  We present a detailed theory for finite-frequency conductivities
Re$[\sigma_{\alpha\beta}(\omega)]$ of quantum Hall stripes, which form at
Landau level $N\geq 2$ close to half filling, in the presence of weak Gaussian
disorder. We use an effective elastic theory to describe the low-energy
dynamics of the stripes with the dynamical matrix being determined through
matching the density-density correlation function obtained in the microscopic
time-dependent Hartree-Fock approximation. We then apply replicas and the
Gaussian variational method to deal with the disorder. Within this method, a
set of saddle point equations for the retarded self energies are obtained,
which are solved numerically to get Re$[\sigma_{\alpha\beta}(\omega)]$. We find
a quantum depinning transition as $\Delta\nu$, the fractional part of the
filling factor, approaches a critical value $\Delta\nu_c$ from below. For
$\Delta\nu<\Delta\nu_c$, the pinned state is realized in a replica symmetry
breaking (RSB) solution, and the frequency-dependent conductivities in both the
directions perpendicular and parallel to the stripes show resonant peaks. These
peaks shift to zero frequency as $\Delta\nu\to \Delta\nu_c$. For
$\Delta\nu\ge\Delta \nu_c$, we find a partial RSB (PRSB) solution in which
there is RSB perpendicular to the stripes, but replica symmetry along the
stripes, leading to free sliding along the stripe direction. The quantum
depinning transition is in the Kosterlitz-Thouless universality class. The
result is consistent with a previous renormalization group analysis.


  The use of blackbox solvers inside neural networks is a relatively new area
which aims to improve neural network performance by including proven, efficient
solvers for complex problems. Existing work has created methods for learning
networks with these solvers as components while treating them as a blackbox.
This work attempts to improve upon existing techniques by optimizing not only
over the primary loss function, but also over the performance of the solver
itself by using Time-cost Regularization. Additionally, we propose a method to
learn blackbox parameters such as which blackbox solver to use or the heuristic
function for a particular solver. We do this by introducing the idea of a
hyper-blackbox which is a blackbox around one or more internal blackboxes.


  Ranking lists are often provided at regular time intervals by one or multiple
rankers in a range of applications, including sports, marketing, and politics.
Most popular methods for rank-order data postulate a linear specification for
the latent scores, which determine the observed ranks, and ignore the temporal
dependence of the ranking lists. To address these issues, novel nonparametric
static (ROBART) and autoregressive (ARROBART) models are introduced, with
latent scores defined as nonlinear Bayesian additive regression tree functions
of covariates. To make inferences in the dynamic ARROBART model, closed-form
filtering, predictive, and smoothing distributions for the latent time-varying
scores are derived. These results are applied in a Gibbs sampler with data
augmentation for posterior inference. The proposed methods are shown to
outperform existing competitors in simulation studies, and the advantages of
the dynamic model are demonstrated by forecasts of weekly pollster rankings of
NCAA football teams.


  Single-Wall Carbon Nanotubes (SWNTs) are among the very few candidates for
single-photon sources operating in the telecom bands since they exhibit large
photon antibunching up to room temperature. However, coupling a nanotube to a
photonic structure is highly challenging because of the random location and
emission wavelength in the growth process. Here, we demonstrate the realization
of a widely tunable single-photon source by using a carbon nanotube inserted in
an original repositionable fiber micro-cavity : we fully characterize the
emitter in the free-space and subsequently form the cavity around the nanotube.
This brings an invaluable insight into the emergence of quantum
electrodynamical effects. We observe an efficient funneling of the emission
into the cavity mode with a strong sub-Poissonian statistics together with an
up to 6-fold Purcell enhancement factor. By exploiting the cavity feeding
effect on the phonon wings, we locked the single-photon emission at the cavity
frequency over a 4~THz-wide band while keeping the mode width below 80~GHz.
This paves the way to multiplexing and multiple qubit coupling.


  This article presents new parabolic and elliptic type gradient estimates for
positive smooth solutions to a nonlinear parabolic equation involving the
Witten Laplacian in the context of smooth metric measure spaces. The metric and
potential here are time dependent and evolve under a super Perelman-Ricci flow.
The estimates are derived under natural lower bounds on the associated
generalised Bakry-\'Emery Ricci curvature tensors and are utilised in
establishing fairly general local and global bounds, Harnack-type inequalities
and Liouville-type global constancy theorems to mention a few. Other
implications and consequences of the results are also discussed.


  We analyse the complexity of learning first-order queries in a
model-theoretic framework for supervised learning introduced by (Grohe and
Tur\'an, TOCS 2004). Previous research on the complexity of learning in this
framework focussed on the question of when learning is possible in time
sublinear in the background structure.
  Here we study the parameterized complexity of the learning problem. We have
two main results. The first is a hardness result, showing that learning
first-order queries is at least as hard as the corresponding model-checking
problem, which implies that on general structures it is hard for the
parameterized complexity class AW[*]. Our second main contribution is a
fixed-parameter tractable agnostic PAC learning algorithm for first-order
queries over sparse relational data (more precisely, over nowhere dense
background structures).


  Congestion prediction represents a major priority for traffic management
centres around the world to ensure timely incident response handling. The
increasing amounts of generated traffic data have been used to train machine
learning predictors for traffic, however this is a challenging task due to
inter-dependencies of traffic flow both in time and space. Recently, deep
learning techniques have shown significant prediction improvements over
traditional models, however open questions remain around their applicability,
accuracy and parameter tuning. This paper proposes an advanced deep learning
framework for simultaneously predicting the traffic flow on a large number of
monitoring stations along a highly circulated motorway in Sydney, Australia,
including exit and entry loop count stations, and over varying training and
prediction time horizons. The spatial and temporal features extracted from the
36.34 million data points are used in various deep learning architectures that
exploit their spatial structure (convolutional neuronal networks), their
temporal dynamics (recurrent neuronal networks), or both through a hybrid
spatio-temporal modelling (CNN-LSTM). We show that our deep learning models
consistently outperform traditional methods, and we conduct a comparative
analysis of the optimal time horizon of historical data required to predict
traffic flow at different time points in the future.


  Surveillance and exploration of large environments is a tedious task. In
spaces with limited environmental cues, random-like search is an effective
approach as it allows the robot to perform online coverage of environments
using simple algorithm designs. One way to generate random-like scanning search
is to use nonlinear dynamical systems to impart chaos into the searching
robot's controller. This will result in the generation of unpredictable yet
deterministic trajectories, allowing designers to control the system and
achieve a high scanning coverage of an area. However, the unpredictability
comes at the cost of increased coverage time and a lack of scalability, both of
which have been ignored by the state-of-the-art chaotic path planners. This
work introduces a new, scalable technique that helps a robot to steer away from
the obstacles and cover the entire search space in a short period of time. The
technique involves coupling and manipulating two chaotic systems to reduce the
coverage time and enable scanning of unknown environments with different online
properties. Using this new technique resulted in an average 49% boost in the
robot's performance compared to the state-of-the-art planners. the overall
search performance of the chaotic planner remained comparable to optimal
systems while still ensuring unpredictable paths.


  We study a family of Maxwell-Higgs models, described by the inclusion of a
function of the scalar field that represent generalized magnetic permeability.
We search for vortex configurations which obey first-order differential
equations that solve the equations of motion. We first deal with the asymptotic
behavior of the field configurations, and then implement a numerical study of
the solutions, the energy density and the magnetic field. We work with the
generalized permeability having distinct profiles, giving rise to new models,
and we investigate how the vortices behave, compared with the solutions of the
corresponding standard models. In particular, we show how to build compact
vortices, that is, vortex solutions with the energy density and magnetic field
vanishing outside a compact region of the plane.


  The residual closure of a subgroup $H$ of a group $G$ is the intersection of
all virtually normal subgroups of $G$ containing $H$. We show that if $G$ is
generated by finitely many cosets of $H$ and if $H$ is commensurated, then the
residual closure of $H$ in $G$ is virtually normal. This implies that separable
commensurated subgroups of finitely generated groups are virtually normal. A
stream of applications to separable subgroups, polycyclic groups, residually
finite groups, groups acting on trees, lattices in products of trees and
just-infinite groups then flows from this main result.


  We discuss the angular correlation function of Sunyaev-Zel'dovich
(SZ)-detected galaxy clusters as a cosmological probe. As a projection of the
real-space cluster correlation function, the angular function samples the
underlying SZ catalog redshift distribution. It offers a way to study cosmology
and cluster evolution directly with the two-dimensional catalog, even before
extensive follow-up observations, thereby facilitating the immediate scientific
return from SZ surveys. As a simple illustration of the information content of
the angular function, we examine its dependence on the parameter pair Om_m,
sigma_8 in flat cosmologies. We discuss sources of modeling uncertainty and
consider application to the future Planck SZ catalog, showing how these two
parameters and the normalization of the SZ flux-mass relation can be
simultaneously found when the local X-ray cluster abundance constraint is
included.


  In real life, success is often contingent upon multiple critical steps that
are distant in time from each other and from the final reward. These critical
steps are challenging to identify with traditional reinforcement learning (RL)
methods that rely on the Bellman equation for credit assignment. Here, we
present a new RL algorithm that uses offline contrastive learning to hone in on
these critical steps. This algorithm, which we call Contrastive Retrospection
(ConSpec), can be added to any existing RL algorithm. ConSpec learns a set of
prototypes for the critical steps in a task by a novel contrastive loss and
delivers an intrinsic reward when the current state matches one of the
prototypes. The prototypes in ConSpec provide two key benefits for credit
assignment: (i) They enable rapid identification of all the critical steps.
(ii) They do so in a readily interpretable manner, enabling out-of-distribution
generalization when sensory features are altered. Distinct from other
contemporary RL approaches to credit assignment, ConSpec takes advantage of the
fact that it is easier to retrospectively identify the small set of steps that
success is contingent upon (and ignoring other states) than it is to
prospectively predict reward at every taken step. ConSpec greatly improves
learning in a diverse set of RL tasks. The code is available at the link:
https://github.com/sunchipsster1/ConSpec


  Depth is one of the keys that make neural networks succeed in the task of
large-scale image recognition. The state-of-the-art network architectures
usually increase the depths by cascading convolutional layers or building
blocks. In this paper, we present an alternative method to increase the depth.
Our method is by introducing computation orderings to the channels within
convolutional layers or blocks, based on which we gradually compute the outputs
in a channel-wise manner. The added orderings not only increase the depths and
the learning capacities of the networks without any additional computation
costs, but also eliminate the overlap singularities so that the networks are
able to converge faster and perform better. Experiments show that the networks
based on our method achieve the state-of-the-art performances on CIFAR and
ImageNet datasets.


  Warm dense matter (WDM) has emerged as one of the frontiers of both
experimental and theoretical physics and is challenging traditional concepts of
plasma, atomic, and condensed-matter physics. While it has become common
practice to model correlated electrons in WDM within the framework of Kohn-Sham
density functional theory, quantitative benchmarks of exchange-correlation (XC)
functionals under WDM conditions are yet incomplete. Here, we present the first
assessment of common XC functionals against exact path-integral Monte Carlo
calculations of the harmonically perturbed thermal electron gas. This system is
directly related to the numerical modeling of X-Ray scattering experiments on
warm dense samples. Our assessment yields the parameter space where common XC
functionals are applicable. More importantly, we pinpoint where the tested XC
functionals fail when perturbations on the electronic structure are imposed. We
indicate the lack of XC functionals that take into account the needs of WDM
physics in terms of perturbed electronic structures.


  We consider a simple setup in which a small quantum dot is strongly connected
to a finite size box. This box can be either a metallic box or a finite size
quantum wire.The formation of the Kondo screening cloud in the box strongly
depends on the ratio between the Kondo temperature and the box level spacing.
By weakly connecting two metallic reservoirs to the quantum dot, a detailed
spectroscopic analysis can be performed. Since the transport channels and the
screening channels are almost decoupled, such a setup allows an easier access
to the measure of finite-size effects associated with the finite extension of
the Kondo cloud.


  We propose a statistical model for static and sliding friction between rough
surfaces. Approximating the contact between rough surfaces by the contact of an
ensemble of one-dimensional viscoelastic elements with a rough rigid surface,
we study the collective behavior of the elements. We find that collective
response of the contacts can lead to macroscopic behavior very different from
the microscopic behavior. Specifically, various observed features of friction
emerge as collective phenomena, without postulating them directly at the
microscale. We discuss how parameters in our model can be related to material
and surface properties of the contacting surfaces. We compare our results to
commonly used rate and state phenomenological models, and propose a new
interpretation of the state variable.


  Fix an integer $d \geq 0$, a field $\mathbb{F}$, and a vector space $V$ over
$\mathbb{F}$ with dimension $d+1$. By a decomposition of $V$ we mean a sequence
$\{V_i\}_{i=0}^d$ of $1$-dimensional subspaces of $V$ whose sum is $V$. For a
linear transformation $A$ from $V$ to $V$, we say $A$ lowers $\{V_i\}_{i=0}^d$
whenever $A V_i = V_{i-1}$ for $0 \leq i \leq d$, where $V_{-1}=0$. We say $A$
raises $\{V_i\}_{i=0}^d$ whenever $A V_i = V_{i+1}$ for $0 \leq i \leq d$,
where $V_{d+1}=0$. An ordered pair of linear transformations $A,B$ from $V$ to
$V$ is called LR whenever there exists a decomposition $\{V_i\}_{i=0}^d$ of $V$
that is lowered by $A$ and raised by $B$. In this case the decomposition
$\{V_i\}_{i=0}^d$ is uniquely determined by $A,B$; we call it the
$(A,B)$-decomposition of $V$. Consider a $3$-tuple of linear transformations
$A$, $B$, $C$ from $V$ to $V$ such that any two of $A$, $B$, $C$ form an LR
pair on $V$. Such a $3$-tuple is called an LR triple on $V$. Let $\alpha$,
$\beta$, $\gamma$ be nonzero scalars in $\mathbb{F}$. The triple $\alpha A,
\beta B, \gamma C$ is an LR triple on $V$, said to be associated to $A,B,C$.
Let $\{V_i\}_{i=0}^d$ be a decomposition of $V$ and let $X$ be a linear
transformation from $V$ to $V$. We say $X$ is tridiagonal with respect to
$\{V_i\}_{i=0}^d$ whenever $X V_i \subseteq V_{i-1} + V_i + V_{i+1}$ for $0
\leq i \leq d$. Let $\cal X$ be the vector space over $\mathbb{F}$ consisting
of the linear transformations from $V$ to $V$ that are tridiagonal with respect
to the $(A,B)$ and $(B,C)$ and $(C,A)$ decompositions of $V$. There is a
special class of LR triples, called $q$-Weyl type. In the present paper, we
find a basis of $\cal X$ for each LR triple that is not associated to an LR
triple of $q$-Weyl type.


  We propose a super-resolution (SR) simulation system that consists of a
physics-based meteorological simulation and an SR method based on a deep
convolutional neural network (CNN). The CNN is trained using pairs of
high-resolution (HR) and low-resolution (LR) images created from meteorological
simulation results for different resolutions so that it can map LR simulation
images to HR ones. The proposed SR simulation system, which performs LR
simulations, can provide HR prediction results in much shorter operating cycles
than those required for corresponding HR simulation prediction system. We apply
the SR simulation system to urban micrometeorology, which is strongly affected
by buildings and human activity. Urban micrometeorology simulations that need
to resolve urban buildings are computationally costly and thus cannot be used
for operational real-time predictions even when run on supercomputers. We
performed HR micrometeorology simulations on a supercomputer to obtain datasets
for training the CNN in the SR method. It is shown that the proposed SR method
can be used with a spatial scaling factor of 4 and that it outperforms
conventional interpolation methods by a large margin. It is also shown that the
proposed SR simulation system has the potential to be used for operational
urban micrometeorology predictions.


  The inclusive top quark pair ($t\bar{t}$) production cross-section
$\sigma_{t\bar{t}}$ has been measured in proton$-$proton collisions at
$\sqrt{s}=13$ TeV, using $36.1$ fb$^{-1}$ of data collected in 2015$-$16 by the
ATLAS experiment at the LHC. Using events with an opposite-charge $e\mu$ pair
and $b$-tagged jets, the cross-section is measured to be:
\begin{equation}\nonumber \sigma_{t\bar{t}} = 826.4 \pm 3.6\,\mathrm{(stat)}\
\pm 11.5\,\mathrm{(syst)}\ \pm 15.7\,\mathrm{(lumi)}\ \pm
1.9\,\mathrm{(beam)}\,\mathrm{pb}, \end{equation} where the uncertainties
reflect the limited size of the data sample, experimental and theoretical
systematic effects, the integrated luminosity, and the LHC beam energy, giving
a total uncertainty of 2.4%. The result is consistent with theoretical QCD
calculations at next-to-next-to-leading order. It is used to determine the top
quark pole mass via the dependence of the predicted cross-section on
$m_t^{\mathrm{pole}}$, giving $m_t^{\mathrm{pole}}=173.1^{+2.0}_{-2.1}$ GeV. It
is also combined with measurements at $\sqrt{s}=7$ TeV and $\sqrt{s}=8$ TeV to
derive ratios and double ratios of $t\bar{t}$ and $Z$ cross-sections at
different energies. The same event sample is used to measure absolute and
normalised differential cross-sections as functions of single-lepton and
dilepton kinematic variables, and the results compared with predictions from
various Monte Carlo event generators.


  A semiclassical approximation for the matrix elements of a quantum chaotic
propagator in the scar function basis has been derived. The obtained expression
is solely expressed in terms of canonical invariant objects. For our purpose,
we have used, the recently developed, semiclassical matrix elements of the
propagator in coherent states, together with the linearization of the flux in
the neighborhood of a classically unstable periodic orbit of chaotic two
dimensional systems. The expression here derived is successfully verified to be
exact for a (linear) cat map, after the theory is adapted to a discrete phase
space appropriate to a quantized torus.


  It is shown in this paper that recent results that below the Fermi
temperature, Fermions obey anomalous semionic statistics, could explain such
apparently diverse phenomena as the magnetism of Pulsars and White Dwarfs on
the one hand and earth like planets, on the other.


  The dynamic process of assisted magnetic switchins has been simulated to
investigate the associated physics. The model uses a Voronoi construction to
determine the physical structure of the nano granular thin film recording
media; and the Landau-Lifshitz-Bloch (LLB) equation is solved to evolve the
magnetic system in time. The reduction of the magnetization is determined over
a range of peak system temperatures and for a number of anisotropy values. The
results show that the HAMR process is not simply magnetization reversal over a
thermally reduced energy barrier. To achieve full magnetization reversal (for
all anisotropies investigated) an applied field strength of at least 6kOe is
required and the peak system temperature must reach at least the Curie point
(Tc). When heated to Tc the magnetization associated with each grain is
destroyed, which invokes the non-precessional linear reversal mode. Reversing
the magnetization through this linear reversal mode is favourable, as the
reversal time is two orders of magnitude smaller than that associated with
precession. Under these conditions, as the temperature decreases to ambient,
the magnetization recovers in the direction of the applied field, completing
the reversal process. Also the model produces results which are consistent with
the concept of thermal writability; when heating the media to Tc, the smaller
grains require a larger field strength to reverse the magnetization.


  We derive the Lagrangian and the transformation laws of N=4 gauged
supergravity coupled to matter multiplets whose sigma-model of the scalars is
SU(1,1)/U(1)x SO(6,6+n)/SO(6)xSO(6+n) and which corresponds to the effective
Lagrangian of the Type IIB string compactified on the T^6/Z_2 orientifold with
fluxes turned on and in presence of n D3-branes. The gauge group is T^12 x G
where G is the gauge group on the brane and T^12 is the gauge group on the bulk
corresponding to the gauged translations of the R-R scalars coming from the R-R
four--form. The N=4 bulk sector of this theory can be obtained as a truncation
of the Scherk-Schwarz spontaneously broken N=8 supergravity. Consequently the
full bulk spectrum satisfies quadratic and quartic mass sum rules, identical to
those encountered in Scherk-Schwarz reduction gauging a flat group. This theory
gives rise to a no scale supergravity extended with partial super-Higgs
mechanism.


  We present optical and ultraviolet (UV) observations of a luminous type Ia
supernova (SN Ia) SN 2015bq characterized by the early flux excess. This SN
reaches a B-band absolute magnitude at $M_B = -19.68 \pm 0.41$ mag and a peak
bolometric luminosity at $L = (1.75 \pm 0.37) \times 10^{43}$ erg s$^{-1}$,
with a relatively small post-maximum decline rate [$\Delta m_{15}(B) = 0.82 \pm
0.05$ mag]. The flux excess observed in the light curves of SN 2015bq a few
days after the explosion, especially seen in the UV bands, might be due to the
radioactive decay of $^{56}$Ni mixed into the surface. The radiation from the
decay of the surface $^{56}$Ni heats the outer layer of this SN. It produces
blue $U-B$ color followed by monotonically reddening in the early phase,
dominated iron-group lines, and weak intermediate-mass elements absorption
features in the early spectra. The scenario of enhanced $^{56}$Ni in the
surface is consistent with a large amount of $^{56}$Ni ($M_{ \rm ^{56}{\rm
Ni}}$ = 0.97 $\pm 0.20$ $M_{\odot}$) synthesized during the explosion. The
properties of SN 2015bq are found to locate between SN 1991T and SN 1999aa,
suggesting the latter two subclasses of SNe Ia may have a common origin.


  Statefinder diagnostic is a useful method which can differ one dark energy
model from the others. The Statefinder pair $\{r, s\}$ is algebraically related
to the equation of state of dark energy and its first time derivative. We apply
in this paper this method to the dilaton dark energy model based on Weyl-Scaled
induced gravitational theory. We investigate the effect of the coupling between
matter and dilaton when the potential of dilaton field is taken as the Mexican
hat form. We find that the evolving trajectory of our model in the $r-s$
diagram is quite different from those of other dark energy models.


  Deep packet inspection is widely recognized as a powerful way which is used
for intrusion detection systems for inspecting, deterring and deflecting
malicious attacks over the network. Fundamentally, almost intrusion detection
systems have the ability to search through packets and identify contents that
match with known attacks. In this paper, we survey the deep packet inspection
implementations techniques, research challenges and algorithms. Finally, we
provide a comparison between the different applied systems.


  The detection of fluorescence with submolecular resolution enables the
exploration of spatially varying photon yields and vibronic properties at the
single-molecule level. By placing individual polycyclic aromatic hydrocarbon
molecules into the plasmon cavity formed by the tip of a scanning tunneling
microscope and a NaCl-covered Ag(111) surface, molecular light emission spectra
are obtained that unravel vibrational progression. In addition, light spectra
unveil a signature of the molecule even when the tunneling current is injected
well separated from the molecular emitter. This signature exhibits a
distance-dependent Fano profile that reflects the subtle interplay between
inelastic tunneling electrons, the molecular exciton and localized plasmons in
at-distance as well as on-molecule fluorescence. The presented findings open
the path to luminescence of a different class of molecules than investigated
before and contribute to the understanding of single-molecule luminescence at
surfaces in a unified picture.


  Nuclear Magnetic Resonance (NMR) Spectroscopy is a widely used technique to
predict the native structure of proteins. However, NMR machines are only able
to report approximate and partial distances between pair of atoms. To build the
protein structure one has to solve the Euclidean distance geometry problem
given the incomplete interval distance data produced by NMR machines. In this
paper, we propose a new genetic algorithm for solving the Euclidean distance
geometry problem for protein structure prediction given sparse NMR data. Our
genetic algorithm uses a greedy mutation operator to intensify the search, a
twin removal technique for diversification in the population and a random
restart method to recover stagnation. On a standard set of benchmark dataset,
our algorithm significantly outperforms standard genetic algorithms.


  We present optical through radio observations of the host galaxies of two
dust obscured, luminous quasars selected in the mid-infrared, at z=2.62 and
z=2.99, including a search for CO emission. Our limits on the CO luminosities
are consistent with these objects having masses of molecular gas <~10^10 solar
masses, several times less than those of luminous submillimeter-detected
galaxies (SMGs) at comparable redshifts. Their near-infrared spectral energy
distributions, however, imply that these galaxies have high stellar masses
(~10^11-12 solar masses). The relatively small reservoirs of molecular gas and
low dust masses are consistent with them being relatively mature systems at
high-z.


  We present AdaFold, a model-based feedback-loop framework for optimizing
folding trajectories. AdaFold extracts a particle-based representation of cloth
from RGB-D images and feeds back the representation to a model predictive
control to re-plan folding trajectory at every time-step. A key component of
AdaFold that enables feedback-loop manipulation is the use of semantic
descriptors extracted from geometric features. These descriptors enhance the
particle representation of the cloth to distinguish between ambiguous point
clouds of differently folded cloths. Our experiments demonstrate AdaFold's
ability to adapt folding trajectories to cloths with varying physical
properties and generalize from simulated training to real-world execution.


  Flares are a major explosive event in our solar system. They are often
followed by coronal mass ejection that has a potential to trigger the
geomagnetic storms. There are various studies aiming to predict when and where
the flares are likely to occur. Most of these studies mainly discuss the
photospheric and chromospheric activity before the flare onset. In this paper
we study the coronal features before the famous large flare occurrence on
December 13th, 2006. Using the data from Hinode/EUV Imaging Spectrometer (EIS),
X-Ray Telescope (XRT), and Solar and Heliospheric Observatory (SOHO) /Extreme
ultraviolet Imaging Telescope (EIT), we discuss the coronal features in the
large scale (~ a few 100 arcsec) before the flare onset. Our findings are as
follows: 1) The upflows in and around active region start growing from ~10 to
30 km /s a day before the flare. 2) The expanding coronal loops are clearly
observed a few hours before the flare. 3) Soft X-ray and EUV intensity are
gradually reduced. 4) The upflows are further enhanced after the flare. From
these observed signatures, we conclude that the outer part of active region
loops with low density were expanding a day before the flare onset, and the
inner part with high density were expanding a few hours before the onset.


  We study pattern formation in a 2-D reaction-diffusion (RD) sub-cellular
model characterizing the effect of a spatial gradient of a plant hormone
distribution on a family of G-proteins associated with root-hair (RH)
initiation in the plant cell Arabidopsis thaliana. The activation of these
G-proteins, known as the Rho of Plants (ROPs), by the plant hormone auxin, is
known to promote certain protuberances on root hair cells, which are crucial
for both anchorage and the uptake of nutrients from the soil. Our mathematical
model for the activation of ROPs by the auxin gradient is an extension of the
model of Payne and Grierson [PLoS ONE, 12(4), (2009)], and consists of a
two-component Schnakenberg-type RD system with spatially heterogeneous
coefficients on a 2-D domain. The nonlinear kinetics in this RD system model
the nonlinear interactions between the active and inactive forms of ROPs. By
using a singular perturbation analysis to study 2-D localized spatial patterns
of active ROPs, it is shown that the spatial variations in the nonlinear
reaction kinetics, due to the auxin gradient, lead to a slow spatial alignment
of the localized regions of active ROPs along the longitudinal midline of the
plant cell. Numerical bifurcation analysis, together with time-dependent
numerical simulations of the RD system are used to illustrate both 2-D
localized patterns in the model, and the spatial alignment of localized
structures.


  The generation of helical magnetic fields during single field inflation due
to an axial coupling of the electromagnetic field to the inflaton is discussed.
We find that such a coupling always leads to a blue spectrum of magnetic fields
during slow roll inflation. Though the helical magnetic fields further evolve
during the inverse cascade in the radiation era after inflation, we conclude
that the magnetic fields generated by such an axial coupling can not lead to
observed field strength on cosmologically relevant scales.


  The exponential growth in scale and relevance of social networks enable them
to provide expansive insights. Predicting missing links in social networks
efficiently can help in various modern-day business applications ranging from
generating recommendations to influence analysis. Several categories of
solutions exist for the same. Here, we explore various feature extraction
techniques to generate representations of nodes and edges in a social network
that allow us to predict missing links. We compare the results of using ten
feature extraction techniques categorized across Structural embeddings,
Neighborhood-based embeddings, Graph Neural Networks, and Graph Heuristics,
followed by modeling with ensemble classifiers and custom Neural Networks.
Further, we propose combining heuristic-based features and learned
representations that demonstrate improved performance for the link prediction
task on social network datasets. Using this method to generate accurate
recommendations for many applications is a matter of further study that appears
very promising. The code for all the experiments has been made public.


  A model for ac-driven systems, based on the
Tang-Wiesenfeld-Bak-Coppersmith-Littlewood automaton for an elastic medium,
exhibits mode-locked steps with frequencies that are irrational multiples of
the drive frequency, when the pinning is spatially quasiperiodic. Detailed
numerical evidence is presented for the large-system-size convergence of such a
mode-locked step. The irrational mode locking is stable to small thermal noise
and weak disorder. Continuous time models with irrational mode locking and
possible experimental realizations are discussed.


  New measurements of galaxy clustering and background radiations provide
improved constraints on the isotropy and homogeneity of the Universe on large
scales. In particular, the angular distribution of radio sources and the X-Ray
Background probe density fluctuations on scales intermediate between those
explored by galaxy surveys and the Cosmic Microwave Background experiments. On
a scale of $\sim 100 \Mpc$ the rms density fluctuations are at the level of
$\sim 10%$ and on scales larger than $300 \Mpc$ the distribution of both mass
and luminous sources safely satisfies the `Cosmological Principle' of isotropy
and homogeneity. The transition with scale from clumpiness to homogeneity can
be phrased in terms of the fractal dimension of the galaxy and mass
distributions.


  This paper deals with the problem of efficient resource allocation in dynamic
infrastructureless wireless networks. Assuming a reactive interference-limited
scenario, each transmitter is allowed to select one frequency channel (from a
common pool) together with a power level at each transmission trial; hence, for
all transmitters, not only the fading gain, but also the number of interfering
transmissions and their transmit powers are varying over time. Due to the
absence of a central controller and time-varying network characteristics, it is
highly inefficient for transmitters to acquire global channel and network
knowledge. Therefore a reasonable assumption is that transmitters have no
knowledge of fading gains, interference, and network topology. Each
transmitting node selfishly aims at maximizing its average reward (or
minimizing its average cost), which is a function of the action of that
specific transmitter as well as those of all other transmitters. This scenario
is modeled as a multi-player multi-armed adversarial bandit game, in which
multiple players receive an a priori unknown reward with an arbitrarily
time-varying distribution by sequentially pulling an arm, selected from a known
and finite set of arms. Since players do not know the arm with the highest
average reward in advance, they attempt to minimize their so-called regret,
determined by the set of players' actions, while attempting to achieve
equilibrium in some sense. To this end, we design in this paper two joint power
level and channel selection strategies. We prove that the gap between the
average reward achieved by our approaches and that based on the best fixed
strategy converges to zero asymptotically. Moreover, the empirical joint
frequencies of the game converge to the set of correlated equilibria. We
further characterize this set for two special cases of our designed game.


  We prove Ornstein-Zernike behaviour in every direction for finite connection
functions of bond percolation on $\mathbb{Z}^{d}$ for $d\geq3$ when $p,$ the
probability of occupation of a bond, is sufficiently close to $1.$ Moreover, we
prove that equi-decay surfaces are locally analytic, strictly convex, with
positive Gaussian curvature.


  We demonstrate the equivalence of two different conjectures in the literature
for the holographic entanglement negativity in AdS$_3$/CFT$_2$, modulo certain
constants. These proposals involve certain algebraic sums of bulk geodesics
homologous to specific combinations of subsystems, and the entanglement wedge
cross section (EWCS) backreacted by a cosmic brane for the conical defect
geometry in the bulk gravitational path integral. It is observed that the
former conjectures reproduce the field theory replica technique results in the
large central charge limit whereas the latter involves constants related to the
Markov gap. In this context we establish an alternative construction for the
EWCS of a single interval in a CFT$_2$ at a finite temperature to resolve an
issue for the latter proposal involving the thermal entropy elimination for the
holographic entanglement negativity. Our construction for the EWCS correctly
reproduces the corresponding field theory results modulo the Markov gap
constant in the large central charge limit.


  We demonstrate that spatial solitons undergo two consecutive spontaneous
symmetry breakings (SSBs), with the increase of the total power, in nonlinear
photonic crystals (PhCs) built as arrays of alternating linear and nonlinear
stripes, in the case when maxima of the effective refractive index coincide
with minima of the self-focusing coefficient, and vice versa, i.e.,the
corresponding linear and nonlinear periodic potentials are in competition. This
setting may be induced, as a virtual PhC, by means of the EIT
(electromagnetically-induced-transparency) technique, in a uniform optical
medium. It may also be realized as a Bose-Einstein condensate (BEC) subject to
the action of combined periodic optical potential and periodically modulated
Feshbach resonance. The first SSB happens at the center of a linear stripe,
pushing a broad low-power soliton into an adjacent nonlinear stripe and
gradually suppressing side peaks in the soliton's shape. Then, the soliton
restores its symmetry, being pinned to the midpoint of the nonlinear stripe.
The second SSB occurs at higher powers, pushing the narrow soliton off the
center of the nonlinear channel,while the soliton keeps its internal symmetry.
The results are obtained by means of numerical and analytical methods. They may
be employed to control switching of light beams by means of the varying power.


  For a scheme $X$ defined over the length $2$ $p$-typical Witt vectors
$W_2(k)$ of a characteristic $p$ field, we introduce total $p$-differentials
which interpolate between Frobenius-twisted differentials and Buium's
$p$-differentials. They form a sheaf over the reduction $X_0$, and behave as if
they were the sheaf of differentials of $X$ over a deeper base below $W_2(k)$.
This allows us to construct the analogues of Gauss-Manin connections and
Kodaira-Spencer classes as in the Katz-Oda formalism. We make connections to
Frobenius lifts, Borger-Weiland's biring formalism, and Deligne--Illusie
classes.


  This paper presents a new `partitional' approach to understanding or
interpreting standard quantum mechanics (QM). The thesis is that the
mathematics (not the physics) of QM is the Hilbert space version of the math of
partitions on a set and, conversely, the math of partitions is a skeletonized
set level version of the math of QM. Since at the set level, partitions are the
mathematical tool to represent distinctions and indistinctions (or definiteness
and indefiniteness), this approach shows how to interpret the key non-classical
QM notion of superposition in terms of (objective) indefiniteness between
definite alternatives (as opposed to seeing it as the sum of `waves'). Hence
this partitional approach substantiates what might be called the Objective
Indefiniteness Interpretation or what Abner Shimony called the Literal
Interpretation of QM.


  This book chapter is an introduction to and an overview of the
information-theoretic, task independent utility function "Empowerment", which
is defined as the channel capacity between an agent's actions and an agent's
sensors. It quantifies how much influence and control an agent has over the
world it can perceive. This book chapter discusses the general idea behind
empowerment as an intrinsic motivation and showcases several previous
applications of empowerment to demonstrate how empowerment can be applied to
different sensor-motor configuration, and how the same formalism can lead to
different observed behaviors. Furthermore, we also present a fast approximation
for empowerment in the continuous domain.


  Drill string communications are important for drilling efficiency and safety.
The design of a low latency drill string communication system with high
throughput and reliability remains an open challenge. In this paper a deep
learning autoencoder (AE) based end-to-end communication system, where
transmitter and receiver implemented as feed forward neural networks, is
proposed for acousticdrill string communications. Simulation shows that the AE
system is able to outperform a baseline non-contiguous OFDM system in terms of
BER and PAPR, operating with lower latency.


In this paper we introduce and study motives for rational homotopy types.


  An analysis of DAMA data (as reconstructed from DAMA publications) confirms
the presence of an annual oscillation, but with a lower significance level than
that claimed by DAMA. The phase of their signal is 0.39 +/- 0.02, corresponding
to a peak value at about May 22, which is consistent with both the DAMA
estimate and the expected phase of a dark-matter signal. However, a spectrogram
analysis also shows evidence for oscillations in the frequency band 11 - 13
year-1, that are similar to oscillations found in spectrograms formed from
measurements of the decay rates of 36Cl and 32Si acquired at the Brookhaven
National Laboratory (BNL). One component of these oscillations (at 11.44
year-1) is prominent in DAMA/NaI data, at the 0.2% significance level (99.8%
confidence level). Analyses of BNL and other nuclear decay (specifically beta
decay and K-capture) measurements point to a solar influence, either by
neutrinos or by some currently unknown form of radiation. The phase of the
annual oscillation in DAMA data is compatible with an influence of dark matter,
and is unlikely to be attributable to a purely solar influence. We also find
that annual oscillations in both 133Ba decay measurements and the Troitsk
tritium-decay measurements are compatible with a cosmic influence but not with
a purely solar influence. These considerations raise the possibility that DAMA
measurements may somehow be influenced by a combination of solar neutrinos,
cosmic neutrinos, and dark matter


  Magnetic ions such as Fe, Mn and Co with localized spins may be adsorbed on
the surface of topological insulators like \Bi. They form scattering centers
for the helical surface states which have a Dirac cone dispersion as long as
the local spins are disordered. However, the local density of states (LDOS) may
be severely modified by the formation of bound states. Commonly only elastic
scattering due to normal and exchange potentials of the adatom is assumed.
Magnetization measurements show, however, that considerable magnetic single ion
anisotropies exist which lead to a splitting of the local impurity spin states
resulting in a singlet ground state. Therefore inelastic scattering processes
of helical Dirac electrons become possible as described by a dynamical local
self energy of second order in the exchange interaction. The self energy
influences bound state formation and leads to significant new anomalies in the
LDOS at low energies and low temperatures which we calculate within T-matrix
approach. We propose that they may be used for spectroscopy of local impurity
spin states by appropriate tuning of chemical potential and magnetic field.


  What is the effect of the combined direct and indirect social influences-peer
pressure (PP)-on a social groups collective decisions? We present a model that
captures PP as a function of the socio-cultural distance between individuals in
a social group. Using this model and empirical data from 15 real-world social
networks we found that the PP level determines how fast a social group reaches
consensus. More importantly, the levels of PP determine the leaders who can
achieve full control of their social groups. PP can overcome barriers imposed
upon a consensus by the existence of tightly connected communities with local
leaders or the existence of leaders with poor cohesiveness of opinions. A
moderate level of PP is also necessary to explain the rate at which innovations
diffuse through a variety of social groups.


  We consider two- and three-dimensional gravity and gravity-capillary solitary
water waves in infinite depth. Assuming algebraic decay rates for the free
surface and velocity potential, we show that the velocity potential necessarily
behaves like a dipole at infinity and obtain a related asymptotic formula for
the free surface. We then prove an identity relating the "dipole moment" to the
kinetic energy. This implies that the leading-order terms in the asymptotics
are nonvanishing and in particular that the angular momentum is infinite.
Lastly we prove a related integral identity which rules out waves of pure
elevation or pure depression.


  We extend a duality theorem of Schneider-Stuhler about $Ext^i[\pi_1,\pi_2]$
proved there for smooth representations of a $p$-adic group $G$ with central
characters to all smooth representations assuming their result for only
irreducible representations by generalities in homological algebra.


  The eruption of multiple flux tubes in a magnetised plasma atmosphere is
proposed as a mechanism for explosive release of energy in plasmas. Linearly
stable isolated flux tubes are shown to be metastable in a box model magnetised
atmosphere in which ends of the field lines are embedded in conducting walls.
The energy released by destabilising such field lines can be a significant
fraction of the gravitational energy stored in the system. This energy can be
released in a fast dynamical time.


  Networks are a general language for representing relational information among
objects. An effective way to model, reason about, and summarize networks, is to
discover sets of nodes with common connectivity patterns. Such sets are
commonly referred to as network communities. Research on network community
detection has predominantly focused on identifying communities of densely
connected nodes in undirected networks.
  In this paper we develop a novel overlapping community detection method that
scales to networks of millions of nodes and edges and advances research along
two dimensions: the connectivity structure of communities, and the use of edge
directedness for community detection. First, we extend traditional definitions
of network communities by building on the observation that nodes can be densely
interlinked in two different ways: In cohesive communities nodes link to each
other, while in 2-mode communities nodes link in a bipartite fashion, where
links predominate between the two partitions rather than inside them. Our
method successfully detects both 2-mode as well as cohesive communities, that
may also overlap or be hierarchically nested. Second, while most existing
community detection methods treat directed edges as though they were
undirected, our method accounts for edge directions and is able to identify
novel and meaningful community structures in both directed and undirected
networks, using data from social, biological, and ecological domains.


  The goal of this paper is to introduce and study analogues of the Euclidean
Funk and Hilbert metrics on open convex subsets $\Omega$ of hyperbolic or
spherical spaces. At least at a formal level, there are striking similarities
among the three cases: Euclidean, spherical and hyperbolic. We start by
defining non-Euclidean analogues of the Euclidean Funk weak metric and we give
three distinct representations of it in each of the non-Euclidean cases, which
parallel the known situation for the Euclidean case. As a consequence, all of
these metrics are shown to be Finslerian, and the associated norms of the
Finsler metrics are described. The theory is developed by using a set of
classical trigonometric identities on the sphere $S^n$ and the hyperbolic space
$\mathbb{H}^n$ and the definition of a cross ratio on the non-Euclidean spaces
of constant curvature. This in turn leads to the concept of projectivity
invariance in these spaces. We then study the geodesics of the Funk and Hilbert
metrics. In the case of Euclidean (respectively spherical, hyperbolic)
geometry, the Euclidean (respectively spherical, hyperbolic) geodesics are Funk
and Hilbert geodesics. Natural projection maps that exist between the spaces
$\mathbb{R}^n$, $\mathbb{H}^n$ and the upper hemisphere demonstrate that the
theories of Hilbert geometry of convex sets in the three spaces of constant
curvature are all equivalent. The same cannot be said about the Funk
geometries.


  In this paper we present a new correlation inequality and use it for proving
an Almost Sure Local Limit Theorem for the so-called Dickman distribution.
Several related results are also proved


  We have developed a statistical technique to test the model assumption of
binary regime switching extension of the geometric Brownian motion (GBM) model
by proposing a new discriminating statistics. Given a time series data, we have
identified an admissible class of the regime switching candidate models for the
statistical inference. By performing several systematic experiments, we have
successfully shown that the sampling distribution of the test statistics
differs drastically, if the model assumption changes from GBM to Markov
modulated GBM, or to semi-Markov modulated GBM. Furthermore, we have
implemented this statistics for testing the regime switching hypothesis with
Indian sectoral indices.


  We prove local-wellposedness of the mKdV equation in $\mathcal{F}L^{s,p}$
spaces using the new method of M. Christ.


  The moduli space of solutions to Nahm's equations of rank (k,k+j) on the
circle, and hence, of SU(2) calorons of charge (k,j), is shown to be equivalent
to the moduli of holomorphic rank 2 bundles on P^1xP^1 trivialized at infinity
with c_2=k and equipped with a flag of degree j along P^1x{0}. An explicit
matrix description of these spaces is given by a monad construction


  Stein [Statist. Sci. 4 (1989) 432--433] proposed the Mat\'{e}rn-type Gaussian
random fields as a very flexible class of models for computer experiments. This
article considers a subclass of these models that are exactly once mean square
differentiable. In particular, the likelihood function is determined in closed
form, and under mild conditions the sieve maximum likelihood estimators for the
parameters of the covariance function are shown to be weakly consistent with
respect to fixed-domain asymptotics.


  Within the framework of modified gravity model namely Slotheon model,
inspired by the theory of extra dimensions, we explore the behaviour of Dark
Energy and the perturbations thereof. The Dark Energy and matter perturbations
equations are then derived and solved numerically by defining certain
dimensionless variables and properly chosen initial conditions. The results are
compared with those for standard quintessence model and $\Lambda$CDM model. The
matter power spectrum is obtained and also compared with that for $\Lambda$CDM
model. It appears that Dark Energy in Slotheon model is more akin to that for
$\Lambda$CDM model than the standard quintessence model.


  Over-the-air computation (AirComp) leverages the signal-superposition
characteristic of wireless multiple access channels to perform mathematical
computations. Initially introduced to enhance communication reliability in
interference channels and wireless sensor networks, AirComp has more recently
found applications in task-oriented communications, namely, for wireless
distributed learning and in wireless control systems. Its adoption aims to
address latency challenges arising from an increased number of edge devices or
IoT devices accessing the constrained wireless spectrum. This paper focuses on
the physical layer of these systems, specifically on the waveform and the
signal processing aspects at the transmitter and receiver to meet the
challenges that AirComp presents within the different contexts and use cases.


  One can assign to four-dimensional N=2 supersymmetric Heterotic string vacua
a set of classification invariants including a lattice $\Lambda_S$ and
vector-valued modular forms. Some of the classification invariants are
constrained by the condition that the Coulomb branch monodromy matrices should
be integer-valued. We computed numerically the period polynomials of
meromorphic cusp forms for some rank-1 $\Lambda_S$; we then computed the
monodromy matrices and extracted general patterns of the constraints on the
invariants. The constraints we got imply that a large fraction of the Heterotic
string vacua we studied satisfy the necessary conditions for a non-linear sigma
model interpretation in the dual Type IIA description. Our computation can also
be used to identify diffeomorphism classes of real six-dimensional manifolds
that cannot be realized by K3-fibred Calabi--Yau threefolds.


  Ultra-light bosons such as axions or axion-like particles (ALPs), are
promising candidates to solve the dark matter problem. A unique way to detect
such ALPs is to search for the periodic oscillation feature of the position
angles of linearly polarized photons emitted from the regions where ALP dark
matter forms a solitonic core. In this work, we use the high-resolution
polarimetric measurements of the radiation near the super-massive black hole
(SMBH) in the center of the Milky Way, i.e., Sagittarius A$^\star$ (Sgr
A$^\star$), by a sub-array of the Event Horizon Telescope to search for the
ultra-light ALPs. We derive upper limits on the ALP-photon coupling of $\sim
10^{-12}{\rm GeV^{-1}}$ for ALP masses of $m\sim (10^{-19}-10^{-18})$eV. Our
results are stronger than that derived from the observations of SN1987A and a
population of supernovae in the mass window of ($10^{-19}-10^{-17}$)eV.
Improved polarimetric measurements with the full Event Horizon Telescope can
further strengthen the constraints.


  Despite recent advances in reputation technologies, it is not clear how
reputation systems can affect human cooperation in social networks. Although it
is known that two of the major mechanisms in the evolution of cooperation are
spatial selection and reputation-based reciprocity, theoretical study of the
interplay between both mechanisms remains almost uncharted. Here, we present a
new individual-based model for the evolution of reciprocal cooperation between
reputation and networks. We comparatively analyze four of the leading moral
assessment rules---shunning, image scoring, stern judging, and simple
standing---and base the model on the giving game in regular networks for
Cooperators, Defectors, and Discriminators. Discriminators rely on a proper
moral assessment rule. By using individual-based models, we show that the four
assessment rules are differently characterized in terms of how cooperation
evolves, depending on the benefit-to-cost ratio, the network-node degree, and
the observation and error conditions. Our findings show that the most tolerant
rule---simple standing---is the most robust among the four assessment rules in
promoting cooperation in regular networks.


  We develop a sparse hierarchical $hp$-finite element method ($hp$-FEM) for
the Helmholtz equation with rotationally invariant variable coefficients posed
on a two-dimensional disk or annulus. The mesh is an inner disk cell (omitted
if on an annulus domain) and concentric annuli cells. The discretization
preserves the Fourier mode decoupling of rotationally invariant operators, such
as the Laplacian, which manifests as block diagonal mass and stiffness
matrices. Moreover, the matrices have a sparsity pattern independent of the
order of the discretization and admit an optimal complexity factorization. The
sparse $hp$-FEM can handle radial discontinuities in the right-hand side and in
rotationally invariant Helmholtz coefficients. We consider examples such as a
high-frequency Helmholtz equation with radial discontinuities, the
time-dependent Schr\"odinger equation, and an extension to a three-dimensional
cylinder domain, with a quasi-optimal solve, via the Alternating Direction
Implicit (ADI) algorithm.


  Photonic-based low-phase-noise microwave generation with real-time frequency
tuning is crucial for a broad spectrum of subjects, including next-generation
wireless communications, radar, metrology, and modern instrumentation. Here,
for the first time to the best of our knowledge, narrow-bandwidth
dual-wavelength microlasers are generated from nearly degenerate polygon modes
in a high-Q active lithium niobate microdisk. The high-Q polygon modes
formation with independently controllable resonant wavelengths and free
spectral ranges is enabled by the weak perturbation of the whispering gallery
microdisk resonators using a tapered fiber. The stable beating signal confirms
the low phase-noise achieved in the tunable laser. Owing to the high spatial
overlap factors between the two nearly degenerate lasing modes as well as that
between the two lasing modes and the pump mode, gain competition between the
two modes is suppressed, leading to stable dual-wavelength laser generation and
in turn the low noise microwave source. The measured microwave signal shows a
linewidth of ~6.87 kHz, a phase noise of ~-123 dBc/Hz, and an electro-optic
tuning efficiency of -1.66 MHz/V.


  We study cohabitation of the poset $P_S$ shooting a club through a given
stationary subset $S$ of $\omega _1$ with finite conditions with other
forcings. Sample results:
  (1) $P_S$ "sometimes" preserves presaturatedness of $NS_{\omega _1}$
  (2) $P_S=P_T$ if $S=T mod NS_{\omega _1}$ (in Boolean algebra sense)
  (3) Cons ( one can embed $Q,$ the poset adding $\aleph _1$ Cohen reals, to
$P_S$ such that reals in $V^Q$ are the same as reals in $V^{P_S}.$ )


  We investigate the fidelity of the measurement-based quantum computation
(MBQC) when it is coupled with boson environment, by measuring cluster state
fidelity and gate fidelity. Two different schemes of cluster state preparation
are studied. In the Controlled-Z (CZ) creation scheme, cluster states are
prepared by entangling all qubits in $|+\rangle$ state with CZ gates on all
neighboring sites. The fidelity shows an oscillation pattern over time
evolution. The influence of environment temperature is evaluated, and
suggestions are given to enhance the performance of MBQC realized in this way.
In the Hamiltonian creation scheme, cluster states are made by cooling a system
with cluster Hamiltonians, of which ground states are cluster states. The
fidelity sudden drop phenomenon is discovered. When the coupling is below a
threshold, MBQC systems are highly robust against the noise. Our main
environment model is the one with a single collective bosonic mode.


  Smoothed Particle Hydrodynamics (SPH) schemes need to be enhanced by
dissipation mechanisms to handle shocks. Most SPH formulations rely on
artificial viscosity and while this is working well in pure shocks, attention
has to be payed to avoid dissipation where it is not wanted. Commonly used
approaches include limiters and time-dependent dissipation parameters. The
former try to distinguish shocks from other types of flows that do not require
dissipation while in the latter approach the dissipation parameters are steered
by some source term ("trigger") and, if not triggered, they decay to a
pre-described floor value. The commonly used source terms trigger on either
compression, $-\nabla\cdot\vec{v}$, or its time derive. Here we explore a novel
way to trigger SPH-dissipation: based on the entropy growth rate between two
time steps we identify "troubled particles" that need to have dissipation added
because they are either passing through a shock wave or become noisy. Our new
scheme is implemented into the Lagrangian hydrodynamics code MAGMA2 and
scrutinized in a number of shock and fluid instability tests. We find excellent
results in shocks and only a moderate (and desired) switch-on in instability
tests, despite our conservatively chosen trigger parameters. The new scheme is
robust, trivial to implement into existing SPH codes and does not add any
computational overhead.


  Although the effects of the electronic excitations during high-energy
radiation damage processes are not currently understood, it is shown that their
role in the interaction of radiation with matter is important. We perform
molecular dynamics simulations of high-energy collision cascades in
bcc-tungsten using the coupled two-temperature molecular dynamics (2T-MD) model
that incorporates both the effects of electronic stopping and electron-phonon
interaction. We compare the combination of these effects on the induced damage
with only the effect of electronic stopping, and conclude in several novel
insights. In the 2T-MD model, the electron-phonon coupling results in less
damage production in the molten region and in faster relaxation of the damage
at short times. These two effects lead to significantly smaller amount of the
final damage at longer times.


  We introduce, and propagate wave-packet solutions of, a single qubit system
in which geometric gauge forces and phases emerge. We investigate under what
conditions non-trivial gauge phenomena arise, and demonstrate how symmetry
breaking is an essential ingredient for realization of the former. We
illustrate how a "magnetic"-lens, for neutral atoms, can be constructed and
find application in the manipulation and interferometry of cold atoms.


  Twitter bot detection has become an increasingly important task to combat
misinformation, facilitate social media moderation, and preserve the integrity
of the online discourse. State-of-the-art bot detection methods generally
leverage the graph structure of the Twitter network, and they exhibit promising
performance when confronting novel Twitter bots that traditional methods fail
to detect. However, very few of the existing Twitter bot detection datasets are
graph-based, and even these few graph-based datasets suffer from limited
dataset scale, incomplete graph structure, as well as low annotation quality.
In fact, the lack of a large-scale graph-based Twitter bot detection benchmark
that addresses these issues has seriously hindered the development and
evaluation of novel graph-based bot detection approaches. In this paper, we
propose TwiBot-22, a comprehensive graph-based Twitter bot detection benchmark
that presents the largest dataset to date, provides diversified entities and
relations on the Twitter network, and has considerably better annotation
quality than existing datasets. In addition, we re-implement 35 representative
Twitter bot detection baselines and evaluate them on 9 datasets, including
TwiBot-22, to promote a fair comparison of model performance and a holistic
understanding of research progress. To facilitate further research, we
consolidate all implemented codes and datasets into the TwiBot-22 evaluation
framework, where researchers could consistently evaluate new models and
datasets. The TwiBot-22 Twitter bot detection benchmark and evaluation
framework are publicly available at https://twibot22.github.io/


  In this paper we propose a simple yet powerful vortex method to numerically
approximate the dynamics of an incompressible flow. The idea is to sample the
distribution of the initial vortices of the fluid flow in question then follow
vortex dynamics along Taylor's Brownian fluid particles. The weak convergences
of this approximation scheme are obtained for 2D and 3D cases, though only for
small time in 3D case. Based on our method, the simulation results are quite
attracting.


  Using ultrafast optical pump-probe spectroscopy, we study the relaxation
dynamics of hot optical phonons in few-layer and multi-layer graphene films
grown by epitaxy on silicon carbide substrates and by chemical vapor deposition
on nickel substrates. In the first few hundred femtoseconds after
photoexcitation, the hot carriers lose most of their energy to the generation
of hot optical phonons which then present the main bottleneck to subsequent
carrier cooling. Optical phonon cooling on short time scales is found to be
independent of the graphene growth technique, the number of layers, and the
type of the substrate. We find average phonon lifetimes in the 2.5-2.55 ps
range. We model the relaxation dynamics of the coupled carrier-phonon system
with rate equations and find a good agreement between the experimental data and
the theory. The extracted optical phonon lifetimes agree very well with the
theory based on anharmonic phonon interactions.


  This paper shows the usefulness of the Perov contraction theorem, which is a
generalization of the classical Banach contraction theorem, for solving Markov
dynamic programming problems. When the reward function is unbounded, combining
an appropriate weighted supremum norm with the Perov contraction theorem yields
a unique fixed point of the Bellman operator under weaker conditions than
existing approaches. An application to the optimal savings problem shows that
the average growth rate condition derived from the spectral radius of a certain
nonnegative matrix is sufficient and almost necessary for obtaining a solution.


  The informed consent process is a complicated procedure involving permissions
as well a variety of entities and actions. In this paper, we discuss the use of
Semantic Web Rule Language (SWRL) to further extend the Informed Consent
Ontology (ICO) to allow for semantic machine-based reasoning to manage and
generate important permission-based information that can later be viewed by
stakeholders. We present four use cases of permissions from the All of Us
informed consent document and translate these permissions into SWRL expressions
to extend and operationalize ICO. Our efforts show how SWRL is able to infer
some of the implicit information based on the defined rules, and demonstrate
the utility of ICO through the use of SWRL extensions. Future work will include
developing formal and generalized rules and expressing permissions from the
entire document, as well as working towards integrating ICO into software
systems to enhance the semantic representation of informed consent for
biomedical research.


  We analyze the quasar two-point correlation function (2pCF) within the
redshift interval $0.8<z<2.2$ using a sample of 52303 quasars selected from the
recent 7th Data Release of the Sloan Digital Sky Survey. Our approach to 2pCF
uses a concept of locally Lorentz (Fermi) frame for determination of the
distance between objects and permutation method of the random catalogue
generation. Assuming the spatially flat cosmological model with given
$\Omega_{\Lambda}=0.726$, we found that the real-space 2pCF is fitted well with
the power-low model within the distance range $1<\sigma<35$ $h^{-1}$ Mpc with
the correlation length $r_{0}=5.85\pm0.33$ $h^{-1}$ Mpc and the slope
$\gamma=1.87\pm0.07$. The redshift-space 2pCF is approximated with
$s_{0}=6.43\pm0.63$ $h^{-1}$ Mpc and $\gamma=1.21\pm0.24$ for $1<s<10$ $h^{-1}$
Mpc, and $s_{0}=7.37\pm0.81$ $h^{-1}$ Mpc and $\gamma=1.90\pm0.24$ for
$10<s<35$ $h^{-1}$ Mpc. For distances $s>10\,h^{-1}$ Mpc the parameter
describing the large-scale infall to density inhomogeneities is
$\beta=0.63\pm0.10$ with the linear bias $b=1.44\pm0.22$ that marginally
(within 2$\sigma$) agrees with the linear theory of cosmological perturbations.
We discuss possibilities to obtain a statistical estimate of the random
component of quasars velocities (different from the large-scale infall). We
note rather slight dependence of quasars velocity dispersion upon the 2pCF
parameters in the region $r<2$ Mpc.


  The atomic structure and mechanical properties of the carbyne (monatomic
linear chains), containing from 2 to 21 carbon atoms, are theoretically
investigated by ab-initio methods. We demonstrate the existence of a stable
cumulene-structure in the inner part of chains with the number of atoms N>=10.
We present a general stress-strain diagram of chains until the moment when they
break, which enables to determine their strength, elasticity and fragility. For
chains with N>=4, the relationship between the strength of the chain and the
binding energy of the edge atom in the chain is established. The existence of
scale-effect and "even-odd" effect for such properties as strength, elasticity
and fragility is observed. We demonstrate that the 5-atom carbon chains show
the maximum strength value.


  A rational theory is proposed to describe the large-scale motion in
turbulence. The fluid element with inner orientational structures is proposed
to be the building block of fluid dynamics. The variance of the orientational
structures then constitutes new fields suitable to describe the vortex state in
turbulence. When the fluid element is assumed to be an open subsystem, the
differentiable manifold description of turbulence ought to be set up, and the
complete fluid dynamics can be deduced from a variational calculus on the
constructed Lagrangian dissipation energy density. The derived dynamical
equations indicate that the vortex evolution is naturally related with the
angular momentum balance.


  The article is devoted to the discussion of the high-throughput approach to
band structures calculations. We present scientific and computational
challenges as well as solutions relying on the developed framework (Automatic
Flow, AFLOW/ACONVASP). The key factors of the method are the standardization
and the robustness of the procedures. Two scenarios are relevant: 1)
independent users generating databases in their own computational systems
(off-line approach) and 2) teamed users sharing computational information based
on a common ground (on-line approach). Both cases are integrated in the
framework: for off-line approaches, the standardization is automatic and fully
integrated for the 14 Bravais lattices, the primitive and conventional unit
cells, and the coordinates of the high symmetry k-path in the Brillouin zones.
For on-line tasks, the framework offers an expandable web interface where the
user can prepare and set up calculations following the proposed standard. Few
examples of band structures are included. LSDA+U parameters (U, J) are also
presented for Nd, Sm, and Eu.


  We present a semicontinuity result, proven in recent joint work with Morrow
and Scholze, relating the mod $p$ singular cohomology of a smooth projective
complex algebraic variety X to the de Rham cohomology of a smooth
characteristic $p$ specialization of X: the rank of the former is bounded above
by that of the latter. The path to this result passes through $p$-adic Hodge
theory and perfectoid geometry, so we survey the relevant aspects of those
subjects as well.


  We prove a generalization of Noether's theorem for optimal control problems
defined on time scales. Particularly, our results can be used for
discrete-time, quantum, and continuous-time optimal control problems. The
generalization involves a one-parameter family of maps which depend also on the
control and a Lagrangian which is invariant up to an addition of an exact delta
differential. We apply our results to some concrete optimal control problems on
an arbitrary time scale.


  We present a scheme which offers a significant reduction in the resources
required to implement linear optics quantum computing. The scheme is a
variation of the proposal of Knill, Laflamme, and Milburn, and makes use of an
incremental approach to the error encoding to boost probability of success.


  At the present work we consider an application of the deformation procedure
that enable us to construct, systematically, scalar field models supporting
multikinks. We introduce a new deformation function in order to realize this
task. We exemplify the procedure with three different starting models already
known in the literature, and the resulting deformed models have rich vacua
structures which are responsible for the appearance of multikink
configurations.


  We investigate the statistical properties of the complexness parameter which
characterizes uniquely complexness (biorthogonality) of resonance eigenstates
of open chaotic systems. Specifying to the regime of isolated resonances, we
apply the random matrix theory to the effective Hamiltonian formalism and
derive analytically the probability distribution of the complexness parameter
for two statistical ensembles describing the systems invariant under time
reversal. For those with rigid spectra, we consider a Hamiltonian characterized
by a picket-fence spectrum without spectral fluctuations. Then, in the more
realistic case of a Hamiltonian described by the Gaussian Orthogonal Ensemble,
we reveal and discuss the r\^ole of spectral fluctuations.


  We give a complete classification of analytic equivalence of germs of
parametric families of systems of complex linear differential equations
unfolding a generic resonant singularity of Poincare rank 1 in dimension $n =
2$ whose leading matrix is a Jordan bloc. The moduli space of analytic
equivalence classes is described in terms of a tuple of formal invariants and a
single analytic invariant obtained from the trace of monodromy, and analytic
normal forms are given. We also explain the underlying phenomena of confluence
of two simple singularities and of a turning point, the associated Stokes
geometry, and the change of order of Borel summability of formal solutions in
dependence on a complex parameter.


  The construction of a network of cell-to-cell contacts makes it possible to
characterize the patterns and spatial organisation of tissues. Such networks
are highly dynamic, depending on the changes of the tissue architecture caused
by cell division, death and migration. Local competitive and cooperative
cell-to-cell interactions influence the choices cells make. We review the
literature on quantitative data of epithelial tissue topology and present a
dynamical network model that can be used to explore the evolutionary dynamics
of a two dimensional tissue architecture with arbitrary cell-to-cell
interactions. In particular, we show that various forms of experimentally
observed types of interactions can be modelled using game theory. We discuss a
model of cooperative and non-cooperative cell-to-cell communication that can
capture the interplay between cellular competition and tissue dynamics. We
conclude with an outlook on the possible uses of this approach in modelling
tumorigenesis and tissue homeostasis.


  The simple method for the calculating of the anomalous dimensions of the
composite operators up to 1/N^2 order is developed. We demonstrate the
effectiveness of this approach by computing the critical exponents of the
$(\otimes\vec\Phi)^{s}$ and $\vec\Phi\otimes(\otimes\vec\partial)^{n}\vec\Phi$
operators in the 1/N^2 order in the nonlinear sigma model. The special
simplifications due to the conformal invariance of the model are discussed.


  Each integrable lowest weight representation of a symmetrizable Kac-Moody Lie
algebra g has a crystal in the sense of Kashiwara, which describes its
combinatorial properties. For a given g, there is a limit crystal, usually
denoted by B(-\infty), which contains all the other crystals. When g is finite
dimensional, a convex polytope, called the Mirkovi\'c-Vilonen polytope, can be
associated to each element in B(-\infty). This polytope sits in the dual space
of a Cartan subalgebra of g, and its edges are parallel to the roots of g. In
this paper, we generalize this construction to the case where g is a symmetric
affine Kac-Moody algebra. The datum of the polytope must however be
complemented by partitions attached to the edges parallel to the imaginary root
\delta. We prove that these decorated polytopes are characterized by conditions
on their normal fans and on their 2-faces. In addition, we discuss how our
polytopes provide an analog of the notion of Lusztig datum for affine Kac-Moody
algebras. Our main tool is an algebro-geometric model for B(-\infty)
constructed by Lusztig and by Kashiwara and Saito, based on representations of
the completed preprojective algebra \Lambda\ of the same type as g. The
underlying polytopes in our construction are described with the help of Buan,
Iyama, Reiten and Scott's tilting theory for the category \Lambda-mod. The
partitions we need come from studying the category of semistable
\Lambda-modules of dimension-vector a multiple of \delta.


  Peer-to-peer (P2P) overlay networks such as BitTorrent and Avalanche are
increasingly used for disseminating potentially large files from a server to
many end users via the Internet. The key idea is to divide the file into many
equally-sized parts and then let users download each part (or, for network
coding based systems such as Avalanche, linear combinations of the parts)
either from the server or from another user who has already downloaded it.
However, their performance evaluation has typically been limited to comparing
one system relative to another and typically been realized by means of
simulation and measurements. In contrast, we provide an analytic performance
analysis that is based on a new uplink-sharing version of the well-known
broadcasting problem. Assuming equal upload capacities, we show that the
minimal time to disseminate the file is the same as for the simultaneous
send/receive version of the broadcasting problem. For general upload
capacities, we provide a mixed integer linear program (MILP) solution and a
complementary fluid limit solution. We thus provide a lower bound which can be
used as a performance benchmark for any P2P file dissemination system. We also
investigate the performance of a decentralized strategy, providing evidence
that the performance of necessarily decentralized P2P file dissemination
systems should be close to this bound and therefore that it is useful in
practice.


  We study electron transport through a domain wall in a ferromagnetic nanowire
subject to spin-dependent scattering. A scattering matrix formalism is
developed to address both coherent and incoherent transport properties. The
coherent case corresponds to elastic scattering by static defects, which is
dominant at low temperatures, while the incoherent case provides a
phenomenological description of the inelastic scattering present in real
physical systems at room temperature. It is found that disorder scattering
increases the amount of spin-mixing of transmitted electrons, reducing the
adiabaticity. This leads, in the incoherent case, to a reduction of conductance
through the domain wall as compared to a uniformly magnetized region which is
similar to the giant magnetoresistance effect. In the coherent case, a
reduction of weak localization, together with a suppression of spin-reversing
scattering amplitudes, leads to an enhancement of conductance due to the domain
wall in the regime of strong disorder. The total effect of a domain wall on the
conductance of a nanowire is studied by incorporating the disordered regions on
either side of the wall. It is found that spin-dependent scattering in these
regions increases the domain wall magnetoconductance as compared to the effect
found by considering only the scattering inside the wall. This increase is most
dramatic in the narrow wall limit, but remains significant for wide walls.


  This study examines the holographic representation of the quantum theory of
transmission lines, which play a crucial role in quantum computing and quantum
information. Utilizing Yurke and Denker's quantum circuit network theory within
the framework of continuous MERA (cMERA) in AdS space, we analyze the
quantization and interactions of transmission lines. The metric is revealed to
be described by the inductance of the quantum circuit, which is AdS-space in
its 0-limit. These results provide new insights into handling and controlling
complex phenomena in quantum circuits, potentially advancing the understanding
of quantum computing and quantum communication.


  The effect of the charge fluctuations on the electronic spectrum and the
Raman spectrum of high temperature superconductors is examined within the slave
boson approach. Instead of using the saddle point approximation for slave
bosons, we confine ourselves to the non-crossing approximation (NCA) in summing
the diagrams for the Green functions, thus obtaining the renormalized hole
spectrum and its lifetime on equal footing. The electronic Raman spectrum is
calculated, showing the characteristic featureless behaviour up to the
frequency of the order of renormalized $\Delta_{pd}$ parameter. The dependence
on the polarization of the incident and the scattered light agrees with
experiments.


  This paper has been withdrawn by the author due to the presented idea is
wrong.


  We show that the mutants of compactified representations constructed by Franz
and Puppe can be written as intersections of real quadrics involving division
algebras and as generalizations of polygon spaces. We also show that these
manifolds are connected sums of products of spheres.


  This paper presents a mathematically exact self-similar solution to the joint
nonsteady problems of vapour diffusion towards a droplet growing in a
vapour-gas medium and of removal of heat released by a droplet into a
vapour-gas medium during vapour condensation. An equation for the temperature
of the droplet is obtained; and it is only at that temperature that the
self-similar solution exists. This equation requires the constancy of the
droplet temperature and even defines it unambiguously throughout the whole
period of the droplet growth. In the case of strong display of heat effects,
when the droplet growth rate decreases significantly, the equation for the
temperature of the droplet is solved analytically. It is shown that the
obtained temperature fully coincides with the one that settles in the droplet
simultaneously with the settlement of its diffusion regime of growth. At the
obtained temperature of the droplet the interrelated nonsteady vapour
concentration and temperature profiles of the vapour-gas medium around the
droplet are expressed in terms of initial (prior to the nucleation of the
droplet) parameters of the vapour-gas medium. The same parameters are used to
formulate the law in accordance with which the droplet is growing in diffusion
regime, and also to define the time that passes after the nucleation of the
droplet till the settlement of diffusion regime of droplet growth, when the
squared radius of the droplet becomes proportionate to time. For the sake of
completeness the case of weak display of heat effects is been studied.


  We present a numerical macrospin model for harmonic voltage detection in
multilayer spintronic devices. The core of the computational backend is based
on the Landau-Lifshitz-Gilbert-Slonczewski equation, which combines high
performance with satisfactory, for large-scale applications, agreement with the
experimental results. We compare the simulations with the experimental findings
in Ta/CoFeB bilayer system for angular- and magnetic field-dependent resistance
measurements, electrically detected magnetisation dynamics, and harmonic Hall
voltage detection. Using simulated scans of the selected system parameters such
as the polar angle $\theta$, magnetisation saturation
($\mu_\textrm{0}M_\textrm{s}$) or uniaxial magnetic anisotropy ($K_\textrm{u}$)
we show the resultant changes in the harmonic Hall voltage, demonstrating the
dominating influence of the $\mu_\textrm{0}M_\textrm{s}$ on the first and
second harmonics. In the spin-diode ferromagnetic resonance (SD-FMR) technique
resonance method the ($\mu_\textrm{0}M_\textrm{s}$, $K_\textrm{u}$) parameter
space may be optimised numerically to obtain a set of viable curves that fit
the experimental data.


  This paper presents a creativity support tool, called FreePub, to collect and
organize scientific material using mindmaps. Mindmaps are visual, graph-based
represenations of concepts, ideas, notes, tasks, etc. They generally take a
hierarchical or tree branch format, with ideas branching into their
subsections. FreePub supports creativity cycles. A user starts such a cycle by
setting up her domain of interest using mindmaps. Then, she can browse mindmaps
and launch search tasks to gather relevant publications from several data
sources. FreePub, besides publications, identifies helpful supporting material
(e.g., blog posts, presentations). All retrieved information from FreePub can
be imported and organized in mindmaps. FreePub has been fully implemented on
top of FreeMind, a popular open-source, mindmapping tool.


  Boundedness of wave operators for Schr\"odinger operators in one space
dimension for a class of singular potentials, admitting finitely many Dirac
delta distributions, is proved. Applications are presented to, for example,
dispersive estimates and commutator bounds.


  We extract energies and widths of the ground states of $^5$He and $^5$Li from
recent single--level R--matrix fits to the spectra of the $^3$H$({\rm
d},\gamma$)$^5$He and the $^3$He$({\rm d},\gamma$)$^5$Li reactions. The widths
obtained differ significantly from the formal R--matrix values but they are
close to those measured as full widths at half maxima of the spectra in various
experiments. The energies are somewhat lower than those given by usual
estimates of the peak positions. The extracted values are close to the
S--matrix poles calculated previously from the multi--term analyses of the
N-$^4$He elastic scattering data.


We determine the image and fibres for solvable base change.


  In this paper we study the deductive properties of a family of 3-valued
paraconsistent logics. We define a notion of standard sequent calculus and
prove that there is no sound and complete standard sequent calculus for these
logics. Moreover, we provide non-standard sound, complete and cut free sequent
calculus for Paraconsistent Weak Kleene Logic using three-sided sequents.


  We present a novel particle filtering algorithm for tracking a moving sound
source using a microphone array. If there are N microphones in the array, we
track all $N \choose 2$ delays with a single particle filter over time. Since
it is known that tracking in high dimensions is rife with difficulties, we
instead integrate into our particle filter a model of the low dimensional
manifold that these delays lie on. Our manifold model is based off of work on
modeling low dimensional manifolds via random projection trees [1]. In
addition, we also introduce a new weighting scheme to our particle filtering
algorithm based on recent advancements in online learning. We show that our
novel TDOA tracking algorithm that integrates a manifold model can greatly
outperform standard particle filters on this audio tracking task.


  It is often of interest to assess whether a function-valued statistical
parameter, such as a density function or a mean regression function, is equal
to any function in a class of candidate null parameters. This can be framed as
a statistical inference problem where the target estimand is a scalar measure
of dissimilarity between the true function-valued parameter and the closest
function among all candidate null values. These estimands are typically defined
to be zero when the null holds and positive otherwise. While there is
well-established theory and methodology for performing efficient inference when
one assumes a parametric model for the function-valued parameter, methods for
inference in the nonparametric setting are limited. When the null holds, and
the target estimand resides at the boundary of the parameter space, existing
nonparametric estimators either achieve a non-standard limiting distribution or
a sub-optimal convergence rate, making inference challenging. In this work, we
propose a strategy for constructing nonparametric estimators with improved
asymptotic performance. Notably, our estimators converge at the parametric rate
at the boundary of the parameter space and also achieve a tractable null
limiting distribution. As illustrations, we discuss how this framework can be
applied to perform inference in nonparametric regression problems, and also to
perform nonparametric assessment of stochastic dependence.


  Consider a surface, enclosing a fixed volume, described by a free-energy
depending only on the local geometry; for example, the Canham-Helfrich energy
quadratic in the mean curvature describes a fluid membrane. The stress at any
point on the surface is determined completely by geometry. In equilibrium, its
divergence is proportional to the Laplace pressure, normal to the surface,
maintaining the constraint on the volume. It is shown that this source itself
can be expressed as the divergence of a position-dependent surface stress. As a
consequence, the equilibrium can be described in terms of a conserved
`effective' surface stress. Various non-trivial geometrical consequences of
this identification are explored. In a cylindrical geometry, the cross-section
can be viewed as a closed planar Euler elastic curve. With respect to an
appropriate centre the effective stress itself vanishes; this provides a
remarkably simple relationship between the curvature and the position along the
loop. In two or higher dimensions, it is shown that the only geometry
consistent with the vanishing of the effective stress is spherical. It is
argued that the appropriate generalization of the loop result will involve
`null' stresses.


  Recently, different works proposed a new way to mine patterns in databases
with pathological size. For example, experiments in genome biology usually
provide databases with thousands of attributes (genes) but only tens of objects
(experiments). In this case, mining the "transposed" database runs through a
smaller search space, and the Galois connection allows to infer the closed
patterns of the original database. We focus here on constrained pattern mining
for those unusual databases and give a theoretical framework for database and
constraint transposition. We discuss the properties of constraint transposition
and look into classical constraints. We then address the problem of generating
the closed patterns of the original database satisfying the constraint,
starting from those mined in the "transposed" database. Finally, we show how to
generate all the patterns satisfying the constraint from the closed ones.


  We report on the sensitivity of SPIRE photometers on the Herschel Space
Observatory. Specifically, we measure the confusion noise from observations
taken during the Science Demonstration Phase of the Herschel Multi-tiered
Extragalactic Survey. Confusion noise is defined to be the spatial variation of
the sky intensity in the limit of infinite integration time, and is found to be
consistent among the different fields in our survey at the level of 5.8, 6.3
and 6.8 mJy/beam at 250, 350 and 500 microns, respectively. These results,
together with the measured instrument noise, may be used to estimate the
integration time required for confusion-limited maps, and provide a noise
estimate for maps obtained by SPIRE.


  Traveling across several order of magnitude in distance, relativistic jets
from strong gravity region to asymptotic flat spacetime region are believed to
consist of several general relativistic magnetohydrodynamic (GRMHD) processes.
We present a semi-analytical approach for modeling the global structures of a
trans-fast magnetosonic relativistic jet, which should be ejected from a plasma
source nearby a black hole in a funnel region enclosed by dense accreting flow
and also disk corona around the black hole. Our model consistently includes the
inflow and outflow part of the GRMHD solution along the magnetic field lines
penetrating the black hole horizon. After the rotational energy of the black
hole is extracted electromagnetically by the negative energy GRMHD inflow, the
huge electromagnetic energy flux then propagates from the inflow to the outflow
region across the plasma source, and in the outflow region the electromagnetic
energy converts to the fluid kinetic energy. Eventually, the accelerated
outflow must exceed the fast-magnetosonic wave speed. We apply the
semi-analytical trans-fast magnetosonic flow model to the black hole
magnetosphere for both parabolic and split-monopole magnetic field
configurations, and discuss the general flow properties; that is, jet
acceleration, jet magnetization, and the locations of some characteristic
surfaces of the black hole magnetosphere. We have confirmed that, at large
distance, the GRMHD jet solutions are in good agreement with the previously
known trans-fast special relativistic magnetohydrodynamic (SRMHD) jet
properties, as expected. The flexibility of the model provides a prompt and
heuristic way to approximate the global GRMHD trans-fast magnetosonic jet
properties.


  One way of carving up the broad "AI ethics and society" research space that
has emerged in recent years is to distinguish between "near-term" and
"long-term" research. While such ways of breaking down the research space can
be useful, we put forward several concerns about the near/long-term distinction
gaining too much prominence in how research questions and priorities are
framed. We highlight some ambiguities and inconsistencies in how the
distinction is used, and argue that while there are differing priorities within
this broad research community, these differences are not well-captured by the
near/long-term distinction. We unpack the near/long-term distinction into four
different dimensions, and propose some ways that researchers can communicate
more clearly about their work and priorities using these dimensions. We suggest
that moving towards a more nuanced conversation about research priorities can
help establish new opportunities for collaboration, aid the development of more
consistent and coherent research agendas, and enable identification of
previously neglected research areas.


  Let $k$ be a field of characteristic zero. This paper studies a problem
proposed by Joseph F. Ritt in 1950. Precisely, we prove that (1) If $p\geq 2$
is an integer, for every integer $i\in\mathbb{N}$, the nilpotency index of the
image of $T_i$ in the ring $k\{T\}/[T^p]$ equals $(i+1)p-i$. (2) For every pair
of integers $(i,j)$, the nilpotency index of the image of $T_iU_j$ in the ring
$k\{T\}/[TU]$ equals $i+j+1$.


  Errors in labels obtained via human annotation adversely affect a model's
performance. Existing approaches propose ways to mitigate the effect of label
error on a model's downstream accuracy, yet little is known about its impact on
a model's disparity metrics. Here we study the effect of label error on a
model's disparity metrics. We empirically characterize how varying levels of
label error, in both training and test data, affect these disparity metrics. We
find that group calibration and other metrics are sensitive to train-time and
test-time label error -- particularly for minority groups. This disparate
effect persists even for models trained with noise-aware algorithms. To
mitigate the impact of training-time label error, we present an approach to
estimate the influence of a training input's label on a model's group disparity
metric. We empirically assess the proposed approach on a variety of datasets
and find significant improvement, compared to alternative approaches, in
identifying training inputs that improve a model's disparity metric. We
complement the approach with an automatic relabel-and-finetune scheme that
produces updated models with, provably, improved group calibration error.


  Let $K$ be a number field and $S$ a finite set of places of $K$ that contains
all of the archimedean places. Let $\varphi: \mathbb{P}^1 \to \mathbb{P}^1$ be
a rational map of degree $d \geq 2$ defined over $K$. Given $\alpha \in
\mathbb{P}^1(K)$ non-preperiodic and $\beta \in \mathbb{P}^1(K)$
non-exceptional, we prove an upper bound of the form $O(|S|^{1+\epsilon})$ on
the number of points in the forward orbit of $\alpha$ that are $S$-integral
relative to $\beta$, extending results of Hsia--Silverman [HS11]. When
$\varphi$ is a power or Latt\`es map, we obtain a stronger upper bound of the
form $O(|S|)$. We also prove uniform bounds when $\varphi$ is a polynomial,
extending results of Krieger et al [KLS+15].