  The periodic flag manifold (in the Sato Grassmannian context) description of
the modified Korteweg--de Vries hierarchy is used to analyse the translational
and scaling self--similar solutions of this hierarchy. These solutions are
characterized by the string equations appearing in the double scaling limit of
the symmetric unitary matrix model with boundary terms. The moduli space is a
double covering of the moduli space in the Sato Grassmannian for the
corresponding self--similar solutions of the Korteweg--de Vries hierarchy, i.e.
of stable 2D quantum gravity. The potential modified Korteweg--de Vries
hierarchy, which can be described in terms of a line bundle over the periodic
flag manifold, and its self--similar solutions corresponds to the symmetric
unitary matrix model. Now, the moduli space is in one--to--one correspondence
with a subset of codimension one of the moduli space in the Sato Grassmannian
corresponding to self--similar solutions of the Korteweg--de Vries hierarchy.


  We construct new families of multi-error-correcting quantum codes for the
amplitude damping channel. Our key observation is that, with proper encoding,
two uses of the amplitude damping channel simulate a quantum erasure channel.
This allows us to use concatenated codes with quantum erasure-correcting codes
as outer codes for correcting multiple amplitude damping errors. Our new codes
are degenerate stabilizer codes and have parameters which are better than the
amplitude damping codes obtained by any previously known construction.


  The core of a terrestrial-type planet consists of a spherical shell of
rapidly rotating, electrically conducting, fluid. Such a body supports two
distinct classes of quasi-geostrophic eigenmodes: fast, primarily hydrodynamic,
inertial modes with period related to the rotation time scale and slow,
primarily magnetic, magnetostrophic modes with much longer periods. Here, we
investigate the properties of these hydromagnetic quasi-geostrophic modes as a
function of non-dimensional parameters controlling the strength of the
background magnetic field, the planetary rotation rate, and the amount of
magnetic dissipation. ... read full length abstract in the paper.


  Robot table tennis systems require a vision system that can track the ball
position with low latency and high sampling rate. Altering the ball to simplify
the tracking using for instance infrared coating changes the physics of the
ball trajectory. As a result, table tennis systems use custom tracking systems
to track the ball based on heuristic algorithms respecting the real time
constrains applied to RGB images captured with a set of cameras. However, these
heuristic algorithms often report erroneous ball positions, and the table
tennis policies typically need to incorporate additional heuristics to detect
and possibly correct outliers. In this paper, we propose a vision system for
object detection and tracking that focus on reliability while providing real
time performance. Our assumption is that by using multiple cameras, we can find
and discard the errors obtained in the object detection phase by checking for
consistency with the positions reported by other cameras. We provide an open
source implementation of the proposed tracking system to simplify future
research in robot table tennis or related tracking applications with strong
real time requirements. We evaluate the proposed system thoroughly in
simulation and in the real system, outperforming previous work. Furthermore, we
show that the accuracy and robustness of the proposed system increases as more
cameras are added. Finally, we evaluate the table tennis playing performance of
an existing method in the real robot using the proposed vision system. We
measure a slight increase in performance compared to a previous vision system
even after removing all the heuristics previously present to filter out
erroneous ball observations.


  We extend a previously successful discussion of the constrained
Schr\"{o}dinger system through the Dirac--Bergmann algorithm to the case of the
Dirac field. In order to follow the analogy, first we discuss the classical
Dirac field as a spinorial variable, by introducing properly defined momenta
and a suitably modified, factor ordered Poisson bracket. According to the
Dirac--Bergmann algorithm two second class Hamiltonian constraints emerge,
leading to a factor ordered Dirac bracket on the full phase space. This becomes
the Poisson bracket on the reduced phase space in the canonical chart adapted
to the shell. The Dirac equation is recovered both as consistency condition on
the full phase space and as canonical equation on the reduced phase space.
Alternatively, considering the Dirac field as odd Grassmann variable, we
present the details of the Dirac--Bergmann algorithm (with either left and righ
derivatives acting on Grassmann valued superfunctions and involving a different
type of generalized Poisson and Dirac brackets). We propose a recipe for the
canonical second quantization of all three versions of the generalized Dirac
brackets, yielding the correct fundamental anticommutator.


  We formulate Positivity Bounds for scattering amplitudes including exchange
of massless particles. We generalize the standard construction through
dispersion relations to include the presence of a branch cut along the real
axis in the complex plane for the Maldestam variable $s$. In general, validity
of these bounds require the cancellation of divergences in the forward limit of
the amplitude, proportional to $t^{-1}$ and $\log(t)$. We show that this is
possible in the case of gravitons if one assumes a Regge behavior of the
amplitude at high energies below the Planck scale, as previously suggested in
the literature, and that the concrete UV behaviour of the amplitude is uniquely
determined by the structure of IR divergences. We thus extend previous results
by including a sub-leading logarithmic term, which we show to be universal. The
bounds that we present here have the potential of constraining very general
models of modified gravity and EFTs of matter coupled to gravitation.


  Relativistic jets carry energy and particles from compact to very large
scales compared with their initial radius. This is possible due to their
remarkable collimation despite their intrinsic unstable nature. In this
contribution, I review the state-of-the-art of our knowledge on instabilities
growing in those jets and several stabilising mechanisms that may give an
answer to the question of the stability of jets. In particular, during the last
years we have learned that the limit imposed by the speed of light sets a
maximum amplitude to the instabilities, contrary to the case of classical jets.
On top of this stabilising mechanism, the fast growth of unstable modes with
small wavelengths prevents the total disruption and entrainment of jets. I also
review several non-linear processes that can have an effect on the collimation
of extragalactic and microquasar jets. Within those, I remark possible causes
for the decollimation and decelleration of FRI jets, as opposed to the
collimated FRII's. Finally, I give a summary of the main reasons why jets can
propagate through such long distances.


  We introduce an analog of the Dirichlet-to-Neumann map for the Maxwell
equation in a bounded domain. We show that it can be approximated by a
pseudodifferential operator on the boundary with a matrix-valued symbol and we
compute the principal symbol. As a consequence, we obtain a parabolic region
free of the transmission eigenvalues associated to the Maxwell equation.


  We demonstrate the existence of a novel quasiparticle: an exciton in a
semiconductor doubly dressed with two photons of different wavelengths: near
infrared cavity photon and terahertz (THz) photon, with the THz coupling
strength approaching the ultra-strong coupling regime. This quasiparticle is
composed of three different bosons, being a mixture of a matter-light
quasiparticle. Our observations are confirmed by a detailed theoretical
analysis, treating quantum mechanically all three bosonic fields. The doubly
dressed quasiparticles retain the bosonic nature of their constituents, but
their internal quantum structure strongly depends on the intensity of the
applied terahertz field.


  The calculation of exclusive observables beyond the one-loop level requires
elaborate techniques for the computation of multi-leg two-loop integrals. We
discuss how the large number of different integrals appearing in actual
two-loop calculations can be reduced to a small number of master integrals. An
efficient method to compute these master integrals is to derive and solve
differential equations in the external invariants for them. As an application
of the differential equation method, we compute the ${\cal O}(\epsilon)$-term
of a particular combination of on-shell massless planar double box integrals,
which appears in the tensor reduction of $2 \to 2$ scattering amplitudes at two
loops.


  We consider a class of Jacobi matrices with unbounded coefficients. This
class is known to exhibit a first-order phase transition in the sense that, as
a parameter is varied, one has purely discrete spectrum below the transition
point and purely absolutely continuous spectrum above the transition point. We
determine the spectral type and solution asymptotics at the transition point.


  A sequence $s(n)$ of integers is MC-finite if for every $m \in \mathbb{N}^+$
the sequence $s^m(n) = s(n) \bmod{m}$ is ultimately periodic. We discuss
various ways of proving and disproving MC-finiteness. Our examples are mostly
taken from set partition functions, but our methods can be applied to many more
integer sequences.


  As development Internet-of-Vehicles (IoV) technology and demand for
Intelligent Transportation Systems (ITS) increase, there is a growing need for
real-time data and communication by vehicle users. Traditional request-based
methods face challenges such as latency and bandwidth limitations. Mode 4 in
Connected Vehicle-to-Everything (C-V2X) addresses latency and overhead issues
through autonomous resource selection. However, Semi-Persistent Scheduling
(SPS) based on distributed sensing may lead to increased collision.
Non-Orthogonal Multiple Access (NOMA) can alleviate the problem of reduced
packet reception probability due to collisions. Moreover, the concept of Age of
Information (AoI) is introduced as a comprehensive metric reflecting
reliability and latency performance, analyzing the impact of NOMA on C-V2X
communication system. AoI indicates the time a message spends in both local
waiting and transmission processes. In C-V2X, waiting process can be extended
to queuing process, influenced by packet generation rate and Resource
Reservation Interval (RRI). The transmission process is mainly affected by
transmission delay and success rate. In C-V2X, a smaller selection window (SW)
limits the number of available resources for vehicles, resulting in higher
collision rates with increased number of vehicles. SW is generally equal to
RRI, which not only affects AoI in queuing process but also AoI in the
transmission process. Therefore, this paper proposes an AoI estimation method
based on multi-priority data type queues and considers the influence of NOMA on
the AoI generated in both processes in C-V2X system under different RRI
conditions. This work aims to gain a better performance of C-V2X system
comparing with some known algorithms.


  An unknotting tunnel in a 3-manifold with boundary is a properly embedded
arc, the complement of an open neighborhood of which is a handlebody. A
geodesic with endpoints on the cusp boundary of a hyperbolic 3-manifold and
perpendicular to the cusp boundary is called a vertical geodesic. Given a
vertical geodesic in a hyperbolic 3-manifold M, we find sufficient conditions
for it to be an unknotting tunnel. In particular, if the vertical geodesic
corresponds to a 4-bracelet, 5-bracelet or 6-bracelet in the universal cover
and has short enough length, it must be an unknotting tunnel. Furthermore, we
consider a vertical geodesic that satisfies the elder sibling property, which
means that in the universal cover, every horoball except the one centered at
infinity is connected to a larger horoball by a lift of the vertical geodesic.
Such a vertical geodesic with length less than ln(2) is then shown to be an
unknotting tunnel.


  We observe experimentally that ensembles of quantum dots in three-dimensional
(3D) photonic crystals reveal strongly nonexponential time-resolved emission.
These complex emission decay curves are analyzed with a continuous distribution
of decay rates. The log-normal distribution describes the decays well for all
studied lattice parameters. The distribution width is identified with
variations of the radiative emission rates of quantum dots with various
positions and dipole orientations in the unit cell. We find a striking sixfold
change of the width of the distribution by varying the lattice parameter. This
interpretation qualitatively agrees with the calculations of the 3D projected
local density of states. We therefore conclude that fluorescence decay of
ensembles of quantum dots is highly nonexponential to an extent that is
controlled by photonic crystals.


  Until the last few decades, investigations of stellar interiors had been
restricted to theoretical studies only constrained by observations of their
global properties and external characteristics. However, in the last thirty
years the field has been revolutionized by the ability to perform seismic
investigations of stellar interiors. This revolution begun with the Sun, where
helioseismology has been yielding information competing with what can be
inferred about the Earth's interior from geoseismology. The last two decades
have witnessed the advent of asteroseismology of solar-like stars, thanks to a
dramatic development of new observing facilities providing the first reliable
results on the interiors of distant stars. The coming years will see a huge
development in this field. In this review we focus on solar-type stars, i.e.,
cool main-sequence stars where oscillations are stochastically excited by
surface convection. After a short introduction and a historical overview of the
discipline, we review the observational techniques generally used, and we
describe the theory behind stellar oscillations in cool main-sequence stars. We
continue with a complete description of the normal mode analyses through which
it is possible to extract the physical information about the structure and
dynamics of the stars. We then summarize the lessons that we have learned and
discuss unsolved issues and questions that are still unanswered.


  In order to deduce properties of dust in astrophysical environments where
dust growth through aggregation is important, knowledge of the way aggregated
particles interact with radiation, and what information is encoded in the
thermal radiation they emit, is needed. The emission characteristics are
determined by the size and structure of the aggregate and the composition and
shape of the constituents. We thus aim at performing computations of
compositionally inhomogeneous aggregates composed of irregularly shaped
constituents. In addition we aim at developing an empirical recipe to compute
the optical properties of such aggregates in a fast and accurate manner. We
performed CDA computations for aggregates of irregularly shaped particles with
various compositions. The constituents of the aggregate are assumed to be in
the Rayleigh regime, and in addition we assume that the dominant interaction of
the aggregate constituents is through dipole-dipole interactions. We computed
the spectral structure of the emission efficiency in the 10 micron region for
aggregates with 30% amorphous carbon and 70% silicates by volume with various
fractions of crystalline and amorphous components. We find that the spectral
appearance of the various components of the aggregate are very different and
depend on their abundances. Most notably, materials that have a very low
abundance appear spectroscopically as if they were in very small grains, while
more abundant materials appear, spectroscopically to reside in larger grains.
We construct a fast empirical approximate method, based on the idea of an
effective medium approximation, to construct the spectra for these aggregates
which almost perfectly reproduces the more exact computations. This new method
is fast enough to be easily implemented in fitting procedures.


  This study presents a novel approach to quantifying uncertainties in Bayesian
model updating, which is effective in sparse or single observations.
Conventional uncertainty quantification metrics such as the Euclidean and
Bhattacharyya distance-based metrics are potential in scenarios with ample
observations. However, their validation is limited in situations with
insufficient data, particularly for nonlinear responses like post-yield
behavior. Our method addresses this challenge by using the latent space of a
Variational Auto-encoder (VAE), a generative model that enables nonparametric
likelihood evaluation. This approach is valuable in updating model parameters
based on nonlinear seismic responses of structure, wherein data scarcity is a
common challenge. Our numerical experiments confirm the ability of the proposed
method to accurately update parameters and quantify uncertainties using limited
observations. Additionally, these numerical experiments reveal a tendency for
increased information about nonlinear behavior to result in decreased
uncertainty in terms of estimations. This study provides a robust tool for
quantifying uncertainty in scenarios characterized by considerable uncertainty,
thereby expanding the applicability of Bayesian updating methods in
data-constrained environments.


  We numerically study the impact of Gaussian barrier height and width on the
gray solitons population in a symmetric and asymmetric potential trap. The gray
solitons are created in a double-well potential by the density engineering
method. Two identical Bose-Einstein condensate fragments are confined and made
to collide by switching off the Gaussian barrier in a double-well potential. We
find that the gray solitons population can be manipulated by Gaussian barrier
height and width. We also study the gray solitons population dependence on the
coupling strength. Moreover, we also study the impact of an asymmetry present
in the double-well potential. We observe that such an asymmetry always swings
the point of collision of the gray solitons. Later, a stationary dark soliton
is created by the phase imprinting method and we observe that the initial
asymmetry in the double-well potential trap sets the dark soliton into
oscillation.


  We describe SemEval-2021 task 6 on Detection of Persuasion Techniques in
Texts and Images: the data, the annotation guidelines, the evaluation setup,
the results, and the participating systems. The task focused on memes and had
three subtasks: (i) detecting the techniques in the text, (ii) detecting the
text spans where the techniques are used, and (iii) detecting techniques in the
entire meme, i.e., both in the text and in the image. It was a popular task,
attracting 71 registrations, and 22 teams that eventually made an official
submission on the test set. The evaluation results for the third subtask
confirmed the importance of both modalities, the text and the image. Moreover,
some teams reported benefits when not just combining the two modalities, e.g.,
by using early or late fusion, but rather modeling the interaction between them
in a joint model.


  We consider the abelian sandpile model and the uniform spanning unicycle on
random planar maps. We show that the sandpile density converges to 5/2 as the
maps get large. For the spanning unicycle, we show that the length and area of
the cycle converges to the hitting time and location of a simple random walk in
the first quadrant. The calculations use the "hamburger-cheeseburger"
construction of Fortuin--Kasteleyn random cluster configurations on random
planar maps.


  Generative artificial intelligence (GAI) is a promising technique towards 6G
networks, and generative foundation models such as large language models (LLMs)
have attracted considerable interest from academia and telecom industry. This
work considers a novel edge-cloud deployment of foundation models in 6G
networks. Specifically, it aims to minimize the service delay of foundation
models by radio resource allocation and task offloading, i.e., offloading
diverse content generation tasks to proper LLMs at the network edge or cloud.
In particular, we first introduce the communication system model, i.e.,
allocating radio resources and calculating link capacity to support generated
content transmission, and then we present the LLM inference model to calculate
the delay of content generation. After that, we propose a novel in-context
learning method to optimize the task offloading decisions. It utilizes LLM's
inference capabilities, and avoids the difficulty of dedicated model training
or fine-tuning as in conventional machine learning algorithms. Finally, the
simulations demonstrate that the proposed edge-cloud deployment and in-context
learning task offloading method can achieve satisfactory generation service
quality without dedicated model training or fine-tuning.


  We develop an existence, uniqueness and regularity theory for general
multidimensional strongly coupled FBSDE using so called decoupling fields. We
begin with a local result and extend it to a global theory via concatenation.
The cornerstone of the global theory is the so called maximal interval which
is, roughly speaking, the largest interval on which reasonable solutions exist.
A method to verify that the maximal interval is the whole interval, for
problems in which this is conjectured, is proposed. As part of our study of the
regularity of solutions constructed we show variational differentiability under
Lipschitz assumptions. Extra emphasis is put on the more special Markovian case
in which assumptions on the Lipschitz continuity for the FBSDE can be weakened
to local ones, and additional regularity properties emerge.


  We investigate a covering problem in $3$-uniform hypergraphs ($3$-graphs):
given a $3$-graph $F$, what is $c_1(n,F)$, the least integer $d$ such that if
$G$ is an $n$-vertex $3$-graph with minimum vertex degree $\delta_1(G)>d$ then
every vertex of $G$ is contained in a copy of $F$ in $G$ ?
  We asymptotically determine $c_1(n,F)$ when $F$ is the generalised triangle
$K_4^{(3)-}$, and we give close to optimal bounds in the case where $F$ is the
tetrahedron $K_4^{(3)}$ (the complete $3$-graph on $4$ vertices).
  This latter problem turns out to be a special instance of the following
problem for graphs: given an $n$-vertex graph $G$ with $m> n^2/4$ edges, what
is the largest $t$ such that some vertex in $G$ must be contained in $t$
triangles? We give upper bound constructions for this problem that we
conjecture are asymptotically tight. We prove our conjecture for tripartite
graphs, and use flag algebra computations to give some evidence of its truth in
the general case.


  We establish the existence and uniqueness of rational conformal maps of
minimal degree $n+1$ for opening up $n$ arcs. In earlier results, the degree
was exponential in $n$. We also discuss two related problems. (a) We establish
existence of rational functions of minimal degree with prescribed critical
values, and show that the number of (suitably normalized) rational functions is
given in terms of the Hurwitz numbers. (b) We consider the problem of finding
rational functions of minimal degree with prescribed critical points, where we
establish existence of solutions by considering certain polynomial equations,
and where the number of normalized solutions is bounded from above by a Catalan
number. We illustrate our results with two examples.


  Ensemble learning is a method that leverages weak learners to produce a
strong learner. However, obtaining a large number of base learners requires
substantial time and computational resources. Therefore, it is meaningful to
study how to achieve the performance typically obtained with many base learners
using only a few. We argue that to achieve this, it is essential to enhance
both classification performance and generalization ability during the ensemble
process. To increase model accuracy, each weak base learner needs to be more
efficiently integrated. It is observed that different base learners exhibit
varying levels of accuracy in predicting different classes. To capitalize on
this, we introduce confidence tensors $\tilde{\mathbf{\Theta}}$ and
$\tilde{\mathbf{\Theta}}_{rst}$ signifies that the $t$-th base classifier
assigns the sample to class $r$ while it actually belongs to class $s$. To the
best of our knowledge, this is the first time an evaluation of the performance
of base classifiers across different classes has been proposed. The proposed
confidence tensor compensates for the strengths and weaknesses of each base
classifier in different classes, enabling the method to achieve superior
results with a smaller number of base learners. To enhance generalization
performance, we design a smooth and convex objective function that leverages
the concept of margin, making the strong learner more discriminative.
Furthermore, it is proved that in gradient matrix of the loss function, the sum
of each column's elements is zero, allowing us to solve a constrained
optimization problem using gradient-based methods. We then compare our
algorithm with random forests of ten times the size and other classical methods
across numerous datasets, demonstrating the superiority of our approach.


  In this article we prove a global result in the spirit of Basener's theorem
regarding the relation between q-pseudoconvexity and q-holomorphic convexity:
we prove that any smoothly bounded strictly q-pseudoconvex open subset of the
complex Euclidean space is (q + 1)-holomorphically convex; moreover, assuming
that the given open set verifies an additional assumption, we prove that it is
q-holomorphically convex. We also prove that any open subset of the complex
n-dimensional Euclidean space is n-holomorphically convex.


  We study dark matter scattering off ${}^4$He and other light nuclei using
chiral effective field theory. We consider scalar DM interactions and include
both one- and two-nucleon scattering processes. The DM interactions and nuclear
wave functions are obtained from chiral effective field theory and we work up
to fourth order in the chiral expansion for the latter to investigate the
chiral convergence. The results for the scattering rates can be used to
determine the sensitivity of planned experiments to detect relatively light
dark matter particles using ${}^4$He. We find that next-to-leading-order scalar
currents are smaller than expected from power counting for scattering off
${}^4$He confirming earlier work. However, the results for two-nucleon
corrections exhibit a linear regulator dependence indicating potential problems
in the applied power counting. We observe a linear correlation between the, in
principle not observable, D-wave probability of various light nuclei and the
scalar two-nucleon matrix elements, again pointing towards potentially missing
contributions.


  Particles in turbulence frequently encounter extreme accelerations between
extended periods of quiescence. The occurrence of extreme events is closely
related to the intermittent spatial distribution of intense flow structures
such as vorticity filaments. This mixed history of flow conditions leads to
very complex particle statistics with a pronounced scale dependence, which
presents one of the major challenges on the way to a non-equilibrium
statistical mechanics of turbulence. Here, we introduce the notion of
persistent Lagrangian acceleration, quantified by the squared particle
acceleration coarse-grained over a viscous time scale. Conditioning Lagrangian
particle data from simulations on this coarse-grained acceleration, we find
remarkably simple, close-to-Gaussian statistics for a range of Reynolds
numbers. This opens the possibility to decompose the complex particle
statistics into much simpler sub-ensembles. Based on this observation, we
develop a comprehensive theoretical framework for Lagrangian single-particle
statistics that captures the acceleration, velocity increments as well as
single-particle dispersion.


  We develop a singular layer transmission model for continuous-variable
quantum key distribution (CVQKD). In CVQKD, the transmit information is carried
by continuous-variable (CV) quantum states, particularly by Gaussian random
distributed position and momentum quadratures. The reliable transmission of the
quadrature components over a noisy link is a cornerstone of CVQKD protocols.
The proposed singular layer uses the singular value decomposition of the
Gaussian quantum channel, which yields an additional degree of freedom for the
phase space transmission. This additional degree of freedom can further be
exploited in a multiple-access scenario. The singular layer defines the
eigenchannels of the Gaussian physical link, which can be used for the
simultaneous reliable transmission of multiple user data streams. Our
transmission model also includes the singular interference avoider (SIA)
precoding scheme. The proposed SIA precoding scheme prevents the eigenchannel
interference to reach an optimal transmission over a Gaussian link. We
demonstrate the results through the adaptive multicarrier quadrature
division-multiuser quadrature allocation (AMQD-MQA) CVQKD multiple-access
scheme. We define the singular model of AMQD-MQA and characterize the
properties of the eigenchannel interference. We propose the SIA precoding of
Gaussian random quadratures and the optimal decoding at the receiver. We show a
random phase space constellation scheme for the Gaussian sub-channels. The
singular layer transmission provides improved simultaneous transmission rates
for the users with unconditional security in a multiple-access scenario,
particularly in crucial low signal-to-noise ratio regimes.


  In this brief review we discuss the generation of Majorana neutrino masses
through the see-saw mechanism, the theory of neutrinoless double-beta decay,
the implications of neutrino oscillation data for the effective Majorana mass,
taking into account the recent Daya Bay measurement of theta_13, and the
interpretation of the results of neutrinoless double-beta decay experiments.


  We calculate mesonic two-point functions in the epsilon-regime of two-flavor
QCD on the lattice with exact chiral symmetry. We use gauge configurations of
size 16^3 32 at the lattice spacing a \sim 0.11 fm generated with dynamical
overlap fermions. The sea quark mass is fixed at \sim 3 MeV and the valence
quark mass is varied in the range 1-4 MeV, both of which are in the
epsilon-regime. We find a good consistency with the expectations from the
next-to-leading order calculation in the epsilon-expansion of (partially
quenched) chiral perturbation theory. From a fit we obtain the pion decay
constant F=87.3(5.6) MeV and the chiral condensate Sigma^{MS}=[239.8(4.0) MeV
]^3 up to next-to-next-to-leading order contributions.


  We construct exact solutions to noncommutative gravity following the
formulation of Chamseddine and show that they are in general accompanied by
Abelian gauge fields which are first order in the noncommutative scale. This
provides a mechanism for generating cosmological electromagnetic fields in an
expanding space-time background, and also leads to multipole-like fields
surrounding black holes. Exact solutions to noncommutative Einstein-Maxwell
theory can give rise to first order corrections to the metric tensor, as well
as to the electromagnetic fields. This leads to first order shifts in the
horizons of charged black holes.


  We present a continuum theory which predicts the steady state propagation of
cracks. The theory overcomes the usual problem of a finite time cusp
singularity of the Grinfeld instability by the inclusion of elastodynamic
effects which restore selection of the steady state tip radius and velocity. We
developed a phase field model for elastically induced phase transitions; in the
limit of small or vanishing elastic coefficients in the new phase, fracture can
be studied. The simulations confirm analytical predictions for fast crack
propagation.


  Is there a unified model for generating molecules considering different
conditions, such as binding pockets and chemical properties? Although
target-aware generative models have made significant advances in drug design,
they do not consider chemistry conditions and cannot guarantee the desired
chemical properties. Unfortunately, merging the target-aware and chemical-aware
models into a unified model to meet customized requirements may lead to the
problem of negative transfer. Inspired by the success of multi-task learning in
the NLP area, we use prefix embeddings to provide a novel generative model that
considers both the targeted pocket's circumstances and a variety of chemical
properties. All conditional information is represented as learnable features,
which the generative model subsequently employs as a contextual prompt.
Experiments show that our model exhibits good controllability in both single
and multi-conditional molecular generation. The controllability enables us to
outperform previous structure-based drug design methods. More interestingly, we
open up the attention mechanism and reveal coupling relationships between
conditions, providing guidance for multi-conditional molecule generation.


  This paper reports the use of Tracker as a pedagogical tool in the effective
learning and teaching of projectile motion in physics. When computer model
building learning processes is supported and driven by video analysis data,
this free Open Source Physics (OSP) tool can provide opportunities for students
to engage in active inquiry-based learning. We discuss the pedagogical use of
Tracker to address some common misconceptions of projectile motion by allowing
students to test their hypothesis by juxtaposing their mental models against
the analysis of real life videos. Initial research findings suggest that
allowing learners to relate abstract physics concepts to real life through
coupling computer modeling with traditional video analysis could be an
innovative and effective way to learn projectile motion. 2015 Resources:
http://iwant2study.org/ospsg/index.php/interactive-resources/physics/02-newtonian-mechanics/01-kinematics/174-projectile-motion


  In an attempt to understand the dynamics of collapsing starless cores, we
have onducted a detailed investigation of the velocity fields of two collapsing
cores, L694-2 and L1197, with high spatial resolution HCN J=1-0 maps and Monte
Carlo radiative transfer alculation.
  It is found that infall motion is most active in the middle and outer layers
outside the central density-flat region, while both the central and outermost
parts of the cores are static or exhibit slower motion. Their peak velocities
are 0.28 km s^{-1} for L694-2 and 0.20 km s^{-1$ for L1197, which could not be
found in simple models. These velocity fields are roughly consistent with the
gravitational collapse models of the isothermal core; However, the velocity
gradients inside the peak velocity position are steeper than those of the
models.
  Our results also show that the density distributions are ~ r^{-2.5} and ~
r^{-1.5} in the outer part for L694-2 and L1197, respectively. HCN abundance
relative to H_2 is spatially almost constant in L694-2 with a value of 7.0 X
10^{-9}, while for L1197, it shows a slight inward increase from 1.7 X 10^{-9}
to 3.5 X 10^{-9}.


  Shape is an important physical property of natural and manmade 3D objects
that characterizes their external appearances. Understanding differences
between shapes and modeling the variability within and across shape classes,
hereinafter referred to as \emph{shape analysis}, are fundamental problems to
many applications, ranging from computer vision and computer graphics to
biology and medicine. This chapter provides an overview of some of the recent
techniques that studied the shape of 3D objects that undergo non-rigid
deformations including bending and stretching. Recent surveys that covered some
aspects such classification, retrieval, recognition, and rigid or nonrigid
registration, focused on methods that use shape descriptors. Descriptors,
however, provide abstract representations that do not enable the exploration of
shape variability. In this chapter, we focus on recent techniques that treated
the shape of 3D objects as points in some high dimensional space where paths
describe deformations. Equipping the space with a suitable metric enables the
quantification of the range of deformations of a given shape, which in turn
enables (1) comparing and classifying 3D objects based on their shape, (2)
computing smooth deformations, i.e. geodesics, between pairs of objects, and
(3) modeling and exploring continuous shape variability in a collection of 3D
models. This article surveys and classifies recent developments in this field,
outlines fundamental issues, discusses their potential applications in computer
vision and graphics, and highlights opportunities for future research. Our
primary goal is to bridge the gap between various techniques that have been
often independently proposed by different communities including mathematics and
statistics, computer vision and graphics, and medical image analysis.


  We show that, in local Calabi-Yau manifolds, the topological open string
partition function transforms as a wavefunction under modular transformations.
Our derivation is based on the topological recursion for matrix models, and it
generalizes in a natural way the known result for the closed topological string
sector. As an application, we derive results for vevs of 1/2 BPS Wilson loops
in ABJM theory at all genera in a strong coupling expansion, for various
representations.


  We investigate the problem of a monostatic pulse-Doppler radar transceiver
trying to detect targets, sparsely populated in the radar's unambiguous
time-frequency region. Several past works employ compressed sensing (CS)
algorithms to this type of problem, but either do not address sample rate
reduction, impose constraints on the radar transmitter, propose CS recovery
methods with prohibitive dictionary size, or perform poorly in noisy
conditions. Here we describe a sub-Nyquist sampling and recovery approach
called Doppler focusing which addresses all of these problems: it performs low
rate sampling and digital processing, imposes no restrictions on the
transmitter, and uses a CS dictionary with size which does not increase with
increasing number of pulses P. Furthermore, in the presence of noise, Doppler
focusing enjoys an SNR increase which scales linearly with P, obtaining good
detection performance even at SNRs as low as -25dB. The recovery is based on
the Xampling framework, which allows reducing the number of samples needed to
accurately represent the signal, directly in the analog-to-digital conversion
process. After sampling, the entire digital recovery process is performed on
the low rate samples without having to return to the Nyquist rate. Finally, our
approach can be implemented in hardware using a previously suggested Xampling
prototype.


  We applied the BEER algorithm to the CoRoT lightcurves from the first five
LRc fields and identified $481$ non-eclipsing BEER candidates with periodic
lightcurve modulations and amplitudes of $0.5-87$ mmag. Medium-resolution
spectra of $281$ candidates were obtained in a seven-night AAOmega
radial-velocity (RV) campaign, with a precision of $\sim1$ km/s. The RVs
confirmed the binarity of $70$ of the BEER candidates, with periods of $0.3-10$
days.


  The existence of a strongly coupled ultraviolet fixed point in 4-dimensional
lattice models as they cross into the conformal window has long been
hypothesized. The SU(3) gauge system with 8 fundamental fermions is a good
candidate to study this phenomenon as it is expected to be very close to the
opening of the conformal window. I study the system using staggered lattice
fermions in the chiral limit. My numerical simulations employ improved lattice
actions that include heavy Pauli-Villars (PV) type bosons. This modification
does not affect the infrared dynamics but greatly reduces the ultraviolet
fluctuations, thus allowing the study of stronger renormalized couplings than
previously possible. I consider two different PV actions and find that both
show an apparent continuous phase transition in the 8-flavor system.
  I investigate the critical behavior using finite size scaling of the
renormalized gradient flow coupling. The finite size scaling curve-collapse
analysis predicts a first order phase transition consistent with discontinuity
exponent $\nu=1/4$ in the system without PV bosons. The scaling analysis with
the PV boson actions is not consistent with a first order phase transition. The
numerical data are well described by "walking scaling" corresponding to a
renormalization group $\beta$ function that just touches zero, $\beta(g^2) \sim
(g^2 - g^2_\star)^2$, though second order scaling cannot be excluded. Walking
scaling could imply that the 8-flavor system is the opening of the conformal
window, an exciting possibility that could be related to t'Hooft anomaly
cancellation of the system.


  We compute the tensor CMB anisotropy power spectrum for singular and
non-singular instantons describing the beginning of an open universe according
to the Euclidean no boundary proposal. Singular instantons occur generically,
whereas non-singular instantons require more contrived scalar field potentials.
For the latter, we consider potentials in which a sharp feature, either
negative or positive, is added to a gently sloping potential. In the first case
one finds a nearly divergent contribution to the low multipole CMB anisotropy,
in conflict with the COBE observations. In the second case the divergence is
weaker, but matching the low multipoles forces the added feature to be large
and narrow. For singular instantons, there is a better match to the
observations, without any such contrivance. The distinction between singular
and nonsingular instantons disappears in the limit as the universe becomes
flat, but is still observable for densities as high as 0.7 of the critical
density.


  With the recent rise of Machine Learning as a candidate to partially replace
classic Financial Mathematics methodologies, we investigate the performances of
both in solving the problem of dynamic portfolio optimization in
continuous-time, finite-horizon setting for a portfolio of two assets that are
intertwined.
  In Financial Mathematics approach we model the asset prices not via the
common approaches used in pairs trading such as a high correlation or
cointegration, but with the cointelation model that aims to reconcile both
short-term risk and long-term equilibrium. We maximize the overall P&L with
Financial Mathematics approach that dynamically switches between a
mean-variance optimal strategy and a power utility maximizing strategy. We use
a stochastic control formulation of the problem of power utility maximization
and solve numerically the resulting HJB equation with the Deep Galerkin method.
  We turn to Machine Learning for the same P&L maximization problem and use
clustering analysis to devise bands, combined with in-band optimization.
Although this approach is model agnostic, results obtained with data simulated
from the same cointelation model as FM give an edge to ML.


  All-dielectric "magnetic light" nanophotonics based on high refractive index
nanoparticles allows controlling magnetic component of light at nanoscale
without having high dissipative losses. The artificial magnetic optical
response of such nanoparticles originates from circular displacement currents
excited inside those structures and strongly depends on geometry and dispersion
of optical materials. Here a new approach for increasing magnetic response via
resonant bianisotropy effect is proposed and analyzed. The key mechanism of
enhancement is based on electric-magnetic interaction between two electrically
and magnetically resonant nanoparticles of all-dielectric dimer nanoantenna. It
was shown that proper geometrical arrangement of the dimer in respect to the
incident illumination direction allows flexible control over all vectorial
components of magnetic polarizability, tailoring the later in the dynamical
range of 100 % and enhancement up to 36 % relative to performances of
standalone spherical particles. The proposed approach provides pathways for
designs of all-dielectric metamaterials and metasurfaces with strong magnetic
response.


  Achieving strong coupling between light and matter is usually a challenge in
Cavity Quantum Electrodynamics (cQED), especially in solid state systems. For
this reason is useful taking advantage of alternative approaches to reach this
regime, and then, generate reliable quantum polaritons. In this work we study a
system composed of a quantized single mode of a mechanical resonator
interacting linearly with both a single mode nanocavity and a two-level single
quantum dot. In particular, we focus on the behavior of the indirect
light-matter interaction when the phonon mode interfaces both parts. By
diagonalization of the Hamiltonian and computing the density matrix in a master
equation approach, we evidence several features of strong coupling between
photons in optical cavities and excitons in a quantum dot. For large energy
detuning between the cavity and the mechanical resonator it is obtained a
phonon-dispersive effective Hamiltonian which is able to retrieve much of the
physics of the conventional Jaynes-Cummings model (JCM). In order to
characterize this mediated coupling, we make a quantitative comparison between
both models and analyze light-matter entanglement and purity of the system
leading to similar results in cQED.


  Inflationary perturbations in multi-field theories can exhibit a transient
tachyonic instability as a consequence of their non-trivial motion in the
internal field space. When an effective single-field description is applicable,
the resulting theory is characterized by fluctuations that propagate with an
$imaginary$ speed of sound. We use the effective field theory of fluctuations
to study such a set-up in a model-independent manner, highlighting the
peculiarities and subtleties that make it different from the standard case. In
particular, perturbations feature exponentially growing and decaying modes
whose relative amplitude is undetermined within the effective field theory.
Nevertheless, we prove that in an interesting limit the dimensionless
bispectrum is in fact universal, depending only on the speed of sound and on
the cutoff scale that limits the validity of the effective theory. Contrary to
the power spectrum, we find that the bispectrum does not display an exponential
enhancement. The amplitude of non-Gaussianities in the equilateral
configuration is similar to the one of conventional models, but it is enhanced
in flattened configurations in a way that is ultraviolet sensitive.


  We apply a formalism recently developed to carry out Generator Coordinate
Method calculations using a set of Hartree- Fock- Bogoliubov wave functions,
where each of the members of the set can be expanded in an arbitrary basis. In
this paper it is assumed that the HFB wave functions are expanded in Harmonic
Oscillator (HO) bases with different oscillator lengths. General expressions to
compute the required matrix elements of arbitrary operators are given. The
application of the present formalism to the case of fission is illustrated with
an example.


  A method is given for determining a mixed social choice out of a
paired-comparison matrix. The method combines a projection procedure introduced
in previous papers of the same authors and a classical method due to Zermelo.
The resulting method is proved to have certain desirable properties, which
include: compliance with a majority principle, clone consistency, and
continuity of the mixing fractions with respect to the data.


  With the constant spread of misinformation on social media networks, a need
has arisen to continuously assess the veracity of digital content. This need
has inspired numerous research efforts on the development of misinformation
detection (MD) models. However, many models do not use all information
available to them and existing research contains a lack of relevant datasets to
train the models, specifically within the South African social media
environment. The aim of this paper is to investigate the transferability of
knowledge of a MD model between different contextual environments. This
research contributes a multimodal MD model capable of functioning in the South
African social media environment, as well as introduces a South African
misinformation dataset. The model makes use of multiple sources of information
for misinformation detection, namely: textual and visual elements. It uses
bidirectional encoder representations from transformers (BERT) as the textual
encoder and a residual network (ResNet) as the visual encoder. The model is
trained and evaluated on the Fakeddit dataset and a South African
misinformation dataset. Results show that using South African samples in the
training of the model increases model performance, in a South African
contextual environment, and that a multimodal model retains significantly more
knowledge than both the textual and visual unimodal models. Our study suggests
that the performance of a misinformation detection model is influenced by the
cultural nuances of its operating environment and multimodal models assist in
the transferability of knowledge between different contextual environments.
Therefore, local data should be incorporated into the training process of a
misinformation detection model in order to optimize model performance.


  The variational auto-encoder has become a leading framework for symbolic
music generation, and a popular research direction is to study how to
effectively control the generation process. A straightforward way is to control
a model using different conditions during inference. However, in music
practice, conditions are usually sequential (rather than simple categorical
labels), involving rich information that overlaps with the learned
representation. Consequently, the decoder gets confused about whether to
"listen to" the latent representation or the condition, and sometimes just
ignores the condition. To solve this problem, we leverage domain adversarial
training to disentangle the representation from condition cues for better
control. Specifically, we propose a condition corruption objective that uses
the representation to denoise a corrupted condition. Minimized by a
discriminator and maximized by the VAE encoder, this objective adversarially
induces a condition-invariant representation. In this paper, we focus on the
task of melody harmonization to illustrate our idea, while our methodology can
be generalized to other controllable generative tasks. Demos and experiments
show that our methodology facilitates not only condition-invariant
representation learning but also higher-quality controllability compared to
baselines.


  Controller Area Network bus systems within vehicular networks are not
equipped with the tools necessary to ward off and protect themselves from
modern cyber-security threats. Work has been done on using machine learning
methods to detect and report these attacks, but common methods are not robust
towards unknown attacks. These methods usually rely on there being a sufficient
representation of attack data, which may not be available due to there either
not being enough data present to adequately represent its distribution or the
distribution itself is too diverse in nature for there to be a sufficient
representation of it. With the use of one-class classification methods, this
issue can be mitigated as only normal data is required to train a model for the
detection of anomalous instances. Research has been done on the efficacy of
these methods, most notably One-Class Support Vector Machine and Support Vector
Data Description, but many new extensions of these works have been proposed and
have yet to be tested for injection attacks in vehicular networks. In this
paper, we investigate the performance of various state-of-the-art one-class
classification methods for detecting injection attacks on Controller Area
Network bus traffic. We investigate the effectiveness of these techniques on
attacks launched on Controller Area Network buses from two different vehicles
during normal operation and while being attacked. We observe that the Subspace
Support Vector Data Description method outperformed all other tested methods
with a Gmean of about 85%.


  In this paper we develop a theory of Fourier-like transforms on the space of
stable graphs. In particular, we introduce a duality theory of stable graphs.
As an application, we derive the holomorphic anomaly equations for general
propagators in the work of Aganagic, Bouchard and Klemm.


  The inner regions of the Galaxy are severely affected by extinction, which
limits our capability to study the stellar populations present there. The Vista
Variables in the Via Lactea (VVV) ESO Public Survey has observed this zone at
near-infrared wavelengths where reddening is highly diminished. By exploiting
the high resolution and wide field-of-view of the VVV images we aim to produce
a deep, homogeneous, and highly complete database of sources that cover the
innermost regions of our Galaxy. To better deal with the high crowding in the
surveyed areas, we have used point spread function (PSF)-fitting techniques to
obtain a new photometry of the VVV images, in the ZYJHKs near-infrared filters
available. Our final catalogs contain close to one billion sources, with
precise photometry in up to five near-infrared filters, and they are already
being used to provide an unprecedented view of the inner Galactic stellar
populations. We make these catalogs publicly available to the community. Our
catalogs allow us to build the VVV giga-CMD, a series of color-magnitude
diagrams of the inner regions of the Milky Way presented as supplementary
videos. We provide a qualitative analysis of some representative CMDs of the
inner regions of the Galaxy, and briefly mention some of the studies we have
developed with this new dataset so far.


  This is a short review of string cosmology. We wish to connect string-scale
physics as closely as possible to observables accessible to current or
near-future experiments. Our possible best hope to do so is a description of
inflation in string theory. The energy scale of inflation can be as high as
that of Grand Unification (GUT). If this is the case, this is the closest we
can possibly get in energy scales to string-scale physics. Hence, GUT-scale
inflation may be our best candidate phenomenon to preserve traces of
string-scale dynamics. Our chance to look for such traces is the primordial
gravitational wave, or tensor mode signal produced during inflation. For
GUT-scale inflation this is strong enough to be potentially visible as a B-mode
polarization of the cosmic microwave background (CMB). Moreover, a GUT-scale
inflation model has a trans-Planckian excursion of the inflaton scalar field
during the observable amount of inflation. Such large-field models of inflation
have a clear need for symmetry protection against quantum corrections. This
makes them ideal candidates for a description in a candidate fundamental theory
like string theory. At the same time the need of large-field inflation models
for UV completion makes them particularly susceptible to preserve imprints of
their string-scale dynamics in the inflationary observables, the spectral index
$n_s$ and the fractional tensor mode power $r$. Hence, we will focus this
review on axion monodromy inflation as a mechanism of large-field inflation in
string theory.


  Server clustering is a common design principle employed by many organisations
who require high availability, scalability and easier management of their
infrastructure. Servers are typically clustered according to the service they
provide whether it be the application(s) installed, the role of the server or
server accessibility for example. In order to optimize performance, manage load
and maintain availability, servers may migrate from one cluster group to
another making it difficult for server monitoring tools to continuously monitor
these dynamically changing groups. Server monitoring tools are usually
statically configured and with any change of group membership requires manual
reconfiguration; an unreasonable task to undertake on large-scale cloud
infrastructures.
  In this paper we present the Cloudlet Control and Management System (C2MS); a
system for monitoring and controlling dynamic groups of physical or virtual
servers within cloud infrastructures. The C2MS extends Ganglia - an open source
scalable system performance monitoring tool - by allowing system administrators
to define, monitor and modify server groups without the need for server
reconfiguration. In turn administrators can easily monitor group and individual
server metrics on large-scale dynamic cloud infrastructures where roles of
servers may change frequently. Furthermore, we complement group monitoring with
a control element allowing administrator-specified actions to be performed over
servers within service groups as well as introduce further customized
monitoring metrics. This paper outlines the design, implementation and
evaluation of the C2MS.


  A new scenario for creation of galactic magnetic fields is proposed which is
operative at the cosmological epoch of the galaxy formation, and which relies
on unconventional properties of dark matter. Namely, it requires existence of
feeble but long range interaction between the dark matter particles and
electrons. In particular, millicharged dark matter particles or mirror
particles with the photon kinetic mixing to the usual photon can be considered.
We show that in rotating protogalaxies circular electric currents can be
generated by the interactions of free electrons with dark matter particles in
the halo, while the impact of such interactions on galactic protons is
considerably weaker. The induced currents may be strong enough to create the
observed magnetic fields on the galaxy scales with the help of moderate dynamo
amplification. In addition, the angular momentum transfer from the rotating gas
to dark matter component could change the dark matter profile and formation of
cusps at galactic centers would be inhibited. The global motion of the ionized
gas could produce sufficiently large magnetic fields also in filaments and
galaxy clusters.


  We show that surface waves along interstellar current sheets closely aligned
with the line of sight lead to pulsar scintillation properties consistent with
those observed. This mechanism naturally produces the length and density scales
of the ISM scattering lenses that are required to explain the magnitude and
dynamical spectrum of the scintillations. In this picture, the parts of warm
ionized interstellar medium that are responsible for the scintillations are
relatively quiescent, with scintillation and scattering resulting from weak
waves propagating along magnetic domain boundary current sheets, which are both
expected from helicity conservation and have been observed in numerical
simulations. The model statistically predicts the spacing and amplitudes of
inverted parabolic arcs seen in Fourier-transformed dynamical spectra of
strongly scintillating pulsars with only 3 parameters. Multi-frequency,
multi-epoch low frequency VLBI observations can quantitatively test this
picture. If successful, in addition to mapping the ISM, this may open the door
to precise nanoarcsecond pulsar astrometry, distance measurements, and emission
studies using these 10AU interferometers in the sky.


  In this paper, we use the linear programming approach to find new upper
bounds for the moments of isotropic measures. These bounds are then utilized
for finding lower packing bounds and energy bounds for projective codes. We
also show that the obtained energy bounds are sharp for several infinite
families of codes.


  We argue that X-ray flaring variability observed in the transient X-ray
pulsar A 0535+26 is due to low-mode magnetospheric instability. This
instability develops at the onset of accretion, in the thin boundary layer
between the accretion disk and neutron star magnetosphere. As a result, the
matter collected in the boundary layer can rapidly fall onto the NS surface
close to the magnetic poles, but not exactly along the field lines by which the
stationary accretion proceeds. This explains the shift in cyclotron line energy
measured using RXTE data in a pre-outburst spike, with respect to the line
energy observed during the main outburst. Furthermore, the instability can
account for the difference in pulse profiles, and their energy evolution that
is different in the pre-outburst flare and main outburst.


  Let $X$ be a continuum and let $\varphi:X\rightarrow X$ be a homeomorphism.
To construct a dynamical system $(X,\varphi)$ with interesting dynamical
properties, the continuum $X$ often needs to have some complicated topological
structure. In this paper, we are interested in one such dynamical property:
transitivity. By now, various examples of continua $X$ have been constructed in
such a way that the dynamical system $(X,\varphi)$ is transitive. Mostly, they
are examples of continua that are not path-connected, such as the pseudo-arc or
the pseudo-circle, or they are examples of locally connected continua (and
every locally connected continuum is path-connected), Wazewski's universal
dendrite and the Sierpinski carpet are such examples.
  In this paper, we present an example of a dynamical system $(X,\varphi)$,
where $\varphi$ is a homeomorphism on the continuum $X$ and $X$ is a
path-connected but not locally connected continuum. We construct a transitive
homeomorphism on the Lelek fan. As a by-product, a non-invertible transitive
map on the Lelek fan is also constructed.


  We study an effective Hamiltonian for the standard $\nu=1/3$ fractional
quantum Hall system in the thin cylinder regime. We give a complete description
of its ground state space in terms of what we call Fragmented Matrix Product
States, which are labeled by a certain family of tilings of the one-dimensional
lattice. We then prove that the model has a spectral gap above the ground
states for a range of coupling constants that includes physical values. As a
consequence of the gap we establish the incompressibility of the fractional
quantum Hall states. We also show that all the ground states labeled by a
tiling have a finite correlation length, for which we give an upper bound. We
demonstrate by example, however, that not all superpositions of tiling states
have exponential decay of correlations.


  This paper introduces the problem of Fine-grained Incident Video Retrieval
(FIVR). Given a query video, the objective is to retrieve all associated
videos, considering several types of associations that range from duplicate
videos to videos from the same incident. FIVR offers a single framework that
contains several retrieval tasks as special cases. To address the benchmarking
needs of all such tasks, we construct and present a large-scale annotated video
dataset, which we call FIVR-200K, and it comprises 225,960 videos. To create
the dataset, we devise a process for the collection of YouTube videos based on
major news events from recent years crawled from Wikipedia and deploy a
retrieval pipeline for the automatic selection of query videos based on their
estimated suitability as benchmarks. We also devise a protocol for the
annotation of the dataset with respect to the four types of video associations
defined by FIVR. Finally, we report the results of an experimental study on the
dataset comparing five state-of-the-art methods developed based on a variety of
visual descriptors, highlighting the challenges of the current problem.


  The capability of the global, electromagnetic gyrokinetic GENE code
interfaced with the transport Tango solver is exploited to address the impact
of fusion alpha particles (in their dual role of fast particles and heating
source) on plasma profiles and performance at JET in the discharges with the
highest quasi-stationary peak fusion power during the DTE2 experimental
campaigns. Employing radially global nonlinear electromagnetic GENE-Tango
simulations, we compare results with/without alpha particles and alpha heating.
Our findings reveal that alpha particles have a negligible impact on turbulent
transport, with GENE-Tango converging to similar plasma profiles regardless of
their inclusion as a kinetic species in GENE. On the other hand, alpha heating
is found to contribute to the peaking of the electron temperature profiles,
leading to a 1keV drop on the on-axis electron temperature when alpha heating
is neglected in Tango. The minimal impact of alpha particles on turbulent
transport in this JET discharge - despite this being the shot with the highest
fusion output - is attributed to the low content of fusion alpha in this
discharge. To assess the potential impact of alpha particles on turbulent
transport in regimes with higher alpha particle density, as expected in ITER
and fusion reactors, we artificially increased the alpha particle concentration
to levels expected for ITER. By performing global nonlinear GENE standalone
simulations, we found that increasing the alpha particle density beyond five
times the nominal value lead to significant overall turbulence destabilization.


  This article revisits and elaborates the significant role of positive
geometry of momentum twistor Grassmannian for planar N=4 SYM scattering
amplitudes. First we establish the fundamentals of positive Grassmannian
geometry for tree amplitudes. Then we formulate this subject around these four
major facets: 1. Deriving the tree and 1-loop BCFW recursion relations solely
from positivity, after introducing the simple building blocks called positive
components. 2. Applying Grassmannian geometry and Pluecker coordinates to
determine the signs in N$^2$MHV homological identities. Most of them in fact
reflect the secret incarnation of the simple 6-term NMHV identity. 3. Deriving
the stacking positivity relation, which is powerful for parameterizing the
matrix representative in terms of positive variables, of a given Grassmannian
geometric configuration. 4. Introducing a highly refined formalism for tree
BCFW recursion relation, which reveals its two-fold simplex-like structures.
First, the BCFW contour in terms of (reduced) Grassmannian geometry
representatives is dissected into a triangle-shape sum, as only a small
fraction of the sum needs to be explicitly identified. Second, this fraction
can be further dissected, according to different growing modes and parameters.
The growing modes possess the shapes of solid simplices of various dimensions,
with which infinite number of BCFW cells can be entirely captured by the
characteristic objects called fully-spanning cells. We find that for a given k,
beyond n=4k+1 there is no more new fully-spanning cell, which signifies the
essential termination of the recursive growth of BCFW cells. As n increases
beyond the termination point, the BCFW contour simply replicates itself
according to the simplex-like patterns, which enables us to master all BCFW
cells once for all without actually identifying most of them.


  We show that the Hermitian analogue of a famous result of Pfister fails. To
do so we provide a Hermitian symmetric polynomial $r$ of total degree 2d such
that any non-zero multiple of it cannot be written as a Hermitian sum of
squares with fewer than $d+1$ squares.


  Monolayer silicene is a front runner in the 2D-Xene family, which also
comprises germanene, stanene, and phosphorene, to name a few, due to its
compatibility with current silicon fabrication technology. Here, we investigate
the utility of 2D-Xenes for straintronics using the ab-initio density
functional theory coupled with quantum transport based on the Landauer
formalism. With a rigorous band structure analysis, we show the effect of
strain on the K-point, and calculate the directional piezoresistances for the
buckled Xenes as per their critical strain limit. Further, we compare the
relevant gauge factors, and their sinusoidal dependences on the transport angle
akin to silicene and graphene. The strain-insensitive transport angles
corresponding to the zero gauge factors are 81 degree and 34 degree for
armchair and zigzag strains, respectively, for silicene and germanene. For
stanene as the strain limit is extended to 10% and notable changes in the
fundamental parameters, the critical angle for stanene along armchair and
zigzag directions are 69 degree and 34 degree respectively. The small values of
gauge factors are attributed to their stable Dirac cones and strain-independent
valley degeneracies. We also explore conductance modulation, which is quantized
in nature and exhibits a similar pattern with other transport parameters
against a change in strain. Based on the obtained results, we propose the
buckled Xenes as an interconnect in flexible electronics and are promising
candidates for various applications in straintronics.


  This paper presents an efficient multi-fidelity Bayesian optimization
approach for analog circuit synthesis. The proposed method can significantly
reduce the overall computational cost by fusing the simple but potentially
inaccurate low-fidelity model and a few accurate but expensive high-fidelity
data. Gaussian Process (GP) models are employed to model the low- and
high-fidelity black-box functions separately. The nonlinear map between the
low-fidelity model and high-fidelity model is also modelled as a Gaussian
process. A fusing GP model which combines the low- and high-fidelity models can
thus be built. An acquisition function based on the fusing GP model is used to
balance the exploitation and exploration. The fusing GP model is evolved
gradually as new data points are selected sequentially by maximizing the
acquisition function. Experimental results show that our proposed method
reduces up to 65.5\% of the simulation time compared with the state-of-the-art
single-fidelity Bayesian optimization method, while exhibiting more stable
performance and a more promising practical prospect.


  We study experimentally the propagation dynamics and interaction of spatial
optical solitons in a bias-free cell filled with nematic liquid crystals. We
reveal and measure long-range effects due to the cell boundaries for a single
nematicon as well as for the interacting in-phase and out-of-phase nematicons.
We discuss the effect of initial beam focusing and relative input angle on the
interaction of in-phase nematicons.


  Let S be a closed orientable surface of genus at least 2 and let G be a
semisimple real algebraic group of non-compact type. We consider a class of
representations from the fundamental group of S to G called positively ratioed
representations. These are Anosov representations with the additional condition
that certain associated cross ratios satisfy a positivity property. Examples of
such representations include Hitchin representations and maximal
representations. Using geodesic currents, we show that the corresponding length
functions for these positively ratioed representations are well-behaved. In
particular, we prove a systolic inequality that holds for all such positively
ratioed representations.


  Markov Chain Monte Carlo (MCMC) methods for sampling probability density
functions (combined with abundant computational resources) have transformed the
sciences, especially in performing probabilistic inferences, or fitting models
to data. In this primarily pedagogical contribution, we give a brief overview
of the most basic MCMC method and some practical advice for the use of MCMC in
real inference problems. We give advice on method choice, tuning for
performance, methods for initialization, tests of convergence, troubleshooting,
and use of the chain output to produce or report parameter estimates with
associated uncertainties. We argue that autocorrelation time is the most
important test for convergence, as it directly connects to the uncertainty on
the sampling estimate of any quantity of interest. We emphasize that sampling
is a method for doing integrals; this guides our thinking about how MCMC output
is best used.


  A fitness landscape is a mapping from a space of discrete genotypes to the
real numbers. A path in a fitness landscape is a sequence of genotypes
connected by single mutational steps. Such a path is said to be accessible if
the fitness values of the genotypes encountered along the path increase
monotonically. We study accessible paths on random fitness landscapes of the
House-of-Cards type, on which fitness values are independent, identically and
continuously distributed random variables. The genotype space is taken to be a
Cartesian power graph $\mathcal{A}^L$, where $L$ is the number of genetic loci
and the allele graph $\mathcal{A}$ encodes the possible allelic states and
mutational transitions on one locus. The probability of existence of accessible
paths between two genotypes at a distance linear in $L$ displays a transition
from 0 to a positive value at a threshold $\beta_c$ for the fitness difference
between the initial and final genotype. We derive a lower bound on $\beta_c$
for general $\mathcal{A}$ and show that this bound is tight for a large class
of allele graphs. Our results generalize previous results for accessibility
percolation on the biallelic hypercube, and compare favorably to published
numerical results for multiallelic Hamming graphs.


  An adaptive modified weak Galerkin method (AmWG) for an elliptic problem is
studied in this paper, in addition to its convergence and optimality. The
modified weak Galerkin bilinear form is simplified without the need of the
skeletal variable, and the approximation space is chosen as the discontinuous
polynomial space as in the discontinuous Galerkin method. Upon a reliable
residual-based a posteriori error estimator, an adaptive algorithm is proposed
together with its convergence and quasi-optimality proved for the lowest order
case. The primary tool is to bridge the connection between the modified weak
Galerkin method and the Crouzeix-Raviart nonconforming finite element. Unlike
the traditional convergence analysis for methods with a discontinuous
polynomial approximation space, the convergence of AmWG is penalty parameter
free. Numerical results are presented to support the theoretical results.


  We present a ~ 5-yr optical light curve of the recurrent Be/X-ray transient
A0538-66 obtained as a by-product of the MACHO Project. These data reveal both
a long-term modulation at P = 420.8 +/- 0.8 d and a short-term modulation at
16.6510 +/- 0.0022 d which, within errors, confirms the previously found
orbital period. Furthermore, the orbital activity is only seen at certain
phases of the 421 d cycle suggesting that the long-term modulation is related
to variations in the Be star envelope.


  A mechanism for double suppression of flavor-changing neutral currents
(FCNCs) and CP violating phases in supersymmetric models is suggested. At
M_{SUSY} they are suppressed due to a nonabelian discrete flavor symmetry, and
the infrared attractive force of gauge interactions in extra dimensions are
used to suppress them at the compactification scale. We present a concrete
model, which is a simple extension of S_{3} invariant minimal supersymmetric
standard model, where only SU(2)_{L} and SU(3)_{C} gauge multiplets are assumed
to propagate in the bulk. We find that a disorder of two orders of magnitude in
soft supersymmetry breaking parameters above the compactification scale may be
allowed to satisfy experimental constraints on FCNC processes and CP violating
phenomena.


  We obtained spectra of 74 globular clusters in M81. These globular clusters
had been identified as candidates in an HST ACS I-band survey. 68 of these 74
clusters lie within 7' of the M81 nucleus. 62 of these clusters are newly
spectroscopically confirmed, more than doubling the number of confirmed M81 GCs
from 46 to 108. We determined metallicities for our 74 observed clusters using
an empirical calibration based on Milky Way globular clusters. We combined our
results with 34 M81 globular cluster velocities and 33 metallicities from the
literature and analyzed the kinematics and metallicity of the M81 globular
cluster system. The mean of the total sample of 107 metallicities is -1.06 +/-
0.07, higher than either M31 or the Milky Way. We suspect this high mean
metallicity is due to an overrepresentation of metal-rich clusters in our
sample created by the spatial limits of the HST I-band survey. The metallicity
distribution shows marginal evidence for bimodality, with metal-rich and
metal-poor peaks approximately matching those of M31 and the Milky Way. The GC
system as a whole, and the metal-poor GCs alone, show evidence of a radial
metallicity gradient. The M81 globular cluster system as a whole shows strong
evidence of rotation, with V_r(deprojected) = 108 +/- 22 km/s overall. This
result is likely biased toward high rotational velocity due to
overrepresentation of metal-rich, inner clusters. The rotation patterns among
globular cluster subpopulations are roughly similar to those of the Milky Way:
clusters at small projected radii and metal-rich clusters rotate strongly,
while clusters at large projected radii and metal-poor clusters show weaker
evidence of rotation.


  Kerr-Schild metrics have been introduced as a linear superposition of the
flat spacetime metric and a squared null vector field, say $\boldsymbol{k}$,
multiplied by some scalar function, say $H$. The basic assumption which led to
Kerr solution was that $\boldsymbol{k}$ be both geodesic and shearfree. This
condition is relaxed here and Kerr-Schild ansatz is revised by treating
Kerr-Schild metrics as {\it exact linear perturbations} of Minkowski spacetime.
The scalar function $H$ is taken as the perturbing function, so that Einstein's
field equations are solved order by order in powers of $H$. It turns out that
the congruence must be geodesic and shearfree as a consequence of third and
second order equations, leading to an alternative derivation of Kerr solution.


  As quantum computing hardware systems continue to advance, the research and
development of performant, scalable, and extensible software architectures,
languages, models, and compilers is equally as important in order to bring this
novel coprocessing capability to a diverse group of domain computational
scientists. For the field of quantum chemistry, applications and frameworks
exists for modeling and simulation tasks that scale on heterogeneous classical
architectures, and we envision the need for similar frameworks on heterogeneous
quantum-classical platforms. Here we present the XACC system-level quantum
computing framework as a platform for prototyping, developing, and deploying
quantum-classical software that specifically targets chemistry applications. We
review the fundamental design features in XACC, with special attention to its
extensibility and modularity for key quantum programming workflow interfaces,
and provide an overview of the interfaces most relevant to simulations of
chemistry. A series of examples demonstrating some of the state-of-the-art
chemistry algorithms currently implemented in XACC are presented, while also
illustrating the various APIs that would enable the community to extend,
modify, and devise new algorithms and applications in the realm of chemistry.


  Matrix completion, where we wish to recover a low rank matrix by observing a
few entries from it, is a widely studied problem in both theory and practice
with wide applications. Most of the provable algorithms so far on this problem
have been restricted to the offline setting where they provide an estimate of
the unknown matrix using all observations simultaneously. However, in many
applications, the online version, where we observe one entry at a time and
dynamically update our estimate, is more appealing. While existing algorithms
are efficient for the offline setting, they could be highly inefficient for the
online setting.
  In this paper, we propose the first provable, efficient online algorithm for
matrix completion. Our algorithm starts from an initial estimate of the matrix
and then performs non-convex stochastic gradient descent (SGD). After every
observation, it performs a fast update involving only one row of two tall
matrices, giving near linear total runtime. Our algorithm can be naturally used
in the offline setting as well, where it gives competitive sample complexity
and runtime to state of the art algorithms. Our proofs introduce a general
framework to show that SGD updates tend to stay away from saddle surfaces and
could be of broader interests for other non-convex problems to prove tight
rates.


  We derive a consistent set of moments equations for CR-magnetohydrodynamics,
assuming a gyrotropic distribution function (DF). Unlike previous efforts we
derive a closure, akin to the M1 closure in radiation hydrodynamics (RHD), that
is valid in both the nearly-isotropic-DF and/or strong-scattering regimes, and
the arbitrarily-anisotropic DF or free-streaming regimes, as well as allowing
for anisotropic scattering and transport/magnetic field structure. We present
the appropriate two-moment closure and equations for various choices of evolved
variables, including the CR phase space distribution function, number density,
total energy, kinetic energy, and their fluxes or higher moments, and the
appropriate coupling terms to the gas. We show that this naturally includes and
generalizes a variety of terms including convection/fluid motion, anisotropic
CR pressure, streaming, diffusion, gyro-resonant/streaming losses, and
re-acceleration. We discuss how this extends previous treatments of CR
transport including diffusion and moments methods and popular forms of the
Fokker-Planck equation, as well as how this differs from the analogous M1-RHD
equations. We also present two different methods for incorporating a reduced
speed of light (RSOL) to reduce timestep limitations: in both we carefully
address where the RSOL (versus true c) must appear for the correct behavior to
be recovered in all interesting limits, and show how current implementations of
CRs with a RSOL neglect some additional terms.


  In this document we shows a first implementation and some preliminary results
of a new theory, facing Machine Learning problems in the frameworks of
Classical Mechanics and Variational Calculus. We give a general formulation of
the problem and then we studies basic behaviors of the model on simple
practical implementations.


  We construct integrable hierarchies of flows for curves in centroaffine
${\mathbb R}^3$ through a natural pre-symplectic structure on the space of
closed unparametrized starlike curves. We show that the induced evolution
equations for the differential invariants are closely connected with the
Boussinesq hierarchy, and prove that the restricted hierarchy of flows on
curves that project to conics in ${\mathbb{RP}}^2$ induces the
Kaup-Kuperschmidt hierarchy at the curvature level.


  In this paper we investigate the Sagnac effect by calculating the difference
in travel time and phase shift observed for photon beams counter--propagating
in a rotating interferometer on a BTZ black hole solution in the context of
scale-dependent gravity, which describes the field around a massive static and
rotating object in $2+1$ gravity.


  The transport of fluids at the nanoscale is fundamental to manifold
biological and industrial processes, ranging from neurotransmission to
ultrafiltration. Yet, it is only recently that well-controlled channels with
cross-sections as small as a few molecular diameters became an experimental
reality. When aqueous electrolytes are confined within such channels, the
Coulomb interactions between the dissolved ions are reinforced due to
dielectric contrast at the channel walls: we dub this effect `interaction
confinement'. Yet, no systematic way of computing these confined interactions
has been proposed beyond the limiting cases of perfectly metallic or perfectly
insulating channel walls. Here, we introduce a new formalism, based on the
so-called surface response functions, that expresses the effective Coulomb
interactions within a two-dimensional channel in terms of the wall's electronic
structure, described to any desired level of precision. We use it to
demonstrate that in few-nanometer-wide channels, the ionic interactions can be
tuned by the wall material's screening length. We illustrate this approach by
implementing these interactions in brownian dynamics simulations of a strongly
confined electrolyte, and show that the resulting ionic conduction can be
adjusted between Ohm's law and a Wien effect behavior. Our results provide a
quantitative approach to tuning nanoscale ion transport through the electronic
properties of the channel wall material.


  The strong intervening absorption system at redshift 1.15 towards the very
bright quasar HE 0515$-$4414 is the most studied absorber for measuring
possible cosmological variations in the fine-structure constant, $\alpha$. We
observed HE 0515$-$4414 for 16.1$\,$h with the Very Large Telescope and present
here the first constraint on relative variations in $\alpha$ with
parts-per-million (ppm) precision from the new ESPRESSO spectrograph:
$\Delta\alpha/\alpha = 1.3 \pm 1.3_{\rm stat} \pm 0.4_{\rm sys}\,{\rm ppm}$.
The statistical uncertainty (1$\sigma$) is similar to the ensemble precision of
previous large samples of absorbers, and derives from the high S/N achieved
($\approx$105 per 0.4$\,$km$\,$s$^{-1}$ pixel). ESPRESSO's design, and
calibration of our observations with its laser frequency comb, effectively
removed wavelength calibration errors from our measurement. The high resolving
power of our ESPRESSO spectrum ($R=145000$) enabled the identification of very
narrow components within the absorption profile, allowing a more robust
analysis of $\Delta\alpha/\alpha$. The evidence for the narrow components is
corroborated by their correspondence with previously detected molecular
hydrogen and neutral carbon. The main remaining systematic errors arise from
ambiguities in the absorption profile modelling, effects from redispersing the
individual quasar exposures, and convergence of the parameter estimation
algorithm. All analyses of the spectrum, including systematic error estimates,
were initially blinded to avoid human biases. We make our reduced ESPRESSO
spectrum of HE 0515$-$4414 publicly available for further analysis. Combining
our ESPRESSO result with 28 measurements, from other spectrographs, in which
wavelength calibration errors have been mitigated, yields a weighted mean
$\Delta\alpha/\alpha = -0.5 \pm 0.5_{\rm stat} \pm 0.4_{\rm sys}\,$ppm at
redshifts 0.6-2.4.


  We prove that the Frobenius structure constructed from the Gromov-Witten
theory for an orbifold projective line with at most three orbifold points is
uniquely determined by the WDVV equations with certain natural initial
conditions.


  We examine the feasibility of gauge invariant descriptions of the gluon
polarization following the proposal that a gauge field can be decomposed into
its physical part and its pure gauge part. We show that gauge invariant angular
momentum currents can be constructed from summations of gauge variant Noether
currents. We present novel expressions of the pure gauge field, which are used
to formulate gauge invariant descriptions of the gluon spin and the photon
spin. We show that the gauge invariant extension of the Chern-Simons current
can describe the spins of the Laguerre-Gauss laser modes. We also discuss the
relation of gauge invariant operators and the parton distributions constructed
from Dirac variables.


  In this paper, we propose a novel concept for engineered molecular
communication (MC) systems inspired by animal olfaction. We focus on a
multi-user scenario where transmitters employ unique mixtures of different
types of signaling molecules to convey their messages to a central receiver,
which is equipped with an array comprising $R$ different types of receptors to
detect the emitted molecule mixtures. The hardware complexity of an MC system
employing \textit{orthogonal} molecule-receptor pairs would linearly scale with
the number of signaling molecule types $Q$ (i.e., $R=Q$). Natural olfaction
systems avoid such high complexity by employing arrays of
\textit{cross-reactive} receptors, where each type of molecule activates
multiple types of receptors and each type of receptor is predominantly
activated by multiple types of molecules albeit with different activation
strengths. For instance, the human olfactory system is believed to discriminate
several thousands of chemicals using only a few hundred receptor types, i.e.,
$Q\gg R$. Motivated by this observation, we first develop an end-to-end MC
channel model that accounts for the key properties of olfaction. Subsequently,
we formulate the molecule mixture recovery as a convex compressive sensing (CS)
problem which can be efficiently solved via available numerical solvers. Our
simulation results confirm the efficiency of the proposed CS problem for the
recovery of the molecular mixture signal and quantify the system performance
for various system parameters.


  In this paper, we quantify the ability of a future measurement of the
Sandage-Loeb test signal from the Cosmic-Dynamic-Experiment-like spectrograph
to constrain some popular modified gravity theories including DGP brane-world
scenario, $f(R)$ modified gravity and $f(T)$ gravity theory. We find that the
Sandage-Loeb test measurements are able to break degeneracies between model
parameters markedly and thus greatly improve cosmological constraints for all
concerned modified gravity theories when combined with the latest observations
of CMB--shift parameter. However, they yield almost the same degeneracy
directions between model parameters as that from the distance ratio data
derived from the latest observations of the cosmic microwave background and
baryonic acoustic oscillations (CMB/BAO). Moreover, for the $f(R)$ modified
gravity, the Sandage-Loeb test could provide completely different bounded
regions in model parameters space as compared to CMB/BAO and thus supplement
strong complementary constraints.


  Motivated by the Langlands program in representation theory, number theory
and geometry, the theory of representations of a reductive $p$-adic group over
a coefficient ring different from the field of complex numbers has been widely
developped during the last two decades. This article provides a survey of basic
results obtained in the 21st century.


  This study was conducted to examine and understand the spending behavior of
low income households (B40), namely households with income of RM3800 and below.
The study focused on the area Kubang Pasu District, Kedah.


  Cities are centers for the integration of capital and incubators of
invention, and attracting venture capital (VC) is of great importance for
cities to advance in innovative technology and business models towards a
sustainable and prosperous future. Yet we still lack a quantitative
understanding of the relationship between urban characteristics and VC
activities. In this paper, we find a clear nonlinear scaling relationship
between VC activities and the urban population of Chinese cities. In such
nonlinear systems, the widely applied linear per capita indicators would be
either biased to larger cities or smaller cities depends on whether it is
superlinear or sublinear, while the residual of cities relative to the
prediction of scaling law is a more objective and scale-invariant metric.
%(i.e., independent of the city size). Such a metric can distinguish the
effects of local dynamics and scaled growth induced by the change of population
size. The spatiotemporal evolution of such metrics on VC activities reveals
three distinct groups of cities, two of which stand out with increasing and
decreasing trends, respectively. And the taxonomy results together with spatial
analysis also signify different development modes between large urban
agglomeration regions. Besides, we notice the evolution of scaling exponents on
VC activities are of much larger fluctuations than on socioeconomic output of
cities, and a conceptual model that focuses on the growth dynamics of different
sized cities can well explain it, which we assume would be general to other
scenarios.


  In this paper mathematical models are formulated in order to simulate heat
production and corresponding temperature changes which accompany the
propagation of an axon potential. Based on earlier experimental results,
several models are proposed. Together with the earlier system of coupled
differential equations derived by the authors for describing the electrical and
mechanical components of signalling in nerve fibres, the novel results permit
to cast the whole process of signalling into one system. The emphasis is on the
mathematical description of coupling forces. The numerical results are
qualitatively similar to experiments.


  We study the most common image and informal description of the optimal
transport problem for quadratic cost, also known as the second boundary value
problem for the Monge--Amp\`{e}re equation -- What is the most efficient way to
fill a hole with a given pile of sand? -- by proving regularity results for
optimal transports between degenerate densities. In particular, our work
contains an analysis of the setting in which holes and sandpiles are
represented by absolutely continuous measures concentrated on bounded convex
domains whose densities behave like nonnegative powers of the distance
functions to the boundaries of these domains.


  We present late-time ($\sim$240-260 days after peak brightness) optical
photometry and nebular (+236 and +264 days) spectroscopy of SN 2018oh, the
brightest Type Ia supernova (SN Ia) observed by the Kepler telescope. The
Kepler/K2 30-minute cadence observations started days before explosion and
continued past peak brightness. For several days after explosion, SN 2018oh had
blue "excess" flux in addition to a normal SN rise. The flux excess can be
explained by the interaction between the SN and a Roche-lobe filling
non-degenerate companion star. Such a scenario should also strip material from
the companion star, that would emit once the SN ejecta become optically thin,
imprinting relatively narrow emission features in its nebular spectrum. We
search our nebular spectra for signs of this interaction, including close
examination of wavelengths of hydrogen and helium transitions, finding no
significant narrow emission. We place upper limits on the luminosity of these
features of $2.6,\ 2.9\ \mathrm{and}\ 2.1\times10^{37}\ \mathrm{erg\ s^{-1}}$
for H$\alpha$, He I $\lambda$5875, and He I $\lambda$6678, respectively.
Assuming a simple model for the amount of swept-up material, we estimate upper
mass limits for hydrogen of $5.4\times10^{-4}\ \mathrm{M_{\odot}}$ and helium
of $4.7\times10^{-4}\ \mathrm{M_{\odot}}$. Such stringent limits are unexpected
for the companion-interaction scenario consistent with the early data. No known
model can explain the excess flux, its blue color, and the lack of late-time
narrow emission features.


  Cued and un-cued cell polarization is a fundamental mechanism in cell
biology. As an alternative to the classical Turing bifurcation, it has been
proposed that the cell polarity might onset by means of the well-known
phenomenon of wave-pinning (Gamba et al, PNAS, 2005). A particularly simple and
elegant model of wave-pinning has been proposed by Edelstein-Keshet and
coworkers (Biop. J., 2008). However, biomolecular networks do communicate with
other networks as well as with the external world. As such, their dynamics has
to be considered as perturbed by extrinsic noises. These noises may have both a
spatial and a temporal correlation, but any case they must be bounded to
preserve the biological meaningfulness of the perturbed parameters. Here we
numerically show that the inclusion of external spatio-temporal bounded
perturbations may sometime destroy the polarized state. The polarization loss
depends on both the extent of temporal and spatial correlations, and on the
kind of adopted noise. Namely, independently of the specific model of noise, an
increase of the spatial correlation induces an increase of the probability of
polarization. However, if the noise is spatially homogeneous then the
polarization is lost in the majority of cases. On the contrary, an increase of
the temporal autocorrelation of the noise induces an effect that depends on the
noise model.


  We construct an extended oriented $(2+\epsilon)$-dimensional topological
field theory, the character field theory $X_G$ attached to a affine algebraic
group in characteristic zero, which calculates the homology of character
varieties of surfaces. It is a model for a dimensional reduction of
Kapustin-Witten theory ($N=4$ $d=4$ super-Yang-Mills in the GL twist), and a
universal version of the unipotent character field theory introduced in
arXiv:0904.1247. Boundary conditions in $X_G$ are given by quantum Hamiltonian
$G$-spaces, as captured by de Rham (or strong) $G$-categories, i.e., module
categories for the monoidal dg category $D(G)$ of $D$-modules on $G$. We show
that the circle integral $X_G(S^1)$ (the center and trace of $D(G)$) is
identified with the category $D(G/G)$ of "class $D$-modules", while for an
oriented surface $S$ (with arbitrary decorations at punctures) we show that
$X_G(S)\simeq{\rm H}_*^{BM}(Loc_G(S))$ is the Borel-Moore homology of the
corresponding character stack. We also describe the "Hodge filtration" on the
character theory, a one parameter degeneration to a TFT whose boundary
conditions are given by classical Hamiltonian $G$-spaces, and which encodes a
variant of the Hodge filtration on character varieties.


  The concept of quantum plasmonic excitations in plasmonic lattices, which
similarly to Frenkel excitons in molecular crystals propagate by hopping from
one nanoparticle to another, is introduced. A consistent quantum theory of such
plasmonic excitons, beginning with the quantization of localized surface
plasmons in a metal nanoparticle and including the radiative relaxation in both
1D and 2D lattices near a reflective substrate surface, is developed. A
possible room-temperature Bose-Einstein condensation in the quantum gas of
plasmonic excitons is also discussed.