title:
Multi-level Monte Carlo methods with the Truncated Euler-Maruyama Scheme
  for Stochastic Differential Equations

abstract:
  In this paper, the truncated Euler-Maruyama (EM) method is employed together
with the Multi-level Monte Carlo (MLMC) method to approximate the expectations
of functions of solutions to stochastic differential equations (SDEs). The
convergence rate and the computational cost of the approximations using the
truncated EM method with the MLMC method are proved when the coefficients of
SDEs fulfill the local Lipschitz and Khasminskii-type conditions. Numerical
examples are given to demonstrate the theoretical results.


title: Harmonic Spheres in the Hilbert-Schmidt Grassmannian

abstract:
  We give the twistor description of harmonic maps of the Riemann sphere into
the Hilbert-Schmidt Grassmannian. The study of such maps is motivated by the
harmonic spheres conjecture formulated in the beginning of this paper.


title:
Quantum effects in nanosystems: good reasons to use phase-space Weyl
  symbols

abstract:
  Bogoliubov transformations have been successfully applied in several
Condensed Matter contexts, e.g., in the theory of superconductors, superfluids,
and antiferromagnets. These applications are based on bulk models where
translation symmetry can be assumed, so that few degrees of freedom in Fourier
space can be `diagonalized' separately, and in this way it is easy to find the
approximate ground state and its excitations. As translation symmetry cannot be
invoked when it comes about nanoscopic systems, the corresponding
multidimensional Bogoliubov transformations are more complicated. For bosonic
systems it is much simpler to proceed using phase-space variables, i.e.,
coordinates and momenta. Interactions can be accounted for by the
self-consistent harmonic approximation, which is naturally developed using
phase-space Weyl symbols. The spin-flop transition in a short antiferromagnetic
chain is illustrated as an example. This approach, rarely used in the past, is
expected to be generally useful to estimate quantum effects, e.g., on phase
diagrams of ordered vs disordered phases.


title: Interchange instability and transport in matter-antimatter plasmas

abstract:
  Symmetric electron-positron plasmas in inhomogeneous magnetic fields are
intrinsically subject to interchange instability and transport. Scaling
relations for the propagation velocity of density blob perturbations relevant
to transport in isothermal magnetically confined electron-positron plasmas are
deduced, including damping effects when Debye lengths are large compared to
Larmor radii. The relations are verified by nonlinear full-F gyrofluid
computations. Results are in favour of sufficient magnetic confinement for
planned electron-positron plasma experiments. The model is generalised to other
matter-antimatter plasmas. Magnetised electron-positron-proton-antiproton
plasmas are susceptible to interchange driven local matter-antimatter
separation, which can be expected to impede (so far unrealised) sustained
laboratory magnetic confinement.


title: Adaptive Feature Abstraction for Translating Video to Text

abstract:
  Previous models for video captioning often use the output from a specific
layer of a Convolutional Neural Network (CNN) as video features. However, the
variable context-dependent semantics in the video may make it more appropriate
to adaptively select features from the multiple CNN layers. We propose a new
approach for generating adaptive spatiotemporal representations of videos for
the captioning task. A novel attention mechanism is developed, that adaptively
and sequentially focuses on different layers of CNN features (levels of feature
"abstraction"), as well as local spatiotemporal regions of the feature maps at
each layer. The proposed approach is evaluated on three benchmark datasets:
YouTube2Text, M-VAD and MSR-VTT. Along with visualizing the results and how the
model works, these experiments quantitatively demonstrate the effectiveness of
the proposed adaptive spatiotemporal feature abstraction for translating videos
to sentences with rich semantics.


title: New Insights into Time Series Analysis II -- No Correlated Observations

abstract:
  Statistical parameters are used in finance, weather, industrial, science,
among other vast number of different fields to draw conclusions. New more
efficient selection methods are mandatory to analyses the huge amount of
astronomical data. The standard and new data-mining parameters to analyses
non-correlated data are used to set the best way to discriminate stochastic and
non-stochastic variations. We introduce 16 modified statistical parameters
covering different features of statistical distribution, like; average,
dispersion, and shape parameters. Many of dispersion and shape parameters are
unbound parameters, i.e. equations which do not require the calculation of the
average. Moreover, the majority of them have lower error than previous ones
that is mainly observed for distributions having few measurements. A set of
non-correlated variability indices, sample size corrections, and a new noise
model as well as tests of different apertures and cutoffs on the data (BAS
approach) are introduced. The number of misselections is reduced by about 520%
using a single waveband and 1200% combining all wavebands. On the other hand,
the even mean also improves the correlated indices introduced in Paper 1
Ferreira Lopes & Cross (2016). The misselection rate is reduced by about 18% if
the even mean is used instead of the mean to compute the correlated indices in
the WFCAM database. Even statistics allows us to improve the effectiveness of
both correlated and non-correlated indices. The correlated variability indices,
proposed in the first paper of this series, are also improved if the even mean
is used. The even parameters will also be useful for classifying light curves
in the last step of this project. We consider that the first step of this
project, where we set new techniques and methods that provide a huge improve on
the efficiency of selection of variable stars, is now complete.


title: Was Thebes Necessary? Contingency in Spatial Modelling

abstract:
  When data is poor we resort to theory modelling. This is a two-step process.
We have first to identify the appropriate type of model for the system under
consideration and then to tailor it to the specifics of the case. To understand
settlement formation, which is the concern of this paper, this not only
involves choosing input parameter values such as site separations but also
input functions which characterises the ease of travel between sites. Although
the generic behaviour of the model is understood, the details are not.
Different choices will necessarily lead to different outputs (for identical
inputs). We can only proceed if choices that are "close" give outcomes are
similar. Where there are local differences it suggests that there was no
compelling reason for one outcome rather than the other. If these differences
are important for the historic record we may interpret this as sensitivity to
contingency. We re-examine the rise of Greek city states as first formulated by
Rihll and Wilson in 1979, initially using the same "retail" gravity model. We
suggest that, whereas cities like Athens owe their position to a combination of
geography and proximity to other sites, the rise of Thebes is the most
contingent, whose success reflects social forces outside the grasp of simple
network modelling.


title:
Behaviour of the order of Tate-Shafarevich groups for the quadratic
  twists of elliptic curves

abstract:
  We present the results of our search for the orders of Tate-Shafarevich
groups for the quadratic twists of elliptic curves. We formulate a general
conjecture, giving for a fixed elliptic curve $E$ over $\Bbb Q$ and positive
integer $k$, an asymptotic formula for the number of quadratic twists $E_d$,
$d$ positive square-free integers less than $X$, with finite group $E_d(\Bbb
Q)$ and $|\Sha(E_d(\Bbb Q))| = k^2$. This paper continues the authors previous
investigations concerning orders of Tate-Shafarevich groups in quadratic twists
of the curve $X_0(49)$. In section 8 we exhibit $88$ examples of rank zero
elliptic curves with $|\Sha(E)| > 63408^2$, which was the largest previously
known value for any explicit curve. Our record is an elliptic curve $E$ with
$|\Sha(E)| = 1029212^2$.


title:
Creation of uni-directional spin-wave emitters by utilizing interfacial
  Dzyaloshinskii-Moriya interaction

abstract:
  We present an analytic and numerical study of the creation of an
uni-directional spin-wave emission in ultra-thin ferromagnetic films sandwiched
in an asymmetric layer stack. For this we extend the analytical description of
spin waves in spin-wave waveguides by the incorporation of the influence of the
interfacial Dzyaloshinskii-Moriya interaction on the spin-wave propagation. By
exploring the model system Ni$_{81}$Fe$_{19}$/Pt we show that it is possible to
achieve an uni-directional spin-wave emission by combining wave-vector
selective excitation sources with the frequency splitting which arises from
interfacial Dzyaloshinskii-Moriya interaction. Hereby we focus on device
feature sizes and spin-wave wavelengths compatible with state-of-the art
excitation and detection schemes. We demonstrate that the optimum operation
conditions for the non-reciprocal emission can be predicted using the presented
analytical formalism


title: On the definition of spacetimes in Noncommutative Geometry, part II

abstract:
  In this second part of the paper, we define spectral spacetimes, a
noncommutative generalization of Lorentzian orientable spacetimes of even
dimension with a spin structure. There are two main differences with spectral
triples: the existence of time-orientation 1-forms and the non-existence of a
distinguished C*-structure on the algebra. If a "reconstructibility condition"
is met, different, yet isomorphic, C*-structures exist. We define a natural
notion of stable causality for spectral spacetimes. We give an example of a
commutative spectral spacetime which is a Wick rotated version of the spectral
triple that must be used in order to recover the usual notion of distance on a
finite graph through Connes' distance formula. We show that this spectral
spacetime is stably causal iff the time-orientation form induces no cycle. We
also provide a noncommutative example, the split Dirac structure, which we
study in some details. This structure is defined thanks to a discrete spinor
bundle on a finite graph, a discrete connection, and operators at the vertices
playing the role of gamma matrices. We give necessary and sufficient conditions
for the split Dirac structure to be a spectral spacetime. These includes the
natural analogues of the properties defining a spin connection in the
continuous case. However the split Dirac structure is not always
reconstructible: we prove that this is the case exactly when there exists a
parallel timelike vector field on the graph. Nonreconstructible split Dirac
structures furnish examples of spectral spacetimes which are not Wick rotations
of usual spectral triples, and are thus genuinely Lorentzian. Moreover we show
that the Dirac operator of the split Dirac structure is related to a Lorentzian
version of a discretization of the Dirac operator introduced earlier by
Marcolli and van Suijlekom.


title:
Portfolio choice, portfolio liquidation, and portfolio transition under
  drift uncertainty

abstract:
  This paper presents several models addressing optimal portfolio choice,
optimal portfolio liquidation, and optimal portfolio transition issues, in
which the expected returns of risky assets are unknown. Our approach is based
on a coupling between Bayesian learning and dynamic programming techniques that
leads to partial differential equations. It enables to recover the well-known
results of Karatzas and Zhao in a framework \`a la Merton, but also to deal
with cases where martingale methods are no longer available. In particular, we
address optimal portfolio choice, portfolio liquidation, and portfolio
transition problems in a framework \`a la Almgren-Chriss, and we build
therefore a model in which the agent takes into account in his decision process
both the liquidity of assets and the uncertainty with respect to their expected
return.


title: New Searches for CPT Violation in Neutral-Meson Oscillations

abstract:
  Classic tests of CPT symmetry have been done in the neutral-meson system.
These have been continued with new results in the framework of the
Standard-Model Extension, where the coefficient for CPT violation is both boost
and direction dependent. Recent contributions and new phenomenological
improvements are discussed with possible new contributions for $b$ and $d$
specific correlated decays at the Belle II asymmetric energy collider.


title:
Cosmic-muon characterization and annual modulation measurement with
  Double Chooz detectors

abstract:
  A study on cosmic muons has been performed for the two identical near and far
neutrino detectors of the Double Chooz experiment, placed at $\sim$120 and
$\sim$300 m.w.e. underground respectively, including the corresponding
simulations using the MUSIC simulation package. This characterization has
allowed to measure the muon flux reaching both detectors to be (3.64 $\pm$
0.04) $\times$ 10$^{-4}$ cm$^{-2}$s$^{-1}$ for the near detector and (7.00
$\pm$ 0.05) $\times$ 10$^{-5}$ cm$^{-2}$s$^{-1}$ for the far one. The seasonal
modulation of the signal has also been studied observing a positive correlation
with the atmospheric temperature, leading to an effective temperature
coefficient of $\alpha_{T}$ = 0.212 $\pm$ 0.024 and 0.355 $\pm$ 0.019 for the
near and far detectors respectively. These measurements, in good agreement with
expectations based on theoretical models, represent one of the first
measurements of this coefficient in shallow depth installations.


title: Non-Collinearity in Small Magnetic Cobalt-Benzene Molecules

abstract:
  Organometallic clusters based on transition metal atoms are interesting
because possible applications in spintronics and quantum information. In
addition to the enhanced magnetism at the nanoscale, the organic ligands may
provide a natural shield again unwanted magnetic interactions with the matrices
required for applications. Here we show that the organic ligands may lead to
non-collinear magnetic order as well as the expected quenching of the magnetic
moments. We use different density functional theory (DFT) methods to study the
experimentally relevant three cobalt atoms surrounded by benzene rings
(Co$_3$Bz$_3$). We found that the benzene rings induce a ground state with
non-collinear magnetization, with the magnetic moments localized on the cobalt
centers and lying on the plane formed by the three cobalt atoms. We further
analyze the magnetism of such a cluster using an anisotropic Heisenberg model
where the involved parameters are obtained by a comparison with the DFT
results. These results may also explain the recent observation of null magnetic
moment of Co$_3$Bz$_3^+$. Moreover, we propose an additional experimental
verification based on electron paramagnetic resonance.


title:
A novel approach to quantifying the sensitivity of current and future
  cosmological datasets to the neutrino mass ordering through Bayesian
  hierarchical modeling

abstract:
  We present a novel approach to derive constraints on neutrino masses from
cosmological data, while taking into account our ignorance of the neutrino mass
ordering. We derive constraints from a combination of current and future
cosmological datasets on the total neutrino mass $M_\nu$ and on the mass
fractions carried by each of the mass eigenstates, after marginalizing over the
(unknown) neutrino mass ordering, either normal (NH) or inverted (IH). The
bounds take therefore into account the uncertainty related to our ignorance of
the mass hierarchy. This novel approach is carried out in the framework of
Bayesian analysis of a typical hierarchical problem. In this context, the
choice of the neutrino mass ordering is modeled via the discrete hyperparameter
$h_{type}$. The preference for either the NH or the IH scenarios is then
encoded in the posterior distribution of $h_{type}$ itself. Current CMB
measurements assign equal odds to the two hierarchies, and are thus unable to
distinguish between them. However, after the addition of BAO measurements, a
weak preference for NH appears, with odds of 4:3 from Planck temperature and
large-scale polarization in combination with BAO (3:2 if small-scale
polarization is also included). Forecasts suggest that the combination of
upcoming CMB (COrE) and BAO surveys (DESI) may determine the neutrino mass
hierarchy at a high statistical significance if the mass is very close to the
minimal value allowed by oscillations, as for NH and $M_\nu=0.06$ eV there is a
9:1 preference of NH vs IH. On the contrary, if $M_\nu$ is of the order of 0.1
eV or larger, even future cosmological observations will be inconclusive. The
unbiased limit on $M_\nu$ we obtain with this innovative statistical strategy
is crucial for ongoing and planned neutrinoless double beta decay searches.


title: On Integer-Forcing Precoding for the Gaussian MIMO Broadcast Channel

abstract:
  Integer-forcing (IF) precoding, also known as downlink IF, is a promising new
approach for communication over multiple-input multiple-output (MIMO) broadcast
channels. Inspired by the integer-forcing linear receiver for multiple-access
channels, it generalizes linear precoding by inducing an effective channel
matrix that is approximately integer, rather than approximately identity.
Combined with lattice encoding and a pre-inversion of the channel matrix at the
transmitter, the scheme has the potential to outperform any linear precoding
scheme, despite enjoying similar low complexity.
  In this paper, a specific IF precoding scheme, called diagonally-scaled exact
IF (DIF), is proposed and shown to achieve maximum spatial multiplexing gain.
For the special case of two receivers, in the high SNR regime, an optimal
choice of parameters is derived analytically, leading to an almost closed-form
expression for the achievable sum rate. In particular, it is shown that the gap
to the sum capacity is upper bounded by 0.27 bits for any channel realization.
For general SNR, a regularized version of DIF (RDIF) is proposed. Numerical
results for two receivers under Rayleigh fading show that RDIF can achieve
performance superior to optimal linear precoding and very close to the sum
capacity.


title: General Relativity from Three-Forms in Seven Dimensions

abstract:
  We consider a certain theory of 3-forms in 7 dimensions, and study its
dimensional reduction to 4D, compactifying the 7-dimensional manifold on the
3-sphere of a fixed radius. We show that the resulting 4D theory is General
Relativity (GR) in Plebanski formulation, modulo corrections that are
negligible for curvatures smaller than Planckian. Possibly the most interesting
point of this construction is that the dimensionally reduced theory is GR with
a non-zero cosmological constant, and the value of the cosmological constant is
directly related to the size of S^3. Realistic values of Lambda correspond to
S^3 of Planck size.


title:
Robust Unsupervised Transient Detection With Invariant Representation
  based on the Scattering Network

abstract:
  We present a sparse and invariant representation with low asymptotic
complexity for robust unsupervised transient and onset zone detection in noisy
environments. This unsupervised approach is based on wavelet transforms and
leverages the scattering network from Mallat et al. by deriving frequency
invariance. This frequency invariance is a key concept to enforce robust
representations of transients in presence of possible frequency shifts and
perturbations occurring in the original signal. Implementation details as well
as complexity analysis are provided in addition of the theoretical framework
and the invariance properties. In this work, our primary application consists
of predicting the onset of seizure in epileptic patients from subdural
recordings as well as detecting inter-ictal spikes.


title:
Approximate Quantum Adders with Genetic Algorithms: An IBM Quantum
  Experience

abstract:
  It has been proven that quantum adders are forbidden by the laws of quantum
mechanics. We analyze theoretical proposals for the implementation of
approximate quantum adders and optimize them by means of genetic algorithms,
improving previous protocols in terms of efficiency and fidelity. Furthermore,
we experimentally realize a suitable approximate quantum adder with the cloud
quantum computing facilities provided by IBM Quantum Experience. The
development of approximate quantum adders enhances the toolbox of quantum
information protocols, paving the way for novel applications in quantum
technologies.


title: Heat dissipation and fluctuations in a driven quantum dot

abstract:
  While thermodynamics is a useful tool to describe the driving of large
systems close to equilibrium, fluctuations dominate the distribution of heat
and work in small systems and far from equilibrium. We study the heat generated
by driving a small system and change the drive parameters to analyse the
transition from a drive leaving the system close to equilibrium to driving it
far from equilibrium. Our system is a quantum dot in a GaAs/AlGaAs
heterostructure hosting a two-dimensional electron gas. The dot is
tunnel-coupled to one part of the two-dimensional electron gas acting as a heat
and particle reservoir. We use standard rate equations to model the driven
dot-reservoir system and find excellent agreement with the experiment.
Additionally, we quantify the fluctuations by experimentally test the
theoretical concept of the arrow of time, predicting our ability to distinguish
whether a process goes in the forward or backward drive direction.


title: Vector-valued multibang control of differential equations

abstract:
  We consider a class of (ill-posed) optimal control problems in which a
distributed vector-valued control is enforced to pointwise take values in a
finite set $\mathcal{M}\subset\mathbb{R}^m$. After convex relaxation, one
obtains a well-posed optimization problem, which still promotes control values
in $\mathcal{M}$. We state the corresponding well-posedness and stability
analysis and exemplify the results for two specific cases of quite general
interest, optimal control of the Bloch equation and optimal control of an
elastic deformation. We finally formulate a semismooth Newton method to
numerically solve a regularized version of the optimal control problem and
illustrate the behavior of the approach for our example cases.


title:
Renormalization group approach to scalar quantum electrodynamics on de
  Sitter

abstract:
  We consider the quantum loop effects in scalar electrodynamics on de Sitter
space by making use of the functional renormalization group approach. We first
integrate out the photon field, which can be done exactly to leading (zeroth)
order in the gradients of the scalar field, thereby making this method suitable
for investigating the dynamics of the infrared sector of the theory. Assuming
that the scalar remains light we then apply the functional renormalization
group methods to the resulting effective scalar theory and focus on
investigating the effective potential, which is the leading order contribution
in the gradient expansion of the effective action. We find symmetry restoration
at a critical renormalization scale $\kappa=\kappa_{\rm cr}$ much below the
Hubble scale $H$. When compared with the results of Serreau and Guilleux
[arXiv:1306.3846 [hep-th], arXiv:1506.06183 [hep-th]] we find that the photon
facilitates symmetry restoration such that it occurs at an RG scale
$\kappa_{\rm cr}$ that is higher than in the case of a pure scalar theory. The
true effective potential is recovered when $\kappa\rightarrow 0$ and in that
limit one obtains the results that agree with those of stochastic inflation,
provided one interprets it in the sense as advocated by Lazzari and Prokopec
[arXiv:1304.0404 [hep-th]].


title: A streamlined approach to particle ALD coating of spherical beads

abstract:
  Conformal Atomic Layer Deposition (ALD) of nanoparticles is an now an
established nanofabrication concept employed by many researchers for
applications such as creating diffusion barriers, tuning catalysis, or masking
a toxic particle core with a biocompatible shell. To conformally coat many
grams of nanoparticles with ALD, long precursor soaking steps, fluidized beds,
vibrating stages, or rotary feedthroughs are typically needed. While these
impressive advancements in ALD techniques dominate literature searches of
particle ALD coating, such methods may lead to a more time-intensive or
cost-prohibitive process than what is required by many typical academic
researchers. Thus we have performed this study to explore the limits of static
planar ALD particle coating, the simplest method to coat nanoparticles with an
ALD film. Using an Arradiance GEMStar6 ALD system, we have explored a fast and
simple static ALD particle coating process. Our protocol produces relatively
small, but still academically useful, quantities of uniformally ALD-coated
nanospheres. This process can be scaled up to nanoparticle samples in the tens
of milligram to gram range. We have demonstrated that we can achieve silica or
titania spherical particle synthesis, and then uniform ALD coating on the
nanoparticles, all within 8-10 hours. The diameter of the chemically
synthesized silica and titania nanoparticles is tunable from 50 nm up to
greater than a micron. The refractive index of the titania nanoparticles is
tunable from approximately 1.7 to 2.7. This report will be most useful for
researchers who are new to particle ALD, or who want to experiment with core
particles conformally covered with ALD shells before moving to a more
complicated, higher throughput ALD method. We provide details for particle
synthesis, storage, and ALD coating along with a comparison to more
conventional approaches.


title: When "Optimal Filtering" Isn't

abstract:
  The so-called "optimal filter" analysis of a microcalorimeter's x-ray pulses
is statistically optimal only if all pulses have the same shape, regardless of
energy. The shapes of pulses from a nonlinear detector can and do depend on the
pulse energy, however. A pulse-fitting procedure that we call "tangent
filtering" accounts for the energy dependence of the shape and should therefore
achieve superior energy resolution. We take a geometric view of the
pulse-fitting problem and give expressions to predict how much the energy
resolution stands to benefit from such a procedure. We also demonstrate the
method with a case study of K-line fluorescence from several 3d transition
metals. The method improves the resolution from 4.9 eV to 4.2 eV at the Cu
K$\alpha$ line (8.0keV).


title: A universal shape function for rising jets

abstract:
  A small drop that splashes into a deep liquid sometimes reappears as a small
rising jet, for example when a water drop splashes into a pool or when coffee
drips into a cup. Here we describe that the growing and rising jet continuously
redistributes its fluid to maintain a universal shape originating from a
surface tension based deceleration of the jet; the shape is universal in the
sense that the shape of the rising jet is the same at all times; only the
scaling depends on fluid parameters and deceleration. An inviscid equation of
motion for the jet is proposed assuming a time dependent but uniform
deceleration; the equation of motion is made dimensionless by using a
generalized time-dependent capillary length ${\lambda_c}$ and is solved
numerically. As a solution a concave shape function is found that is fully
determined by three measurable physical parameters: deceleration, mass density
and surface tension; it is found that the surface tension based deceleration of
the jet scales quadratic with the size of the jet base. Deceleration values
derived from the jet shape are in good agreement with deceleration values
calculated from the time plot of the height of the rising jet.


title:
Leavitt path algebras with bounded index of nilpotence and simple
  modules over them

abstract:
  In this paper we completely describe graphically Leavitt path algebras with
bounded index of nilpotence and show that each graded simple module $S$ over a
Leavitt path algebra with bounded index of nilpotence is graded
$\Sigma$-injective, that is, $S^{(\alpha)}$ is graded injective for any
cardinal $\alpha$. Furthermore, we characterize Leavitt path algebras over
which each simple module is $\Sigma$-injective. We have shown that each simple
module over a Leavitt path algebra $L_K(E)$ is $\Sigma$-injective if and only
if the graph $E$ contains no cycles, and there is a positive integer $d$ such
that the length of any path in $E$ is less than or equal to $d$ and the number
of distinct paths ending at any vertex $v$ (including $v$) is less than or
equal to $d$.


title:
Why does steady-state magnetic reconnection have a maximum local rate of
  order 0.1?

abstract:
  Simulations suggest collisionless steady-state magnetic reconnection of
Harris-type current sheets proceeds with a rate of order 0.1, independent of
dissipation mechanism. We argue this long-standing puzzle is a result of
constraints at the magnetohydrodynamic (MHD) scale. We perform a scaling
analysis of the reconnection rate as a function of the opening angle made by
the upstream magnetic fields, finding a maximum reconnection rate close to 0.2.
The predictions compare favorably to particle-in-cell simulations of
relativistic electron-positron and non-relativistic electron-proton
reconnection. The fact that simulated reconnection rates are close to the
predicted maximum suggests reconnection proceeds near the most efficient state
allowed at the MHD-scale. The rate near the maximum is relatively insensitive
to the opening angle, potentially explaining why reconnection has a similar
fast rate in differing models.

categories: physics.plasm-ph astro-ph.EP astro-ph.HE astro-ph.SR physics.space-ph


title: Accurate barrier heights using diffusion Monte Carlo

abstract:
  Fixed node diffusion Monte Carlo (DMC) has been performed on a test set of
forward and reverse barrier heights for 19 non-hydrogen-transfer reactions, and
the nodal error has been assessed. The DMC results are robust to changes in the
nodal surface, as assessed by using different mean-field techniques to generate
single determinant wave functions. Using these single determinant nodal
surfaces, DMC results in errors of 1.5(5) kcal/mol on barrier heights. Using
the large data set of DMC energies, we attempted to find good descriptors of
the fixed node error. It does not correlate with a number of descriptors
including change in density, but does correlate with the gap between the
highest occupied and lowest unoccupied orbital energies in the mean-field
calculation.


title: Charge ordering and correlation effects in the extended Hubbard model

abstract:
  We study the half filled extended Hubbard model on a two-dimensional square
lattice using cluster dynamical mean field theory on clusters of size 8-20. We
show that the model exhibits metallic, Mott insulating, and charge ordered
phases, and determine the location of the charge ordering phase transition line
and the properties of the ordered and disordered phase as a function of
temperature, local interaction, and nearest neighbor interaction. We find
strong non-local correlations in the uniform phase and a pronounced screening
effect in the vicinity of the phase transition, where non-local interactions
push the system towards metallic behavior. In contrast, correlations in the
ordered phase are mostly local to the unit cell. Extrapolation to the
thermodynamic limit and control of all sources of errors allow us to assess the
regime of applicability of simpler approximation schemes for systems with
non-local interactions. We also demonstrate how strong non-local
electron-electron interactions can increase electron mobility by turning a
charge ordered insulator into a metal.


title: Browsix: Bridging the Gap Between Unix and the Browser

abstract:
  Applications written to run on conventional operating systems typically
depend on OS abstractions like processes, pipes, signals, sockets, and a shared
file system. Porting these applications to the web currently requires extensive
rewriting or hosting significant portions of code server-side because browsers
present a nontraditional runtime environment that lacks OS functionality.
  This paper presents Browsix, a framework that bridges the considerable gap
between conventional operating systems and the browser, enabling unmodified
programs expecting a Unix-like environment to run directly in the browser.
Browsix comprises two core parts: (1) a JavaScript-only system that makes core
Unix features (including pipes, concurrent processes, signals, sockets, and a
shared file system) available to web applications; and (2) extended JavaScript
runtimes for C, C++, Go, and Node.js that support running programs written in
these languages as processes in the browser. Browsix supports running a POSIX
shell, making it straightforward to connect applications together via pipes.
  We illustrate Browsix's capabilities via case studies that demonstrate how it
eases porting legacy applications to the browser and enables new functionality.
We demonstrate a Browsix-enabled LaTeX editor that operates by executing
unmodified versions of pdfLaTeX and BibTeX. This browser-only LaTeX editor can
render documents in seconds, making it fast enough to be practical. We further
demonstrate how Browsix lets us port a client-server application to run
entirely in the browser for disconnected operation. Creating these applications
required less than 50 lines of glue code and no code modifications,
demonstrating how easily Browsix can be used to build sophisticated web
applications from existing parts without modification.


title: Adiabatic invariants for the regular region of the Dicke model

abstract:
  Adiabatic invariants are introduced and shown to provide an approximate
second integral of motion for the non-integrable Dicke model, in the energy
region where the system exhibits a regular dynamics. This low-energy region is
always present and has been described both in a semiclassical and a full
quantum analysis. Its Peres lattices exhibit that many observables vary
smoothly with energy, along lines which beg for a formal description. It is
shown how the adiabatic invariants provide a rationale to their presence in
many cases. They are built employing the Born-Oppenheimer approximation, valid
when a fast system is coupled to a much slower one. As the Dicke model has a
one bosonic and one fermionic degree of freedom, two versions of the
approximation are used, depending on which one is the faster. In both cases a
noticeably accord with exact numerical results is obtained. The employment of
the adiabatic invariants provides a simple and clear theoretical framework to
study the physical phenomenology associated to this energy regime, far beyond
the energies where the quadratic approximation can be employed.


title: Physics at the LHC Run-2 and Beyond

abstract:
  These lecture notes discuss methods, recent results and future prospects in
proton-proton physics at the Large Hadron Collider.


title: Controlling Perceptual Factors in Neural Style Transfer

abstract:
  Neural Style Transfer has shown very exciting results enabling new forms of
image manipulation. Here we extend the existing method to introduce control
over spatial location, colour information and across spatial scale. We
demonstrate how this enhances the method by allowing high-resolution controlled
stylisation and helps to alleviate common failure cases such as applying ground
textures to sky regions. Furthermore, by decomposing style into these
perceptual factors we enable the combination of style information from multiple
sources to generate new, perceptually appealing styles from existing ones. We
also describe how these methods can be used to more efficiently produce large
size, high-quality stylisation. Finally we show how the introduced control
measures can be applied in recent methods for Fast Neural Style Transfer.


title:
Minimizing the Union: Tight Approximations for Small Set Bipartite
  Vertex Expansion

abstract:
  In the Minimum k-Union problem (MkU) we are given a set system with n sets
and are asked to select k sets in order to minimize the size of their union.
Despite being a very natural problem, it has received surprisingly little
attention: the only known approximation algorithm is an
$O(\sqrt{n})$-approximation due to [Chlamt\'a\v{c} et al APPROX '16]. This
problem can also be viewed as the bipartite version of the Small Set Vertex
Expansion problem (SSVE), which we call the Small Set Bipartite Vertex
Expansion problem (SSBVE). SSVE, in which we are asked to find a set of k nodes
to minimize their vertex expansion, has not been as well studied as its
edge-based counterpart Small Set Expansion (SSE), but has recently received
significant attention, e.g. [Louis-Makarychev APPROX '15]. However, due to the
connection to Unique Games and hardness of approximation the focus has mostly
been on sets of size $k = \Omega(n)$, while we focus on the case of general
$k$, for which no polylogarithmic approximation is known.
  We improve the upper bound for this problem by giving an
$n^{1/4+\varepsilon}$ approximation for SSBVE for any constant $\varepsilon >
0$. Our algorithm follows in the footsteps of Densest $k$-Subgraph (DkS) and
related problems, by designing a tight algorithm for random models, and then
extending it to give the same guarantee for arbitrary instances. Moreover, we
show that this is tight under plausible complexity conjectures: it cannot be
approximated better than $O(n^{1/4})$ assuming an extension of the so-called
"Dense vs Random" conjecture for DkS to hypergraphs. We show that the same
bound is also matched by an integrality gap for a super-constant number of
rounds of the Sherali-Adams LP hierarchy, and an even worse integrality gap for
the natural SDP relaxation. Finally, we design a simple bicriteria $\tilde
O(\sqrt{n})$ approximation for the more general SSVE problem.


title:
Analysis on 60 GHz Wireless Communications with Beamwidth-Dependent
  Misalignment

abstract:
  High speed wireless access on 60 GHz spectrum relies on high-gain directional
antennas to overcome the severe signal attenuation. However, perfect alignment
between transmitting and receiving antenna beams is rare in practice and
overheard signals from concurrent transmissions may cause significant
interference. In this paper we analyze the impact of antenna beam misalignment
on the system performance of 60 GHz wireless access. We quantify the signal
power loss caused by beam misalignment and the interference power accumulated
from neighboring concurrent transmissions whose signals are leaked either via
the main-beam pointing in the similar direction or via side-lobe emission, and
derive the probability distribution of the signal to interference plus noise
power ratio (SINR). For scenarios where interfering transmitters are
distributed uniformly at random, we derive upper and lower bounds on the
cumulative distribution function (abbreviated as CDF or c.d.f.) of SINR, which
can be easily applied to evaluate system performance. We validate our
analytical results by simulations where random nodes are uniformly distributed
within a circular hall, and evaluate the sensitivity of average throughput and
outage probability against two parameters: the half-power (3 dB) beamwidth to
main-lobe beamwidth ratio and the beam misalignment deviation to main-lobe
beamwidth ratio. Our results indicate that the derived lower bound performs
well when the half-power beamwidth to main-lobe beamwidth ratio or the number
of concurrent transmission links is small. When the number of active links is
high, it is desirable in antenna design to balance the degradation caused by
beam misalignment (wider beam is better) and the interference from concurrent
transmission (narrower beam is better).


title:
Star formation and gas flows in the centre of the NUGA galaxy NGC 1808
  observed with SINFONI

abstract:
  NGC 1808 is a nearby barred spiral galaxy which hosts young stellar clusters
in a patchy circumnuclear ring with a radius of $\sim 240\,\mathrm{pc}$. In
order to study the gaseous and stellar kinematics and the star formation
properties of the clusters, we perform seeing-limited $H+K$-band near-infrared
integral-field spectroscopy with SINFONI of the inner $\sim 600\,\mathrm{pc}$.
From the $M_\mathrm{BH}-\sigma_*$ relation, we find a black hole mass of a few
$10^7\,M_\odot$. We estimate the age of the young stellar clusters in the
circumnuclear ring to be $\lesssim 10\,\mathrm{Myr}$. No age gradient along the
ring is visible. However, the starburst age is comparable to the travel time
along the ring, indicating that the clusters almost completed a full orbit
along the ring during their life time. In the central $\sim 600\,\mathrm{pc}$,
we find a hot molecular gas mass of $\sim 730\,M_\odot$ which, with standard
conversion factors, corresponds to a large cold molecular gas reservoir of
several $10^8\,M_\odot$, in accordance with CO measurements from the
literature. The gaseous and stellar kinematics show several deviations from
pure disc motion, including a circumnuclear disc and signs of a nuclear bar
potential. In addition, we confirm streaming motions on $\sim 200\,\mathrm{pc}$
scale that have recently been detected in CO(1-0) emission. Due to our enhanced
angular resolution of $<1\,\mathrm{arcsec}$, we find further streaming motion
within the inner arcsecond, that have not been detected until now. Despite the
flow of gas towards the centre, no signs for significant AGN activity are
found. This raises the questions what determines whether the infalling gas will
fuel an AGN or star formation.


title:
Characterization of ${\cal B}(\infty)$ using marginally large tableaux
  and rigged configurations in the $A_n$ case via integer sequences

abstract:
  Rigged configurations are combinatorial objects prominent in the study of
solvable lattice models. Marginally large tableaux are semi-standard Young
tableaux of special form that give a realization of the crystals ${\cal
B}(\infty)$. We introduce cascading sequences to characterize marginally large
tableaux. Then we use cascading sequences and a non-explicit crystal
isomorphism between marginally large tableaux and rigged configurations to give
a characterization of the latter set, and to give an explicit bijection between
the two sets.


title:
Sub-shot-noise transmission measurement using optically gated single
  photons

abstract:
  Harnessing the unique properties of quantum mechanics offers the possibility
to deliver new technologies that can fundamentally outperform their classical
counterparts. These technologies only deliver advantages when components
operate with performance beyond specific thresholds. For optical quantum
metrology, the biggest challenge that impacts on performance thresholds is
optical loss. Here we demonstrate how including an optical delay and an optical
switch in a feed-forward configuration with a stable and efficient correlated
photon pair source reduces the detector efficiency required to enable quantum
enhanced sensing down to the detection level of single photons. When the switch
is active, we observe a factor of improvement in precision of 1.27 for
transmission measurement on a per input photon basis, compared to the
performance of a laser emitting an ideal coherent state and measured with the
same detection efficiency as our setup. When the switch is inoperative, we
observe no quantum advantage.


title:
Demonstrating an absolute quantum advantage in direct absorption
  measurement

abstract:
  Engineering apparatus that harness quantum theory offers practical advantages
over current technology. A fundamentally more powerful prospect is the
long-standing prediction that such quantum technologies could out-perform any
future iteration of their classical counterparts, no matter how well the
attributes of those classical strategies can be improved. Here, we
experimentally demonstrate such an instance of \textit{absolute} advantage per
photon probe in the precision of optical direct absorption measurement. We use
correlated intensity measurements of spontaneous parametric downconversion
using a commercially available air-cooled CCD, a new estimator for data
analysis and a high heralding efficiency photon-pair source. We show this
enables improvement in the precision of measurement, per photon probe, beyond
what is achievable with an ideal coherent state (a perfect laser) detected with
$100\%$ efficient and noiseless detection. We see this absolute improvement for
up to $50\%$ absorption, with a maximum observed factor of improvement of 1.46.
This equates to around $32\%$ reduction in the total number of photons
traversing an optical sample, compared to any future direct optical absorption
measurement using classical light.


title:
Correlations between Supermassive Black Holes and their Hosts in Active
  Galaxies

abstract:
  In the last decades several correlations between the mass of the central
supermassive black hole (BH) and properties of the host galaxy - such as bulge
luminosity and mass, central stellar velocity dispersion, S\'ersic index,
spiral pitch angle etc. - have been found and point at a coevolution scenario
of BH and host galaxy. In this article, I review some of these relations for
inactive galaxies and discuss the findings for galaxies that host an active
galactic nucleus/quasar. I present the results of our group that finds that
active galaxies at $z\lesssim 0.1$ do not follow the BH mass - bulge luminosity
relation. Furthermore, I show near-infrared integral-field spectroscopic data
that suggest that young stellar populations cause the bulge overluminosity and
indicate that the host galaxy growth started first. Finally, I discuss
implications for the BH-host coevolution.


title: Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlo

abstract:
  Recently there have been exciting developments in Monte Carlo methods, with
the development of new MCMC and sequential Monte Carlo (SMC) algorithms which
are based on continuous-time, rather than discrete-time, Markov processes. This
has led to some fundamentally new Monte Carlo algorithms which can be used to
sample from, say, a posterior distribution. Interestingly, continuous-time
algorithms seem particularly well suited to Bayesian analysis in big-data
settings as they need only access a small sub-set of data points at each
iteration, and yet are still guaranteed to target the true posterior
distribution. Whilst continuous-time MCMC and SMC methods have been developed
independently we show here that they are related by the fact that both involve
simulating a piecewise deterministic Markov process. Furthermore we show that
the methods developed to date are just specific cases of a potentially much
wider class of continuous-time Monte Carlo algorithms. We give an informal
introduction to piecewise deterministic Markov processes, covering the aspects
relevant to these new Monte Carlo algorithms, with a view to making the
development of new continuous-time Monte Carlo more accessible. We focus on how
and why sub-sampling ideas can be used with these algorithms, and aim to give
insight into how these new algorithms can be implemented, and what are some of
the issues that affect their efficiency.


title: Chern-Simons-matter dualities with $SO$ and $USp$ gauge groups

abstract:
  In the last few years several dualities were found between the low-energy
behaviors of Chern-Simons-matter theories with unitary gauge groups coupled to
scalars, and similar theories coupled to fermions. In this paper we generalize
those dualities to orthogonal and symplectic gauge groups. In particular, we
conjecture dualities between $SO(N)_k$ Chern-Simons theories coupled to $N_f$
real scalars in the fundamental representation, and $SO(k)_{-N+N_f/2}$ coupled
to $N_f$ real (Majorana) fermions in the fundamental. For $N_f=0$ these are
just level-rank dualities of pure Chern-Simons theories, whose precise form we
clarify. They lead us to propose new gapped boundary states of topological
insulators and superconductors. For $k=1$ we get an interesting low-energy
duality between $N_f$ free Majorana fermions and an $SO(N)_1$ Chern-Simons
theory coupled to $N_f$ scalar fields (with $N_f \leq N-2$).


title:
On a phase field approximation of the planar Steiner problem: existence,
  regularity, and asymptotic of minimizers

abstract:
  In this article, we consider and analyse a small variant of a functional
originally introduced in \cite{BLS,LS} to approximate the (geometric) planar
Steiner problem. This functional depends on a small parameter $\varepsilon>0$
and resembles the (scalar) Ginzburg-Landau functional from phase transitions.
In a first part, we prove existence and regularity of minimizers for this
functional. Then we provide a detailed analysis of their behavior as
$\varepsilon\to0$, showing in particular that sublevel sets Hausdorff converge
to optimal Steiner sets. Applications to the average distance problem and
optimal compliance are also discussed.


title: Cointegrated Continuous-time Linear State Space and MCARMA Models

abstract:
  In this paper we define and characterize cointegrated continuous-time linear
state-space models. A main result is that a cointegrated continuous-time linear
state-space model can be represented as a sum of a L\'evy process and a
stationary linear state-space model. Moreover, we prove that the class of
cointegrated multivariate L\'evy-driven autoregressive moving-average (MCARMA)
processes, the continuous-time analogues of the classical vector ARMA
processes, is equivalent to the class of cointegrated continuous-time linear
state space models. Necessary and sufficient conditions for MCARMA processes to
be cointegrated are given as well extending the results of Comte for MCAR
processes. The conditions depend on the autoregressive polynomial. Finally, we
investigate cointegrated continuous-time linear state-space models observed on
a discrete time-grid and derive an error correction form for this model. The
error correction form is based on an infinite linear filter in contrast to the
finite linear filter for VAR models.


title: On transparent embeddings of point-line geometries

abstract:
  We introduce the class of transparent embeddings for a point-line geometry
$\Gamma = ({\mathcal P},{\mathcal L})$ as the class of full projective
embeddings $\varepsilon$ of $\Gamma$ such that the preimage of any projective
line fully contained in $\varepsilon({\mathcal P})$ is a line of $\Gamma$. We
will then investigate the transparency of Pl\"ucker embeddings of projective
and polar grassmannians and spin embeddings of half-spin geometries and dual
polar spaces of orthogonal type. As an application of our results on
transparency, we will derive several Chow-like theorems for polar grassmannians
and half-spin geometries.


title: Kinematics of Einstein-Cartan universes

abstract:
  We analyse the kinematics of cosmological spacetimes with nonzero torsion, in
the framework of the classical Einstein-Cartan gravity. After a brief
introduction to the basic features of spaces with non-vanishing torsion, we
consider a family of observers moving along timelike worldlines and focus on
their kinematic behaviour. In so doing, we isolate the irreducible variables
monitoring the observers' motion and derive their evolution formulae and
associated constraint equations. Our aim is to identify the effects of
spacetime torsion, and the changes they introduce into the kinematics of the
standard, torsion-free, cosmological models. We employ a fully geometrical
approach, imposing no restrictions on the material content, or any a priori
couplings between torsion and spin. Also, we do not apply the familiar
splitting of the equations, into a purely Riemannian component plus a
torsion/spin part, at the start of our study, but only introduce it at the very
end. With the general formulae at hand, we use the Einstein-Cartan field
equations to incorporate explicitly the spin of the matter. The resulting
formulae fully describe the kinematics of dynamical spacetimes within the
framework of the Einstein-Cartan gravity, while in the special case of the
so-called Weyssenhoff fluid, they recover results previously reported in the
literature.


title: Testing submodularity and other properties of valuation functions

abstract:
  We show that for any constant $\epsilon > 0$ and $p \ge 1$, it is possible to
distinguish functions $f : \{0,1\}^n \to [0,1]$ that are submodular from those
that are $\epsilon$-far from every submodular function in $\ell_p$ distance
with a constant number of queries.
  More generally, we extend the testing-by-implicit-learning framework of
Diakonikolas et al. (2007) to show that every property of real-valued functions
that is well-approximated in $\ell_2$ distance by a class of $k$-juntas for
some $k = O(1)$ can be tested in the $\ell_p$-testing model with a constant
number of queries. This result, combined with a recent junta theorem of Feldman
and Vondrak (2016), yields the constant-query testability of submodularity. It
also yields constant-query testing algorithms for a variety of other natural
properties of valuation functions, including fractionally additive (XOS)
functions, OXS functions, unit demand functions, coverage functions, and
self-bounding functions.


title: On the fiber product of Riemann surfaces

abstract:
  Let $S_{0}, S_{1}$ and $S_{2}$ be connected Riemann surfaces and let
$\beta_{1}:S_{1} \to S_{0}$ and $\beta_{2}:S_{2} \to S_{0}$ be surjective
holomorphic maps. The associated fiber product
  $S_{1} \times_{(\beta_{1},\beta_{2})} S_{2}$ has the structure of a singular
Riemann surface, endowed with a canonical map $\beta$ to $S_{0}$ satisfying
that $\beta_{j} \circ \pi_{j}=\beta$, where $\pi_{j}$ is coordinate projection
onto $S_{j}$. In this paper we provide a Fuchsian description of the fiber
product and obtain that if one the maps $\beta_{j}$ is a regular branched
cover, then all its irreducible components are isomorphic.
  In the case that both $\beta_{j}$ are of finite degree, we observe that the
number of irreducible components is bounded above by the greatest common
divisor of the two degrees; we study the irreducibility of the fiber product.
  In the case that $S_{0}=\widehat{\mathbb C}$, and $S_{1}$ and $S_{2}$ are
compact, we define the strong field of moduli of the pair $(S_{1}
\times_{(\beta_{1},\beta_{2})} S_{2},\beta)$ and observe that this field
coincides with the minimal field containing the fields of moduli of both pairs
$(S_{1},\beta_{1})$ and $(S_{2},\beta_{2})$. Finally, in the case that the
fiber product is a connected Riemann surface, we provide an isogenous
decomposition of its Jacobian variety.


title: Conservative discretization of the Landau collision integral

abstract:
  We describe a density-, momentum-, and energy-conserving discretization of
the nonlinear Landau collision integral. The method is suitable for both the
finite-element and discontinuous Galerkin methods and does not require
structured meshes. The conservation laws for the discretization are proven
algebraically and demonstrated numerically for an axially symmetric nonlinear
relaxation problem using a finite-element implementation.


title: Chern classes with modulus

abstract:
  In this paper, we construct Chern classes from the relative $K$-theory of
modulus pairs to the relative motivic cohomology defined by Binda-Saito. An
application to relative motivic cohomology of henselian dvr is given.


title:
Gaia Assorted Mass Binaries Long Excluded from SLoWPoKES (GAMBLES):
  Identifying Ultra-Wide Binary Pairs with Components of Diverse Mass

abstract:
  The formation and evolution of binary star systems still remain key questions
in modern astronomy. Wide binary pairs (separations $>10^3$ AU) are
particularly intriguing because their low binding energies make it difficult
for the stars to stay gravitationally bound over extended timescales,and thus
probe the dynamics of binary formation and dissolution. Our previous SLoWPoKES
I \& II catalogs provided the largest and most complete sample of wide binary
pairs of low masses. Here we present an extension of these catalogs to a broad
range of stellar masses: the Gaia Assorted Mass Binaries Long Excluded from
SloWPoKES (GAMBLES), comprising 8,660 statistically significant wide pairs that
we make available in a living online database. Within this catalog we identify
a subset of 543 long-lived (dissipation timescale $>$1.5 Gyr) candidate binary
pairs, of assorted mass, with typical separations between $10^3-10^{5.5}$ AU
($0.002-1.5$ pc), using the published distances and proper motions from the
Tycho-Gaia Astrometric Solution and Sloan Digital Sky Survey photometry. Each
pair has at most a false positive probability of 0.05; the total expectation is
2.44 false binaries in our sample. Among these, we find 22 systems with 3
components, 1 system with 4 components, and 15 pairs consisting of at least 1
possible red giant. We find the largest long-lived binary separation to be
nearly 3.2 pc; even so, $>76\%$ of GAMBLES long-lived binaries have large
binding energies and dissipation lifetimes longer than 1.5 Gyr. Finally, we
find the distribution of binary separations is clearly bimodal, corroborating
the finding from SloWPoKES and suggesting multiple pathways for the formation
and dissipation of the widest binaries in the Galaxy.


title: Dimers in piecewise Temperleyan domains

abstract:
  We study the large-scale behavior of the height function in the dimer model
on the square lattice. Richard Kenyon has shown that the fluctuations of the
height function on Temperleyan discretizations of a planar domain converge in
the scaling limit (as the mesh size tends to zero) to the Gaussian Free Field
with Dirichlet boundary conditions. We extend Kenyon's result to a more general
class of discretizations.
  Moreover, we introduce a new factorization of the coupling function of the
double-dimer model into two discrete holomorphic functions, which are similar
to discrete fermions defined in [Stas, Stas07].For Temperleyan discretizations
with appropriate boundary modifications, the results of Kenyon imply that the
expectation of the double-dimer height function converges to a harmonic
function in the scaling limit. We use the above factorization to extend this
result to the class of all polygonal discretizations, that are not necessarily
Temperleyan. Furthermore, we show that, quite surprisingly, the expectation of
the double-dimer height function in the Temperleyan case is exactly discrete
harmonic (for an appropriate choice of Laplacian) even before taking the
scaling limit.


title: Hunting For Eclipses: High Speed Observations of Cataclysmic Variables

abstract:
  We present new time-resolved photometry of 74 cataclysmic variables (CVs), 47
of which are eclipsing. 13 of these eclipsing systems are newly discovered. For
all 47 eclipsing systems we show high cadence (1-20 seconds) light curves
obtained with the high-speed cameras ultracam and ultraspec. We provide new or
refined ephemerides, and supply mid-eclipse times for all observed eclipses. We
assess the potential for light curve modelling of all 47 eclipsing systems to
determine their system parameters, finding 20 systems which appear to be
suitable for future study.


title: Spans of cospans

abstract:
  We discuss the notion of a span of cospans and define, for them, horizonal
and vertical composition. These compositions satisfy the interchange law if
working in a topos $\mathbf{C}$ and if the span legs are monic. A bicategory is
then constructed from $\mathbf{C}$-objects, $\mathbf{C}$-cospans, and doubly
monic spans of $\mathbf{C}$-cospans. The primary motivation for this
construction is an application to graph rewriting.


title: Experiments with Conflict Analysis in Mixed Integer Programming

abstract:
  The analysis of infeasible subproblems plays an import role in solving mixed
integer programs (MIPs) and is implemented in most major MIP solvers. There are
two fundamentally different concepts to generate valid global constraints from
infeasible subproblems. The first is to analyze the sequence of implications
obtained by domain propagation that led to infeasibility. The result of the
analysis are one or more sets of contradicting variable bounds from which
so-called conflict constraints can be generated. This concept has its origin in
solving satisfiability problems and is similarly used in constraint
programming. The second is to analyze infeasible linear programming (LP)
relaxations. The dual LP solution provides a set of multipliers that can be
used to generate a single new globally valid linear constraint. The main
contribution of this short paper is an empirical evaluation of two ways to
combine these approaches. Experiments are carried out on general MIP instances
from standard public test sets such as MIPLIB; the presented algorithms have
been implemented within the non-commercial MIP solver SCIP. Moreover, we
present a pool-based approach to manage conflicts which addresses the way a MIP
solver traverses the search tree better than aging strategies known from SAT
solving.


title:
Electrically Pumped Single Transverse-Mode Coupled Waveguide Lasers by
  Parity-time (PT) Symmetry

abstract:
  We demonstrate single transverse-mode operation of broad-area coupled
waveguide lasers enabled by parity-time (PT) symmetry. The PT symmetric laser
operates on coupled waveguide cavities with electrically tuned gain and loss.
Such counterintuitive waveguide design enables PT symmetric breaking, causing
unique mode selection and ultimately enabling single mode operation. By
electrically tuning the loss in the loss region of the coupled waveguide
cavity, several different PT-symmetric regimes are analyzed theoretically, and
the corresponding PT symmetric phase transition is demonstrated experimentally
in the coupled waveguide laser.


title: The World of Fast Moving Objects

abstract:
  The notion of a Fast Moving Object (FMO), i.e. an object that moves over a
distance exceeding its size within the exposure time, is introduced. FMOs may,
and typically do, rotate with high angular speed. FMOs are very common in
sports videos, but are not rare elsewhere. In a single frame, such objects are
often barely visible and appear as semi-transparent streaks.
  A method for the detection and tracking of FMOs is proposed. The method
consists of three distinct algorithms, which form an efficient localization
pipeline that operates successfully in a broad range of conditions. We show
that it is possible to recover the appearance of the object and its axis of
rotation, despite its blurred appearance. The proposed method is evaluated on a
new annotated dataset. The results show that existing trackers are inadequate
for the problem of FMO localization and a new approach is required. Two
applications of localization, temporal super-resolution and highlighting, are
presented.


title: Image-based localization using LSTMs for structured feature correlation

abstract:
  In this work we propose a new CNN+LSTM architecture for camera pose
regression for indoor and outdoor scenes. CNNs allow us to learn suitable
feature representations for localization that are robust against motion blur
and illumination changes. We make use of LSTM units on the CNN output, which
play the role of a structured dimensionality reduction on the feature vector,
leading to drastic improvements in localization performance. We provide
extensive quantitative comparison of CNN-based and SIFT-based localization
methods, showing the weaknesses and strengths of each. Furthermore, we present
a new large-scale indoor dataset with accurate ground truth from a laser
scanner. Experimental results on both indoor and outdoor public datasets show
our method outperforms existing deep architectures, and can localize images in
hard conditions, e.g., in the presence of mostly textureless surfaces, where
classic SIFT-based methods fail.


title:
New constraint qualifications for mathematical programs with equilibrium
  constraints via variational analysis

abstract:
  In this paper, we study the mathematical program with equilibrium constraints
(MPEC) formulated as a mathematical program with a parametric generalized
equation involving the regular normal cone. Compared with the usual way of
formulating MPEC through a KKT condition, this formulation has the advantage
that it does not involve extra multipliers as new variables, and it usually
requires weaker assumptions on the problem data. Using the so-called first
order sufficient condition for metric subregularity, we derive verifiable
sufficient conditions for the metric subregularity of the involved set-valued
mapping, or equivalently the calmness of the perturbed generalized equation
mapping.


title: Active Brownian particles moving in a random Lorentz gas

abstract:
  Biological microswimmers often inhabit a porous or crowded environment such
as soil. In order to understand how such a complex environment influences their
spreading, we numerically study non-interacting active Brownian particles
(ABPs) in a two-dimensional random Lorentz gas. Close to the percolation
transition in the Lorentz gas, they perform the same subdiffusive motion as
ballistic and diffusive particles. However, due to their persistent motion they
reach their long-time dynamics faster than passive particles and also show
superdiffusive motion at intermediate times. While above the critical obstacle
density $\eta_c$ the ABPs are trapped, their long-time diffusion below $\eta_c$
is strongly influenced by the propulsion speed $v_0$. With increasing $v_0$,
ABPs are stuck at the obstacles for longer times. Thus, for large propulsion
speed, the long-time diffusion constant decreases more strongly in a denser
obstacle environment than for passive particles. This agrees with the behavior
of an effective swimming velocity and persistence time, which we extract from
the velocity autocorrelation function.


title: Translation-Invariant Parent Hamiltonians of Valence Bond Crystals

abstract:
  We present a general method to construct translation-invariant and SU(2)
symmetric antiferromagnetic parent Hamiltonians of valence bond crystals (VBC).
The method is based on a canonical mapping transforming S=1/2 spin operators
into a bilinear form of a new set of dimer fermion operators. We construct
parent Hamltonians of the columnar- and the staggered-VBC on the square
lattice, for which the VBC is an eigenstate in all regimes and the exact ground
state in some region of the phase diagram. We study the depart from the exact
VBC regime upon tuning the anisotropy by means of the hierarchical mean field
theory and exact diagonalization on finite clusters. In both Hamiltonians, the
VBC phase extends over the exact regime and transits to a columnar
antiferromagnet (CAFM) through a window of intermediate phases, revealing an
intriguing competition of correlation lengths at the VBC-CAFM transition. The
method can be readily applied to construct other VBC parent Hamiltonians in
different lattices and dimensions.


title:
Proposal for enhanced resolution in nanoscale NMR: quantum sensing with
  pulses of finite duration

abstract:
  The nitrogen vacancy (NV) color center in diamond is an enormously important
platform for the development of quantum sensors, including for single spin and
single molecule NMR. Detection of weak single-spin signals is greatly enhanced
by repeated sequences of microwave pulses; in these dynamical decoupling (DD)
techniques, the key control parameters swept in the experiment are the time
intervals, $\tau$, between pulses. Here we show that, in fact, the pulse
duration offers a powerful additional control parameter. While previously, a
non-negligible pulse-width has been considered simply a source of experimental
error, here we elucidate the underlying quantum dynamics: we identify a
landscape of quantum-state crossings which are usually closed (inactive) but
may be controllably activated (opened) by adjusting the pulse-width from zero.
We identify these crossings with recently observed but unexpected dips (so
called spurious dips) seen in the quantum coherence of the NV spin. With this
new understanding, both the position and strength of these sharp features may
be accurately controlled; they co-exist with the usual broader coherence dips
of short-duration microwave pulses, but their sharpness allows for higher
resolution spectroscopy with quantum diamond sensors, or their analogues.


title:
Indirect acquisition of information in quantum mechanics: states
  associated with tail events

abstract:
  The problem of reconstructing information on a physical system from data
acquired in long sequences of direct (projective) measurements of some simple
physical quantities - histories - is analyzed within quantum mechanics; that
is, the quantum theory of indirect measurements, and, in particular, of
non-demolition measurements is studied. It is shown that indirect measurements
of time-independent features of physical systems can be described in terms of
quantum-mechanical operators belonging to an algebra of asymptotic observables.
Our proof involves associating a natural measure space with certain sets of
histories of a system and showing that quantum-mechanical states of the system
determine probability measures on this space. Our main result then says that
functions on that space of histories measurable at infinity (i.e., functions
that only depend on the tails of histories) correspond to operators in the
algebra of asymptotic observables.


title: Phenomenology of a Higgs triplet model at future $e^{+}e^{-}$ colliders

abstract:
  In this work, we investigate the prospects of future $e^{+}e^{-}$ colliders
in testing a Higgs triplet model with a scalar triplet and a scalar singlet
under $SU(2)$. The parameters of the model are fixed so that the lightest
$CP-$even state corresponds to the Higgs particle observed at the LHC at around
$125$ GeV. This study investigates if the second heaviest $CP-$even, the
heaviest $CP-$odd and the singly charged states can be observed at existing and
future colliders by computing their accessible production and decay channels.
In general, the LHC is not well equipped to produce a Higgs boson which is not
mainly doublet-like, so we turn our focus to lepton colliders. We find
distinctive features of this model in cases when the second heaviest $CP-$even
Higgs is triplet-like, singlet-like or a mixture. These features could
distinguish the model from other scenarios at future $e^{+}e^{-}$ colliders.


title:
Learning Generic Sentence Representations Using Convolutional Neural
  Networks

abstract:
  We propose a new encoder-decoder approach to learn distributed sentence
representations that are applicable to multiple purposes. The model is learned
by using a convolutional neural network as an encoder to map an input sentence
into a continuous vector, and using a long short-term memory recurrent neural
network as a decoder. Several tasks are considered, including sentence
reconstruction and future sentence prediction. Further, a hierarchical
encoder-decoder model is proposed to encode a sentence to predict multiple
future sentences. By training our models on a large collection of novels, we
obtain a highly generic convolutional sentence encoder that performs well in
practice. Experimental results on several benchmark datasets, and across a
broad range of applications, demonstrate the superiority of the proposed model
over competing methods.


title: Planck scale operators, inflation and fine tuning

abstract:
  Ultraviolet completion of the standard model plus gravity at and beyond the
Planck scale is a daunting problem to which no generally accepted solution
exists. Principal obstacles include (a) lack of data at the Planck scale (b)
nonrenormalizability of gravity and (c) unitarity problem. Here we make a
simple observation that, if one treats all Planck scale operators of equal
canonical dimension democratically, one can tame some of the undesirable
features of these models. With a reasonable amount of fine tuning one can
satisfy slow roll conditions required in viable inflationary models. That
remains true even when the number of such operators becomes very large.


title: Generating Near-Bipartite Bricks

abstract:
  A $3$-connected graph $G$ is a brick if, for any two vertices $u$ and $v$,
the graph $G-\{u,v\}$ has a perfect matching. Deleting an edge $e$ from a brick
$G$ results in a graph with zero, one or two vertices of degree two. The
bicontraction of a vertex of degree two consists of contracting the two edges
incident with it; and the retract of $G-e$ is the graph $J$ obtained from it by
bicontracting all its vertices of degree two. An edge $e$ is thin if $J$ is
also a brick. Carvalho, Lucchesi and Murty [How to build a brick, Discrete
Mathematics 306 (2006), 2383-2410] showed that every brick, distinct from
$K_4$, the triangular prism $\overline{C_6}$ and the Petersen graph, has a thin
edge. Their theorem yields a generation procedure for bricks, using which they
showed that every simple planar solid brick is an odd wheel.
  A brick $G$ is near-bipartite if it has a pair of edges $\alpha$ and $\beta$
such that $G-\{\alpha,\beta\}$ is bipartite and matching covered; examples are
$K_4$ and $\overline{C_6}$. The significance of near-bipartite graphs arises
from the theory of ear decompositions of matching covered graphs.
  The object of this paper is to establish a generation procedure which is
specific to the class of near-bipartite bricks. In particular, we prove that if
$G$ is any near-bipartite brick, distinct from $K_4$ and $\overline{C_6}$, then
$G$ has a thin edge $e$ so that the retract $J$ of $G-e$ is also
near-bipartite.
  In a subsequent work, with Marcelo H. de Carvalho, we use the results of this
paper to prove a generation theorem for simple near-bipartite bricks.


title:
$K-$structure of ${\cal U}(\mathfrak{g})$ for
  $\mathfrak{s}\mathfrak{u}(n,1)$ and $\mathfrak{s}\mathfrak{o}(n,1)$

abstract:
  Let $G$ be the adjoint group of a real simple Lie algebra $\mathfrak{g}_0$
equal either $\mathfrak{s}\mathfrak{u}(n,1)$ or
$\mathfrak{s}\mathfrak{o}(n,1),$ $K$ its maximal compact subgroup, ${\cal
U}(\mathfrak{g})$ the universal enveloping algebra of the complexification
$\mathfrak{g}$ of $\mathfrak{g}_0$ and ${\cal U}(\mathfrak{g})^K$ its
subalgebra of $K-$invariant elements. By a result of F. Knopp [3] ${\cal
U}(\mathfrak{g})$ is free as a ${\cal U}(\mathfrak{g})^K-$module, so there
exists a $K-$submodule $E$ of ${\cal U}(\mathfrak{g})$ such that the
multiplication defines an isomorphism of $K-$modules ${\cal
U}(\mathfrak{g})^K\otimes E\longrightarrow{\cal U}(\mathfrak{g}).$ We prove
that $E$ is equivalent to the regular representation of $K,$ i.e. that the
multiplicity of every $\delta\in\hat{K}$ in $E$ equals its dimension. As a
consequence we get that for any finitedimensional complex $K-$module $V$ the
space $({\cal U}(\mathfrak{g})\otimes V)^K$ of $K-$invariants is free ${\cal
U}(\mathfrak{g})^K-$module of rank $\dim\,V.$


title:
Langmuir Wave Electric Fields Induced by Electron Beams in the
  Heliosphere

abstract:
  Solar electron beams responsible for type III radio emission generate
Langmuir waves as they propagate out from the Sun. The Langmuir waves are
observed via in-situ electric field measurements. These Langmuir waves are not
smoothly distributed but occur in discrete clumps, commonly attributed to the
turbulent nature of the solar wind electron density. Exactly how the density
turbulence modulates the Langmuir wave electric fields is understood only
qualitatively. Using weak turbulence simulations, we investigate how solar wind
density turbulence changes the probability distribution functions, mean value
and variance of the beam-driven electric field distributions. Simulations show
rather complicated forms of the distribution that are dependent upon how the
electric fields are sampled. Generally the higher magnitude of density
fluctuations reduce the mean and increase the variance of the distribution in a
consistent manor to the predictions from resonance broadening by density
fluctuations. We also demonstrate how the properties of the electric field
distribution should vary radially from the Sun to the Earth and provide a
numerical prediction for the in-situ measurements of the upcoming Solar Orbiter
and Solar Probe Plus spacecraft.


title:
Turbulent momentum transport due to the beating between different
  tokamak flux surface shaping effects

abstract:
  Introducing up-down asymmetry into the tokamak magnetic equilibria appears to
be a feasible method to drive fast intrinsic toroidal rotation in future large
devices. In this paper we investigate how the intrinsic momentum transport
generated by up-down asymmetric shaping scales with the mode number of the
shaping effects. Making use the gyrokinetic tilting symmetry (Ball et al (2016)
Plasma Phys. Control. Fusion 58 045023), we study the effect of envelopes
created by the beating of different high-order shaping effects. This reveals
that the presence of an envelope can change the scaling of the momentum flux
from exponentially small in the limit of large shaping mode number to just
polynomially small. This enhancement of the momentum transport requires the
envelope to be both up-down asymmetric and have a spatial scale on the order of
the minor radius.


title: FDTD subcell graphene model beyond the thin-film approximation

abstract:
  A subcell technique for calculation of optical properties of graphene with
the finite-difference time-domain (FDTD) method is presented. The technique
takes into account the surface conductivity of graphene which allows the
correct calculation of its dispersive response for arbitrarily polarized
incident waves interacting with the graphene.The developed technique is
verified for a planar graphene sheet configuration against the exact analytical
solution. Based on the same test case scenario, we also show that the subcell
technique demonstrates a superior accuracy and numerical efficiency with
respect to the widely used thin-film FDTD approach for modeling graphene. We
further apply our technique to the simulations of a graphene metamaterial
containing periodically spaced graphene strips (graphene strip-grating) and
demonstrate good agreement with the available theoretical results.


title: Existence to nonlinear parabolic problems with unbounded weights

abstract:
  We consider the weighted parabolic problem of the type \begin{equation*}
\begin{split} \left\{\begin{array}{ll} u_t-\mathrm{div}(\omega_2(x)|\nabla
u|^{p-2} \nabla u )= \lambda \omega_1(x) |u|^{p-2}u,& x\in\Omega, u(x,0)=f(x),&
x\in\Omega, u(x,t)=0,& x\in\partial\Omega,\ t>0, \end{array}\right. \end{split}
\end{equation*} for quite a general class of possibly unbounded weights $
\omega_1,\omega_2$ satisfying the Hardy-type inequality. We prove existence of
a global weak solution in the weighted Sobolev spaces provided that $\lambda$
is smaller than the optimal constant in the inequality.


title: Evidence for a break in the spectrum of astrophysical neutrinos

abstract:
  The announcement by the IceCube Collaboration of the observation of 53
astrophysical neutrino candidates in the energy range 0.03 \alt E_\nu/PeV \alt
2 has been greeted with a great deal of justified excitement. Herein we provide
fits of single and a broken power-law energy-spectra to these high-energy
starting events (HESEs). By comparing our statistical results from fits to
(background-free) shower HESE data with the spectral shape of muon neutrinos
recently reported by the IceCube Collaboration, we show that there is (3
\sigma) evidence for a break in the spectrum of astrophysical neutrinos. After
that we use the fitted result to predict the rate of Glashow events (in the ~
6.3 PeV region) and double-bang tau neutrino events (in the PeV region) just at
the threshold of IceCube detection.


title:
3D Simulation of Spindle Gravitational Collapse of a Collisionless
  Particle System

abstract:
  We simulate the spindle gravitational collapse of a collisionless particle
system in a 3D numerical relativity code and compare the qualitative results
with the old work done by Shapiro and Teukolsky(ST). The simulation starts from
the prolate-shaped distribution of particles and a spindle collapse is
observed. The peak value and its spatial position of curvature invariants are
monitored during the time evolution. We find that the peak value of the
Kretschmann invariant takes a maximum at some moment, when there is no apparent
horizon, and its value is greater for a finer resolution, which is consistent
with what is reported in ST. We also find a similar tendency for the Weyl
curvature invariant. Therefore, our results lend support to the formation of a
naked singularity as a result of the axially symmetric spindle collapse of a
collisionless particle system in the limit of infinite resolution. However,
unlike in ST, our code does not break down then but go well beyond.We find that
the peak values of the curvature invariants start to gradually decrease with
time for a certain period of time. Another notable difference from ST is that,
in our case, the peak position of the Kretschmann curvature invariant is always
inside the matter distribution.


title: Lacunary Arithmetic convergence

abstract:
  In this article we introduce and study the lacunary arithmetic convergent
sequence space $AC_{\theta}$. Using the idea of strong Ces\`{a}ro summable
sequence and arithmetic convergence we define $AC_{\sigma_1}$ and study the
relations between $AC_{\theta}$ and $AC_{\sigma_1}$. Finally using modulus
function we define $AC_{\theta}(f)$ and study some interesting results.


title:
Combinatorial construction of Gelfand-Tsetlin modules for
  $\mathfrak{gl}_n$

abstract:
  We propose a new effective method of constructing explicitly Gelfand -Tsetlin
modules for $\mathfrak{gl}_n$. We obtain a large family of simple modules that
have a basis consisting of Gelfand-Tsetlin tableaux, the action of the Lie
algebra is given by the Gelfand-Tsetlin formulas and with all Gelfand-Tsetlin
multiplicities equal $1$. As an application of our construction we prove
necessary and sufficient condition for the Gelfand and Graev's continuation
construction to define a module which was conjectured by Lemire and Patera.


title: Image Segmentation Using Overlapping Group Sparsity

abstract:
  Sparse decomposition has been widely used for different applications, such as
source separation, image classification and image denoising. This paper
presents a new algorithm for segmentation of an image into background and
foreground text and graphics using sparse decomposition. First, the background
is represented using a suitable smooth model, which is a linear combination of
a few smoothly varying basis functions, and the foreground text and graphics
are modeled as a sparse component overlaid on the smooth background. Then the
background and foreground are separated using a sparse decomposition framework
and imposing some prior information, which promote the smoothness of
background, and the sparsity and connectivity of foreground pixels. This
algorithm has been tested on a dataset of images extracted from HEVC standard
test sequences for screen content coding, and is shown to outperform prior
methods, including least absolute deviation fitting, k-means clustering based
segmentation in DjVu, and shape primitive extraction and coding algorithm.


title:
Map-aided Dead-reckoning --- A Study on Locational Privacy in Insurance
  Telematics

abstract:
  We present a particle-based framework for estimating the position of a
vehicle using map information and measurements of speed. Two measurement
functions are considered. The first is based on the assumption that the lateral
force on the vehicle does not exceed critical limits derived from physical
constraints. The second is based on the assumption that the driver approaches a
target speed derived from the speed limits along the upcoming trajectory.
Performance evaluations of the proposed method indicate that end destinations
often can be estimated with an accuracy in the order of $100\,[m]$. These
results expose the sensitivity and commercial value of data collected in many
of today's insurance telematics programs, and thereby have privacy implications
for millions of policyholders. We end by discussing the strengths and
weaknesses of different methods for anonymization and privacy preservation in
telematics programs.


title:
An efficient surrogate model for emulation and physics extraction of
  large eddy simulations

abstract:
  In the quest for advanced propulsion and power-generation systems,
high-fidelity simulations are too computationally expensive to survey the
desired design space, and a new design methodology is needed that combines
engineering physics, computer simulations and statistical modeling. In this
paper, we propose a new surrogate model that provides efficient prediction and
uncertainty quantification of turbulent flows in swirl injectors with varying
geometries, devices commonly used in many engineering applications. The novelty
of the proposed method lies in the incorporation of known physical properties
of the fluid flow as {simplifying assumptions} for the statistical model. In
view of the massive simulation data at hand, which is on the order of hundreds
of gigabytes, these assumptions allow for accurate flow predictions in around
an hour of computation time. To contrast, existing flow emulators which forgo
such simplications may require more computation time for training and
prediction than is needed for conducting the simulation itself. Moreover, by
accounting for coupling mechanisms between flow variables, the proposed model
can jointly reduce prediction uncertainty and extract useful flow physics,
which can then be used to guide further investigations.


title: The Coriolis Effect Further Described in the Seventeenth Century

abstract:
  Claude Francis Milliet Dechales described the Coriolis effect in his 1674
Cursus seu Mundus Mathematicus. Dechales discussed and illustrated the
deflection of both falling bodies and of projectiles launched toward the poles
that should occur on a rotating Earth. Interestingly, this was done as an
argument against the Earth's rotation, the deflections not having been observed
at the time. Dechales's work follows on that of Giovanni Battista Riccioli, who
had also described the effect in his Almagestum Novum of 1651.


title:
Kondo temperature when the Fermi level is near a step in the conduction
  density of states

abstract:
  The (111) surface of Cu, Ag and Au is characterized by a band of surface
Shockley states, with constant density of states beginning slightly below the
Fermi energy. These states as well as bulk states hybridize with magnetic
impurities which can be placed above the surface. We calculate the
characteristic low-temperature energy scale, the Kondo temperature $T_K$ of the
impurity Anderson model, as the bottom of the conduction band $D_s$ crosses the
Fermi energy $\epsilon_F$. We find simple power laws $T_K \simeq
|D_s-\epsilon_F|^{\eta}$, where $\eta$ depends on the sign of $D_s-\epsilon_F$,
the ratio between surface and bulk hybridizations with the impurity
$\Delta_s/\Delta_b$ and the ratio between on-site and Coulomb energy $E_d/U$ in
the model.


title:
Fullness and Connes' $\boldsymbol{\tau}$ invariant of type III tensor
  product factors

abstract:
  We show that the tensor product $M \mathbin{\overline{\otimes}} N$ of any two
full factors $M$ and $N$ (possibly of type ${\rm III}$) is full and we compute
Connes' invariant $\tau(M \mathbin{\overline{\otimes}} N)$ in terms of
$\tau(M)$ and $\tau(N)$. The key novelty is an enhanced spectral gap property
for full factors of type ${\rm III}$. Moreover, for full factors of type ${\rm
III}$ with almost periodic states, we prove an optimal spectral gap property.
As an application of our main result, we also show that for any full factor $M$
and any non-type ${\rm I}$ amenable factor $P$, the tensor product factor $M
\mathbin{\overline{\otimes}} P$ has a unique McDuff decomposition, up to stable
unitary conjugacy.


title:
The many scales to cosmic homogeneity: Use of multiple tracers from the
  SDSS

abstract:
  We carry out multifractal analyses of multiple tracers namely the main galaxy
sample, the LRG sample and the quasar sample from the SDSS to test the
assumption of cosmic homogeneity and identify the scale of transition to
homogeneity, if any. We consider the behaviour of the scaled number counts and
the scaling relations of different moments of the galaxy number counts in
spheres of varying radius $R$ to calculate the spectrum of the
Minkowski-Bouligand general dimension $D_{q} (R)$ for $-4 \leq q \leq 4$. The
present analysis provides us the opportunity to study the spectrum of the
generalized dimension $D_{q}(R)$ for multiple tracers of the cosmic density
field over a wide range of length scales and allows us to confidently test the
validity of the assumption of cosmic homogeneity. Our analysis indicates that
the SDSS main galaxy sample is homogeneous on a length scales of $80\, h^{-1}\,
{\rm Mpc} $ and beyond whereas the SDSS quasar sample and the SDSS LRG sample
show transition to homogeneity on an even larger length scales at $\sim 150\,
h^{-1}\, {\rm Mpc}$ and $\sim 230\, h^{-1}\, {\rm Mpc}$ respectively. These
differences in the scale of homogeneity arise due to the effective mass and
redshift scales probed by the different tracers in a Universe where structures
form hierarchically. Our results reaffirm the validity of cosmic homogeneity on
large scales irrespective of the tracers used and strengthens the foundations
of the Standard Model of Cosmology.


title:
Perturbed gradient flow trees and $A_\infty$-algebra structures on Morse
  cochain complexes

abstract:
  We elaborate on an idea of M. Abouzaid of equipping the Morse cochain complex
of a smooth Morse function on a closed oriented manifold with the structure of
an $A_\infty$-algebra. This is a variation on K. Fukaya's definition of
Morse-$A_\infty$-categories for closed oriented manifolds involving families of
Morse functions. The purpose of this article is to provide a coherent and
detailed treatment of Abouzaid's approach including a discussion of all
relevant analytic notions and results.


title: Deep Restricted Boltzmann Networks

abstract:
  Building a good generative model for image has long been an important topic
in computer vision and machine learning. Restricted Boltzmann machine (RBM) is
one of such models that is simple but powerful. However, its restricted form
also has placed heavy constraints on the models representation power and
scalability. Many extensions have been invented based on RBM in order to
produce deeper architectures with greater power. The most famous ones among
them are deep belief network, which stacks multiple layer-wise pretrained RBMs
to form a hybrid model, and deep Boltzmann machine, which allows connections
between hidden units to form a multi-layer structure. In this paper, we present
a new method to compose RBMs to form a multi-layer network style architecture
and a training method that trains all layers jointly. We call the resulted
structure deep restricted Boltzmann network. We further explore the combination
of convolutional RBM with the normal fully connected RBM, which is made trivial
under our composition framework. Experiments show that our model can generate
descent images and outperform the normal RBM significantly in terms of image
quality and feature quality, without losing much efficiency for training.


title:
Nucleon form factors and couplings with $N_\mathrm{f} = 2 + 1$ Wilson
  fermions

abstract:
  We present updated results on the nucleon electromagnetic form factors and
axial coupling calculated using CLS ensembles with $N_\mathrm{f}=2+1$ dynamical
flavours of Wilson fermions. The measurements are performed on large, fine
lattices with a pseudoscalar mass reaching down to 200 MeV. The
truncated-solver method is employed to reduce the variance of the measurements.
Estimation of the matrix elements is challenging due to large contamination
from excited states and further investigation is necessary to bring these
effects under control.


title:
Enhanced qubit readout using locally-generated squeezing and inbuilt
  Purcell-decay suppression

abstract:
  We introduce and analyze a dispersive qubit readout scheme where two-mode
squeezing is generated directly in the measurement cavities. The resulting
suppression of noise enables fast, high- fidelity readout of naturally weakly
coupled qubits, and the possibility to protect strongly coupled qubits from
decoherence by weakening their coupling. Unlike other approaches exploiting
squeezing, our setup avoids the difficult task of transporting and injecting
with high fidelity an externally-generated squeezed state. Our setup is also
surprisingly robust against unwanted non-QND backaction effects, as
interference naturally suppresses Purcell decay: the system acts as its own
Purcell filter. Our setup is compatible with the experimental state-of-the-art
in circuit QED systems, but the basic idea could also be realized in other
systems.


title: Multiquark Resonances

abstract:
  Multiquark resonances are undoubtedly experimentally observed. The number of
states and the amount of details on their properties has been growing over the
years. It is very recent the discovery of two pentaquarks and the confirmation
of four tetraquarks, two of which had not been observed before. We mainly
review the theoretical understanding of this sector of particle physics
phenomenology and present some considerations attempting a coherent description
of the so called X and Z resonances. The prominent problems plaguing
theoretical models, like the absence of selection rules limiting the number of
states predicted, motivate new directions in model building. Data are reviewed
going through all of the observed resonances with particular attention to their
common features and the purpose of providing a starting point to further
research.


title: Weak containment of measure preserving group actions

abstract:
  We survey recent progress in the theory of weak containment of measure
preserving group actions.


title: Planar triangulations, bridgeless planar maps and Tamari intervals

abstract:
  We present a direct bijection between planar 3-connected triangulations and
bridgeless planar maps, which were first enumerated by Tutte (1962) and Walsh
and Lehman (1975) respectively. Previously known bijections by Wormald (1980)
and Fusy (2010) are all defined recursively. Our direct bijection passes by a
new class of combinatorial objects called "sticky trees". We also present
bijections between sticky trees, intervals in the Tamari lattices and closed
flows on forests. With our bijections, we recover several known enumerative
results about these objects. We thus show that sticky trees can serve as a
nexus of bijective links among all these equi-enumerated objects.


title: Effective potential for relativistic scattering

abstract:
  We consider quantum inverse scattering with singular potentials and calculate
the Sine-Gordon model effective potential in the laboratory and centre-of-mass
frames. The effective potentials are frame dependent but closely resemble the
zero-momentum potential of the equivalent Ruijsenaars-Schneider model.


title:
R-mode frequencies of rapidly and differentially rotating relativistic
  neutron stars

abstract:
  R-modes of neutron stars could be a source of gravitational waves for ground
based detectors. If the precise frequency $\sigma$ is known, guided
gravitational wave searches with enhanced detectability are possible. Because
of its physical importance many authors have calculated the r-mode frequency.
For the dominant mode, the associated gravitational wave frequency is 4/3 times
the angular velocity of the star $\Omega$, subject to various corrections of
which relativistic and rotational corrections are the most important. This has
led several authors to investigate the dependence of the r-mode frequency on
factors such as the relativistic compactness parameter ($M/R$) and the angular
velocity of stars with different equations of state. The results found so far,
however, are almost independent of the equation of state. Here we investigate
the effect of rapid rotation and differential rotation on $\sigma$. We evolve
the perturbation equations using the Cowling approximation by applying finite
differencing methods to compute the r-mode frequency for a series of rotating
neutron stars with polytropic equations of state. We find that rotational
effects in the r-mode frequency can be larger than relativistic effects for
rapidly spinning stars with low compactness, reducing the observed frequency.
Differential rotation also acts to decrease $\sigma$, but its effect inscreases
with the compactness. The results presented here are relevant to the design of
gravitational wave and electromagnetic r-mode searches.