  Quantum measurement is a fundamental cornerstone of experimental quantum
computations. The main issues in current quantum measurement strategies are the
high number of measurement rounds to determine a global optimal measurement
output and the low success probability of finding a global optimal measurement
output. Each measurement round requires preparing the quantum system and
applying quantum operations and measurements with high-precision control in the
physical layer. These issues result in extremely high-cost measurements with a
low probability of success at the end of the measurement rounds. Here, we
define a novel measurement for quantum computations called dense quantum
measurement. The dense measurement strategy aims at fixing the main drawbacks
of standard quantum measurements by achieving a significant reduction in the
number of necessary measurement rounds and by radically improving the success
probabilities of finding global optimal outputs. We provide application
scenarios for quantum circuits with arbitrary unitary sequences, and prove that
dense measurement theory provides an experimentally implementable solution for
gate-model quantum computer architectures.


  The ground state properties of N=Z doubly closed shell nuclei are studied
within correlated basis function theory. A truncated version of the Urbana v14
realistic potential, with spin, isospin and tensor components, is adopted,
together with state dependent correlations. Fermi hypernetted chain integral
equation and single operator chain approximation are used to evaluate density,
distribution function and ground state energy of 16O and 40Ca. The results
favourably compare with the available, variational MonteCarlo estimates and
provide a first substantial check of the accuracy of the cluster summation
method for state dependent correlations. We achieve in finite nuclei at least
the same level of accuracy in the treatment of non central interactions and
correlations as in nuclear matter. This opens the way for a microscopic study
of medium heavy nuclei ground state using present days realistic hamiltonians.


  The ability to adapt medical image segmentation networks for a novel class
such as an unseen anatomical or pathological structure, when only a few
labelled examples of this class are available from local healthcare providers,
is sought-after. This potentially addresses two widely recognised limitations
in deploying modern deep learning models to clinical practice,
expertise-and-labour-intensive labelling and cross-institution generalisation.
This work presents the first 3D few-shot interclass segmentation network for
medical images, using a labelled multi-institution dataset from prostate cancer
patients with eight regions of interest. We propose an image alignment module
registering the predicted segmentation of both query and support data, in a
standard prototypical learning algorithm, to a reference atlas space. The
built-in registration mechanism can effectively utilise the prior knowledge of
consistent anatomy between subjects, regardless whether they are from the same
institution or not. Experimental results demonstrated that the proposed
registration-assisted prototypical learning significantly improved segmentation
accuracy (p-values<0.01) on query data from a holdout institution, with varying
availability of support data from multiple institutions. We also report the
additional benefits of the proposed 3D networks with 75% fewer parameters and
an arguably simpler implementation, compared with existing 2D few-shot
approaches that segment 2D slices of volumetric medical images.


  We consider the population transfer process in a Lambda-type atomic medium of
unequal oscillator strengths by stimulated Raman adiabatic passage via
bright-state (b-STIRAP) taking into account propagation effects. Using both
analytic and numerical methods we show that the population transfer efficiency
is sensitive to the ratio q_p/q_s of the transition oscillator strengths. We
find that the case q_p>q_s is more detrimental for population transfer process
as compared to the case where $q_p \leq q_s$. For this case it is possible to
increase medium dimensions while permitting efficient population transfer. A
criterion determining the interaction adiabaticity in the course of propagation
process is found. We also show that the mixing parameter characterizing the
population transfer propagates superluminally.


  Although fully elastic when static, granular media become transiently elastic
when being slowly sheared -- during which both the elastic energy and stress
relax. Starting from this observation, we cogently derive the framework for
granular hydrodynamics, a set of differential equations consistent with general
principles of physics, especially reversible and irreversible thermodynamics.
In addition, an expression for the granular elastic energy is reviewed and
further discussed.


  Many unstable periodic orbits of the planar circular restricted 3-body
problem (PCRTBP) persist as invariant tori when a periodic forcing is added to
the equations of motion. In this study, we compute tori corresponding to
exterior Jupiter-Europa and interior Jupiter-Ganymede PCRTBP resonant periodic
orbits in a concentric circular restricted 4-body problem (CCR4BP). Motivated
by the 2:1 Laplace resonance between Europa and Ganymede's orbits, we then
attempt the continuation of a Jupiter-Europa 3:4 resonant orbit from the CCR4BP
into the Jupiter-Ganymede PCRTBP. We strongly believe that the resulting
dynamical object is a KAM torus lying near but not on the 3:2 Jupiter-Ganymede
resonance.


  We propose a joint source-channel-network coding scheme, based on compressive
sensing principles, for wireless networks with AWGN channels (that may include
multiple access and broadcast), with sources exhibiting temporal and spatial
dependencies. Our goal is to provide a reconstruction of sources within an
allowed distortion level at each receiver. We perform joint source-channel
coding at each source by randomly projecting source values to a lower
dimensional space. We consider sources that satisfy the restricted eigenvalue
(RE) condition as well as more general sources for which the randomness of the
network allows a mapping to lower dimensional spaces. Our approach relies on
using analog random linear network coding. The receiver uses compressive
sensing decoders to reconstruct sources. Our key insight is the fact that,
compressive sensing and analog network coding both preserve the source
characteristics required for compressive sensing decoding.


  Combining complementary information from multiple modalities is intuitively
appealing for improving the performance of learning-based approaches. However,
it is challenging to fully leverage different modalities due to practical
challenges such as varying levels of noise and conflicts between modalities.
Existing methods do not adopt a joint approach to capturing synergies between
the modalities while simultaneously filtering noise and resolving conflicts on
a per sample basis. In this work we propose a novel deep neural network based
technique that multiplicatively combines information from different source
modalities. Thus the model training process automatically focuses on
information from more reliable modalities while reducing emphasis on the less
reliable modalities. Furthermore, we propose an extension that multiplicatively
combines not only the single-source modalities, but a set of mixtured source
modalities to better capture cross-modal signal correlations. We demonstrate
the effectiveness of our proposed technique by presenting empirical results on
three multimodal classification tasks from different domains. The results show
consistent accuracy improvements on all three tasks.


  Observations of stellar surfaces - except for the Sun - are hampered by their
tiny angular extent, while observed spectral lines are smeared by averaging
over the stellar surface, and by stellar rotation. Exoplanet transits can be
used to analyze stellar atmospheric structure, yielding high-resolution spectra
across spatially highly resolved stellar surfaces, free from effects of spatial
smearing and the rotational wavelength broadening present in full-disk spectra.
During a transit, stellar surface portions successively become hidden, and
differential spectroscopy between various transit phases provides spectra of
those surface segments then hidden behind the planet. The small area subtended
by even a large planet (about 1% of a main-sequence star) offers high spatial
resolution but demands very precise observations. We demonstrate the
reconstruction of photospheric FeI line profiles at a spectral resolution
R=80,000 across the surface of the solar-type star HD209458. Any detailed
understanding of stellar atmospheres requires modeling with 3-dimensional
hydrodynamics. The properties predicted by such models are mapped onto the
precise spectral-line shapes, asymmetries and wavelength shifts, and their
variation from the center to the limb across any stellar disk. This method
provides a tool for testing and verifying such models. The method will soon
become applicable to more diverse types of stars, thanks to new spectrometers
on very large telescopes, and since ongoing photometric searches are expected
to discover additional bright host stars of transiting exoplanets.


  The recent discovery of the universal I-Love-Q relations connecting the
moment of inertia, tidal deformability, and the spin-induced quadrupole moment
of compact stars is intriguing and totally unexpected. In this paper, we
provide numerical evidence showing that the universality can be attributed to
the incompressible limit of the I-Love-Q relations. The fact that modern
equations of state are stiff, with an effective adiabatic index larger than
about two, above the nuclear density range is the key to establishing the
universality for neutron stars and quark stars with typical compactness from
about 0.1 to 0.3. On the other hand, the I-Love-Q relations of low-mass neutron
stars near the minimum mass limit depend more sensitively on the underlying
equation of state because these stars are composed mainly of softer matter at
low densities. However, the I-Love-Q relations for low-mass quark stars can
still be represented accurately by the incompressible limit. We also study the
I-Love relation connecting the moment of inertia and tidal deformability
analytically in Newtonian gravity and show why the I-Love-Q relation is weakly
dependent on the underlying equation of state and can be attributed to its
incompressible limit.


  In this work, we introduce a novel approach based on algebraic topology to
enhance graph convolution and attention modules by incorporating local
topological properties of the data. To do so, we consider the framework of
sheaf neural networks, which has been previously leveraged to incorporate
additional structure into graph neural networks' features and construct more
expressive, non-isotropic messages. Specifically, given an input simplicial
complex (e.g. generated by the cliques of a graph or the neighbors in a point
cloud), we construct its local homology sheaf, which assigns to each node the
vector space of its local homology. The intermediate features of our networks
live in these vector spaces and we leverage the associated sheaf Laplacian to
construct more complex linear messages between them. Moreover, we extend this
approach by considering the persistent version of local homology associated
with a weighted simplicial complex (e.g., built from pairwise distances of
nodes embeddings). This i) solves the problem of the lack of a natural choice
of basis for the local homology vector spaces and ii) makes the sheaf itself
differentiable, which enables our models to directly optimize the topology of
their intermediate features.


  The superconducting pairing in Sr$_2$RuO$_4$ is widely considered to be
chiral $p$-wave with $\vec{d}_{\boldsymbol k} \sim (k_x + ik_y)\hat{z}$, which
belongs to the $E_u$ representation of the crystalline $D_{4h}$ group. However,
this superconducting order appears hard to reconcile with a number of key
experiments. In this paper, based on symmetry analysis we discuss the
possibility of odd-parity pairing with inherent three-dimensional (3D)
character enforced by the inter-orbital interlayer coupling and the sizable
spin-orbit coupling (SOC) in the material. We focus on a yet unexplored $E_u$
pairing, which contains finite $(k_z \hat x$, $k_z \hat y)$-component in the
gap function. Under appropriate circumstances a novel time-reversal invariant
nematic pairing can be realized. This nematic superconducting state could make
contact with some puzzling observations on Sr$_2$RuO$_4$, such as the absence
of spontaneous edge current and no evidences of split transitions under
uniaxial strains.


  Recently video diffusion models have emerged as expressive generative tools
for high-quality video content creation readily available to general users.
However, these models often do not offer precise control over camera poses for
video generation, limiting the expression of cinematic language and user
control. To address this issue, we introduce CamCo, which allows fine-grained
Camera pose Control for image-to-video generation. We equip a pre-trained
image-to-video generator with accurately parameterized camera pose input using
Pl\"ucker coordinates. To enhance 3D consistency in the videos produced, we
integrate an epipolar attention module in each attention block that enforces
epipolar constraints to the feature maps. Additionally, we fine-tune CamCo on
real-world videos with camera poses estimated through structure-from-motion
algorithms to better synthesize object motion. Our experiments show that CamCo
significantly improves 3D consistency and camera control capabilities compared
to previous models while effectively generating plausible object motion.
Project page: https://ir1d.github.io/CamCo/


  In this paper, we prove that for every Finsler $n$-sphere $(S^n, F)$ for
$n\ge 3$ with reversibility $\lambda$ and flag curvature $K$ satisfying
$(\frac{\lambda}{\lambda+1})^2<K\le 1$, either there exist infinitely many
prime closed geodesics or there exists one elliptic closed geodesic whose
linearized Poincar\'e map has at least one eigenvalue which is of the form
$\exp(\pi i \mu)$ with an irrational $\mu$. Furthermore, there always exist
three prime closed geodesics on any $(S^3, F)$ satisfying the above pinching
condition.


  Chameleon, environmentally dependent dilaton, and symmetron gravity are three
models of modified gravity in which the effects of the additional scalar degree
of freedom are screened in dense environments. They have been extensively
studied in laboratory, cosmological, and astrophysical contexts. In this paper,
we present a preliminary investigation into whether additional constraints can
be provided by studying these scalar fields around black holes. By looking at
the properties of a static, spherically symmetric black hole, we find that the
presence of a non-uniform matter distribution induces a non-constant scalar
profile in chameleon and dilaton, but not necessarily symmetron gravity. An
order of magnitude estimate shows that the effects of these profiles on
in-falling test particles will be sub-leading compared to gravitational waves
and hence observationally challenging to detect.


  We tackle the problem of inferring node labels in a partially labeled graph
where each node in the graph has multiple label types and each label type has a
large number of possible labels. Our primary example, and the focus of this
paper, is the joint inference of label types such as hometown, current city,
and employers, for users connected by a social network. Standard label
propagation fails to consider the properties of the label types and the
interactions between them. Our proposed method, called EdgeExplain, explicitly
models these, while still enabling scalable inference under a distributed
message-passing architecture. On a billion-node subset of the Facebook social
network, EdgeExplain significantly outperforms label propagation for several
label types, with lifts of up to 120% for recall@1 and 60% for recall@3.


  Graphene exhibits unconventional two-dimensional electronic properties
resulting from the symmetry of its quasiparticles, which leads to the concepts
of pseudospin and electronic chirality. Here we report that scanning tunneling
microscopy can be used to probe these unique symmetry properties at the
nanometer scale. They are reflected in the quantum interference pattern
resulting from elastic scattering off impurities, and they can be directly read
from its fast Fourier transform. Our data, complemented by theoretical
calculations, demonstrate that the pseudospin and the electronic chirality in
epitaxial graphene on SiC(0001) correspond to the ones predicted for ideal
graphene.


  Inhomogeneous distribution of the pinning force in superconductor results in
a magnetization asymmetry. A model considering the field distribution in
superconductor was developed and symmetric and asymmetric magnetization loops
of porous and textured Bi_{1.8}Pb_{0.3}Sr_{1.9}Ca_{2}Cu_{3}O_{x} were fitted.
It is found that the thermal equilibrium magnetization realizes in crystals
smaller than some size depending on temperature and magnetic field.


  Understanding the reactivity and spectroscopy of aqueous solutions at the
atomistic level is crucial for the elucidation and design of chemical
processes. However, the simulation of these systems requires addressing the
formidable challenges of treating the quantum nature of both the electrons and
nuclei. Exploiting our recently developed methods that provide acceleration by
up to two orders of magnitude, we combine path integral simulations with
on-the-fly evaluation of the electronic structure at the hybrid density
functional theory level to capture the interplay between nuclear quantum
effects and the electronic surface. Here we show that this combination provides
accurate structure and dynamics, including the full infra-red and Raman spectra
of liquid water. This allows us to demonstrate and explain the failings of
lower-level density functionals for dynamics and vibrational spectroscopy when
the nuclei are treated quantum mechanically. These insights thus provide a
foundation for the reliable investigation of spectroscopy and reactivity in
aqueous environments.


  Referring Image Segmentation~(RIS) leveraging transformers has achieved great
success on the interpretation of complex visual-language tasks. However, the
quadratic computation cost makes it resource-consuming in capturing long-range
visual-language dependencies. Fortunately, Mamba addresses this with efficient
linear complexity in processing. However, directly applying Mamba to
multi-modal interactions presents challenges, primarily due to inadequate
channel interactions for the effective fusion of multi-modal data. In this
paper, we propose ReMamber, a novel RIS architecture that integrates the power
of Mamba with a multi-modal Mamba Twister block. The Mamba Twister explicitly
models image-text interaction, and fuses textual and visual features through
its unique channel and spatial twisting mechanism. We achieve competitive
results on three challenging benchmarks with a simple and efficient
architecture. Moreover, we conduct thorough analyses of ReMamber and discuss
other fusion designs using Mamba. These provide valuable perspectives for
future research. The code has been released at:
https://github.com/yyh-rain-song/ReMamber.


  The question whether excess electrons in SrTiO3 form free or trapped carriers
is a crucial aspect for the electronic properties of this important material.
This fundamental ambiguity prevents a consistent interpretation of the puzzling
experimental situation, where results support one or the other scenario
depending on the type of experiment that is conducted. Using density functional
theory corrected with an on-site Coulomb interaction U, it is established that
excess electrons form small polarons if the electron density is higher than ~
1%. For densities below this critical value, the electrons stay delocalized or
become large polarons. Our modeling of oxygen deficient SrTiO3 provides an
alternative picture with respect to previous theoretical studies endowing firm
evidence for the observed, temperature-driven metal-insulator transition in
samples with homogeneously distributed oxygen vacancies. Small polarons
confined to Ti(3+) sites are immobile at low temperature but can be thermally
activated into a conductive state.


  We describe ZEUS-MP: a Multi-Physics, Massively-Parallel, Message-Passing
code for astrophysical fluid dynamics simulations in 3 dimensions. ZEUS-MP is a
follow-on to the sequential ZEUS-2D and ZEUS-3D codes developed and
disseminated by the Laboratory for Computational Astrophysics
(lca.ncsa.uiuc.edu) at NCSA. V1.0 released 1/1/2000 includes the following
physics modules: ideal hydrodynamics, ideal MHD, and self-gravity. Future
releases will include flux-limited radiation diffusion, thermal heat
conduction, two-temperature plasma, and heating and cooling functions. The
covariant equations are cast on a moving Eulerian grid with Cartesian,
cylindrical, and spherical polar coordinates currently supported.
Parallelization is done by domain decomposition and implemented in F77 and MPI.
The code is portable across a wide range of platforms from networks of
workstations to massively parallel processors. Some parallel performance
results are presented as well as an application to turbulent star formation.


  Let P be a set of n > 2 points in general position in the plane and let G be
a geometric graph with vertex set P. If the number of empty triangles uvw in P
for which the subgraph of G induced by {u,v,w} is not connected is at most n-3,
then G contains a non-self intersecting spanning tree.


  An exact solution of Einstein-Cartan-Maxwell (ECM) field equations
representing a charged domain wall given by the jump on the electric charge and
spin density across the wall is obtained from the Riemannian theory of
distributions. The Gauss-Coddazzi equations are used to show that spin, charge
and Cartan torsion increases the repulsive character of the domain wall. Taub
and Vilenkin walls are discussed as well as their relations to wormhole
geometry. The electric and torsion fields are constants at the wall.


  In this paper, we report recent developments of the HAL QCD method for two
hadron systems which contain quark annihilation processes using all-to-all
quark propagators. We employ the hybrid method for all-to-all propagators,
which combines a low-mode spectral decomposition of the quark propagator and
stochastic estimators for remaining high modes, to evaluate the HAL QCD
potentials for the first time. Using this method, we investigate the $I= 1,2$
$\pi \pi$ scatterings at $m_{\pi} \approx 870$ MeV. In the $I=2$ study, we
study how statistical fluctuations of the HAL QCD potentials are increased due
to stochastic estimators in the hybrid method, compared with the conventional
one without them. We find that we can reduce statistical fluctuations by
dilutions of stochastic noises in order to obtain sufficiently precise results,
which turn out to be consistent with conventional results without all-to-all
propagators. In the $I=1$ $\pi \pi$ case, which contains quark annihilation
processes, we find that statistical fluctuations are further enhanced due to
noise contaminations in annihilation processes. We, however, confirm that we
can also reduce such statistical fluctuations to obtain the potential with a
reasonable precision as long as we further increase a degree of dilutions at a
price of large numerical costs and take an appropriate scheme for the
potential.


  Worldwide commitments to net zero greenhouse emissions have accelerated
investments in renewable energy resources. The requirements for operating and
planning power systems are becoming stringent because of the need to take into
account the uncertainty associated with renewable generation. Several modeling
frameworks that consider the inherent uncertainty in the operation and planning
of the power system have been extensively studied. Stochastic optimization has
been the most popular approach among these frameworks due to its intuitive
representation, especially when formulated using discrete probabilistic
scenarios to represent the random variables. Although many scenarios
representing all possible uncertain operating conditions would be needed to
accurate evaluate stochastic operation and planning models, the size of the
scenario set impacts computational complexity, posing a significant tradeoff
between uncertainty detail representation and computational tractability.
  During the last decade, a large body of research has focused on developing
new scenario aggregation methods to derive reduced scenario sets that show
properties similar to the original scenario set while decreasing computational
burden. This review provides an up-to-date, comprehensive classification and
analysis of the literature related to scenario aggregation methods for
addressing power system optimization problems. First, we present a general
framework and the aggregation methodologies. Then, the main studies related to
temporal and spatial scenario aggregation are described, followed by a
bibliometric analysis of the main publication sources, authors, and application
problems. Finally, we provide a numerical analysis and discuss 16 aggregation
methods for the transmission expansion planning problem. Finally,
recommendations, opportunities, and conclusions are discussed.


  We study the cohomological physics of fivebranes in type II and heterotic
string theory. We give an interpretation of the one-loop term in type IIA,
which involves the first and second Pontrjagin classes of spacetime, in terms
of obstructions to having bundles with certain structure groups. Using a
generalization of the Green-Schwarz anomaly cancelation in heterotic string
theory which demands the target space to have a String structure, we observe
that the "magnetic dual" version of the anomaly cancelation condition can be
read as a higher analog of String structure, which we call Fivebrane structure.
This involves lifts of orthogonal and unitary structures through higher
connected covers which are not just 3- but even 7-connected. We discuss the
topological obstructions to the existence of Fivebrane structures. The dual
version of the anomaly cancelation points to a relation of String and Fivebrane
structures under electric-magnetic duality.


  In view of ongoing experiments to trap ultracold spin-polarized $^6$Li, we
study various properties of an interacting Fermi gas in a harmonic trap taking
the discrete nature of the unperturbed harmonic trap levels into account
exactly. As $^6$Li has a rather large and negative scattering length, we focus
on the effects of the attractive atom-atom interaction on several thermodynamic
properties and on the momentum and density distributions.
  The dependence of the chemical potential, the specific heat and the density
and momentum distributions on the number of particles in the trap is obtained.
We also calculate the energy of the gas. Comparison is made with results of a
semiclassical calculation and with the properties of a non-interacting gas. We
find that the effect of the interactions is rather large for realistic trap
frequencies. Hence, it is important to include these interactions in any
quantitative predictions relevant for experiments.


  Heavy-flavoured jets have been studied in photoproduction at HERA. This
includes the first measurement of dijet angular distributions in D*
photoproduction and the ratio of the vector/(vector + pseudoscalar) production
rate for charm mesons.


  Breakthroughs in unsupervised domain adaptation (uDA) can help in adapting
models from a label-rich source domain to unlabeled target domains. Despite
these advancements, there is a lack of research on how uDA algorithms,
particularly those based on adversarial learning, can work in distributed
settings. In real-world applications, target domains are often distributed
across thousands of devices, and existing adversarial uDA algorithms -- which
are centralized in nature -- cannot be applied in these settings. To solve this
important problem, we introduce FRuDA: an end-to-end framework for distributed
adversarial uDA. Through a careful analysis of the uDA literature, we identify
the design goals for a distributed uDA system and propose two novel algorithms
to increase adaptation accuracy and training efficiency of adversarial uDA in
distributed settings. Our evaluation of FRuDA with five image and speech
datasets show that it can boost target domain accuracy by up to 50% and improve
the training efficiency of adversarial uDA by at least 11 times.


  Deep Neural Networks (DNNs) have recently been achieving state-of-the-art
performance on a variety of computer vision related tasks. However, their
computational cost limits their ability to be implemented in embedded systems
with restricted resources or strict latency constraints. Model compression has
therefore been an active field of research to overcome this issue.
Additionally, DNNs typically require massive amounts of labeled data to be
trained. This represents a second limitation to their deployment. Domain
Adaptation (DA) addresses this issue by allowing knowledge learned on one
labeled source distribution to be transferred to a target distribution,
possibly unlabeled. In this paper, we investigate on possible improvements of
compression methods in DA setting. We focus on a compression method that was
previously developed in the context of a single data distribution and show
that, with a careful choice of data to use during compression and additional
regularization terms directly related to DA objectives, it is possible to
improve compression results. We also show that our method outperforms an
existing compression method studied in the DA setting by a large margin for
high compression rates. Although our work is based on one specific compression
method, we also outline some general guidelines for improving compression in DA
setting.


  The Multipath effect in Time-of-Flight(ToF) cameras still remains to be a
challenging problem that hinders further processing of 3D data information.
Based on the evidence from previous literature, we explored the possibility of
using machine learning techniques to correct this effect. Firstly, we created
two new datasets of of ToF images rendered via ToF simulator of LuxRender.
These two datasets contain corners in multiple orientations and with different
material properties. We chose scenes with corners as multipath effects are most
pronounced in corners. Secondly, we used this dataset to construct a learning
model to predict real valued corrections to the ToF data using Random Forests.
We found out that in our smaller dataset we were able to predict real valued
correction and improve the quality of depth images significantly by removing
multipath bias. With our algorithm, we improved relative per-pixel error from
average value of 19% to 3%. Additionally, variance of the error was lowered by
an order of magnitude.


  We propose a recipe on how to build a general, powerful, scalable (GPS) graph
Transformer with linear complexity and state-of-the-art results on a diverse
set of benchmarks. Graph Transformers (GTs) have gained popularity in the field
of graph representation learning with a variety of recent publications but they
lack a common foundation about what constitutes a good positional or structural
encoding, and what differentiates them. In this paper, we summarize the
different types of encodings with a clearer definition and categorize them as
being $\textit{local}$, $\textit{global}$ or $\textit{relative}$. The prior GTs
are constrained to small graphs with a few hundred nodes, here we propose the
first architecture with a complexity linear in the number of nodes and edges
$O(N+E)$ by decoupling the local real-edge aggregation from the fully-connected
Transformer. We argue that this decoupling does not negatively affect the
expressivity, with our architecture being a universal function approximator on
graphs. Our GPS recipe consists of choosing 3 main ingredients: (i)
positional/structural encoding, (ii) local message-passing mechanism, and (iii)
global attention mechanism. We provide a modular framework $\textit{GraphGPS}$
that supports multiple types of encodings and that provides efficiency and
scalability both in small and large graphs. We test our architecture on 16
benchmarks and show highly competitive results in all of them, show-casing the
empirical benefits gained by the modularity and the combination of different
strategies.


  The Josephson Junction model is applied to the experimental implementation of
classical bifurcation in a quadrupolar Nuclear Magnetic Resonance system. There
are two regimes, one linear and one nonlinear which are implemented by the
radio-frequency term and the quadrupolar term of the Hamiltonian of a spin
system respectively. Those terms provide an explanation of the symmetry
breaking due to bifurcation. Bifurcation depends on the coexistence of both
regimes at the same time in different proportions. The experiment is performed
on a lyotropic liquid crystal sample of an ordered ensemble of $^{133}$Cs
nuclei with spin $I=7/2$ at room temperature. Our experimental results confirm
that bifurcation happens independently of the spin value and of the physical
system. With this experimental spin scenario, we confirm that a quadrupolar
nuclei system could be described analogously to a symmetric two--mode
Bose--Einstein condensate.


  We formulate a kinetic model of DNA replication that quantitatively describes
recent results on DNA replication in the in vitro system of Xenopus laevis
prior to the mid-blastula transition. The model describes well a large amount
of different data within a simple theoretical framework. This allows one, for
the first time, to determine the parameters governing the DNA replication
program in a eukaryote on a genome-wide basis. In particular, we have
determined the frequency of origin activation in time and space during the cell
cycle. Although we focus on a specific stage of development, this model can
easily be adapted to describe replication in many other organisms, including
budding yeast.


  With the advent of wide-spread global and continental-scale spatiotemporal
datasets, increased attention has been given to covariance functions on spheres
over time. This paper provides results for stationary covariance functions of
random fields defined over $d$-dimensional spheres cross time. Specifically, we
provide a bridge between the characterization in \cite{berg-porcu} for
covariance functions on spheres cross time and Gneiting's lemma
\citep{gneiting2002} that deals with planar surfaces.
  We then prove that there is a valid class of covariance functions similar in
form to the Gneiting class of space-time covariance functions
\citep{gneiting2002} that replaces the squared Euclidean distance with the
great circle distance. Notably, the provided class is shown to be positive
definite on every $d$-dimensional sphere cross time, while the Gneiting class
is positive definite over $\R^d \times \R$ for fixed $d$ only.
  In this context, we illustrate the value of our adapted Gneiting class by
comparing examples from this class to currently established nonseparable
covariance classes using out-of-sample predictive criteria. These comparisons
are carried out on two climate reanalysis datasets from the National Centers
for Environmental Prediction and National Center for Atmospheric Research. For
these datasets, we show that examples from our covariance class have better
predictive performance than competing models.


  Nanomechanical shuttles transferring small groups of electrons or even
individual electrons from one electrode to another offer a novel approach to
the problem of controlled charge transport. Here, we report the fabrication of
shuttle-junctions consisting of a 20 nm diameter gold nanoparticle embedded
within the gap between two gold electrodes. The nanoparticle is attached to the
electrodes through a monolayer of flexible organic molecules which play the
role of springs so that when a sufficient voltage bias is applied, then
nanoparticle starts to oscillate transferring electrons from one electrode to
the other. Current-voltage characteristics for the fabricated devices have been
measured and compared with the results of our computer simulations.


  Hard cases of pronoun resolution have been used as a long-standing benchmark
for commonsense reasoning. In the recent literature, pre-trained language
models have been used to obtain state-of-the-art results on pronoun resolution.
Overall, four categories of training and evaluation objectives have been
introduced. The variety of training datasets and pre-trained language models
used in these works makes it unclear whether the choice of training objective
is critical. In this work, we make a fair comparison of the performance and
seed-wise stability of four models that represent the four categories of
objectives. Our experiments show that the objective of sequence ranking
performs the best in-domain, while the objective of semantic similarity between
candidates and pronoun performs the best out-of-domain. We also observe a
seed-wise instability of the model using sequence ranking, which is not the
case when the other objectives are used.


  A generalization of Chern-Simons gauge theory is formulated in any dimension
and arbitrary gauge group where gauge fields and gauge parameters are
differential forms of any degree. The quaternion algebra structure of this
formulation is shown to be equivalent to a three Z(2)-gradings structure, thus
clarifying the quaternion role in a previous formulation.


  Let X_0=0, X_1, X_2, ..., be an aperiodic random walk generated by a sequence
xi_1, xi_2, ..., of i.i.d. integer-valued random variables with common
distribution p(.) having zero mean and finite variance. For an N-step
trajectory X=(X_0,X_1,...,X_N) and a monotone convex function V: R^+ -> R^+
with V(0)=0, define V(X)= sum_{j=1}^{N-1} V(|X_j|). Further, let I_{N,+}^{a,b}
be the set of all non-negative paths X compatible with the boundary conditions
X_0=a, X_N=b. We discuss asymptotic properties of X in I_{N,+}^{a,b} w.r.t. the
probability distribution P_{N}^{a,b}(X)= (Z_{N}^{a,b})^{-1} exp{-lambda V(X)}
prod_{i=0}^{N-1} p(X_{i+1}-X_i) as N -> infinity and lambda -> 0, Z_{N}^{a,b}
being the corresponding normalization. If V(.) grows not faster than
polynomially at infinity, define H(lambda) to be the unique solution to the
equation lambda H^2 V(H) =1. Our main result reads that as lambda -> 0, the
typical height of X_{[alpha N]} scales as H(lambda) and the correlations along
X decay exponentially on the scale H(lambda)^2. Using a suitable blocking
argument, we show that the distribution tails of the rescaled height decay
exponentially with critical exponent 3/2. In the particular case of linear
potential V(.), the characteristic length H(lambda) is proportional to
lambda^{-1/3} as lambda -> 0.


  The COBE detection of CMB anisotropies provides the best way of fixing the
amplitude of fluctuations on the largest scales. This normalization is usually
given for an n=1 spectrum, including only the anisotropy caused by the Sachs-
Wolfe effect. This is certainly not a good approximation for a model containing
any reasonable amount of baryonic matter. In fact, even tilted S-W spectra are
not a good fit to models like CDM. Here we normalize standard CDM (sCDM) to the
2-year COBE data, and quote the best amplitude in terms of the conventionally
used measures of power. We also give normalizations for some specific variants
of this standard model, and we indicate how the normalization depends on the
assumed values of n, Omega_B and H_0. For sCDM we find <Q>=19.9\pm1.5uK,
corresponding to sigma_8=1.34\pm0.10, with the normalization at large scales
being B=(8.16\pm1.04)\times10^5 (Mpc/h)^4, and other numbers given in the
Table. The measured rms temperature fluctuation smoothed on 10deg is a little
low relative to this normalization. This is mainly due to the low quadrupole in
the data: when the quadrupole is removed, the measured value of sigma(10) is
quite consistent with the best-fitting <Q>. The use of <Q> should be preferred
over sigma(10), when its value can be determined for a particular theory, since
it makes full use of the data.


  This work considers the multi-access caching system proposed by Hachem et
al., where each user has access to L neighboring caches in a cyclic wrap-around
fashion. We first propose a placement strategy called the consecutive cyclic
placement, which achieves the maximal local caching gain. Then under the
consecutive cyclic placement, we derive the optimal coded caching gain from the
perspective of Placement Delivery Array (PDA), thus obtaining a lower bound on
the rate of PDA. Finally, under the consecutive cyclic placement, we construct
a class of PDA, leading to a multi-access coded caching scheme with linear
subpacketization, which achieves our derived lower bound for some parameters;
while for other parameters, the achieved coded caching gain is only 1 less than
the optimal one. Analytical and numerical comparisons of the proposed scheme
with existing schemes are provided to validate the performance.


  In this paper, we will first introduce a novel multiscale representation
(MSR) for shapes. Based on the MSR, we will then design a surface inpainting
algorithm to recover 3D geometry of blood vessels. Because of the nature of
irregular morphology in vessels and organs, both phantom and real inpainting
scenarios were tested using our new algorithm. Successful vessel recoveries are
demonstrated with numerical estimation of the degree of arteriosclerosis and
vessel occlusion.


  We report a detailed study of the electronic structure of the MgB$_{2}$ with
different lattice constants by using the full-potential linearized augmented
plane wave(FPLAPW) method. It is found that the lattice parameters have great
effect on the $\sigma$ band of Boron. Our results indicate that increasing
lattice constant along the {\it c} axis will increase the density of
states(DOS) at the Fermi level, making the $\sigma$ band upward shift, and
increasing hole number in the $\sigma$ band. So, the superconducting transition
temperature T$_{c}$ will be raised correspondingly. Changing the lattice
constant along {\it a} axis has an opposite effect to that of along {\it c}
axis. Our result is in agreement with experiment. A possible way of searching
for higher T$_{c}$ superconductor has been indicated, i.e., making MgB$_{2}$ to
have longer {\it c} axis and shorter {\it a, b} axis by doping.


  Selected results of original numeric simulations of non-linear magnetostatic
spin waves and microwave-frequency magnetic chaos in ferrite films are
expounded, as third part of the work whose first two parts are recent arXive
preprints 1204.0200 and 1204.2423 . Especially we consider crucial role of
parametric processes in creating the chaos and simultaneously obstacles to its
synchronization, and examine some possibilities of good enough synchronization
(to an extent allowing its use for direct secure communication in microwave
band).


  The Kechris-Pestov-Todorcevic correspondence connects extreme amenability of
non-Archimedean Polish groups with Ramsey properties of classes of finite
structures. The purpose of the present paper is to recast it as one of the
instances of a more general construction, allowing to show that Ramsey-type
statements actually appear as natural combinatorial expressions of the
existence of fixed points in certain compactifications of groups, and that
similar correspondences in fact exist in various dynamical contexts.


  In this paper we study finite p-solvable groups having irreducible complex
characters chi in Irr(G) which take roots of unity values on the p-singular
elements of G.


  As recent advancements in physics and astronomy rapidly rewrite textbooks,
there is a growing need in keeping abreast of the latest knowledge in these
fields. Reading preprints is one of the effective ways to do this. By having
journal clubs where people can read and discuss journals together, the benefits
of reading journals become more prevalent. We present an investigative study of
understanding the factors that affect the success of preprint journal clubs in
astronomy, more commonly known as Astro-ph/Astro-Coffee (hereafter called AC).
A survey was disseminated to understand how institutions from different
countries implement AC. We interviewed 9 survey respondents and from their
responses we identified four important factors that make AC successful:
commitment (how the organizer and attendees participate in AC), environment
(how conducive and comfortable AC is conducted), content (the discussed topics
in AC and how they are presented), and objective (the main goal/s of conducting
AC). We also present the format of our AC, an elective class which was
evaluated during the Spring Semester 2020 (March 2020 - June 2020). Our
evaluation with the attendees showed that enrollees (those who are enrolled and
are required to present papers regularly) tend to be more committed in
attending compared to audiences (those who are not enrolled and are not
required to present papers regularly). In addition, participants tend to find
papers outside their research field harder to read. Finally, we showed an
improvement in the weekly number of papers read after attending AC of those who
present papers regularly, and a high satisfaction rating of our AC. We
summarize the areas of improvement in our AC implementation, and we encourage
other institutions to evaluate their own AC in accordance with the four
aforementioned factors to assess the effectiveness of their AC in reaching
their goals.


  The resistivity of a dense crystalline array of semiconductor nanocrystals
(NCs) depends in a sensitive way on the level of doping as well as on the NC
size and spacing. The choice of these parameters determines whether electron
conduction through the array will be characterized by activated
nearest-neighbor hopping or variable-range hopping (VRH). Thus far, no general
theory exists to explain how these different behaviors arise at different
doping levels and for different types of NCs. In this paper we examine a simple
theoretical model of an array of doped semiconductor NCs that can explain the
transition from activated transport to VRH. We show that in sufficiently small
NCs, the fluctuations in donor number from one NC to another provide sufficient
disorder to produce charging of some NCs, as electrons are driven to vacate
higher shells of the quantum confinement energy spectrum. This
confinement-driven charging produces a disordered Coulomb landscape throughout
the array and leads to VRH at low temperature. We use a simple computer
simulation to identify different regimes of conduction in the space of
temperature, doping level, and NC diameter. We also discuss the implications of
our results for large NCs with external impurity charges and for NCs that are
gated electrochemically.


  We present a consistent microscopic study of spin pumping effects for both
metallic and insulating ferromagnets. As for metallic case, we present a simple
quantum mechanical picture of the effect as due to the electron spin flip as a
result of a nonadiabatic (off-diagonal) spin gauge field. The effect of
interface spin-orbit interaction is briefly discussed. We also carry out
field-theoretic calculation to discuss on the equal footing the spin current
generation and torque effects such as enhanced Gilbert damping constant and
shift of precession frequency both in metallic and insulating cases. For thick
ferromagnetic metal, our study reproduces results of previous theories such as
the correspondence between the dc component of the spin current and enhancement
of the damping. For thin metal and insulator, the relation turns out to be
modified. For the insulating case, driven locally by interface $sd$ exchange
interaction due to magnetic proximity effect, physical mechanism is distinct
from the metallic case. Further study of proximity effect and interface
spin-orbit interaction would be crucial to interpret experimental results in
particular for insulators.


  We outline the theory and practice of measuring the four Stokes parameters of
spectral lines in emission/absorption observations. We apply these concepts to
our Arecibo HI absorption line data and present the results. We include a
detailed discussion of instrumental effects arising from polarized beam
structure and its interaction with the spatially extended emission line
structure. At Arecibo, linear polarization (Stokes (Q,U)) has much larger
instrumental effects than circular (Stokes V). We show how to reduce the
instrumental contributions to V and to evaluate upper limits to its remaining
instrumental errors by using the (Q,U) results. These efforts work well for
opacity spectra but not for emission spectra. Arecibo's large central blockage
exacerbates these effects, particularly for emission profiles, and other
telescopes with weaker sidelobes are not as susceptible. We present graphical
results for 41 sources; we analyze these absorption spectra in terms of
Gaussian components, which number 136, and present physical parameters
including magnetic field for each.


  In the paper "Broersma and Hoede, {\it Path graphs}, J. Graph Theory {\bf 13}
(1989) 427-444", the authors proposed a problem whether there is a triple of
mutually nonisomorphic connected graphs which have an isomorphic connected
$P_3$-graph. For a long time, this problem remains unanswered. In this paper,
we give it a negative answer that there is no such triple, and thus completely
solve this problem.


  We investigate two-parameter quantum groups corresponding to the general
linear and special linear Lie algebras gl_n and sl_n. We show that these
quantum groups can be realized as Drinfel'd doubles of certain Hopf subalgebras
with respect to Hopf pairings. Using the Hopf pairing, we construct a
corresponding R-matrix and a quantum Casimir element. We discuss isomorphisms
among these quantum groups and connections with multiparameter quantum groups.


  To realize the practical implementation of device-independent quantum key
distribution~(DIQKD), the main difficulty is that its security relies on the
detection-loophole-free violation of the Clauser-Horne-Shimony-Holt~(CHSH)
inequality, i.e. the CHSH value $S>2$, which is easily destroyed by the loss in
transmission channels. One of the simplest methods to circumvent it is to
utilize the entanglement swapping relay~(ESR). Here, we propose and
experimentally test an improved version of the heralded nonlocality amplifier
protocol based on the ESR, and numerically show that our scheme is much more
robust against the transmission loss than the previously developed protocol. In
the experiment, we observe that the obtained probability distribution is in
excellent agreement with those expected by the numerical simulation with
experimental parameters which are precisely characterized in a separate
measurement. Moreover, we experimentally estimate the nonlocality of the
heralded state after the transmission of 10~dB loss just before detection. It
is estimated to be $S=2.104>2$, which indicates that our final state possesses
strong nonlocality even with various experimental imperfections. Our result
clarifies an important benchmark of the ESR protocol, and paves the way towards
the long-distance realization of the loophole-free CHSH-violation as well as
DIQKD.


  Besides the lot of advantages offered by the 3D stacking of devices in an
integrated circuit there is a chance of device damage due to rise in peak
temperature value. Hence, in order to make use of all the potential benefits of
the vertical stacking a thermal aware design is very essential. The first step
for designing a thermal aware architecture is to analyze the hotspot
temperature generated by the devices. In this paper we are presenting the
results of our thermal analysis experiments of a 3D heterogeneous structure
with three layers. The bottom layer had eight identical processors at 2.4 GHz
and the top layer was with four memory units. The intermediate layer was a
thermal interface material (TIM). The 2D thermal analysis of the top and bottom
layers was also done separately. In the next step simulations were carried out
by varying TIM thickness and conductivity to study its affect on hotspot
temperature so as to optimize the temperature distribution.


  To achieve interoperability between unconnected ledgers, hash time lock
contracts (HTLCs) are commonly used for cross-chain asset exchange. The
solution tolerates transaction failure, and can "make the best out of worst''
by allowing transacting agents to at least keep their original assets in case
of an abort. Nonetheless, as an undesired outcome, reoccurring transaction
failures prompt a critical and analytical examination of the protocol. In this
study, we propose a game-theoretic framework to study the strategic behaviors
of agents taking part in cross-chain atomic swaps implemented with HTLCs. We
study the success rate of the transaction as a function of the exchange rate of
the swap, the token price and its volatility, among other variables. We
demonstrate that in an attempt to maximize one's own utility as asset price
changes, either agent might withdraw from the swap. An extension of our model
confirms that collateral deposits can improve the transaction success rate,
motivating further research towards collateralization without a trusted third
party. A second model variation suggests that a swap is more likely to succeed
when agents dynamically adjust the exchange rate in response to price
fluctuations.


  We develop a formalism for the resummation of target mass corrections in
off-forward two-photon amplitudes given by a chronological product of
electromagnetic currents, arising in e.g. deeply virtual Compton scattering.
The method is based on a relation of composite operators with a definite twist
to harmonic tensors, which form an irreducible representation of the Lorentz
group. We give an application of the framework for the matrix elements of
twist-two operators.


  We construct an adaptive wavelet estimator that attains minimax near-optimal
rates in a wide range of Besov balls. The convergence rates are affected only
by the weakest dependence amongst the channels, and take into account both
noise sources.


  In 1959, Batchelor predicted that the stationary statistics of passive
scalars advected in fluids with small diffusivity $\kappa$ should display a
$|k|^{-1}$ power spectrum along an inertial range contained in the
viscous-convective range of the fluid model. This prediction has been
extensively tested, both experimentally and numerically, and is a core
prediction of passive scalar turbulence.
  In this article we provide a rigorous proof of a version of Batchelor's
prediction in the $\kappa \to 0$ limit when the scalar is subjected to a
spatially-smooth, white-in-time stochastic source and is advected by the 2D
Navier-Stokes equations or 3D hyperviscous Navier-Stokes equations in
$\mathbb{T}^d$ forced by sufficiently regular, nondegenerate stochastic
forcing. Although our results hold for fluids at arbitrary Reynolds number,
this value is fixed throughout. Our results rely on the quantitative
understanding of Lagrangian chaos and passive scalar mixing established in our
recent works. Additionally, in the $\kappa \to 0$ limit, we obtain
statistically stationary, weak solutions in $H^{-\epsilon}$ to the
stochastically-forced advection problem without diffusivity. These solutions
are almost-surely not locally integrable distributions with non-vanishing
average anomalous flux and satisfy the Batchelor spectrum at all sufficiently
small scales. We also prove an Onsager-type criticality result which shows that
no such dissipative, weak solutions with a little more regularity can exist.


  We investigate the efficiency of single timeslice stochastic sources for the
calculation of light meson masses on the lattice as one varies the quark mass.
Simulations are carried out with Nf = 2 flavours of non-perturbatively O(a)
improved Wilson fermions for pion masses in the range of 450 - 760 MeV. Results
for pseudoscalar and vector meson two-point correlation functions computed
using stochastic as well as point sources are presented and compared. At fixed
computational cost the stochastic approach reduces the variance considerably in
the pseudoscalar channel for all simulated quark masses. The vector channel is
more affected by the intrinsic stochastic noise. In order to obtain stable
estimates of the statistical errors and a more pronounced plateau for the
effective vector meson mass, a relatively large number of stochastic sources
must be used.


  Let $\mathfrak{o}$ be the ring of integers of a non-archimedean local field
with the maximal ideal $\wp$ and the finite residue field of characteristic
$p.$ Let $\mathbf{G}$ be the General Linear or Special Linear group with
entries from the finite quotients $\mathfrak{o}/\wp^\ell$ of $\mathfrak{o}$ and
$\mathbf{U}$ be the subgroup of $\mathbf{G}$ consisting of upper triangular
unipotent matrices. We prove that the induced representation
$\mathrm{Ind}^{\mathbf{G}}_{\mathbf{U}}(\theta)$ of $\mathbf{G}$ obtained from
a ${\it non-degenerate}$ character $\theta$ of $\mathbf{U}$ is multiplicity
free for all $\ell \geq 2.$ This is analogous to the multiplicity one theorem
regarding Gelfand-Graev representation for the finite Chevalley groups. We
prove that for many cases the regular representations of $\mathbf{G}$ are
characterized by the property that these are the constituents of the induced
representation $\mathrm{Ind}^{\mathbf{G}}_{\mathbf{U}}(\theta)$ for some
non-degenerate character $\theta$ of $\mathbf{U}$. We use this to prove that
the restriction of a regular representation of General Linear groups over
$\mathfrak{O}/\wp^\ell$ to the Special Linear groups is multiplicity free for
all $\ell \geq 2$ and also obtain the corresponding branching rules in many
cases.


  A specific class of partially entangled states known as
Knill-Laflamme-Milburn states (or KLM states) has been proved to be useful in
relation to quantum information processing [Knill et al., Nature 409, 46
(2001)]. Although the usage of such states is widely investigated, considerably
less effort has been invested into experimentally accessible preparation
schemes. This paper discusses the possibility to employ a tunable controlled
phase gate to generate an arbitrary Knill-Laflamme-Milburn state. In the first
part, the idea of using the controlled phase gate is explained on the case of
two-qubit KLM states. Optimization of the proposed scheme is then discussed for
the framework of linear optics. Subsequent generalization of the scheme to
arbitrary n-qubit KLM state is derived in the second part of this paper.


  A sharp vanishing theorem for the $L^p$ cohomology torsion of Riemannian
manifolds with pinched negative curvature is given. It follows that certain
negatively curved homogeneous spaces cannot be quasiisometric to better pinched
manifolds.


  The rapid-chase theory of response priming defines a set of behavioral
criteria that indicate feedforward processing of visual stimulus features
rather than recurrent processing. These feedforward criteria are strong
predictions from a feedforward model that argues that sequentially presented
prime and target stimuli lead to strictly sequential waves of visuomotor
processing that can still be traced in continuous motor output, for instance,
in pointing movements, muscle forces, or EEG readiness potentials. The
feedforward criteria make it possible to evaluate whether some continuous motor
output is consistent with feedforward processing, even though the neuronal
processes themselves are not readily observable. This paper is intended as an
auxiliary resource that states the criteria with some degree of formal
precision.


  A discussion on the contribution of Peshkov, Bertin, Ginelli and Chate,
arxiv:1404.3275v1, in this special issue.


  In quantum mechanics, continuously measuring an observable steers the system
into one eigenstate of that observable. This property has interesting and
useful consequences when the observable is a joint property of two remotely
separated qubits. In particular, if the measurement of the two-qubit joint
observable is performed in a way that is blind to single-qubit information,
quantum back-action generates correlation of the discord type even if the
measurement is weak and inefficient. We demonstrate the ability to generate
these quantum correlations in a circuit-QED setup by performing a weak joint
readout of two remote, non-interacting, superconducting transmon qubits using
the two non-degenerate modes of a Josephson Parametric Converter (JPC).
Single-qubit information is erased from the output in the limit of large gain
and with properly tailored cavity drive pulses. Our results of the measurement
of discord are in quantitative agreement with theoretical predictions, and
demonstrate the utility of the JPC as a which-qubit information eraser.


  The present status of anisotropy studies for the highest energy cosmic rays
is presented including the first full sky survey. Directions and prospects for
the future are also discussed in light of new statistical methods and the last
quantities of data expected in the near future from the Pierre Auger
Observatory.


  Multiple-choice load balancing has been a topic of intense study since the
seminal paper of Azar, Broder, Karlin, and Upfal. Questions in this area can be
phrased in terms of orientations of a graph, or more generally a k-uniform
random hypergraph. A (d,b)-orientation is an assignment of each edge to d of
its vertices, such that no vertex has more than b edges assigned to it.
Conditions for the existence of such orientations have been completely
documented except for the "extreme" case of (k-1,1)-orientations. We consider
this remaining case, and establish:
  - The density threshold below which an orientation exists with high
probability, and above which it does not exist with high probability.
  - An algorithm for finding an orientation that runs in linear time with high
probability, with explicit polynomial bounds on the failure probability.
  Previously, the only known algorithms for constructing (k-1,1)-orientations
worked for k<=3, and were only shown to have expected linear running time.


  When using reinforcement learning (RL) algorithms it is common, given a large
state space, to introduce some form of approximation architecture for the value
function (VF). The exact form of this architecture can have a significant
effect on an agent's performance, however, and determining a suitable
approximation architecture can often be a highly complex task. Consequently
there is currently interest among researchers in the potential for allowing RL
algorithms to adaptively generate (i.e. to learn) approximation architectures.
One relatively unexplored method of adapting approximation architectures
involves using feedback regarding the frequency with which an agent has visited
certain states to guide which areas of the state space to approximate with
greater detail. In this article we will: (a) informally discuss the potential
advantages offered by such methods; (b) introduce a new algorithm based on such
methods which adapts a state aggregation approximation architecture on-line and
is designed for use in conjunction with SARSA; (c) provide theoretical results,
in a policy evaluation setting, regarding this particular algorithm's
complexity, convergence properties and potential to reduce VF error; and
finally (d) test experimentally the extent to which this algorithm can improve
performance given a number of different test problems. Taken together our
results suggest that our algorithm (and potentially such methods more
generally) can provide a versatile and computationally lightweight means of
significantly boosting RL performance given suitable conditions which are
commonly encountered in practice.


  Networks are powerful data structures, but are challenging to work with for
conventional machine learning methods. Network Embedding (NE) methods attempt
to resolve this by learning vector representations for the nodes, for
subsequent use in downstream machine learning tasks.
  Link Prediction (LP) is one such downstream machine learning task that is an
important use case and popular benchmark for NE methods. Unfortunately, while
NE methods perform exceedingly well at this task, they are lacking in
transparency as compared to simpler LP approaches.
  We introduce ExplaiNE, an approach to offer counterfactual explanations for
NE-based LP methods, by identifying existing links in the network that explain
the predicted links. ExplaiNE is applicable to a broad class of NE algorithms.
An extensive empirical evaluation for the NE method `Conditional Network
Embedding' in particular demonstrates its accuracy and scalability.


  Over-parameterized neural language models (LMs) can memorize and recite long
sequences of training data. While such memorization is normally associated with
undesired properties such as overfitting and information leaking, our work
casts memorization as an unexplored capability of LMs. We propose the first
symmetric encryption algorithm with autoregressive language models (SELM). We
show that autoregressive LMs can encode arbitrary data into a compact
real-valued vector (i.e., encryption) and then losslessly decode the vector to
the original message (i.e., decryption) via random subspace optimization and
greedy decoding. While SELM is not amenable to conventional cryptanalysis, we
investigate its security through a novel empirical variant of the classic
IND-CPA (indistinguishability under chosen-plaintext attack) game and show
promising results on security. Our code and datasets are available at
https://github.com/OSU-NLP-Group/SELM.


  We are exploring the design and implementation of artificial expressions,
kinetic audio-visual representations of real-time physiological data that
reflect emotional and cognitive state. In this work, we demonstrate a
prototype, the Enactive Mandala, which maps real-time EEG signals to modulate
ambient music and animated visual music. Transparent real-time audio-visual
feedback of brainwave qualities supports intuitive insight into the connection
between thoughts and physiological states.


  We study a new type of separation between quantum and classical communication
complexity which is obtained using quantum protocols where all parties are
efficient, in the sense that they can be implemented by small quantum circuits
with oracle access to their inputs. More precisely, we give an explicit partial
Boolean function that can be computed in the
quantum-simultaneous-with-entanglement model of communication, however, every
interactive randomized protocol is of exponentially larger cost. Furthermore,
all the parties in the quantum protocol can be implemented by quantum circuits
of small size with blackbox access to the inputs. Our result qualitatively
matches the strongest known separation between quantum and classical
communication complexity and is obtained using a quantum protocol where all
parties are efficient.


  We reexamine a recent result within a nonrelativistic constituent quark model
(NRCQM) which maintains that the uuds\bar s component in the proton has its
uuds subsystem in P state, with its \bar s in S state (configuration I). When
the result are corrected, contrary to the previous result, we find that all the
empirical signs of the form factors data can be described by the lowest-lying
uuds\bar s configuration with \bar s in P state that has its uuds subsystem in
$S$ state (configuration II). Further, it is also found that the removal of the
center-of-mass (CM) motion of the clusters will enhance the contributions of
the transition current considerably. We also show that a reasonable description
of the existing form factors data can be obtained with a very small probability
P_{s\bar s}=0.025% for the uuds\bar s component. We further see that the
agreement of our prediction with the data for G_A^s at low-q^2 region can be
markedly improved by a small admixture of configuration I. It is also found
that by not removing CM motion, P_{s\bar s} would be overestimated by about a
factor of four in the case when transition dominates over direct currents.
Then, we also study the consequence of a recent estimate reached from analyzing
the existing data on quark distributions that P_{s\bar s} lies between 2.4-2.9%
which would lead to a large size for the five-quark (5q) system, as well as a
small bump in both G^s_E+\eta G^s_M and G^s_E in the region of q^2 =< 0.1
GeV^2.


  Motivated by the vacuum selection problem of string/M theory, we study a new
geometric invariant of a positive Hermitian line bundle $(L, h)\to M$ over a
compact K\"ahler manifold: the expected distribution of critical points of a
Gaussian random holomorphic section $s \in H^0(M, L)$ with respect to the Chern
connection $\nabla_h$. It is a measure on $M$ whose total mass is the average
number $\mathcal{N}^{crit}_h$ of critical points of a random holomorphic
section. We are interested in the metric dependence of $\mathcal{N}^{crit}_h$,
especially metrics $h$ which minimize $\mathcal{N}^{crit}_h$. We concentrate on
the asymptotic minimization problem for the sequence of tensor powers $(L^N,
h^N)\to M$ of the line bundle and their critical point densities
$\mathcal{K}^{crit}_{N,h}(z)$. We prove that $\mathcal{K}^{crit}_{N,h}(z)$ has
a complete asymptotic expansion in $N$ whose coefficients are curvature
invariants of $h$. The first two terms in the expansion of
$\mathcal{N}^{crit}_{N,h}$ are topological invariants of $(L, M)$. The third
term is a topological invariant plus a constant $\beta_2(m)$ (depending only on
the dimension $m$ of $M$) times the Calabi functional $\int_M \rho^2 dV_h$,
where $\rho$ is the scalar curvature of the K\"ahler metric $\omega_h:=\frac i2
\Theta_h$. We give an integral formula for $\beta_2(m)$ and show, by a computer
assisted calculation, that $\beta_2(m)>0$ for $m\leq 5$, hence that
$\mathcal{N}^{crit}_{N,h}$ is asymptotically minimized by the Calabi extremal
metric (when one exists). We conjecture that $\beta_2(m)>0$ in all dimensions,
i.e. the Calabi extremal metric is always the asymptotic minimizer.


  In 1995 a 9SDH-2 Pelletron from NEC was installed at IFUNAM (Instituto de
Fisica, Universidad Nacional Autonoma de Mexico). Two beam lines have been
operational since then and two new lines have been built. In order to perform
the planned projects in this grown facility, an upgrading of the original
manual control system is required. The proposed new control system takes
advantage of the existing devices and incorporates the electronics needed for
the newer beam lines. The control software from NEC, has been modified to
accommodate the larger requirements. It runs on the same dedicated computer but
receives commands from a new installed host. Both computers communicate through
a local network sharing the accelerator database. The new host computer also
handles all parameters related to the new lines. In the future, the old
computer will be replaced in order to expand the possibilities of the system
and use a friendlier graphical interface. In this work we present the changes
made to the control software, the new acquisition and control devices installed
and the integration of the old and new systems. Finally, the beam control
procedure based on the analysis of the beam profile that is under development
is also shown.


  In this paper we fit the observed galactic cosmic ray electron spectrum from
a few MeV to 1 TeV. New data from Voyager from 5-60 MeV beyond the heliopause
is used along with high energy data from the PAMELA, FERMI and AMS-2
instruments in Earth orbit. Using a Monte Carlo diffusion model for galactic
propagation we obtain a source rigidity spectrum with a spectral index =-2.25
independent of energy below 10 GeV, possibly steepening above 10 GeV to 2.40 at
the highest energies. This spectrum will fit the electron data over 5 orders of
magnitude to within + 10% at both low and high energies. This steepening of the
electron source spectrum could be an important feature of the acceleration
process, e.g., synchrotron loss during acceleration could steepen the source
spectrum. This fit requires only a single break in the rigidity dependence of
the diffusion coefficient by ~1.0 power in the exponent at about 1.0 GV. The
calculations also predict the distribution of electrons perpendicular to the
galactic disk. The galaxy does act as a calorimeter for electrons in the energy
range 0.1-10 GeV where ~80% of the electrons are trapped. At higher energies
the electrons escape the galactic disk rapidly. At energies ~1 TEV the
electrons loose most of their energy by synchrotron and inverse Compton
emission within < 0.5 Kpc of their origin near the galactic equator. At
energies < 0.1 GeV, because of the increase in the diffusion coefficient below
~1 GV, and the absence of other significant loss processes, the electrons
escape and form a difficult to detect, but important galactic halo population.


  State estimation for nonlinear state space models is a challenging task.
Existing assimilation methodologies predominantly assume Gaussian posteriors on
physical space, where true posteriors become inevitably non-Gaussian. We
propose Deep Bayesian Filtering (DBF) for data assimilation on nonlinear state
space models (SSMs). DBF constructs new latent variables $h_t$ on a new latent
(``fancy'') space and assimilates observations $o_t$. By (i) constraining the
state transition on fancy space to be linear and (ii) learning a Gaussian
inverse observation operator $q(h_t|o_t)$, posteriors always remain Gaussian
for DBF. Quite distinctively, the structured design of posteriors provides an
analytic formula for the recursive computation of posteriors without
accumulating Monte-Carlo sampling errors over time steps. DBF seeks the
Gaussian inverse observation operators $q(h_t|o_t)$ and other latent SSM
parameters (e.g., dynamics matrix) by maximizing the evidence lower bound.
Experiments show that DBF outperforms model-based approaches and latent
assimilation methods in various tasks and conditions.


  In this paper, we consider Abelian varieties over function fields that arise
as twists of Abelian varieties by cyclic covers of irreducible quasi-projective
varieties. Then, in terms of Prym varieties associated to the cyclic covers, we
prove a structure theorem on their Mordell-Weil group. Our results give an
explicit method for construction of elliptic curves, hyper- and super-elliptic
Jacobians that have large ranks over function fields of certain varieties.


  We address a recently introduced model describing a system of periodically
coupled nonlinear phase oscillators submitted to multiplicative white noises,
wherein a ratchet-like transport mechanism arises through a symmetry-breaking
noise-induced nonequilibrium phase transition. Numerical simulations of this
system reveal amazing novel features such as negative zero-bias conductance and
anomalous hysteresis, explained resorting to a strong-coupling analysis in the
thermodynamic limit. Using an explicit mean-field approximation we explore the
whole ordered phase finding a transition from anomalous to normal hysteresis
inside this phase, estimating its locus and identifying (within this scheme) a
mechanism whereby it takes place.


  Trimming is a common operation in CAD, and, in its simplest formulation,
consists in removing superfluous parts from a geometric entity described via
splines (a spline patch). After trimming the geometric description of the patch
remains unchanged, but the underlying mesh is unfitted with the physical
object. We discuss the main problems arising when solving elliptic PDEs on a
trimmed domain. First we prove that, even when Dirichlet boundary conditions
are weakly enforced using Nitsche's method, the resulting method suffers lack
of stability. Then, we develop novel stabilization techniques based on a
modification of the variational formulation, which allow us to recover
well-posedness and guarantee accuracy. Optimal a priori error estimates are
proven, and numerical examples confirming the theoretical results are provided.


  Randomized mechanisms, which map a set of bids to a probability distribution
over outcomes rather than a single outcome, are an important but ill-understood
area of computational mechanism design. We investigate the role of randomized
outcomes (henceforth, "lotteries") in the context of a fundamental and
archetypical multi-parameter mechanism design problem: selling heterogeneous
items to unit-demand bidders. To what extent can a seller improve her revenue
by pricing lotteries rather than items, and does this modification of the
problem affect its computational tractability? Our results show that the
answers to these questions hinge on whether consumers can purchase only one
lottery (the buy-one model) or purchase any set of lotteries and receive an
independent sample from each (the buy-many model). In the buy-one model, there
is a polynomial-time algorithm to compute the revenue-maximizing envy-free
prices (thus overcoming the inapproximability of the corresponding item pricing
problem) and the revenue of the optimal lottery system can exceed the revenue
of the optimal item pricing by an unbounded factor as long as the number of
item types exceeds 4. In the buy-many model with n item types, the profit
achieved by lottery pricing can exceed item pricing by a factor of O(log n) but
not more, and optimal lottery pricing cannot be approximated within a factor of
O(n^eps) for some eps>0, unless NP has subexponential-time randomized
algorithms. Our lower bounds rely on a mixture of geometric and algebraic
techniques, whereas the upper bounds use a novel rounding scheme to transform a
mechanism with randomized outcomes into one with deterministic outcomes while
losing only a bounded amount of revenue.


  The Ericksen-Leslie model for nematic liquid crystals in a bounded domain
with general Leslie and isotropic Ericksen stress is studied in the case of a
non-isothermal and incompressible fluid. This system is shown to be locally
well-posed in the $L_p$-setting, and a dynamic theory is developed. The
equilibria are identified and shown to be normally stable. In particular, a
local solution extends to a unique, global strong solution provided the initial
data are close to an equilibrium or the solution is eventually bounded in the
topology of the natural state manifold. In this case, the solution converges
exponentially to an equilibrium, in the topology of the state manifold. The
above results are proven {\em without} any structural assumptions on the Leslie
coefficients and in particular {\em without} assuming Parodi's relation.


  Percolation problems appear in a large variety of different contexts ranging
from the design of composite materials to vaccination strategies on community
networks. The key observable for many applications is the percolation
threshold. Unlike the universal critical exponents, the percolation threshold
depends explicitly on the specific system properties. As a consequence,
theoretical approaches to the percolation threshold are rare and generally
tailored to the specific application.
  Yet, any percolating cluster forms a discrete network the emergence of which
can be cast as a graph problem and analyzed using branching processes. We
propose a general mapping of any kind of percolation problem onto a branching
process which provides rigorous lower bounds of the percolation threshold.
These bounds progressively tighten as we incorporate more information into the
theory. We showcase our approach for different continuum problems finding
accurate predictions with almost no effort. Our approach is based on first
principles and does not require fitting parameters. As such it offers an
important theoretical reference in a field that is dominated by simulation
studies and heuristic fit functions.


  We present an action for minimal massive gravity (MMG) in three dimensions in
terms of a dreibein and an independent spin connection. Furthermore, the
construction provides an action principle for an infinite family of so-called
third-way consistent generalizations of the three-dimensional Einstein field
equations, including exotic massive gravity and new higher-order
generalizations. It allows to systematically construct the matter couplings for
these models, including the couplings to fermions, depending on the spin
connection. In particular, we construct different supersymmetric extensions of
MMG, and derive their second order fermionic field equations. This establishes
a new class of three-dimensional supergravity theories and we discuss their
limit to topological massive supergravity. Finally, we identify the landscape
of (A)dS vacua of the supersymmetric models. We analyze the spectrum and the
unitarity properties of these vacua. We recover the known AdS vacua of MMG
which are bulk and boundary unitary.


  We show that in dimensions $n \geq 12$, a non-flat complete gradient
shrinking solitons with uniformly positive isotropic curvature (PIC) must be a
quotient of either the round sphere $S^n$ or the cylinder $S^{n-1} \times
\mathbb{R}$. We also observe that in dimensions $n \geq 5$, a complete gradient
shrinking soliton that is strictly PIC and weakly PIC2 must be a quotient of
either the round sphere $S^n$ or the cylinder $S^{n-1} \times \mathbb{R}$.


  We report about a nuclear track imaging system which is designed to study in
detail the ionization topology of charged particle tracks in a low-pressure
gas. The detection method is based on a time projection chamber (TPC) filled
with low-pressure triethylamine (TEA). Ionization electrons produced by
energetic charged particles are three-dimensionally imaged by recording light
from electron avalanches with an intensified CCD system. The detector permits
to inves-tigate the spatial ionization distributions of particle tracks in gas,
of equivalent length and resolution in tissue of 4 mm and 40 nm (RMS),
respectively. We explain the relevance of this technique for dosimetry,
describe the experimental method and the basic operation parameters. First
results of the chamber response to protons and alpha particles are presented.


  The calculations of three-body direct nuclear reactions with nonlocal optical
potentials are performed for the first time using the framework of Faddeev-type
scattering equations. Important nonlocality effect is found for transfer
reactions like d+16O -> p + 17O often improving the description of the
experimental data.


  We propose a novel graph-driven generative model, that unifies multiple
heterogeneous learning tasks into the same framework. The proposed model is
based on the fact that heterogeneous learning tasks, which correspond to
different generative processes, often rely on data with a shared graph
structure. Accordingly, our model combines a graph convolutional network (GCN)
with multiple variational autoencoders, thus embedding the nodes of the graph
i.e., samples for the tasks) in a uniform manner while specializing their
organization and usage to different tasks. With a focus on healthcare
applications (tasks), including clinical topic modeling, procedure
recommendation and admission-type prediction, we demonstrate that our method
successfully leverages information across different tasks, boosting performance
in all tasks and outperforming existing state-of-the-art approaches.


  We consider the spaces $L^p(X,\nu;V)$, where $X$ is a separable Banach space,
$\mu$ is a centred non-degenerate Gaussian measure, $\nu:=Ke^{-U}\mu$ with
normalizing factor $K$ and $V$ is a separable Hilbert space. In this paper we
prove a vector-valued Poincar\'e inequality for functions $F\in
W^{1,p}(X,\nu;V)$, which allows us to show that for every $p\in(1,+\infty)$ and
every $k\in\mathbb N$ the norm in $W^{k,p}(X,\nu)$ is equivalent to the graph
norm of $D_H^k$ (the $k$-th Malliavin derivative) in $L^p(X,\nu)$. To conclude,
we show exponential decay estimates for $(T^V(t))_{t\geq0}$ as
$t\rightarrow+\infty$. Useful tools are the study of the asymptotic behaviour
of the scalar perturbed Ornstein-Uhlenbeck $(T(t))_{t\geq0}$, and pointwise
estimates for $|D_HT(t)f|_H^p$ by means both of $T(t)|D_Hf|^p_H$ and of
$T(t)|f|^p$.


  Despite the remarkable results that can be achieved by data-driven
intelligent fault diagnosis techniques, they presuppose the same distribution
of training and test data as well as sufficient labeled data. Various operating
states often exist in practical scenarios, leading to the problem of domain
shift that hinders the effectiveness of fault diagnosis. While recent
unsupervised domain adaptation methods enable cross-domain fault diagnosis,
they struggle to effectively utilize information from multiple source domains
and achieve effective diagnosis faults in multiple target domains
simultaneously. In this paper, we innovatively proposed a weighted joint
maximum mean discrepancy enabled multi-source-multi-target unsupervised domain
adaptation (WJMMD-MDA), which realizes domain adaptation under
multi-source-multi-target scenarios in the field of fault diagnosis for the
first time. The proposed method extracts sufficient information from multiple
labeled source domains and achieves domain alignment between source and target
domains through an improved weighted distance loss. As a result,
domain-invariant and discriminative features between multiple source and target
domains are learned with cross-domain fault diagnosis realized. The performance
of the proposed method is evaluated in comprehensive comparative experiments on
three datasets, and the experimental results demonstrate the superiority of
this method.


  In his 1910 "Five Variables" paper, Cartan solved the equivalence problem for
the geometry of $(2, 3, 5)$ distributions and in doing so demonstrated an
intimate link between this geometry and the exceptional simple Lie groups of
type $\textrm{G}_2$. He claimed to produce a local classification of all such
(complex) distributions which have infinitesimal symmetry algebra of dimension
at least $6$ (and which satisfy a natural uniformity condition), but in 2013
Doubrov and Govorov showed that this classification misses a particular
distribution $\bf E$. We produce a closed form for the Fefferman-Graham ambient
metric $\widetilde{g}_{\bf E}$ of the conformal class induced by (a real form
of) $\bf E$, expanding the small catalogue of known explicit, closed-form
ambient metrics. We show that the holonomy group of $\widetilde{g}_{\bf E}$ is
the exceptional group $\textrm{G}_2^*$ and use that metric to give explicitly a
projective structure with normal projective holonomy equal to that group.
  We also present some simple but apparently novel observations about ambient
metrics of general left-invariant conformal structures that were used in the
determination of the explicit formula for $\widetilde{g}_{\bf E}$.


  We describe the various Halpha morphologies of Virgo Cluster and isolated
spiral galaxies, and associate the Halpha morphologies with the types of
environmental interactions which have altered the cluster galaxies. The spatial
distributions of Halpha and R-band emission are used to divide the star
formation morphologies of the 52 Virgo Cluster spirals into several categories:
normal (37%), anemic (6%), enhanced (6%), and (spatially) truncated (52%).
Truncated galaxies are further subdivided based on their inner star formation
rates into truncated/normal (37%), truncated/compact (6%), truncated/anemic
(8%), and truncated/enhanced (2%). The fraction of anemic galaxies is
relatively small (6-13%) in both environments, suggesting that starvation is
not a major factor in the reduced star formation rates of Virgo spirals. The
majority of Virgo spiral galaxies have their Halpha disks truncated (52%),
whereas truncated Halpha disks are rarer in isolated galaxies (12%). Most of
the Halpha-truncated galaxies have relatively undisturbed stellar disks and
normal-to-slightly enhanced inner disk star formation rates, suggesting that
ICM-ISM stripping is the main mechanism causing the reduced star formation
rates of Virgo spirals. In other galaxies, the Halpha morphologies are more
consistent with a tidal origin or perhaps outer cluster HI accretion. These
results indicate that most Virgo spiral galaxies experience ICM-ISM stripping,
many experience significant tidal effects, and many experience both.
(abridged).


  Feynman's functional formulation of statistical mechanics is used to study
the renormalizability of the well known Linear Chiral Sigma Model in the
presence of fermionic fields at finite temperature in an alternative way. It is
shown that the renormalization conditions coincide with those of the zero
temperature model.


  The Schr{\"o}dinger problem is an entropy minimisation problem on the space
of probability measures. Its optimal value is a cost between two probability
measures. In this article we investigate some regularity properties of this
cost: continuity with respect to the marginals and time derivative of the cost
along probability measures valued curves.


  The celebrated Poincar\'e and Friedrichs inequalities estimate the
$\mathbb{L}_p$-norm of a function by the $\mathbb{L}_p$-norm of the gradient.
We prove the Poincar\'e inequality for a domain $\Omega\subset \mathbb{R}^n$
and for a hypersurface $\mathcal{C}\subset\mathbb{R}^n$ based on open mapping
theorem of Banach only. For a cylinder which has a hypersurface as a base, is
prove stronger inequality, involving only the surface derivatives. Similar
inequalities for the uniform $C$-norm are proved as well. We also estimate
$\mathbb{H}^m_p$-norm of functions prove inequalities for some generalizations
of the mentioned inequalities.
  We also prove Poincar\'e-Korns and Friedrichs-Korns inequalities for
vector-func\-ti\-ons estimating the $\mathbb{L}_p$-norm of a function by the
$\mathbb{L}_p$-norm of the deformation tensor only on domains and on
hypersurfaces. The proofs are based on the paper \cite{Du10} of the author on
Korns inequalities. And again, the norm of the function in a cylinder is
estimated by is the deformation tensor on the base of the cylinder.


  Word embeddings are one of the most fundamental technologies used in natural
language processing. Existing word embeddings are high-dimensional and consume
considerable computational resources. In this study, we propose WordTour,
unsupervised one-dimensional word embeddings. To achieve the challenging goal,
we propose a decomposition of the desiderata of word embeddings into two parts,
completeness and soundness, and focus on soundness in this paper. Owing to the
single dimensionality, WordTour is extremely efficient and provides a minimal
means to handle word embeddings. We experimentally confirmed the effectiveness
of the proposed method via user study and document classification.


  A new numerical method for solving a scalar ordinary differential equation
with a given initial condition is introduced. The method is using a numerical
integration procedure for an equivalent integral equation and is called in this
paper an integrating method. Bound to specific constraints, the method returns
an approximate solution assuredly within a given tolerance provided by a user.
This makes it different from a large variety of single- and multi-step methods
for solving initial value problems that provide results up to some undefined
error in the form O(h^k), where h is a step size and k is concerned with the
method's accuracy. Advantages and disadvantages of the method are presented.
Some improvements in order to avoid the latter are also made. Numerical
experiments support these theoretical results.


  Text generation has become one of the most important yet challenging tasks in
natural language processing (NLP). The resurgence of deep learning has greatly
advanced this field by neural generation models, especially the paradigm of
pretrained language models (PLMs). In this paper, we present an overview of the
major advances achieved in the topic of PLMs for text generation. As the
preliminaries, we present the general task definition and briefly describe the
mainstream architectures of PLMs for text generation. As the core content, we
discuss how to adapt existing PLMs to model different input data and satisfy
special properties in the generated text. We further summarize several
important fine-tuning strategies for text generation. Finally, we present
several future directions and conclude this paper. Our survey aims to provide
text generation researchers a synthesis and pointer to related research.


  Period study of 321 fundamental mode galactic field RR Lyrae type stars
(RRab), which had appropriate data in ASAS and SuperWASP surveys, brighter than
12.5 mag in maximum light was performed. We found 100 stars to be definitely
modulated. In 25 cases, previously unknown modulation was revealed and 8 new
candidates for Blazhko stars were identified. In 18 previously found Blazhko
stars, no modulation was detectable. Multiple modulation was revealed for eight
stars that were previously proposed to show simple modulation. In total, there
were twelve stars with some peculiarity in their modulation in the sample. This
brings the incidence rate of multiple/irregularly-modulated stars to 12 %. The
ratio of the modulation periods of five of the double-modulated stars was
within the ratios of small integers. One of stars studied, IK Hya, showed a
very interesting frequency spectrum, which we interpret as changing Blazhko
period between 71.81 and 75.57 days and an additional 1403-day-long cycle
analogous to a four-year cycle of the prototype RR Lyr. The limits of the
shorter period produce a beating period that is approximately twice as big as a
1403-day period. The newly revealed Blazhko star RZ CVn seems to undergo
changes in the amplitude of the modulation, as well as in the basic pulsation
and Blazhko periods. We found that the incidence rate of the Blazhko RR Lyraes
is at least 31 %, more likely even higher. It was also found that the majority
of the Blazhko variables show triplet structures in their frequency spectra and
that in 89 % of these cases, the peak with larger amplitude is on the
right-hand side of the main pulsation component.


  We study a model for quantum gravity on a circle in which the notion of a
classical metric tensor is replaced by a quantum metric with an inhomogeneous
transformation law under diffeomorphisms. This transformation law corresponds
to the co--adjoint action of the Virasoro algebra, and resembles that of the
connection in Yang--Mills theory. The transformation property is motivated by
the diffeomorphism invariance of the one dimensional Schr\"odinger equation.
The quantum distance measured by the metric corresponds to the phase of a
quantum mechanical wavefunction. The dynamics of the quantum gravity theory are
specified by postulating a Riemann metric on the space $Q$ of quantum metrics
and taking the kinetic energy operator to be the resulting laplacian on the
configuration space $Q/\rm Diff_0(S^1)$. The resulting metric on the
configuration space is analyzed and found to have singularities. The
second--quantized Schr\"odinger equation is derived, some exact solutions are
found, and a generic wavefunction behavior near one of the metric singularities
is described. Finally some further directions are indicated, including an
analogue of the Yamabe problem of differential geometry.


  In this paper we discuss some of the recent developments on derived
equivalences in algebraic geometry.


  In this paper the magnetic behaviour of SmFeAsO and SmFeAs(O0.85F0.15)
samples is presented and discussed. Molar susceptibility of SmFeAsO exhibits a
local peak at T around 140K due to the establishment of a long range
antiferromagnetic ordering of the Fe moments in Fe-As layers. This feature has
already been observed with different techniques, and frequently ascribed to the
onset of a Spin Density Wave (SDW). At TN around 6K another peak, which we
attribute to the establishment of antiferromagnetic ordering of Sm ion
sublattice, is observed. Furthermore, a temperature independent signal (Pauli
paramagnetism, Landau and core diamagnetism...) is also present in the magnetic
behaviour of this sample. In SmFeAs(O0.85F0.15) the antiferromagnetic ordering
in Fe-As plane is suppressed and superconductivity occurs at T = 52 K, whereas
the antiferromagnetic ordering of Sm ions at low temperature persists, leading
to the coexistence and competition between superconducting and magnetic
orderings. Above the transition temperature, after the subtraction of the Sm
ion sublattice paramagnetic contribution and of the temperature independent
contribution to the experimental susceptibility data, a Curie-Weiss behaviour
for Fe is observed, with a magnetic moment of 1.4 Bohr magneton.


  Millisecond dips in the RXTE/PCA light curve of Sco X-1 were reported
recently (Chang et al. 2006), which were interpreted as the occultation of
X-rays from Sco X-1 caused by Trans-Neptunian Objects (TNO) of hundred-meter
size. Inconclusive signatures of possible instrumental effects in many of these
dip events related to high-energy cosmic rays were later found (Jones et al.
2006) and the TNO interpretation became shaky. Here we report more detailed
analysis aiming at distinguishing true occultation events from those related to
cosmic rays. Based on some indicative criteria derived from housekeeping data
and two-channel spectral information, we suggest that about 10% of the dips are
probable events of occultation. The total number of TNOs of size from 60 m to
100 m is estiamted to be about 10^{15} accordingly. Limited by the coarser time
resolution of standard data modes of RXTE/PCA, however, definite results cannot
be obtained. Adequately configured observations with RXTE or other new
instruments in the future are very much desired.