimensional Euclidean space that are invariant
under a circle action, and in most cases the monopole charge is equal to the
instanton charge. A key ingredient is the identification of a new set of
constraints on ADHM instanton data that are sufficient to ensure the circle
invariance. Unlike for Euclidean monopoles, the formulae for the squared Higgs
field magnitude in the examples we construct are rational functions of the
coordinates. Using these formulae, we compute and illustrate the energy density
of the monopoles. We also prove, for particular monopoles, that the number of
zeros of the Higgs field is greater than the monopole charge, confirming
numerical results established earlier for Euclidean monopoles. We also present
some one-parameter families of monopoles analogous to known scattering events
for Euclidean monopoles within the geodesic approximation.


  The available R-matrix parametrization of experimental data on the excitation
functions for the elastic and inelastic p-Be7 scattering at the collision
energies up to 3.4 MeV is used to generate the corresponding partial-wave cross
sections in the states with J^pi=0+. Thus obtained data are considered as
experimental partial cross sections and are fitted using the semi-analytic
two-channel Jost matrix with proper analytic structure and some adjustable
parameters. Then the spectral points are sought as zeros of the Jost matrix
determinant (which correspond to the S-matrix poles) at complex energies. The
correct analytic structure makes it possible to calculate the fitted Jost
matrix on any sheet of the Riemann surface whose topology involves not only the
square-root but also the logarithmic branching caused by the Coulomb
interaction. In this way, two overlapping 0+ resonances at the excitation
energies ~1.79 MeV and ~1.96 MeV have been found.


  In the search for more efficient and less environmentally harmful cooling
technologies, the field of magnetocalorics is considered a promising
alternative. To generate cooling spans, rotating permanent magnet assemblies
are used to cyclically magnetize and demagnetize magnetocaloric materials,
which change their temperature under the application of a magnetic field. In
this work, an axial rotary permanent magnet assembly, aimed for
commercialization, is computationally designed using topology and shape
optimization. This is efficiently facilitated in an isogeometric analysis
framework, where harmonic mortaring is applied to couple the rotating
rotor-stator system of the multipatch model. Inner, outer and co-rotating
assemblies are compared and optimized designs for different magnet masses are
determined. These simulations are used to homogenize the magnetic flux density
in the magnetocaloric material. The resulting torque is analyzed for different
geometric parameters. Additionally, the influence of anisotropy in the active
magnetic regenerators is studied in order to guide the magnetic flux. Different
examples are analyzed and classified to find an optimal magnet assembly for
magnetocaloric cooling.


  Most network-based speech recognition methods are based on the assumption
that the labels of two adjacent speech samples in the network are likely to be
the same. However, assuming the pairwise relationship between speech samples is
not complete. The information a group of speech samples that show very similar
patterns and tend to have similar labels is missed. The natural way overcoming
the information loss of the above assumption is to represent the feature data
of speech samples as the hypergraph. Thus, in this paper, the three
un-normalized, random walk, and symmetric normalized hypergraph Laplacian based
semi-supervised learning methods applied to hypergraph constructed from the
feature data of speech samples in order to predict the labels of speech samples
are introduced. Experiment results show that the sensitivity performance
measures of these three hypergraph Laplacian based semi-supervised learning
methods are greater than the sensitivity performance measures of the Hidden
Markov Model method (the current state of the art method applied to speech
recognition problem) and graph based semi-supervised learning methods (i.e. the
current state of the art network-based method for classification problems)
applied to network created from the feature data of speech samples.


  Performing Bayesian inference via Markov chain Monte Carlo (MCMC) can be
exceedingly expensive when posterior evaluations invoke the evaluation of a
computationally expensive model, such as a system of partial differential
equations. In recent work [Conrad et al. JASA 2016, arXiv:1402.1694], we
described a framework for constructing and refining local approximations of
such models during an MCMC simulation. These posterior--adapted approximations
harness regularity of the model to reduce the computational cost of inference
while preserving asymptotic exactness of the Markov chain. Here we describe two
extensions of that work. First, we prove that samplers running in parallel can
collaboratively construct a shared posterior approximation while ensuring
ergodicity of each associated chain, providing a novel opportunity for
exploiting parallel computation in MCMC. Second, focusing on the
Metropolis--adjusted Langevin algorithm, we describe how a proposal
distribution can successfully employ gradients and other relevant information
extracted from the approximation. We investigate the practical performance of
our strategies using two challenging inference problems, the first in
subsurface hydrology and the second in glaciology. Using local approximations
constructed via parallel chains, we successfully reduce the run time needed to
characterize the posterior distributions in these problems from days to hours
and from months to days, respectively, dramatically improving the tractability
of Bayesian inference.


  Raman-assisted hopping may be used to realize the anyon Hubbard model in
one-dimensional optical lattices. We propose a feasible scenario that
significantly improves the proposal of [T. Keilmann et al., Nature Commun. 2,
361 (2011)], allowing as well for an exact realization of the two-body
hard-core constraint, and for controllable effective interactions without the
need of Feshbach resonances. We show that the combination of anyonic statistics
and two-body hard-core constraint leads to a rich ground state physics,
including Mott insulators with attractive interactions, pair superfluids, dimer
phases, and multicritical points. Moreover, the anyonic statistics results in a
novel two-component superfluid of holon and doublon dimers, characterized by a
large but finite compressibility and a multipeaked momentum distribution, which
may be easily revealed experimentally.


  We present results on the broadband nature of the power spectrum $S(\omega)$,
$\omega\in(0,2\pi)$, for a large class of nonuniformly expanding maps with
summable and nonsummable decay of correlations. In particular, we consider a
class of intermittent maps $f:[0,1]\to[0,1]$ with $f(x)\approx x^{1+\gamma}$
for $x\approx 0$, where $\gamma\in(0,1)$. Such maps have summable decay of
correlations when $\gamma\in(0,\frac12)$, and $S(\omega)$ extends to a
continuous function on $[0,2\pi]$ by the classical Wiener-Khintchine Theorem.
We show that $S(\omega)$ is typically bounded away from zero for H\"older
observables.
  Moreover, in the nonsummable case $\gamma\in[\frac12,1)$, we show that
$S(\omega)$ is defined almost everywhere with a continuous extension $\tilde
S(\omega)$ defined on $(0,2\pi)$, and $\tilde S(\omega)$ is typically
nonvanishing.


  The effects of Ag15+ (120 MeV) swift heavy ion irradiation on the structural
and morphological properties of epitaxial La0.25Pr0.375Ca0.375MnO3 (LPCMO) thin
films was investigated by x-ray scattering and atomic force microscopy (AFM)
techniques. LPCMO films of thickness ~ 280 {\AA} were irradiated with an Ag15+
ion beam at different fluences of 1E11, 5E11, and 1E12 ions/cm2. XRD results
suggested the development of the tensile stress along the out-of-plane
direction of the LPCMO film upon ion irradiation which increased on increasing
the ion fluence. The morphology of the film also modified with the irradiation
and an increase in the fluence of the ion beam enhanced the in-plane
height-height correlation length scale (grain size) with a loss of the fractal
behaviour.


  Seymour proved that the chromatic numbers and the list chromatic numbers of
loop-free finite matroids are the same. In this paper we prove the same
statement for infinite, loop-free finitary matroids.


  We propose tunnel junctions of a Hall bar and a superconducting lead, for
observing Cooper-pair tunneling into singlet fractional quantum Hall edge
states. These tunnel junctions provide a natural means of extracting precise
information of the spin polarization and the filling factor of the state. The
low energy regime of one of the set-ups is governed by a novel quantum
entangled fixed point.


  Even distribution of irregular workload to processing units is crucial for
efficient parallelization in many applications. In this work, we are concerned
with a spatial partitioning called rectilinear partitioning (also known as
generalized block distribution) of sparse matrices. More specifically, in this
work, we address the problem of symmetric rectilinear partitioning of a square
matrix. By symmetric, we mean the rows and columns of the matrix are
identically partitioned yielding a tiling where the diagonal tiles (blocks)
will be squares. We first show that the optimal solution to this problem is
NP-hard, and we propose four heuristics to solve two different variants of this
problem. We present a thorough analysis of the computational complexities of
those proposed heuristics. To make the proposed techniques more applicable in
real life application scenarios, we further reduce their computational
complexities by utilizing effective sparsification strategies together with an
efficient sparse prefix-sum data structure. We experimentally show the proposed
algorithms are efficient and effective on more than six hundred test matrices.
With sparsification, our methods take less than 3 seconds in the Twitter graph
on a modern 24 core system and output a solution whose load imbalance is no
worse than 1%.


  Graphene and graphene-based materials exhibit exceptional optical and
electrical properties with great promise for novel applications in light
detection. However, several challenges prevent the full exploitation of these
properties in commercial devices. Such challenges include the limited linear
dynamic range (LDR) of graphene-based photodetectors, the lack of efficient
generation and extraction of photoexcited charges, the smearing of photoactive
junctions due to hot-carriers effects, large-scale fabrication and ultimately
the environmental stability of the constituent materials. In order to overcome
the aforementioned limits, different approaches to tune the properties of
graphene have been explored. A new class of graphene-based devices has emerged
where chemical functionalisation, hybridisation with light-sensitising
materials and the formation of heterostructures with other 2D materials have
led to improved performance, stability or versatility. For example,
intercalation of graphene with FeCl$_3$ is highly stable in ambient conditions
and can be used to define photo-active junctions characterized by an
unprecedented LDR while graphene oxide (GO) is a very scalable and versatile
material which supports the photodetection from UV to THz frequencies.
Nanoparticles and quantum dots have been used to enhance the absorption of
pristine graphene and to enable high gain thanks to the photogating effect. In
the same way, hybrid detectors made from stacked sequences of graphene and
layered transition-metal dichalcogenides enabled a class of detectors with high
gain and responsivity. In this work we will review the performance and advances
in functionalised graphene and hybrid photodetectors, with particular focus on
the physical mechanisms governing the photoresponse in these materials, their
performance and possible future paths of investigation.


  The vibrational frequencies of a plate under tension are given by the
eigenvalues $\omega$ of the equation $\Delta^2u-\tau\Delta u=\omega u$. This
paper determines the eigenfunctions and eigenvalues of this bi-Laplace problem
on the ball under natural (free) boundary conditions. In particular, the
fundamental modes --- the eigenfunctions of the lowest nonzero eigenvalue ---
are identified and found to have simple angular dependence.


  We report on the mass-to-light ratio determination based on a newly selected
binary galaxy sample, which includes a large number of pairs whose separations
exceed a few hundred kpc. The probability distributions of the projected
separation and the velocity difference have been calculated considering the
contamination of optical pairs, and the mass-to-light ratio has been determined
based on the maximum likelihood method. The best estimate of $M/L$ in the B
band for 57 pairs is found to be 28 $\sim$ 36 depending on the orbital
parameters and the distribution of optical pairs (solar unit, $H_0=50$ km
s$^{-1}$ Mpc$^{-1}$). The best estimate of $M/L$ for 30 pure spiral pairs is
found to be 12 $\sim$ 16. These results are relatively smaller than those
obtained in previous studies, but consistent with each other within the errors.
Although the number of pairs with large separation is significantly increased
compared to previous samples, $M/L$ does not show any tendency of increase, but
found to be almost independent of the separation of pairs beyond 100 kpc. The
constancy of $M/L$ beyond 100 kpc may indicate that the typical halo size of
spiral galaxies is less than $\sim 100$ kpc.


  Learning the dynamics of spatiotemporal events is a fundamental problem.
Neural point processes enhance the expressivity of point process models with
deep neural networks. However, most existing methods only consider temporal
dynamics without spatial modeling. We propose Deep Spatiotemporal Point Process
(\ours{}), a deep dynamics model that integrates spatiotemporal point
processes. Our method is flexible, efficient, and can accurately forecast
irregularly sampled events over space and time. The key construction of our
approach is the nonparametric space-time intensity function, governed by a
latent process. The intensity function enjoys closed form integration for the
density. The latent process captures the uncertainty of the event sequence. We
use amortized variational inference to infer the latent process with deep
networks. Using synthetic datasets, we validate our model can accurately learn
the true intensity function. On real-world benchmark datasets, our model
demonstrates superior performance over state-of-the-art baselines. Our code and
data can be found at the https://github.com/Rose-STL-Lab/DeepSTPP.


  The gravitational wave event GW170817 associated with the short gamma-ray
burst (GRB) 170817A confirms that binary neutron star (BNS) mergers are one of
the origins of short GRBs. The associated kilonova emission, radioactively
powered by nucleosynthesized heavy elements, was also detected. Black
hole-neutron star (BH-NS) mergers have been argued to be another promising
origin candidate of short GRBs and kilonovae. Numerical simulations show that
the ejecta in BH-NS mergers is geometrically much more anisotropic than the BNS
merger case. In this paper, we investigate observational signatures of kilonova
emission from the anisotropic ejecta in BH-NS mergers. We find that a bump
appears on the bolometric luminosity light curve due to the inhomogeneous mass
distribution in the latitudinal direction. The decay slope of the single-band
light curve becomes flatter and the spectrum also deviates from a
single-temperature blackbody radiation spectrum due to the gradient in the
velocity distribution of the ejecta. Future detection or non-detection of such
signatures would be useful to test the mass ejection geometry in BH-NS mergers.


  The Plan Execution Interchange Language (PLEXIL) is a synchronous language
developed by NASA to support autonomous spacecraft operations. In this paper,
we propose a rewriting logic semantics of PLEXIL in Maude, a high-performance
logical engine. The rewriting logic semantics is by itself a formal interpreter
of the language and can be used as a semantic benchmark for the implementation
of PLEXIL executives. The implementation in Maude has the additional benefit of
making available to PLEXIL designers and developers all the formal analysis and
verification tools provided by Maude. The formalization of the PLEXIL semantics
in rewriting logic poses an interesting challenge due to the synchronous nature
of the language and the prioritized rules defining its semantics. To overcome
this difficulty, we propose a general procedure for simulating synchronous set
relations in rewriting logic that is sound and, for deterministic relations,
complete. We also report on two issues at the design level of the original
PLEXIL semantics that were identified with the help of the executable
specification in Maude.


  We analyze, within the framework of unified brane gravity, the weak-field
perturbations caused by the presence of matter on a 3-brane. Although deviating
from the Randall-Sundrum approach, the masslessness of the graviton is still
preserved. In particular, the four-dimensional Newton force law is recovered,
but serendipitously, the corresponding Newton constant is shown to be
necessarily lower than the one which governs FRW cosmology. This has the
potential to puzzle out cosmological dark matter. A subsequent conjecture
concerning galactic dark matter follows.


  We investigate the non-equilibrium electronic structure and characteristic
time scales in a candidate excitonic insulator, Ta$_2$NiSe$_5$, using time- and
angle-resolved photoemission spectroscopy with a temporal resolution of 50 fs.
Following a strong photoexcitation, the band gap closes transiently within 100
fs, i.e., on a time scale faster than the typical lattice vibrational period.
Furthermore, we find that the characteristic time associated with the rise of
the photoemission intensity above the Fermi energy decreases with increasing
excitation strength, while the relaxation time of the electron population
towards equilibrium shows an opposite behaviour. We argue that these
experimental observations can be consistently explained by an excitonic origin
of the band gap in the material. The excitonic picture is supported by
microscopic calculations based on the non-equilibrium Green's function
formalism for an interacting two-band system. We interpret the speedup of the
rise time with fluence in terms of an enhanced scattering probability between
photo-excited electrons and excitons, leading to an initially faster decay of
the order parameter. We show that the inclusion of electron-phonon coupling at
a semi-classical level changes only the quantitative aspects of the proposed
dynamics, while the qualitative features remain the same. The experimental
observations and microscopic calculations allow us to develop a simple and
intuitive phenomenological model that captures the main dynamics after
photoexcitation in Ta$_2$NiSe$_5$.


  We extend the notions of Hochschild and cyclic homology to morphisms from
algebraic spaces to algebraic stacks. Using this, we obtain generalizations to
log schemes in the sense of Fontaine and Illusie of these homology theories.


  The visual surface brightness of K/M giants and dwarfs with near-solar
metallicity differ slightly in agreement with the gravity effects predicted by
recent theoretical models. We show that M-dwarfs display also a metallicity
dependence of the surface brightness in the infrared $K$-band in agreement with
theory. Based on these results, we present improved Barnes-Evans type relations
and estimate the radii of 60 single or presumed M and K-dwarfs


  In this thesis, the properties of mixtures of Bose-Einstein condensates at $T
= 0$ have been investigated using quantum Monte Carlo (QMC) methods and Density
Functional Theory (DFT) with the aim of understanding physics beyond the
mean-field theory in Bose-Bose mixtures.


  Gravitational interactions between a protoplanetary disk and its embedded
planet is one of the formation mechanisms of gaps and rings found in recent
ALMA observations. To quantify the gap properties measured in not only surface
density but also rotational velocity profiles, we run two-dimensional
hydrodynamic simulations of protoplanetary disks by varying three parameters:
the mass ratio $q$ of a planet to a central star, the ratio of the disk scale
height $h_p$ to the orbital radius $r_p$ of the planet, and the viscosity
parameter $\alpha$. We find the gap depth $\delta_\Sigma$ in the gas surface
density depends on a single dimensionless parameter $K\equiv
q^2(h_p/r_p)^{-5}\alpha^{-1}$ as $\delta_\Sigma = (1 + 0.046K)^{-1}$,
consistent with the previous results of Kanagawa et al. (2015a). The gap depth
$\delta_V$ in the rotational velocity is given by $\delta_V= 0.007 (h_p/r_p)
K^{1.38}/(1 +0.06K^{1.03})$. The gap width, in both surface density and
rotational velocity, has a minimum of about $4.7 h_p$ when the planet mass
$M_p$ is around the disk thermal mass $M_{\text{th}}$, while it increases in a
power-law fashion as $M_p/M_{\text{th}}$ increases or decrease from unity. Such
a minimum in the gap width arises because spirals from sub-thermal planets have
to propagate before they shock the disk gas and open a gap. We compare our
relations for the gap depth and width with the previous results, and discuss
their applicability to observations.


  We study the multi-dimensional persistence of Carlsson and Zomorodian and
obtain a finer classification based upon the higher tor-modules of a
persistence module. We propose a variety structure on the set of isomorphism
classes of these modules, and present several examples. We also provide a
geometric interpretation for the higher tor-modules of homology modules of
multi-filtered simplicial complexes.


  We study phase structures of quantum field theories in fuzzy geometries.
Several examples of fuzzy geometries as well as QFT's on such geometries are
considered. They are fuzzy spheres and beyond as well as noncommutative
deformations of BTZ blackholes. Analysis is done analytically and through
simulations. Several features like novel stripe phases as well as spontaneous
symmetry breaking avoiding Colemen, Mermin, Wagner theorem are brought out.
Also we establish that these phases are stable due to topological obstructions.


  We present experimental phase functions of three types of millimeter-sized
dust grains consisting of enstatite, quartz and volcanic material from Mount
Etna, respectively. The three grains present similar sizes but different
absorbing properties. The measurements are performed at 527 nm covering the
scattering angle range from 3 to 170 degrees. The measured phase functions show
two well defined regions i) soft forward peaks and ii) a continuous increase
with the scattering angle at side- and back-scattering regions. This behavior
at side- and back-scattering regions are in agreement with the observed phase
functions for the Fomalhaut and HR 4796A dust rings. Further computations and
measurements (including polarization) for millimeter sized-grains are needed to
draw some conclusions about the fluffy or compact structure of the dust grains.


  The Simons Observatory (SO) is a ground-based cosmic microwave background
experiment currently being deployed to Cerro Toco in the Atacama Desert of
Chile. The initial deployment of SO, consisting of three 0.46m-diameter
small-aperture telescopes and one 6m-primary large-aperture telescope, will
field over 60,000 transition-edge sensors that will observe at frequencies
between 30 GHz and 280 GHz. SO will read out its detectors using
Superconducting Quantum Interference Device (SQUID) microwave-frequency
multiplexing $\mu$mux, a form of frequency division multiplexing where an
RF-SQUID couples each TES bolometer to a superconducting resonator tuned to a
unique frequency. Resonator frequencies are spaced roughly every 2 MHz between
4 and 6 GHz, allowing for multiplexing factors on the order of 1000. One
challenge of $\mu$mux is matching each tracked resonator with its corresponding
physical detector. Variations in resonator fabrication, and frequency shifts
between cooldowns caused by trapped flux can cause the measured resonance
frequencies to deviate significantly from their designed values. In this study,
we introduce a method for pairing measured and designed resonators by
constructing a bipartite graph based on the two resonator sets, and assigning
edge weights based on measured resonator and detector properties such as
resonance frequency, detector pointing, and assigned bias lines. Finding the
minimum-cost matching for a given set of edge weights is a well-studied problem
that can be solved very quickly, and this matching tells us the best assignment
of measured resonators to designed detectors for our input parameters. We will
present results based on the first on-sky measurements from SAT1, the first SO
MF small-aperture telescope.


  The use of high-dimensional data for targeted therapeutic interventions
requires new ways to characterize the heterogeneity observed across subgroups
of a specific population. In particular, models for partially exchangeable data
are needed for inference on nested datasets, where the observations are assumed
to be organized in different units and some sharing of information is required
to learn distinctive features of the units. In this manuscript, we propose a
nested Common Atoms Model (CAM) that is particularly suited for the analysis of
nested datasets where the distributions of the units are expected to differ
only over a small fraction of the observations sampled from each unit. The
proposed CAM allows a two-layered clustering at the distributional and
observational level and is amenable to scalable posterior inference through the
use of a computationally efficient nested slice-sampler algorithm. We further
discuss how to extend the proposed modeling framework to handle discrete
measurements, and we conduct posterior inference on a real microbiome dataset
from a diet swap study to investigate how the alterations in intestinal
microbiota composition are associated with different eating habits. We further
investigate the performance of our model in capturing true distributional
structures in the population by means of a simulation study.


  For a knot diagram $K$, the classical knot group $\pi_1(K)$ is a free group
modulo relations determined by Wirtinger-type relations on the classical
crossings. The classical knot group is invariant under the Reidemeister moves.
In this paper, we define a set of quotient groups associated to a knot diagram
$K$. These quotient groups are invariant under the Reidemeister moves and the
set includes the extended knot groups defined by Boden et al and Silver and
Williams.


  Answering a question of J. Rosenberg, we construct the first examples of
infinite characters on $GL_n(\mathbf{K})$ for a global field $\mathbf{K}$ and
$n\geq 2.$ The case $n=2$ is deduced from the following more general result.
Let $G$ a non amenable countable subgroup acting on locally finite tree $X$.
Assume either that the stabilizer in $G$ of every vertex of $X$ is finite or
that the closure of the image of $G$ in ${\rm Aut}(X)$ is not amenable. We show
that $G$ has uncountably many infinite dimensional irreducible unitary
representations $(\pi, \mathcal{H})$ of $G$ which are traceable, that is, such
that the $C^*$-subalgebra of $\mathcal{B}(\mathcal{H})$ generated by $\pi(G)$
contains the algebra of the compact operators on $\mathcal{H}.$ In the case
$n\geq 3,$ we prove the existence of infinitely many characters for
$G=SL_n(R)$, where $n\geq 3$ and $R$ is an integral domain such that $G$ is not
amenable. In particular, the group $SL_n(\mathbf{Z})$ has infinitely many such
characters for $n\geq 2.$


  We start by describing a symmetry enforced nodal line semi-metal (NLSM) in
the 2D flat form of honeycomb Group - V and its non trivial thermo-electric
response. We will then proceed to show that, upon buckling, the system
undergoes its dirac-merging phase transitions. Further buckling leads to these
unpinned Dirac cones annihilating in pairs at two distinct critical angle
leading to a second topological phase transition to an insulating state. We
then show that this seemingly innocuous insulating state is indeed a weak
topological crystalline insulator. Furthermore, upon closer look, this
insulating state turns out to be a Higher Order Topological Insulator (HOTI)
that is protected by $\mathcal{S}_6$ symmetry. In a broader context, we will
see that the the topological properties of buckled Group - $V$ stem from the
fact that they topologically belong to the class of Obstructed Atomic Limit
(OAL) insulators. Combining all these, we will prove that annihilating pairs of
Dirac fermions necessitate a topological phase transition from the critical
semi-metallic phase to an OAL insulator phase. We also uncover the rich set of
phases in the phase diagram in case of annihilating Dirac fermions and study
their entanglement properties using entanglement entropy. Finally, based on the
non-trivial topology of these systems, we propose the conceptual design of a
quantized switch that is protected by topology. Last part of the thesis
involves the remarkable discovery of a spin polarized 2D electron/hole gas at
the surfaces of a well known system - LiCoO2.


  Video games have played a crucial role in entertainment since their
development in the 1970s, becoming even more prominent during the lockdown
period when people were looking for ways to entertain them. However, at that
time, players were unaware of the significant impact that playtime could have
on their feelings. This has made it challenging for designers and developers to
create new games since they have to control the emotional impact that these
games will take on players. Thus, the purpose of this study is to look at how a
player's emotions are affected by the duration of the game. In order to achieve
this goal, a framework for emotion detection is created. According to the
experiment's results, the volunteers' general ability to express emotions
increased from 20 to 60 minutes. In comparison to shorter gameplay sessions,
the experiment found that extended gameplay sessions did significantly affect
the player's emotions. According to the results, it was recommended that in
order to lessen the potential emotional impact that playing computer and video
games may have in the future, game producers should think about creating
shorter, entertaining games.


  ML models are increasingly deployed in settings with real world interactions
such as vehicles, but unfortunately, these models can fail in systematic ways.
To prevent errors, ML engineering teams monitor and continuously improve these
models. We propose a new abstraction, model assertions, that adapts the
classical use of program assertions as a way to monitor and improve ML models.
Model assertions are arbitrary functions over a model's input and output that
indicate when errors may be occurring, e.g., a function that triggers if an
object rapidly changes its class in a video. We propose methods of using model
assertions at all stages of ML system deployment, including runtime monitoring,
validating labels, and continuously improving ML models. For runtime
monitoring, we show that model assertions can find high confidence errors,
where a model returns the wrong output with high confidence, which
uncertainty-based monitoring techniques would not detect. For training, we
propose two methods of using model assertions. First, we propose a bandit-based
active learning algorithm that can sample from data flagged by assertions and
show that it can reduce labeling costs by up to 40% over traditional
uncertainty-based methods. Second, we propose an API for generating
"consistency assertions" (e.g., the class change example) and weak labels for
inputs where the consistency assertions fail, and show that these weak labels
can improve relative model quality by up to 46%. We evaluate model assertions
on four real-world tasks with video, LIDAR, and ECG data.


  We focus on the statistics of word occurrences and of the waiting times
between such occurrences in Blogs. Due to the heterogeneity of words'
frequencies, the empirical analysis is performed by studying classes of
"frequently-equivalent" words, i.e. by grouping words depending on their
frequencies. Two limiting cases are considered: the dilute limit, i.e. for
those words that are used less than once a day, and the dense limit for
frequent words. In both cases, extreme events occur more frequently than
expected from the Poisson hypothesis. These deviations from Poisson statistics
reveal non-trivial time correlations between events that are associated with
bursts of activities. The distribution of waiting times is shown to behave like
a stretched exponential and to have the same shape for different sets of words
sharing a common frequency, thereby revealing universal features.


  A holomorphic representation formula for special parabolic hyperspheres is
given.


  We compute the one-loop renormalization of the Planck mass for type II string
theories compactified to four dimensions on symmetric orbifolds that preserve
${\cal N}=2$ supersymmetry. Depending on the orbifold, the effect can be as
large as to compete with the standard tree-level value.


  This paper discusses the letter entitled "Network analysis of the state space
of discrete dynamical systems" by A. Shreim et al. [Physical Review Letters,
98, 198701 (2007)]. We found that some theoretical analyses are wrong and the
proposed indicators based on two parameters of the state-mapping network cannot
discriminate the dynamical complexity of the discrete dynamical systems
composed of a 1-D Cellular Automata.


  The standard quantitative metric for evaluating enrichment capacity known as
$\textit{LogAUC}$ depends on a cutoff parameter that controls what the minimum
value of the log-scaled x-axis is. Unless this parameter is chosen carefully
for a given ROC curve, one of the two following problems occurs: either (1)
some fraction of the first inter-decoy intervals of the ROC curve are simply
thrown away and do not contribute to the metric at all, or (2) the very first
inter-decoy interval contributes too much to the metric at the expense of all
following inter-decoy intervals. We fix this problem with LogAUC by showing a
simple way to choose the cutoff parameter based on the number of decoys which
forces the first inter-decoy interval to always have a stable, sensible
contribution to the total value. Moreover, we introduce a normalized version of
LogAUC known as $\textit{enrichment score}$, which (1) enforces stability by
selecting the cutoff parameter in the manner described, (2) yields scores which
are more intuitively meaningful, and (3) allows reliably accurate comparison of
the enrichment capacities exhibited by different ROC curves, even those
produced using different numbers of decoys. Finally, we demonstrate the
advantage of enrichment score over unbalanced metrics using data from a real
retrospective docking study performed using the program $\textit{DOCK 3.7}$ on
the target receptor TRYB1 included in the $\textit{DUDE-Z}$ benchmark.


  A previous research on multivariate approach to the calculation of
reverberation chamber correlation matrices is used to calculate the number of
independent positions in a mode-stirred reverberation chamber. Anomalies and
counterintuitive behavior are observed in terms of number of correlated matrix
elements with respect to increasing frequency. This is ascribed to the regular
geometry forming the baseline cavity (screened room) of a reverberation
chamber, responsible for localizing energy and preserving regular modes
(bouncing ball modes). Smooth wall deformations are introduced in order to
create underlying Lyapunov instability of rays and then destroy survived
regular modes. Numerical full-wave simulations are performed for a
reverberation chamber with corner hemispheres and (off-)center wall spherical
caps. Field sampling is performed by moving a mechanical carousel stirrer. It
is found that wave-chaos inspired baseline geometries improve chamber
performances in terms of lowest usable frequencies and number of independent
cavity realizations of mechanical stirrers.


  In this paper, we compute the one-level density of low-lying zeros of
Dirichlet $L$-functions in a family weighted by special values of Dirichlet
$L$-functions at a fixed $s \in [1/2, 1)$. We verify both Fazzari's conjecture
and the first author's conjecture on the weighted one-level density for our
family of $L$-functions.


  In this paper, we study recurrence and transience of L\'evy-type processes,
that is, Feller processes associated with pseudo-differential operators. Since
the recurrence property of L\'evy-type processes in dimensions greater than two
is vacuous and the recurrence and transience of one-dimensional L\'evy-type
processes have been very well investigated, in this paper we are focused on the
two-dimensional case only. In particular, we study perturbations of
two-dimensional L\'evy-type processes which do not affect their recurrence and
transience properties, we derive sufficient conditions for their recurrence and
transience in terms of the corresponding L\'evy measure and we provide some
comparison conditions for the recurrence and transience also in terms of the
L\'evy measures.


  The noncollinear spin textures provide promising avenues to stabilize exotic
magnetic phases and excitations. They have attracted vast attention owning to
their nontrivial band topology in the past decades. Distinct from the
conventional route of involving the Dzyaloshinskii-Moriya interaction in a
honeycomb magnet, the interplay of bond-dependent Kitaev and $\Gamma$
interactions, originating from the spin-orbit coupling and octahedra crystal
field in real materials, has demonstrated to be another source to generate
noncollinear spin textures with multiple spins in a magnetic unit cell.
Notably, earlier works have revealed a triple-meron crystal (TmX) consisting of
eighteen spins in the frustrated Kitaev-$\Gamma$ model. Aligning with previous
efforts, here we attempt to identify that the TmX hosts several peculiar
features with the help of the linear spin-wave theory. To begin with, the
symmetric anisotropic exchanges are beneficial for the existence of
nonreciprocal magnons, which are stabilized by an external magnetic field.
Further, within the regime of TmX, successive topological phase transitions
occur, accompanied by the changes of Chern number in value and thermal Hall
conductivity in sign. In addition, topological nature of magnons is also
verified by the onset of chiral edge modes in a nanoribbon geometry. Our
findings pave the way to study topological phenomena of noncollinear spin
textures in potential Kitaev materials.