  Words are sequences of letters over a finite alphabet. We study two
intimately related topics for this object: quasi-randomness and limit theory.
With respect to the first topic we investigate the notion of uniform
distribution of letters over intervals, and in the spirit of the famous
Chung--Graham--Wilson theorem for graphs we provide a list of word properties
which are equivalent to uniformity. In particular, we show that uniformity is
equivalent to counting 3-letter subsequences.
  Inspired by graph limit theory we then investigate limits of convergent word
sequences, those in which all subsequence densities converge. We show that
convergent word sequences have a natural limit, namely Lebesgue measurable
functions of the form $f:[0,1]\to[0,1]$. Via this theory we show that every
hereditary word property is testable, address the problem of finite forcibility
for word limits and establish as a byproduct a new model of random word
sequences.
  Along the lines of the proof of the existence of word limits, we can also
establish the existence of limits for higher dimensional structures. In
particular, we obtain an alternative proof of the result by Hoppen, Kohayakawa,
Moreira, R\'ath and Sampaio [{\it J. Combin. Theory Ser. B 103(1):93--113,
2013}] establishing the existence of permutons.


  From the string partition function, we discuss the mass-shell and GSO
projection conditions valid for Kaluza-Klein (KK) as well as massless states in
the heterotic string theory compactified on a nonprime orbifold. Based on the
obtained conditions we construct a 4D string standard model, which is embedded
in a 6D SUSY GUT by including KK states above the compactification scale. We
discuss the stringy threshold corrections to gauge couplings, including the
Wilson line effects.


  We experimentally demonstrate a polarization-entangled photon source at 810
nm using a type-II phase-matched PPKTP crystal pumped by a low-cost, broadband
laser diode with a central wavelength of 405 nm and a typical bandwidth of 0.53
nm. The PPKTP crystal is placed in a Sagnac-loop to realize the compact size
and high stability. The downconverted biphotons, the signal and the idler, have
typical bandwidths of 5.57 nm and 7.32 nm. We prepare two Bell states |Psi+>
and |Psi-> with the fidelities of 0.948+-0.004 and 0.963+-0.002. In
polarization correlation measurement, the visibilities are all higher than
96.2%, and in the Bell inequality test, the S value can achieve 2.78+-0.01. To
our knowledge, this experiment is the first to combine a multi-mode pump laser
with a Sagnac-loop configuration. This high-quality and low-cost entangled
photon source may have many practical applications in quantum information
processing.


  Let $K$ be a number field with ring of integers $\mathcal{O}_K$ and let $G$
be a \mbox{finite group of} odd order. Given a $G$-Galois $K$-algebra $K_h$,
let $A_h$ be the square root of the inverse different of $K_h/K$, which exists
by Hilbert's formula. If $K_h/K$ is weakly ramified, then $A_h$ is locally free
over $\mathcal{O}_{K}G$ by a result of B. Erez, in which case it determines a
class in the locally free class group $\mbox{Cl}(\mathcal{O}_KG)$ of
$\mathcal{O}_KG$. Such a class in $\mbox{Cl}(\mathcal{O}_KG)$ is said to be
$A$-realizable, and tame $A$-realizable if $K_h/K$ is tame. Let
$\mathcal{A}(\mathcal{O}_KG)$ and $\mathcal{A}^t(\mathcal{O}_KG)$ denote the
sets of all $A$-realizable classes and tame $A$-realizable classes,
respectively. For $G$ abelian, we will show that the two sets
$\mathcal{A}(\mathcal{O}_KG)$ and $\mathcal{A}^t(\mathcal{O}_KG)$ are equal
when extended scalars to the maximal order in $KG$.


  Bayesian optimization (BO) is a powerful technology for optimizing noisy
expensive-to-evaluate black-box functions, with a broad range of real-world
applications in science, engineering, economics, manufacturing, and beyond. In
this paper, we provide an overview of recent developments, challenges, and
opportunities in BO for design of next-generation process systems. After
describing several motivating applications, we discuss how advanced BO methods
have been developed to more efficiently tackle important problems in these
applications. We conclude the paper with a summary of challenges and
opportunities related to improving the quality of the probabilistic model, the
choice of internal optimization procedure used to select the next sample point,
and the exploitation of problem structure to improve sample efficiency.


  The equation of state with light clusters for nuclear and stellar matter is
determined using chemical equilibrium constants evaluated from the analysis of
the recently published (Xe$+$Sn) heavy ion data, corresponding to three
reactions with different isotopic contents of the emission source. The measured
multiplicities are used to extract the thermodynamic properties, and an
in-medium correction to the ideal gas internal partition function of the
clusters is included in the analysis. This in-medium correction and its
respective uncertainty are calculated via a Bayesian analysis, with the unique
hypothesis that the different nuclear species in a given sample must correspond
to a unique common value for the density of the expanding source. Different
parameter sets for the correction are tested, and the effect of the radius of
the clusters on the thermodynamics and on the chemical equilibrium constants is
also addressed. It is shown that the equilibrium constants obtained are almost
independent of the isospin content of the analysed systems. Finally, a
comparison with a relativistic mean field model proves that data are consistent
with a universal in-medium correction of the scalar $\sigma$-meson coupling for
nucleons bound in clusters. The obtained value, $g_s/g_s^0 = 0.92 \pm 0.02$, is
larger than that obtained in a previous study not including in-medium effects
in the data analysis. This result implies a smaller effect on the binding
energy of the clusters and, as a consequence, larger melting densities, and an
increased cluster contribution in supernova matter.


  Online shopping has become a valuable modern convenience, but blind or low
vision (BLV) users still face significant challenges using it, because of: 1)
inadequate image descriptions and 2) the inability to filter large amounts of
information using screen readers. To address those challenges, we propose
Revamp, a system that leverages customer reviews for interactive information
retrieval. Revamp is a browser integration that supports review-based
question-answering interactions on a reconstructed product page. From our
interview, we identified four main aspects (color, logo, shape, and size) that
are vital for BLV users to understand the visual appearance of a product. Based
on the findings, we formulated syntactic rules to extract review snippets,
which were used to generate image descriptions and responses to users' queries.
Evaluations with eight BLV users showed that Revamp 1) provided useful
descriptive information for understanding product appearance and 2) helped the
participants locate key information efficiently.


  When neutrinos propagate over long distances, the mass eigenstate components
of a flavor eigenstate will become spatially separated due to their different
group velocities. This can happen over terrestrial distance scales if the
neutrino energy is of order MeV and if the neutrino is localized (in a quantum
mechanical sense) to subatomic scales. For example, if the Heisenberg
uncertainty in the neutrino position is below 0.01 Angstrom, neutrino
decoherence can be observed in reactor neutrinos using a large liquid
scintillator detector.


  We examine various entropic inflation scenarios, under the light of
eternality. After describing the inflation realization and the normal condition
for inflation to last at the background level, we investigate the conditions
for eternal inflation with the effect of thermal fluctuations produced from
standard radiation and from the holographic screen. Furthermore, we incorporate
stochastic quantum fluctuations through a phenomenological, Langevin analysis,
studying whether they can affect the inflation eternality. In
single-holographic-screen scenarios eternality can be easily obtained, while in
double-screen considerations inflation is eternal only in the high-energy
regime. Thus, from the cosmological point of view, one should take these into
account before he can consider entropic gravity as a candidate for the
description of nature. However, form the string theory point of view, inflation
eternality may form the background for the "Landscape" of string/M theory
vacua, leading to new perspectives in entropy gravity.


  e present a detailed study of the retrieved optical parameters, electrical
permittivity, magnetic permeability and refractive index, of the coupled
fishnet metamaterial structures as a function of the separation between layers.
For the weak coupling case, the retrieved parameters are very close to the
one-functional-layer results and converge relatively fast. For the strong
coupling case, the retrieved parameters are completely different than the one
unit fishnet results. We also demonstrate that the high value of the figure of
merit (FOM=|Re(n)/Im(n)|) for the strongly coupled structures is due to the
fact that the real part of the negative $n$ moves away from the maximum of the
imaginary part of n (close to the resonance), where the losses are high.


  The recent observation of high-energy neutrinos from the 2017 flare of the
blazar TXS~0506+056, together with counterparts across the whole
electromagnetic spectrum, opens up new possibilities for investigating the
properties of this class of objects as well as the traversed medium.
Propagation effects such as the attenuation of the very-high-energy gamma-ray
component by the extragalactic background light are well known, and usually
taken into account when fitting spectral energy distributions of objects. Other
effects such as those of intergalactic magnetic fields are, however, often
neglected. In this work, we present a comprehensive study of the influence of
these fields and the extragalactic background light on the determination of the
intrinsic gamma-ray spectrum of this blazar.


  Maintenance decisions range from the simple detection of faults to ultimately
predicting future failures and solving the problem. These traditionally human
decisions are nowadays increasingly supported by data and the ultimate aim is
to make them autonomous. This paper explores the challenges encountered in data
driven maintenance, and proposes to consider four aspects in a maturity
framework: data / decision maturity, the translation from the real world to
data, the computability of decisions (using models) and the causality in the
obtained relations. After a discussion of the theoretical concepts involved,
the exploration continues by considering a practical fault detection and
identification problem. Two approaches, i.e. experience based and model based,
are compared and discussed in terms of the four aspects in the maturity
framework. It is observed that both approaches yield the same decisions, but
still differ in the assignment of causality. This confirms that a maturity
assessment not only concerns the type of decision, but should also include the
other proposed aspects.


  It is often useful, if not necessary, to reason about the syntactic structure
of an expression in an interpreted language (i.e., a language with a
semantics). This paper introduces a mathematical structure called a syntax
framework that is intended to be an abstract model of a system for reasoning
about the syntax of an interpreted language. Like many concrete systems for
reasoning about syntax, a syntax framework contains a mapping of expressions in
the interpreted language to syntactic values that represent the syntactic
structures of the expressions; a language for reasoning about the syntactic
values; a mechanism called quotation to refer to the syntactic value of an
expression; and a mechanism called evaluation to refer to the value of the
expression represented by a syntactic value. A syntax framework provides a
basis for integrating reasoning about the syntax of the expressions with
reasoning about what the expressions mean. The notion of a syntax framework is
used to discuss how quotation and evaluation can be built into a language and
to define what quasiquotation is. Several examples of syntax frameworks are
presented.


  User pairing in Non-Orthogonal Multiple-Access (NOMA) uplink based on channel
state information is investigated considering some predefined power allocation
schemes. The base station divides the set of users into disjunct pairs and
assigns the available resources to these pairs. The combinatorial problem of
user pairing to achieve the maximum sum rate is analyzed in the large system
limit for various scenarios, and some optimum and sub-optimum algorithms with a
polynomial-time complexity are proposed. In the first scenario, $2M$ users and
the base station have a single-antenna and communicate over $M$ subcarriers.
The performance of optimum pairing is derived for $M\rightarrow \infty$ and
shown to be superior to random pairing and orthogonal multiple access
techniques. In the second setting, a novel NOMA scheme for a multi-antenna base
station and single carrier communication is proposed. In this case, the users
need not be aware of the pairing strategy. Furthermore, the proposed NOMA
scheme is generalized to multi-antenna users. It is shown that random and
optimum user pairing perform similarly in the large system limit, but optimum
pairing is significantly better in finite dimensions. It is shown that the
proposed NOMA scheme outperforms a previously proposed NOMA scheme with signal
alignment.


  Constructing a smart wheelchair on a commercially available powered
wheelchair (PWC) platform avoids a host of seating, mechanical design and
reliability issues but requires methods of predicting and controlling the
motion of a device never intended for robotics. Analog joystick inputs are
subject to black-box transformations which may produce intuitive and adaptable
motion control for human operators, but complicate robotic control approaches;
furthermore, installation of standard axle mounted odometers on a commercial
PWC is difficult. In this work, we present an integrated hardware and software
system for predicting the motion of a commercial PWC platform that does not
require any physical or electronic modification of the chair beyond plugging
into an industry standard auxiliary input port. This system uses an RGB-D
camera and an Arduino interface board to capture motion data, including visual
odometry and joystick signals, via ROS communication. Future motion is
predicted using an autoregressive sparse Gaussian process model. We evaluate
the proposed system on real-world short-term path prediction experiments.
Experimental results demonstrate the system's efficacy when compared to a
baseline neural network model.


  Given a globally hyperbolic spacetime $M$, we show the existence of a {\em
smooth spacelike} Cauchy hypersurface $S$ and, thus, a global diffeomorphism
between $M$ and $\R \times S$.


  We show that Type IIB string theory on AdS_3 X S^3 X M_4 with p units of NS
flux contains an integrable subsector, isomorphic to the minimal (p,1) bosonic
string. To this end, we construct a topological string theory with target space
Euclidean AdS_3 X S^3. We use a variant of Hamiltonian reduction to prove its
equivalence to the minimal (p,1) string. The topological theory is then
embedded in the physical ten-dimensional IIB string theory. Correlators of
tachyons in the minimal string are mapped to correlators of spacetime chiral
primaries in the IIB theory, in the presence of background 5-form RR flux. We
also uncover a ground ring structure in AdS_3 X S^3 analogous to the well-known
ground ring of the minimal string. This tractable model provides a literal
incarnation of the idea that the holographic direction of AdS space is the
Liouville field. We discuss a few generalizations, in particular we show that
the N=4 topological string on an A_{p-1} ALE singularity also reduces to the
(p,1) minimal string.


  We conduct a comprehensive study on the sub-GeV millicharge dark matter
produced through the freeze-in mechanism. We discuss in general the mixing
mechanism, encompassing both kinetic mixing and mass mixing, between the
$U(1)_X$ hidden sector and the standard model, which can generate millicharge
carried by the dark fermions from the hidden sector. We discuss in depth how
such millicharge is generated, and clarify several misunderstandings regarding
this subject in the literature. Without employing an effective field theory
approach, where the photon field directly mixed with the additional $U(1)$, we
analyze a general renormalizable model and investigate the complete evolution
of the hidden sector particles. Due to the substantial self-interactions among
hidden sector particles, the evolution of the hidden sector temperature plays a
crucial role, which is addressed concurrently with the number densities of
hidden sector particles by solving a set of coupled Boltzmann equations. We
thoroughly examine eight benchmark models from six distinct cases. Some of our
key findings from the analysis of these benchmark models may be generalizable
and applicable to broader freeze-in scenarios. We also explore the possibility
that the $\mathcal{O}$(keV) $U(1)_X$ dark photon is a viable dark matter
candidate, even though it can contribute at most $\sim 5\%$ to the total
observed dark matter relic density.


  We show that tilting modules and parity sheaves on the affine Grassmannian
are related through the geometric Satake correspondence, when the
characteristic is bigger than an explicit bound.


  We present a free form mass reconstruction of the massive lensing cluster
MACSJ0416.1-2403 using the latest Hubble Frontier Fields data. Our model
independent method finds that the extended lensing pattern is generated by two
elongated, closely projected clusters of similar mass. Our lens model
identifies new lensed images with which we improve the accuracy of the dark
matter distribution. We find that the bimodal mass distribution is nearly
coincident with the bimodal X-ray emission, but with the two dark matter peaks
lying closer together than the centroids of the X-ray emisison. We show this
can be achieved if the collision has occurred close to the plane and such that
the cores are deflected around each other. The projected mass profiles of both
clusters are well constrained because of the many interior lensed images,
leading to surprisingly flat mass profiles of both components in the region
15-100 kpc. We discuss the extent to which this may be generated by tidal
forces in our dynamical model which are large during an encounter of this type
as the cores "graze" each other. The relative velocity between the two cores is
estimated to be about 1200 km/s and mostly along the line of sight so that our
model is consistent with the relative redshift difference between the two cD
galaxies (dz = 0.04).


  The hierarchical galaxy formation scenario in the Cold Dark Matter cosmogony
with a non-vanishing cosmological constant and geometrically flat space has
been very successful in explaining the large-scale distribution of galaxies.
However, there have been claims that the scenario predicts too many satellite
galaxies associated with massive galaxies compared to observations, called the
missing satellite galaxy problem. Isolated groups of galaxies hosted by
passively evolving massive early-type galaxies are ideal laboratories for
finding the missing physics in the current theory. Here we report from a deep
spectroscopic survey of such satellite systems that isolated massive early-type
galaxies with no recent star formation through wet mergers or accretion have
almost no satellite galaxies fainter than the r-band absolute magnitude of
about Mr =-14. If only early-type satellites are used, the cutoff is at
somewhat brighter magnitude of about Mr =-15. Such a cutoff has not been found
in other nearby satellite galaxy systems hosted by late-type galaxies or those
with merger features. Various physical properties of satellites depend strongly
on the host-centric distance. Our observation indicates that the satellite
galaxy luminosity function is largely determined by the interaction of
satellites with the environment provided by their host, which sheds light on
the missing satellite galaxy problem.


  Humans perceive the world using multi-modal sensory inputs such as vision,
audition, and touch. In this work, we investigate the cross-modal connection
between vision and touch. The main challenge in this cross-domain modeling task
lies in the significant scale discrepancy between the two: while our eyes
perceive an entire visual scene at once, humans can only feel a small region of
an object at any given moment. To connect vision and touch, we introduce new
tasks of synthesizing plausible tactile signals from visual inputs as well as
imagining how we interact with objects given tactile data as input. To
accomplish our goals, we first equip robots with both visual and tactile
sensors and collect a large-scale dataset of corresponding vision and tactile
image sequences. To close the scale gap, we present a new conditional
adversarial model that incorporates the scale and location information of the
touch. Human perceptual studies demonstrate that our model can produce
realistic visual images from tactile data and vice versa. Finally, we present
both qualitative and quantitative experimental results regarding different
system designs, as well as visualizing the learned representations of our
model.


  We present here the results of an analysis carried out by biologists and
roboticists with the aim of modeling bird locomotion kinematics for robotics
purposes. The aim was to develop a bio-inspired kinematic model of the bird leg
from biological data. We first acquired and processed kinematic data for
sagittal and top views obtained by X-ray radiography of quails walking. Data
processing involved filtering and specific data reconstruction in three
dimensions, as two-dimensional views cannot be synchronized. We then designed a
robotic model of a bird-like leg based on a kinematic analysis of the
biological data. Angular velocity vectors were calculated to define the number
of degrees of freedom (DOF) at each joint and the orientation of the rotation
axes.


  A Nevanlinna function is a function which is analytic in the open upper half
plane and has a non-negative imaginary part there. In this paper we study a
fractional linear transformation for a Nevanlinna function $n$ with a suitable
asymptotic expansion at $\infty$, that is an analogue of the Schur
transformation for contractive analytic functions in the unit disc. Applying
the transformation $p$ times we find a Nevanlinna function $n_p$ which is a
fractional linear transformation of the given function $n$. The main results
concern the effect of this transformation to the realizations of $n$ and $n_p$,
by which we mean their representations through resolvents of self-adjoint
operators in Hilbert space. Our tools are block operator matrix
representations, $u$--resolvent matrices, and reproducing kernel Hilbert
spaces.


  Due to the scale of social video sharing, User Generated Content (UGC) is
getting more attention from academia and industry. To facilitate
compression-related research on UGC, YouTube has released a large-scale
dataset. The initial dataset only provided videos, limiting its use in quality
assessment. We used a crowd-sourcing platform to collect subjective quality
scores for this dataset. We analyzed the distribution of Mean Opinion Score
(MOS) in various dimensions, and investigated some fundamental questions in
video quality assessment, like the correlation between full video MOS and
corresponding chunk MOS, and the influence of chunk variation in quality score
aggregation.


  Using the HST/WFC3 and ACS multi-band imaging data taken in CANDELS and
3D-HST, we study the general properties and the diversity of the progenitors of
the Milky Way (MWs) and local massive galaxy (MGs) at 0.5 < z < 3.0, based on a
constant cumulative number density analysis. After careful data reduction and
stacking analysis, we conduct a radially resolved pixel SED fitting to obtain
the radial distributions of the stellar mass and rest-frame colors. The stellar
mass of MWs increases in self-similar way, irrespective of the radial distance,
while that of MGs grows in inside-out way where they obtain ~ 75% of the total
mass at outer (> 2.5 kpc) radius since z ~ 2. Although the radial mass profiles
evolve in distinct ways, the formation and quenching of the central dense
region (or bulge) ahead of the outer disk formation are found to be common for
both systems. The sudden reddening of bulge at z ~ 1.6 and z ~ 2.4 for MWs and
MGs, respectively, suggests the formation of bulge and would give a clue to the
different gas accretion histories and quenching. A new approach to evaluate the
morphological diversity is conducted by using the average surface density
profile and its dispersion. The variety of the radial mass profiles for MGs
peaks at higher redshift (z > 2.8), and then rapidly converges to more uniform
shape at z < 1.5, while that for MWs remains in the outer region over the
redshift. Compared with the observed star formation rates and color profiles,
the evolution of variety is consistently explained by the star formation
activities.


  For a preloaded impact oscillator under superharmonic excitation of order 2,
the Hertzian non linearity constitutes the precursor of vibroimpacts
established over a wide frequency range. The theoretical study is performed by
using the shooting method with an arc length continuation. Experimental results
obtained from a devoted test rig agree with theoretical ones. Particularly, the
threeshold level of the excitation necessary to induce vibroimpacts is
confirmed.


  The thermal dynamics in thermo-mechanical systems exhibits a much slower time
scale compared to the structural dynamics. In this work, we use the method of
multiple scales to reduce the thermo-mechanical structural models with a
slowly-varying temperature distribution in a systematic manner. In the process,
we construct a reduction basis that adapts according to the instantaneous
temperature distribution of the structure, facilitating an efficient reduction
in the number of unknown. As a proof of concept, we demonstrate the method on a
range of linear and nonlinear beam examples and obtain a consistently better
accuracy and reduction in the number of unknowns than standard the Galerkin
projection using a constant basis.


  For cosmic microwave background (CMB) polarization observations, calibration
of detector polarization angles is essential. We have developed a fully remote
controlled calibration system with a sparse wire grid that reflects linearly
polarized light along the wire direction. The new feature is a
remote-controlled system for regular calibration, which has not been possible
in sparse wire grid calibrators in past experiments. The remote control can be
achieved by two electric linear actuators that load or unload the sparse wire
grid into a position centered on the optical axis of a telescope between the
calibration time and CMB observation. Furthermore, the sparse wire grid can be
rotated by a motor. A rotary encoder and a gravity sensor are installed on the
sparse wire grid to monitor the wire direction. They allow us to achieve
detector angle calibration with expected systematic error of $0.08^{\circ}$.
The calibration system will be installed in small-aperture telescopes at Simons
Observatory.


  A flat plate turbulent boundary layer (TBL) is experimentally subjected to a
family of 22 favorable-adverse pressure gradients (FAPGs) by using a ceiling
panel of variable convex curvature. We define a FAPG as a sequence of
streamwise pressure gradients in the order of favorable followed by adverse,
similar to the pressure gradient sequence over the suction side of an airfoil.
The adverse pressure gradient region of this configuration is studied using
particle image velocimetry (PIV) in the streamwise--wall-normal plane. The
streamwise mean and Reynolds stresses are presented and discussed in this work.
Although favorable and adverse pressure gradients are known to evoke opposing
responses from a TBL, the current adverse pressure gradient (APG) that followed
a favorable pressure gradient (FPG) was not found to 'reverse' the effect of
the FPG. Instead, a complex response that is neither characteristic of a ZPG
nor an APG TBL was observed. The Reynolds stresses showed a bimodal structure,
with the outer-scaled stresses strengthening along the streamwise direction in
$y < ~ 0.2 \delta$ and weakening in $y > ~ 0.2\delta$, where $y$ is the
wall-normal coordinate, and $\delta$, the local boundary layer thickness. These
were signatures of a new internal layer, previously observed in bump/hill
flows, formed due to the pressure gradient sign change from favorable to
adverse. The non-typical structure of and trends in the statistics were more
significant in the stronger pressure gradient cases, where the stronger
upstream FPG seemed to have exerted a stronger influence on the downstream APG.
The current dataset with 22 cases provided a well-resolved picture of the
breakdown of equilibrium of the ZPG TBL under an FAPG configuration. The
statistics for all the cases are included under the ancillary file section.


  We present a new method for constructing maps of the secondary temperature
fluctuations imprinted on the cosmic microwave background (CMB) radiation by
photons propagating through the evolving cosmic gravitational potential. Large
cosmological N-body simulations are used to calculate the complete non-linear
evolution of the peculiar gravitational potential. Tracing light rays back
through the past lightcone of a chosen observer accurately captures the
temperature perturbations generated by linear (the integrated Sachs-Wolfe or
ISW effect) and non-linear (the Rees-Sciama or RS effect) evolution. These
effects give rise to three kinds of non-linear features in the temperature
maps. (a) In overdense regions, converging flows of matter induce cold spots of
order 100 Mpc in extent which can dominate over the ISW effect at high
redshift, and are surrounded by hot rings. (b) In underdense regions, the RS
effect enhances ISW cold spots which can be surrounded by weak hot rings. (c)
Transverse motions of large lumps of matter produce characteristic dipole
features, consisting of adjacent hot and cold spots separated by a few tens of
Megaparsecs. These non-linear features are not easily detectable; they modulate
the ISW sky maps at about the 10 percent level. The RS effect causes the
angular power spectrum to deviate from linear theory at l~50 and generates
non-Gaussianity, skewing the one-point distribution function to negative
values. Cold spots of similar angular size, but much smaller amplitude than the
CMB cold spot reported by Cruz et al. are produced. Joint analysis of our maps
and the corresponding galaxy distribution may enable techniques to be developed
to detect these non-linear, non-Gaussian features. Our maps are available at
http://astro.dur.ac.uk/~cai/ISW


  We study three-dimensional Chern-Simons theory with complex gauge group
SL(2,C), which has many interesting connections with three-dimensional quantum
gravity and geometry of hyperbolic 3-manifolds. We show that, in the presence
of a single knotted Wilson loop in an infinite-dimensional representation of
the gauge group, the classical and quantum properties of such theory are
described by an algebraic curve called the A-polynomial of a knot. Using this
approach, we find some new and rather surprising relations between the
A-polynomial, the colored Jones polynomial, and other invariants of hyperbolic
3-manifolds. These relations generalize the volume conjecture and the
Melvin-Morton-Rozansky conjecture, and suggest an intriguing connection between
the SL(2,C) partition function and the colored Jones polynomial.


  For a ring R and system L of linear homogeneous equations, we call a coloring
of the nonzero elements of R minimal for L if there are no monochromatic
solutions to L and the coloring uses as few colors as possible. For a rational
number q and positive integer n, let E(q,n) denote the equation
$\sum_{i=0}^{n-2} q^{i}x_i = q^{n-1}x_{n-1}$. We classify the minimal colorings
of the nonzero rational numbers for each of the equations E(q,3) with q in
{3/2,2,3,4}, for E(2,n) with n in {3,4,5,6}, and for x_1+x_2+x_3=4x_4. These
results lead to several open problems and conjectures on minimal colorings.


  We consider a long topological Josephson junction formed on a conducting 2D
surface of a 3D topological insulator (TI). The superconducting correlations
are proximity-induced by s-wave superconductors covering the surface. The 1D
spacing between the coverings is either unfilled or filled by a magnetic
insulator. Generally, the Josephson current mediated by the TI surface is
determined by scattering modes as well as by the states localized around the
junction (Andreev bound states or Andreev bands). We find out that it is
crucial to take into account both contributions to determine the current--phase
relation of the topological Josephson junction. We analyze the dependence of
the Josephson current on the thickness of the junction as well as the
deviations from the sinusoidal shape of the current--phase relation.


  For affine stochastic differential equation with uniformly distributed time
delay the local asymptotic properties of the likelihood function are studied.
Local asymptotic normality, local asymptotic mixed normality, periodic local
asymptotic mixed normality or local asymptotic quadraticity is proved for
different values of the parameter. Applications to the asymptotic behaviour of
the maximum likelihood estimator of the parameter based on continuous sample
are given.


  Estimating depth from a single image is a challenging visual task. Compared
to relative depth estimation, metric depth estimation attracts more attention
due to its practical physical significance and critical applications in
real-life scenarios. However, existing metric depth estimation methods are
typically trained on specific datasets with similar scenes, facing challenges
in generalizing across scenes with significant scale variations. To address
this challenge, we propose a novel monocular depth estimation method called
ScaleDepth. Our method decomposes metric depth into scene scale and relative
depth, and predicts them through a semantic-aware scale prediction (SASP)
module and an adaptive relative depth estimation (ARDE) module, respectively.
The proposed ScaleDepth enjoys several merits. First, the SASP module can
implicitly combine structural and semantic features of the images to predict
precise scene scales. Second, the ARDE module can adaptively estimate the
relative depth distribution of each image within a normalized depth space.
Third, our method achieves metric depth estimation for both indoor and outdoor
scenes in a unified framework, without the need for setting the depth range or
fine-tuning model. Extensive experiments demonstrate that our method attains
state-of-the-art performance across indoor, outdoor, unconstrained, and unseen
scenes. Project page: https://ruijiezhu94.github.io/ScaleDepth


  Recent experimental and theoretical developments have motivated interest in a
more detailed exploration of heavy ion collisions in the range sqrt(sNN)=5-15
GeV. In contrast to interactions at the full RHIC energy of sqrt(sNN)=200 GeV,
such collisions result in systems characterized by much higher baryon chemical
potential, muB. Extensions of lattice QCD calculations to non-zero values of
muB suggest that a critical point may exist in this region of the QCD phase
diagram. Discovery of the critical point or, equivalently, determining the
location where the phase transition from partonic to hadronic matter switches
from a smooth crossover to 1st order would establish a major landmark in the
phase diagram. Initial studies of Pb+Pb collisions in this energy range have
revealed several unexpected features in the data. In response to these results,
it has been suggested that the existing RHIC accelerator and experiments can be
used to further the investigation of this important physics topic. This
proceeding briefly summarizes the theoretical and experimental situation with
particular emphasis on the conclusions from a RIKEN BNL workshop held in March
of 2006.


  Current and field profiles, and magnetization and ac losses are calculated
for arrays of infinitely long superconducting tapes in the critical state in a
perpendicularly applied magnetic field. The tapes are arranged both
horizontally and in a matrix configuration, which is the geometry found in many
actual high-T_c superconducting tapes. The finite thickness of the tapes and
the effects of demagnetizing fields are considered. Systematic results for the
magnetization and ac losses of the tapes are obtained as function of the
geometry and separation of the constituent tapes. Results allow to understand
some unexplained features observed in experiments, as well as to propose some
future directions.


  This article extends the works of Gon\c{c}alves, Guaschi, Ocampo [GGO] and
Marin [MAR2] on finite subgroups of the quotients of generalized braid groups
by the derived subgroup of their pure braid group. We get explicit criteria for
subgroups of the (complex) reflection group to lift to subgroups of this
quotient. In the specific case of the classical braid group, this enables us to
describe all its finite subgroups : we show that every odd-order finite group
can be embedded in it, when the number of strands goes to infinity. We also
determine a complete list of the irreducible reflection groups for which this
quotient is a Bieberbach group.


  In the settings of Euclidean Jordan algebras, normal decomposition systems
(or Eaton triples), and structures induced by complete isometric hyperbolic
polynomials, we consider the problem of optimizing a certain combination (such
as the sum) of spectral and linear$/$distance functions over a spectral set. To
present a unified theory, we introduce a new system called Fan-Theobald-von
Neumann system which is a triple $(V,W,{\lambda})$, where $V$ and $W$ are real
inner product spaces and ${\lambda}:V\rightarrow W$ is a norm preserving map
satisfying a Fan-Theobald-von Neumann type inequality together with a condition
for equality. In this general setting, we show that optimizing a certain
combination of spectral and linear$/$distance functions over a set of the form
$E={\lambda}^{-1}(Q)$ in $V$, where $Q$ is a subset of $W$, is equivalent to
optimizing a corresponding combination over the set ${\lambda}(E)$ and relate
the attainment of the optimal value to a commutativity concept. We also study
related results for convex functions in place of linear$/$distance functions.
Particular instances include the classical results of Fan and Theobald, von
Neumann, results of Tam, Lewis, and Bauschke et al., and recent results of
Ramirez et al. As an application, we present a commutation principle for
variational inequality problems over such a system.


  Using Hermite's formulation of polynomial stability conditions, static output
feedback (SOF) controller design can be formulated as a polynomial matrix
inequality (PMI), a (generally nonconvex) nonlinear semidefinite programming
problem that can be solved (locally) with PENNON, an implementation of a
penalty method. Typically, Hermite SOF PMI problems are badly scaled and
experiments reveal that this has a negative impact on the overall performance
of the solver. In this note we recall the algebraic interpretation of Hermite's
quadratic form as a particular Bezoutian and we use results on polynomial
interpolation to express the Hermite PMI in a Lagrange polynomial basis, as an
alternative to the conventional power basis. Numerical experiments on benchmark
problem instances show the substantial improvement brought by the approach, in
terms of problem scaling, number of iterations and convergence behavior of
PENNON.


  Using a directional spherical wavelet analysis we detect the integrated
Sachs-Wolfe (ISW) effect, indicated by a positive correlation between the
first-year Wilkinson Microwave Anisotropy Probe (WMAP) and NRAO VLA Sky Survey
(NVSS) data. Detections are made using both a directional extension of the
spherical Mexican hat wavelet and the spherical butterfly wavelet. We examine
the possibility of foreground contamination and systematics in the WMAP data
and conclude that these factors are not responsible for the signal that we
detect. The wavelet analysis inherently enables us to localise on the sky those
regions that contribute most strongly to the correlation. On removing these
localised regions the correlation that we detect is reduced in significance, as
expected, but it is not eliminated, suggesting that these regions are not the
sole source of correlation between the data. This finding is consistent with
predictions made using the ISW effect, where one would expect weak correlations
over the entire sky. In a flat universe the detection of the ISW effect
provides direct and independent evidence for dark energy. We use our detection
to constrain dark energy parameters by deriving a theoretical prediction for
the directional wavelet covariance statistic for a given cosmological model.
Comparing these predictions with the data we place constraints on the
equation-of-state parameter $w$ and the vacuum energy density $\Omega_\Lambda$.
We also consider the case of a pure cosmological constant, i.e. $w=-1$. For
this case we rule out a zero cosmological constant at greater than the 99.9%
significance level. All parameter estimates that we obtain are consistent with
the standand cosmological concordance model values.


  We consider the weak turbulence of whistler waves in the in low-\beta\ inner
magnetosphere of the Earth. Whistler waves with frequencies, originating in the
ionosphere, propagate radially outward and can trigger nonlinear induced
scattering by thermal electrons provided the wave energy density is large
enough. Nonlinear scattering can substantially change the direction of the wave
vector of whistler waves and hence the direction of energy flux with only a
small change in the frequency. A portion of whistler waves return to the
ionosphere with a smaller perpendicular wave vector resulting in diminished
linear damping and enhanced ability to pitch-angle scatter trapped electrons.
In addition, a portion of the scattered wave packets can be reflected near the
ionosphere back into the magnetosphere. Through multiple nonlinear scatterings
and ionospheric reflections a long-lived wave cavity containing turbulent
whistler waves can be formed with the appropriate properties to efficiently
pitch-angle scatter trapped electrons. The primary consequence on the Earth's
radiation belts is to reduce the lifetime of the trapped electron population.


  We report the results of a study of $B^{\pm}\to K^{\pm}\eta_c$ and
$B^{\pm}\to K^{\pm}\eta_c(2S)$ decays followed by $\eta_c$ and $\eta_c(2S)$
decays to $(K_SK\pi)^0$. The results are obtained from a data sample containing
535 million $B\bar{B}$-meson pairs collected by the Belle experiment at the
KEKB $e^+e^-$ collider. We measure the products of the branching fractions
${\mathcal B}(B^{\pm}\to K^{\pm}\eta_c){\mathcal B}(\eta_c\to K_S
K^{\pm}\pi^{\mp})=(26.7\pm 1.4(stat)^{+2.9}_{-2.6}(syst)\pm 4.9(model))\times
10^{-6}$ and ${\mathcal B}(B^{\pm}\to K^{\pm}\eta_c(2S)){\mathcal
B}(\eta_c(2S)\to K_S
K^{\pm}\pi^{\mp})=(3.4^{+2.2}_{-1.5}(stat+model)^{+0.5}_{-0.4} syst))\times
10^{-6}$. Interference with the non-resonant component leads to significant
model uncertainty in the measurement of these product branching fractions. Our
analysis accounts for this interference and allows the model uncertainty to be
reduced. We also obtain the following charmonia masses and widths:
$M(\eta_c)=(2985.4\pm 1.5(stat)^{+0.5}_{-2.0}(syst))$ MeV/$c^2$,
$\Gamma(\eta_c)=(35.1\pm 3.1(stat)^{+1.0}_{-1.6}(syst))$ MeV/$c^2$,
$M(\eta_c(2S))=(3636.1^{+3.9}_{-4.2}(stat+model)^{+0.7}_{-2.0}(syst))$
MeV/$c^2$,
$\Gamma(\eta_c(2S))=(6.6^{+8.4}_{-5.1}(stat+model)^{+2.6}_{-0.9}(syst))$
MeV/$c^2$.


  Augmented Language Models (ALMs) empower large language models with the
ability to use tools, transforming them into intelligent agents for real-world
interactions. However, most existing frameworks for ALMs, to varying degrees,
are deficient in the following critical features: flexible customization,
collaborative democratization, and holistic evaluation. We present gentopia, an
ALM framework enabling flexible customization of agents through simple
configurations, seamlessly integrating various language models, task formats,
prompting modules, and plugins into a unified paradigm. Furthermore, we
establish gentpool, a public platform enabling the registration and sharing of
user-customized agents. Agents registered in gentpool are composable such that
they can be assembled together for agent collaboration, advancing the
democratization of artificial intelligence. To ensure high-quality agents,
gentbench, an integral component of gentpool, is designed to thoroughly
evaluate user-customized agents across diverse aspects such as safety,
robustness, efficiency, etc. We release gentopia on Github and will
continuously move forward.


  Harmonic Hilbert spaces on locally compact abelian groups are reproducing
kernel Hilbert spaces (RKHSs) of continuous functions constructed by Fourier
transform of weighted $L^2$ spaces on the dual group. It is known that for
suitably chosen subadditive weights, every such space is a Banach algebra with
respect to pointwise multiplication of functions. In this paper, we study RKHSs
associated with subconvolutive functions on the dual group. Sufficient
conditions are established for these spaces to be symmetric Banach
$^*$-algebras with respect to pointwise multiplication and complex conjugation
of functions (here referred to as RKHAs). In addition, we study aspects of the
spectra and state spaces of RKHAs. Sufficient conditions are established for an
RKHA on a compact abelian group $G$ to have the same spectrum as the
$C^*$-algebra of continuous functions on $G$. We also consider one-parameter
families of RKHSs associated with semigroups of self-adjoint Markov operators
on $L^2(G)$, and show that in this setting subconvolutivity is a necessary and
sufficient condition for these spaces to have RKHA structure. Finally, we
establish embedding relationships between RKHAs and a class of Fourier--Wermer
algebras that includes spaces of dominating mixed smoothness used in
high-dimensional function approximation.


  Recently there has been a growing interest in fairness-aware recommender
systems including fairness in providing consistent performance across different
users or groups of users. A recommender system could be considered unfair if
the recommendations do not fairly represent the tastes of a certain group of
users while other groups receive recommendations that are consistent with their
preferences. In this paper, we use a metric called miscalibration for measuring
how a recommendation algorithm is responsive to users' true preferences and we
consider how various algorithms may result in different degrees of
miscalibration for different users. In particular, we conjecture that
popularity bias which is a well-known phenomenon in recommendation is one
important factor leading to miscalibration in recommendation. Our experimental
results using two real-world datasets show that there is a connection between
how different user groups are affected by algorithmic popularity bias and their
level of interest in popular items. Moreover, we show that the more a group is
affected by the algorithmic popularity bias, the more their recommendations are
miscalibrated.


  The number of effective relativistic neutrino species represents a
fundamental probe of the thermal history of the early Universe, and as such of
the Standard Model of Particle Physics. Traditional approaches to the neutrino
decoupling are either very technical and computationally expensive, or assume
that neutrinos decouple instantaneously. In this work, we aim to fill the gap
between these two approaches by modeling the neutrino decoupling in terms of
two simple coupled differential equations for the electromagnetic and neutrino
sector temperatures, in which all the relevant interactions are taken into
account and which allows for a straightforward implementation of BSM species.
Upon including finite temperature QED corrections we reach an accuracy on
$N_{\rm eff}$ in the SM of $0.01$. We illustrate the usefulness of this
approach to the neutrino decoupling by considering, in a model independent
manner, the impact of MeV thermal dark matter on $N_{\rm eff}$. We show that
Planck rules out electrophilic and neutrinophilic thermal dark matter particles
of $m< 3.0\,\text{MeV}$ at 95\% CL regardless of their spin, and of their
annihilation being $s$-wave or $p$-wave. We point out that thermal dark matter
particles with non-negligible interactions with both electrons and neutrinos
are more elusive to CMB observations than purely electrophilic or
neutrinophilic ones. In addition, assisted by the accuracy of our approach, we
show that CMB Stage-IV experiments will generically test thermal dark matter
particles with $m \lesssim 15\,\text{MeV}$. We make publicly available the
codes developed for this study at https://github.com/MiguelEA/nudec_BSM .


  In this paper, we survey some mathematical developments that followed from
the discovery of simple supercuspidal representations of p-adic groups.


  Room temperature Co K-edge extended x-ray absorption fine structure (EXAFS),
x-ray absorption near edge structure (XANES) including pre-edge and x-ray
diffraction (XRD) studies are carried out on LaCoO3 and PrCoO3. The Co-O,
Co-La/Pr and Co-Co bond lengths are obtained from EXAFS analysis and compared
with those obtained from XRD. The EXAFS analysis of data indicates that CoO6
octahedron is distorted in both LaCoO3 and PrCoO3. Such distortion is expected
in orthorhombic PrCoO3 but not in rhombohedral LaCoO3. This distortion in CoO6
octahedron is attributed to Jahn-Teller active Co3+ ion in intermediate spin
state in these compounds. Higher shell studies reveal that Debye-Waller (DW)
factors of Co-Pr and Co-Co bonds in PrCoO3 are more in comparison to Co-La and
Co-Co bonds in LaCoO3 indicating that these bonds are structurally more
disordered in PrCoO3. The comparison of Co-Co bond lengths and corresponding DW
factors indicates that the structural disorder plays an important role in
deciding the insulating properties of these compounds. XANES studies have shown
changes in the intensities and positions of different near edge features.


  Streets networks provide an invaluable source of information about the
different temporal and spatial patterns emerging in our cities. These streets
are often represented as graphs where intersections are modelled as nodes and
streets as links between them. Previous work has shown that raster
representations of the original data can be created through a learning
algorithm on low-dimensional representations of the street networks. In
contrast, models that capture high-level urban network metrics can be trained
through convolutional neural networks. However, the detailed topological data
is lost through the rasterisation of the street network. The models cannot
recover this information from the image alone, failing to capture complex
street network features. This paper proposes a model capable of inferring good
representations directly from the street network. Specifically, we use a
variational autoencoder with graph convolutional layers and a decoder that
outputs a probabilistic fully-connected graph to learn latent representations
that encode both local network structure and the spatial distribution of nodes.
We train the model on thousands of street network segments and use the learnt
representations to generate synthetic street configurations. Finally, we
proposed a possible application to classify the urban morphology of different
network segments by investigating their common characteristics in the learnt
space.


  Recent advances in machine learning models allowed robots to identify objects
on a perceptual nonsymbolic level (e.g., through sensor fusion and natural
language understanding). However, these primarily black-box learning models
still lack interpretation and transferability and require high data and
computational demand. An alternative solution is to teach a robot on both
perceptual nonsymbolic and conceptual symbolic levels through hybrid
neurosymbolic learning approaches with expert feedback (i.e., human-in-the-loop
learning). This work proposes a concept for this user-centered hybrid learning
paradigm that focuses on robotic surgical situations. While most recent
research focused on hybrid learning for non-robotic and some generic robotic
domains, little work focuses on surgical robotics. We survey this related
research while focusing on human-in-the-loop surgical robotic systems. This
evaluation highlights the most prominent solutions for autonomous surgical
robots and the challenges surgeons face when interacting with these systems.
Finally, we envision possible ways to address these challenges using online
apprenticeship learning based on implicit and explicit feedback from expert
surgeons.


  Relativistic transformation of electrode potential has been derived to
explain time dilation in electrode processes. The newly formulated Lorentz
transformation of the electrode potential is explained in terms of the
generation of spin 2-boson gravitons from the fusion of spin-1 boson
virtual-photons followed by their eventual escape in higher dimensions.
Gravitational transformations of electrode potential have also been derived
that explains decrease in the cell potential at the lower gravitational field.
The dropping of electrode potential at the lower gravitational field is also
explained in terms of the greater flux of gravitons escaping into higher
dimensions at lower gravitational fields than at higher gravitational fields.
Similarly potential energy associated with the spin of magnetically active
nuclei in applied magnetic field within NMR spectrometer has been shown to be
Lorentz variant that mathematically proves Hamiltonian describing the energy of
magnetically active nuclei to be Lorentz variant. Relativistic and
gravitational transformations of electrode potential and potential energy of
magnetically active nuclei under applied magnetic field are shown analogous to
one another.


  Using data collected from the AMS websites, and the internet in general, we
compute the weight-enumerator of the set of 145 AMS fellows who passed away
before Aug. 2022, according to the statistics [Age, Number of Publications,
Number of Citations]. Using Maple and elementary calculus, we deduced from it
the numbers stated in the title, as well as much more detailed and fascinating
statistical information. For example, while the correlation coefficient between
the number of publications and number of citations is, not surprisingly,
positive, it is far lower than one would expect, being a mere 0.5797 . The
appendices contain the rankings according to longevity, number of publications,
and number of citations.


  COVID-19 pandemic elucidated that knowledge systems will be instrumental in
cases where accurate information needs to be communicated to a substantial
group of people with different backgrounds and technological resources.
However, several challenges and obstacles hold back the wide adoption of
virtual assistants by public health departments and organizations. This paper
presents the Instant Expert, an open-source semantic web framework to build and
integrate voice-enabled smart assistants (i.e. chatbots) for any web platform
regardless of the underlying domain and technology. The component allows
non-technical domain experts to effortlessly incorporate an operational
assistant with voice recognition capability into their websites. Instant Expert
is capable of automatically parsing, processing, and modeling Frequently Asked
Questions pages as an information resource as well as communicating with an
external knowledge engine for ontology-powered inference and dynamic data
utilization. The presented framework utilizes advanced web technologies to
ensure reusability and reliability, and an inference engine for natural
language understanding powered by deep learning and heuristic algorithms. A use
case for creating an informatory assistant for COVID-19 based on the Centers
for Disease Control and Prevention (CDC) data is presented to demonstrate the
framework's usage and benefits.


  We consider space discretizations of the matrix Zakharov-Shabat AKNS scheme,
in particular the discrete matrix non-linear Scrhr\"odinger (DNLS) model, and
the matrix generalization of the Ablowitz-Ladik (AL) model, which is the more
widely acknowledged discretization. We focus on the derivation of solutions via
local Darboux transforms for both discretizations, and we derive novel
solutions via generic solutions of the associated discrete linear equations.
The continuum analogue is also discussed, and as an example we identify
solutions of the matrix NLS equation in terms of the heat kernel. In this frame
we also derive a discretization of the Burgers equation via the analogue of the
Cole-Hopf transform. Using the basic Darboux transforms for each scheme we
identify both matrix DNLS-like and AL hierarchies, i.e. we extract the
associated Lax pairs, via the dressing process. We also discuss the global
Darboux transform, which is the discrete analogue of the integral transform,
through the discrete Gelfand-Levitan-Marchenko (GLM) equation. The derivation
of the discrete matrix GLM equation and associated solutions are also presented
together with explicit linearizations. Particular emphasis is given in the
discretization schemes, i.e. forward/backward in the discrete matrix DNLS
scheme versus symmetric in the discrete matrix AL model.


  We have investigated the optical spectral behavior of a large sample of Fermi
blazars (40 FSRQs and 13 BL Lacs), and found two new universal optical spectral
behaviors. In the low state the optical spectrum gradually becomes softer
(steeper) or harder (flatter) but more and more slowly when the brightness
increases, and then tends to stable in the high state, which are briefly named
the redder-stable-when-brighter (RSWB) and bluer-stable-when-brighter (BSWB)
behaviors, respectively. 34 FSRQs and 7 BL Lacs exhibit clear RSWB behavior,
and 2 FSRQs and 5 BL Lacs show distinct BSWB behavior, which mean that FSRQs
favor more RSWB than BSWB behavior, while BL Lacs have no clear preference
among both behaviors. We have put forward a unified nonlinear formula to
quantitatively characterize the optical spectral behaviors of FSRQs and BL
Lacs, which can fit both kinds of behaviors very well. We argue that the RSWB
and BSWB behaviors originate from the same mechanism, and they are the
universal optical spectral behaviors for blazars. The frequently observed
redder-when-brighter (RWB) and bluer-when-brighter (BWB) trends can be
considered to be the approximations of the behaviors of RSWB and BSWB,
respectively. The rarely observed stable-when-brighter (SWB) trend can also be
viewed as an approximation or a special case of the RSWB or BSWB behavior. We
have developed a model with two constant-spectral-index components which can
not only explain well both two kinds of optical spectral behaviors, but also
successfully interpret the differential behaviors between FSRQs and BL Lacs.


  High-resolution absorption spectroscopy toward bright background sources has
had a paramount role in understanding early galaxy formation, the evolution of
the intergalactic medium and the reionisation of the Universe. However, these
studies are now approaching the boundaries of what can be achieved at
ground-based 8-10m class telescopes. The identification of primeval systems at
the highest redshifts, within the reionisation epoch and even into the dark
ages, and of the products of the first generation of stars and the chemical
enrichment of the early Universe, requires observing very faint targets with a
signal-to-noise ratio high enough to detect very faint spectral signatures. In
this paper, we describe the giant leap forward that will be enabled by ANDES,
the high-resolution spectrograph for the ELT, in these key science fields,
together with a brief, non-exhaustive overview of other extragalactic research
topics that will be pursued by this instrument, and its synergistic use with
other facilities that will become available in the early 2030s.


  Predicting traffic conditions has been recently explored as a way to relieve
traffic congestion. Several pioneering approaches have been proposed based on
traffic observations of the target location as well as its adjacent regions,
but they obtain somewhat limited accuracy due to a lack of mining road
topology. To address the effect attenuation problem, we suggest taking into
account the traffic of surrounding locations(wider than the adjacent range). We
propose an end-to-end framework called DeepTransport, in which Convolutional
Neural Networks (CNN) and Recurrent Neural Networks (RNN) are utilized to
obtain spatial-temporal traffic information within a transport network
topology. In addition, an attention mechanism is introduced to align spatial
and temporal information. Moreover, we constructed and released a real-world
large traffic condition dataset with a 5-minute resolution. Our experiments on
this dataset demonstrate our method captures the complex relationship in the
temporal and spatial domains. It significantly outperforms traditional
statistical methods and a state-of-the-art deep learning method.


  Periodicity analysis of unevenly collected data is a relevant issue in
several scientific fields. In astrophysics, for example, we have to find the
fundamental period of light or radial velocity curves which are unevenly
sampled observations of stars. Classical spectral analysis methods are
unsatisfactory to solve the problem. In this paper we present a neural network
based estimator system which performs well the frequency extraction in unevenly
sampled signals. It uses an unsupervised Hebbian nonlinear neural algorithm to
extract, from the interpolated signal, the principal components which, in turn,
are used by the MUSIC frequency estimator algorithm to extract the frequencies.
The neural network is tolerant to noise and works well also with few points in
the sequence. We benchmark the system on synthetic and real signals with the
Periodogram and with the Cramer-Rao lower bound.


  We propose a series representation for the Virasoro fusion and modular
kernels at any irrational central charge. Two distinct, yet closely related
formulas are needed for the cases $c\in \mathbb C \backslash (-\infty,1]$ and
$c <1$. We also conjecture that the formulas have a well-defined limit as the
central charge approaches rational values. Our proposal for $c <1$ agrees
numerically with the fusion transformation of the four-point spherical
conformal blocks, whereas our proposal for $c\in \mathbb C \backslash
(-\infty,1]$ agrees numerically with Ponsot and Teschner's integral formula for
the fusion kernel. The case of the modular kernel is studied as a special case
of the fusion kernel.


  We propose networking superconducting quantum circuits by transducing their
excitations (typically 4-8 GHz) to 100-500 MHz photons for transmission via
cryogenic coaxial cables. Counter-intuitively, this frequency downconversion
reduces noise and transmission losses. We introduce a multi-octave
asymmetrically threaded SQUID circuit (MOATS) capable of the required
efficient, high-rate transduction. For a 100-meter cable with $Q_i = 10^5$ at
10 mK, our approach achieves single-photon fidelities of 0.962 at 200 MHz
versus 0.772 at 8 GHz, and triples the lower bound on quantum channel capacity.
This method enables kilometer-scale quantum links while maintaining high
fidelities, combining improved performance with the practical advantages of
flexible, compact coaxial cables.


  The nonconvex and nonsmooth finite-sum optimization problem with linear
constraint has attracted much attention in the fields of artificial
intelligence, computer, and mathematics, due to its wide applications in
machine learning and the lack of efficient algorithms with convincing
convergence theories. A popular approach to solve it is the stochastic
Alternating Direction Method of Multipliers (ADMM), but most stochastic
ADMM-type methods focus on convex models. In addition, the variance reduction
(VR) and acceleration techniques are useful tools in the development of
stochastic methods due to their simplicity and practicability in providing
acceleration characteristics of various machine learning models. However, it
remains unclear whether accelerated SVRG-ADMM algorithm (ASVRG-ADMM), which
extends SVRG-ADMM by incorporating momentum techniques, exhibits a comparable
acceleration characteristic or convergence rate in the nonconvex setting. To
fill this gap, we consider a general nonconvex nonsmooth optimization problem
and study the convergence of ASVRG-ADMM. By utilizing a well-defined potential
energy function, we establish its sublinear convergence rate $O(1/T)$, where
$T$ denotes the iteration number. Furthermore, under the additional
Kurdyka-Lojasiewicz (KL) property which is less stringent than the frequently
used conditions for showcasing linear convergence rates, such as strong
convexity, we show that the ASVRG-ADMM sequence has a finite length and
converges to a stationary solution with a linear convergence rate. Several
experiments on solving the graph-guided fused lasso problem and regularized
logistic regression problem validate that the proposed ASVRG-ADMM performs
better than the state-of-the-art methods.


  We investigate the dynamics of a dark-bright soliton in a harmonic potential
using a mean-field approach via coupled nonlinear Schr\"odinger equations
appropriate to multicomponent Bose-Einstein condensates. We use a modified
perturbed dynamical variational Lagrangian approximation, where the
perturbation is due to the trap, taken as a Thomas-Fermi profile. The
wavefunction ansatz is taken as the correct hyperbolic tangent and secant
solutions in the scalar case for the dark and bright components of the soliton,
respectively. We also solve the problem numerically with psuedo-spectral
Runge-Kutta methods. We find, analytically and numerically, for weak trapping
the internal modes are nearly independent of center of mass motion of the
dark-bright soliton. In contrast, in tighter traps the internal modes couple
strongly to the center of mass motion, showing that for dark-bright solitons in
a harmonic potential the center of mass and relative degrees of freedom are not
independent. This result is robust against noise in the initial condition and
should, therefore, be experimentally observable.


  The problem of factorising positive integer $N$ into two integer factors $x$
and $y$ is first reformulated as an optimisation problem over the positive
integer domain of either of the Diophantine polynomials $Q_N(x,y)=N^2(N-xy)^2 +
x(x-y)^2$ or $R_N(x,y) = N^2(N-xy)^2 + (x-y)^2 + x$, of each of which the
optimal solution is unique with $x\le \sqrt{N} \le y$, and $x=1$ if and only if
$N$ is prime. An algorithm in the context of Adiabatic Quantum Computation is
then proposed for the general factorisation problem.


  Rough paths theory allows for a pathwise theory of solutions to differential
equations driven by highly irregular signals. The fundamental observation of
rough paths theory is that if one can define "iterated integrals" above a
signal, then one can construct solutions to differential equations driven by
the signal.
  The typical examples of the signals of interest are stochastic processes such
as (fractional) Brownian motion. However, rough paths theory is not inherently
random and therefore can treat irregular deterministic driving signals such as
a (multivariate) Weierstrass function. To the authors' best knowledge, no
explicit construction of a rough path (the "iterated integrals") above a
multivariate Weierstrass function has been constructed, nor has there been an
explicit solution to a differential equation driven by a multivariate
Weierstrass function. This note supplies a construction of a rough path above a
multivariate Weierstrass function. We conclude with some illustrations and some
examples of solving differential equations driven by rough Weierstrass
functions.


  We demonstrate that the dispersion of surface plasmon polaritons in a
periodically perforated gold film can be efficiently manipulated by femtosecond
laser pulses with the wavelengths far from the intrinsic resonances of gold.
Using a time- and frequency- resolved pump-probe technique we observe shifting
of the plasmon polariton resonances with response times from 200 to 800 fs
depending on the probe photon energy, through which we obtain comprehensive
insight into the electron dynamics in gold. We show that Wood anomalies in the
optical spectra provide pronounced resonances in differential transmission and
reflection with magnitudes up to 3% for moderate pump fluences of 0.5 mJ/cm^2.


  We propose a visual-linguistic representation learning approach within a
self-supervised learning framework by introducing a new operation, loss, and
data augmentation strategy. First, we generate diverse features for the
image-text matching (ITM) task via soft-masking the regions in an image, which
are most relevant to a certain word in the corresponding caption, instead of
completely removing them. Since our framework relies only on image-caption
pairs with no fine-grained annotations, we identify the relevant regions to
each word by computing the word-conditional visual attention using multi-modal
encoder. Second, we encourage the model to focus more on hard but diverse
examples by proposing a focal loss for the image-text contrastive learning
(ITC) objective, which alleviates the inherent limitations of overfitting and
bias issues. Last, we perform multi-modal data augmentations for
self-supervised learning via mining various examples by masking texts and
rendering distortions on images. We show that the combination of these three
innovations is effective for learning a pretrained model, leading to
outstanding performance on multiple vision-language downstream tasks.


  We point out an example of a projective family $\pi : X \to S$, a
$\pi$-pseudoeffective divisor $D$ on $X$, and a subvariety $V \subset X$ for
which the asymptotic multiplicity $\sigma_V(D;X/S)$ is infinite. This shows
that the divisorial Zariski decomposition is not always defined for
pseudoeffective divisors in the relative setting.


  This work is devoted to new constructions of symplectically fat fiber
bundles. The latter are constructed in two ways: using the Kirwan map and
expressing the fatness condition in terms of the isotropy representation
related to the G-structure over some homogeneous spaces.


  Let K be a totally real Galois number field. C. J. Hillar proved that if f in
Q[x_1,...,x_n] is a sum of m squares in K[x_1,...,x_n], then f is a sum of N(m)
squares in Q[x_1,...,x_n]. Modifying Hillar's proof, we improve the improve the
bound given for N(m), the proof being constructive as well.


  Dynamic Difficulty Adjustment (DDA) is a viable approach to enhance a
player's experience in video games. Recently, Reinforcement Learning (RL)
methods have been employed for DDA in non-competitive games; nevertheless, they
rely solely on discrete state-action space with a small search space. In this
paper, we propose a continuous RL-based DDA methodology for a visual working
memory (VWM) game to handle the complex search space for the difficulty of
memorization. The proposed RL-based DDA tailors game difficulty based on the
player's score and game difficulty in the last trial. We defined a continuous
metric for the difficulty of memorization. Then, we consider the task
difficulty and the vector of difficulty-score as the RL's action and state,
respectively. We evaluated the proposed method through a within-subject
experiment involving 52 subjects. The proposed approach was compared with two
rule-based difficulty adjustment methods in terms of player's score and game
experience measured by a questionnaire. The proposed RL-based approach resulted
in a significantly better game experience in terms of competence, tension, and
negative and positive affect. Players also achieved higher scores and win
rates. Furthermore, the proposed RL-based DDA led to a significantly less
decline in the score in a 20-trial session.


  This paper addresses mesh restoration problems, i.e., denoising and
completion, by learning self-similarity in an unsupervised manner. For this
purpose, the proposed method, which we refer to as Deep Mesh Prior, uses a
graph convolutional network on meshes to learn the self-similarity. The network
takes a single incomplete mesh as input data and directly outputs the
reconstructed mesh without being trained using large-scale datasets. Our method
does not use any intermediate representations such as an implicit field because
the whole process works on a mesh. We demonstrate that our unsupervised method
performs equally well or even better than the state-of-the-art methods using
large-scale datasets.


  We prove for Gibbs-Markov maps that the number of visits to a sequence of
shrinking sets with bounded cylindrical lengths converges in distribution to a
Poisson law. Applying to continued fractions, this result extends Doeblin's
Poisson limit theorem.


  The demand for high-performance materials, along with advanced synthesis
technologies such as additive manufacturing and 3D printing, has spurred the
development of hierarchical composites with superior properties. However,
computational modelling of such composites using physics-based solvers, while
enabling the discovery of optimal microstructures, have prohibitively high
computational cost hindering their practical application. To this extent, we
show that Neural Operators (NOs) can be used to learn and predict the strain
evolution in 2D digital composites. Specifically, we consider three
architectures, namely, Fourier NO (FNO), Wavelet NO (WNO), and Multi-wavelet NO
(MWT). We demonstrate that by providing a few initial strain frames as input,
NOs can accurately predict multiple future time steps in an extremely
data-efficient fashion, especially WNO. Further, once trained, NOs forecast the
strain trajectories for completely unseen boundary conditions. Among NOs, only
FNO offers super-resolution capabilities for estimating strains at multiple
length scales, which can provide higher material and pixel-wise resolution. We
also show that NOs can generalize to arbitrary geometries with finer domain
resolution without the need for additional training. Based on all the results
presented, we note that the FNO exhibits the best performance among the NOs,
while also giving minimum inference time that is almost three orders magnitude
lower than the conventional finite element solutions. Thus, FNOs can be used as
a surrogate for accelerated simulation of the strain evolution in complex
microstructures toward designing the next composite materials.


  We study adiabatic limits of Ricci-flat Kahler metrics on a Calabi-Yau
manifold which is the total space of a holomorphic fibration when the volume of
the fibers goes to zero. By establishing some new a priori estimates for the
relevant complex Monge-Ampere equation, we show that the Ricci-flat metrics
collapse (away from the singular fibers) to a metric on the base of the
fibration. This metric has Ricci curvature equal to a Weil-Petersson metric
that measures the variation of complex structure of the Calabi-Yau fibers. This
generalizes results of Gross-Wilson for K3 surfaces to higher dimensions.


  Present physics theory deems that the inertial mass characteristic of matter
is the result of the interaction of that matter with a newly defined additional
field called the Higgs Field after its principle researcher. Stated briefly,
the Higgs field mechanism endows "gauge bosons" in a "gauge theory" with mass,
through absorption of "Nambu-Goldstone bosons" arising in spontaneous "symmetry
breaking".
  Present physics theory deems that the gravitational mass characteristic of
matter is the result of that matter "curving" or "warping" space and time
according to the matter's presence through a mechanism not yet discovered nor
defined.
  Present physics recognizes that inertial mass and gravitational mass are
equal as an empirical fact based on highly precise experiments. But, for
example, the Earth in its orbit around the Sun experiences attraction toward
the Sun involving its gravitational mass, mg, and simultaneously experiences
that attraction balanced by Earth's orbital centripetal force involving its
inertial mass, mi.
  G M mg / r^2 = mi v^2 / r
  That the matter of planet Earth is being endowed "gauge theory bosons with
mass through absorption of Nambu-Goldstone bosons symmetry breaking in a Higgs
Field" while simultaneously "warping or curving its region of space" is beyond
the unreasonable and is simply inconceivable.
  The resolution of this issue and phenomenon is presented in the following.


  Fine-tuning is the de facto way to leverage large pretrained language models
to perform downstream tasks. However, it modifies all the language model
parameters and therefore necessitates storing a full copy for each task. In
this paper, we propose prefix-tuning, a lightweight alternative to fine-tuning
for natural language generation tasks, which keeps language model parameters
frozen, but optimizes a small continuous task-specific vector (called the
prefix). Prefix-tuning draws inspiration from prompting, allowing subsequent
tokens to attend to this prefix as if it were "virtual tokens". We apply
prefix-tuning to GPT-2 for table-to-text generation and to BART for
summarization. We find that by learning only 0.1\% of the parameters,
prefix-tuning obtains comparable performance in the full data setting,
outperforms fine-tuning in low-data settings, and extrapolates better to
examples with topics unseen during training.


  In this paper, a function on any pair of graphs is defined whose properties
are similar to the properties of dot product in vector space. This function
enables us to define graph orthogonality and, also, a new metric on isomorphism
classes of $n$-vertex graphs. Using dot product of graphs, a coordinate system
for graphs is provided which benefits us in graph isomorphism and related
problems.


  In the light-cone gauge choice for Abelian and non-Abelian gauge fields, the
vector boson propagator carries in it an additional ``spurious'' or
``unphysical'' pole intrinsic to the choice requiring a careful mathematical
treatment. Research in this field over the years has shown us that mathematical
consistency only is not enough to guarantee physically meaningful results.
Whatever the prescription invoked to handle such an object, it has to preserve
causality in the process. On the other hand the covariantization technique is a
well suited one to tackle gauge dependent poles in the Feynman integrals,
dispensing the use of {\em ad hoc} prescriptions. In this work we show that the
covariantization technique in the light-cone gauge is a direct consequence of
the canonical quantization of the theory.


  While historically, economists have been primarily occupied with analyzing
the behaviour of the markets, electronic trading gave rise to a new class of
unprecedented problems associated with market fairness, transparency and
manipulation. These problems stem from technical shortcomings that are not
accounted for in the simple conceptual models used for theoretical market
analysis. They, thus, call for more pragmatic market design methodologies that
consider the various infrastructure complexities and their potential impact on
the market procedures. First, we formally define temporal fairness and then
explain why it is very difficult for order-matching policies to ensure it in
continuous markets. Subsequently, we introduce a list of system requirements
and evaluate existing "fair" market designs in various practical and
adversarial scenarios. We conclude that they fail to retain their properties in
the presence of infrastructure inefficiencies and sophisticated technical
manipulation attacks. Based on these findings, we then introduce Libra, a
"fair" policy that is resilient to gaming and tolerant of technical
complications. Our security analysis shows that it is significantly more robust
than existing designs, while Libra's deployment (in a live foreign currency
exchange) validated both its considerably low impact on the operation of the
market and its ability to reduce speed-based predatory trading.


  A crucial aspect of understanding planet formation is determining the
binarity of the host stars. Results from radial velocity surveys and the
follow-up of Kepler exoplanet candidates have demonstrated that stellar
binarity certainly does not exclude the presence of planets in stable orbits
and the configuration may in fact be relatively common. Here we present new
results for the 30 Arietis system which confirms that the B component hosts
both planetary and stellar companions. Keck AO imaging provides direct
detection of the stellar companion and additional radial velocity data are
consistent with an orbiting star. We present a revised orbit of the known
planet along with photometry during predicted transit times. Finally, we
provide constraints on the properties of the stellar companion based on orbital
stability considerations.


  Let $R(k_1, \cdots, k_r)$ denote the classical $r$-color Ramsey number for
integers $k_i \ge 2$. The Diagonal Conjecture (DC) for classical Ramsey numbers
poses that if $k_1, \cdots, k_r$ are integers no smaller than 3 and $k_{r-1}
\leq k_r$, then $R(k_1, \cdots, k_{r-2}, k_{r-1}-1, k_r +1) \leq R(k_1, \cdots,
k_r)$. We obtain some implications of this conjecture, present evidence for its
validity, and discuss related problems.
  Let $R_r(k)$ stand for the $r$-color Ramsey number $R(k, \cdots, k)$. It is
known that $\lim_{r \rightarrow \infty} R_r(3)^{1/r}$ exists, either finite or
infinite, the latter conjectured by Erd\H{o}s. This limit is related to the
Shannon capacity of complements of $K_3$-free graphs. We prove that if DC
holds, and $\lim_{r \rightarrow \infty} R_r(3)^{1/r}$ is finite, then $\lim_{r
\rightarrow \infty} R_r(k)^{1/r}$ is finite for every integer $k \geq 3$.


  In this research, we consider the commercial aircraft trajectory optimization
problem for a general cruise model with arbitrary spatial wind fields to be
solved using the Pontryagin maximum principle. The model features two
fundamental controls, namely, throttle setting (which appears as a singular
control) and heading angle (appearing as a regular control). For a constrained
problem with minimum time-fuel objective, we show that the optimal heading
angle is fully defined through the classic Zermelo navigation identity. We also
show that the optimal throttle setting can be characterized through a complete
feedback function. The switching-point algorithm is employed to solve a case
study where we inspect the optimality conditions and graph the optimal controls
together with the optimal state and co-state variables.


  Models of Galactic 1.275 MeV emission produced by the decay of the
radionuclide $^{22}$Na have been computed. Several frequency-spatial
distributions of novae have been investigated using recent results of nova
rates and spatial distributions of novae in our Galaxy. These models allow us
to estimate the lower-limit of the $^{22}$Na mass ejected per ONe nova
detectable with the future spectrometer (SPI) of the INTEGRAL observatory as a
function of the frequency-spatial distribution of ONe novae in the Galaxy.
Calculations using recent estimations of the expected $^{22}$Na mass ejected
per ONe nova show that the detection of the Galactic emission of 1.275 MeV
photons will be difficult with the future spectrometer of the INTEGRAL
observatory, whereas the cumulative emission around the Galactic center has
some chances to be detected during the deep survey of the central radian of the
Galaxy.


  What happens to the QCD vacuum when a time-periodic circularly polarized
laser field with a sufficiently large intensity and frequency is applied? Based
on the Floquet formalism for periodically driven systems and the systematic
low-energy effective theory of QCD, we show that for a sufficiently large
frequency and above a critical intensity, the QCD vacuum is unstable against
the chiral soliton lattice of pions; a crystalline structure of topological
solitons that spontaneously breaks parity and continuous translational
symmetries. Our work would pave the way for novel "Floquet vacuum engineering."


  Our main goal in this paper is to answer new positive cases of the natural
generalized version of Hartshorne's celebrated question on cofiniteness of
local cohomology modules, and consequently of Huneke's conjecture on the
finiteness of their sets of associated primes. Our approach, by means of which
we extend several results from the literature, is essentially based on spectral
sequence techniques and connections to numerical invariants such as the
cohomological dimension and the Gorenstein projective dimension. We also
provide, over a polynomial ring, a rather pathological example of a non weakly
Laskerian module (i.e., it admits a quotient with infinitely many associated
primes) whose first local cohomology module is non-zero and has finitely many
associated primes.


  The lowest order Josephson coupling, $J_1(\theta)\cos(\phi)$, between two
d-wave superconductors with phase-difference $\phi$ across the junction
vanishes when their relative orientation is rotated by $\theta=\pi/4$. However,
in the presence of inhomogeneity, $J_{1}(\mathbf{r})$ is non-zero locally, with
a sign that fluctuates in space. We show that such a random $J_1$ generates a
global second-harmonic Josephson coupling, $J_2\cos(2\phi)$, with a sign that
favors $\phi = \pm \pi/2$, i.e., spontaneous breaking of time reversal
symmetry. The magnitude of $J_2$ is substantially enhanced if the spatial
correlations of $J_1(\mathbf{r})$ extend over large distances, such as would be
expected in the presence of large amplitude twist-angle angle disorder or
significant local electronic nematicity. We argue that this effect likely
accounts for the recent observations in twisted Josephson junctions between
high temperature superconductors.


  In this paper we prove a weak comparison principle for a reaction-diffusion
system without uniqueness of solutions. We apply the abstract results to the
Lotka-Volterra system with diffusion, a generalized logistic equation and to a
model of fractional-order chemical autocatalysis with decay. Morever, in the
case of the Lotka-Volterra system a weak maximum principle is given, and a
suitable estimate in the space of essentially bounded functions $L^{\infty}$ is
proved for at least one solution of the problem.


  Exoplanets with short orbit period reside very close to their host stars.
They transition very rapidly between different sectors of the circumstellar
space environment along their orbit, leading to large variations of the
magnetic field in the vicinity of the planet on short timescales. This rapid
change of the magnetic flux through the conducting and resistive layer of the
planetary upper atmosphere may drive currents that dissipate in the form of
Joule Heating. Here, we estimate the amount of Joule Heating dissipation in the
upper atmosphere of Trappist-1e, and two hypothetical planets orbiting the Sun
in close-in orbits. We find that the rapid orbital motion could drive a
significant amount of atmospheric heating and could significantly affect the
planetary atmosphere escape rate. Thus, the process should be accounted for
when studying the long-term evolution of exoplanetary atmospheres.


  We empirically investigate the (negative) expected accuracy as an alternative
loss function to cross entropy (negative log likelihood) for classification
tasks. Coupled with softmax activation, it has small derivatives over most of
its domain, and is therefore hard to optimize. A modified, leaky version is
evaluated on a variety of classification tasks, including digit recognition,
image classification, sequence tagging and tree tagging, using a variety of
neural architectures such as logistic regression, multilayer perceptron, CNN,
LSTM and Tree-LSTM. We show that it yields comparable or better accuracy
compared to cross entropy. Furthermore, the proposed objective is shown to be
more robust to label noise.


  Multiple-scale and broad-scale assessments often require rescaling the
original data to a consistent grain size for analysis. Rescaling categorical
raster data by spatial aggregation is common in large area ecological
assessments. However, distortion and loss of information are associated with
aggregation. Using a majority rule generally results in dominant classes
becoming more pronounced and rare classes becoming less pronounced. Using
nearest neighbor techniques generally maintains the global proportion of each
category in the original map but can lead to disaggregation. In this paper we
implement the spatial scan statistic for spatial aggregation of categorical
raster maps and describe the behavior of the technique at the local level
(aggregation unit) and global level (map). We also contrast the spatial scan
statistic technique with the majority rule and nearest neighbor approaches. In
general, the scan statistic technique behaved inverse the majority rule
approach in that rare classes rather than abundant classes were preserved. We
suggest the scan statistic techniques should be used for spatial aggregation of
categorical maps when preserving heterogeneity and information from rare
classes are important goals of the study or assessment.


  We have investigated an applicability of the scotch-tape method to
fabricating thin crystals of Fe chalcogenide FeTe1-xSx. Thin crystals with a
typical thickness of 40 nm were expectedly left on a Si substrate. Thin films
prepared using this process will develop both detailed studies on intrinsic
nature of Fe-based superconductivity and application to superconducting
devices.


  The transverse mass spectra of Omega, J/psi and psi' in Pb+Pb collisions at
158 AGeV are studied within a hydrodynamical model of the quark gluon plasma
expansion and hadronization. The model reproduces the existing data with the
common hadronization parameters: temperature T=T_H = 170 MeV and average
collective transverse velocity v_T = 0.2.


  In the last decades, dynamical mean-field theory (DMFT) and its diagrammatic
extensions have been successfully applied to describe local and nonlocal
correlation effects in correlated electron systems. Unfortunately, except for
the exact solution, it is impossible to fulfill both the Pauli principle and
conservation laws at the same time. Consequently, fundamental observables such
as the kinetic and potential energies are ambiguously defined. In this work, we
propose an approach to overcome the ambiguity in the calculation of the
potential energy within the ladder dynamical vertex approximation (D$\Gamma$A)
by introducing an effective mass renormalization parameter in both the charge
and the spin susceptibility of the system. We then apply our method to the
half-filled single-band Hubbard model on a three-dimensional bipartite cubic
lattice. We find that: (i) at weak-to-intermediate coupling, a reasonable
modification of the transition temperature $\TN$ to the antiferromagnetically
ordered state with respect to previous ladder D$\Gamma$A calculations without
charge renormalization. This is in good agreement with dual fermion and Monte
Carlo results; (ii) the renormalization of charge fluctuations in our new
approach leads to a unique value for the potential energy which is
substantially lower than corresponding ones from DMFT and non-self-consistent
ladder D$\Gamma$A; and (iii) the hierarchy of the kinetic energies between the
DMFT and the ladder D$\Gamma$A in the weak coupling regime is restored by the
consideration of charge renormalization.


  In this research, we study the change in the performance of machine learning
(ML) classifiers when various linguistic preprocessing methods of a dataset
were used, with the specific focus on linguistically-backed embeddings in
Convolutional Neural Networks (CNN). Moreover, we study the concept of Feature
Density and confirm its potential to comparatively predict the performance of
ML classifiers, including CNN. The research was conducted on a Formspring
dataset provided in a Kaggle competition on automatic cyberbullying detection.
The dataset was re-annotated by objective experts (psychologists), as the
importance of professional annotation in cyberbullying research has been
indicated multiple times. The study confirmed the effectiveness of Neural
Networks in cyberbullying detection and the correlation between classifier
performance and Feature Density while also proposing a new approach of training
various linguistically-backed embeddings for Convolutional Neural Networks.


  Vehicle acceleration and deceleration maneuvers at traffic signals results in
significant fuel and energy consumption levels. Green light optimal speed
advisory systems require reliable estimates of signal switching times to
improve vehicle fuel efficiency. Obtaining these estimates is difficult for
actuated signals where the length of each green indication changes to
accommodate varying traffic conditions. This study details a four-step Long
Short-Term Memory deep learning-based methodology that can be used to provide
reasonable switching time estimates from green to red and vice versa while
being robust to missing data. The four steps are data gathering, data
preparation, machine learning model tuning, and model testing and evaluation.
The input to the models included controller logic, signal timing parameters,
time of day, traffic state from detectors, vehicle actuation data, and
pedestrian actuation data. The methodology is applied and evaluated on data
from an intersection in Northern Virginia. A comparative analysis is conducted
between different loss functions including the mean squared error, mean
absolute error, and mean relative error used in LSTM and a new loss function is
proposed. The results show that while the proposed loss function outperforms
conventional loss functions in terms of overall absolute error values, the
choice of the loss function is dependent on the prediction horizon. In
particular, the proposed loss function is outperformed by the mean relative
error for very short prediction horizons and mean squared error for very long
prediction horizons.


  The search for new topological materials and states of matter is presently at
the forefront of quantum materials research. One powerful approach to novel
topological phases beyond the thermodynamic space is to combine different
topological/functional materials into a single materials platform in the form
of superlattices. However, despite some previous efforts, there has been a
significant gap between theories and experiments in this direction. Here, we
provide the first detailed set of experimentally-verifiable phase diagrams of
topological superlattices composed of archetypal topological insulator (TI),
Bi$_{2}$Se$_{3}$, and normal insulator (NI), In$_{2}$Se$_{3}$, by combining
molecular-level materials control, low-temperature magnetotransport
measurements, and field theoretical calculations. We show how the electronic
properties of topological superlattices evolve with unit-layer thicknesses and
utilize the weak antilocalization effect as a tool to gain quantitative
insights into the evolution of conducting channels within each set of
heterostructures. This orchestrated study opens the door to the possibility of
creating a variety of artificial-topological-phases by combining topological
materials with various other functional building blocks such as superconductors
and magnetic materials.


  We develop a framework for multiscale analysis of elliptic operators with
high-contrast random coefficients. For a general class of such operators, we
provide a detailed spectral analysis of the corresponding homogenised limit
operator. By combining stochastic techniques with operator theory, we link
objects defined on an abstract probability space to their counterparts in the
physical space. In particular, we show that the key characteristics of the
limit operator can be obtained from a single "typical" realisation in the
physical space. Under some lenient assumptions on the configuration of the
random inclusions, we fully characterise the limit of the spectra of the
high-contrast operators in question, which unlike in the periodic setting is
shown to be different to the spectrum of the homogenised operator. Introducing
a new notion of statistically relevant limiting spectrum, we describe the
connection between these two sets.


  We survey a number of models from physics, statistical mechanics, probability
theory and combinatorics, which are each described in terms of an orthogonal
polynomial ensemble. The most prominent example is apparently the Hermite
ensemble, the eigenvalue distribution of the Gaussian Unitary Ensemble (GUE),
and other well-known ensembles known in random matrix theory like the Laguerre
ensemble for the spectrum of Wishart matrices. In recent years, a number of
further interesting models were found to lead to orthogonal polynomial
ensembles, among which the corner growth model, directed last passage
percolation, the PNG droplet, non-colliding random processes, the length of the
longest increasing subsequence of a random permutation, and others. Much
attention has been paid to universal classes of asymptotic behaviors of these
models in the limit of large particle numbers, in particular the spacings
between the particles and the fluctuation behavior of the largest particle.
Computer simulations suggest that the connections go even farther and also
comprise the zeros of the Riemann zeta function. The existing proofs require a
substantial technical machinery and heavy tools from various parts of
mathematics, in particular complex analysis, combinatorics and variational
analysis. Particularly in the last decade, a number of fine results have been
achieved, but it is obvious that a comprehensive and thorough understanding of
the matter is still lacking. Hence, it seems an appropriate time to provide a
surveying text on this research area.