  Neuromorphic photonic computing has emerged as a competitive computing
paradigm to overcome the bottlenecks of the von-Neumann architecture. Linear
weighting and nonlinear spiking activation are two fundamental functions of a
photonic spiking neural network (PSNN). However, they are separately
implemented with different photonic materials and devices, hindering the
large-scale integration of PSNN. Here, we propose, fabricate and experimentally
demonstrate a photonic neuro-synaptic chip enabling the simultaneous
implementation of linear weighting and nonlinear spiking activation based on a
distributed feedback (DFB) laser with a saturable absorber (DFB-SA). A
prototypical system is experimentally constructed to demonstrate the parallel
weighted function and nonlinear spike activation. Furthermore, a four-channel
DFB-SA array is fabricated for realizing matrix convolution of a spiking
convolutional neural network, achieving a recognition accuracy of 87% for the
MNIST dataset. The fabricated neuro-synaptic chip offers a fundamental building
block to construct the large-scale integrated PSNN chip.


  The real number system is geometrically extended to include three new
anticommuting square roots of plus one, each such root representing the
direction of a unit vector along the orthonormal coordinate axes of Euclidean
3-space. The resulting geometric (Clifford) algebra provides a geometric basis
for the famous Pauli matrices which, in turn, proves the consistency of the
rules of geometric algebra. The flexibility of the concept of geometric numbers
opens the door to new understanding of the nature of space-time, and of Pauli
and Dirac spinors as points on the Riemann sphere, including Lorentz boosts.


  Economic data are often generated by stochastic processes that take place in
continuous time, though observations may occur only at discrete times. For
example, electricity and gas consumption take place in continuous time. Data
generated by a continuous time stochastic process are called functional data.
This paper is concerned with comparing two or more stochastic processes that
generate functional data. The data may be produced by a randomized experiment
in which there are multiple treatments. The paper presents a method for testing
the hypothesis that the same stochastic process generates all the functional
data. The test described here applies to both functional data and multiple
treatments. It is implemented as a combination of two permutation tests. This
ensures that in finite samples, the true and nominal probabilities that each
test rejects a correct null hypothesis are equal. The paper presents upper and
lower bounds on the asymptotic power of the test under alternative hypotheses.
The results of Monte Carlo experiments and an application to an experiment on
billing and pricing of natural gas illustrate the usefulness of the test.


  Under certain conditions, a scheme can be reconstructed from its category of
quasi-coherent sheaves. The Tannakian reconstruction theorem provides another
example where a geometric object can be reconstructed from an associated
category, in this case the category of its finite dimensional representations.
Lurie's result that the pseudofunctor which sends a geometric stack to its
category of quasi-coherent sheaves is fully faithful provides a conceptual
explanation for why this works.
  In this paper we prove a generalized Tannakian recognition theorem, in order
to characterize a part of the image of the extension of the above pseudofunctor
to algebraic stacks in the sense of Naumann. This allows us to further
investigate a conjecture by Richard Pink about categories of filtered modules,
which were defined by Fontaine and Laffaille to construct p-adic Galois
representations.
  In order to do this we give a new characterization of Adams Hopf algebroids,
which also allows us to answer a question posed by Mark Hovey.


  This is a survey or exposition of a particular collection of results and open
problems involving snarks --- simple "cubic" (3-valent) graphs for which, for
nontrivial reasons, the edges cannot be 3-colored. The results and problems
here are rooted in a series of papers by Laszlo Kaszonyi that were published in
the early 1970s. The problems posed in this survey paper can be tackled without
too much specialized mathematical preparation, and in particular seem well
suited for interested undergraduate mathematics students to pursue as
independent research projects. This survey paper is intended to facilitate
research on these problems.


  Broad-band observations of the solar photosphere began in Meudon in 1875
under the auspices of Jules Janssen. For his part, Henri Deslandres initiated
imaging spectroscopy in 1892 at Paris observatory. He invented, concurrently
with George Hale in Kenwood (USA) but quite independently, the
spectroheliograph designed for monochromatic imagery of the solar atmosphere.
Deslandres developed two kinds of spectrographs: the ''spectroh{\'e}liographe
des formes'', i.e. the narrow bandpass instrument to reveal chromospheric
structures (such as filaments, prominences, plages and active regions); and the
''spectroh{\'e}liographe des vitesses'', i.e. the section spectroheliograph to
record line profiles of cross sections of the Sun with a 20''-30'' spatial
step. This second apparatus was intended to measure the velocities (more
exactly the Dopplershifts) of dynamic features. Deslandres moved to Meudon in
1898 with his instruments and tested various combinations, in order to improve
the spectral and spatial resolutions, leading to the final large quadruple
spectroheliograph in 1908. CaII K systematic observations started at this date
and were followed in 1909 by H$\alpha$. The service was organized by Lucien
d'Azambuja and continues today. Optical and mechanical parts were revisited in
1989 and the digital technology was introduced in 2002. Full line profiles are
registered for all pixels of the Sun since 2018, so that the instrument
produces now data-cubes. The collection is one of the longest available (more
than 100 000 observations). It contains sporadic images from 1893 to 1907
(during the development phase) and systematic observations along 10 solar
cycles since 1908, in H$\alpha$ and CaII K lines. This paper summarizes 130
years of observations, instrumental research and technical advances.


  The stabilizer group for an $n$-qubit state $\ket{\phi}$ is the set of all
invertible local operators (ILO) $g=g_1\otimes g_2\otimes \cdots\otimes g_n,$ $
g_i\in \mathcal{GL}(2,\mathbb{C})$ such that $\ket{\phi}=g\ket{\phi}.$
Recently, G. Gour $et$ $al.$ \cite{GKW} presented that almost all $n$-qubit
state $\ket{\psi}$ own a trivial stabilizer group when $n\ge 5.$ In this
article, we consider the case when the stabilizer group of an $n$-qubit
symmetric pure state $\ket{\psi}$ is trivial. First we show that the stabilizer
group for an n-qubit symmetric pure state $\ket{\phi}$ is nontrivial when $n\le
4$. Then we present a class of $n$-qubit symmetric states $\ket{\phi}$ with the
trivial stabilizer group. At last, we prove that an $n$-qubit symmetric pure
state owns a trivial stabilizer group when its diversity number is bigger than
5, which confirms the main result of \cite{GKW} partly.


  In this paper, we introduce a combinatorial path model of representation of
the quantum affine algebra of type $D_n$, inspired by Mukhin and Young's
combinatorial path models of representations of the quantum affine algebras of
types $A_n$ and $B_n$. In particular, we give a combinatorial formula for
$q$-characters of fundamental modules of type $D_{n}$ by assigning each path to
a monomial or binomial. By counting our paths, a new expression on dimensions
of fundamental modules of type $D_n$ is obtained.


  Grammar-based compression, where one replaces a long string by a small
context-free grammar that generates the string, is a simple and powerful
paradigm that captures many popular compression schemes. Given a grammar, the
random access problem is to compactly represent the grammar while supporting
random access, that is, given a position in the original uncompressed string
report the character at that position. In this paper we study the random access
problem with the finger search property, that is, the time for a random access
query should depend on the distance between a specified index $f$, called the
\emph{finger}, and the query index $i$. We consider both a static variant,
where we first place a finger and subsequently access indices near the finger
efficiently, and a dynamic variant where also moving the finger such that the
time depends on the distance moved is supported.
  Let $n$ be the size the grammar, and let $N$ be the size of the string. For
the static variant we give a linear space representation that supports placing
the finger in $O(\log N)$ time and subsequently accessing in $O(\log D)$ time,
where $D$ is the distance between the finger and the accessed index. For the
dynamic variant we give a linear space representation that supports placing the
finger in $O(\log N)$ time and accessing and moving the finger in $O(\log D +
\log \log N)$ time. Compared to the best linear space solution to random
access, we improve a $O(\log N)$ query bound to $O(\log D)$ for the static
variant and to $O(\log D + \log \log N)$ for the dynamic variant, while
maintaining linear space. As an application of our results we obtain an
improved solution to the longest common extension problem in grammar compressed
strings. To obtain our results, we introduce several new techniques of
independent interest, including a novel van Emde Boas style decomposition of
grammars.


  We derive the second-order hydrodynamic equation for reactive multi-component
systems from the relativistic Boltzmann equation. In the reactive system,
particles can change their species under the restriction of the imposed
conservation laws during the collision process. Our derivation is based on the
renormalization group (RG) method, in which the Boltzmann equation is solved in
an organized perturbation method as faithfully as possible and possible secular
terms are resummed away by a suitable setting of the initial value of the
distribution function. The microscopic formulae of the relaxation times and the
lengths are explicitly given as well as those of the transport coefficients for
the reactive multi-component system. The resultant hydrodynamic equation with
these formulae has nice properties that it satisfies the positivity of the
entropy production rate and the Onsager's reciprocal theorem, which ensure the
validity of our derivation.


  We evaluate the Wightman function, the mean field squared and the vacuum
expectation value (VEV) of the energy-momentum tensor for a scalar field with
Robin boundary condition on a spherical shell in the background of a constant
negative curvature space. For the coefficient in the boundary condition there
is a critical value above which the scalar vacuum becomes unstable. In both
interior and exterior regions, the VEVs are decomposed into the boundary-free
and sphere-induced contributions. For the latter, rapidly convergent integral
representations are provided. In the region inside the sphere, the eigenvalues
are expressed in terms of the zeros of the combination of the associated
Legendre function and its derivative and the decomposition is achieved by
making use of the Abel-Plana type summation formula for the series over these
zeros. The sphere-induced contribution to the VEV of the field squared is
negative for Dirichlet boundary condition and positive for Neumann one. At
distances from the sphere larger than the curvature scale of the background
space the suppression of the vacuum fluctuations in the gravitational field
corresponding to the negative curvature space is stronger compared with the
case of the Minkowskian bulk. In particular, the decay of the VEVs with the
distance is exponential for both massive and massless fields. The corresponding
results are generalized for spaces with spherical bubbles and for cosmological
models with negative curvature spaces.


  Contributions of the direct quark mechanism are studied in the nonmesonic
weak decays of light hypernuclei. The $\Lambda N \to NN$ transition is
described by the one pion exchange mechanism and the direct quark mechanism,
induced by the four-quark vertices in the effective weak Hamiltonian. By
employing a realistic wave function of the $\Lambda$ inside the hypernuclei,
nonmesonic decay rates of $^4_{\Lambda}$H, $^4_{\Lambda}$He, and
$^5_{\Lambda}$He are calculated. The results show that the direct quark
mechanism is significantly large and gives a large $\Delta I =3/2$ contribution
in the J=0 channel. The relative phase between the one-pion exchange and the
direct-quark contributions is determined so that the effective weak Hamiltonian
for quarks give both of them consistently. We find that the sum of these two
contributions reproduce the current available experimental data fairly well.


  Zirconium alloys are widely used in the nuclear industry because of their
high strength, good corrosion resistance and low neutron absorption
cross-section. However, zirconium has strong affinity for hydrogen which leads
to hydrogen concentration build-up over time. It is well known that the
formation of hydrides will degrade the material and leads to, for example,
delayed hydride cracking during high burn up. Even though zirconium hydrides
have been studied for several decades, there still remain some controversies
regarding the formation mechanisms, exact crystal structure, and stability of
various hydride phases. This study uses high resolution synchrotron radiation
as a probing tool to observe the precipitation and dissolution of hydrides in
highly pure zirconium powder during in-situ hydrogen charging. The experiment
enabled the direct observation of the hydride formation and phase
transformations. It, also, provided high quality data for crystal structure
determination.


  The accidental degeneracy appearing in cycloacenes as triplets and
quadruplets is explained with the concept of segmentation, introduced here with
the aim of describing the effective disconnection of $\pi$ orbitals on these
organic compounds. For periodic systems with time reversal symmetry, the
emergent nodal domains are shown to divide the atomic chains into simpler
carbon structures analog to benzene rings, diallyl chains, anthracene
(triacene) chains and tetramethyl-naphtalene skeletal forms. The common
electronic levels of these segments are identified as members of degenerate
multiplets of the global system. The peculiar degeneracy of M\"obius cycloacene
is also explained by segmentation. In the last part, it is shown that the
multiplicity of energies for cycloacene can be foreseen by studying the
continuous limit of the tight-binding model; the degeneracy conditions are put
in terms of Chebyshev polynomials. The results obtained in this work have
important consequences on the physics of electronic transport in organic wires,
together with their artificial realizations.


  We study the grain properties and location of the forsterite crystals in the
circumstellar environment of the pre-planetary nebula (PPN) IRAS 17150-3224 in
order to learn more about the as yet poorly understood evolutionary phase prior
to the PPN. We use the best-fit model for IRAS 17150-3224 of Meixner et al.
(2002) and add forsterite to this model. We investigate different spatial
distributions and grain sizes of the forsterite crystals in the circumstellar
environment. We compare the spectral bands of forsterite in the mid-infrared
and at 69 micrometre in radiative transport models to those in ISO-SWS and
Herschel/PACS observations. We can reproduce the non-detection of the
mid-infrared bands and the detection of the 69 micrometre feature with models
where the forsterite is distributed in the whole outflow, in the superwind
region, or in the AGB-wind region emitted previous to the superwind, but we
cannot discriminate between these three models. To reproduce the observed
spectral bands with these three models, the forsterite crystals need to be
dominated by a grain size population of 2 micrometre up to 6 micrometre. We
hypothesise that the large forsterite crystals were formed after the superwind
phase of IRAS 17150-3224, where the star developed an as yet unknown hyperwind
with an extremely high mass-loss rate (10^-3 Msol/yr). The high densities of
such a hyperwind could be responsible for the efficient grain growth of both
amorphous and crystalline dust in the outflow. Several mechanisms are discussed
that might explain the lower-limit of 2 micrometre found for the forsterite
grains, but none are satisfactory. Among the mechanisms explored is a possible
selection effect due to radiation pressure based on photon scattering on
micron-sized grains.


  Shadowgraphy is a technique widely used to diagnose objects or systems in
various fields in physics and engineering. In shadowgraphy, an optical beam is
deflected by the object and then the intensity modulation is captured on a
screen placed some distance away. However, retrieving quantitative information
from the shadowgrams themselves is a challenging task because of the non-linear
nature of the process. Here, a novel method to retrieve quantitative
information from shadowgrams, based on computational geometry, is presented for
the first time. This process can be applied to proton radiography for electric
and magnetic field diagnosis in high-energy-density plasmas and has been
benchmarked using a toroidal magnetic field as the object, among others. It is
shown that the method can accurately retrieve quantitative parameters with
error bars less than 10%, even when caustics are present. The method is also
shown to be robust enough to process real experimental results with simple pre-
and post-processing techniques. This adds a powerful new tool for research in
various fields in engineering and physics for both techniques.


  The symmetric regularized long wave system (SRLW) is a model for the weakly
nonlinear ion acoustic and space-charge waves, which was introduced by C.
Seyler and D. Fenstermacher. In this paper, we investigated the wellposedness
and controllability properties of the generalized symmetric regularized long
wave system (g-SRLW) in different structures (periodic and bounded domains).
Firstly, the wellposedness and the exact controllability results for both
linear and nonlinear g-SRLW system posed on the one-dimensional torus are
obtained under the effect of a distributed moving control. Second, we consider
the g-SRLW system in a bounded interval with some Dirichlet-Neumann conditions
and we show that the system is not spectrally controllable (No finite linear
combination of eigenfunctions associated with the state equations, other than
zero, can be steered to zero). Although the system is not spectrally
controllable, it can be shown that it is approximately controllable.


  In single-molecule force spectroscopy experiments, a biomolecule is attached
to a force probe via polymer linkers, and the total extension -- of molecule
plus apparatus -- is monitored as a function of time. In a typical unfolding
experiment at constant force, the total extension jumps between two values that
correspond to the folded and unfolded states of the molecule. For several
biomolecular systems the committor, which is the probability to fold starting
from a given extension, has been used to extract the molecular activation
barrier (a technique known as "committor inversion"). In this work, we study
the influence of the force probe, which is much larger than the molecule being
measured, on the activation barrier obtained by committor inversion. We use a
two-dimensional framework in which the diffusion coefficient of the molecule
and of the pulling device can differ. We systematically study the free energy
profile along the total extension obtained from the committor, by numerically
solving the Onsager equation and using Brownian dynamics simulations. We
analyze the dependence of the extracted barrier on the linker stiffness,
molecular barrier height, and diffusion anisotropy, and thus, establish the
range of validity of committor inversion. Along the way, we showcase the
committor of 2-dimensional diffusive models and illustrate how it is affected
by barrier asymmetry and diffusion anisotropy.


  Lattice parameter, electronic structure, mechanical and thermodynamic
properties of ThN are systematically studied using the projector-augmented-wave
method and the generalized gradient approximation based on the density
functional theory. The calculated electronic structure indicates the important
contributions of Th 6\emph{d}and 5\emph{f} states to the Fermi-level electron
occupation. Through Bader analysis it is found that the effective valencies in
ThN can be represented as Th$^{+1.82}$ N$^{-1.82}$. Elastic constant
calculations shows that ThN is mechanically stable and elastically anisotropic.
Furthermore, the melting curve of ThN is presented up to 120 GPa. Based on the
phonon dispersion data, our calculated specific heat capacities including both
lattice and conduction-electron contributions agree well with experimental
results in a wide range of temperature.


  Melting temperatures at ambient pressure of systems of isosceles
Lennard-Jones trimers with angles ranging from 70 degrees to 100 degrees are
determined. Two crystal structures are considered: a distorted body centered
cubic structure and a distorted face centered cubic structure with preferred
angles of 77 and 96 degrees, respectively. Liquid dynamics are slowed down when
the angle is increased. A trimer angle of 83 degrees yields the largest
distance between isochrones and the melting temperature, suggesting that this
value gives the optimal glass-forming ability. It is conjectured that better
glass-formers may be found at angles larger than the ones considered in this
study.


  Classical and quantum aspects of physical systems that can be described by
Riemannian non degenerate superspaces are analyzed from the topological and
geometrical points of view. For the N=1 case the simplest supermetric
introduced in [Physics Letters B \textbf{661}, (2008),186] have the correct
number of degrees of freedom for the fermion fields and the super-momentum
fulfil the mass shell condition, in sharp contrast with other cases in the
literature where the supermetric is degenerate. This fact leads a deviation of
the 4-impulse (e.g. mass constraint) that can be mechanically interpreted as a
modification of the Newton's law. Quantum aspects of the physical states and
the basic states and the projection relation between them, are completely
described due the introduction of a new Majorana-Weyl representation of the
generators of the underlying group manifold. A new oscillatory fermionic effect
in the $B_{0}$ part of the vaccum solution involving the chiral and antichiral
components of this Majorana bispinor is explicitly shown.


  This paper addresses the three concepts of \textit{ consistency, stability
and convergence } in the context of compact finite volume schemes for systems
of nonlinear hyperbolic conservation laws. The treatment utilizes the framework
of "balance laws". Such laws express the relevant physical conservation laws in
the presence of discontinuities. Finite volume approximations employ this
viewpoint, and the present paper can be regarded as being in this category. It
is first shown that under very mild conditions a weak solution is indeed a
solution to the balance law. The schemes considered here allow the computation
of several quantities per mesh cell (e.g., slopes) and the notion of
consistency must be extended to this framework. Then a suitable convergence
theorem is established, generalizing the classical convergence theorem of Lax
and Wendroff. Finally, the limit functions are shown to be entropy solutions by
using a notion of "Godunov compatibility", which serves as a substitute to the
entropy condition.


  Let $\mathfrak{g}$ be a complex semisimple Lie algebra with associated
Yangian $Y_\hbar\mathfrak{g}$. In the mid-1990s, Khoroshkin and Tolstoy
formulated a conjecture which asserts that the algebra
$\mathrm{D}Y_\hbar\mathfrak{g}$ obtained by doubling the generators of
$Y_\hbar\mathfrak{g}$, called the Yangian double, provides a realization of the
quantum double of the Yangian. We provide a uniform proof of this conjecture
over $\mathbb{C}[\![\hbar]\!]$ which is compatible with the theory of quantized
enveloping algebras. As a byproduct, we identify the universal $R$-matrix of
the Yangian with the canonical element defined by the pairing between the
Yangian and its restricted dual.


  We present the study of millisecond-resolved polymer brush swelling dynamics
using infrared spectroscopy with a custom-built quantum cascade laser-based
infrared spectrometer at a 1 kHz sampling rate after averaging. By cycling the
humidity of the environment of the polymer brush, we are able to measure the
swelling dynamics sequentially at different wavenumbers. The high sampling rate
provides us with information on the reconformation of the brush at a higher
temporal resolution than previously reported. Using spectroscopic ellipsometry,
we study the brush swelling dynamics as a reference experiment and to correct
artefacts of the infrared measurement approach. This technique informs on the
changes in the brush thickness and refractive index. Our results indicate that
the swelling dynamics of the polymer brush are poorly described by Fickian
diffusion and the Berens-Hopfenberg formalism, pointing toward more complicated
underlying transport.


  We introduce the notion of numerical functors to generalise Eilenberg &
MacLane's polynomial functors to modules over a binomial base ring. After
shewing how these functors are encoded by modules over a certain ring, we
record a precise criterion for a numerical (or polynomial) functor to admit a
strict polynomial structure in the sense of Friedlander & Suslin. We also
provide several characterisations of analytic functors.


  We present new policy mirror descent (PMD) methods for solving reinforcement
learning (RL) problems with either strongly convex or general convex
regularizers. By exploring the structural properties of these overall highly
nonconvex problems we show that the PMD methods exhibit fast linear rate of
convergence to the global optimality. We develop stochastic counterparts of
these methods, and establish an ${\cal O}(1/\epsilon)$ (resp., ${\cal
O}(1/\epsilon^2)$) sampling complexity for solving these RL problems with
strongly (resp., general) convex regularizers using different sampling schemes,
where $\epsilon$ denote the target accuracy. We further show that the
complexity for computing the gradients of these regularizers, if necessary, can
be bounded by ${\cal O}\{(\log_\gamma \epsilon) [(1-\gamma)L/\mu]^{1/2}\log
(1/\epsilon)\}$ (resp., ${\cal O} \{(\log_\gamma \epsilon )
(L/\epsilon)^{1/2}\}$)for problems with strongly (resp., general) convex
regularizers. Here $\gamma$ denotes the discounting factor. To the best of our
knowledge, these complexity bounds, along with our algorithmic developments,
appear to be new in both optimization and RL literature. The introduction of
these convex regularizers also greatly expands the flexibility and
applicability of RL models.


  A fundemantal and unanswered question for the widely shared goal of
electrifying passenger vehicles is how the price of electricity, which can vary
greatly across countries and regions, affects buying behavior. I make use of a
natural experiment in Norway in the period 2021-2022 when large price
differences between north and south emerged to estimate the effect of
electricity prices on the decision to purchase a pure battery-electric vehicle.
Simple difference estimates along the border of the price zones as well as a
difference-in-difference regression model suggest a significant but
economically modest effect of a 2-4\% reduction in the probability of
purchasing an electric vehicle in the high price zone. A counterfactual
simulation suggests that there would have been about 3000 to 6000 fewer
electric vehicles sold in the high-price south compared to a scenario where the
south had equally low prices as in the north.


  Software development meets the various challenges of rapidly growing markets.
To address such challenges projects to design and adopt specific development
approaches. However, various project management approaches do not consider the
uncertainties that exist in projects. In this paper, we present findings from a
case study in which we explore how to apply the Management Uncertainty Software
Project (MUPS) approach. We do so by the empirical investigation at a public
organization in Brazil. The objective of this study is to contribute to the
body of knowledge regarding the potential benefits of MUSP approach. The
conclusions of the empirical study will help both researchers and practitioners
to understand better which benefits are already being realized in practice, and
how they can best be realized.


  Graph neural networks (GNNs) have been widely used in graph-structured data
computation, showing promising performance in various applications such as node
classification, link prediction, and network recommendation. Existing works
mainly focus on node-wise correlation when doing weighted aggregation of
neighboring nodes based on attention, such as dot product by the dense vectors
of two nodes. This may cause conflicting noise in nodes to be propagated when
doing information propagation. To solve this problem, we propose a General
Information Propagation Algorithm (GIPA in short), which exploits more
fine-grained information fusion including bit-wise and feature-wise
correlations based on edge features in their propagation. Specifically, the
bit-wise correlation calculates the element-wise attention weight through a
multi-layer perceptron (MLP) based on the dense representations of two nodes
and their edge; The feature-wise correlation is based on the one-hot
representations of node attribute features for feature selection. We evaluate
the performance of GIPA on the Open Graph Benchmark proteins (OGBN-proteins for
short) dataset and the Alipay dataset of Alibaba. Experimental results reveal
that GIPA outperforms the state-of-the-art models in terms of prediction
accuracy, e.g., GIPA achieves an average ROC-AUC of $0.8901\pm 0.0011$, which
is better than that of all the existing methods listed in the OGBN-proteins
leaderboard.


  We show that the polarized proton-antiproton Drell-Yan process is ideal to
probe the pretzelosity distribution ($h_{1T}^\perp$), which is one of the new
transverse-momentum-dependent parton distributions of the nucleon. We present
predictions of the $\cos(2\phi + \phi_a - \phi_b)$ asymmetry in the
transversely polarized proton-antiproton Drell-Yan process at PAX kinematics
and find that the results are significantly larger compared with those of the
$\sin(3\phi_h - \phi_S)$ asymmetry in the semi-inclusive deep inelastic
scattering process at HERMES, COMPASS, and JLab kinematics. We conclude that
the $\cos(2\phi + \phi_a - \phi_b)$ asymmetry in the PAX experiment can probe
the new physical quantity of the pretzelosity distribution.


  We consider a codimension two scalar theory with brane-localised Higgs type
potential. The six-dimensional field has Dirichlet boundary condition on the
bounds of the transverse compact space. The regularisation of the brane
singularity yields renormalisation group evolution for the localised couplings
at the classical level. In particular, a tachyonic mass term grows at large
distances and hits a Landau pole. We exhibit a peculiar value of the bare
coupling such that the running mass parameter becomes large precisely at the
compactification scale, and the effective four-dimensional zero mode is
massless. Above the critical coupling, spontaneous symmetry breaking occurs and
there is a very light state.


  The InterPlanetary File System (IPFS) is an hyper-media distribution
protocol, addressed by content and identities. It aims to make the web faster,
safer, and more open. The JavaScript implementation of IPFS runs on the
browser, benefiting from the mass adoption potential that it yields. Startrail
takes advantage of the IPFS ecosystem and strives to further evolve it, making
it more scalable and performant through the implementation of an adaptive
network caching mechanism. Our solution aims to add resilience to IPFS and
improve its overall scalability, by avoiding overloading the nodes providing
highly popular content, particularly during flash-crowd-like conditions where
popularity and demand grow suddenly. We add a novel crucial key component to
enable an IPFS-based decentralized Content Distribution Network (CDN).
Following a peer-to-peer architecture, it runs on a scalable, highly available
network of untrusted nodes that distribute immutable and authenticated objects
which are cached progressively towards the sources of requests.


  We summarize recent progress in the studies of the short-rang correlations
(SRC) in nuclei in high energy electron and hadron nucleus scattering and
suggest directions for the future high energy studies aimed at establishing
detailed structure of two-nucleon SRCs, revealing structure of three nucleon
SRC correlations and discovering non-nucleonic degrees of freedom in nuclei.


  We investigate the compactness, masses and radii of realistic neutron stars
(NSs) and quark stars (QSs) within the Eddington-inspired Born-Infeld (EiBI)
theory of gravity, and the energy conditions of their apparent equation of
states (EOSs). We show that the maximum compactness and maximum masses
constraints extracted from the recent pulsars masses and radii observations can
provide the upper and lower limits of $\kappa$ value of EiBI theory. By using
BSP parameter set of relativistic mean field (RMF) model to describe NS core
EOS including hyperons, it can be estimated that $ (2.7 \le \kappa_g \le 7.9)
\times$ $\rm 10^{-2} m^5 kg^{-1} s^{-2}$. If we use
confined-isospin-density-dependent-mass (CIDDM) model with additional scalar
Coulomb term with QSK046 parameter set to describe QS EOS, we can obtain lesser
value i.e., $ (1.6 \le \kappa_g\le 2.2) \times$ $\rm 10^{-2} m^5 kg^{-1}
s^{-2}$. We have also observed that for large $\kappa$ values, mass-radius
relations of NSs and QSs do not exceed causality restrictions because the
compactness of NS and QS are saturated after passing certain large critical
value. This observation is in agreement with the results obtained in
Ref.\cite{Delsate12} for the case of pressure-less stars. We have also found
that if $\kappa$ larger than certain non-zero value, the CIDDM with vector
Coulomb model prediction of QS can reach the maximum mass $\gtrsim$ 2
$M_\odot$. We have found also that if the NS or QS EOS becomes stiffer, the
upper limit of $\kappa$ from compactness constraint becomes smaller and lower
limit of $\kappa$ from maximum masses constraint becomes larger. We also
observe that the uncertainty of the systematic in canonical mass compact stars
radii measurements data can affect the $\kappa$ range. It is also shown that
the non-physical apparent EOS of NSs and QSs can satisfy the energy conditions.


  We revisit Nagaoka ferromagnetism in the U=oo Hubbard model within the
dynamical mean-field theory (DMFT) using the recently developed continuous time
quantum Monte Carlo method as the impurity solver. The stability of Nagaoka
ferromagnetism is studied as a function of the temperature, the doping level,
and the next-nearest-neighbor lattice hopping t'. We found that the nature of
the phase transition as well as the stability of the ferromagnetic state is
very sensitive to the t' hopping. Negative t'=-0.1t stabilizes ferromagnetism
up to higher doping levels. The paramagnetic state is reached through a first
order phase transition. Alternatively, a second order phase transition is
observed at t'=0. Very near half-filling, the coherence temperature T_{coh} of
the paramagnetic metal becomes very low and ferromagnetism evolves out of an
incoherent metal rather than conventional Fermi liquid. We use the DMFT results
to benchmark slave-boson method which might be useful in more complicated
geometries.


  Vehicle re-identification (Re-ID) aims to retrieve images with the same
vehicle ID across different cameras. Current part-level feature learning
methods typically detect vehicle parts via uniform division, outside tools, or
attention modeling. However, such part features often require expensive
additional annotations and cause sub-optimal performance in case of unreliable
part mask predictions. In this paper, we propose a weakly-supervised
Part-Attention Network (PANet) and Part-Mentored Network (PMNet) for Vehicle
Re-ID. Firstly, PANet localizes vehicle parts via part-relevant channel
recalibration and cluster-based mask generation without vehicle part
supervisory information. Secondly, PMNet leverages teacher-student guided
learning to distill vehicle part-specific features from PANet and performs
multi-scale global-part feature extraction. During inference, PMNet can
adaptively extract discriminative part features without part localization by
PANet, preventing unstable part mask predictions. We address this Re-ID issue
as a multi-task problem and adopt Homoscedastic Uncertainty to learn the
optimal weighing of ID losses. Experiments are conducted on two public
benchmarks, showing that our approach outperforms recent methods, which require
no extra annotations by an average increase of 3.0% in CMC@5 on VehicleID and
over 1.4% in mAP on VeRi776. Moreover, our method can extend to the occluded
vehicle Re-ID task and exhibits good generalization ability.


  Reiman produced a quadratic inequality for the size of bipartite graphs of
girth six. We get its counterpart for girth eight, a cubic inequality. It is
optimal in as far as it admits the algebraic structure of generalized
quadrangles as case of equality. This enables us to obtain the optimal estimate
e ~ v^(4/3) for balanced bipartite graphs. We also get an optimal estimate for
very unbalanced graphs.


  An exact boson mapping of the reduced BCS (equal strength) pairing
Hamiltonian is considered. In the mapping, fermion pair operators are mapped
exactly to the corresponding bosons. The image of the mapping results in a
Bose-Hubbard model with level dependent hopping. Though the resultant
Bose-Hubbard Hamiltonian is non-Hermitian, all eigenvalues are real when Uk/t<
1, where k is the total number of bosons. When U/t=1, a part of spectrum of the
Bose-Hubbard Hamiltonian corresponds exactly to the whole spectrum of the
reduced BCS pairing Hamiltonian.


  Understanding how matter behaves at the highest densities and temperatures is
a major open problem in both nuclear physics and relativistic astrophysics.
This physics is often encapsulated in the so-called high-temperature nuclear
equation of state, which influences compact binary mergers, core-collapse
supernovae, and many more phenomena. One such case is the type (either black
hole or neutron star) and mass of the remnant of the core collapse of a massive
star. For each of six candidate equations of state, we use a very large suite
of spherically symmetric supernova models to generate a suite of synthetic
populations of such remnants. We then compare these synthetic populations to
the observed remnant population. We thus provide a novel constraint on the
high-temperature nuclear equation of state and describe which EOS candidates
are more or less favored by this metric.


  We briefly review the turbulent mean-field dynamo action in protoneutron
stars that are subject to convective and neutron finger instabilities during
the early evolutionary phase. By solving the mean-field induction equation with
the simplest model of $\alpha$-quenching we estimate the strength of the
generated magnetic field. If the initial period of the protoneutron star is
short, then the generated large-scale field is very strong ($> 3 \times
10^{13}$G) and exceeds the small-scale field at the neutron star surface, while
if the rotation is moderate, then the pulsars are formed with more or less
standard dipole fields ($< 3 \times 10^{13}$G) but with surface small-scale
magnetic fields stronger than the dipole field. If rotation is very slow, then
the mean-field dynamo does not operate, and the neutron star has no global
field.


  Precisely measuring $\theta_{13}$ is one of the highest priority in neutrino
oscillation study. Reactor experiments can cleanly determine $\theta_{13}$.
Past reactor neutrino experiments are reviewed and status of next precision
$\theta_{13}$ experiments are presented. Daya Bay is designed to measure
$\sin^22\theta_{13}$ to better than 0.01 and Double Chooz and RENO are designed
to measure it to 0.02-0.03. All are heading to full operation in 2010. Recent
improvements in neutrino moment measurement are also briefed.


  We present quantum networks for a n-qubit controlled gate C^{n-1}(U) which
use a higher dimensional (qudit) ancilla as a catalyser. In its simplest form
the network has only n two-particle gates (qubit-qudit) -- this is the minimum
number of two-body interactions needed to couple all n+1 subsystems (n qubits
plus one ancilla). This class of controlled gates includes the generalised
Toffoli gate C^{n-1}(X) on n qubits, which plays an important role in several
quantum algorithms and error correction. A particular example implementing this
model is given by the dispersive limit of a generalised Jaynes-Cummings
Hamiltonian of an effective spin-s interacting with a cavity mode.


  One of the main practical applications of quasi-Monte Carlo (QMC) methods is
the valuation of financial derivatives. We aim to give a short introduction
into option pricing and show how it is facilitated using QMC. We give some
practical examples for illustration.


  Abundances of 18 chemical elements have been derived for 27 A/Am and 16 F
stars members of the Pleiades and Coma Berenices open clusters. We have
specifically computed, with the Montr\'eal code, a series of evolutionary
models for two A stars members of these two clusters. None of the models
reproduces entirely the overall shape of the abundances patterns. The inclusion
of competing processes such as rotational mixing in the radiative zones of
these stars seems necessary to improve the agreement between observed and
predicted abundances patterns.


  Recent advancements in superconducting circuits have enabled the experimental
study of collective behavior of precisely controlled intermediate-scale
ensembles of qubits. In this work, we demonstrate an atomic frequency comb
formed by individual artificial atoms strongly coupled to a single resonator
mode. We observe periodic microwave pulses that originate from a single
coherent excitation dynamically interacting with the multi-qubit ensemble. We
show that this revival dynamics emerges as a consequence of the constructive
and periodic rephasing of the five superconducting qubits forming the vacuum
Rabi split comb. In the future, similar devices could be used as a memory with
in-situ tunable storage time or as an on-chip periodic pulse generator with
non-classical photon statistics.


  We prove the stability of entropy weak solutions of a class of scalar
conservation laws with non-local flux arising in traffic modelling. We obtain
an estimate of the dependence of the solution with respect to the kernel
function, the speed and the initial datum. Stability is obtained from the
entropy condition through doubling of variable technique. We finally provide
some numerical simulations illustrating the dependencies above for some cost
functionals derived from traffic flow applications.


  In Heterogeneous mobile ad hoc networks (MANETs) congestion occurs with
limited resources. Due to the shared wireless channel and dynamic topology,
packet transmissions suffer from interference and fading. In heterogeneous ad
hoc networks, throughput via a given route is depending on the minimum data
rate of all its links. In a route of links with various data rates, if a high
data rate node forwards more traffic to a low data rate node, there is a chance
of congestion, which leads to long queuing delays in such routes. Since hop
count is used as a routing metric in traditional routing, it do not adapt well
to mobile nodes. A congestion-aware routing metric for MANETs should
incorporate transmission capability, reliability, and congestion around a link.
In this paper, we propose to develop a hop-by-hop congestion aware routing
protocol which employs a combined weight value as a routing metric, based on
the data rate, queuing delay, link quality and MAC overhead. Among the
discovered routes, the route with minimum cost index is selected, which is
based on the node weight of all the in-network nodes. Simulation results prove
that our proposed routing protocol attains high throughput and packet delivery
ratio, by reducing the packet drop and delay.


  We propose the general idea that 't Hooft anomalies of generalized global
symmetries can be understood in terms of the properties of solitonic defects,
which generically are non-topological defects. The defining property of such
defects is that they act as sources for background fields of generalized
symmetries. 't Hooft anomalies arise when solitonic defects are charged under
these generalized symmetries. We illustrate this idea for several kinds of
anomalies in various spacetime dimensions. A systematic exploration is
performed in 3d for 0-form, 1-form, and 2-group symmetries, whose 't Hooft
anomalies are related to two special types of solitonic defects, namely vortex
line defects and monopole operators. This analysis is supplemented with
detailed computations of such anomalies in a large class of 3d gauge theories.
Central to this computation is the determination of the gauge and 0-form
charges of a variety of monopole operators: these involve standard gauge
monopole operators, but also fractional gauge monopole operators, as well as
monopole operators for 0-form symmetries. The charges of these monopole
operators mainly receive contributions from Chern-Simons terms and fermions in
the matter content. Along the way, we interpret the vanishing of the global
gauge and ABJ anomalies, which are anomalies not captured by local anomaly
polynomials, as the requirement that gauge monopole operators and mixed
monopole operators for 0-form and gauge symmetries have non-fractional integer
charges.


  We consider the matrix spherical function related to the compact symmetric
pair $(G,K)=(\mathrm{SU}(n+m),\mathrm{S}(\mathrm{U}(n)\times\mathrm{U}(m)))$.
The irreducible $K$ representations $(\pi,V)$ in the ${\rm U}(n)$ part are
considered and the induced representation $\mathrm{Ind}_K^G\pi$ splits
multiplicity free. In this case, the irreducible $K$ representations in the
${\rm U}(n)$ part are studied. The corresponding spherical functions can be
approximated in terms of the simpler matrix-valued functions. We can determine
the explicit spherical functions using the action of a differential operator.
We consider several cases of irreducible $K$ representations and the
orthogonality relations are also described.


  In this note, the corrigendum to our earlier paper "Recover the source and
initial value simultaneously in a parabolic equation" [2014 Inverse Problems 30
065013] is given.


  Background: To assist policy makers in taking adequate decisions to stop the
spread of COVID-19 pandemic, accurate forecasting of the disease propagation is
of paramount importance. Materials and Methods: This paper presents a deep
learning approach to forecast the cumulative number of COVID-19 cases using
Bidirectional Long Short-Term Memory (Bi-LSTM) network applied to multivariate
time series. Unlike other forecasting techniques, our proposed approach first
groups the countries having similar demographic and socioeconomic aspects and
health sector indicators using K-Means clustering algorithm. The cumulative
cases data for each clustered countries enriched with data related to the
lockdown measures are fed to the Bidirectional LSTM to train the forecasting
model. Results: We validate the effectiveness of the proposed approach by
studying the disease outbreak in Qatar. Quantitative evaluation, using multiple
evaluation metrics, shows that the proposed technique outperforms state-of-art
forecasting approaches. Conclusion: Using data of multiple countries in
addition to lockdown measures improve accuracy of the forecast of daily
cumulative COVID-19 cases.


  We investigate the influence of the nonextensive q-statistics and kinetic
theory on galactic scales through the analysis of a devised sample of Spiral
Rotation Curves. Largely supported by recent developments on the foundations of
statistical mechanics and a plethora of astrophysical applications, the theory
also provides an alternative interpretation to the empirical cored dark matter
profiles observed in galaxies. We show that the observations could well be
fitted with reasonable values for the mass model parameters, encouraging
further investigation into q-statistcs on the distribution of dark matter from
both observational and theoretical points of view.


  A method for obtaining asteroseismological information of a Gamma Doradus
oscillating star showing at least three pulsation frequencies is presented.
This method is based on a first-order asymptotic g-mode expression, in
agreement with the internal structure of Gamma Doradus stars. The information
obtained is twofold: 1) a possible identification of the radial order n and
degree l of observed frequencies (assuming that these have the same l), and 2)
an estimate of the integral of the buoyancy frequency (Brunt-Vaisala) weighted
over the stellar radius along the radiative zone. The accuracy of the method as
well as its theoretical consistency are also discussed for a typical Gamma
Doradus stellar model. Finally, the frequency ratios method has been tested
with observed frequencies of the Gamma Doradus star HD 12901. The number of
representative models verifying the complete set of constraints (the location
in the HR diagram, the Brunt-Vaisala frequency integral, the observed
metallicity and frequencies and a reliable identification of n and l) is
drastically reduced to six.


  In a growing number of materials, phonons have been found to generate a
thermal Hall effect, but the underlying mechanism remains unclear. Inspired by
previous studies that revealed the importance of Tb$^{3+}$ ions in generating
the thermal Hall effect in a family of pyrochlores, we investigated the role of
Tm$^{3+}$ ions in TmVO$_{4}$, a paramagnetic insulator with a different crystal
structure. We observe a negative thermal Hall conductivity in TmVO$_{4}$ with a
magnitude such that the Hall angle, $|\kappa_{xy}$/$\kappa_{xx}|$, is
approximately 1 x 10$^{-3}$ at $H$ = 15 T and $T$ = 20 K, typical for a
phonon-generated thermal Hall effect. In contrast to the negligible
$\kappa_{xy}$ found in the nonmagnetic pyrochlore analog (where the Tb$^{3+}$
ions are replaced with Y$^{3+}$), we observe a negative $\kappa_{xy}$ in
YVO$_{4}$ with a Hall angle of magnitude comparable to that of TmVO$_{4}$. This
shows that the Tm$^{3+}$ ions are not essential for the thermal Hall effect in
this family of materials. Interestingly, at an intermediate Y concentration of
$x$ = 0.3 in Tm$_{1-x}$Y$_{x}$VO$_{4}$, $\kappa_{xy}$ was found to have a
positive sign, pointing to the importance of impurities in the thermal Hall
effect of phonons.


  The sensitivity of entanglement to the thermal and squeezed reservoirs'
parameters is investigated regarding entanglement decay and what is called
sudden-death of entanglement, ESD, for a system of two qubit pairs. The
dynamics of information is investigated by means of the information disturbance
and exchange information. We show that for squeezed reservoir, we can keep both
of the entanglement and information survival for a long time. The sudden death
of information is seen in the case of thermal reservoir.


  One of the most important topics in the study of the dynamics of open quantum
system is information exchange between system and environment. Based on the
features of a back-flow information from an environment to a system, an
approach is provided to detect non-Markovianity for unital dynamical maps. The
method takes advantage of non-contractive property of the von Neumann entropy
under completely positive and trace preserving unital maps. Accordingly, for
the dynamics of a single qubit as an open quantum system, the sign of the
time-derivative of the density matrix eigenvalues of the system determines the
non-Markovianity of unital quantum dynamical maps. The main characteristics of
the measure is to make the corresponding calculations and optimization
procedure simpler.


  We consider a network of interacting resonators and analyze the physical
ingredients that enable the emergence of relaxation-free and decoherence-free
subspaces. We investigate two different situations: i) when the whole network
interacts with a common reservoir and ii) when each resonator, strongly coupled
to each other, interacts with its own reservoir. Our main result is that both
subspaces are generated when all the resonators couple with the same group of
reservoir modes, thus building up a correlation (among these modes), which has
the potential to shield particular network states against relaxation and/or
decoherence.


  A number of ferromagnetic superconductors have been recently discovered which
are believed to be in the so-called "equal spin pairing" (ESP) state. In the
ESP state the Cooper pairs condense forming order parameters
$\Delta_{\uparrow\uparrow}, \Delta_{\downarrow\downarrow}$ which are decoupled
in the spin-sector. We show that these three-dimensional systems should
generically support topologically protected surface Majorana arcs and bulk Weyl
fermions as gapless excitations. Similar protected low-energy exotic
quasiparticles should also appear in the recently discovered
non-centrosymmteric superconductors in the presence of a Zeeman field. The
protected surface arcs can be probed by angle-resolved photoemission (ARPES) as
well as scanning tunneling microscope (STM) experiments.


  Support vector machine (SVM) and neural networks (NN) have strong
complementarity. SVM focuses on the inner operation among samples while NN
focuses on the operation among the features within samples. Thus, it is
promising and attractive to combine SVM and NN, as it may provide a more
powerful function than SVM or NN alone. However, current work on combining them
lacks true integration. To address this, we propose a sample attention memory
network (SAMN) that effectively combines SVM and NN by incorporating sample
attention module, class prototypes, and memory block to NN. SVM can be viewed
as a sample attention machine. It allows us to add a sample attention module to
NN to implement the main function of SVM. Class prototypes are representatives
of all classes, which can be viewed as alternatives to support vectors. The
memory block is used for the storage and update of class prototypes. Class
prototypes and memory block effectively reduce the computational cost of sample
attention and make SAMN suitable for multi-classification tasks. Extensive
experiments show that SAMN achieves better classification performance than
single SVM or single NN with similar parameter sizes, as well as the previous
best model for combining SVM and NN. The sample attention mechanism is a
flexible module that can be easily deepened and incorporated into neural
networks that require it.


  We consider the iron pnictides in terms of a proximity to a Mott insulator.
The superexchange interactions contain competing nearest-neighbor and
next-nearest-neighbor components. In the undoped parent compound, these
frustrated interactions lead to a two-sublattice collinear antiferromagnet
(each sublattice forming a Neel ordering), with a reduced magnitude for the
ordered moment. Electron or hole doping, together with the frustration effect,
suppresses the magnetic ordering and allows a superconducting state. The
exchange interactions favor a d-wave superconducting order parameter; in the
notation appropriate for the Fe square lattice, its orbital symmetry is
$d_{xy}$. A number of existing and future experiments are discussed in light of
the theoretical considerations.


  A locally uniform random permutation is generated by sampling $n$ points
independently from some absolutely continuous distribution $\rho$ on the plane
and interpreting them as a permutation by the rule that $i$ maps to $j$ if the
$i$th point from the left is the $j$th point from below. As $n$ tends to
infinity, decreasing subsequences in the permutation will appear as curves in
the plane, and by interpreting these as level curves, a union of decreasing
subsequences gives rise to a surface. In a recent paper by the author it was
shown that, for any $r\ge0$, under the correct scaling as $n$ tends to
infinity, the surface of the largest union of $\lfloor r\sqrt{n}\rfloor$
decreasing subsequences approaches a limit in the sense that it will come close
to a maximizer of a specific variational integral (and, under reasonable
assumptions, that the maximizer is essentially unique). In the present paper we
show that there exists a continuous maximizer, provided that $\rho$ has bounded
density and support.
  The key ingredient in the proof is a new theorem about real functions of two
variables that are increasing in both variables: We show that, for any constant
$C$, any such function can be made continuous without increasing the diameter
of its image or decreasing anywhere the product of its partial derivatives
clipped by $C$, that is the minimum of the product and $C$.


  The nature of statistics, statistical mechanics and consequently the
thermodynamics of stochastic systems is largely determined by how the number of
states $W(N)$ depends on the size $N$ of the system. Here we propose a scaling
expansion of the phasespace volume $W(N)$ of a stochastic system. The
corresponding expansion coefficients (exponents) define the universality class
the system belongs to. Systems within the same universality class share the
same statistics and thermodynamics. For sub-exponentially growing systems such
expansions have been shown to exist. By using the scaling expansion this
classification can be extended to all stochastic systems, including correlated,
constraint and super-exponential systems. The extensive entropy of these
systems can be easily expressed in terms of thee scaling exponents. Systems
with super-exponential phasespace growth contain important systems, such as
magnetic coins that combine combinatorial and structural statistics. We discuss
other applications in the statistics of networks, aging, and cascading random
walks.


  All spaces are assumed to be separable and metrizable. Ostrovsky showed that
every zero-dimensional Borel space is $\sigma$-homogeneous. Inspired by this
theorem, we obtain the following results: assuming $\mathsf{AD}$, every
zero-dimensional space is $\sigma$-homogeneous; assuming $\mathsf{AC}$, there
exists a zero-dimensional space that is not $\sigma$-homogeneous; assuming
$\mathsf{V=L}$, there exists a coanalytic zero-dimensional space that is not
$\sigma$-homogeneous. Along the way, we introduce two notions of hereditary
rigidity, and give alternative proofs of results of van Engelen, Miller and
Steel. It is an open problem whether every analytic zero-dimensional space is
$\sigma$-homogeneous.


  This review presents an overview and analysis of the body of research on
special relativity theory (SRT) education at the secondary and lower
undergraduate level. There is currently a growing international interest in
implementing SRT in pre-university education as an introduction to modern
physics. For this reason, insights into learning opportunities and challenges
in SRT education are needed. The field of research in SRT education is still at
an early stage, especially at the level of secondary education, and there is a
shortage of empirical evaluation of learning outcomes. In order to guide future
research directions, there is a need for an overview and synthesis of the
results reported so far. We have selected 40 articles and categorized them
according to reported learning difficulties, teaching approaches, and research
tools. Analysis shows that students at all educational levels experience
learning difficulties with the use of frames of reference, the postulates of
SRT, and relativistic effects. In the reported teaching sequences,
instructional materials, and learning activities, these difficulties are
approached from different angles. Some teaching approaches focus on thought
experiments to express conceptual features of SRT, while others use virtual
environments to provide realistic visualization of relativistic effects. From
the reported teaching approaches, three learning objectives can be identified:
to foster conceptual understanding, to foster understanding of the history and
philosophy of science, and to gain motivation and confidence toward SRT and
physics in general. In order to quantitatively compare learning outcomes of
different teaching strategies, a more thorough evaluation of assessment tools
is required.


  Normalizing flows transform a simple base distribution into a complex target
distribution and have proved to be powerful models for data generation and
density estimation. In this work, we propose a novel type of normalizing flow
driven by a differential deformation of the Wiener process. As a result, we
obtain a rich time series model whose observable process inherits many of the
appealing properties of its base process, such as efficient computation of
likelihoods and marginals. Furthermore, our continuous treatment provides a
natural framework for irregular time series with an independent arrival
process, including straightforward interpolation. We illustrate the desirable
properties of the proposed model on popular stochastic processes and
demonstrate its superior flexibility to variational RNN and latent ODE
baselines in a series of experiments on synthetic and real-world data.


  We have studied quasi one-dimensional few-particle systems consisting of one
to six ultracold fermionic atoms in two different spin states with attractive
interactions. We probe the system by deforming the trapping potential and by
observing the tunneling of particles out of the trap. For even particle numbers
we observe a tunneling behavior which deviates from uncorrelated
single-particle tunneling indicating the existence of pair correlations in the
system. From the tunneling timescales we infer the differences in interaction
energies of systems with different number of particles which show a strong
odd-even effect, similar to the one observed for neutron separation experiments
in nuclei.


  Objective of this study is to examine the impact of twelve specifications
namely No. of Rotors, Max Flight Time(min.), Operating Range (m), Wingspan(mm),
Weight(g), Payload Capacity(g), Max Speed(m/s), Max Flying Altitude(m), GPS
Compatibility, Autonomous Flight, Collision Avoidance, Flight Battery (mAh) on
the price of the drones. Using Stepwise Multiple Linear Regression analysis,
our study shows that at {\alpha}=0.05; Max Flight Time (min.) (p-value=<0.001),
Wingspan (mm) (p-value=<0.001), and Autonomous Flight capability
(p-value=0.006) are the significant impact factors, while GPS Compatibility
(p-value=0.057), and Collision Avoidance (p-value=0.077) are marginally
significant factors affecting the price of drones.


  The electroweak sector of the Standard Model contains three generations of
charged leptons $\ell^-\in\{e^-,\mu^-,\tau^-\}$ as exact replicas of each
other, except for their Yukawa couplings to the Higgs that determine their
masses. The Yukawas, and thereby, the masses, are not predicted but are
parameters in the theory. A basic tenet in the formalism, known as lepton
universality, is equality of the couplings to the electroweak gauge bosons
$\{\gamma, Z, W^-\}$ among all three generations, and has mostly stood the test
of time. However, precision tests in $B$ decays have recently posed serious
challenges to lepton flavor universality, potentially pointing to New Physics
beyond the Standard Model. In this work we summarize the latest LHCb results on
lepton flavor universality tests in the $b\to s\ell^-\ell^+$ electroweak
penguin sector and mention further prospects with the upgraded LHCb detector.


  Smoothed analysis of complexity bounds and condition numbers has been done,
so far, on a case by case basis. In this paper we consider a reasonably large
class of condition numbers for problems over the complex numbers and we obtain
smoothed analysis estimates for elements in this class depending only on
geometric invariants of the corresponding sets of ill-posed inputs. These
estimates are for a version of smoothed analysis proposed in this paper which,
to the best of our knowledge, appears to be new. Several applications to linear
and polynomial equation solving show that estimates obtained in this way are
easy to derive and quite accurate.


  In industrial applications, complex tasks require human collaboration since
the robot doesn't have enough dexterity. However, the robots are still
implemented as tools and not as collaborative intelligent systems. To ensure
safety in the human-robot collaboration, we introduce a system that presents a
new method that integrates low-cost wearable mocap, and an improved collision
avoidance algorithm based on the artificial potential fields. Wearable optical
motion capturing allows to track the human hand position with high accuracy and
low latency on large working areas. To increase the efficiency of the proposed
algorithm, two obstacle types are discriminated according to their collision
probability. A preliminary experiment was performed to analyze the algorithm
behavior and to select the best values for the obstacle's threshold angle
$\theta_{OBS}$, and for the avoidance threshold distance $d_{AT}$. The second
experiment was carried out to evaluate the system performance with $d_{AT}$ =
0.2 m and $\theta_{OBS}$ = 45 degrees. The third experiment evaluated the
system in a real collaborative task. The results demonstrate the robust
performance of the robotic arm generating smooth collision-free trajectories.
The proposed technology will allow consumer robots to safely collaborate with
humans in cluttered environments, e.g., factories, kitchens, living rooms, and
restaurants.


  We present a consistent analysis of the signal as well as the irreducible
background for the search of the SM Higgs boson in the ZZ decay channel at the
LHC. Soft-gluons effects are resummed up to next-to-leading logarithmic
accuracy, and the results are compared to those obtained with fixed order
calculations and the MC@NLO event generator. The soft-gluon effects are
typically modest but should be taken into account when precise predictions are
demanded. Our results show that the signal over background ratio can be
significantly enhanced with a cut on the transverse momentum pt(ZZ) of the ZZ
pair. We also introduce a fully transverse angular variable that could give
information about the CP nature of the Higgs boson.


  We present results from a survey of the internal kinematics of 49
star-forming galaxies at z$\,\sim\,$2 in the CANDELS fields with the
Keck/MOSFIRE spectrograph (SIGMA, Survey in the near-Infrared of Galaxies with
Multiple position Angles). Kinematics (rotation velocity $V_{rot}$ and
integrated gas velocity dispersion $\sigma_g$) are measured from nebular
emission lines which trace the hot ionized gas surrounding star-forming
regions. We find that by z$\,\sim\,$2, massive star-forming galaxies
($\log\,M_*/M_{\odot}\gtrsim10.2$) have assembled primitive disks: their
kinematics are dominated by rotation, they are consistent with a marginally
stable disk model, and they form a Tully-Fisher relation. These massive
galaxies have values of $V_{rot}/\sigma_g$ which are factors of 2-5 lower than
local well-ordered galaxies at similar masses. Such results are consistent with
findings by other studies. We find that low mass galaxies
($\log\,M_*/M_{\odot}\lesssim10.2$) at this epoch are still in the early stages
of disk assembly: their kinematics are often supported by gas velocity
dispersion and they fall from the Tully-Fisher relation to significantly low
values of $V_{rot}$. This "kinematic downsizing" implies that the process(es)
responsible for disrupting disks at z$\,\sim\,$2 have a stronger effect and/or
are more active in low mass systems. In conclusion, we find that the period of
rapid stellar mass growth at z$\,\sim\,$2 is coincident with the nascent
assembly of low mass disks and the assembly and settling of high mass disks.


A short review on a neutrino magnetic moment is presented.


  We propose a scheme of "$R$-type" photoassociative adiabatic passage (PAP) to
create polar molecular condensates from two different species of ultracold
atoms. Due to the presence of a quasi-coherent population trapping state in the
scheme, it is possible to associate atoms into molecules with a
\textit{low-power} photoassociation (PA) laser. One remarkable advantage of our
scheme is that a tunable atom-molecule coupling strength can be achieved by
using a time-dependent PA field, which exhibits larger flexibility than using a
tunable magnetic field. In addition, our results show that the PA intensity
required in the "$R$-type" PAP could be greatly reduced compared to that in a
conventional "$\Lambda $-type" one.


  We tackle the problem of template estimation when data have been randomly
transformed under an isometric group action in the presence of noise. In order
to estimate the template, one often minimizes the variance when the influence
of the transformations have been removed (computation of the Fr{\'e}chet mean
in quotient space). The consistency bias is defined as the distance (possibly
zero) between the orbit of the template and the orbit of one element which
minimizes the variance. In this article we establish an asymptotic behavior of
the consistency bias with respect to the noise level. This behavior is linear
with respect to the noise level. As a result the inconsistency is unavoidable
as soon as the noise is large enough. In practice, the template estimation with
a finite sample is often done with an algorithm called max-max. We show the
convergence of this algorithm to an empirical Karcher mean. Finally, our
numerical experiments show that the bias observed in practice cannot be
attributed to the small sample size or to a convergence problem but is indeed
due to the previously studied inconsistency.


  Finding new phase is a fundamental task in physics. Landau's theory explained
the deep connection between symmetry breaking and phase transition commonly
occurring in magnetic, superconducting and super uid systems. The discovery of
the quantum Hall effect led to Z topological phases which could be different
for same symmetry and are characterized by the discrete values of the Berry
phases. By studying 1D trimer lattices we report new phases characterized by
Berry phases which are piecewise continuous rather than discrete numbers. The
phase transition occurs at the discontinuity point. With time-dependent
changes, trimer lattices also give a 2D phases characterized by very specific
2D Berry phases of half period. These Berry phases change smoothly within a
phase while change discontinuously at the transition point. We further
demonstrate the existence of adiabatic pumping for each phase and gain assisted
enhanced pumping. The non-reciprocity of the pumping process makes the system a
good optical diode.


  We calculate the dynamic structure factor S (omega, q) of spinless fermions
in one dimension with quadratic energy dispersion k^2/2m and long range
density-density interaction whose Fourier transform f_q is dominated by small
momentum-transfers q << q_0 << k_F. Here q_0 is a momentum-transfer cutoff and
k_F is the Fermi momentum. Using functional bosonization and the known
properties of symmetrized closed fermion loops, we obtain an expansion of the
inverse irreducible polarization to second order in the small parameter q_0 /
k_F. In contrast to perturbation theory based on conventional bosonization, our
functional bosonization approach is not plagued by mass-shell singularities.
For interactions which can be expanded as f_q = f_0 + f_0^{2} q^2/2 + O (q^4)
with finite f_0^{2} we show that the momentum scale q_c = 1/ | m f_0^{2} |
separates two regimes characterized by a different q-dependence of the width
gamma_q of the collective zero sound mode and other features of S (omega, q).
For q_c << q << k_F we find that the line-shape in this regime is
non-Lorentzian with an overall width gamma_q of order q^3/(m q_c) and a
threshold singularity at the lower edge.


  The detection of non-baryonic dark matter through its gamma-ray annihilation
in the centre of our galaxy has been studied. The gamma fluxes according to
different models have been simulated and compared to those expected to be
observed with the Alpha Magnetic Spectrometer (AMS), during a long-term mission
on board of the International Space Station. Under the assumption that the dark
matter halo is composed of the lightest, stable supersymmetric particle, the
neutralino, the results of the simulations in the framework of mSUGRA models,
show that with a cuspy dark matter halo or a clumpy halo, the annihilation
gamma-ray signal would be detected by AMS. More optimistic perspectives are
obtained with the Anomaly Mediated Supersymmetry Breaking (AMSB) model. The
latter leads also to a cosmologically important 6Li abundance. Finally, the
discovery potential for the massive Kaluza-Klein dark matter candidates has
been evaluated and their detection looks feasible.


  The inspiral of supermassive black-hole binaries in gas-rich environment is
driven by the presence of an accretion disc and viscous interactions tend to
align the spin of the black holes with the orbital angular momentum of the
disc. Recent work introduced a new iterative approach to describe the alignment
process and the resulting non-linear evolution of the surrounding warped
accretion disc. Their model predicted that black-hole spins reach either full
alignment or a critical obliquity where solutions to the warp equations cease
to exist. In this paper, we show that this critical region corresponds to the
disc breaking phenomenon, where the disc is disrupted into two or more discrete
sections. We use 3D hydrodynamical simulations to (i) recover the predictions
of the semi-analytic model and (ii) unveil a richer phenomenology where the
disc exhibits either unsuccessful, single and multiple breaks. We additionally
identify hydrodynamic effects such as spiral arms that are able to stabilise
the disc against breaking beyond criticality. Our results show that when disc
breaking occurs, the ability of black holes and disc to align is compromised
and in some cases even prevented as the binary inspirals.


  Dementia is associated with language disorders which impede communication.
Here, we automatically learn linguistic disorder patterns by making use of a
moderately-sized pre-trained language model and forcing it to focus on
reformulated natural language processing (NLP) tasks and associated linguistic
patterns. Our experiments show that NLP tasks that encapsulate contextual
information and enhance the gradient signal with linguistic patterns benefit
performance. We then use the probability estimates from the best model to
construct digital linguistic markers measuring the overall quality in
communication and the intensity of a variety of language disorders. We
investigate how the digital markers characterize dementia speech from a
longitudinal perspective. We find that our proposed communication marker is
able to robustly and reliably characterize the language of people with
dementia, outperforming existing linguistic approaches; and shows external
validity via significant correlation with clinical markers of behaviour.
Finally, our proposed linguistic disorder markers provide useful insights into
gradual language impairment associated with disease progression.


  Associated to a complex Hadamard matrix $H\in M_N(\mathbb C)$ is the complex
probability measure $\mu\in\mathcal P(\mathbb C)$ describing the distribution
of $\varphi(a,b)=<a,Hb>$, where $a,b\in\mathbb T^N$ are random. This measure is
called "glow" of the matrix, due to the analogy with the Gale-Berlekamp
switching game, where $H,a,b$ are real. We prove here that: (1) $\mu$ becomes
complex Gaussian in the $N\to\infty$ limit, (2) the universality holds as well
at order 2, (3) the order 3 term seems to be quite interesting, particularly
for the master Hadamard matrices, (4) in the Fourier matrix case, some of the
higher order terms control counting problems for circulant Hadamard matrices.


  Current state-of-the-art human activity recognition is focused on the
classification of temporally trimmed videos in which only one action occurs per
frame. We propose a simple, yet effective, method for the temporal detection of
activities in temporally untrimmed videos with the help of untrimmed
classification. Firstly, our model predicts the top k labels for each untrimmed
video by analysing global video-level features. Secondly, frame-level binary
classification is combined with dynamic programming to generate the temporally
trimmed activity proposals. Finally, each proposal is assigned a label based on
the global label, and scored with the score of the temporal activity proposal
and the global score. Ultimately, we show that untrimmed video classification
models can be used as stepping stone for temporal detection.


  Systematic ensemble photoluminescence studies have been performed on type-I
InP-quantum dots in Al0.20Ga0.80InP barriers, emitting at approximately 1.85 eV
at 5 K. The influence of different barrier configurations as well as the
incorporation of additional tunnel barriers on the optical properties has been
investigated. The confinement energy between the dot barrier and the
surrounding barrier layers, which is the sum of the band discontinuities for
the valence and the conduction bands, was chosen to be approximately 190 meV by
using Al0.50Ga0.50InP. In combination with 2 nm thick AlInP tunnel barriers,
the internal quantum efficiency of these barrier configurations can be
increased by up to a factor of 20 at elevated temperatures with respect to
quantum dots without such layers.


  We study the observability for a Standard Model-like Higgs boson at an
upgraded Tevatron via the modes $p \bar p \to gg \to h \to \ww \to \ljj$ and
$\ll$. We find that with c. m. energy of 2 TeV and an integrated luminosity of
30 fb$^{-1}$ the signal may be observable for the mass range of $135 {\gev}
\lsim \mh \lsim 180$ GeV at a $3-5\sigma$ statistical level. We conclude that
the upgraded Tevatron may have the potential to detect a SM-like Higgs boson in
the mass range from the LEP2 reach to 180 GeV.


  In this paper, we numerically study the magnetic transport properties of
disordered Weyl semimetals (WSM) in the ultra-quantum limit. We find a positive
magnetic conductivity for the long-range disorder, although the system tends to
have negative magnetic conductivity for the weak short-range disorder.
Remarkably, for long-range disorder, such a positive magnetic conductivity
cannot be described by the semiclassical Boltzmann transport theory even in the
weak disorder limit, and the back-scattering assisted by the high Landau levels
is always important. Our results have significant implications for the positive
magnetic conductivity recently discovered in the WSM systems, and point out two
physical mechanisms: (i) the long-range correlated disorder suppresses the
back-scattering among the zeroth Landau level modes; (ii) with increasing the
magnetic field, the back-scattering assisted by the high Landau levels will
also be suppressed.


  A new catalogue of extrasolar planets is presented by re-analysing a
selection of published radial velocity data sets using EXOFIT (Balan & Lahav
2009). All objects are treated on an equal footing within a Bayesian framework,
to give orbital parameters for 94 exoplanetary systems. Model selection
(between one- and two-planet solutions) is then performed, using both a visual
flagging method and a standard chi-square analysis, with agreement between the
two methods for 99% of the systems considered. The catalogue is to be made
available online, and this 'proof of concept' study may be maintained and
extended in the future to incorporate all systems with publicly available
radial velocity data, as well as transit and microlensing data.


  De-noising plays a crucial role in the post-processing of spectra. Machine
learning-based methods show good performance in extracting intrinsic
information from noisy data, but often require a high-quality training set that
is typically inaccessible in real experimental measurements. Here, using
spectra in angle-resolved photoemission spectroscopy (ARPES) as an example, we
develop a de-noising method for extracting intrinsic spectral information
without the need for a training set. This is possible as our method leverages
the self-correlation information of the spectra themselves. It preserves the
intrinsic energy band features and thus facilitates further analysis and
processing. Moreover, since our method is not limited by specific properties of
the training set compared to previous ones, it may well be extended to other
fields and application scenarios where obtaining high-quality multidimensional
training data is challenging.


  Digital devices are now ubiquitous and have the potential to be used to
support positive changes in human lives and promote psychological well-being.
This paper presents three interactive systems that we created focusing on
introspection activities, leveraging tangible interaction and spatial augmented
reality. More specifically, we describe anthropomorphic augmented avatars that
display the users' inner states using physiological sensors. We also present a
first prototype of an augmented sandbox specifically dedicated to promoting
mindfulness activities.


  In the 1+1-dimensional dilatonic background of Callan et al.
\cite{Callan1992}, we collide fields. Real and ghost fields are considered
separately. The colliding ghost fields in the lineland creates particle-like
wormholes. These structures, however, collapse to a black hole whenever the
supporting ghosts are removed.


  We show that the open cluster Trumpler 20, contrary to the earlier findings,
is actually an old Galactic open cluster. New CCD photometry and
high-resolution spectroscopy are used to derive the main parameters of this
cluster. At [Fe/H]=-0.11 for a single red giant star, the metallicity is
slightly subsolar. The best fit to the color-magnitude diagrams is achieved
using a 1.3 Gyr isochrone with convective overshoot. The cluster appears to
have a significant reddening at E(B-V)=0.46 (for B0 spectral type), although
for red giants this high reddening yields the color temperature exceeding the
spectroscopic T_eff by about 200 K. Trumpler 20 is a very rich open cluster,
containing at least 700 members brighter than M_V=+4. It may extend over the
field-of-view available in our study at 20'x20'.


  I give an overview of recent developments in the structure and classification
theory of separable, simple, nuclear C*-algebras. I will in particular focus on
the role of quasidiagonality and amenability for classification, and on the
regularity conjecture and its interplay with internal and external
approximation properties.


  This chapter introduces numerical simulations provided by a 2D biomechanical
model of the tongue. These simulations help in understanding the influence of
the lingual mechanical characteristics onto the anticipation phenomena that are
measured on acoustic and articulatory speech data.


  In this paper, we present multimodal 2D +3D face recognition method using
block based curvelet features. The 3D surface of face (Depth Map) is computed
from the stereo face images using stereo vision technique. The statistical
measures such as mean, standard deviation, variance and entropy are extracted
from each block of curvelet subband for both depth and intensity images
independently.In order to compute the decision score, the KNN classifier is
employed independently for both intensity and depth map. Further, computed
decision scoresof intensity and depth map are combined at decision level to
improve the face recognition rate. The combination of intensity and depth map
is verified experimentally using benchmark face database. The experimental
results show that the proposed multimodal method is better than individual
modality.


  We propose a new variational quantum algorithm named Variational Open Quantum
Eigensolver (VOQE) for solving steady states of open quantum systems described
by either Lindblad master equations or non-Hermitian Hamiltonians. In VOQE,
density matrices of mixed states are represented by pure states in doubled
Hilbert space. We give a framework for building circuit ansatz which we call
the Hermitian-preserving ansatz (HPA) to restrict the searching space. We also
give a method to efficiently measure the operators' expectation values by
post-selection measurements. We show the workflow of VOQE on solving steady
states of the LMEs of the driven XXZ model and implement VOQE to solve the
spectrum of the non-Hermitian Hamiltonians of the Ising spin chain in an
imaginary field.


  We study the tight-binding model with two distinct hoppings $(t_L, t_S)$ on
the two-dimensional hexagonal golden-mean tiling and examine the confined
states with $E=0$, where $E$ is the eigenenergy. Some confined states found in
the case $t_L=t_S$ are exact eigenstates even for the system with $t_L \neq
t_S$, where their amplitudes are smoothly changed. By contrast, the other
states are no longer eigenstates of the system with $t_L \neq t_S$. This may
imply the existence of macroscopically degenerate states which are
characteristic of the system with $t_L=t_S$, and that a discontinuity appears
in the number of the confined states in the thermodynamic limit.


  The inclusive spectrum of \pi^0 production has been measured in pp collisions
at \sqrt{s} = 900 GeV and 7 TeV with the ALICE experiment. The preliminary
results of these measurements are presented, and perspectives for \pi^0
measurements with heavy ions are discussed.


  Given a LHS (Lattice of Hilbert spaces) $V_J$ and a symmetric operator $A$ in
$V_J$, in the sense of partial inner product spaces, we define a generalized
resolvent for $A$ and study the corresponding spectral properties. In
particular, we examine, with help of the KLMN theorem, the question of
generalized eigenvalues associated to points of the continuous (Hilbertian)
spectrum. We give some examples, including so-called frame multipliers.


  In this paper the magnetic geodesic flow on a 2-torus is considered. We study
a semi-hamiltonian quasi-linear PDEs which is equivalent to the existence of
polynomial in momenta first integral of magnetic geodesic flow on fixed energy
level. It is known that diagonal metric associated with this system is Egorov
one if degree of the first integral is equal to 2 or 3. In this paper we prove
this fact in the case of existence of the first integral of any degree.


  We adopt the "translation" as well as other techniques to express several
identities conjectured by Z.-W. Sun in arXiv:1102.5649v47 by means of known
formulas for $1/\pi$ involving Domb and other Ap\'ery-like sequences.


  The present work critically investigates the influence of low melting glasses
on the fabrication of metal contacts, with the goal of advancing applications
of bismuth based oxide glass and screen printed silver contacts for use in
integrated circuits (ICs), solar cells, and sensors. In this study, novel
electrode contacts were fabricated by screen printing composite pastes composed
of mainly silver powder, Bi2O3 glass powder, and acyclic binder, and then
firing the pastes in a belt furnace. The microstructures of the composite films
after firing at 830 to 890 {\deg}C were observed under different corrosion
conditions, and the resulting layers were analyzed with X ray diffraction (XRD)
and the transfer length method (TLM). A series of investigations to determine
the influence of Bi2O3 glass in silver paste involved various tests, including
differential thermal analysis (DTA), scanning electron microscopy (SEM),
electron probe X ray microanalysis (EPMA), secondary ion mass spectrometry
(SIMS) and transmission electron microscopy (TEM), to determine the effects of
Bi2O3 mixed with silver and the efficacy of the resulting metal contacts in IC
fabrications. It was observed that the additive, Bi2O3 glass, controlled the
melting of the silver into the glass, influencing the precipitation of Ag
crystallites. In addition, an increase in the firing temperature caused
excessive growth of Ag crystallites and current leakage, and the size and the
relationship of the Ag crystallites in the Bi2O3 glass were confirmed.


  This paper presents an accurate and robust fourth order gas-kinetic scheme on
two dimensional unstructured hybrid mesh for incompressible and compressible
viscous flows. For generalized Riemann problem and Navier-Stokes solution, the
gas-kinetic scheme (GKS) provides a time-accurate flux solver using a different
way in the reconstruction at a cell interface in which two slopes for the
equilibrium state are used. Different from the previous one-stage time-stepping
method, the two-stage Lax-Wendroff type time stepping method is applied in this
paper. Compared to standard four-stage fourth-order Runge-Kutta method, the
two-stage fourth order time accurate method reduces the complexity of the
adoption of time derivative of the flux function. To achieve fourth order
accuracy, a finite volume method for GKS using cubic spline reconstruction is
proposed on both structured grid and unstructured hybrid mesh. When dealing
with flow discontinuities, the original spline scheme is replaced by the one
blended with shock-capturing WENO scheme. Many one and two-dimensional test
cases, including Couette flow, Shu-Osher problem, Woodward-Colella blast
problem, two-dimensional Riemann problem, viscous shock tube flow, supersonic
flow over a forward-facing step, and hypersonic flow over a circular cylinder,
are carried out to demonstrate the performance of the proposed scheme.


  We introduce the modified planar rotator method (MPRS), a physically inspired
machine learning method for spatial/temporal regression. MPRS is a
non-parametric model which incorporates spatial or temporal correlations via
short-range, distance-dependent ``interactions'' without assuming a specific
form for the underlying probability distribution. Predictions are obtained by
means of a fully autonomous learning algorithm which employs equilibrium
conditional Monte Carlo simulations. MPRS is able to handle scattered data and
arbitrary spatial dimensions. We report tests on various synthetic and
real-word data in one, two and three dimensions which demonstrate that the MPRS
prediction performance (without parameter tuning) is competitive with standard
interpolation methods such as ordinary kriging and inverse distance weighting.
In particular, MPRS is a particularly effective gap-filling method for rough
and non-Gaussian data (e.g., daily precipitation time series). MPRS shows
superior computational efficiency and scalability for large samples. Massive
data sets involving millions of nodes can be processed in a few seconds on a
standard personal computer.


  We provide recipe theorems for the Bollob\`as and Riordan polynomial
$\mathcal{R}$ defined on classes of ribbon graphs with half-edges introduced in
arXiv:1310.3708[math.GT]. We also define a generalized transition polynomial
$Q$ on this new category of ribbon graphs and establish a relationship between
$Q$ and $\mathcal{R}$.


  I review the arguments most often raised against a fundamental coupling of
classical spacetime to quantum matter. I show that an experiment by Page and
Geilker does not exclude such a semiclassical theory but mandates an inclusion
of an objective mechanism for wave function collapse. In this regard, I present
a classification of semiclassical models defined by the way in which the wave
function collapse is introduced. Two related types of paradoxes that have been
discussed in the context of the necessity to quantize the gravitational field
can be shown to not constrain the possibility of a semiclassical coupling. A
third paradox, the possibility to signal faster than light via semiclassical
gravity, is demonstrably avoided if certain conditions are met by the
associated wave function collapse mechanism. In conclusion, all currently
discussed models of semiclassical gravity can be made consistent with
observation. Their internal theoretical consistency remains an open question.


  We present a theoretical description for a lasing scheme for atoms with three
internal levels in a $V$-configuration and interacting with an optical cavity.
The use of a $V$-level system allows for an efficient closed lasing cycle to be
sustained on a dipole-forbidden transition without the need for incoherent
repumping. This is made possible by utilizing an additional dipole-allowed
transition. We determine the lasing threshold and emission frequency by
performing a stability analysis of the non-lasing solution. In the lasing
regime, we use a mean-field Floquet method (MFFM) to calculate the lasing
intensity and emission frequency. This MFFM predicts the lasing transition to
be accompanied by the breaking of a continuous $U(1)$ symmetry in a single
Fourier component of the total field. In addition, we use the MFFM to derive
bistable lasing and non-lasing solutions that highlight the non-linear nature
of this system. We then test the bistability by studying hysteresis when slowly
ramping external parameters across the threshold and back. Furthermore, we also
compare our mean-field results to a second-order cumulant approach. The work
provides simple methods for understanding complex physics that occur in cold
atom lasers with narrow line transitions.


  In the two decades since the appearance of the book "Bose-Einstein
Condensation" in 1995, there have been a number of developments in our
understanding of dense matter. After a brief overview of neutron star structure
and the Bose-Einstein condensed phases that have been proposed, we describe
selected topics, including neutron and proton pairing gaps, the physics of the
inner crust of neutron stars, where a neutron fluid penetrates a lattice of
nuclei, meson condensates, and pairing in dense quark matter. Especial emphasis
is placed on basic physical effects and on connections to the physics of cold
atomic gases.


  There are several on-going projects to search for stars orbiting around an
invisible companion. A fraction of such candidates may be a triple, instead of
a binary, consisting of an inner binary black hole (BBH) and an outer orbiting
star. In this paper, we propose a methodology to search for a signature of such
an inner BBH, possibly a progenitor of gravitational-wave sources discovered by
{\it LIGO}, from the precise radial velocity (RV) follow-up of the outer star.
We first describe a methodology using an existing approximate RV formula for
coplanar circular triples. We apply this method and constrain the parameters of
a possible inner binary objects in 2M05215658+4359220, which consists of a red
giant and an unseen companion. Next we consider co-planar but non-circular
triples. We compute numerically the RV variation of a tertiary star orbiting
around an inner BBH, generate mock RV curves, and examine the feasibility of
the BBH detection for our fiducial models. We conclude that the short-cadence
RV monitoring of a star-BH binary provides an interesting and realistic method
to constrain and/or search for possible inner BBHs. Indeed a recent discovery
of a star--BH binary system LB-1 may imply that there are a large number of
such unknown objects in our Galaxy, which are ideal targets for the methodology
proposed here.


  It is shown that in the complex trajectory representation of quantum
mechanics, the Born's Psi^{\star}\Psi probability density can be obtained from
the imaginary part of the velocity field of particles on the real axis.
Extending this probability axiom to the complex plane, we first attempt to find
a probability density by solving an appropriate conservation equation. The
characteristic curves of this conservation equation are found to be the same as
the complex paths of particles in the new representation. The boundary
condition in this case is that the extended probability density should agree
with the quantum probability rule along the real line. For the simple,
time-independent, one-dimensional problems worked out here, we find that a
conserved probability density can be derived from the velocity field of
particles, except in regions where the trajectories were previously suspected
to be nonviable. An alternative method to find this probability density in
terms of a trajectory integral, which is easier to implement on a computer and
useful for single particle solutions, is also presented. Most importantly, we
show, by using the complex extension of Schrodinger equation, that the desired
conservation equation can be derived from this definition of probability
density.


  We report a non-trivial feature of the vacuum structure of free massive or
massless Dirac fields in the hyperbolic de Sitter spacetime. Here we have two
causally disconnected regions, say $R$ and $L$ separated by another region,
$C$. We are interested in the field theory in $R\cup L$ to understand the long
range quantum correlations between $R$ and $L$. There are local modes of the
Dirac field having supports individually either in $R$ or $L$, as well as
global modes found via analytically continuing the $R$ modes to $L$ and vice
versa. However, we show that unlike the case of a scalar field, the analytic
continuation does not preserve the orthogonality of the resulting global modes.
Accordingly, we need to orthonormalise them following the Gram-Schmidt
prescription, prior to the field quantisation in order to preserve the
canonical anti-commutation relations. We observe that this prescription
naturally incorporates a spacetime independent continuous parameter,
$\theta_{\rm RL}$, into the picture. Thus interestingly, we obtain a naturally
emerging one-parameter family of $\alpha$-like de Sitter vacua. The values of
$\theta_{\rm RL}$ yielding the usual thermal spectra of massless created
particles are pointed out. Next, using these vacua, we investigate both
entanglement and R\'enyi entropies of either of the regions and demonstrate
their dependence on $\theta_{\rm RL}$.