  Emulators, or reduced complexity climate models, are surrogate Earth system
models that produce projections of key climate quantities with minimal
computational resources. Using time-series modelling or more advanced machine
learning techniques, data-driven emulators have emerged as a promising avenue
of research, producing spatially resolved climate responses that are visually
indistinguishable from state-of-the-art Earth system models. Yet, their lack of
physical interpretability limits their wider adoption. In this work, we
introduce FaIRGP, a data-driven emulator that satisfies the physical
temperature response equations of an energy balance model. The result is an
emulator that \textit{(i)} enjoys the flexibility of statistical machine
learning models and can learn from data, and \textit{(ii)} has a robust
physical grounding with interpretable parameters that can be used to make
inference about the climate system. Further, our Bayesian approach allows a
principled and mathematically tractable uncertainty quantification. Our model
demonstrates skillful emulation of global mean surface temperature and spatial
surface temperatures across realistic future scenarios. Its ability to learn
from data allows it to outperform energy balance models, while its robust
physical foundation safeguards against the pitfalls of purely data-driven
models. We also illustrate how FaIRGP can be used to obtain estimates of
top-of-atmosphere radiative forcing and discuss the benefits of its
mathematical tractability for applications such as detection and attribution or
precipitation emulation. We hope that this work will contribute to widening the
adoption of data-driven methods in climate emulation.


  Previous research shows that women are more altruist than men in dictator
game experiments. Yet, little is known whether women are expected to be more
altruist than men. Here we elicit third-parties' beliefs about dictators'
donations conditional on knowing the gender of the dictator. Our data provide
evidence of three main findings: (i) women are expected to be more altruist
than men; (ii) both men and women have correct beliefs about the level of
altruism among men; and (iii) both men and women overestimate the level of
altruism among women. In doing so, our results uncover a perception gap
according to which, although women are more altruist than men, they are
expected to be even more altruist than they actually are.


  We study electron spin decoherence in a two-electron double quantum dot due
to the hyperfine interaction, under spin-echo conditions as studied in recent
experiments. We develop a semi-classical model for the interaction between the
electron and nuclear spins, in which the time-dependent Overhauser fields
induced by the nuclear spins are treated as classical vector variables.
Comparison of the model with experimentally-obtained echo signals allows us to
quantify the contributions of various processes such as coherent Larmor
precession and spin diffusion to the nuclear spin evolution.


  We show that the solutions of the Bogomolny equations for the Abelian Higgs
model on a two-dimensional torus, can be expanded in powers of a quantity
epsilon measuring the departure of the area from the critical area. This allows
a precise determination of the shape of the solutions for all magnetic fluxes
and arbitrary position of the Higgs field zeroes. The expansion is carried out
to 51 orders for a couple of representative cases, including the unit flux
case. We analyse the behaviour of the expansion in the limit of large areas, in
which case the solutions approach those on the plane. Our results suggest
convergence all the way up to infinite area.


  We propose Neural Crossbreed, a feed-forward neural network that can learn a
semantic change of input images in a latent space to create the morphing
effect. Because the network learns a semantic change, a sequence of meaningful
intermediate images can be generated without requiring the user to specify
explicit correspondences. In addition, the semantic change learning makes it
possible to perform the morphing between the images that contain objects with
significantly different poses or camera views. Furthermore, just as in
conventional morphing techniques, our morphing network can handle shape and
appearance transitions separately by disentangling the content and the style
transfer for rich usability. We prepare a training dataset for morphing using a
pre-trained BigGAN, which generates an intermediate image by interpolating two
latent vectors at an intended morphing value. This is the first attempt to
address image morphing using a pre-trained generative model in order to learn
semantic transformation. The experiments show that Neural Crossbreed produces
high quality morphed images, overcoming various limitations associated with
conventional approaches. In addition, Neural Crossbreed can be further extended
for diverse applications such as multi-image morphing, appearance transfer, and
video frame interpolation.


  Videogames developed in the 1970s and 1980s were modest programs created in a
couple of months by a single person, who played the roles of designer, artist
and programmer. Since then, videogames have evolved to become a multi-million
dollar industry. Today, AAA game development involves hundreds of people
working together over several years. Management and engineering requirements
have changed at the same pace. Although many of the processes have been adapted
over time, this is not quite true for quality assurance tasks, which are still
done mainly manually by human beta testers due to the specific peculiarities of
videogames. This paper presents an approach to automate this beta testing.


  Let $\overline{p}(n)$ be the number of overpartitions of $n$, we establish
and give a short elementary proof of the following congruence
\[\overline{p}({{4}^{\alpha }}(40n+35))\equiv 0 \, (\bmod \, 40),\] where
$\alpha ,n $ are nonnegative integers. By letting $\alpha =0$ we proved a
conjecture of Hirschhorn and Sellers. Some new congruences for
$\overline{p}(n)$ modulo 3 and 5 have also been found, including the following
two infinite families of Ramanujan-type congruences: for any integers $n\ge 0$
and $\alpha \ge 1$, \[\overline{p}({{5}^{2\alpha +1}}(5n+1))\equiv
\overline{p}({{5}^{2\alpha +1}}(5n+4))\equiv 0 \, (\bmod \, 5).\]


  Given a (smooth) complex analytic family of compact complex manifolds, we
prove that the central fibre must be Moishezon if the other fibres are
Moishezon. Using a "strongly Gauduchon metric" on the central fibre whose
existence was proved in our previous work on limits of projective manifolds, we
show that the irreducible components of the relative Barlet space of divisors
contained in the fibres are proper over the base even under the weaker
assumption that the $\partial\bar\partial$-lemma hold on all the fibres except,
possibly, the central one. This implies that the algebraic dimension of the
central fibre cannot be lower than that of the generic fibre. Since the latter
is already maximal thanks to the Moishezon assumption, the central fibre must
be of maximal algebraic dimension, hence Moishezon.


  Here we present an alternative approach, requiring only basic tools of
differential geometry. This method was conceived by Kijowski and first
presented during the IV Marcel Grossman Meeting on General Relativity in Rome
(1986). It was later published in a generalized form by J. Jezierski, J.
Kijowski in 1987 (Positivity of total energy in general relativity, Physical
Review D {\bf 36} (1987), 1041-4). We summarize these results briefly and
present a new foliation gauge.


  The classical theorem of Milnor on pullback rings states that the category of
projective modules over a pullback ring is equivalent to a certain category of
gluing triples consisting of projective modules. We prove an analogous result
on the level of derived categories, where the equivalence has to be replaced by
an epivalence.


  The lowest-mass stars, brown dwarfs and giant exoplanets span a minimum in
the mass-radius relationship that probes the fundamental physics of extreme
states of matter, magnetism, and fusion. This White Paper outlines scientific
opportunities and the necessary resources for modeling and measuring the
mass-radius relationship in this regime.


  The question of whether the pseudogap in high $T_c$ cuprates is related to
super conducting precursor effects or to the existence of extrinsic bosonic
massive excitations is investigated on the basis of the Boson-Fermion model.
The characteristic three peak structure of the electronic spectral function and
the temperature dependent Fermi vector derived here are signatures for a two
component scenario which can be tested by ARPES and BIS experiments.


  Dialogue policy plays an important role in task-oriented spoken dialogue
systems. It determines how to respond to users. The recently proposed deep
reinforcement learning (DRL) approaches have been used for policy optimization.
However, these deep models are still challenging for two reasons: 1) Many
DRL-based policies are not sample-efficient. 2) Most models don't have the
capability of policy transfer between different domains. In this paper, we
propose a universal framework, AgentGraph, to tackle these two problems. The
proposed AgentGraph is the combination of GNN-based architecture and DRL-based
algorithm. It can be regarded as one of the multi-agent reinforcement learning
approaches. Each agent corresponds to a node in a graph, which is defined
according to the dialogue domain ontology. When making a decision, each agent
can communicate with its neighbors on the graph. Under AgentGraph framework, we
further propose Dual GNN-based dialogue policy, which implicitly decomposes the
decision in each turn into a high-level global decision and a low-level local
decision. Experiments show that AgentGraph models significantly outperform
traditional reinforcement learning approaches on most of the 18 tasks of the
PyDial benchmark. Moreover, when transferred from the source task to a target
task, these models not only have acceptable initial performance but also
converge much faster on the target task.


  We present a detailed comparative systematic study using a sample of 221
Narrow-line Seyfert 1 (NLSy1) galaxies in comparison to a redshift matched
sample of 154 Broad-line Seyfert 1 (BLSy1) galaxies based on their observations
using ROSAT and/or XMM-Newton telescopes in soft X-ray band (0.1-2.0 keV). A
homogeneous analysis is carried out to estimate their soft X-ray photon indices
($\Gamma^{s}_{X}$) and its correlations with other parameters of nuclear
activities such as Eddington ratios (R$_\mathrm{Edd}$), bolometric luminosities
(L$_\mathrm{bol}$), black hole masses (M$_\mathrm{BH}$) and the widths of the
broad component of H$\beta$ lines (FWHM(H$\beta$)). In our analysis, we found
clear evidence of the difference in the $\Gamma^{s}_{X}$ and R$_\mathrm{Edd}$
distributions among NLSy1 and BLSy1 galaxies, with steeper $\Gamma^{s}_{X}$ and
higher R$_\mathrm{Edd}$ for the former. Such a difference also exists in the
spectral indices distribution in hard X-ray ($\Gamma^{h}_{X}$), based on the
analysis of 53 NLSy1 and 46 BLSy1 galaxies in the 2-10 keV energy band. The
difference in R$_\mathrm{Edd}$ distributions does exist even after applying the
average correction for the difference in the inclination angle of NLSy1 and
BLSy1 galaxies. We also estimated R$_\mathrm{Edd}$, based on SED fitting of 34
NLSy1 and 30 BLSy1 galaxies over the 0.3-10 keV energy band and found that
results are still consistent with R$_\mathrm{Edd}$ estimates based on the
optical bolometric luminosity. Our analysis suggests that the higher
R$_\mathrm{Edd}$ in NLSy1 is responsible for its steeper X-ray spectral slope
compared to the BLSy1, consistent with the disc-corona model as proposed for
the luminous AGNs.


  We demonstrate dynamic and arbitrary multisite two-photon excitation in three
dimensions using the holographic projection method. Rapid response (fourth
dimension) is achieved through high-speed noniterative calculation of the
hologram using a video graphics accelerator board. We verify that the projected
asymmetric spot configurations have sufficient spatiotemporal photon density
for localized two-photon excitation. This system is a significant advance and
can be applied to time-resolved photolysis of caged compounds in biological
cells and complex neuronal networks, nonlinear microfabrication and volume
holographic optical storage.


  Considering a random binary tree with $n$ labelled leaves, we use a pruning
procedure on this tree in order to construct a $\beta(3/2,1/2)$-coalescent
process. We also use the continuous analogue of this construction, i.e. a
pruning procedure on Aldous's continuum random tree, to construct a continuous
state space process that has the same structure as the $\beta$-coalescent
process up to some time change. These two constructions unable us to obtain
results on the coalescent process such as the asymptotics on the number of
coalescent events or the law of the blocks involved in the last coalescent
event.


  In this paper, we introduce $q$-analogues of the Barnes multiple zeta
functions. We show that these functions can be extended meromorphically to the
whole plane, and moreover, tend to the Barnes multiple zeta functions when
$q\uparrow 1$ for all complex numbers.


  Magnetars are regarded as the most magnetized neutron stars in the Universe.
Aiming to unveil what kinds of stars and supernovae can create magnetars, we
have performed a state-of-the-art spatially resolved spectroscopic X-ray study
of the supernova remnants (SNRs) Kes 73, RCW 103, and N49, which host magnetars
1E 1841-045, 1E 161348-5055, and SGR 0526-66, respectively. The three SNRs are
O- and Ne-enhanced and are evolving in the interstellar medium with densities
of >1--2 cm$^{-3}$. The metal composition and dense environment indicate that
the progenitor stars are not very massive. The progenitor masses of the three
magnetars are constrained to be < 20 Msun (11--15 Msun for Kes 73, < 13 Msun
for RCW 103, and ~13 --17 Msun for N49). Our study suggests that magnetars are
not necessarily made from very massive stars, but originate from stars that
span a large mass range. The explosion energies of the three SNRs range from
$10^{50}$ erg to ~2$\times 10^{51}$ erg, further refuting that the SNRs are
energized by rapidly rotating (millisecond) pulsars. We report that RCW 103 is
produced by a weak supernova explosion with significant fallback, as such an
explosion explains the low explosion energy (~$10^{50}$ erg), small observed
metal masses ($M_{\rm O}\sim 4\times 10^{-2}$ Msun and $M_{\rm Ne}\sim 6\times
10^{-3}$ Msun), and sub-solar abundances of heavier elements such as Si and S.
Our study supports the fossil field origin as an important channel to produce
magnetars, given the normal mass range ($M_{\rm ZAMS} < 20$ Msun) of the
progenitor stars, the low-to-normal explosion energy of the SNRs, and the fact
that the fraction of SNRs hosting magnetars is consistent with the magnetic OB
stars with high fields.


  This paper proposes a classification network to image semantic retrieval
(NIST) framework to counter the image retrieval challenge. Our approach
leverages the successful classification network GoogleNet based on
Convolutional Neural Networks to obtain the semantic feature matrix which
contains the serial number of classes and corresponding probabilities. Compared
with traditional image retrieval using feature matching to compute the
similarity between two images, NIST leverages the semantic information to
construct semantic feature matrix and uses the semantic distance algorithm to
compute the similarity. Besides, the fusion strategy can significantly reduce
storage and time consumption due to less classes participating in the last
semantic distance computation. Experiments demonstrate that our NIST framework
produces state-of-the-art results in retrieval experiments on MIRFLICKR-25K
dataset.


  Epitaxial bilayer films of Bi(110) and Ni host a time-reversal symmetry (TRS)
breaking superconducting order with an unexpectedly high transition temperature
$T_c = 4.1$ K. Using time-domain THz spectroscopy, we measure the low energy
electrodynamic response of a Bi/Ni bilayer thin film from $0.2$ THz to $2$ THz
as a function of temperature and magnetic field. We analyze the data in the
context of a BCS-like superconductor with a finite normal-state scattering
rate. In zero magnetic field, all states in the film become fully gapped,
providing important constraints into possible pairing symmetries. Our data
appears to rule out the odd-frequency pairing that is natural for many
ferromagnetic-superconductor interfaces. By analyzing the magnetic
field-dependent response in terms of a pair-breaking parameter, we determine
that superconductivity develops over the entire bilayer sample which may point
to the $p$-wave like nature of unconventional superconductivity.


  Isomap algorithm is a representative manifold learning algorithm. The
algorithm simplifies the data analysis process and is widely used in
neuroimaging, spectral analysis and other fields. However, the classic Isomap
algorithm becomes unwieldy when dealing with large data sets. Our object is to
accelerate the classical algorithm with quantum computing, and propose the
quantum Isomap algorithm. The algorithm consists of two sub-algorithms. The
first one is the quantum Floyd algorithm, which calculates the shortest
distance for any two nodes. The other is quantum Isomap algorithm based on
quantum Floyd algorithm, which finds a low-dimensional representation for the
original high-dimensional data. Finally, we analyze that the quantum Floyd
algorithm achieves exponential speedup without sampling. In addition, the time
complexity of quantum Isomap algorithm is $O(dNpolylogN)$. Both algorithms
reduce the time complexity of classical algorithms.


  We discuss the stabilization of the compact dimension for a class of
five-dimensional orbifold supergravity models. Supersymmetry is broken by the
superpotential on a boundary. Classically, the size $L$ of the fifth dimension
is undetermined, with or without supersymmetry breaking, and the effective
potential is of no-scale type. The size $L$ is fixed by quantum corrections to
the K\"ahler potential, the Casimir energy and Fayet-Iliopoulos (FI) terms
localized at the boundaries. For an FI scale of order $M_\mathrm{GUT}$, as in
heterotic string compactifications with anomalous $\U1$ symmetries, one obtains
$L \sim 1/M_\mathrm{GUT}$. A small mass is predicted for the scalar fluctuation
associated with the fifth dimension, $m_{\rho} \lesssim m_{3/2}/(L M)$.


  We prove hybrid subconvexity bounds for a wide class of twisted L-functions
$L(s,f\times \chi)$ at the central point, including a new instance of the Weyl
subconvexity bound.


  A novel multi-level method for partial differential equations with uncertain
parameters is proposed. The principle behind the method is that the error
between grid levels in multi-level methods has a spatial structure that is by
good approximation independent of the actual grid level. Our method learns this
structure by employing a sequence of convolutional neural networks, that are
well-suited to automatically detect local error features as latent quantities
of the solution. Furthermore, by using the concept of transfer learning, the
information of coarse grid levels is reused on fine grid levels in order to
minimize the required number of samples on fine levels. The method outperforms
state-of-the-art multi-level methods, especially in the case when complex PDEs
(such as single-phase and free-surface flow problems) are concerned, or when
high accuracy is required.


  In this paper we consider the unstable chaotic attractor of the Toda
potential and stabilize it by a control in integral form. In order to obtain
stability results, we propose a special technique which is based on the idea of
reduction of integro-differential equations to ordinary differential equations
system.


  We study grand unified theories based on an SU(5)xSU(5) gauge group in which
the GUT scale, M_{GUT}, is the VEV of an exact or approximate modulus, and in
which fast proton decay is avoided through a combination of a large triplet
mass and small triplet couplings. These features are achieved by discrete
symmetries. In many of our models, M_{GUT} is generated naturally by the
balance of higher dimension terms that lift the GUT modulus potential, and soft
supersymmetry breaking masses. The theories often lead to interesting patterns
of quark and lepton masses. We also discuss some distinctions between grand
unified theories and string unification.


  We propose and analyze numerical methods for the Heath-Jarrow-Morton (HJM)
model. To construct the methods, we first discretize the infinite dimensional
HJM equation in maturity time variable using quadrature rules for approximating
the arbitrage-free drift. This results in a finite dimensional system of
stochastic differential equations (SDEs) which we approximate in the weak and
mean-square sense using the general theory of numerical integration of SDEs.
The proposed numerical algorithms are computationally highly efficient due to
the use of high-order quadrature rules which allow us to take relatively large
discretization steps in the maturity time without affecting overall accuracy of
the algorithms. Convergence theorems for the methods are proved. Results of
some numerical experiments with European-type interest rate derivatives are
presented.


  We report on nonlinear transport measurements in a two-dimensional electron
gas hosted in GaAs/AlGaAs heterostructures. Upon application of direct current,
the low-temperature differential resistivity acquires a positive correction,
which exhibits a pronounced maximum followed by a plateau. With increasing
temperature, the nonlinearity diminishes and disappears. These observations can
be understood in terms of a crossover from the Bloch-Gr\"uneisen regime to the
quasielastic scattering regime as the electrons are heated by direct current.
Calculations considering the interaction of electrons with acoustic phonons
provide a reasonable description of our experimental findings.


  In this work, we report a high remnant polarization, 2Pr >70$\mu$C/cm$^2$ in
thermally processed atomic layer deposited Hf0.5Zr0.5O2 (HZO) film on Silicon
with NH3 plasma exposed thin TiN interlayer and Tungsten (W) as a top
electrode. The effect of interlayer on the ferroelectric properties of HZO is
compared with standard Metal-Ferroelectric-Metal and
Metal-Ferroelectric-Semiconductor structures. X-Ray Diffraction shows that the
Orthorhombic (o) phase increases as TiN is thinned. However, the strain in the
o-phase is highest at 2 nm TiN and then relaxes significantly for the no-TiN
case. HRTEM images reveal that the ultra-thin TiN acts as a seed layer for the
local epitaxy in HZO potentially increasing the strain to produce a 2X
improvement in the remnant polarization. Finally, the HZO devices are shown to
be wake-up-free, and exhibit endurance >10^6 cycles. This study opens a pathway
to achieve epitaxial ferroelectric HZO films on Si with improved memory
performance.


  We establish that any even permutation from A_n moving at least [3n/4] + o(n)
points is the commutator of a generating pair of A_n and a generating pair of
S_n. From this we deduce an exponential lower bound on the number of systems of
transitivity in alternating and symmetric groups.


  Genome-wide Association Studies (GWASes) identify genomic variations that are
statistically associated with a trait, such as a disease, in a group of
individuals. Unfortunately, careless sharing of GWAS statistics might give rise
to privacy attacks. Several works attempted to reconcile secure processing with
privacy-preserving releases of GWASes. However, we highlight that these
approaches remain vulnerable if GWASes utilize overlapping sets of individuals
and genomic variations. In such conditions, we show that even when relying on
state-of-the-art techniques for protecting releases, an adversary could
reconstruct the genomic variations of up to 28.6% of participants, and that the
released statistics of up to 92.3% of the genomic variations would enable
membership inference attacks. We introduce I-GWAS, a novel framework that
securely computes and releases the results of multiple possibly interdependent
GWASes. I-GWAS continuously releases privacy-preserving and noise-free GWAS
results as new genomes become available.


  Usually, single-crystal material has a longer carrier diffusion length due to
fewer defects. Here, we report a nano/amorphous copper oxide and selenium (COS)
composite film prepared by radio frequency magnetron co-sputtering of CuO and
Se and post annealing. The photo-generated carriers in the COS film can diffuse
very far (3.147 mm). Additionally, the COS film can strongly absorb light over
the entire solar spectrum region (250-2500 nm) (average absorptance is ~80%).
These results indicate that the COS composite is an excellent material and can
be used in solar cells and other photo-electric devices.


  We study meson-meson scattering in a soluble model which describes
asymptotically free mesons and confined quark-antiquark pairs via coupled
channels. Concretely, the two scattered mesons are assumed to interact through
s-channel meson-exchange diagrams. Furthermore, we develop a perturbative
expansion of the model, and show that the thus found resonance pole positions,
including contributions up to fourth order in perturbation theory, completely
fail to reproduce the exact results. This shows that the resonance predictions
based on perturbative approximations in quark models may be highly unreliable.


  We investigate strongly correlated spin-1 ultracold bosons with
antiferromagnetic interactions in a cubic optical lattice, based on bosonic
dynamical mean-field theory. Rich phase diagrams of the system are mapped out
at both zero and finite temperature, and in particular the existence of a
spin-singlet condensate is established. Interestingly, at finite temperature,
we find that the superfluid can be heated into a Mott insulator with even (odd)
filling via a first- (second-) order phase transition, analogous to the
Pomeranchuk effect in $^{3}$He. Moreover, for typical experimental setups, we
estimate the critical temperatures for different ordered phases and our results
suggest that direct experimental observation of these phases is promising.


  Let $C$ be a curve over a complete discretely valued field $K$. We give
tropical descriptions of the weight function attached to a pluricanonical form
on $C$ and the essential skeleton of $C$. We show that the Laplacian of the
weight function equals the pluricanonical divisor on Berkovich skeleta, and we
describe the essential skeleton of $C$ as a combinatorial skeleton of the
Berkovich skeleton of the minimal $snc$-model. In particular, if $C$ has
semi-stable reduction, then the essential skeleton coincides with the minimal
skeleton. As an intermediate step, we describe the base loci of logarithmic
pluricanonical line bundles on minimal $snc$-models.


  In this paper, some subtleties in the measurement of the transverse
polarization of the produced hadrons on symmetric colliders -- such as the
Large Hadron Collider when conducting the $pp$ collisions -- are revealed. It
can be proved that the transverse polarization of the produced particles with
opposite pseudorapidity takes exactly opposite values if the normal vector of
the production plane is defined in a convention-dependent way, regardless of
whether parity is conserved or not in the production process. The analysis
shows that, due to the symmetry of the initial state, the $\Lambda_b$
transverse polarization measured by the CMS collaboration in Phys. Rev. D 97,
072010 (2018) should be exactly equal to zero. A modified measurement of the
$\Lambda_b$ polarization for CMS and ATLAS is proposed, the result of which can
be compared to the LHCb measurement.


  Observations have shown that the disk frequency and the fraction of accreting
pre-main-sequence stars decrease with the age of the population and that some
stars appear to have disks while their accretion has stopped. Still, it is
unclear how disk-bearing stars stop their accretion. To provide insight into
the last stages of accretion in low-mass young stars, we conducted a survey of
disk-bearing stars that are thought to be non-accretors to identify stars still
accreting at very low rates. Here we present the first catalog of the survey of
170 disk-bearing non-accreting stars in Chamaeleon I, Orion OB1, Upper
Scorpius, $\gamma$ Velorum, and Upper Centaurus Lupus, using He I
$\lambda$10830 as a sensitive probe of accretion. We classify the line profiles
into six types and argue that those showing redshifted and/or blueshifted
absorption are still accreting. Using these classifications, we found that,
among disk-bearing stars previously classified as non-accretors, at least
20-30% are still accreting, with a larger fraction of those at younger
population ages. While the difference between the outer disk signature and
accretion status is unclear, we find a difference between the inner disk excess
and accretion status. There is no preference in the mass of the newly
identified accretors, suggesting that the processes inhibiting accretion do not
directly depend on mass in the typical mass range of T Tauri stars. Lastly, we
found that at a low accretion level, the H$\alpha$ width at the 10% height
criteria mischaracterizes a larger fraction of accretors than the line's
equivalent width.


  We consider a model composed of Landau quasiparticle states with patched
Fermi surfaces (FS) sandwiched by states with flat FS to simulate the ``cold''
spot regions in cuprates. We calculate the one particle irreducible function
and the self-energy up to two-loop order. Using renormalization group arguments
we show that in the forward scattering channel the renormalized coupling
constant is never infrared stable due to the flat FS sectors. Furthemore we
show that the self-energy scales with energy as ${\rm Re} \Sigma \sim \omega
\ln \omega $ as $\omega \to 0$, and thus the Fermi liquid state within each FS
patch is turned into a marginal Fermi liquid.


  We provide an exposition of a `horizontal' generalization of Goodman's
surgery operation on (pseudo-)Anosov flows. This operation is performed by
cutting along a specific kind of annulus that is transverse to the flow and
regluing with a Dehn twist of the appropriate sign. We then show that
performing horizontal Goodman surgery on a transitive pseudo-Anosov flow yields
an almost equivalent flow, i.e. the original flow and the surgered flow are
orbit equivalent after drilling out a finite collection of closed orbits. We
obtain some almost equivalence results by applying this theorem on examples of
the surgery operation. Along the way, we also show a structural stability
result for pseudo-Anosov flows.


  In recent decades the analysis of data has become increasingly computational.
Correspondingly, this has changed how scientific and statistical work is
shared. For example, it is now commonplace for underlying analysis code and
data to be proffered alongside journal publications and conference talks.
Unfortunately, sharing code faces several challenges. First, it is often
difficult to take code from one computer and run it on another. Code
configuration, version, and dependency issues often make this challenging.
Secondly, even if the code runs, it is often hard to understand or interact
with the analysis. This makes it difficult to assess the code and its findings,
for example, in a peer review process. In this review we describe the
combination of two computing technologies that help make analyses shareable,
interactive, and completely reproducible. These technologies are (1) analysis
containerization, which leverages virtualization to fully encapsulate analysis,
data, code and dependencies into an interactive and shareable format, and (2)
code notebooks, a literate programming format for interacting with analyses.
The fusion of these two technologies offers significant advantages over using
either individually. This review surveys how the combination enhances the
accessibility and reproducibility of code, analyses, and ideas.


  This manuscript presents verification cases that are developed to study the
electrothermal instability (ETI). Specific verification cases are included to
ensure that the unit physics components necessary to model the ETI are
accurate, providing a path for fluid-based codes to effectively simulate ETI in
the linear and nonlinear growth regimes. Two software frameworks with different
algorithmic approaches are compared for accuracy in their ability to simulate
diffusion of a magnetic field, linear growth of the ETI, and a fully nonlinear
ETI evolution. The nonlinear ETI simulations show early time agreement, with
some differences emerging, as noted in the wavenumber spectrum, late into the
nonlinear development of ETI. A sensitivity study explores the role of
equation-of-state (EOS), vacuum density, and vacuum resistivity. EOS and vacuum
resistivity are found to be the most critical factors in the modeling of
nonlinear ETI development.


  In 2013, Marcus, Spielman, and Srivastava resolved the famous Kadison-Singer
conjecture. It states that for $n$ independent random vectors $v_1,\cdots, v_n$
that have expected squared norm bounded by $\epsilon$ and are in the isotropic
position in expectation, there is a positive probability that the determinant
polynomial $\det(xI - \sum_{i=1}^n v_iv_i^\top)$ has roots bounded by $(1 +
\sqrt{\epsilon})^2$. An interpretation of the Kadison-Singer theorem is that we
can always find a partition of the vectors $v_1,\cdots,v_n$ into two sets with
a low discrepancy in terms of the spectral norm (in other words, rely on the
determinant polynomial).
  In this paper, we provide two results for a broader class of polynomials, the
hyperbolic polynomials. Furthermore, our results are in two generalized
settings:
  $\bullet$ The first one shows that the Kadison-Singer result requires a
weaker assumption that the vectors have a bounded sum of hyperbolic norms.
  $\bullet$ The second one relaxes the Kadison-Singer result's distribution
assumption to the Strongly Rayleigh distribution.
  To the best of our knowledge, the previous results only support determinant
polynomials [Anari and Oveis Gharan'14, Kyng, Luh and Song'20]. It is unclear
whether they can be generalized to a broader class of polynomials. In addition,
we also provide a sub-exponential time algorithm for constructing our results.


  The popularity of local meshless methods in the field of numerical
simulations has increased greatly in recent years. This is mainly due to the
fact that they can operate on scattered nodes and that they allow a direct
control over the approximation order and basis functions. In this paper we
analyse two popular variants of local strong form meshless methods, namely the
radial basis function-generated finite differences (RBF-FD) using polyharmonic
splines (PHS) augmented with monomials, and the weighted least squares (WLS)
approach using only monomials. Our analysis focuses on the accuracy and
stability of the numerical solution computed on scattered nodes in a two- and
three-dimensional domain. We show that while the WLS variant is a better choice
when lower order approximations are sufficient, the RBF-FD variant exhibits a
more stable behavior and a higher accuracy of the numerical solution for higher
order approximations, but at the cost of higher computational complexity.


  We experimentally study the phase space distribution (PSD) of a mechanical
resonator that is simultaneously coupled to two electromagnetic cavities. The
first one, operating in the microwave band, is employed for inducing either
cooling or self-excited oscillation, whereas the second one, operating in the
optical band, is used for displacement detection. A tomography technique is
employed for extracting the PSD from the signal reflected by the optical
cavity. Measurements of PSD are performed in steady state near the threshold of
self-excited oscillation while sweeping the microwave cavity detuning. In
addition, we monitor the time evolution of the transitions from an
optomechanically cooled state to a state of self excited oscillation. This
transition is induced by abruptly switching the microwave driving frequency
from the red-detuned region to the blue-detuned one. The experimental results
are compared with theoretical predictions that are obtained by solving the
Fokker-Planck equation. The feasibility of generating quantum superposition
states in the system under study is briefly discussed.


  A class of discrete flavor-symmetry-based models predicts constrained
neutrino mass matrix schemes that lead to specific neutrino mass sum-rules
(MSR). We show how these theories may constrain the absolute scale of neutrino
mass, leading in most of the cases to a lower bound on the neutrinoless double
beta decay effective amplitude.


  The Aditya-L1 is the first space-based solar observatory of the Indian Space
Research Organization (ISRO). The spacecraft will carry seven payloads
providing uninterrupted observations of the Sun from the first Lagrangian
point. Aditya-L1 comprises four remote sensing instruments, {\it viz.} a
coronagraph observing in visible and infrared, a full disk imager in Near
Ultra-Violet (NUV), and two full-sun integrated spectrometers in soft X-ray and
hard X-ray. In addition, there are three instruments for in-situ measurements,
including a magnetometer, to study the magnetic field variations during
energetic events. Aditya-L1 is truly a mission for multi-messenger solar
astronomy from space that will provide comprehensive observations of the Sun
across the electromagnetic spectrum and in-situ measurements in a broad range
of energy, including magnetic field measurements at L1.


  We investigate the pre-disruption gravitational dynamics and post-disruption
hydrodynamics of the tidal disruption of stars by supermassive black hole
(SMBH) binaries. We focus on binaries with relatively low mass primaries
($10^6M_{\odot}$), moderate mass ratios, and separations with reasonably long
gravitational wave inspiral times (tens of Myr). First, we generate a large
ensemble (between 1 and 10 million) of restricted three-body integrations to
quantify the statistical properties of tidal disruptions by circular SMBH
binaries of initially-unbound stars. Compared to the reference case of a
disruption by a single SMBH, the binary potential induces significant variance
into the specific energy and angular momentum of the star at the point of
disruption. Second, we use Newtonian numerical hydrodynamics to study the
detailed evolution of the fallback debris from 120 disruptions randomly
selected from the three-body ensemble (excluding only the most deeply
penetrating encounters). We find that the overall morphology of the debris is
greatly altered by the presence of the second black hole, and the accretion
rate histories display a wide range of behaviors, including order of magnitude
dips and excesses relative to control simulations that include only one black
hole. Complex evolution persists, in some cases, for many orbital periods of
the binary. We find evidence for power in the accretion curves on timescales
related to the binary orbital period, though there is no exact periodicity. We
discuss our results in the context of future wide-field surveys, and comment on
the prospects of identifying and characterizing the subset of events occurring
in nuclei with binary SMBHs.


  Actors and critics in actor-critic reinforcement learning algorithms are
functionally separate, yet they often use the same network architectures. This
case study explores the performance impact of network sizes when considering
actor and critic architectures independently. By relaxing the assumption of
architectural symmetry, it is often possible for smaller actors to achieve
comparable policy performance to their symmetric counterparts. Our experiments
show up to 99% reduction in the number of network weights with an average
reduction of 77% over multiple actor-critic algorithms on 9 independent tasks.
Given that reducing actor complexity results in a direct reduction of run-time
inference cost, we believe configurations of actors and critics are aspects of
actor-critic design that deserve to be considered independently, particularly
in resource-constrained applications or when deploying multiple actors
simultaneously.


  Research into electronic nanomaterials has recently seen a growing focus into
the synthesis of structures with unconventional curved geometries including
bent wires in planar systems and three-dimensional architectures obtained by
rolling up nanomembranes. The inclusion of these geometries has led to the
prediction and observation of a series of novel effects that either result from
shape-driven modifications of the electronic motion or from an intrinsic change
of electronic and magnetic properties due to peculiar confinement effects.
Moreover, local strains often generated by curvature also trigger the
appearance of new phenomena due to the essential role played by
electromechanical coupling in solids. Here we review the recent developments in
the discovery of these shape-, confinement- and strain-induced curvature
effects at the nanoscale, and discuss their potential use in electronic and
spintronic devices.


  We are interested in the following validation problem for computational
reductions: for algorithmic problems $P$ and $P^\star$, is a given candidate
reduction indeed a reduction from $P$ to $P^\star$? Unsurprisingly, this
problem is undecidable even for very restricted classes of reductions. This
leads to the question: Is there a natural, expressive class of reductions for
which the validation problem can be attacked algorithmically? We answer this
question positively by introducing an easy-to-use graphical specification
mechanism for computational reductions, called cookbook reductions. We show
that cookbook reductions are sufficiently expressive to cover many classical
graph reductions and expressive enough so that SAT remains NP-complete (in the
presence of a linear order). Surprisingly, the validation problem is decidable
for natural and expressive subclasses of cookbook reductions.


  It is fairly common to use code-mixing on a social media platform to express
opinions and emotions in multilingual societies. The purpose of this task is to
detect the sentiment of code-mixed social media text. Code-mixed text poses a
great challenge for the traditional NLP system, which currently uses
monolingual resources to deal with the problem of multilingual mixing. This
task has been solved in the past using lexicon lookup in respective sentiment
dictionaries and using a long short-term memory (LSTM) neural network for
monolingual resources. In this paper, we (my codalab username is kongjun)
present a system that uses a bilingual vector gating mechanism for bilingual
resources to complete the task. The model consists of two main parts: the
vector gating mechanism, which combines the character and word levels, and the
attention mechanism, which extracts the important emotional parts of the text.
The results show that the proposed system outperforms the baseline algorithm.
We achieved fifth place in Spanglish and 19th place in Hinglish.The code of
this paper is availabled at : https://github.com/JunKong5/Semveal2020-task9


  Bekenstein's generalized second law (GSL) of thermodynamics asserts that the
sum of black-hole entropy, $S_{\text{BH}}=Ac^3/4\hbar G$ (here $A$ is the
black-hole surface area), and the ordinary entropy of matter and radiation
fields in the black-hole exterior region never decreases. We here re-analyze an
intriguing gedanken experiment which was designed by Bekenstein to challenge
the GSL. In this historical gedanken experiment an entropy-bearing box is
lowered into a charged Reissner-Nordstr\"om black hole. For the GSL to work,
the resulting increase in the black-hole surface area (entropy) must compensate
for the loss of the box's entropy. We show that if the box can be lowered
adiabatically all the way down to the black-hole horizon, as previously assumed
in the literature, then for near-extremal black holes the resulting increase in
black-hole surface-area (due to the assimilation of the box by the black hole)
may become too small to compensate for the loss of the box's entropy. In order
to resolve this apparent violation of the GSL, we here suggest to use a
generalized version of the hoop conjecture. In particular, assuming that a
physical system of mass $M$ and electric charge $Q$ forms a black hole if its
circumference radius $r_{\text{c}}$ is equal to (or smaller than) the
corresponding Reissner-Nordstr\"om black-hole radius
$r_{\text{RN}}=M+\sqrt{M^2-Q^2}$, we prove that a new (and larger) horizon is
already formed before the entropy-bearing box reaches the horizon of the
original near-extremal black hole. This result, which seems to have been
overlooked in previous analyzes of the composed black-hole-box system, ensures
the validity of Bekenstein's GSL in this famous gedanken experiment.


  This document is a specialized technical description of one of the potential
implementations of a second layer protocol over Gravity, a
blockchain-/token-agnostic decentralized oracle protocol. The SuSy protocol
prescribes an implementation of cross-chain transfers of digital assets
(tokens) in blockchain networks that support smart contracts, focused primarily
on popular blockchains with varying architectures, consensuses and
cryptography. SuSy is centered exclusively around technical implementation of
transfers, without bringing any incentive models for cross-chain transfer
providers. In addition, we describe the most popular inter-chain communication
solutions such as Polkadot, Cosmos Hub, Rainbow and RenVM, as a backdrop for
the new solution proposed in this paper.


  In this paper, we investigate Bauer's method for the matrix spectral
factorization of an r-channel matrix product filter which is a halfband
autocorrelation matrix. We regularize the resulting matrix spectral factors by
an averaging approach and by multiplication by a unitary matrix. This leads to
the approximate and exact orthogonal SA4 multiscaling functions. We also find
the corresponding orthogonal multiwavelet functions, based on the QR
decomposition.


  One kind of spontaneous (2+1)-dimensional Lorentz symmetry breaking is
discussed. The symmetry breaking pattern is $SO(2,1)\rightarrow SO(1,1)$. Using
the coset construction formalism, we derive the Goldstone covariant derivative
and the associated covariant gauge field. Finally, the two-derivative
low-energy effective action of the Nambu-Goldstone bosons is obtained.


  Since the last century, deterministic compartmental models have emerged as
powerful tools to predict and control epidemic outbreaks, in many cases helping
to mitigate their impacts. A key quantity for these models is the so-called
Basic Reproduction Number, that measures the number of secondary infections
produced by an initial infected individual in a fully susceptible population.
Some methods have been developed to allow the direct computation of this
quantity provided that some conditions are fulfilled, such that the model has a
pre-pandemic disease-free equilibrium state. This condition is only fulfilled
when the populations are stationary. In the case of vector-borne diseases, this
implies that the vector birth and death rates need to be balanced, what is not
fulfilled in many realistic cases in which the vector population grow or
decrease. Here we develop a vector-borne epidemic model with growing and
decaying vector populations and study the conditions under which the standard
methods to compute $R_0$ work and discuss an alternative when they fail. We
also show that growing vector populations produce a delay in the epidemic
dynamics when compared to the case of the stationary vector population.
Finally, we discuss the conditions under which the model can be reduced to the
SIR model with fewer compartments and parameters, which helps in solving the
problem of parameter unidentifiability of many vector-borne epidemic models.


  In this article, we prove a new bound for the least prime ideal in the
Chebotarev density theorem, which improves the main theorem of Zaman [Funct.
Approx. Comment. Math. 57 (2017), no.1, 115-142] by a factor of $5/2$. Our main
improvement comes from a new version of Tur\'an's power sum method. The key new
idea is to use Harnack's inequality for harmonic functions to derive a superior
lower bound for the generalised Fej\'er kernel.


  This paper details the development of an integrated AC electro-osmotic (ACEO)
microfluidic pump for dilute electrolytes consisting of a long serpentine
microchannel lined with three dimensional (3D) stepped electrode arrays. Using
low AC voltage (1 Volt rms, 1 kHz), power (5 mW) and current (3.5 mA) in water,
the pump is capable of generating a 1.4 kPa head pressure, a 100-fold increase
over prior ACEO pumps, and a 1.37 mm/sec effective slip velocity over the
electrodes without flow reversal. The integrated ACEO pump can utilize low
ionic strength solutions such as distilled water as the working solution to
pump physiological strength (100 mM) biological solutions in separate
microfluidic devices, with potential applications in portable or implantable
biomedical microfluidic devices. As a proof-of-concept experiment, the use of
the ACEO pumps for DNA hybridization in a microfluidic microarray is
demonstrated.


  Within linearized perturbation theory, black holes decay to their final
stationary state through the well-known spectrum of quasinormal modes. Here we
numerically study whether nonlinearities change this picture. For that purpose
we study the ringdown frequencies of gauge-invariant second-order gravitational
perturbations induced by self-coupling of linearized perturbations of
Schwarzschild black holes. We do so through high-accuracy simulations in the
time domain of first and second-order Regge-Wheeler-Zerilli type equations, for
a variety of initial data sets. We consider first-order even-parity
$(\ell=2,m=\pm 2)$ perturbations and odd-parity $(\ell=2,m=0)$ ones, and all
the multipoles that they generate through self-coupling. For all of them and
all the initial data sets considered we find that ---in contrast to previous
predictions in the literature--- the numerical decay frequencies of
second-order perturbations are the same ones of linearized theory, and we
explain the observed behavior. This would indicate, in particular, that when
modeling or searching for ringdown gravitational waves, appropriately including
the standard quasinormal modes already takes into account nonlinear effects.


  We present an analysis of the X-ray time lags for the highly variable Seyfert
1 galaxy NGC 4051, based on a series of XMM-Newton observations taken in 2009.
We investigate the Fourier frequency dependent time lags in the light curves
between the 0.3--1.0 keV and 2.0--5.0 keV energy bands as a function of source
flux, including simultaneous modelling of the resulting lag-frequency spectra.
We find the shape of the lag-frequency spectra to vary significantly and
systematically with source flux. We model the lag-frequency spectra using
simple transfer functions, and find that two time lag components are required,
one in each energy band. The simplest acceptable fits have only the relative
contribution of the lagged component in the hard band varying with flux level,
which can be associated with changes in the energy spectrum. We discuss the
interpretation of these results in terms of the currently popular models for
X-ray time lags.


  In this paper we prove a multiplicity result concerning the critical points
of a class of functionals involving local and nonlocal nonlinearities. We apply
our result to the nonlinear Schrodinger-Maxwell system and to the nonlinear
elliptic Kirchhoff equation assuming on the local nonlinearity the general
hypotheses introduced by Berestycki and Lions.


  A $G$-grading on a complex semisimple Lie algebra $L$, where $G$ is a finite
abelian group, is called quasi-good if each homogeneous component is
1-dimensional and 0 is not in the support of the grading.
  Analogous to classical root systems, we define a finite root system $R$ to be
some subset of a finite symplectic abelian group satisfying certain axioms.
There always corresponds to $R$ a semisimple Lie algebra $L(R)$ together with a
quasi-good grading on it. Thus one can construct nice basis of $L(R)$ by means
of finite root systems.
  We classify finite maximal abelian subgroups $T$ in $\Aut(L)$ for complex
simple Lie algebras $L$ such that the grading induced by the action of $T$ on
$L$ is quasi-good, and show that the set of roots of $T$ in $L$ is always a
finite root system. There are five series of such finite maximal abelian
subgroups, which occur only if $L$ is a classical simple Lie algebra.


  This article is an account of the scientific work of Hugo Duminil-Copin at
the time of his award in 2022 of the Fields Medal "for solving longstanding
problems in the probabilistic theory of phase transitions in statistical
physics, especially in dimensions three and four''.


  Consider a rigid body having a fixed point in a superposition of two constant
force fields (for example, gravitational and magnetic). Introducing the
condition of Kowalevski type, O.I.Bogoyavlensky (1984) has found the first
integral generalizing that of Kowalevski and pointed out the integrable case
with two invariant relations, which reduces to the 1st Appelrot class when one
of the fields vanishes. The article presents a new case with two invariant
relations integrable in Jacobi sense and generalizing the 2nd and 3rd classes
of Appelrot.


  Let $Y$ be a compact complex manifold embedded in a complex manifold with
unitary flat normal bundle. Our interest is in a sort of the linearizability
problem of a neighborhood of $Y$. As a higher-codimensional generalization of
Ueda's result, we give a sufficient condition for the existence of a
non-singular holomorphic foliation on a neighborhood of $Y$ which includes $Y$
as a leaf with unitary-linear holonomy. We apply this result to the existence
problem of a smooth Hermitian metric with semi-positive curvature on a nef line
bundle.


  In this paper we present a new routing paradigm that generalizes
opportunistic routing for wireless multihop networks. In multirate anypath
routing, each node uses both a set of next hops and a selected transmission
rate to reach a destination. Using this rate, a packet is broadcast to the
nodes in the set and one of them forwards the packet on to the destination. To
date, there has been no theory capable of jointly optimizing both the set of
next hops and the transmission rate used by each node. We solve this by
introducing two polynomial-time routing algorithms and provide the proof of
their optimality. The proposed algorithms run in roughly the same running time
as regular shortest-path algorithms, and are therefore suitable for deployment
in routing protocols. We conducted measurements in an 802.11b testbed network,
and our trace-driven analysis shows that multirate anypath routing performs on
average 80% and up to 6.4 times better than anypath routing with a fixed rate
of 11 Mbps. If the rate is fixed at 1 Mbps instead, performance improves by up
to one order of magnitude.


  Inspired by the fact that human eyes continue to develop tracking ability in
early and middle childhood, we propose to use tracking as a proxy task for a
computer vision system to learn the visual representations. Modelled on the
Catch game played by the children, we design a Catch-the-Patch (CtP) game for a
3D-CNN model to learn visual representations that would help with video-related
tasks. In the proposed pretraining framework, we cut an image patch from a
given video and let it scale and move according to a pre-set trajectory. The
proxy task is to estimate the position and size of the image patch in a
sequence of video frames, given only the target bounding box in the first
frame. We discover that using multiple image patches simultaneously brings
clear benefits. We further increase the difficulty of the game by randomly
making patches invisible. Extensive experiments on mainstream benchmarks
demonstrate the superior performance of CtP against other video pretraining
methods. In addition, CtP-pretrained features are less sensitive to domain gaps
than those trained by a supervised action recognition task. When both trained
on Kinetics-400, we are pleasantly surprised to find that CtP-pretrained
representation achieves much higher action classification accuracy than its
fully supervised counterpart on Something-Something dataset. Code is available
online: github.com/microsoft/CtP.


  We prove nonlinear Landau damping in optimal weighted Gevrey-3 spaces for
solutions of the confined Vlasov-Poisson system on $\T^d\times\R^d$ which are
small perturbations of homogeneous Penrose-stable equilibria.
  We also prove the existence of nonlinear scattering operators associated to
the confined Vlasov-Poisson evolution, as well as suitable injectivity
properties and Lipschitz estimates (also in weighted Gevrey-3 spaces) on these
operators.
  Our results give definitive answers to two well-known open problems in the
field, both of them stated in the recent review of Bedrossian [4, Section 6].


  Most transport theorems---that is, a formula for the rate of change of an
integral in which both the integrand and domain of integration depend on
time---involve domains that evolve according to a flow map. Such domains are
said to be convecting. Here a transport theorem for nonconvecting domains
evolving on an embedded manifold is established. While the domain is not
convecting, it is assumed that the boundary of the domain does evolve according
to a flow map is some generalized sense. The proof relies on considering the
evolving set as a fixed set in one higher dimension and then using the
divergence theorem. The domains considered can be irregular in the sense that
their boundaries need only be Lipschitz. Tools from geometric measure theory
are used to deal with this irregularity.


  We prove an implicit function theorem for C^k-maps from arbitrary topological
vector spaces over valued fields to Banach spaces (for k at least 2). As a
tool, we show the C^k-dependence of fixed points on parameters for suitable
families of contractions of a Banach space. Similar results are obtained for k
times strictly differentiable maps, and for k times Lipschitz differentiable
maps. In the real case, our results subsume an implicit function theorem for
Keller C^k_c-maps from arbitrary topological vector spaces to Banach spaces.


  One of the interesting features in unification models and supersymmetric
unification models is that the chiral states of quarks and leptons in a family
including a right-handed neutrino can be fitted neatly into a fundamental
spinor representation (f.s) of dimension 16 for the SO(10) gauge group.
However, it is shown in this paper that such a fundamental spinor
representation of SO(10) for Weyl fermions will generate global
(non-perturbative) gauge anomalies (of new type) when restricting to the
$SU(2)\otimes SU(2)\otimes SU(2) \otimes SU(2)$ gauge subgroup. Such an example
is the four SU(2) factors obtained through the reduction of the subgroup
$SU(2)\otimes SO(7)$ of SO(10) with the SO(7) to the three SU(2) factors. The
branching rule in this case is given by $(f.s)\rightarrow (2-1-2-2)\oplus
(2-2-1-2)$ in terms of dimensions. A consistent gauge theory implies the gauge
symmetry in a gauge subgroup, and then needs to be well-defined when
restricting to the gauge subgroup. Consequently, a consistent SO(10) quantum
theory needs to satisfy our selection rule $N_f+N_{mf}=even\geq 4$, namely the
total number of generations with $N_f$ ordinary fermion families and $N_{mf}$
mirror fermion families is even and larger than three, and the three
generations of chiral fermions in this content can not correspond to a
consistent theory. Then we expect that there exist at least one additional
fermion family including a right-handed neutrino or at least one family of
mirror fermions including a left-handed mirror neutrino if SO(10) unification
theory is relevant to our realistic world. The next possibility is to have
total six generations that may subject to stringent


  According to the Campbell-Magaard theorem, any analytical spacetime can be
locally and analytically embedded into a five-dimensional pseudo-Riemannian
Ricci-flat manifold. We find explicitly this embedding for Godel's universe.
The embedding space is Ricci-flat and has a non-Lorentzian signature of type
(++--). We also show that the embedding found is global.


  A review of the renormalization group approach to the proof of non
perturbative ultraviolet stability in scalar field theories in dimension d=2,3.


  For the high granularity and high energy resolution, Silicon Strip Detector
(SSD) is widely applied in assembling telescopes to measure the charged
particles in heavy ion reactions. In this paper, we present a novel method to
achieve track recognition in the SSD telescopes of the Compact Spectrometer for
Heavy Ion Experiment (CSHINE). Each telescope consists of a single-sided
silicon strip detector (SSSSD) and a double-sided silicon strip detector
(DSSSD) backed by $3 \times 3$ CsI(Tl) crystals. Detector calibration and track
reconstruction are implemented. Special decoding algorithm is developed for the
multi-track recognition procedure to deal with the multi-hit effect convoluted
by charge sharing and the missing signals with certain probability. It is
demonstrated that the track recognition efficiency of the method is
approximately 90\% and 80\% for the DSSSD-CsI and SSSSD-DSSSD events,
respectively.


  We analyze the decomposition problem of multivariate polynomial-exponential
functions from truncated series and present new algorithms to compute their
decomposition. Using the duality between polynomials and formal power series,
we first show how the elements in the dual of an Artinian algebra correspond to
polynomial-exponential functions. They are also the solutions of systems of
partial differential equations with constant coefficients. We relate their
representation to the inverse system of the roots of the characteristic
variety. Using the properties of Hankel operators, we establish a
correspondence between polynomial exponential series and Artinian Gorenstein
algebras. We generalize Kronecker theorem to the multivariate case, by showing
that the symbol of a Hankel operator of finite rank is a polynomial-exponential
series and by connecting the rank of the Hankel operator with the decomposition
of the symbol. A generalization of Prony's approach to multivariate
decomposition problems is presented , exploiting eigenvector methods for
solving polynomial equations. We show how to compute the frequencies and
weights of a minimal polynomial-exponential decomposition , using the first
coefficients of the series. A key ingredient of the approach is the flat
extension criteria, which leads to a multivariate generalization of a rank
condition for a Carath{\'e}odory-Fej{\'e}r decomposition of multivariate Hankel
matrices. A new algorithm is given to compute a basis of the Artinian
Gorenstein algebra, based on a Gram-Schmidt orthogonalization process and to
decompose polynomial-exponential series. A general framework for the
applications of this approach is described and illustrated in different
problems. We provide Kronecker-type theorems for convolution operators, showing
that a convolution operator (or a cross-correlation operator) is of finite
rank, if and only if, its symbol is a polynomial-exponential function, and we
relate its rank to the decomposition of its symbol. We also present
Kronecker-type theorems for the reconstruction of measures as weighted sums of
Dirac measures from moments and for the decomposition of polynomial-exponential
functions from values. Finally, we describe an application of this method for
the sparse interpolation of polylog functions from values.


  Traditional Scene Understanding problems such as Object Detection and
Semantic Segmentation have made breakthroughs in recent years due to the
adoption of deep learning. However, the former task is not able to localise
objects at a pixel level, and the latter task has no notion of different
instances of objects of the same class. We focus on the task of Instance
Segmentation which recognises and localises objects down to a pixel level. Our
model is based on a deep neural network trained for semantic segmentation. This
network incorporates a Conditional Random Field with end-to-end trainable
higher order potentials based on object detector outputs. This allows us to
reason about instances from an initial, category-level semantic segmentation.
Our simple method effectively leverages the great progress recently made in
semantic segmentation and object detection. The accurate instance-level
segmentations that our network produces is reflected by the considerable
improvements obtained over previous work.


  In this work we investigate how children ages 5-12 perceive, understand, and
use generative AI models such as a text-based LLMs ChatGPT and a visual-based
model DALL-E. Generative AI is newly being used widely since chatGPT. Children
are also building mental models of generative AI. Those haven't been studied
before and it is also the case that the children's models are dynamic as they
use the tools, even with just very short usage. Upon surveying and
experimentally observing over 40 children ages 5-12, we found that children
generally have a very positive outlook towards AI and are excited about the
ways AI may benefit and aid them in their everyday lives. In a forced choice,
children robustly associated AI with positive adjectives versus negative ones.
We also categorize what children are querying AI models for and find that
children search for more imaginative things that don't exist when using a
visual-based AI and not when using a text-based one. Our follow-up study
monitored children's responses and feelings towards AI before and after
interacting with GenAI models. We even find that children find AI to be less
scary after interacting with it. We hope that these findings will shine a light
on children's mental models of AI and provide insight for how to design the
best possible tools for children who will inevitably be using AI in their
lifetimes. The motivation of this work is to bridge the gap between
Human-Computer Interaction (HCI) and Psychology in an effort to study the
effects of AI on society. We aim to identify the gaps in humans' mental models
of what AI is and how it works. Previous work has investigated how both adults
and children perceive various kinds of robots, computers, and other
technological concepts. However, there is very little work investigating these
concepts for generative AI models and not simply embodied robots or physical
technology.


  This paper proposes a nonlinear estimator for the robust reconstruction of
process and sensor faults for a class of uncertain nonlinear systems. The
proposed fault estimation method augments the system dynamics with an
ultra-local (in time) internal state-space representation (a finite chain of
integrators) of the fault vector. Next, a nonlinear state observer is designed
based on the known parts of the augmented dynamics. This nonlinear filter
(observer) reconstructs the fault signal as well as the states of the augmented
system. We provide sufficient conditions that guarantee stability of the
estimation error dynamics: firstly, asymptotic stability (i.e., exact fault
estimation) in the absence of perturbations induced by the fault model mismatch
(mismatch between internal ultra-local model for the fault and the actual fault
dynamics), uncertainty, external disturbances, and measurement noise and,
secondly, Input-to-State Stability (ISS) of the estimation error dynamics is
guaranteed in the presence of these perturbations. In addition, to support
performance-based estimator design, we provide Linear Matrix Inequality (LMI)
conditions for $\mathcal{L}_2$-gain and $\mathcal{L}_2-\mathcal{L}_\infty$
induced norm and cast the synthesis of the estimator gains as a semi-definite
program where the effect of model mismatch and external disturbances on the
fault estimation error is minimized in the sense of $\mathcal{L}_2$-gain, for
an acceptable $\mathcal{L}_2-\mathcal{L}_\infty$ induced norm with respect to
measurement noise. The latter result facilitates a design that explicitly
addresses the performance trade-off between noise sensitivity and robustness
against model mismatch and external disturbances. Finally, numerical results
for a benchmark system illustrate the performance of the proposed
methodologies.


  Distribution shift is an important concern in deep image classification,
produced either by corruption of the source images, or a complete change, with
the solution involving domain adaptation. While the primary goal is to improve
accuracy under distribution shift, an important secondary goal is uncertainty
estimation: evaluating the probability that the prediction of a model is
correct. While improving accuracy is hard, uncertainty estimation turns out to
be frustratingly easy. Prior works have appended uncertainty estimation into
the model and training paradigm in various ways. Instead, we show that we can
estimate uncertainty by simply exposing the original model to corrupted images,
and performing simple statistical calibration on the image outputs. Our
frustratingly easy methods demonstrate superior performance on a wide range of
distribution shifts as well as on unsupervised domain adaptation tasks,
measured through extensive experimentation.


  A huge swath of parameter space in the context of the Minimal Supersymmetric
Standard Model (MSSM) has been ruled at after run I of the LHC. Various
exclusion contours in the $m_{\tilde{g}}-\m_{\tilde{\chi}_{1}^{0}}$ plane were
derived by the experimental collaborations, all based on three-body gluino
decay topologies. These limits are however extremely model dependent and do not
always reflect the level of exclusion. If the gluino-neutralino spectrum is
compressed, then the current mass limits can be drastically reduced. In such
situations, the radiative decay of the gluino $\gino \ra g \neut{1}$ can be
dominant and used as a sensitive probe of small mass splittings. We examine the
sensitivity of constraints of some Run I experimental searches on this decay
after recasting them within the \texttt{MadAnalysis5} framework. The recasted
searches are now part of the \texttt{MadAnalysis5} Public Analysis Database. We
also design a dedicated search strategy and investigate its prospects to
uncover this decay mode of the gluino at run II of the LHC. We emphasize that a
multijet search strategy may be more sensitive than a monojet one, even in the
case of very small mass differences.


  Stellar limb darkening affects a wide range of astronomical measurements and
is frequently modelled with a parametric model using polynomials in the cosine
of the angle between the line of sight and the emergent intensity.
Two-parameter laws are particularly popular for cases where one wishes to fit
freely for the limb darkening coefficients (i.e. an uninformative prior) due to
the compact prior volume and the fact that more complex models rarely obtain
unique solutions with present data. In such cases, we show that the two limb
darkening coefficients are constrained by three physical boundary conditions,
describing a triangular region in the two-dimensional parameter space. We show
that uniformly distributed samples may be drawn from this region with optimal
efficiency by a technique developed by computer graphical programming:
triangular sampling. Alternatively, one can make draws using a uniform,
bivariate Dirichlet distribution. We provide simple expressions for these
parametrizations for both techniques applied to the case of quadratic,
square-root and logarithmic limb darkening laws. For example, in the case of
the popular quadratic law, we advocate fitting for q_1 = (u_1+u_2)^2 and q_2 =
0.5u_1(u_1+u_2)^{-1} with uniform priors in the interval [0,1] to implement
triangular sampling easily. Employing these parametrizations allows one to
derive model parameters which fully account for our ignorance about the
intensity profile, yet never explore unphysical solutions, yielding robust and
realistic uncertainty estimates. Furthermore, in the case of triangular
sampling with the quadratic law, our parametrization leads to significantly
reduced mutual correlations and provides an alternative geometric explanation
as to why naively fitting the quadratic limb darkening coefficients
precipitates strong correlations in the first place.


  We consider mean trajectories of multiple tracking points on a rigid body
that conducts Brownian motion in the absence and presence of an external force
field. Based on a na\"{\i}ve representation of rigid body - polygon and
polyhedron where hydrodynamic interactions are neglected, we study the Langevin
dynamics of these Brownian polygons and polyhedra. Constant force, harmonic
force and an exponentially decaying force are investigated as examples. In two
dimensional space, depending on the magnitude and form of the external force
and the isotropy and anisotropy of the body, mean trajectories of these
tracking points can exhibit three regimes of interactions: convergence, where
the mean trajectories converge to either a point or a single trajectory;
alignment, where the mean trajectories juxtapose in parallel; twist, where the
mean trajectories twist and intertwine, forming a plait structure. Moreover, we
have shown that in general a rigid body can sample from these regimes and
transit between them. And its Brownian behavior could be modified during such
transition. Notably, from a polygon in two dimensional space to a polyhedron in
three dimensional space, the alignment and twist regimes disappear and there is
only the convergence regime survived, due to the two more rotational degrees of
freedom in three dimensional space.


  The Lovelock Lagrangian is for even dimension D obtained from Weil
polynomials on the Lie algebra of the Lorentz group SO(1,D-1). The procedure
for generating it is related to the Weil homomorphism that converts Lie algebra
invariants into cohomology classes.


  Modern (sub-)millimeter interferometers enable the measurement of the cool
gas and dust emission of high-redshift galaxies (z>5). However, at these
redshifts the cosmic microwave background (CMB) temperature is higher,
approaching, and even exceeding, the temperature of cold dust and molecular gas
observed in the local Universe. In this paper, we discuss the impact of the
warmer CMB on (sub-)millimeter observations of high-redshift galaxies. The CMB
affects the observed (sub-)millimeter dust continuum and the line emission
(e.g. carbon monoxide, CO) in two ways: (i) it provides an additional source of
(both dust and gas) heating; and (ii) it is a non-negligible background against
which the line and continuum emission are measured. We show that these two
competing processes affect the way we interpret the dust and gas properties of
high-redshift galaxies using spectral energy distribution models. We quantify
these effects and provide correction factors to compute what fraction of the
intrinsic dust (and line) emission can be detected against the CMB as a
function of frequency, redshift and temperature. We discuss implications on the
derived properties of high-redshift galaxies from (sub-)millimeter data.
Specifically, the inferred dust and molecular gas masses can be severely
underestimated for cold systems if the impact of the CMB is not properly taken
into account.


  Consider the global wellposedness problem for nonlinear
  Schr\"odinger equation \[ i\partial_t u = [-\tfrac{1}{2} \Delta + V(x)] u \pm
|u|^{4/(d-2)} u, \ u(0) \in \Sigma(\mathbf{R}^d), \] where $\Sigma$ is the
weighted Sobolev space $\dot{H}^1 \cap |x|^{-1} L^2$. The case $V(x) =
\tfrac{1}{2}|x|^2$ was recently treated by the author. This note generalizes
the results to a class of "approximately quadratic" potentials.
  We closely follow the previous concentration compactness arguments for the
harmonic oscillator. A key technical difference is that in the absence of a
concrete formula for the linear propagator, we apply more general tools from
microlocal analysis, including a Fourier integral parametrix of Fujiwara.


  [Abridged] We calculate the structural evolution and nucleosynthesis of a
grid of models covering the metallicity range: -6.5 < [Fe/H] < -3.0 (plus Z=0),
and mass range: 0.85 < M < 3.0 Msun, amounting to 20 stars in total. In this
paper, the first of a series describing and analysing this large data set, we
present the resulting stellar yields. Many of the models experience violent
nuclear burning episodes not seen at higher metallicities. We refer to these
events as `Dual Flashes'. These events have also been reported by previous
studies. Some of the material processed by the Dual Flashes is dredged up
causing significant surface pollution with a distinct chemical composition. We
also analyse the yields in terms of C and N, comparing them to the observed
CEMP abundances. At the lowest metallicities ([Fe/H] < -4.0) we find the yields
to contain ~1 to 2 dex too much carbon, in agreement with all previous studies.
At higher metallicities ([Fe/H] = -3.0), where the observed data set is much
larger, all our models produce yields with [C/Fe] values consistent with those
observed in the most C-rich CEMPs. However it is only the low-mass models that
undergo the Dual Shell Flash (which occurs at the start of the TPAGB) that can
best reproduce the C and N observations. Normal Third Dredge-Up can not
reproduce the observations because at these metallicities intermediate mass
models (M > 2 Msun) suffer HBB which converts the C to N thus lowering [C/N]
well below the observations, whilst if TDU were to occur in the low-mass (M < 1
Msun) models (we do not find it to occur in our models), the yields would be
expected to be C-rich only, which is at odds with the `dual pollution' of C and
N generally observed in the CEMPs.


  The two-dimensional quantum Heisenberg antiferromagnet at zero temperature
with two kinds of locally frustrating defects - isolated ferromagnetic bonds
and impurity spins, is studied. For a quantum spin, coupled
antiferromagnetically to the two sublattices, we find a local ground state
transition. In the case of a ferromagnetic bond, the local magnetization is
found to remain finite even for strong coupling, contrary to previous results,
derived within the linear spin-wave approximation. Our results are based on an
analytic approach, suitable to treat strong defect-environment interaction, as
well as exact diagonalization studies. Technical details and some extension of
this work can be found in cond-mat/9712281.


  The edges of graphene nanoribbons (GNRs) have attracted much interest due to
their potentially strong influence on GNR electronic and magnetic properties.
Here we report the ability to engineer the microscopic edge termination of high
quality GNRs via hydrogen plasma etching. Using a combination of
high-resolution scanning tunneling microscopy and first-principles
calculations, we have determined the exact atomic structure of plasma-etched
GNR edges and established the chemical nature of terminating functional groups
for zigzag, armchair and chiral edge orientations. We find that the edges of
hydrogen-plasma-etched GNRs are generally flat, free of structural
reconstructions and are terminated by hydrogen atoms with no rehybridization of
the outermost carbon edge atoms. Both zigzag and chiral edges show the presence
of edge states.


  For a d-dimensional cellular automaton with d $\ge$ 1 we introduce a rescaled
entropy which estimates the growth rate of the entropy at small scales by
generalizing previous approaches [1, 9]. We also define a notion of Lyapunov
exponent and proves a Ruelle inequality as already established for d = 1 in
[16, 15]. Finally we generalize the entropy formula for 1-dimensional
permutative cellular automata [18] to the rescaled entropy in higher
dimensions. This last result extends recent works [17] of Shinoda and Tsukamoto
dealing with the metric mean dimensions of two-dimensional symbolic dynamics.


  In this paper, we study the Cauchy problem with decaying initial data for the
nonlocal modified Korteweg-de Vries equation (nonlocal mKdV)
  \[q_t(x,t)+q_{xxx}(x,t)-6q(x,t)q(-x,-t)q_x(x,t)=0,\]
  which can be viewed as a generalization of the local classical mKdV equation.
We first formulate the Riemann-Hilbert problem associated with the Cauchy
problem of the nonlocal mKdV equation. Then we apply the Deift-Zhou nonlinear
steepest-descent method to analyze the long-time asymptotics for the solution
of the nonlocal mKdV equation. In contrast with the classical mKdV equation, we
find some new and different results on long-time asymptotics for the nonlocal
mKdV equation and some additional assumptions about the scattering data are
made in our main results.


  We study non-equilibrium microcavity-polariton condensates (MPCs) in a
harmonic potential trap theoretically. We calculate and analyze the steady
state, collective-excitation modes and instability of MPCs. Within excitation
modes, there exist Nambu-Goldstone modes that can reveal the pattern of the
spontaneous symmetry breaking of MPCs. Bifurcation of the stable and unstable
modes is identified in terms of the pumping power and spot size. The unstable
mechanism associated with the inward supercurrent flow is characterized by the
existence of a supersonic region within the condensate.


  Semiconductor nanowires have opened new research avenues in quantum transport
owing to their confined geometry and electrostatic tunability. They have
offered an exceptional testbed for superconductivity, leading to the
realization of hybrid systems combining the macroscopic quantum properties of
superconductors with the possibility to control charges down to a single
electron. These advances brought semiconductor nanowires to the forefront of
efforts to realize topological superconductivity and Majorana modes. A prime
challenge to benefit from the topological properties of Majoranas is to reduce
the disorder in hybrid nanowire devices. Here, we show ballistic
superconductivity in InSb semiconductor nanowires. Our structural and chemical
analyses demonstrate a high-quality interface between the nanowire and a NbTiN
superconductor which enables ballistic transport. This is manifested by a
quantized conductance for normal carriers, a strongly enhanced conductance for
Andreev-reflecting carriers, and an induced hard gap with a significantly
reduced density of states. These results pave the way for disorder-free
Majorana devices.


  The purpose of this paper is to study the $L^2$ boundedness of operators of
the form \[ f\mapsto \psi(x) \int f(\gamma_t(x)) K(t) dt, \] where
$\gamma_t(x)$ is a $C^\infty$ function defined on a neighborhood of the origin
in $(t,x)\in \R^N\times \R^n$, satisfying $\gamma_0(x)\equiv x$, $\psi$ is a
$C^\infty$ cutoff function supported on a small neighborhood of $0\in \R^n$,
and $K$ is a "multi-parameter singular kernel" supported on a small
neighborhood of $0\in \R^N$. The goal is, given an appropriate class of kernels
$K$, to give conditions on $\gamma$ such that every operator of the above form
is bounded on $L^2$. The case when $K$ is a Calder\'on-Zygmund kernel was
studied by Christ, Nagel, Stein, and Wainger; we generalize their conditions to
the case when $K$ has a "multi-parameter" structure. For example, when $K$ is
given by a "product kernel." Even when $K$ is a Calder\'on-Zygmund kernel, our
methods yield some new results. This is the first paper in a three part series,
the later two of which are joint with E. M. Stein. The second paper deals with
the related question of $L^p$ boundedness, while the third paper deals with the
special case when $\gamma$ is real analytic.


  We determine the subgroup of automorphisms acting trivially on the second
integral cohomology for hyperkaehler manifolds which are deformation equivalent
to O'Grady's sporadic examples. In particular, we prove that this subgroup is
trivial in the ten dimensional case and isomorphic to
$(\mathbb{Z}/2\mathbb{Z})^{\times 8}$ in the six dimensional case. Furthermore
we study the fixed loci of the automorphisms in the six dimensional case.


  We propose a scenario for dynamical supersymmetry breaking in string
compactifications based on geometric engineering of quiver gauge theories. In
particular we show that the runaway behavior of fractional branes at del Pezzo
singularities can be stabilized by a flux superpotential in compact models. Our
construction relies on homological mirror symmetry for orientifolds.


  Major shifts in the global system of science and technology are destabilizing
the global status order and demonstrating the capacity for emerging countries
like China and India to exert greater influence. In order to measure changes in
the global scientific system, we develop a framework to assess the hierarchical
position of countries in the international scientific collaboration network.
Using a machine-learning model to identify the leaders of 5,966,623 scientific
teams that collaborated across international borders, we show that Chinese
scientists substantially narrowed their leadership deficit with scientists from
the US, UK, and EU between 1990 and 2023 in absolute terms. Consequently, China
and the US are on track to reach an equal number of team leaders engaged in
bilateral collaborations between 2027 and 2028. Nevertheless, Chinese progress
has been considerably slower in per-collaborator terms: after adjusting for the
number of non-leaders from each country, our models do not predict parity
between the US and China until after 2087. These dynamics extend to 11 critical
technology areas central to ongoing diplomacy between the two nations, such AI,
Semiconductors, and Advanced Communications, and to China's scientific
leadership with respect to the European Union and the United Kingdom. Thus,
while China's elite scientists are achieving leadership in the international
scientific community, China's scientific enterprise continues to face
developmental constraints. We conclude by reviewing several steps that Chinese
science is taking to overcome these constraints, by increasing its engagement
in scientific training and research in signatory nations to the Belt and Road
Initiative.


  In the large variety of models such as 3D and 2D Fermi-gas model with
hard-core repulsion, 3D and 2D Hubbard model, and Shubin-Vonsovsky model we
demonstrate the possibility of triplrt p-wave pairing at low electron density.
We show that the critical temperature of the p-wave pairing can be strongly
increased in a spin-polarized case or in a two-band situation already at low
density and reach experimentally observable values of (1-5)K. We also discuss
briefly d-wave pairing and high-Tc superconductivity with Tc~100K which arises
in the t-J model in the range of parameters realistic for cuprates.


  This paper is a survey of author's mathematical and logical study of the
problem of quantization of fields.


  We present the consistent approach to finding the discrete transformations in
the representation spaces of the proper Poincar\'e group. To this end we use
the possibility to establish a correspondence between involutory automorphisms
of the proper Poincar\'e group and the discrete transformations. As a result,
we derive rules of the discrete transformations for arbitrary spin-tensor
fields without the use of relativistic wave equations. Besides, we construct
explicitly fields carrying representations of the extended Poincar\'e group,
which includes the discrete transformations as well.


  We make use of the Next Generation model atmospheres by Allard et al. (1997)
and Hauschildt, Allard & Baron (1999) to compute theoretical models for low and
very low-mass stars for selected metallicities in the range Z= 0.0002 to 0.002.
On this basis, we present theoretical predictions covering the sequence of
H-burning stars as observed in galactic globulars from the faint end of the
Main Sequence up to, and beyond, the cluster Turn Off. The role played by the
new model atmospheres is discussed, showing that present models appear in
excellent agreement with models by Baraffe et al. (1997) as computed on quite
similar physical basis. One finds that the theoretical mass-luminosity
relations based on this updated set of models, are in good agreement with the
empirical data provided by Henry & McCarthy (1993). Comparison with HST
observation discloses that the location in the Color-Magnitude diagram of the
lower Main Sequence in galactic globular clusters appears again in good
agreement with the predicted sensitive dependence of these sequences on the
cluster metallicity.


  In this note we prove that certain twisted flag varieties carry Ulrich
bundles.


  We present efficient implementations of a number of operations for quantum
computers. These include controlled phase adjustments of the amplitudes in a
superposition, permutations, approximations of transformations and
generalizations of the phase adjustments to block matrix transformations. These
operations generalize those used in proposed quantum search algorithms.


  Massive particles with self interactions of the order of 0.2 barn/GeV are
intriguing Dark Matter candidates from an astrophysical point of view. Current
and past experiments for direct detection of massive Dark Matter particles are
focusing to relatively low cross sections with ordinary matter, however they
cannot rule out very large cross sections, $\sigma/M > 0.01$ barn/GeV, due to
atmosphere and material shielding. Cosmology places a strong indirect limit for
the presence of large interactions among Dark Matter and baryons in the
Universe, however such a limit cannot rule out the existence of a small
sub-dominant component of Dark Matter with non negligible interactions with
ordinary matter in our galactic halo. Here, the possibility of the existence of
bound states with ordinary matter, for a similar Dark Matter candidate with not
negligible interactions, is considered. The existence of bound states, with
binding energy larger than $\sim$1 meV, would offer the possibility to test in
laboratory capture cross sections of the order of a barn (or larger). The
signature of the detection for a mass increasing of cryogenic samples, due to
the possible particle accumulation, would allow the investigation of these Dark
Matter candidates with mass up to the GUT scale. A proof of concept for a
possible detection set-up and the evaluation of some noise sources are
described.


  This thesis is concerned with the calculation of fixed moments of the
O(a_s^3) heavy flavor contributions to the Wilson coefficients of the structure
function F_2(x,Q^2) in the limit Q^2 >> m^2, neglecting power corrections. The
massive Wilson coefficients in the asymptotic region are given as convolutions
of massive operator matrix elements (OMEs) and the known light flavor Wilson
coefficients. The former derive from the twist--2 operators emerging in the
light--cone--expansion and are calculated at the 3--loop level for fixed
moments. We also compute the massive OMEs which are needed to evaluate heavy
flavor parton distributions in the variable flavor number scheme to the same
order. All contributions to the Wilson coefficients and OMEs but the genuine
constant terms at O(a_s^3) of the OMEs are derived in terms of quantities,
which are known for general values in the Mellin variable N. For the OMEs
A_{Qg}^(3), A_{qg,Q}^(3) and A_{gg,Q}^(3) the moments N = 2 to 10, for
A_{Qq}^{(3), PS} to N = 12, and for A_{qq,Q}^{(3), NS}, A_{qq,Q}^{(3), PS},
A_{gq,Q}^(3)}to N=14 are computed. These terms contribute to the light flavor
'+'-combinations. For the flavor non-singlet terms, we calculate as well the
odd moments N=1 to 13, corresponding to the light flavor '-'-combinations. We
also obtain moments of the terms ~ T_F of the 3-loop anomalous dimensions in an
independent calculation, which agree with results given in the literature. The
mathematical structure of the occurring momentum integrals and of the final
results in terms of harmonic sums is discussed. We study applications of the
same techniques to the polarized and transversity case at the NLO and NNLO
level as well.


  We use confocal microscopy to study the motions of particles in concentrated
colloidal systems. Near the glass transition, diffusive motion is inhibited, as
particles spend time trapped in transient ``cages'' formed by neighboring
particles. We measure the cage sizes and lifetimes, which respectively shrink
and grow as the glass transition approaches. Cage rearrangements are more
prevalent in regions with lower local concentrations and higher disorder.
Neighboring rearranging particles typically move in parallel directions,
although a nontrivial fraction move in anti-parallel directions, usually from
pairs of particles with initial separations corresponding to the local maxima
and minima of the pair correlation function $g(r)$, respectively.


  The wealth of structural phases seen in the rare-earth disilicate compounds
promises an equally rich range of interesting magnetic properties. We report on
the crystal growth by the optical floating zone method of members of the
rare-earth disilicate family, $R_{2}$Si$_{2}$O$_{7}$ (with $R=$ Er, Ho, and
Tm). Through a systematic study, we have optimised the growth conditions for
Er$_{2}$Si$_{2}$O$_{7}$. We have grown, for the first time using the floating
zone method, crystal boules of Ho$_{2}$Si$_{2}$O$_{7}$ and
Tm$_{2}$Si$_{2}$O$_{7}$ compounds. We show that the difficulties encountered in
the synthesis of polycrystalline and single crystal samples are due to the
similar thermal stability ranges of different rare-earth silicate compounds in
the temperature-composition phase diagrams of the $R$-Si-O systems. The
addition of a small amount of SiO$_{2}$ excess allowed the amount of impurity
phases present in the powder samples to be minimised. The phase composition
analysis of the powder X-ray diffraction data collected on the as-grown boules
revealed that they were of single phase, except in the case of thulium
disilicate, which comprised of two phases. All growths resulted in multi-grain
boules, from which sizable single crystals could be isolated. The optimum
conditions used for the synthesis and crystal growth of polycrystalline and
single crystal $R_{2}$Si$_{2}$O$_{7}$ materials are reported. Specific heat
measurements of erbium and thulium disilicate compounds confirm an
antiferromagnetic phase transition below $T_{\mathrm{N}}=$ 1.8 K for D-type
Er$_{2}$Si$_{2}$O$_{7}$ and a Schottky anomaly centered around 3.5 K in C-type
Tm$_{2}$Si$_{2}$O$_{7}$, suggesting the onset of short-range magnetic
correlations. Magnetic susceptibility data of E-type Ho$_{2}$Si$_{2}$O$_{7}$
reveals an antiferromagnetic ordering of the Ho spins below $T_\mathrm{{N}}=$
2.3 K.


  The sequential fully implicit (SFI) method was introduced along with the
development of the multiscale finite volume (MSFV) framework, and has received
considerable attention in recent years. Each time step for SFI consists of an
outer loop to solve the coupled system, in which there is one inner Newton loop
to implicitly solve the pressure equation and another loop to implicitly solve
the transport equations. Limited research has been conducted that deals with
the outer coupling level to investigate the convergence performance. In this
paper we extend the basic SFI method with several nonlinear acceleration
techniques for improving the outer-loop convergence. Specifically, we consider
numerical relaxation, quasi-Newton (QN) and Anderson acceleration (AA) methods.
The acceleration techniques are adapted and studied for the first time within
the context of SFI for coupled flow and transport in porous media. We reveal
that the iterative form of SFI is equivalent to a nonlinear block Gauss-Seidel
(BGS) process. The effectiveness of the acceleration techniques is demonstrated
using several challenging examples. The results show that the basic SFI method
is quite inefficient, suffering from slow convergence or even convergence
failure. In order to better understand the behaviors of SFI, we carry out
detailed analysis on the coupling mechanisms between the sub-problems. Compared
with the basic SFI method, superior convergence performance is achieved by the
acceleration techniques, which can resolve the convergence difficulties
associated with various types of coupling effects. We show across a wide range
of flow conditions that the acceleration techniques can stabilize the iterative
process, and largely reduce the outer iteration count.


  In this note, we go over the recent soft photon model and Faddeev-Jackiw
quantization of the massless quantum electrodynamics in the eikonal limit to
some extent. Throughout our readdressing, we observe that the gauge potentials
in both approaches become pure gauges and the associated eikonal Faddeev-Jackiw
quantum bracket matches with the soft quantum bracket. These observations and
the fact that the gauge fields in two cases localize in two-dimensional plane
(even if it is spatial in soft photon case and $1+1$-dimensional Minkowski in
the eikonal case) imply that there might be an interesting relation between
these two distinct perspectives.


  The traditional approach to studying student understanding presents a
question and uses the student answers to make inferences about their knowledge.
However, this method does not capture the range of possible alternative ideas
available to students. We use a new approach, asking students to generate a
plausible explanation for every choice of a multiple-choice question, to
capture a range of explanations that students can generate in answering physics
questions. Asking 16 students to provide explanations in this way revealed
alternative possibilities for student thinking that would not have been
captured if they only provided one solution. The findings show two ways these
alternatives can be productive for learning physics: (i) even students who
ultimately chose the wrong answer could often generate the correct explanation
and (ii) many incorrect explanations contained elements of correct physical
reasoning. We discuss the instructional implications of this multiple-choice
questioning approach and of student alternative ideas.