  We propose a high dimensional classification method that involves
nonparametric feature augmentation. Knowing that marginal density ratios are
the most powerful univariate classifiers, we use the ratio estimates to
transform the original feature measurements. Subsequently, penalized logistic
regression is invoked, taking as input the newly transformed or augmented
features. This procedure trains models equipped with local complexity and
global simplicity, thereby avoiding the curse of dimensionality while creating
a flexible nonlinear decision boundary. The resulting method is called Feature
Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by
generalizing the Naive Bayes model, writing the log ratio of joint densities as
a linear combination of those of marginal densities. It is related to
generalized additive models, but has better interpretability and computability.
Risk bounds are developed for FANS. In numerical analysis, FANS is compared
with competing methods, so as to provide a guideline on its best application
domain. Real data analysis demonstrates that FANS performs very competitively
on benchmark email spam and gene expression data sets. Moreover, FANS is
implemented by an extremely fast algorithm through parallel computing.


  The linear compressibility of two-dimensional fatty acid mesophases has
determined by grazing incidence x-ray diffraction. Surface pressure vs
molecular area isotherms were reconstructed from these measurements, and the
linear compressibility (relative distortion along a given direction for
isotropic applied stress) was determined both in the sample plane and in a
plane normal to the aliphatic chain director (transverse plane). The linear
compressibilities range over two orders of magnitude from 0.1 to 10 m/N and are
distributed depending on their magnitude in 4 different sets which we are able
to associate with different molecular mechanisms. The largest compressibilities
(10m/N) are observed in the tilted phases. They are apparently independent of
the chain length and could be related to the reorganization of the headgroup
hydrogen-bounded network, whose role should be revalued. Intermediate
compressibilities are observed in phases with quasi long-range order
(directions normal to the molecular tilt in L_2 or L_2' phases, S phase), and
could be related to the ordering of these phases. The lowest compressibilities
are observed in the solid untilted CS phase and for 1 direction of the S and
L_2'' phases. They are similar to the compressibility of crystalline polymers
and correspond to the interactions between methyl groups in the crystal.
Finally, negative compressibilities are observed in the transverse plane for
L_2' and L_2'' phases and can be traced to subtle reorganizations upon
untilting.


  We observed a test globule, B 335 in U, B, g, r, and I, and together with the
2MASS survey, this data set gives a well-defined spectral energy distribution
(SED) of a large number of stars. The SED of each star depends on the
interstellar extinction, the distance to the star, and its intrinsic SED. The
method is based on the use of stellar atmospheric models to represent the
intrinsic SEDs of the stars. Formally, it is then possible to determine the
spectral class of each star and thereby its distance. For some of the stars we
have optical spectra, allowing us to compare the photometric classification to
the spectrometric.
  We can identify one star at the front side of the globule. It has a
photometric distance of 90 pc. The closest star behind the B 335 globule has a
distance of only \approx 120 pc and we therefore determine the distance to B
335 as 90-120 pc. Our deep U image shows a relatively bright south-western rim
of the globule, and we investigate whether it might be due to a local
enhancement of the radiation field. A candidate source, located 1.5 arcminutes
outside our field, would be the field star, HD 184982. This star has an entry
in the Hipparcos Catalogue and its distance is 140-200 pc. However, we come to
the conclusion that the bright SW rim is more likely due to the wing of the
point-spread-function (PSF) of this star.


  We study the quantum chaos in the Bose-Fermi Kondo model in which the
impurity spin interacts with conduction electrons and a bosonic bath at the
intermediate temperature in the large $N$ limit. The out-of-time-ordered
correlator is calculated based on the Bethe-Salpeter equation and the Lyapunov
exponent $\lambda_L$ is extracted. Our calculation shows that the Lyapunov
exponent monotonically increases as the Kondo coupling $J_K$ increases, and it
can reach an order of $\lambda_L\sim T$ as $J_K$ approaches the $MCK$ point.
Furthermore, we also demonstrate that $\lambda_L$ decreases monotonously as the
impurity and bosonic bath coupling $g$ increases, which is contrary to the
general expectation that the most chaotic property occurs at the quantum
critical point with the non-Fermi liquid nature.


  Resilience curves have been the primary approach for conceptualizing and
representing the resilience behavior of communities during hazard events;
however, the use of resilience curves has remained as a mere conceptual and
visual tool with limited data-driven characterization and empirical grounding.
Empirical characterizations of resilience curves provide essential insights
regarding the manner in which differently impacted systems of communities
absorb perturbations and recover from disruptions. To address this gap, this
study examines human mobility resilience patterns following multiple
weather-related hazard events in the United States by analyzing more than 2000
empirical resilience curves constructed from high-resolution location-based
mobility data. These empirical resilience curves are then classified using
k-means clustering based on various features into archetypes. Three main
archetypes of human mobility resilience are identified: Type I, with rapid
recovery after mild impact; Type II, exhibiting bimodal recovery after moderate
impact; and Type III, showing slower recovery after severe impact. The results
also reveal critical thresholds, such as the bimodal recovery breakpoint at a
20% impact extent, at which the recovery rate decreases, and the critical
functional threshold at a 60% impact extent, above which recovery rate would be
rather slow. The results show that a critical functional recovery rate of 2.5%
per day is necessary to follow the bimodal resilience archetype when impact
extent exceeds more than 20%. These findings provide novel and important
insights into different resilience curve archetypes and their fundamental
properties. Departing from using resilience curves as a mere concept and visual
tool, the data-driven specification of resilience curve archetypes and their
properties improve our understanding of the resilience patterns...


  Given a numerical function $h:\mathbb Z_{\geq 0}\to\mathbb Z_{\geq 0}$ with
$h(0)>0$, the Hilbert depth of $h$ is
$\operatorname{hdepth}(h)=\max\{d\;:\;\sum\limits_{j=0}^k
(-1)^{k-j}\binom{d-j}{k-j}h(j)\geq 0\text{ for all }k\leq d\}$; see
arXiv:2309.10521 . In this note, we study the Hilbert depth of the functions
$h_2(j)=aj^2+bj+e$, $j\geq 0$, and $h_3(j)=aj^3+bj^2+cj+e$, $j\geq 0$, where
$a,b,c,e$ are some integers with $a,e>0$. We prove that if $b<0$ and $b^2\leq
4ae$ then $\operatorname{hdepth}(h_2)\leq 11$, and, if $b<0$and $b^2>4ae$ then
$\operatorname{hdepth}(h_2)\leq 13$. Also, we show that if $b<0$ and $b^2\leq
3ac$ then $\operatorname{hdepth}(h_3)\leq 67$.


  We propose a minimal nonlinear model of brittle crack propagation by
considering only the motion of the crack-tip atom. The model captures many
essential features of steady-state crack velocity and is in excellent
quantitative agreement with many-body dynamical simulations. The model exhibits
lattice-trapping. For loads just above this, the crack velocity rises sharply,
reaching a limiting value well below that predicted by elastic continuum
theory. We trace the origin of the low limiting velocity to the anharmonicity
of the potential well experienced by the crack-tip atom.


  With the OPAL detector at LEP we measured at energies around the Z0 peak the
Bose-Einstein Correlations (BECs) of neutral pion pairs. We compare the results
of this measurement with former results obtained at LEP for hadrons including
those obtained from Fermi-Dirac Correlations (FDCs).


  Let $k\ge 2$ be a positive integer and $P^+(n)$ the greatest prime factor of
a positive integer $n$ with convention $P^+(1)=1$. For any $\theta\in
\left[\frac 1{2k},\frac{17}{32k}\right)$, set
$$T_{k,\theta}(x)=\sum_{\substack{p_1\cdot\cdot\cdot p_k\le x\\
P^+(\gcd(p_1-1,...,p_k-1))\ge (p_1\cdot\cdot\cdot p_k)^\theta}}1,$$ where the
$p'$s are primes. It is proved that
$$T_{k,\theta}(x)\ll_{k}\frac{x^{1-\theta(k-1)}}{(\log x)^2},$$ which, together
with the lower bound $$T_{k,\theta}(x)\gg_{k}\frac{x^{1-\theta(k-1)}}{(\log
x)^2}$$ obtained by Wu in 2019, answer a 2015 problem of Luca, Menares and
Pizarro-Madariaga on the exact order of magnitude of $T_{k,\theta}(x)$.
  A main novelty in the proof is that, instead of using the Brun--Titchmarsh
theorem to estimate the $k^{th}$ movement of primes in arithmetic progressions,
we transform the movement to an estimation involving taking primes
simultaneously by linear shifts of primes.


  The increasing observational evidence of galactic outflows is considered as a
sign of active galactic nucleus (AGN) feedback in action. However, the physical
mechanism responsible for driving the observed outflows remains unclear, and
whether it is due to momentum, energy, or radiation is still a matter of
debate. The observed outflow energetics, in particular the large measured
values of the momentum ratio ($\dot{p}/(L/c) \sim 10$) and energy ratio
($\dot{E}_k/L \sim 0.05$), seems to favour the energy-driving mechanism; and
most observational works have focused their comparison with wind energy-driven
models. Here we show that AGN radiation pressure on dust can adequately
reproduce the observed outflow energetics (mass outflow rate, momentum flux,
and kinetic power), as well as the scalings with luminosity, provided that the
effects of radiation trapping are properly taken into account. In particular,
we predict a sub-linear scaling for the mass outflow rate ($\dot{M} \propto
L^{1/2}$) and a super-linear scaling for the kinetic power ($\dot{E}_k \propto
L^{3/2}$), in agreement with the observational scaling relations reported in
the most recent compilation of AGN outflow data. We conclude that AGN radiative
feedback can account for the global outflow energetics, at least equally well
as the wind energy-driving mechanism, and therefore both physical models should
be considered in the interpretation of future AGN outflow observations.


  Some connections between operator theory and wavelet analysis: Since the mid
eighties, it has become clear that key tools in wavelet analysis rely crucially
on operator theory. While isolated variations of wavelets, and wavelet
constructions had previously been known, since Haar in 1910, it was the advent
of multiresolutions, and subband filtering techniques which provided the tools
for our ability to now easily create efficient algorithms, ready for a rich
variety of applications to practical tasks. Part of the underpinning for this
development in wavelet analysis is operator theory. This will be presented in
the lectures, and we will also point to a number of developments in operator
theory which in turn derive from wavelet problems, but which are of independent
interest in mathematics. Some of the material will build on chapters in a new
wavelet book, co-authored by the speaker and Ola Bratteli, see
http://www.math.uiowa.edu/~jorgen/ .


  We present a comprehensive picture of the Cl0218.3-0510 protocluster at
$z=1.623$ across 10 co-moving Mpc. Using filters that tightly bracket the
Balmer and 4000 Angstrom breaks of the protocluster galaxies we obtain precise
photometric redshifts resulting in a protocluster galaxy sample that is 89+/-5%
complete and has a contamination of only 12+/-5%. Both star forming and
quiescent protocluster galaxies are located allowing us to map the structure of
the forming cluster for the first time. The protocluster contains 6 galaxy
groups, the largest of which is the nascent cluster. Only a small minority of
the protocluster galaxies are in the nascent cluster (11%) or in the other
galaxy groups (22%), as most protocluster galaxies reside between the groups.
Unobscured star forming galaxies predominantly reside between the
protocluster's groups, whereas red galaxies make up a large fraction of the
groups' galactic content, so observing the protocluster through only one of
these types of galaxies results in a biased view of the protocluster's
structure. The structure of the protocluster reveals how much mass is available
for the future growth of the cluster and we use the Millennium Simulation,
scaled to a Planck cosmology, to predict that Cl0218.3-0510 will evolve into a
2.7x 10^14 Msun cluster by the present day.


  Recently discovered superconducting infinite-layer nickelates $R$NiO$_2$
($R$=Nd, La, Pr) attracts increasing attention as a similar system to cuprates.
Both $R$NiO$_2$ and YBCO cuprates display the three-dimensional (3D) CDW with
wave vector ${\bf q}\sim(2\pi/3,0,q_z)$, while $q_z$ is non-zero and
incommensurate in the former system. Here, we reveal that the characteristic
CDW in $R$NiO$_2$ can be naturally explained as the quantum interference
between paramagnons, by focusing on the following characteristics of
$R$NiO$_2$: (i) prominent three-dimensionality in the Fermi surface and (ii)
large self-hole-doping ($\sim 14$%). This mechanism predicts the emergence of
the $d_{x^2-y^2}$-wave bond order at a secondary 3D nesting vector ${\bf
q}^c\sim(2\pi/3,0,q^c_z)$ $(q^c_z=0.2\pi\sim 2\pi/3)$. The obtained strong bond
fluctuations lead to the non-Fermi liquid electronic states and superconducting
states in nickelates.


  Quantum information stored in local operators spreads over other degrees of
freedom of the system during time evolution, known as scrambling. This process
is conveniently characterized by the out-of-time-order commutators (OTOC),
whose time dependence reveals salient aspects of the system's dynamics. Here we
study the spatially local spin correlation function i.e., the expectation value
of spin commutator and the corresponding OTOC of Dirac--Weyl systems in one,
two, and three spatial dimensions. The OTOC can be written as the square of the
expectation value of the commutator and the variance of the commutator. In
principle, the problem features two energy scales, the chemical potential, and
the high energy cutoff. We find that only the latter is dominant, therefore the
time evolution is separated into only two different regions. The spin
correlation function grows linearly with time initially and decays as $t^{-2}$
for late times. The OTOC reveals a universal $t^2$ initial growth from both the
commutator and the variance while its late time decay, $t^{-2}$ originates from
the variance of the commutator. This late time decay is identified as a
characteristic signature or Dirac-Weyl fermions. These features remain present
also at finite temperatures. Our results indicate that Dirac--Weyl systems are
slow information scramblers and are essential when additional channels for
scrambling, i.e., interaction or disorder are analyzed.


  In the 17th and 18th centuries, several natural philosophers studied the
phenomenon of refraction and attempted to obtain the Snell law from various
assumptions. Lacking experimental data, it was generally believed that light
travels faster in a refracting medium than in air. In the present article, I
review the contributions to the problem of light refraction by Descartes,
Fermat, Huygens, Leibniz, Newton, Clairaut, and finally Maupertuis who
established a principle of least action based on his own approach to the
problem.


  We develop a structure theory for nilpotent symplectic alternating algebras.
We then give a classification of all nilpotent symplectic alternating algebras
of dimension up to 10 over any field. The study reveals a new subclasses of
powerful groups that we call powerfully nilpotent groups and powerfully soluble
groups.


  We theoretically study semi-supervised clustering in sparse graphs in the
presence of pairwise constraints on the cluster assignments of nodes. We focus
on bi-cluster graphs, and study the impact of semi-supervision for varying
constraint density and overlap between the clusters. Recent results for
unsupervised clustering in sparse graphs indicate that there is a critical
ratio of within-cluster and between-cluster connectivities below which clusters
cannot be recovered with better than random accuracy. The goal of this paper is
to examine the impact of pairwise constraints on the clustering accuracy. Our
results suggests that the addition of constraints does not provide automatic
improvement over the unsupervised case. When the density of the constraints is
sufficiently small, their only impact is to shift the detection threshold while
preserving the criticality. Conversely, if the density of (hard) constraints is
above the percolation threshold, the criticality is suppressed and the
detection threshold disappears.


  The online advertising market, with its thousands of auctions run per second,
presents a daunting challenge for advertisers who wish to optimize their spend
under a budget constraint. Thus, advertising platforms typically provide
automated agents to their customers, which act on their behalf to bid for
impression opportunities in real time at scale. Because these proxy agents are
owned by the platform but use advertiser funds to operate, there is a strong
practical need to balance reliability and explainability of the agent with
optimizing power. We propose a generalizable approach to optimizing bidding
policies in production environments by learning from real data using offline
reinforcement learning. This approach can be used to optimize any
differentiable base policy (practically, a heuristic policy based on principles
which the advertiser can easily understand), and only requires data generated
by the base policy itself. We use a hybrid agent architecture that combines
arbitrary base policies with deep neural networks, where only the optimized
base policy parameters are eventually deployed, and the neural network part is
discarded after training. We demonstrate that such an architecture achieves
statistically significant performance gains in both simulated and at-scale
production bidding environments. Our approach does not incur additional
infrastructure, safety, or explainability costs, as it directly optimizes
parameters of existing production routines without replacing them with black
box-style models like neural networks.


  In this paper we construct a graded universal enveloping algebra of a
$G$-graded Lie algebra, where $G$ is not necessarily an abelian group. If the
grading group is abelian, then it coincides with the classical construction. We
prove the existence and uniqueness of the graded enveloping algebra. As
consequences, we prove a graded variant of Witt's Theorem on the universal
enveloping algebra of the free Lie algebra, and the graded version of Ado's
Theorem, which states that every finite-dimensional Lie algebra admits a
faithful finite dimensional representation. Furthermore we investigate if a Lie
grading is equivalent to an abelian grading.


  In this paper, we formulate a construction of ideal coset invariants for
surface-links in $4$-space using invariants for knots and links in $3$-space.
We apply the construction to the Kauffman bracket polynomial invariant and
obtain an invariant for surface-links called the Kauffman bracket ideal coset
invariant of surface-links. We also define a series of new invariants
$\{{\mathbf K}_{2n-1}(\mathcal L) | n=2, 3, 4, \ldots\}$ for surface-links
$\mathcal L$ by using skein relations, which are more effective than the
Kauffman bracket ideal coset invariant to distinguish given surface-links.


  The canonical statistical model analysis of strange and multistrange hadron
production in central A-A relative to p-p/p-A collisions is presented over the
energy range from $\sqrt s=8.73$ GeV up to $\sqrt s =130$ GeV. It is shown that
the relative enhancement of strange particle yields from p-p/p-A to A-A
collisions substantially increases with decreasing collision energy. It is
largest at $\sqrt s= 8.7$ GeV, where the enhancement of $\Omega,\Xi$ and
$\Lambda$ is of the order of 100, 20 and 3, respectively. In terms of the model
these results are due to the canonical suppression of particle thermal phase
space at lower energies, which increases with the strangeness content of the
particle and with decreasing size of the collision fireball. The comparison of
the model with existing data on energy dependence of the kaon/pion ratio is
also discussed.


  The local Gauss law of quantum chromodynamics on a finite lattice is
investigated. It is shown that it implies a gauge invariant, additive law
giving rise to a gauge invariant ${\mathbb Z}_3$-valued global charge in QCD.
The total charge contained in a region of the lattice is equal to the flux
through its boundary of a certain ${\mathbb Z}_3$-valued, additive quantity.
Implications for continuous QCD are discussed.


  We start with a revision study of two coupled spin-$1/2$ under the influence
of Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interaction and a magnetic
field. We first show the role of idle levels, i.e., levels that do not couple
to the external magnetic field, when the system is working as a heat engine as
well as when it is a refrigerator. Then we extend the results reported in [PRE.
92, (2015) 022142] by showing that it is not necessary to change both the
magnetic field as well as the coupling parameters to break the extensive
property of the work extracted globally from two coupled spin-$1/2$ as has been
demonstrated there. Then we study the role of increasing the number of coupled
spins on efficiency, extractable work, and coefficient of performance (COP).
First, we consider two- and three-coupled spin-$1/2$ Heisenberg
$\mathrm{XXX}$-chain. We prove that the latter can outperform the former in
terms of efficiency, extractable work, and COP. Then we consider the Ising
model, where the number of interacting spins ranges from two to six. We show
that only when the number of interacting spins is odd the system can work as a
heat engine in the strong coupling regime. The enhancements in efficiency and
COP are explored in detail. Finally, this model confirms the idea that
entanglement and quantum correlations are not the reasons behind the
enhancements observed in efficiency, extracatable work, and COP, but only due
to the structure of the energy levels of the Hamiltonian of the working
substance. In addition to this, the extensive property of global work as well,
is not affected by entanglement and quantum correlations.


  Calculating dipole moments with high-order basis sets is generally only
possible for the light molecules, such as water. A simple, yet highly effective
strategy of obtaining high-order dipoles with small, computationally less
expensive basis sets is described. Using the finite field method for computing
dipoles, energies calculated with small basis sets can be extrapolated to
produce dipoles that are comparable to those obtained in high order
calculations. The method reduces computational resources by approximately 50%
(allowing the calculation of reliable dipole moments for larger molecules) and
simultaneously improves the agreement with experimentally measured infrared
transition intensities. For atmospherically important molecules which are
typically too large to consider the use of large basis sets, this procedure
will provide the necessary means of improving calculated spectral intensities
by several percent.


  Supermassive primordial stars in hot, atomically-cooling haloes at $z \sim$
15 - 20 may have given birth to the first quasars in the universe. Most
simulations of these rapidly accreting stars suggest that they are red, cool
hypergiants, but more recent models indicate that some may have been bluer and
hotter, with surface temperatures of 20,000 - 40,000 K. These stars have
spectral features that are quite distinct from those of cooler stars and may
have different detection limits in the near infrared (NIR) today. Here, we
present spectra and AB magnitudes for hot, blue supermassive primordial stars
calculated with the TLUSTY and CLOUDY codes. We find that photometric
detections of these stars by the James Webb Space Telescope (JWST) will be
limited to $z \lesssim$ 10 - 12, lower redshifts than those at which red stars
can be found, because of quenching by their accretion envelopes. With moderate
gravitational lensing, Euclid and the Wide-Field Infrared Space Telescope
(WFIRST) could detect blue supermassive stars out to similar redshifts in
wide-field surveys.


  In this paper, we classify the nondegenerate ruled surfaces in the
three-dimensional Lorentz-Minkowski space that are homothetic self-similar
solutions for the inverse mean curvature flow. This classification shows the
existence of two classes of non-cylindrical homothetic solitons: one with
lightlike rulings and another one with non-lightlike rulings.


  In this paper we analyse logic of false belief in intuitionistic setting.
This logic, studied in its classical version by Steinsvold, Fan, Gilbert and
Venturi, describes the following situation: a formula F is not satisfied in a
given world, but we still believe in it (or we think that it should be
accepted). Another interpretations are also possible: e.g. that we do not
accept F but it is imposed on us by a kind of council or advisory board. From
the mathematical point of view, the idea is expressed by an adequate form of
modal operator W which is interpreted in relational frames with neighborhoods.
We discuss monotonicity of forcing, soundness, completeness and several other
issues. We present also some simple systems in which confirmation of previously
accepted formula is modelled.


  The matrix elements of local operators such as the electromagnetic current,
the energy momentum tensor, angular momentum, and the moments of structure
functions have exact representations in terms of light-cone Fock state
wavefunctions of bound states such as hadrons. We illustrate all of these
properties by giving explicit light-cone wavefunctions for the two-particle
Fock state of the electron in QED, thus connecting the Schwinger anomalous
magnetic moment to the spin and orbital momentum carried by its Fock state
constituents. We also compute the QED one-loop radiative corrections for the
form factors for the graviton coupling to the electron and photon. Although the
underlying model is derived from elementary QED perturbative couplings, it in
fact can be used to simulate much more general bound state systems by applying
spectral integration over the constituent masses while preserving all of the
Lorentz properties, giving explicit realization of the spin sum rules and other
local matrix elements. The role of orbital angular momentum in understanding
the "spin crisis" problem for relativistic systems is clarified. We also prove
that the anomalous gravitomagnetic moment B(0) vanishes for any composite
system. This property is shown to follow directly from the Lorentz boost
properties of the light-cone Fock representation and holds separately for each
Fock state component. We show how the QED perturbative structure can be used to
model bound state systems while preserving all Lorentz properties. We thus
obtain a theoretical laboratory to test the consistency of formulae which have
been proposed to probe the spin structure of hadrons.


  The relation between the observed UV continuum slope ($\beta$) and the
infrared excess (IRX) is used as a powerful probe to understand the nature of
dust attenuation law in high-redshift galaxies. We present a study of 83
UV-selected galaxies between redshift 0.5 and 0.7 from the AstroSat UV Deep
Field north (AUDFn) that encloses the GOODS-north field. Using empirical
relation, we estimate the observed IRX of 52 galaxies that are detected in
either one or both of the Herschel PACS 100$\mu$m and 160$\mu$m bands. We
further utilize the multi-band photometric data in 14 - 18 filters from the
UVIT, KPNO, HST, Spitzer, and Herschel telescopes to perform spectral energy
distribution (SED) modeling. Both the observed and model-derived IRX - $\beta$
values show a large scatter within the span of previously known relations,
signifying diversity in dust attenuation. We found a distinct relation between
the best-fit power law slope of the modified Calzetti relation ($\delta$) in
the IRX - $\beta$ plane: where the steeper SMC-like attenuation law prefers
lower $\delta$ values. Our SED model based IRX - $\beta$ relation shows a
preference for steeper SMC-like attenuation which we further confirm from the
agreement between extinction-corrected star formation rates derived using
H$\alpha$ emission line and the observed FUV plus reprocessed far-IR fluxes.
The current study reveals a strong positive correlation between IRX and the
galaxy stellar mass between $10^{9.5}$ and $10^{11.0}$ M$_{\odot}$, signifying
increased dust production in more massive star-forming galaxies.


  We introduce the notion of cascade connection of multiparametric discrete
time-invariant linear dynamical systems with unit delay. This allows us to
construct the explicit example of conservative realization of a decomposable
operator-valued function $\theta (z_1, z_2)=\theta_2(z_2)\theta_1(z_1)$, where
$\theta_1$ and $\theta_2$ are inner operator-valued functions on the unit disk,
vanishing at zero, and discuss some properties of such realization.


  In this paper we introduce the Temporo-Spatial Vision Transformer (TSViT), a
fully-attentional model for general Satellite Image Time Series (SITS)
processing based on the Vision Transformer (ViT). TSViT splits a SITS record
into non-overlapping patches in space and time which are tokenized and
subsequently processed by a factorized temporo-spatial encoder. We argue, that
in contrast to natural images, a temporal-then-spatial factorization is more
intuitive for SITS processing and present experimental evidence for this claim.
Additionally, we enhance the model's discriminative power by introducing two
novel mechanisms for acquisition-time-specific temporal positional encodings
and multiple learnable class tokens. The effect of all novel design choices is
evaluated through an extensive ablation study. Our proposed architecture
achieves state-of-the-art performance, surpassing previous approaches by a
significant margin in three publicly available SITS semantic segmentation and
classification datasets. All model, training and evaluation codes are made
publicly available to facilitate further research.


  This paper presents an efficient coupling of the 3D Stokes flow interacting
with an effective perforated periodic heterogeneous anisotropic 2D plate. The
effective model was obtained by the asymptotic analysis in earlier works and
here an effective numerical algorithm is given. By $Q_3$ or bi-cubic spacial
interpolation the time-dependent problem was reduced to an algebraic system of
ordinary differential equation in time. Different examples were given,
demonstrating the influence of the structural plate parameters on the solution.


  The nature of the first Pop III stars is still a mystery and the energy
distribution of the first supernovae is completely unexplored. For the first
time we account simultaneously for the unknown initial mass function (IMF),
stellar mixing, and energy distribution function (EDF) of Pop III stars in the
context of a cosmological model for the formation of a MW-analogue. Our
data-calibrated semi-analytic model is based on a N-body simulation and follows
the formation and evolution of both Pop III and Pop II/I stars in their proper
timescales. We discover degeneracies between the adopted Pop III unknowns, in
the predicted metallicity and carbonicity distribution functions and the
fraction of C-enhanced stars. Nonetheless, we are able to provide the first
available constraints on the EDF, $dN/dE_\star \propto E_{\star}^{-\alpha_e}$
with $1\leq \alpha_e \leq2.5$. In addition, the characteristic mass of the Pop
III IMF should be $m_{\rm ch}<100\:{\rm M_\odot}$, assuming a mass range
consistent with hydrodynamical simulations (0.1-1000$\:{\rm M_\odot}$).
Independent of the assumed Pop III properties, we find that all [C/Fe]>+0.7
stars (with [Fe/H]<-2.8) have been enriched by Pop III supernovae at a $>20\%$
level, and all [C/Fe]>+2 stars at a $>95\%$ level. All very metal-poor stars
with $\rm [C/Fe]<0$ are predicted to be predominantly enriched by Pop III
hypernovae and/or pair instabillity supernovae. To better constrain the
primordial EDF, it is absolutely crucial to have a complete and accurate
determination of the metallicity distribution function, and the properties of
C-enhanced metal-poor stars (frequency and [C/Fe]) in the Galactic halo.


  This is the introduction to the section on Quantum Mechanics in the
centennial collection of noteworthy articles appearing in The Physical Review
and Physical Review Letters through 1983, since it all began in 1893. The
selections for this section are "Can Quantum-Mechanical Description of Physical
Reality Be Considered Complete?" by Einstein, Podolsky and Rosen; Bohr's
response, with the same title; Bohm's first hidden variables paper: "A
Suggested Interpretation of the Quantum Theory in Terms of `Hidden' Variables.
I"; Aharonov and Bohm's "Significance of Electromagnetic Potentials in the
Quantum Theory"; and "Experimental Test of Bell's Inequalities Using
Time-Varying Analyzers" by Aspect, Dalibard and Roger.


  We discuss the uncertainty on processes computed using next-to-next-to
leading (NNLO) parton distributions (PDFs) due to the neglect of higher order
perturbative corrections in the PDF determination, in the specific case of
Higgs production in gluon fusion. By studying the behaviour of the perturbative
series for this process, we show that this uncertainty is negligible in
comparison to the theoretical uncertainty on the matrix element. We then take
this as a case study for the use of the Cacciari-Houdeau method for the
estimate of theoretical uncertainties, and show that the method provides an
effective way of treating theoretical uncertainties on the matrtix element and
the PDF on the same footing.


  This paper presents a novel method for layout of undirected graphs, where
nodes (vertices) are constrained to lie on a set of nested, simple, closed
curves. Such a layout is useful to simultaneously display the structural
centrality and vertex distance information for graphs in many domains,
including social networks. Closed curves are a more general constraint than the
previously proposed circles, and afford our method more flexibility to preserve
vertex relationships compared to existing radial layout methods. The proposed
approach modifies the multidimensional scaling (MDS) stress to include the
estimation of a vertex depth or centrality field as well as a term that
penalizes discord between structural centrality of vertices and their alignment
with this carefully estimated field. We also propose a visualization strategy
for the proposed layout and demonstrate its effectiveness using three social
network datasets.


  A generic degenerate Lagrangian system of even and odd fields is examined in
algebraic terms of the Grassmann-graded variational bicomplex. Its
Euler-Lagrange operator obeys Noether identities which need not be independent,
but satisfy first-stage Noether identities, and so on. We show that, if a
certain necessary and sufficient condition holds, one can associate to a
degenerate Lagrangian system the exact Koszul-Tate complex with the boundary
operator whose nilpotency condition restarts all its Noether and higher-stage
Noether identities. This complex provides a sufficient analysis of the
degeneracy of a Lagrangian system for the purpose of its BV quantization.


  The bipartite graph structure has shown its promising ability in facilitating
the subspace clustering and spectral clustering algorithms for large-scale
datasets. To avoid the post-processing via k-means during the bipartite graph
partitioning, the constrained Laplacian rank (CLR) is often utilized for
constraining the number of connected components (i.e., clusters) in the
bipartite graph, which, however, neglects the distribution (or normalization)
of these connected components and may lead to imbalanced or even ill clusters.
Despite the significant success of normalized cut (Ncut) in general graphs, it
remains surprisingly an open problem how to enforce a one-step normalized cut
for bipartite graphs, especially with linear-time complexity. In this paper, we
first characterize a novel one-step bipartite graph cut (OBCut) criterion with
normalized constraints, and theoretically prove its equivalence to a trace
maximization problem. Then we extend this cut criterion to a scalable subspace
clustering approach, where adaptive anchor learning, bipartite graph learning,
and one-step normalized bipartite graph partitioning are simultaneously modeled
in a unified objective function, and an alternating optimization algorithm is
further designed to solve it in linear time. Experiments on a variety of
general and large-scale datasets demonstrate the effectiveness and scalability
of our approach.


  The linear algorithm of the the full non-linear large scale structure of
Gaussian random fields is extended here to to perform non-linear CRs. The
procedure consists of: (1) Using linear CR of low resolution data to construct
a high resolution realization of the underlying field, as if the linear theory
is valid; (2) Taking the linear CR backwards in time, by the linear theory, to
set initial conditions for an N-body simulation; (3) Forwarding the field in
time by an N-body code. An intermediate step might be introduced to `linearize'
the low resolution data.
  The non-linear CR can be applied to any observational data set that is
linearly related to the underlying field. Here it is applied to the IRAS 1.2Jy
catalog using 843 data points within a sphere of $6000 Km/s$, to reconstruct
the full non-linear large scale structure of our `local' universe.


  Phase-coupled oscillators serve as paradigmatic models of networks of weakly
interacting oscillatory units in physics and biology. The order parameter which
quantifies synchronization was so far found to be chaotic only in systems with
inhomogeneities. Here we show that even symmetric systems of identical
oscillators may not only exhibit chaotic dynamics, but also chaotically
fluctuating order parameters. Our findings imply that neither inhomogeneities
nor amplitude variations are necessary to obtain chaos, i.e., nonlinear
interactions of phases give rise to the necessary instabilities.


  The TAC (Turkish Accelerator Center) IR FEL Oscillator facility, which has
been supported by Turkish State Planning Organization (SPO) since 2006, will be
based on a 15-40 MeV electron linac accompanying two different undulators with
2.5 cm and 9 cm periods in order to obtain IR FEL ranging between 2-250
microns. The electron linac will consist of two sequenced modules, each housing
two 9-cell superconducting TESLA cavities for cw operation. It is planned that
the TAC IR FEL facility will be completed in 2012 at Golbasi campus of Ankara
University. This facility will give an opportunity to the scientists and
industry to use FEL in research and development in Turkey and our region. In
this study, the results of optimization studies and present plans about
construction process of the facility are presented.


  We define an integral form of the deformed W-algebra of type gl_r, and
construct its action on the K-theory groups of moduli spaces of rank r stable
sheaves on a smooth projective surface S, under certain assumptions. Our
construction generalizes the action studied by Nakajima, Grojnowski and
Baranovsky in cohomology, although the appearance of deformed W-algebras by
generators and relations is a new feature. Physically, this action encodes the
AGT correspondence for 5d supersymmetric gauge theory on S x circle.


  We consider the form of Hubble diagrams that would be constructed by
observers in universes that are homogeneous but anisotropic, when averaged over
suitably large length-scales. This is achieved by ray-tracing in different
directions on the sky in families of exact inhomogeneous cosmological solutions
of Einstein's equations, in order to determine the redshifts and luminosity
distances that observers in these space-times would infer for distant
astrophysical objects. We compare the results of this procedure to the Hubble
diagrams that would be obtained by direct use of the large-scale-averaged
anisotropic cosmological models, and find that observables calculated in the
averaged model closely agree with those obtained from ray-tracing in all cases
where a statistical homogeneity scale exists. In contrast, we find that in
cosmologies with spaces that contain no statistical homogeneity scale that
Hubble diagrams inferred from the averaged cosmological model can differ
considerably from those that observers in the space-time would actually
construct. We hope that these results will be of use for understanding and
interpreting recent observations that suggest that large-scale anisotropy may
have developed in the late Universe.


  Temporal inhomogeneities observed in various natural and social phenomena
have often been characterized in terms of scaling behaviors in the
autocorrelation function with a decaying exponent $\gamma$, the interevent time
distribution with a power-law exponent $\alpha$, and the burst size
distributions. Here the interevent time is defined as a time interval between
two consecutive events in the event sequence, and the burst size denotes the
number of events in a bursty train detected for a given time window. In order
to understand such temporal scaling behaviors implying a hierarchical temporal
structure, we devise a hierarchical burst model by assuming that each observed
event might be a consequence of the multi-level causal or decision-making
process. By studying our model analytically and numerically, we confirm the
scaling relation $\alpha+\gamma=2$, established for the uncorrelated interevent
times, despite of the existence of correlations between interevent times. Such
correlations between interevent times are supported by the stretched
exponential burst size distributions, for which we provide an analytic
argument. In addition, by imposing conditions for the ordering of events, we
observe an additional feature of log-periodic behavior in the autocorrelation
function. Our modeling approach for the hierarchical temporal structure can
help us better understand the underlying mechanisms behind complex bursty
dynamics showing temporal scaling behaviors.


  High-Entropy Materials are composed of multiple elements on comparatively
simpler lattices. Due to the multicomponent nature of such materials, the
atomic scale sampling is computationally expensive due to the combinatorial
complexity. We propose a genetic algorithm based methodology for sampling such
complex chemically-disordered materials. Genetic Algorithm based Atomistic
Sampling Protocol (GAASP) variants can generate low and well as high-energy
structures. GAASP low-energy variant in conjugation with metropolis criteria
avoids the premature convergence as well as ensures the detailed balance
condition. GAASP can be employed to generate the low-energy structures for
thermodynamic predictions as well as diverse structures can be generated for
machine learning applications.


  We consider one-level additive Schwarz preconditioners for a family of
Helmholtz problems with absorption and increasing wavenumber $k$. These
problems are discretized using the Galerkin method with nodal conforming finite
elements of any (fixed) order on meshes with diameter $h = h(k)$, chosen to
maintain accuracy as $k$ increases. The action of the preconditioner requires
solution of independent (parallel) subproblems (with impedance boundary
conditions) on overlapping subdomains of diameter $H$ and overlap $\delta\leq
H$. The solutions of these subproblems are linked together using
prolongation/restriction operators defined using a partition of unity. In
numerical experiments (with $\delta \sim H$) for a model interior impedance
problem, we observe robust (i.e. $k-$independent) GMRES convergence as $k$
increases. This provides a highly-parallel, $k-$robust one-level domain
decomposition method. We provide supporting theory by studying the
preconditioner applied to a range of absorptive problems, $k^2\mapsto k^2+
\mathrm{i} \varepsilon$, with absorption parameter $\varepsilon$. Working in
the Helmholtz ``energy'' inner product, and using the underlying theory of
Helmholtz boundary-value problems, we prove a $k-$independent upper bound on
the norm of the preconditioned matrix, valid for all $\vert \varepsilon\vert
\lesssim k^2$. We also prove a strictly-positive lower bound on the distance of
the field of values of the preconditioned matrix from the origin which holds
when $\varepsilon/k$ is constant or growing arbitrarily slowly with $k$. These
results imply robustness of the preconditioner for the corresponding absorptive
problem as k increases and give theoretical support for the observed robustness
of the preconditioner for the pure Helmholtz problem.


  The string equations of motion for some homogeneous (Kantowski-Sachs, Bianchi
I and Bianchi IX) background spacetimes are given, and solved explicitly in
some simple cases. This is motivated by the recent developments in string
cosmology, where it has been shown that, under certain circumstances, such
spacetimes appear as string-vacua.
  Both tensile and null strings are considered. Generally, it is much simpler
to solve for the null strings since then we deal with the null geodesic
equations of General Relativity plus some additional constraints.
  We consider in detail an ansatz corresponding to circular strings, and we
discuss the possibility of using an elliptic-shape string ansatz in the case of
homogeneous (but anisotropic) backgrounds.


  The aim of this paper is to analyse the evolution of the COVID-19 pandemic in
Rio Grande do Sul by applying graph-theoretical tools, particularly spectral
clustering techniques, on weighted graphs defined on the set of 167
municipalities in the state with population 10,000 or more, which are based on
data provided by government agencies and other sources. To respond to this
outbreak, the state has adopted a system by which pre-determined regions are
assigned flags on a weekly basis, and different measures go into effect
according to the flag assigned. Our results suggest that considering a flexible
approach to the regions themselves might be a useful additional tool to give
more leeway to cities with lower incidence rates, while keeping the focus on
public safety. Moreover, simulations show the dampening effect of isolation on
the dissemination of the disease.


  The phase diagram of correlated, disordered electron systems is calculated
within dynamical mean-field theory using the H\"older mean local density of
states. A critical disorder strength is determined in the
Anderson-Falicov-Kimball model and the arithmetically and the geometrically
averages are found to be just particular means used respectively to detect or
not the Anderson localization. Correlated metal, Mott insulator and Anderson
insulator phases, as well as coexistence and crossover regimes are analyzed in
this new perspective.


  Aspect-based Sentiment Analysis (ABSA) seeks to predict the sentiment
polarity of a sentence toward a specific aspect. Recently, it has been shown
that dependency trees can be integrated into deep learning models to produce
the state-of-the-art performance for ABSA. However, these models tend to
compute the hidden/representation vectors without considering the aspect terms
and fail to benefit from the overall contextual importance scores of the words
that can be obtained from the dependency tree for ABSA. In this work, we
propose a novel graph-based deep learning model to overcome these two issues of
the prior work on ABSA. In our model, gate vectors are generated from the
representation vectors of the aspect terms to customize the hidden vectors of
the graph-based models toward the aspect terms. In addition, we propose a
mechanism to obtain the importance scores for each word in the sentences based
on the dependency trees that are then injected into the model to improve the
representation vectors for ABSA. The proposed model achieves the
state-of-the-art performance on three benchmark datasets.


  In this paper we give local error estimates in Sobolev norms for the Galerkin
method applied to strongly elliptic pseudodifferential equations on a polygon.
By using the K-operator, an operator which averages the values of the Galerkin
solution, we construct improved approximations.


  Many powerful machine learning models are based on the composition of
multiple processing layers, such as deep nets, which gives rise to nonconvex
objective functions. A general, recent approach to optimise such "nested"
functions is the method of auxiliary coordinates (MAC). MAC introduces an
auxiliary coordinate for each data point in order to decouple the nested model
into independent submodels. This decomposes the optimisation into steps that
alternate between training single layers and updating the coordinates. It has
the advantage that it reuses existing single-layer algorithms, introduces
parallelism, and does not need to use chain-rule gradients, so it works with
nondifferentiable layers. With large-scale problems, or when distributing the
computation is necessary for faster training, the dataset may not fit in a
single machine. It is then essential to limit the amount of communication
between machines so it does not obliterate the benefit of parallelism. We
describe a general way to achieve this, ParMAC. ParMAC works on a cluster of
processing machines with a circular topology and alternates two steps until
convergence: one step trains the submodels in parallel using stochastic
updates, and the other trains the coordinates in parallel. Only submodel
parameters, no data or coordinates, are ever communicated between machines.
ParMAC exhibits high parallelism, low communication overhead, and facilitates
data shuffling, load balancing, fault tolerance and streaming data processing.
We study the convergence of ParMAC and propose a theoretical model of its
runtime and parallel speedup. We develop ParMAC to learn binary autoencoders
for fast, approximate image retrieval. We implement it in MPI in a distributed
system and demonstrate nearly perfect speedups in a 128-processor cluster with
a training set of 100 million high-dimensional points.


  We reconsider the commonly held assumption that warm debris disks are tracers
of terrestrial planet formation. The high occurrence rate inferred for
Earth-mass planets around mature solar-type stars based on exoplanet surveys
(roughly 20%) stands in stark contrast to the low incidence rate (less than
2-3%) of warm dusty debris around solar-type stars during the expected epoch of
terrestrial planet assembly (roughly 10 Myr). If Earth-mass planets at AU
distances are a common outcome of the planet formation process, this
discrepancy suggests that rocky planet formation occurs more quickly and/or is
much neater than traditionally believed, leaving behind little in the way of a
dust signature. Alternatively, the incidence rate of terrestrial planets has
been overestimated or some previously unrecognized physical mechanism removes
warm dust efficiently from the terrestrial planet region. A promising removal
mechanism is gas drag in a residual gaseous disk with a surface density of
roughly or somewhat more than 0.001% of the minimum mass solar nebula.


  We show that on a metric graph of genus $g$, a divisor of degree $n$
generically has $g(n-g+1)$ Weierstrass points. For a sequence of generic
divisors on a metric graph whose degrees grow to infinity, we show that the
associated Weierstrass points become distributed according to the Zhang
canonical measure. In other words, the limiting distribution is determined by
effective resistances on the metric graph. This distribution result has an
analogue for complex algebraic curves, due to Neeman, and for curves over
non-Archimedean fields, due to Amini.


  Strong resilience properties of dynamical flow networks are analyzed for
distributed routing policies. The latter are characterized by the property that
the way the inflow at a non-destination node gets split among its outgoing
links is allowed to depend only on local information about the current particle
densities on the outgoing links. The strong resilience of the network is
defined as the infimum sum of link-wise flow capacity reductions under which
the network cannot maintain the asymptotic total inflow to the destination node
to be equal to the inflow at the origin. A class of distributed routing
policies that are locally responsive to local information is shown to yield the
maximum possible strong resilience under such local information constraints for
an acyclic dynamical flow network with a single origin-destination pair. The
maximal strong resilience achievable is shown to be equal to the minimum node
residual capacity of the network. The latter depends on the limit flow of the
unperturbed network and is defined as the minimum, among all the
non-destination nodes, of the sum, over all the links outgoing from the node,
of the differences between the maximum flow capacity and the limit flow of the
unperturbed network. We propose a simple convex optimization problem to solve
for equilibrium limit flows of the unperturbed network that minimize average
delay subject to strong resilience guarantees, and discuss the use of tolls to
induce such an equilibrium limit flow in transportation networks. Finally, we
present illustrative simulations to discuss the connection between cascaded
failures and the resilience properties of the network.


  Accreting compact objects show variations in source flux over a broad range
of timescales and in all wavebands. The light curves typically show a lognormal
distribution of flux and a linear relation between flux and rms. It has been
demonstrated that an exponential transform of an underlying (and unobserved)
Gaussian stochastic process provides a very good description of the light
curves with these observed properties. Recently, a non-stationary power
spectrum was observed on fast timescales (~ days) in the active galaxy, IRAS
13224--3809, as well as a non-lognormal flux distribution and non-linear
rms-flux relation. Here, we investigate the affects of piecewise non-stationary
power spectra on the resultant flux distribution and rms-flux relation. We
demonstrate that the simple "exponentiation" model successfully reproduces the
observed quantities, even when the light curves are non-stationary. We also
demonstrate how non-lognormal flux distributions and rms-flux relations
inconsistent with a linear model can be erroneously produced from poorly
sampled PSDs. This is of particular importance for AGN surveys where very long
baselines are required to sample the PSD down to low enough frequencies.


  In this paper, we develop a dynamic exploration/ exploitation (exr/exp)
strategy for contextual recommender systems (CRS). Specifically, our methods
can adaptively balance the two aspects of exr/exp by automatically learning the
optimal tradeoff. This consists of optimizing a utility function represented by
a linearized form of the probability distributions of the rewards of the
clicked and the non-clicked documents already recommended. Within an offline
simulation framework we apply our algorithms to a CRS and conduct an evaluation
with real event log data. The experimental results and detailed analysis
demonstrate that our algorithms outperform existing algorithms in terms of
click-through-rate (CTR).


  We investigate the reduced Maxwell-Bloch (RMB) equations which describe the
propagation of short optical pulses in dielectric materials with resonant
non-degenerate transitions. The general Nth-order periodic solutions are
provided by means of the Darboux transformation, and from two different
limiting cases of the obtained general periodic solutions, the Nth-order
degenerate periodic and Nth-order rational solutions containing several free
parameters with compact determinant representations are derived, respectively.
Explicit expressions of these solutions from first to second order are
presented. Typical nonlinear wave patterns for the four components of the RMB
equations such as single-peak, double-peak-double-dip, double-peak and
single-dip structures in the second-order rational solutions are shown. This
kind of the rational solutions correspond to rogue waves in the reduced
Maxwell-Bloch equations.


  We propose a new framework for imitation learning -- treating imitation as a
two-player ranking-based game between a policy and a reward. In this game, the
reward agent learns to satisfy pairwise performance rankings between behaviors,
while the policy agent learns to maximize this reward. In imitation learning,
near-optimal expert data can be difficult to obtain, and even in the limit of
infinite data cannot imply a total ordering over trajectories as preferences
can. On the other hand, learning from preferences alone is challenging as a
large number of preferences are required to infer a high-dimensional reward
function, though preference data is typically much easier to collect than
expert demonstrations. The classical inverse reinforcement learning (IRL)
formulation learns from expert demonstrations but provides no mechanism to
incorporate learning from offline preferences and vice versa. We instantiate
the proposed ranking-game framework with a novel ranking loss giving an
algorithm that can simultaneously learn from expert demonstrations and
preferences, gaining the advantages of both modalities. Our experiments show
that the proposed method achieves state-of-the-art sample efficiency and can
solve previously unsolvable tasks in the Learning from Observation (LfO)
setting. Project video and code can be found at
https://hari-sikchi.github.io/rank-game/


  Extracting useful information from noisy near-term quantum simulations
requires error mitigation strategies. A broad class of these strategies rely on
precise characterization of the noise source. We study the robustness of
probabilistic error cancellation and tensor network error mitigation when the
noise is imperfectly characterized. We adapt an Imry-Ma argument to predict the
existence of a threshold in the robustness of these error mitigation methods
for random spatially local circuits in spatial dimensions $D \geq 2$: noise
characterization disorder below the threshold rate allows for error mitigation
up to times that scale with the number of qubits. For one-dimensional circuits,
by contrast, mitigation fails at an $\mathcal{O}(1)$ time for any imperfection
in the characterization of disorder. As a result, error mitigation is only a
practical method for sufficiently well-characterized noise. We discuss further
implications for tests of quantum computational advantage, fault-tolerant
probes of measurement-induced phase transitions, and quantum algorithms in
near-term devices.


  Learning graphical conditional independence structures is an important
machine learning problem and a cornerstone of causal discovery. However, the
accuracy and execution time of learning algorithms generally struggle to scale
to problems with hundreds of highly connected variables -- for instance,
recovering brain networks from fMRI data. We introduce the best order score
search (BOSS) and grow-shrink trees (GSTs) for learning directed acyclic graphs
(DAGs) in this paradigm. BOSS greedily searches over permutations of variables,
using GSTs to construct and score DAGs from permutations. GSTs efficiently
cache scores to eliminate redundant calculations. BOSS achieves
state-of-the-art performance in accuracy and execution time, comparing
favorably to a variety of combinatorial and gradient-based learning algorithms
under a broad range of conditions. To demonstrate its practicality, we apply
BOSS to two sets of resting-state fMRI data: simulated data with
pseudo-empirical noise distributions derived from randomized empirical fMRI
cortical signals and clinical data from 3T fMRI scans processed into cortical
parcels. BOSS is available for use within the TETRAD project which includes
Python and R wrappers.


  Existing research on action recognition treats activities as monolithic
events occurring in videos. Recently, the benefits of formulating actions as a
combination of atomic-actions have shown promise in improving action
understanding with the emergence of datasets containing such annotations,
allowing us to learn representations capturing this information. However, there
remains a lack of studies that extend action composition and leverage multiple
viewpoints and multiple modalities of data for representation learning. To
promote research in this direction, we introduce Home Action Genome (HOMAGE): a
multi-view action dataset with multiple modalities and view-points supplemented
with hierarchical activity and atomic action labels together with dense scene
composition labels. Leveraging rich multi-modal and multi-view settings, we
propose Cooperative Compositional Action Understanding (CCAU), a cooperative
learning framework for hierarchical action recognition that is aware of
compositional action elements. CCAU shows consistent performance improvements
across all modalities. Furthermore, we demonstrate the utility of co-learning
compositions in few-shot action recognition by achieving 28.6% mAP with just a
single sample.


  In this paper we show that the dramatic increase in the number of research
articles indexed in the Web of Science database impacts the commonly observed
distributions of citations within these articles. First, we document that the
growing number of physics articles in recent years is due to existing journals
publishing more and more papers rather than more new journals coming into being
as it happens in computer science. And second, even though the references from
the more recent papers generally cover a longer time span, the newer papers are
cited more frequently than the older ones if the uneven paper growth is not
corrected for. Nevertheless, despite this change in the distribution of
citations, the citation behavior of scientists does not seem to have changed.


  We prove a general result that relates certain pushouts of $E_k$-algebras to
relative tensors over $E_{k+1}$-algebras. Specializations include a number of
established results on classifying spaces, resolutions of modules, and
(co)homology theories for ring spectra. The main results apply when the
category in question has centralizers.
  Among our applications, we show that certain quotients of the dual Steenrod
algebra are realized as associative algebras over $HF_p \wedge HF_p$ by
attaching single $E_1$-algebra relation, generalizing previous work at the
prime $2$. We also construct a filtered $E_2$-algebra structure on the sphere
spectrum, and the resulting spectral sequence for the stable homotopy groups of
spheres has $E_1$-term isomorphic to a regrading of the $E_1$-term of the May
spectral sequence.


  We provide a general construction procedure for antilinearly invariant
complex root spaces. The proposed method is generic and may be applied to any
Weyl group allowing to take any element of the group as a starting point for
the construction. Worked out examples for several specific Weyl groups are
presented, focusing especially on those cases for which no solutions were found
previously. When applied in the defining relations of models based on root
systems this usually leads to non-Hermitian models, which are nonetheless
physically viable in a self-consistent sense as they are antilinearly invariant
by construction. We discuss new types of Calogero models based on these complex
roots. In addition we propose an alternative construction leading to q-deformed
roots. We employ the latter type of roots to formulate a new version of affine
Toda field theories based on non-simply laced roots systems. These models
exhibit on the classical level a strong-weak duality in the coupling constant
equivalent to a Lie algebraic duality, which is known for the quantum version
of the undeformed case.


  String gas cosmology is an approach towards studying the effects of
superstring theory on early universe cosmology which is based on new symmetries
and new degrees of freedom of string theory. Within this context, it appears
possible to stabilize the moduli which describe the size and shape of the extra
spatial dimensions without the need of introducing many extra tools such as
warping and fluxes. In this lecture, the recent progress towards moduli
stabilization in string gas cosmology is reviewed, and outstanding problems for
the scenario are discussed.


  This paper seeks to expand the scope of the alkaline seepage site
hydrothermal mound scenario of Russell et al, by appealing to its wider canvas
for hypothesizing self-assembly of gregite clusters via interplay of forces
within the gel phase of FeS membranes: directed heat transport a la
Rayleigh-Benard convection for dissociation, vs oriented attachment (small
clusters) and magnetic forces (large clusters) for association, the latter
assisted by magnetic mound constituents. The directed movement of tiny clusters
through cluster layers are reminiscent of processes like budding, molecular
motors, pre-RNA world on the lines of Cairns-Smith's hypothesis, and optical
polarity. Higher rate of (soft) multinucleate formation vs growth rate of
(rigid) microcrystals, correlates with icosahedral (forbidden
crystallographically!) framboidal morphology. This pattern indicates a link to
phylotaxis, thus reinforcing the quasi-periodicity connection which can provide
a natural access to features like surface limit, anomalous transport and low
thermal conductivity, while facilitating diffusion through clusters. And
magnetism offers a hierarchy of features: primordial multicellularity; phase
correlations of assembled molecules; overcoming thermal decoherence. These
dynamical nested structures offer possibilities for iterative computations,
adaptive learning, and coherent quantum searches. The link between enzymatic
FeS clusters and the Hadean ocean floor is seen as part of a larger conceptual
framework uncovering a role for Magnetism and the Origin of Life.


  Cumulative effect in social contagions underlies many studies on the spread
of innovation, behaviors, and influence. However, few large-scale empirical
studies are conducted to validate the existence of cumulative effect in the
information diffusion on social networks. In this paper, using the
population-scale dataset from the largest Chinese microblogging website, we
conduct a comprehensive study on the cumulative effect in information
diffusion. We base our study on the diffusion network of each message, where
nodes are the involved users and links are the following relationships among
them. We find that multiple exposures to the same message indeed increase the
possibility of forwarding it. However, additional exposures cannot further
improve the chance of forwarding when the number of exposures crosses its peak
at two. This finding questions the cumulative effect hypothesis in information
diffusion. Furthermore, to clarify the forwarding preference among users, we
investigate both the structural motif of the diffusion network and the temporal
pattern of information diffusion process among users. The patterns provide
vital insight for understanding the variation of message popularity and explain
the characteristics of diffusion networks.


  In General Relativity, the rotation of a gravitating body like the Earth
influences the motion of orbiting test particles or satellites in a
non-Newtonian way. This causes, e.g., a precession of the orbital plane known
as the Lense-Thirring effect and a precession of the spin of a gyroscope known
as the Schiff effect. Here, we discuss a third effect first introduced by Cohen
and Mashhoon called the gravitomagnetic clock effect. It describes the
difference in proper time of counterrevolving clocks after a revolution of
$2\pi$. For two clocks on counterrotating equatorial circular orbits around the
Earth, the effect is about $10^{-7}$ seconds per revolution, which is quite
large. We introduce a general relativistic definition of the gravitomagnetic
clock effect which is valid for arbitrary pairs of orbits. This includes
rotations in the same direction and different initial conditions, which are
crucial if the effect can be detected with existing satellites or with payloads
on nondedicated missions. We also derive the post-Newtonian expansion of the
general relativistic expression and calculate the effect for the example of a
satellite of a Global Navigation Satellite System compared to a geostationary
satellite.


  Aging in Caenorhabditis elegans is controlled, in part, by the insulin-like
signaling and heat shock response pathways. Following thermal stress,
expression levels of small heat shock protein 16.2 show a spatial patterning
across the 20 intestinal cells that reside along the length of the worm. Here,
we present a hypothesized mechanism that could lead to this patterned response
and develop a mathematical model of this system to test our hypothesis. We
propose that the patterned expression of heat shock protein is caused by a
diffusion-driven instability within the pseudocoelom, or fluid-filled cavity,
that borders the intestinal cells in C. elegans. This instability is due to the
interactions between two classes of insulin like peptides that serve
antagonistic roles. We examine output from the developed model and compare it
to experimental data on heat shock protein expression. Furthermore, we use the
model to gain insight on possible biological parameters in the system. The
model presented is capable of producing patterns similar to what is observed
experimentally and provides a first step in mathematically modeling
aging-related mechanisms in C. elegans.


  With over 60M articles, Wikipedia has become the largest platform for open
and freely accessible knowledge. While it has more than 15B monthly visits, its
content is believed to be inaccessible to many readers due to the lack of
readability of its text. However, previous investigations of the readability of
Wikipedia have been restricted to English only, and there are currently no
systems supporting the automatic readability assessment of the 300+ languages
in Wikipedia. To bridge this gap, we develop a multilingual model to score the
readability of Wikipedia articles. To train and evaluate this model, we create
a novel multilingual dataset spanning 14 languages, by matching articles from
Wikipedia to simplified Wikipedia and online children encyclopedias. We show
that our model performs well in a zero-shot scenario, yielding a ranking
accuracy of more than 80% across 14 languages and improving upon previous
benchmarks. These results demonstrate the applicability of the model at scale
for languages in which there is no ground-truth data available for model
fine-tuning. Furthermore, we provide the first overview on the state of
readability in Wikipedia beyond English.


  Generative adversarial networks (GANs) are an exciting alternative to
algorithms for solving density estimation problems---using data to assess how
likely samples are to be drawn from the same distribution. Instead of
explicitly computing these probabilities, GANs learn a generator that can match
the given probabilistic source. This paper looks particularly at this matching
capability in the context of problems with one-dimensional outputs. We identify
a class of function decompositions with properties that make them well suited
to the critic role in a leading approach to GANs known as Wasserstein GANs. We
show that Taylor and Fourier series decompositions belong to our class, provide
examples of these critics outperforming standard GAN approaches, and suggest
how they can be scaled to higher dimensional problems in the future.


  The spin-charge-orbital complex structures of manganites are studied using
topological concepts. The key quantity is the "winding number" w associated
with the Berry-phase connection of an e_g electron parallel-transported through
Jahn-Teller centers, along zigzag one-dimensional paths in an antiferromagnetic
environment of t_{2g} spins. From these concepts, it is shown that the
"bi-stripe" and "Wigner-crystal" states observed experimentally have different
w's. Predictions for the spin structure of the charge-ordered states for
heavily doped manganites are discussed.


  We show that fixed dimensional klt weak Fano pairs with alpha-invariants and
volumes bounded away from $0$ and the coefficients of the boundaries belong to
the set of hyperstandard multiplicities $\Phi(\mathscr{R})$ associated to a
fixed finite set $\mathscr{R}$ form a bounded family. We also show
$\alpha(X,B)^{d-1}\mathrm{vol}(-(K_X+B))$ are bounded from above for all klt
weak Fano pairs $(X,B)$ of a fixed dimension $d$.


  We measure the thickness of the heavy water layer trapped under the stress
corrosion fracture surface of silica using neutron reflectivity experiments. We
show that the penetration depth is 65-85 \aa ngstr\"{o}ms, suggesting the
presence of a damaged zone of $\approx$ 100 \aa ngstr\"{o}ms extending ahead of
the crack tip during its propagation. This estimate of the size of the damaged
zone is compatible with other recent results.


  Future electroweak precision measurements in the Circular Electron Positron
Collider (CEPC) project would significantly improve the precision of
electroweak oblique parameters. We evaluate the expected precision through
global fits, and study the corresponding sensitivity to weakly interacting
fermionic dark matter. Three models with electroweak multiplets in the dark
sector are investigated as illuminating examples. We find that the CEPC data
can probe up to TeV scales and explore some regions where direct detection
cannot reach, especially when the models respect the custodial symmetry.


  In human microbiome studies, sequencing reads data are often summarized as
counts of bacterial taxa at various taxonomic levels specified by a taxonomic
tree. This paper considers the problem of analyzing two repeated measurements
of microbiome data from the same subjects. Such data are often collected to
assess the change of microbial composition after certain treatment, or the
difference in microbial compositions across body sites. Existing models for
such count data are limited in modeling the covariance structure of the counts
and in handling paired multinomial count data. A new probability distribution
is proposed for paired-multinomial count data, which allows flexible covariance
structure and can be used to model repeatedly measured multivariate count data.
Based on this distribution, a test statistic is developed for testing the
difference in compositions based on paired multinomial count data. The proposed
test can be applied to the count data observed on a taxonomic tree in order to
test difference in microbiome compositions and to identify the subtrees with
different subcompositions. Simulation results indicate that proposed test has
correct type 1 errors and increased power compared to some commonly used
methods. An analysis of an upper respiratory tract microbiome data set is used
to illustrate the proposed methods.


  By considering the Bredon analogue of complete cohomology of a group, we show
that every group in the class $\LHFF$ of type Bredon-$\FP_\infty$ admits a
finite dimensional model for $\EFG$.
  We also show that abelian-by-infinite cyclic groups admit a $3$-dimensional
model for the classifying space for the family of virtually nilpotent
subgroups. This allows us to prove that for $\mF,$ the class of virtually
cyclic groups, the class of $\LHFF$-groups contains all locally virtually
soluble groups and all linear groups over $\mathbb C$ of integral
characteristic.


  A recent paper by Ge et al. performs a series of experiments with two full
spectral fitting codes, pPXF and starlight, finding that the two yield
consistent results when the input spectrum is not heavily reddened. For E(B-V)
> 0.2, however, they claim starlight leads to severe biases in the derived
properties. Counterintuitively, and at odds with previous simulations, they
find that this behaviour worsens significantly as the signal-to-noise ratio of
the input spectrum increases. This communication shows that this is entirely
due to an A_V < 1 mag condition imposed while initializing the Markov chains in
the code. This choice is normally irrelevant in real-life galaxy work but can
become critical in artificial experiments. Alleviating this usually harmless
initialization constraint changes the Ge et al. results completely, as was
explained to the authors before their publication. We replicate their spectral
fitting experiments, finding much smaller biases. Furthermore both bias and
scatter in the derived properties all converge as S/N increases, as one would
expect. We also show how the very output of the code provides ways of
diagnosing anomalies in the fits. The code behaviour has been documented in
careful and extensive experiments in the literature, but the biased analysis of
Ge et al. is just not representative of starlight at all.


  In this paper, we present Lyapunov-based robust and adaptive controllers for
the finite time stabilization of a perturbed chain of integrators with bounded
uncertainties. The proposed controllers can be designed for integrator chains
of any arbitrary length. The uncertainty bounds are known in the robust control
problem whereas they are unknown in the adaptive control problem. Both
controllers are developed from a class of finite time stabilization controllers
for pure integrator chains. Lyapunov-based design permits to calculate upper
bound on convergence time.


  The design and preparation of novel quantum materials with atomic precision
are crucial for exploring new physics and for device applications. Electron
irradiation has demonstrated as an effective method for preparing novel quantum
materials and quantum structures that could be challenging to obtain otherwise.
It features the advantages of precise control over the patterning of such new
materials and their integration with other materials with different
functionalities. Here, we present a new strategy for fabricating freestanding
monolayer SiC within nanopores of a graphene membrane. By regulating the energy
of the incident electron beam and the in-situ heating temperature in a scanning
transmission electron microscope (STEM), we can effectively control the
patterning of nanopores and subsequent growth of monolayer SiC within the
graphene lattice. The resultant SiC monolayers seamlessly connect with the
graphene lattice, forming a planar structure distinct by a wide direct bandgap.
Our in-situ STEM observations further uncover that the growth of monolayer SiC
within the graphene nanopore is driven by a combination of bond rotation and
atom extrusion, providing new insights into the atom-by-atom self-assembly of
freestanding two-dimensional (2D) monolayers.


  In this paper we explore predicting facial or lip video features from
electroencephalography (EEG) features and predicting EEG features from recorded
facial or lip video frames using deep learning models. The subjects were asked
to read out loud English sentences shown to them on a computer screen and their
simultaneous EEG signals and facial video frames were recorded. Our model was
able to generate very broad characteristics of the facial or lip video frame
from input EEG features. Our results demonstrate the first step towards
synthesizing high quality facial or lip video from recorded EEG features. We
demonstrate results for a data set consisting of seven subjects.


  We announce the discovery of a ~2 Jupiter-mass planet in an eccentric 11-year
orbit around the K7/M0 dwarf GJ 328. Our result is based on 10 years' worth of
radial velocity (RV) data from the Hobby-Eberly and Harlan J. Smith telescopes
at McDonald Observatory, and from the Keck Telescope at Mauna Kea. Our analysis
of GJ 328's magnetic activity via the Na I D features reveals a long-period
stellar activity cycle, which creates an additional signal in the star's RV
curve with amplitude 6-10 m/s. After correcting for this stellar RV
contribution, we see that the orbit of the planet is more eccentric than
suggested by the raw RV data. GJ 328b is currently the most massive,
longest-period planet discovered around a low-mass dwarf.


  We consider accretion of matter onto a low mass black hole surrounded by
ionized medium. We show that, because of higher mobility of protons than
electrons, the black hole would acquire positive electric charge. If the black
hole's mass is about or below $10^{20}$ g, the electric field at the horizon
can reach the critical value which leads to vacuum instability and
electron--positron pair production by the Schwinger mechanism. Since the
positrons are ejected by the emergent electric field, while electrons are
back--captured, the black hole operates as an antimatter factory which
effectively converts protons into positrons.


  Elementary sub-Riemannian geometry on the Heisenberg group H(n) provides a
compact picture of symplectic geometry. Any Hamiltonian diffeomorphism on
$R^{2n}$ lifts to a volume preserving bi-Lipschitz homeomorphisms of H(n), with
the use of its generating function. Any curve of a flow of such homeomorphisms
deviates from horizontality by the Hamiltonian of the flow. From the metric
point of view this means that any such curve has Hausdorff dimension 2 and the
$\mathcal{H}^{2}$ (area) density equal to the Hamiltonian. The non-degeneracy
of the Hofer distance is a direct consequence of this fact.


  The two tone intermodulation distortion arising in MgB2 thin films
synthesized by hybrid physical-chemical vapour deposition is studied in order
to probe the influence of the two bands on the nonlinear response of this
superconductor. The measurements are carried out by using a dielectrically
loaded copper cavity operating at 7 GHz. Microwave data on samples having
critical temperatures above 41 K, very low resistivity values, and residual
resistivity ratio larger than 10, are shown. The dependence of the nonlinear
surface losses and of the third order intermodulation products on the power
feeding the cavity and on the temperature is analyzed. At low power, the signal
arising from distortion versus temperature shows the intrinsic s-wave behavior
expected for this compound. Data are compared with measurements performed on Nb
and YBCO thin films using the same technique.


  A Hamiltonian and action principle formalism for deriving three-dimensional
gyroviscous magnetohydrodynamic models is presented. The uniqueness of the
approach in constructing the gyroviscous tensor from first principles and its
ability to explain the origin of the gyromap and the gyroviscous terms are
highlighted. The procedure allows for the specification of free functions,
which can be used to generate a wide range of gyroviscous models. Through the
process of reduction, the noncanonical Hamiltonian bracket is obtained and
briefly analysed.


  In this paper, we establish the Pexiderized stability of coboundaries and
cocycles and use them to investigate the Hyers--Ulam stability of some
functional equations. We prove that for each Banach algebra $A$, Banach
$A$-bimodule $X$ and positive integer $n, H^n(A,X)=0$ if and only if the $n$-th
cohomology group approximately vanishes.


  In the paper, we are concerned with degenerate stochastic differential
equations with jumps. Firstly, we establish two support theorems for the
solutions of the degenerate stochastic equations, under different (sufficient)
conditions. Secondly, we apply one of our support theorems to a class of
degenerate stochastic evolution equations (i.e., infinite-dimensional
stochastic differential equations) with jumps to get a characterisation of
path-independence for the densities of their Girsanov transformations.


  We consider the finite sample properties of the regularized high-dimensional
Cox regression via lasso. Existing literature focuses on linear models or
generalized linear models with Lipschitz loss functions, where the empirical
risk functions are the summations of independent and identically distributed
(iid) losses. The summands in the negative log partial likelihood function for
censored survival data, however, are neither iid nor Lipschitz. We first
approximate the negative log partial likelihood function by a sum of iid
non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the
lasso penalized Cox regression using pointwise arguments to tackle the
difficulty caused by the lack of iid and Lipschitz property.


  We map the three dimensional extent of the Virgo Over-density by combining
distance information from RR Lyrae variables and projected spatial information
from SEKBO (Keller et al. 2008) and Sloan Digital Sky Survey (SDSS) DR6
photometry. The Virgo Over-density is seen to comprise two filaments 14.5 x 3
degrees and 10 x 3 degrees and a circular structure 3 degrees in diameter.
Together the three features span 38 degrees of right ascension and declinations
of +2 to -15 degrees. RR Lyrae variables place the two filamentary features at
heliocentric distances of 20 and 17 kpc respectively, with projected dimensions
of 5 x 1 kpc and 3 x 1 kpc.


  We develop relative oscillation theory for general Sturm-Liouville
differential expressions of the form \[
  \frac{1}{r}\left(-\frac{\mathrm d}{\mathrm dx} p \frac{\mathrm d}{\mathrm dx}
+ q\right) \] and prove perturbation results and invariance of essential
spectra in terms of the real coefficients $p$, $q$, $r$. The novelty here is
that we also allow perturbations of the weight function $r$ in which case the
unperturbed and the perturbed operator act in different Hilbert spaces.


  This paper presents a detailed kinematic and chemical analysis of 16 members
of the Kapteyn moving group. The group does not appear to be chemically
homogenous. However, the kinematics and the chemical abundance patterns seen in
14 of the stars in this group are similar to those observed in the well-studied
cluster, Omega Centauri. Some members of this moving group may be remnants of
the tidal debris of Omega Cen, left in the Galactic disk during the merger
event which deposited Omega Cen into the Milky Way.


  The structure, vibrational dynamics and thermodynamics of a chiral surface,
Cu(532), has been calculated using a local approach and the harmonic
approximation, with interatomic potentials based on the embedded atom method.
The relaxation of atomic positions to the optimum configuration results in a
complex relaxation pattern with strong contractions in the bond length of atoms
near the kink and the step site and an equivalently large expansion near the
least under-coordinated surface atoms. The low coordination of the atoms on the
surface affects substantially the vibrational dynamics and thermodynamics of
this system. The local vibrational density of states show a deviation from the
bulk behavior that persist down to the 10th layer resulting in a substantial
contribution of the vibrational entropy to the excess free energy amounting to
about 90 meV per unit cell at 300K.


  Sonic crystal acoustic screens have been in progressive research and
development in the last two decades as a technical solution for mitigating
traffic noise. Their behaviour is quite different from that observed in
classical barriers, with the latter being based on physically blocking the
direct sound propagation path (only allowing diffracted noise to reach sensible
receivers), and sonic crystals providing attenuation efficiency based on the
creation of band-gaps at specific frequency ranges, due to the Bragg's
interference phenomenon. The distinct physical mechanisms of these two types of
noise barriers complicates the use of classical simplified or even numerical
models developed for traditional barriers to simulate and predict the
attenuation performance of a sonic crystal, and alternative methods become thus
required. In the acoustics scientific literature, several authors have proposed
estimation and simulation methods based on different numerical tools to predict
the sound insulation provided by these new noise abatement solutions. This
paper presents a comparative evaluation of some of these methods, with emphasis
to the assessment of their accuracy versus memory usage in order to determine
which one is the most suitable for optimization methodologies in the design of
new devices with improved acoustic performance.


  We propose to use atmospheric neutrinos as a powerful probe of new physics
beyond the Standard Model via neutrino trident production. The final state with
double muon tracks simultaneously produced from the same vertex is a
distinctive signal at large Cherenkov detectors. We calculate the expected
event numbers of trident production in the Standard Model. To illustrate the
potential of this process to probe new physics we obtain the sensitivity on new
vector/scalar bosons with coupling to muon and tau neutrinos.


  We analyze four different approaches to estimate a multivariate probability
density (or the log-density) and its first and second order derivatives. Two
methods, local log-likelihood and local Hyv\"arinen score estimation, are in
terms of weighted scoring rules with local quadratic models. The other two
approaches are matching of local moments and kernel density estimation. All
estimators depend on a general kernel, and we use the Gaussian kernel to
provide explicit examples. Asymptotic properties of the estimators are derived
and compared. In terms of rates of convergence, a refined local moment matching
estimator is the best.


  We study the boundary terms of the spectral action of the noncommutative
space, defined by the spectral triple dictated by the physical spectrum of the
standard model, unifying gravity with all other fundamental interactions. We
prove that the spectral action predicts uniquely the gravitational boundary
term required for consistency of quantum gravity with the correct sign and
coefficient. This is a remarkable result given the lack of freedom in the
spectral action to tune this term.


  Magnetic skyrmions are particle-like topological excitations recently
discovered in chiral magnets. Their small size, topological protection and the
ease with which they can be manipulated by electric currents generated much
interest in using skyrmions for information storage and processing. Recently,
it was suggested that skyrmions with additional degrees of freedom can exist in
magnetically frustrated materials. Here, we show that dynamics of skyrmions and
antiskyrmions in nanostripes of frustrated magnets is strongly affected by
complex spin states formed at the stripe edges. These states create multiple
edge channels which guide the skyrmion motion. Non-trivial topology of edge
states gives rise to complex current-induced dynamics, such as emission of
skyrmion-antiskyrmion pairs. The edge state topology can be controlled with an
electric current through the exchange of skyrmions and antiskyrmions between
the edges of a magnetic nanostructure. These results can lead to conceptually
new electronic devices.


  This expository paper focuses on free Lie $K$-algebras and the basic PBW
theorem. We argue in various ways that the basic PBW theorem is a quite close
consequence of the Magnus-Witt theorems concerning free Lie algebras.


  Motivated by the recent work of Louko and Molgado, we consider the
Ashtekar-Horowitz-Boulware model using the projection operator formalism. This
paper uses the techniques developed in a recent paper of Klauder and Little to
overcome the potential difficulties of this particular model. We also extend
the model by including a larger class of functions than previously considered
and evaluate the classical limit of the model.


  In this paper we consider the energy and momentum transport in
(1+1)-dimension conformal field theories (CFTs) that are deformed by an
irrelevant operator $T\bar{T}$, using the integrability based generalized
hydrodynamics, and holography. The two complementary methods allow us to study
the energy and momentum transport after the in-homogeneous quench, derive the
exact non-equilibrium steady states (NESS) and calculate the Drude weights and
the diffusion constants. Our analysis reveals that all of these quantities
satisfy universal formulae regardless of the underlying CFT, thereby
generalizing the universal formulae for these quantities in pure CFTs. As a
sanity check, we also confirm that the exact momentum diffusion constant agrees
with the conformal perturbation. These fundamental physical insights have
important consequences for our understanding of the $T\bar{T}$-deformed CFTs.
First of all, they provide the first check of the $T\bar{T}$-deformed
$\mathrm{AdS}_3$/$\mathrm{CFT}_2$ correspondence from the dynamical standpoint.
And secondly, we are able to identify a remarkable connection between the
$T\bar{T}$-deformed CFTs and reversible cellular automata.


  Modeling emotional-cognition is in a nascent stage and therefore wide-open
for new ideas and discussions. In this paper the author looks at the modeling
problem by bringing in ideas from axiomatic mathematics, information theory,
computer science, molecular biology, non-linear dynamical systems and quantum
computing and explains how ideas from these disciplines may have applications
in modeling emotional-cognition.


  We report a characterization of surfaces of the dichalcogenide TaSe$_2$ using
scanning tunneling microscopy and spectroscopy (STM/S) at 150 mK. When the top
layer has the 2H structure and the layer immediately below the 1T structure, we
find a singular spatial dependence of the tunneling conductance below 1 K,
changing from a zero bias peak on top of Se atoms to a gap in between Se atoms.
The zero bias peak is additionally modulated by the commensurate $3a_0 \times
3a_0$ charge density wave of 2H-TaSe$_2$. Multilayers of 2H-TaSe$_2$ show a
spatially homogeneous superconducting gap with a critical temperature also of 1
K. We discuss possible origins for the peculiar tunneling conductance in single
layers.


  Analysis of the gravitational source for the Schwarzschild metric indicates
that the time and the radial components of the energy momentum tensor are
equal. Imposing such a condition on cosmology, we propose a cosmological model
that is a modification of the Friedman-Robertson-Walker (FRW) universe. An
accelerating universe emerges as a natural consequence of this ansatz.


  We demonstrate wavelength conversion of QAM signals including 32GBd QPSK and
10GBd 16QAM in a 50cm long high index doped glass spiral waveguide. The quality
of the generated idlers over a 10nm bandwidth is sufficient to achieve a BER
performance below the HD FEC threshold (less than 3.8 x 10-3), with an OSNR
penalty of less than 0.3 dB compared to the original signal. Our results
confirm that this is a promising platform for nonlinear optical signal
processing, a result of both very low linear propagation loss (less than 0.07
dB/cm) and the large material bandgap that ensures negligible nonlinear loss at
telecom wavelengths.


  The refractive index (RI) of cells and tissues is crucial in pathophysiology
as a noninvasive and quantitative imaging contrast. Although its measurements
have been demonstrated using three-dimensional quantitative phase imaging
methods, these methods often require bulky interferometric setups or multiple
measurements, which limits the measurement sensitivity and speed. Here, we
present a single-shot RI imaging method that visualizes the RI of the in-focus
region of a sample. By exploiting spectral multiplexing and optical transfer
function engineering, three color-coded intensity images of a sample with three
optimized illuminations were simultaneously obtained in a single-shot
measurement. The measured intensity images were then deconvoluted to obtain the
RI image of the in-focus slice of the sample. As a proof of concept, a setup
was built using Fresnel lenses and a liquid-crystal display. For validation
purposes, we measured microspheres of known RI and cross-validated the results
with simulated results. Various static and highly dynamic biological cells were
imaged to demonstrate that the proposed method can conduct single-shot RI slice
imaging of biological samples with subcellular resolution.


  We present the results of our calculations of the parity nonconserving
electric dipole amplitudes ($E1_{PNC}$) for the $6s ~ ^2S_{1/2} - 5d ~
^2D_{3/2;5/2}$ transitions of $^{133}$Cs employing a relativistic
coupled-cluster (RCC) method. $E1_{PNC}$ values for the nuclear spin
independent (NSI) and nuclear spin dependent (NSD) parity non-conservation
(PNC) effects for different hyperfine levels of the $6s ~ ^2S_{1/2} - 5d ~
^2D_{3/2}$ transition and only due to the NSD PNC interaction Hamiltonian for
all possible hyperfine levels of the $6s ~ ^2S_{1/2} - 5d ~ ^2D_{5/2}$
transition are given. We have also performed calculations of several properties
that are relevant for assessing the reliability of the calculations of the
amplitudes of the above mentioned transitions. We highlight the importance of
correlation effects by giving the results of both the Dirac-Fock (DF) and RCC
contributions. Approximate contributions to these properties from the Breit and
quantum electrodynamics (QED) interactions have also been evaluated. Plausible
experimental schemes to measure these transition amplitudes by light shift
techniques and interference involving induced Stark shifts are outlined.