title:
The initial boundary value problem for free-evolution formulations of
  General Relativity

abstract:
  We consider the initial boundary value problem for free-evolution
formulations of general relativity coupled to a parametrized family of
coordinate conditions that includes both the moving puncture and harmonic
gauges. We concentrate primarily on boundaries that are geometrically
determined by the outermost normal observer to spacelike slices of the
foliation. We present high-order-derivative boundary conditions for the gauge,
constraint violating and gravitational wave degrees of freedom of the
formulation. Second order derivative boundary conditions are presented in terms
of the conformal variables used in numerical relativity simulations. Using
Kreiss-Agranovich-Metivier theory we demonstrate, in the frozen coefficient
approximation, that with sufficiently high order derivative boundary conditions
the initial boundary value problem can be rendered boundary stable. The precise
number of derivatives required depends on the gauge. For a choice of the gauge
condition that renders the system strongly hyperbolic of constant multiplicity,
well-posedness of the initial boundary value problem follows in this
approximation. Taking into account the theory of pseudo-differential operators,
it is expected that the nonlinear problem is also well-posed locally in time.


title:
Variations of Power-Expected-Posterior Priors in Normal Regression
  Models

abstract:
  The power-expected-posterior (PEP) prior is an objective prior for Gaussian
linear models, which leads to consistent model selection inference, under the
M-closed scenario, and tends to favor parsimonious models. Recently, two new
forms of the PEP prior were proposed which generalize its applicability to a
wider range of models. The properties of these two PEP variants within the
context of the normal linear model are examined thoroughly, focusing on the
prior dispersion and on the consistency of the induced model selection
procedure. Results show that both PEP variants have larger variances than the
unit-information g-prior and that they are M-closed consistent as the limiting
behavior of the corresponding marginal likelihoods matches that of the BIC. The
consistency under the M-open case, using three different model misspecification
scenarios is further investigated.


title:
A quantitative analysis of tilt in the Caf\'e Wall illusion: a
  bioplausible model for foveal and peripheral vision

abstract:
  The biological characteristics of human visual processing can be investigated
through the study of optical illusions and their perception, giving rise to
intuitions that may improve computer vision to match human performance.
Geometric illusions are a specific subfamily in which orientations and angles
are misperceived. This paper reports quantifiable predictions of the degree of
tilt for a typical geometric illusion called Caf\'e Wall, in which the mortar
between the tiles seems to tilt or bow. Our study employs a common bioplausible
model of retinal processing and we further develop an analytic processing
pipeline to quantify and thus predict the specific angle of tilt. We further
study the effect of resolution and feature size in order to predict the
different perceived tilts in different areas of the fovea and periphery, where
resolution varies as the eye saccades to different parts of the image. In the
experiments, several different minimal portions of the pattern, modeling
monocular and binocular foveal views, are investigated across multiple scales,
in order to quantify tilts with confidence intervals and explore the difference
between local and global tilt.


title:
Quantum-Many-Body Intermetallics: Phase Stability of Fe$_3$Al and
  Small-Gap Formation in Fe$_2$VAl

abstract:
  Various intermetallic compounds harbor subtle electronic correlation effects.
To elucidate this fact for the Fe-Al system, we perform a realistic many-body
investigation based on the combination of density functional theory with
dynamical mean-field theory in a charge self-consistent manner. A better
characterization and understanding of the phase stability of bcc-based
D0$_3$-Fe$_3$Al through an improved description of the correlated charge
density and the magnetic-energy is achevied. Upon replacement of one Fe
sublattice by V, the Heusler compound Fe$_2$VAl is realized, known to display
bad-metal behavior and increased specific heat. We here document a charge-gap
opening at low temperatures in line with previous experimental work. The gap
structure does not match conventional band theory and is reminiscent of
(pseudo)gap charateristics in correlated oxides.


title: Relative equivariant motives and modules

abstract:
  We introduce and study various categories of (equivariant) motives of
(versal) flag varieties. We relate these categories with certain categories of
parabolic (Demazure) modules. We show that the motivic decomposition type of a
versal flag variety depends on the direct sum decomposition type of the
parabolic module. To do this we use localization techniques of Kostant-Kumar in
the context of generalized oriented cohomology as well as the Rost nilpotence
principle for algebraic cobordism and its generic version. As an application,
we obtain new proofs and examples of indecomposable Chow motives of versal flag
varieties.


title:
Spectra of Certain Holographic ABJM Wilson Loops in Higher Rank
  Representations

abstract:
  The holographic configurations dual to Wilson loops in higher rank
representations in the ABJM theory are described by branes with electric flux
along their world volumes. In particular, D2 and D6 branes with electric flux
play a central role as potential dual to totally symmetric and totally
antisymmetric representations, respectively. We compute the spectra of
excitations of these brane configurations in both, the bosonic and fermionic
sectors. We highlight a number of aspects that distinguish these configurations
from their D3 and D5 cousins including new peculiar mixing terms in the
fluctuations. We neatly organize the spectrum of fluctuations into the
corresponding supermultiplets.


title:
Resonance interaction energy between two accelerated identical atoms in
  a coaccelerated frame and the Unruh effect

abstract:
  We investigate the resonance interaction energy between two uniformly
accelerated identical atoms, interacting with the scalar field or the
electromagnetic field in the vacuum state, in the reference frame
coaccelerating with the atoms. We assume that one atom is excited and the other
in the ground state, and that they are prepared in their correlated symmetric
or antisymmetric state. Using perturbation theory, we separate, at the second
order in the atom-field coupling, the contributions of vacuum fluctuations and
radiation reaction field to the energy shift of the interacting system. We show
that only the radiation reaction term contributes to the resonance interaction
between the two atoms, while Unruh thermal fluctuations, related to the vacuum
fluctuations contribution, do not affect the resonance interatomic interaction.
We also show that the resonance interaction between two uniformly accelerated
atoms, recently investigated in the comoving (locally inertial) frame, can be
recovered in the coaccelerated frame, without the additional assumption of the
Fulling-Davies-Unruh temperature for the quantum fields (as necessary for the
Lamb-shift, for example). This indicates, in the case considered, the
equivalence between the coaccelerated frame and the locally inertial frame.


title: Two coupled, driven Ising spin systems working as an Engine

abstract:
  Miniaturized heat engines constitutes a fascinating field of current
research. They are being studied theoretically as well as experimentally, with
experiments involving colloidal particles and harmonic traps and even bacterial
baths acting like thermal baths. They are interesting to study because usual
equilibrium thermodynamic notions can not be applied directly to these systems.
These systems are micron sized or even smaller and they are subjected to laud
thermal fluctuations. Thus one needs to study the behavior of such systems in
terms of these fluctuations. Average thermodynamic quantities like work done,
heat exchanged, efficiency loose meaning unless otherwise supported by their
full probability distributions. Earlier studies on micro-engines are concerned
with applying Carnot or Stirling engine protocols to miniaturized systems,
where system undergoes typical two isothermal and two adiabatic changes. Unlike
these models we for the first time, study a prototype system of two classical
Ising spins driven by time dependent, phase different, external magnetic
fields. These spins are {\it simultaneously} in contact with two heat
reservoirs at different temperatures for the full duration of the driving
protocol. Performance of the model as an engine or a refrigerator depends only
on a single parameter namely the phase between two external drivings. We study
this system in terms of fluctuations in efficiency and coefficient of
performance (COP). We also find full distributions of these quantities
numerically and also study the tails of these distributions. We also study
reliability of this engine. We find the fluctuations dominate mean values of
efficiency and COP and their probability distributions are broad with power law
tails.


title:
Limiting Hamilton-Jacobi Equation for the Large Scale Asymptotics of a
  Subdiffusion Jump-Renewal Equation

abstract:
  Subdiffusive motion takes place at a much slower timescale than diffusive
motion. As a preliminary step to studying reaction-subdiffusion pulled fronts,
we consider here the hyperbolic limit $(t,x) \to (t/\varepsilon,
x/\varepsilon)$ of an age-structured equation describing the subdiffusive
motion of, e.g., some protein inside a biological cell. Solutions of the
rescaled equations are known to satisfy a Hamilton-Jacobi equation in the
formal limit $\varepsilon \to 0$. In this work we derive uniform Lipschitz
estimates, and establish the convergence towards the viscosity solution of the
limiting Hamilton-Jacobi equation. The two main obstacles overcome in this work
are the non-existence of an integrable stationary measure, and the importance
of memory terms in subdiffusion.


title: Surface-modified Wannier-Stark states in a 1D optical lattice

abstract:
  We study the energy spectrum of atoms trapped in a vertical 1D optical
lattice in close proximity to a reflective surface. We propose an effective
model to describe the interaction between the atoms and the surface at any
distance. Our model includes the long-range Casimir-Polder potential together
with a short-range Lennard-Jones potential, which are considered
non-perturbatively with respect to the optical lattice potential. We find an
intricate energy spectrum which contains a pair of loosely-bound states
localized close to the surface in addition to a surface-modified Wannier-Stark
ladder at long distances. Atomic interferometry involving those loosely-bound
atom-surface states is proposed to probe the adsorption dynamics of atoms on
mirrors.


title: Quantum Neural Machine Learning - Backpropagation and Dynamics

abstract:
  The current work addresses quantum machine learning in the context of Quantum
Artificial Neural Networks such that the networks' processing is divided in two
stages: the learning stage, where the network converges to a specific quantum
circuit, and the backpropagation stage where the network effectively works as a
self-programing quantum computing system that selects the quantum circuits to
solve computing problems. The results are extended to general architectures
including recurrent networks that interact with an environment, coupling with
it in the neural links' activation order, and self-organizing in a dynamical
regime that intermixes patterns of dynamical stochasticity and persistent
quasiperiodic dynamics, making emerge a form of noise resilient dynamical
record.


title:
Walker-Independent Features for Gait Recognition from Motion Capture
  Data

abstract:
  MoCap-based human identification, as a pattern recognition discipline, can be
optimized using a machine learning approach. Yet in some applications such as
video surveillance new identities can appear on the fly and labeled data for
all encountered people may not always be available. This work introduces the
concept of learning walker-independent gait features directly from raw joint
coordinates by a modification of the Fisher Linear Discriminant Analysis with
Maximum Margin Criterion. Our new approach shows not only that these features
can discriminate different people than who they are learned on, but also that
the number of learning identities can be much smaller than the number of
walkers encountered in the real operation.


title: Volterra-type Ornstein-Uhlenbeck processes in space and time

abstract:
  We propose a novel class of tempo-spatial Ornstein-Uhlenbeck processes as
solutions to L\'evy-driven Volterra equations with additive noise and
multiplicative drift. After formulating conditions for the existence and
uniqueness of solutions, we derive an explicit solution formula and discuss
distributional properties such as stationarity, second-order structure and
short versus long memory. Furthermore, we analyze in detail the path properties
of the solution process. In particular, we introduce different notions of
c\`adl\`ag paths in space and time and establish conditions for the existence
of versions with these regularity properties. The theoretical results are
accompanied by illustrative examples.


title:
Low Frequency Carbon Radio Recombination Lines I: Calculations of
  Departure Coefficients

abstract:
  In the first paper of this series, we study the level population problem of
recombining carbon ions. We focus our study on high quantum numbers
anticipating observations of Carbon Radio Recombination Lines to be carried out
by the LOw Frequency ARray (LOFAR). We solve the level population equation
including angular momentum levels with updated collision rates up to high
principal quantum numbers. We derive departure coefficients by solving the
level population equation in the hydrogenic approximation and including low
temperature dielectronic recombination effects. Our results in the hydrogenic
approximation agree well with those of previous works. When comparing our
results including dielectronic recombination we find differences which we
ascribe to updates in the atomic physics (e.g., collision rates) and to the
approximate solution method of the statistical equilibrium equations adopted in
previous studies. A comparison with observations is discussed in an
accompanying article, as radiative transfer effects need to be considered.


title: Phase diagram of the off-diagonal Aubry-Andr\'e model

abstract:
  We study a one-dimensional quasiperiodic system described by the off-diagonal
Aubry-Andr\'{e} model and investigate its phase diagram by using the symmetry
and the multifractal analysis. It was shown in a recent work ({\it Phys. Rev.
B} {\bf 93}, 205441 (2016)) that its phase diagram was divided into three
regions, dubbed the extended, the topologically-nontrivial localized and the
topologically-trivial localized phases, respectively. Out of our expectation,
we find an additional region of the extended phase which can be mapped into the
original one by a symmetry transformation. More unexpectedly, in both
"localized" phases, most of the eigenfunctions are neither localized nor
extended. Instead, they display critical features, that is, the minimum of the
singularity spectrum is in a range $0<\gamma_{min}<1$ instead of $0$ for the
localized state or $1$ for the extended state. Thus, a mixed phase is found
with a mixture of localized and critical eigenfunctions.


title: On the White Dwarf Mass Problem of Cataclysmic Variables

abstract:
  Recent observations show that the white dwarfs (WDs) in cataclysmic Variables
(CVs) have an average mass significantly higher than isolated WDs and WDs in
post-common envelope binaries (PCEBs), which are thought to the progenitors of
CVs. This suggests that either the WDs have grown in mass during the PCEB/CV
evolution or the binaries with low-mass WDs are unable to evolve to be CVs. In
this paper, we calculate the evolution of accreting WD binaries with updated
hydrogen accumulation efficiency and angular momentum loss prescriptions. We
show that thermal timescale mass transfer is not effective in changing the
average WD mass distribution. The WD mass discrepancy is most likely related to
unstable mass transfer in WD binaries in which an efficient mechanism of
angular momentum loss is required.


title: Theory Vision, LHCP 2016

abstract:
  I give my perspective on promising directions for high energy physics in
coming years.


title: Randomized Independent Component Analysis

abstract:
  Independent component analysis (ICA) is a method for recovering statistically
independent signals from observations of unknown linear combinations of the
sources. Some of the most accurate ICA decomposition methods require searching
for the inverse transformation which minimizes different approximations of the
Mutual Information, a measure of statistical independence of random vectors.
Two such approximations are the Kernel Generalized Variance or the Kernel
Canonical Correlation which has been shown to reach the highest performance of
ICA methods. However, the computational effort necessary just for computing
these measures is cubic in the sample size. Hence, optimizing them becomes even
more computationally demanding, in terms of both space and time. Here, we
propose a couple of alternative novel measures based on randomized features of
the samples - the Randomized Generalized Variance and the Randomized Canonical
Correlation. The computational complexity of calculating the proposed
alternatives is linear in the sample size and provide a controllable
approximation of their Kernel-based non-random versions. We also show that
optimization of the proposed statistical properties yields a comparable
separation error at an order of magnitude faster compared to Kernel-based
measures.

categories: stat.ML cs.LG cs.SY math.PR math.ST stat.TH


title: Traceable Coulomb Blockade Thermometry

abstract:
  We present a measurement and analysis scheme for determining traceable
thermodynamic temperature at cryogenic temperatures using Coulomb blockade
thermometry. The uncertainty of the electrical measurement is improved by
utilizing two sampling digital voltmeters instead of the traditional lock-in
technique. The remaining uncertainty is dominated by that of the numerical
analysis of the measurement data. Two analysis methods are demonstrated:
numerical fitting of the full conductance curve and measuring the height of the
conductance dip. The complete uncertainty analysis shows that using either
analysis method the relative combined standard uncertainty (k = 1) in
determining the thermodynamic temperature in the temperature range from 20 mK
to 200 mK is below 0.5 %. In this temperature range, both analysis methods
produced temperature estimates that deviated from 0.39 % to 0.67 % from the
reference temperatures provided by a superconducting reference point device
calibrated against the Provisional Low Temperature Scale of 2000.


title: Quantum Tunneling In Deformed Quantum Mechanics with Minimal Length

abstract:
  In the deformed quantum mechanics with a minimal length, one WKB connection
formula through a turning point is derived. We then use it to calculate
tunnelling rates through potential barriers under the WKB approximation.
Finally, the minimal length effects on two examples of quantum tunneling in
nuclear and atomic physics are discussed


title:
The Centroid Shifts of Light Beams Reflected from Multi-Layers and the
  Effects of Angular Momentum Manifestations

abstract:
  Laguerre-Gaussian (LG) beams reflected from a multi-layered dielectric
experience a shift in their centroid that is different than that from a single
interface. This has been previously investigated for linearly polarized beams
and, to a much lesser extent, beams with spin angular momentum. Here a
combination of perturbation and computational analyses is used to provide a
unified quantification of these shifts in layered dielectrics with two parallel
interfaces. The approach is then extended to consider the qualitatively new
behavior that results when the light is endowed with an intrinsic orbital
angular momentum--i.e. vortex beams. Destructive interference causes singular
lateral shifts in the centroid of the reflected vortex beam for which spin
alone produces only a mild modulation. In the case of total internal
reflection, both spin and intrinsic orbital angular momentum contribute to an
enhancement of these lateral shifts as the interlayer thickness is decreased.
This is just the opposite of the trend associated with longitudinal shifts. Two
geometries are considered: air/glass/air and glass/air/glass multi-layers. A
commonly available glass is used to show that vortex beams can result in
centroid shifts on the order of microns for beams with a significant reflection
coefficient.


title: Double polarisation experiments in meson photoproduction

abstract:
  One of the remaining challenges within the standard model is to gain a good
understanding of QCD in the non-perturbative regime. A key step towards this
aim is baryon spectroscopy, investigating the spectrum and the properties of
baryon resonances. To gain access to resonances with small $\pi N$ partial
width, photoproduction experiments provide essential information. Partial wave
analyses need to be performed to extract the contributing resonances. Here, a
complete experiment is required to unambiguously determine the contributing
amplitudes. This involves the measurement of carefully chosen single and double
polarisation observables. In a joint endeavour by MAMI, ELSA, and Jefferson
Laboratory, a new generation of experiments with polarised beams, polarised
proton and neutron targets, and $4\pi$ particle detectors have been performed
in recent years. Many results of unprecedented quality were recently published
by all three experiments, and included by the various partial wave analysis
groups in their analyses, leading to substantial improvements, e.g. a more
precise determination of resonance parameters. An overview of recent results is
given, with an emphasis on results from the CBELSA/TAPS experiment, and their
impact on our understanding of the nucleon excitation spectrum is discussed.


title: Distribution results on polynomials with bounded roots

abstract:
  For $d \in \mathbb{N}$ the well-known Schur-Cohn region $\mathcal{E}_d$
consists of all $d$-dimensional vectors $(a_1,\ldots,a_d)\in\mathbb{R}^d$
corresponding to monic polynomials $X^d+a_1X^{d-1}+\cdots+a_{d-1}X+a_d$ whose
roots all lie in the open unit disk. This region has been extensively studied
over decades. Recently, Akiyama and Peth\H{o} considered the subsets
$\mathcal{E}_d^{(s)}$ of the Schur-Cohn region that correspond to polynomials
of degree $d$ with exactly $s$ pairs of nonreal roots. They were especially
interested in the $d$-dimensional Lebesgue measures
$v_d^{(s)}:=\lambda_d(\mathcal{E}_d^{(s)})$ of these sets and their arithmetic
properties, and gave some fundamental results. Moreover, they posed two
conjectures that we prove in the present paper. Namely, we show that in the
totally complex case $d=2s$ the formula \[ \frac{v_{2s}^{(s)}}{v_{2s}^{(0)}} =
2^{2s(s-1)}\binom {2s}s \] holds for all $s\in\mathbb{N}$ and in the general
case the quotient $v_d^{(s)}/v_d^{(0)}$ is an integer for all choices $d\in
\mathbb{N}$ and $s\le d/2$. We even go beyond that and prove explicit
formul\ae{} for $v_d^{(s)} / v_d^{(0)}$ for arbitrary $d\in \mathbb{N}$, $s\le
d/2$. The ingredients of our proofs comprise Selberg type integrals,
determinants like the Cauchy double alternant, and partial Hilbert matrices.


title: Model reduction for LPV systems based on approximate modal decomposition

abstract:
  The paper presents a novel model order reduction technique for large-scale
linear parameter varying (LPV) systems. The approach is based on decoupling the
original dynamics into smaller dimensional LPV subsystems that can be
independently reduced by parameter varying reduction methods. The decomposition
starts with the construction of a modal transformation that separates the modal
subsystems. Hierarchical clustering is applied then to collect the dynamically
similar modal subsystems into larger groups. The subsystems formed from the
groups are then independently reduced. This approach substantially differs from
most of the previously proposed LPV model reduction techniques, since it
performs manipulations on the LPV model and not on a set of linear
time-invariant (LTI) models defined at fixed scheduling parameter values.
Therefore the model interpolation, which is the most challenging part of most
reduction techniques, is avoided. The applicability of the developed algorithm
is thoroughly investigated and demonstrated by numerical case studies.


title: Solar Physics at the Einstein Tower

abstract:
  The solar observatory Einstein Tower (Einsteinturm) at the Telegrafenberg in
Potsdam is both a landmark of modern architecture and an important place for
solar physics. Originally built for high-resolution spectroscopy and measuring
the gravitational redshift, research shifted over the years to understanding
the active Sun and its magnetic field. Nowadays, telescope and spectrographs
are used for research and development, i.e., testing instruments and in
particular polarization optics for advanced instrumentation deployed at major
European and international astronomical and solar telescopes. In addition, the
Einstein Tower is used for educating and training of the next generation
astrophysicists as well as for education and public outreach activities
directed at the general public. This article comments on the observatory's
unique architecture and the challenges of maintaining and conserving the
building. It describes in detail the characteristics of telescope,
spectrographs, and imagers; it portrays some of the research and development
activities.


title:
The Hilbert function of bigraded algebras in
  $k[\mathbb{P}^1\times\mathbb{P}^1]$

abstract:
  We classify the Hilbert functions of bigraded algebras in $k[x_1, x_2, y_1,
y_2]$ introducing a numerical function called Ferrers function.


title: Model Checking and Validity in Propositional and Modal Inclusion Logics

abstract:
  Propositional and modal inclusion logic are formalisms that belong to the
family of logics based on team semantics. This article investigates the model
checking and validity problems of these logics. We identify complexity bounds
for both problems, covering both lax and strict team semantics. By doing so, we
come close to finalising the programme that ultimately aims to classify the
complexities of the central reasoning problems for modal and propositional
dependence, independence, and inclusion logics.


title:
Multi-wavelength Temporal Variability of the Blazar 3C 454.3 during 2014
  Activity Phase

abstract:
  We present a multi-wavelength temporal analysis of the blazar 3C 454.3 during
the high $\gamma$-ray active period from May-December, 2014. Except for X-rays,
the period is well sampled at near-infrared (NIR)-optical by the \emph{SMARTS}
facility and the source is detected continuously on daily timescale in the
\emph{Fermi}-LAT $\gamma$-ray band. The source exhibits diverse levels of
variability with many flaring/active states in the continuously sampled
$\gamma$-ray light curve which are also reflected in the NIR-optical light
curves and the sparsely sampled X-ray light curve by the \emph{Swift}-XRT.
Multi-band correlation analysis of this continuous segment during different
activity periods shows a change of state from no lags between IR and
$\gamma$-ray, optical and $\gamma$-ray, and IR and optical to a state where
$\gamma$-ray lags the IR/optical by $\sim$3 days. The results are consistent
with the previous studies of the same during various $\gamma$-ray flaring and
active episodes of the source. This consistency, in turn, suggests an extended
localized emission region with almost similar conditions during various
$\gamma$-ray activity states. On the other hand, the delay of $\gamma$-ray with
respect to IR/optical and a trend similar to IR/optical in X-rays along with
strong broadband correlations favor magnetic field related origin with X-ray
and $\gamma$-ray being inverse Comptonized of IR/optical photons and external
radiation field, respectively.


title: The Digital Synaptic Neural Substrate: Size and Quality Matters

abstract:
  We investigate the 'Digital Synaptic Neural Substrate' (DSNS) computational
creativity approach further with respect to the size and quality of images that
can be used to seed the process. In previous work we demonstrated how combining
photographs of people and sequences taken from chess games between weak players
can be used to generate chess problems or puzzles of higher aesthetic quality,
on average, compared to alternative approaches. In this work we show
experimentally that using larger images as opposed to smaller ones improves the
output quality even further. The same is also true for using clearer or less
corrupted images. The reasons why these things influence the DSNS process is
presently not well-understood and debatable but the findings are nevertheless
immediately applicable for obtaining better results.


title:
Semiring Programming: A Declarative Framework for Generalized Sum
  Product Problems

abstract:
  To solve hard problems, AI relies on a variety of disciplines such as logic,
probabilistic reasoning, machine learning and mathematical programming.
Although it is widely accepted that solving real-world problems requires an
integration amongst these, contemporary representation methodologies offer
little support for this.
  In an attempt to alleviate this situation, we introduce a new declarative
programming framework that provides abstractions of well-known problems such as
SAT, Bayesian inference, generative models, and convex optimization. The
semantics of programs is defined in terms of first-order structures with
semiring labels, which allows us to freely combine and integrate problems from
different AI disciplines.


title:
SuperMann: a superlinearly convergent algorithm for finding fixed points
  of nonexpansive operators

abstract:
  Operator splitting techniques have recently gained popularity in convex
optimization problems arising in various control fields. Being fixed-point
iterations of nonexpansive operators, such methods suffer many well known
downsides, which include high sensitivity to ill conditioning and parameter
selection, and consequent low accuracy and robustness. As universal solution we
propose SuperMann, a Newton-type algorithm for finding fixed points of
nonexpansive operators. It generalizes the classical Krasnosel'skii-Mann
scheme, enjoys its favorable global convergence properties and requires exactly
the same oracle. It is based on a novel separating hyperplane projection
tailored for nonexpansive mappings which makes it possible to include steps
along any direction. In particular, when the directions satisfy a Dennis-Mor\'e
condition we show that SuperMann converges superlinearly under mild
assumptions, which, surprisingly, do not entail nonsingularity of the Jacobian
at the solution but merely metric subregularity. As a result, SuperMann
enhances and robustifies all operator splitting schemes for structured convex
optimization, overcoming their well known sensitivity to ill conditioning.


title: Nonlinear Quantum Hall effects in Rarita-Schwinger gas

abstract:
  Emergence of higher spin relativistic fermionic materials becomes a new
favorite in the study of condensed matter physics. Massive Rarita-Schwinger
3/2-spinor was known owning very exotic properties, such as the superluminal
fermionic modes and even being unstable in an external magnetic field. Due to
the superluminal modes and the non-trivial constraints on the Rarita-Schwinger
gas, we exposit anomalous properties of the Hall effects in (2+1)-dimensions
which subvert the well-known quantum Hall paradigms. First, the Hall
conductance of a pure Rarita-Schwinger gas is step-like but not
plateau-quantized, instead of the linear dependence on the filling factor for a
pure spin-1/2 Dirac gas. In reality, the Hall conductance of the Dirac gas is
of quantized integer plateaus with the unit $\frac{e^2}h$ due to the
localization away from the Landau level centers. If the general localization
rule is applicable to the disordered Rarita-Schwinger gas, the Hall plateaus
are also expected to appear but they are nonlinearly dependent on the Landau
level index. Furthermore, there is a critical magnetic field beyond which
higher Landau levels become unstable. This confines the filling factor of the
system. We also show that the non-hermitness of the effective Hamiltonian is
not crucial to the nonlinearity of the quantum Hall conductance.


title:
Early Warning System for Seismic Events in Coal Mines Using Machine
  Learning

abstract:
  This document describes an approach to the problem of predicting dangerous
seismic events in active coal mines up to 8 hours in advance. It was developed
as a part of the AAIA'16 Data Mining Challenge: Predicting Dangerous Seismic
Events in Active Coal Mines. The solutions presented consist of ensembles of
various predictive models trained on different sets of features. The best one
achieved a winning score of 0.939 AUC.


title: Wind generated rogue waves in an annular wave flume

abstract:
  We investigate experimentally the statistical properties of a wind-generated
wave field and the spontaneous formation of rogue waves in an annular flume.
Unlike many experiments on rogue waves, where waves are mechanically generated,
here the wave field is forced naturally by wind as it is in the ocean. What is
unique about the present experiment is that the annular geometry of the tank
makes waves propagating circularly in an {\it unlimited-fetch} condition.
Within this peculiar framework, we discuss the temporal evolution of the
statistical properties of the surface elevation. We show that rogue waves and
heavy-tail statistics may develop naturally during the growth of the waves just
before the wave height reaches a stationary condition. Our results shed new
light on the formation of rogue waves in a natural environment.


title:
Iterative observer-based state and parameter estimation for linear
  systems

abstract:
  We propose an iterative method for joint state and parameter estimation using
measurements on a time interval [0,T] for systems that are backward output
stabilizable. Since this time interval is fixed, errors in initial state may
have a big impact on the parameter estimate. We propose to use the back and
forth nudging (BFN) method for estimating the system's initial state and a
Gauss--Newton step between BFN iterations for estimating the system parameters.
Taking advantage of results on the optimality of the BFN method, we show that
for systems with skew-adjoint generators, the initial state and parameter
estimate minimizing an output error cost functional is an attractive fixed
point for the proposed method. We treat both linear source estimation and
bilinear parameter estimation problems.


title:
BayesBinMix: an R Package for Model Based Clustering of Multivariate
  Binary Data

abstract:
  The BayesBinMix package offers a Bayesian framework for clustering binary
data with or without missing values by fitting mixtures of multivariate
Bernoulli distributions with an unknown number of components. It allows the
joint estimation of the number of clusters and model parameters using Markov
chain Monte Carlo sampling. Heated chains are run in parallel and accelerate
the convergence to the target posterior distribution. Identifiability issues
are addressed by implementing label switching algorithms. The package is
demonstrated and benchmarked against the Expectation-Maximization algorithm
using a simulation study as well as a real dataset.


title: Graphs vertex-partitionable into strong cliques

abstract:
  A graph is said to be well-covered if all its maximal independent sets are of
the same size. In 1999, Yamashita and Kameda introduced a subclass of
well-covered graphs, called localizable graphs and defined as graphs having a
partition of the vertex set into strong cliques, where a clique in a graph is
strong if it intersects all maximal independent sets. Yamashita and Kameda
observed that all well-covered trees are localizable, pointed out that the
converse inclusion fails in general, and asked for a characterization of
localizable graphs.
  In this paper we obtain several structural and algorithmic results about
localizable graphs. Our results include a proof of the fact that every very
well-covered graph is localizable and characterizations of localizable graphs
within the classes of line graphs, triangle-free graphs, $C_4$-free graphs, and
cubic graphs, each leading to a polynomial time recognition algorithm. On the
negative side, we prove NP-hardness of recognizing localizable graphs within
the classes of weakly chordal graphs, complements of line graphs, and graphs of
independence number three. Furthermore, using localizable graphs we disprove a
conjecture due to Zaare-Nahandi about $k$-partite well-covered graphs having
all maximal cliques of size $k$. Our results unify and generalize several
results from the literature.


title:
On the Liouville type theorems for self-similar solutions to the
  Navier-Stokes equations

abstract:
  We prove Liouville type theorems for the self-similar solutions to the
Navier-Stokes equations. One of our results generalizes the previous ones by
Ne\v{c}as-R\.{u}\v{z}i\v{c}ka-\v{S}verak and Tsai. Using the Liouville type
theorem we also remove a scenario of asymtotically self-similar blow-up for the
Navier-Stokes equations with the profile belonging to $L^{p, \infty} (\Bbb
R^3)$ with $p> \frac{3}{2}$.


title:
Estimate of the number of fragments formed during the rapid radial
  expansion of a ring

abstract:
  In recent paper (Goloveshkin and Myagkov 2014) we proposed a two-dimensional
energy-based model of fragmentation of rapidly expanding cylinder under plane
strain conditions. The model allowed one to estimate the average fragment
length and the number of fragments produced by ductile fracture of the
cylinder. In present note we show that the proposed approach can be used to
estimate the number of fragments in a problem of fragmentation of an expanding
ring.


title:
Bridging the Gap between Crosslinking Chemistry and Directed Assembly of
  Metasurfaces Using Electrohydrodynamic Flow

abstract:
  Advances in understanding chemical and physical driving forces in
self-assembly allow the fabrication of unique nanoarchitectures with
subwavelength building blocks as the basis for plasmonic and metamaterial
devices. Chemical crosslinking of colloidal nanospheres has produced among the
smallest gap spacings, necessary to obtain regions of greatly enhanced electric
field, hotspots, which are critical to tailor light-matter interactions.
However, obtaining uniform electromagnetic response of dense nanoantennas over
large area for use in devices remains challenging. In this work,
electrohydrodynamic (EHD) flow and chemical crosslinking is combined to form
dense, yet discrete, Au nanosphere clusters (oligomers) on a working electrode.
EHD provides a long range driving force to bring nanospheres together and
anhydride crosslinking yields 0.9 nm gap spacings. Using selective chemistry,
nanospheres are simultaneously crosslinked onto a block copolymer template,
producing oligomers with a narrower wavelength band width and higher hotspot
intensity than monolayer structures produced without a template. We investigate
nanoantenna response via full wave simulations, ultraviolet-visible
spectroscopy, and surface enhanced Raman scattering (SERS). Nanoantennas
exhibit uniform hotspot intensity and gap spacing. Simulations show field
enhancements of 600, correlating well with measured average SERS enhancement of
1.4x10^9. Nanoantenna substrates produce a SERS signal with a relative standard
deviation of 10% measured over a 1 mm2 area, crucial for nano-optical devices
such as optical sensors, among other applications. Understanding long range
(EHD flow) and short range (chemical crosslinking) driving forces provides the
control for assembling colloidal nanoparticles in architectures for large area
plasmonic and metasurface device fabrication.


title: Patching and the completed homology of locally symmetric spaces

abstract:
  Under an assumption on the existence of p-adic Galois representations, we
carry out Taylor--Wiles patching (in the derived category) for the completed
homology of the locally symmetric spaces associated to GL(n) over a number
field. We use our construction to show that standard conjectures on completed
homology imply `big R = big T' theorems. In the case that n=2 and p splits
completely in the number field, we relate our construction to the p-adic local
Langlands correspondence for GL(2,Q_p).


title: High order paracontrolled calculus

abstract:
  We develop in this work a general version of paracontrolled calculus that
allows to treat analytically within this paradigm some singular partial
differential equations with the same efficiency as regularity structures. This
work deals with the analytic side of the story and offers a toolkit for the
study of such equations, under the form of a number of continuity results for
some operators. We illustrate the efficiency of this elementary approach on the
examples of the 3-dimensional generalised parabolic Anderson model equation and
the generalised KPZ equation driven by a (1+1)-dimensional space/time white
noise.


title: Two-dimensional collective Hamiltonian for chiral and wobbling modes

abstract:
  A two-dimensional collective Hamiltonian (2DCH) on both azimuth and polar
motions in triaxial nuclei is proposed to investigate the chiral and wobbling
modes. In the 2DCH, the collective potential and the mass parameters are
determined from three-dimensional tilted axis cranking (TAC) calculations. The
broken chiral and signature symmetries in the TAC solutions are restored by the
2DCH. The validity of the 2DCH is illustrated with a triaxial rotor
($\gamma=-30^\circ$) coupling to one $h_{11/2}$ proton particle and one
$h_{11/2}$ neutron hole. By diagonalizing the 2DCH, the angular momenta and
energy spectra are obtained. These results agree with the exact solutions of
the particle rotor model (PRM) at high rotational frequencies. However, at low
frequencies, the energies given by the 2DCH are larger than those by the PRM
due to the underestimation of the mass parameters. In addition, with increasing
angular momentum, the transitions from the chiral vibration to chiral rotation
and further to longitudinal wobbling motion have been presented in the 2DCH.


title:
Some comments about "Penalising model component complexity" by Simpson
  et al. (2017)

abstract:
  This note discusses the paper "Penalising model component complexity" by
Simpson et al. (2017). While we acknowledge the highly novel approach to prior
construction and commend the authors for setting new-encompassing principles
that will Bayesian modelling, and while we perceive the potential connection
with other branches of the literature, we remain uncertain as to what extent
the principles exposed in the paper can be developed outside specific models,
given their lack of precision. The very notions of model component, base model,
overfitting prior are for instance conceptual rather than mathematical and we
thus fear the concept of penalised complexity may not further than extending
first-guess priors into larger families, thus failing to establish reference
priors on a novel sound ground.


title:
Power corrections to the electromagnetic spectral function and the
  dilepton rate in QCD plasma within operator product expansion in D=4

abstract:
  We evaluate the electromagnetic spectral function in QCD plasma in a
nonperturbative background of in-medium quark and gluon condensates by
incorporating the leading order power corrections in a systematic framework
within the ambit of the operator product expansion in D=4 dimension. We
explicitly show that the mixing of the composite operators removes mass
singularities and renders Wilson coefficients finite and well defined. As a
spectral property, we then obtain the nonperturbative dilepton production rate
from QCD plasma. The operator product expansion automatically restricts the
dilepton rate to the intermediate mass range, which is found to be enhanced due
to the power corrections. We also compare our result with those from
nonperturbative calculations, e.g., lattice QCD and effective QCD models based
on Polyakov loop.


title:
Characterisation by Local Means of Anisotropic Lizorkin--Triebel Spaces
  with Mixed Norms

abstract:
  This is a contribution to the theory of Lizorkin--Triebel spaces having mixed
Lebesgue norms and quasi-homogeneous smoothness. We discuss their
characterisation in terms of general quasi-norms based on convolutions. In
particular, this covers the case of local means, in Triebel's terminology. The
main step is an extension of some crucial inequalities due to Rychkov to the
case with mixed norms.


title:
The Dirichlet Series for the Liouville Function and the Riemann
  Hypothesis

abstract:
  This paper investigates the analytic properties of the Liouville function's
Dirichlet series that obtains from the function F(s)= zeta(2s)/zeta(s), where s
is a complex variable and zeta(s) is the Riemann zeta function. The paper
employs a novel method of summing the series by casting it as an infinite
number of sums over sub-series that exhibit a certain symmetry and rapid
convergence. In this procedure, which heavily invokes the prime factorization
theorem, each sub-series has the property that it oscillates in a predictable
fashion, rendering the analytic properties of the Dirichlet series
determinable. With this method, the paper demonstrates that, for every integer
with an even number of primes in its factorization, there is another integer
that has an odd number of primes (multiplicity counted) in its factorization.
Furthermore, by showing that a sufficient condition derived by Littlewood
(1912) is satisfied, the paper demonstrates that the function F(s) is analytic
over the two half-planes Re(s) > 1/2 and Re(s)<1/2. This establishes that the
nontrivial zeros of the Riemann zeta function can only occur on the critical
line Re(s)=1/2.


title: Minimal completely asymmetric (4; n)-regular matchstick graphs

abstract:
  A matchstick graph is a graph drawn with straight edges in the plane such
that the edges have unit length, and non-adjacent edges do not intersect. We
call a matchstick graph $(m;n)$-regular if every vertex has only degree $m$ or
$n$. In this article we present the latest known $(4;n)$-regular matchstick
graphs for $4\leq n\leq11$ with a minimum number of vertices and a completely
asymmetric structure. We call a matchstick graph completely asymmetric, if the
following conditions are complied. 1) The graph is rigid. 2) The graph has no
point, rotational or mirror symmetry. 3) The graph has an asymmetric outer
shape. 4) The graph can not be decomposed into rigid subgraphs and rearrange to
a similar graph which contradicts to any of the other conditions.


title: Rapid crystallization of externally produced ions in a Penning trap

abstract:
  We have studied the cooling dynamics, formation process and geometric
structure of mesoscopic crystals of externally produced magnesium ions in a
Penning trap. We present a cooling model and measurements for a combination of
buffer gas cooling and laser cooling which has been found to reduce the ion
kinetic energy by eight orders of magnitude from several hundreds of eV to
micro-eV and below within seconds. With ion numbers of the order of 1000 to
100000, such cooling leads to the formation of ion Coulomb crystals which
display a characteristic shell structure in agreement with theory of
non-neutral plasmas. We show the production and characterization of two-species
ion crystals as a means of sympathetic cooling of ions lacking a suitable
laser-cooling transition.


title:
Numerical investigation of local defectiveness control of diblock
  copolymer patterns

abstract:
  We numerically investigate local defectiveness control of self-assembled
diblock copolymer patterns through appropriate substrate design. We use a
nonlocal Cahn-Hilliard (CH) equation for the phase separation dynamics of
diblock copolymers. We discretize the nonlocal CH equation by an
unconditionally stable finite difference scheme on a tapered trench design and,
in particular, we use Dirichlet, Neumann, and periodic boundary conditions. The
value at the Dirichlet boundary comes from an energy-minimizing equilibrium
lamellar profile. We solve the resulting discrete equations using a
Gauss-Seidel iterative method. We perform various numerical experiments such as
effects of channel width, channel length, and angle on the phase separation
dynamics. The simulation results are consistent with the previous experimental
observations.


title: Regenerative Soot-VIII: Sputtering and formation of C1 and C2

abstract:
  Photoemission spectroscopy of the regenerative soot in neon's glow discharge
plasma reveals the contributions from the sputtered atomic and molecular carbon
species. We present the pattern of sputtering and the formation of monatomic C1
and diatomic C2 as a function of the discharge current, the support gas
pressure and the number densities of the excited and ionized neon as the active
constituents of the carbonaceous plasma.


title: Matrices about the lattice paths

abstract:
  From the matrix point of view, we use the recursion to discuss four
combinatorial numbers in terms of the integer lattice paths, this is different
from Andr\'a's method (Andra). We give four tables and matrices, and their
relations, and give their matrix decompositions. By their relations, we give
the explicit formulas of the special combinatorial numbers.


title:
Avoiding the Goldstone Boson Catastrophe in general renormalisable field
  theories at two loops

abstract:
  We show how the infra-red divergences associated to Goldstone bosons in the
minimum condition of the two-loop Landau-gauge effective potential can be
avoided in general field theories. This extends the resummation formalism
recently developed for the Standard Model and the MSSM, and we give compact,
infra-red finite expressions in closed form for the tadpole equations. We also
show that the results at this loop order are equivalent to (and are most easily
obtained by) imposing an "on-shell" condition for the Goldstone bosons.
Moreover, we extend the approach to show how the infra-red divergences in the
calculation of the masses of neutral scalars (such as the Higgs boson) can be
eliminated. For the mass computation, we specialise to the gaugeless limit and
extend the effective potential computation to allow the masses to be determined
without needing to solve differential equations for the loop functions --
opening the door to fast, infra-red safe determinations of the Higgs mass in
general theories.


title: Gridlan: a Multi-purpose Local Grid Computing Framework

abstract:
  In scientific computing, more computational power generally implies faster
and possibly more detailed results. The goal of this study was to develop a
framework to submit computational jobs to powerful workstations underused by
nonintensive tasks. This is achieved by using a virtual machine in each of
these workstations, where the computations are done. This group of virtual
machines is called the Gridlan. The Gridlan framework is intermediate between
the cluster and grid computing paradigms. The Gridlan is able to profit from
existing cluster software tools, such as resource managers like Torque, so a
user with previous experience in cluster operation can dispatch jobs
seamlessly. A benchmark test of the Gridlan implementation shows the system's
suitability for computational tasks, principally in embarrassingly parallel
computations.


title: A G2-QCD neutron star

abstract:
  The determination of the properties of neutron stars from the underlying
theory, QCD, is still an unsolved problem. This is mainly due to the difficulty
to obtain reliable results for the equation of state for cold, dense QCD. As an
alternative route to obtain qualitative insights, we determine the structure of
a neutron star for a modified version of QCD: By replacing the gauge group
SU(3) with the exceptional Lie group G2, it is possible to perform lattice
simulations at finite density, while still retaining neutrons. Here, results of
these lattice simulations are used to determine the mass-radius relation of a
neutron star for this theory. The results show that phase changes express
themselves in this relation. Also, the radius of the most massive neutron stars
is found to vary very little, which would make radius determinations much
simpler if this would also be true in QCD.

categories: astro-ph.HE astro-ph.SR hep-lat hep-ph nucl-th


title: Finite symmetries in agent-based epidemic models

abstract:
  We present an algorithm which explores permutation symmetries to describe the
time evolution of agent-based epidemic models. The main idea to improve
computation times relies on restricting the stochastic process to one sector of
the vector space, labeled by a single permutation eigenvalue. In this scheme,
the transition matrix reduces to block diagonal form, enhancing computational
performance.


title: Fundamental energy cost for quantum measurement

abstract:
  Measurements and feedback are essential in the control of any device
operating at the quantum scale and exploiting the features of quantum physics.
As the number of quantum components grows, it becomes imperative to consider
the energetic expense of such elementary operations. Here, we derive energy
requirements for general quantum measurement, extending previous models and
obtaining stronger bounds in relevant situations, and then study two important
classes of measurements in detail. One is the projective measurement, where we
obtain the exact cost rather than a lower bound, and the other is the so-called
inefficient measurement, in which we explicitly show that energy extraction is
possible. As applications, we derive the energy-precision trade-off in quantum
Zeno stabilisation schemes and the exact energy expense for quantum error
correction. Our results constitute fundamental energetic limitations against
which to benchmark implementations of future quantum devices as they grow in
complexity.


title: The fundamental diagram of urbanization

abstract:
  The process of urbanization is one of the most important phenomenon of our
societies and it is only recently that the availability of massive amounts of
geolocalized historical data allows us to address quantitatively some of its
features. Here, we discuss how the number of buildings evolves with population
and we show on different datasets (Chicago, $1930-2010$; London, $1900-2015$;
New York City, $1790-2013$; Paris, $1861-2011$) that this `fundamental diagram'
evolves in a possibly universal way with three distinct phases. After an
initial pre-urbanization phase, the first phase is a rapid growth of the number
of buildings versus population. In a second regime, where residences are
converted into another use (such as offices or stores for example), the
population decreases while the number of buildings stays approximatively
constant. In another subsequent phase, the number of buildings and the
population grow again and correspond to a re-densification of cities. We
propose a stochastic model based on these simple mechanisms to reproduce the
first two regimes and show that it is in excellent agreement with empirical
observations. These results bring evidences for the possibility of constructing
a minimal model that could serve as a tool for understanding quantitatively
urbanization and the future evolution of cities.


title:
On the local equivalence between the canonical and the microcanonical
  distributions for quantum spin systems

abstract:
  We study a quantum spin system on the $d$-dimensional hypercubic lattice
$\Lambda$ with $N=L^d$ sites with periodic boundary conditions. We take an
arbitrary translation invariant short-ranged Hamiltonian. For this system, we
consider both the canonical ensemble with inverse temperature $\beta_0$ and the
microcanonical ensemble with the corresponding energy $U_N(\beta_0)$. For an
arbitrary self-adjoint operator $\hat{A}$ whose support is contained in a
hypercubic block $B$ inside $\Lambda$, we prove that the expectation values of
$\hat{A}$ with respect to these two ensembles are close to each other for large
$N$ provided that $\beta_0$ is sufficiently small and the number of sites in
$B$ is $o(N^{1/2})$. This establishes the equivalence of ensembles on the level
of local states in a large but finite system. The result is essentially that of
Brandao and Cramer (here restricted to the case of the canonical and the
microcanonical ensembles), but we prove improved estimates in an elementary
manner. We also review and prove standard results on the thermodynamic limits
of thermodynamic functions and the equivalence of ensembles in terms of
thermodynamic functions. The present paper assumes only elementary knowledge on
quantum statistical mechanics and quantum spin systems.


title:
Event-Triggered Communication and Control for Multi-Agent Average
  Consensus

abstract:
  In this chapter we look at one of the canonical driving examples for
multi-agent systems: average consensus. In this scenario, a group of agents
seek to agree on the average of their initial states. Depending on the
particular application, such states might correspond to sensor measurements,
estimates about the position of a target, or some other data that needs to be
fused. Due to its numerous applications in networked systems, many algorithmic
solutions exist to the multi-agent average consensus problem; however, a
majority of them rely on agents having continuous or periodic availability of
information from other agents. Unfortunately, this assumption leads to
inefficient implementations in terms of energy consumption, communication
bandwidth, network congestion, and processor usage. Motivated by these
observations, our main goal here is the design of provably correct distributed
event-triggered strategies that autonomously decide when communication and
control updates should occur so that the resulting asynchronous network
executions still achieve average consensus.


title:
Markovian nature, completeness, regularity and correlation properties of
  Generalized Poisson-Kac processes

abstract:
  We analyze some basic issues associated with Generalized Poisson-Kac (GPK)
stochastic processes, starting from the extended notion of the Markovian
condition. The extended Markovian nature of GPK processes is established, and
the implications of this property derived: the associated adjoint formalism for
GPK processes is developed essentially in an analogous way as for the
Fokker-Planck operator associated with Langevin equations driven by Wiener
processes. Subsequently, the regularity of trajectories is addressed: the
occurrence of fractality in the realizations of GPK is a long-term emergent
property, and its implication in thermodynamics is discussed. The concept of
completeness in the stochastic description of GPK is also introduced. Finally,
some observations on the role of correlation properties of noise sources and
their influence on the dynamic properties of transport phenomena are addressed,
using a Wiener model for comparison.


title: More on Diophantine sextuples

abstract:
  A rational Diophantine m-tuple is a set of m nonzero rationals such that the
product of any two of them increased by 1 is a perfect square. The first
rational Diophantine quadruple was found by Diophantus, while Euler proved that
there are infinitely many rational Diophantine quintuples. In 1999, Gibbs found
the first example of a rational Diophantine sextuple, and Dujella, Kazalicki,
Mikic and Szikszai recently proved that there exist infinitely many rational
Diophantine sextuples.
  In this paper, generalizing the work of Piezas, we describe a method for
generating new parametric formulas for rational Diophantine sextuples.


title:
Two-dimensional relative peripheral refractive error induced by Fractal
  Contact Lenses for myopia control

abstract:
  Purpose: To assess the peripheral refraction induced by Fractal Contact
Lenses (FCLs) in myopic eyes by means of a two-dimensional Relative Peripheral
Refractive Error (RPRE) map.
  Methods: FCLs prototypes were specially manufactured and characterized. This
study involved twenty-six myopic subjects ranging from -0.50 D to -7.00 D. The
two-dimensional RPRE was measured with an open-field autorefractor by means of
tracking targets distributed in a square grid from -30 degrees (deg) nasal to
30 deg temporal and 15 deg superior to -15 deg inferior. Corneal topographies
were taken in order to assess correlations between corneal asphericity, lens
decentration and RPRE represented in vector components M, J0 and J45.
  Results: The mean power of the FCLs therapeutic zones was 1.32 +/- 0.28 D.
Significant correlations were found between the corneal asphericity and vector
components of the RPRE in the nacked eyes. FCLs were decentered a mean of 0.7
+/- 0.19 mm to the temporal cornea. M decreased asymmetrically between nasal
and temporal retina after fitting the FCLs with a significant increment of the
myopic shift besides 10 deg (p<0.05) and the induced myopic shift at 25 deg and
30 deg decreased with FCLs decentration to temporal cornea. The peak of maximum
myopic shift at the peripheral retina (M= -1.3 D) was located at 20 deg.
Two-dimensional maps showed uniform significant differences in extreme
positions of the visual field in comparison with the horizontal RPRE for M and
J0, but not for J45.
  Conclusions: FCLs measured in myopic eyes showed a similar performance than
the reported in previous ray-tracing studies with a small bias explained by the
manufacturing process and the lens decentration. Two-dimensional maps are
preferable for assessing J45 changes due to the lens.


title:
Symmetric Non-Rigid Structure from Motion for Category-Specific Object
  Structure Estimation

abstract:
  Many objects, especially these made by humans, are symmetric, e.g. cars and
aeroplanes. This paper addresses the estimation of 3D structures of symmetric
objects from multiple images of the same object category, e.g. different cars,
seen from various viewpoints. We assume that the deformation between different
instances from the same object category is non-rigid and symmetric. In this
paper, we extend two leading non-rigid structure from motion (SfM) algorithms
to exploit symmetry constraints. We model the both methods as energy
minimization, in which we also recover the missing observations caused by
occlusions. In particularly, we show that by rotating the coordinate system,
the energy can be decoupled into two independent terms, which still exploit
symmetry, to apply matrix factorization separately on each of them for
initialization. The results on the Pascal3D+ dataset show that our methods
significantly improve performance over baseline methods.


title: Structural Properties of Stiff Elastic Networks

abstract:
  Networks of elastic beams can deform either by stretching or bending of their
members. The primary mode of deformation (bending or stretching) crucially
depends on the specific details of the network architecture. In order to shed
light on the relationship between microscopic geometry and macroscopic
mechanics, we characterize the structural features of networks which deform
uniformly, through the stretching of the beams only. We provide a convenient
set of geometrical criteria to identify such networks, and derive the values of
their effective elastic moduli. The analysis of these criteria elucidates the
variability of mechanical response of elastic networks. In particular, our
study rationalizes the difference in mechanical behavior of cellular and fiber
networks.


title: Quasidiagonal traces and crossed products

abstract:
  Let $A$ be a simple, exact, separable, unital $C^*$-algebra and let $\alpha
\colon G \rightarrow Aut(A)$ be an action of a finite group $G$ with the weak
tracial Rokhlin property. We show that every trace on $A \rtimes_{\alpha} G$ is
quasidiagonal provided that all traces on $A$ are quasidiagonal. As an
application, we study the behavior of finite decomposition rank under taking
crossed products by finite group actions with the weak tracial Rokhlin
property. Moreover, we discuss the stability of the property that all traces
are quasidiagonal under taking crossed products of finite group actions with
finite Rokhlin dimension with commuting towers.


title:
Spherical character of a supercuspidal representation as weighted
  orbital integral

abstract:
  Let $\rm E/\rm F$ be an unramified quadratic extension of local non
archimedean fields of characteristic 0. Let $\underline{H}$ be an algebraic
reductive group, defined and split over $\rm F$. We assume that the split
connected component of the center of $\underline{H}$ is trivial. Let $(\tau,V)$
be a $\underline{H}(\rm F)$-distinguished supercuspidal representation of
$\underline{H}(\rm E)$. Using the recent results of C. Zhang, and the geometric
side of a local relative trace formula obtained by P. Delorme, P. Harinck and
S. Souaifi, we describe spherical characters associated to $\underline{H}(\rm
F)$-invariant linear forms on $V$ in terms of weighted orbital integrals of
matrix coefficients of $\tau$.


title:
Formal Series of Generalised Functions and Their Application to
  Deformation Quantisation

abstract:
  Foundations of the formal series $*$ -- calculus in deformation quantisation
are discussed. Several classes of continuous linear functionals over algebras
applied in classical and quantum physics are introduced. The notion of
nonnegativity in formal series calculus is proposed. Problems with defining
quantum states over the set of formal series are analysed.


title: The Conformal Limit of Inflation in the Era of CMB Polarimetry

abstract:
  We argue that the non-detection of primordial tensor modes has taught us a
great deal about the primordial universe. In single-field slow-roll inflation,
the current upper bound on the tensor-to-scalar ratio, $r < 0.07$ $(95 \%
~CL)$, implies that the Hubble slow-roll parameters obey $\varepsilon \ll
\eta$, and therefore establishes the existence of a new hierarchy. We dub this
regime the conformal limit of (slow-roll) inflation, and show that it includes
Starobinsky-like inflation as well as all viable single-field models with a
sub-Planckian field excursion. In this limit, all primordial correlators are
constrained by the full conformal group to leading non-trivial order in
slow-roll. This fixes the power spectrum and the full bispectrum, and leads to
the "conformal" shape of non-Gaussianity. The size of non-Gaussianity is
related to the running of the spectral index by a consistency condition, and
therefore it is expected to be small. In passing, we clarify the role of
boundary terms in the $\zeta$ action, the order to which constraint equations
need to be solved, and re-derive our results using the Wheeler-deWitt
formalism.


title: Deconstruction and conditional erasure of quantum correlations

abstract:
  We define the deconstruction cost of a tripartite quantum state on systems
$ABE$ as the minimum rate of noise needed to apply to the $AE$ systems, such
that there is negligible disturbance to the marginal state on the $BE$ systems,
while the system $A$ of the resulting state is locally recoverable from the $E$
system alone. We refer to such actions as deconstruction operations and
protocols implementing them as state deconstruction protocols. State
deconstruction generalizes Landauer erasure of a single-party quantum state as
well the erasure of correlations of a two-party quantum state. We find that the
deconstruction cost of a tripartite quantum state on systems $ABE$ is equal to
its conditional quantum mutual information (CQMI) $I(A;B|E)$, thus giving the
CQMI an operational interpretation in terms of a state deconstruction protocol.
We also define a related task called conditional erasure, in which the goal is
to apply noise to systems $AE$ in order to decouple system $A$ from systems
$BE$, while causing negligible disturbance to the marginal state of systems
$BE$. We find that the optimal rate of noise for conditional erasure is also
equal to the CQMI $I(A;B|E)$. State deconstruction and conditional erasure lead
to operational interpretations of the quantum discord and squashed
entanglement, which are quantum correlation measures based on the CQMI. We find
that the quantum discord is equal to the cost of simulating einselection, the
process by which a quantum system interacts with an environment, resulting in
selective loss of information in the system. The squashed entanglement is equal
to half the minimum rate of noise needed for deconstruction/conditional erasure
if Alice has available the best possible system $E$ to help in the
deconstruction/conditional erasure task.


title:
Tilings of non-convex Polygons, skew-Young Tableaux and determinantal
  Processes

abstract:
  This paper studies random lozenge tilings of general non-convex polygonal
regions. We show that the pairwise interaction of the non-convexities leads
asymptotically to new kernels and thus to new statistics for the tiling
fluctuations.
  The precise geometrical figure here consists of a hexagon with cuts along
opposite edges. For this model we take limits when the size of the hexagon and
the cuts tend to infinity, while keeping certain geometric data fixed in order
to guarantee interaction beyond the limit. We show in this paper that the
kernel for the finite tiling model can be expressed as a multiple integral,
where the number of integrations is related to the fixed geometric data above.
The limiting kernel is believed to be a universal master kernel.


title:
Radiative conductivity and abundance of post-perovskite in the lowermost
  mantle

abstract:
  Thermal conductivity of the lowermost mantle governs the heat flow out of the
core energizing planetary-scale geological processes. Yet, there are no direct
experimental measurements of thermal conductivity at relevant
pressure-temperature conditions of Earth's core-mantle boundary. Here we
determine the radiative conductivity of post-perovskite at near core-mantle
boundary conditions by optical absorption measurements in a laser-heated
diamond anvil cell. Our results show that the radiative conductivity of
Mg0.9Fe0.1SiO3 post-perovskite (< 1.2 W/m/K) is ~ 40% smaller than bridgmanite
at the base of the mantle. By combining this result with the present-day
core-mantle heat flow and available estimations on the lattice thermal
conductivity we conclude that post-perovskite is as abundant as bridgmanite in
the lowermost mantle which has profound implications for the dynamics of the
deep Earth.


title:
Smooth anti-reflective three-dimensional textures for liquid-phase
  crystallized silicon thin-film solar cells on glass

abstract:
  Recently, liquid-phase crystallization of thin silicon films has emerged as a
promising candidate for thin-film photovoltaics. On 10 \mu m thin absorbers,
wafer-equivalent morphologies and open-circuit voltages were reached, leading
to a record efficiency of 12.1%. However, short-circuit current densities are
still limited, mainly due to optical losses at the glass-silicon interface.
While nano-structures at this interface have been shown to efficiently reduce
reflection, up to now these textures caused an increase in recombination.
Therefore, optical gains were mitigated due to electronic losses. Here, the
SMooth Anti-Reflective Three-dimensional (SMART) texture is introduced in order
to overcome this trade-off. By smoothing nanoimprinted SiOx nano-pillar arrays
with spin-coated TiOx layers, light-trapping properties of laser-crystallized
silicon solar cells could significantly be improved as successfully shown in
three-dimensional simulations and in experiment. At the same time, the smooth
surface morphology of SMART textures allows preserving electronic material
quality equivalent to that of planar reference samples and reaching Voc values
above 640 mV in 8 \mu m thin liquid-phase crystallized silicon solar cells.
Furthermore, the short-circuit current density jsc could be increased from 21.0
mA cm-2 for planar reference cells with already optimized anti-reflective
interlayer stacks to 23.3 mA cm-2 on SMART textures, corresponding to a
relative increase of 11%.


title:
On differential operators on complete symmetric varieties of type $A_1$
  and $A_2$

abstract:
  In this paper, we will look at the algebra of global differential operators
$D_X$ on wonderful compactifications $X$ of symmetric spaces $G/H$ of type
$A_1$ and $A_2$. We will first construct a global differential operator on
these varieties that does not come from the infinitesimal action of
$\mathfrak{g}$. We will then focus on type $A_2$, where we will show that $D_X$
is an algebra of finite type, and that for any invertible sheaf ${\cal L}$ on
$X$, $H^{0}(X,{\cal L})$ is either 0 or a simple left $D_{X,{\cal L}}$-module.
Finally, we will show with the help of local cohomology that this is still true
for higher cohomology groups $H^{i}(X,{\cal L})$.


title: A classification of harmonic Maass forms

abstract:
  We give a classification of the Harish-Chandra modules generated by the
pullback to $\text{SL}_2(\mathbb R)$ of harmonic Maass forms for congruence
subgroups of $\text{SL}_2(\mathbb Z)$ with exponential growth allowed at the
cusps. We assume that the weight is integral but include vector-valued forms.
Due to the weak growth condition, these modules need not be irreducible.
Elementary Lie algebra considerations imply that there are 9 possibilities, and
we show, by giving explicit examples, that all of them arise from harmonic
Maass forms. Finally, we briefly discuss the case of forms that are not
harmonic but rather are annihilated by a power of the Laplacian, where much
more complicated Harish-Chandra modules can arise.


title:
Stiffness of the C-terminal disordered linker affects the geometry of
  the active site in endoglucanase Cel8A

abstract:
  Cellulosomes are complex multi-enzyme machineries which efficiently degrade
plant cell-wall polysaccharides. The multiple domains of the cellulosome
proteins are often tethered together by intrinsically disordered regions. The
properties and functions of these disordered linkers are not well understood.
In this work, we study endoglucanase Cel8A, which is a relevant enzymatic
component of the cellulosomes of Clostridium thermocellum. We use both all-atom
and coarse-grained simulations to investigate how the equilibrium conformations
of the catalytic domain of Cel8A are affected by the disordered linker at its C
terminus. We find that when the endoglucanase is bound to its substrate, the
effective stiffness of the linker can influence the distances between groups of
amino-acid residues throughout the entire enzymatic domain. In particular,
variations in the linker stiffness can lead to small changes in the geometry of
the active-site cleft. We suggest that such geometrical changes may, in turn,
have an effect on the catalytic activity of the enzyme.


title:
Energy dependence of hadron polarization in $e^+e^-\to hX$ at high
  energies

abstract:
  The longitudinal polarization of hyperons in $e^+e^-$ annihilation at high
energies depends on the longitudinal polarization of the quark produced at the
$e^+e^-$ annihilation vertex whereas the spin alignment of vector mesons is
independent of it. They exhibit very different energy dependences. We use the
longitudinal polarization of Lambda hyperon and the spin alignment of $K^*$ as
examples and present numerical results of energy dependences. We present the
results at the leading twist with perturbative QCD evolutions of fragmentation
functions at the leading order.


title:
Vertex operators for production of baryon resonances in nucleon-gamma
  collisions with preserving gauge invariance and analyticity

abstract:
  Vertex operators for photo- and electro-production of baryon states with
arbitrary spin-parity, $ \gamma + N\to B(J^P)$, are constructed. The operators
obey gauge invariance and analyticity constraints. Analyticity is realized as a
requirement of the generalized Siegert theorem for vertex form factors.


title: Parallel transport along Seifert manifolds and fractional monodromy

abstract:
  The notion of fractional monodromy was introduced by Nekhoroshev,
Sadovski\'{i} and Zhilinski\'{i} as a generalization of standard (`integer')
monodromy in the sense of Duistermaat from torus bundles to singular torus
fibrations. In the present paper we prove a general result that allows to
compute fractional monodromy in various integrable Hamiltonian systems. In
particular, we show that the non-triviality of fractional monodromy in 2
degrees of freedom systems with a Hamiltonian circle action is related only to
the fixed points of the circle action. Our approach is based on the study of a
specific notion of parallel transport along Seifert manifolds.


title:
Lines of Constant Physics in a Five-Dimensional Gauge-Higgs Unification
  Scenario

abstract:
  We report on the progress in the study of a five-dimensional SU(2)
Gauge-Higgs Unification model. In this non-perturbative study, the Higgs
mechanism is triggered by the spontaneous breaking of a global symmetry. In the
same region of the phase diagram, we observe both dimensional reduction and the
ratio of Higgs and Z boson masses to take the value known from experiment. We
present the first results on the construction of a line of constant physics in
this region, including the prediction for the mass scale of the first excited
states of the Higgs and gauge bosons.


title: Hofer-Zehnder capacity and Bruhat graph

abstract:
  We find bounds for the Hofer-Zehnder capacity of coadjoint orbits of compact
Lie groups with respect to the Kostant--Kirillov--Souriau symplectic form in
terms of the combinatorics of their Bruhat graph. We show that our bounds are
sharp for coadjoint orbits of the unitary group and equal to the diameter of a
weighted Cayley graph.


title:
SafeGuardPF: Safety Guaranteed Reactive Potential Fields for Mobile
  Robots in Unknown and Dynamic Environments

abstract:
  An autonomous navigation with proven collision avoidance in unknown and
dynamic environments is still a challenge, particularly when there are moving
obstacles. A popular approach to collision avoidance in the face of moving
obstacles is based on model predictive algorithms, which, however, may be
computationally expensive. Hence, we adopt a reactive potential field approach
here. At every cycle, the proposed approach requires only current robot states
relative to the closest obstacle point to find the potential field in the
current position; thus, it is more computationally efficient and more suitable
to scale up for multiple agent scenarios. Our main contribution here is to
write the reactive potential field based motion controller as a hybrid
automaton, and then formally verify its safety using differential dynamic
logic. In particular, we can guarantee a passive safety property, which means
that collisions cannot occur if the robot is to blame, namely a collision can
occur only if the robot is at rest. The proposed controller and verification
results are demonstrated via simulations and implementation on a Pioneer P3-AT
robot.


title: Fast symmetric additive covariance smoothing

abstract:
  We propose a fast bivariate smoothing approach for symmetric surfaces that
has a wide range of applications. We show how it can be applied to estimate the
covariance function in longitudinal data as well as multiple additive
covariances in functional data with complex correlation structures. Our
symmetric smoother can handle (possibly noisy) data sampled on a common, dense
grid as well as irregularly or sparsely sampled data. Estimation is based on
bivariate penalized spline smoothing using a mixed model representation and the
symmetry is used to reduce computation time compared to the usual non-symmetric
smoothers. We outline the application of our approach in functional principal
component analysis and demonstrate its practical value in two applications. The
approach is evaluated in extensive simulations. We provide documented open
source software implementing our fast symmetric bivariate smoother building on
established algorithms for additive models.


title:
Scaling betweenness centrality using communication-efficient sparse
  matrix multiplication

abstract:
  Betweenness centrality (BC) is a crucial graph problem that measures the
significance of a vertex by the number of shortest paths leading through it. We
propose Maximal Frontier Betweenness Centrality (MFBC): a succinct BC algorithm
based on novel sparse matrix multiplication routines that performs a factor of
$p^{1/3}$ less communication on $p$ processors than the best known
alternatives, for graphs with $n$ vertices and average degree $k=n/p^{2/3}$. We
formulate, implement, and prove the correctness of MFBC for weighted graphs by
leveraging monoids instead of semirings, which enables a surprisingly succinct
formulation. MFBC scales well for both extremely sparse and relatively dense
graphs. It automatically searches a space of distributed data decompositions
and sparse matrix multiplication algorithms for the most advantageous
configuration. The MFBC implementation outperforms the well-known CombBLAS
library by up to 8x and shows more robust performance. Our design methodology
is readily extensible to other graph problems.


title: Is the deconvolution layer the same as a convolutional layer?

abstract:
  In this note, we want to focus on aspects related to two questions most
people asked us at CVPR about the network we presented. Firstly, What is the
relationship between our proposed layer and the deconvolution layer? And
secondly, why are convolutions in low-resolution (LR) space a better choice?
These are key questions we tried to answer in the paper, but we were not able
to go into as much depth and clarity as we would have liked in the space
allowance. To better answer these questions in this note, we first discuss the
relationships between the deconvolution layer in the forms of the transposed
convolution layer, the sub-pixel convolutional layer and our efficient
sub-pixel convolutional layer. We will refer to our efficient sub-pixel
convolutional layer as a convolutional layer in LR space to distinguish it from
the common sub-pixel convolutional layer. We will then show that for a fixed
computational budget and complexity, a network with convolutions exclusively in
LR space has more representation power at the same speed than a network that
first upsamples the input in high resolution space.


title:
Dispersion relations and bending losses of cylindrical and spherical
  shells, slabs, and slot waveguides

abstract:
  We derive formulas for Whispering Gallery Mode resonances and bending losses
in infinite cylindrical dielectric shells and sets of concentric cylindrical
shells. The formulas also apply to spherical shells and to sections of bent
waveguides. The derivation is based on a WKB treatment of Helmholtz equation
and can in principle be extended to any number of concentric shells. A
distinctive limit analytically arises in the analysis when two shells are
brought at very close distance to one another. In that limit, the two shells
act as a slot waveguide. If the two shells are sufficiently apart, we identify
a structural resonance between the individual shells, which can either lead to
a substantial enhancement or suppression of radiation losses.


title: Singular curves and Baker-Akhiezer functions

abstract:
  We present the concept of Baker-Akhiezer functions on singular complex
curves. For this purpose, we translate the algebraic presentation of such
curves in [Se, Chapter~IV] into the analytic setting. Generalised divisors and
their interplay with partial desingularisations are the fundament of the
construction of Baker-Akhiezer functions.


title:
Formation and stability of metastable skyrmionic spin structures with
  various topologies in an ultrathin film

abstract:
  We observe metastable localized spin configurations with topological charges
ranging from $Q=-3$ to $Q=2$ in a (Pt$_{0.95}$Ir$_{0.05}$)/Fe bilayer on
Pd$(111)$ surface by performing spin dynamics simulations, using a classical
Hamiltonian parametrized by ab initio calculations. We demonstrate that the
frustration of the isotropic exchange interactions is responsible for the
creation of these various types of skyrmionic structures. The
Dzyaloshinsky--Moriya interaction present due to the breaking of inversion
symmetry at the surface energetically favors skyrmions with $Q=-1$, distorts
the shape of the other objects, and defines a preferred orientation for them
with respect to the underlying lattice.


title:
On the construction of solutions to the free-surface incompressible
  ideal magnetohydrodynamic equations

abstract:
  We consider a free boundary problem for the incompressible ideal
magnetohydrodynamic equations that describes the motion of the plasma in
vacuum. The magnetic field is tangent and the total pressure vanishes along the
plasma-vacuum interface. Under the Taylor sign condition of the total pressure
on the free surface, we prove the local well-posedness of the problem in
Sobolev spaces.


title: Chiral-scale effective theory including a dilatonic meson

abstract:
  A scale-invariant chiral effective Lagrangian is constructed for octet pions
and a dilaton figuring as Nambu-Goldstone bosons with vector mesons
incorporated as hidden gauge fields. The Lagrangian is built to the
next-to-leading order in chiral-scale counting without baryon fields and then
to leading order including baryons. The resulting theory is hidden
scale-symmetric and local symmetric. We also discuss some possible applications
of the present Lagrangian.


title: Distributed Consistent Data Association

abstract:
  Data association is one of the fundamental problems in multi-sensor systems.
Most current techniques rely on pairwise data associations which can be
spurious even after the employment of outlier rejection schemes. Considering
multiple pairwise associations at once significantly increases accuracy and
leads to consistency. In this work, we propose two fully decentralized methods
for consistent global data association from pairwise data associations. The
first method is a consensus algorithm on the set of doubly stochastic matrices.
The second method is a decentralization of the spectral method proposed by
Pachauri et al.. We demonstrate the effectiveness of both methods using
theoretical analysis and experimental evaluation.


title:
Spin-polarized scanning tunneling microscopy characteristics of
  skyrmionic spin structures exhibiting various topologies

abstract:
  The correct identification of topological magnetic objects in experiments is
an important issue. In the present work we report on the characterization of
metastable skyrmionic spin structures with various topological charges
($Q=-3,-2,-1,0,+1,+2$) in the (Pt$_{1-x}$Ir$_{x}$)Fe/Pd(111) ultrathin magnetic
film by performing spin-polarized scanning tunneling microscopy (SP-STM)
calculations. We find that an out-of-plane magnetized tip already results in
distinguished SP-STM contrasts for the different skyrmionic structures
corresponding to their symmetries. Our work also establishes an understanding
of the relationship between in-plane SP-STM contrasts and skyrmionic topologies
through an investigation of the variation of the in-plane angle between the
spins along the perimeter of the structures, which can be characterized by the
local vorticity or linear density of the winding number. For spin structures
exhibiting a uniform sign of the local vorticity throughout the whole
skyrmionic area, we demonstrate that (i) $|Q|$ can be determined from a single
SP-STM image taken by any in-plane magnetized tip, and (ii) an in-plane tip
magnetization rotation provides the sign of $Q$ independently of the sign of
the effective spin polarization in the tunnel junction. We also discuss cases
where the local vorticity is changing sign. Finally, by increasing the Ir
content of the PtIr overlayer, we find an appearing secondary outer ring
in-plane SP-STM contrast that is indicative of attractive skyrmions or
antiskyrmions.


title: Content of Local Cohomology, Parameter Ideals, and Robust Algebras

abstract:
  This paper continues the investigation of quasilength, of content of local
cohomology with respect to generators of the support ideal, and of robust
algebras begun in joint work of Hochster and Huneke. We settle several
questions raised by Hochster and Huneke. In particular, we give a family of
examples of top local cohomology modules both in equal characteristic 0 and in
positive prime characteristic that are nonzero but have content 0. We use the
notion of a robust forcing algebra (the condition turns out to be strictly
stronger than the notion of a solid forcing algebra in, for example, equal
characteristic 0) to define a new closure operation on ideals. We prove that
this new notion of closure coincides with tight closure for ideals in complete
local domains of positive characteristic, which requires proving that forcing
algebras for instances of tight closure are robust, and study several related
problems. This gives, in effect, a new characterization of tight closure in
complete local domains of positive characteristic. As a byproduct, we also
answer a question of Lyubeznik in the negative.


title:
Strong-field ionization via high-order Coulomb corrected strong-field
  approximation

abstract:
  Signatures of the Coulomb corrections in the photoelectron momentum
distribution during laser-induced ionization of atoms or ions in tunneling and
multiphoton regimes are investigated analytically in the case of an
one-dimensional problem. High-order Coulomb corrected strong-field
approximation is applied, where the exact continuum state in the S-matrix is
approximated by the eikonal Coulomb-Volkov state including the second-order
corrections to the eikonal. Although, without high-order corrections our theory
coincides with the known analytical R-matrix (ARM) theory, we propose a
simplified procedure for the matrix element derivation. Rather than matching
the eikonal Coulomb-Volkov wave function with the bound state as in the
ARM-theory to remove the Coulomb singularity, we calculate the matrix element
via the saddle-point integration method as by time as well as by coordinate,
and in this way avoiding the Coulomb singularity. The momentum shift in the
photoelectron momentum distribution with respect to the ARM-theory due to
high-order corrections is analyzed for tunneling and multiphoton regimes. The
relation of the quantum corrections to the tunneling delay time is discussed


title:
Lorentz Covariant Canonical Symplectic Algorithms for Dynamics of
  Charged Particles

abstract:
  In this paper, the Lorentz covariance of algorithms is introduced. Under
Lorentz transformation, both the form and performance of a Lorentz covariant
algorithm are invariant. To acquire the advantages of symplectic algorithms and
Lorentz covariance, a general procedure for constructing Lorentz covariant
canonical symplectic algorithms (LCCSA) is provided, based on which an explicit
LCCSA for dynamics of relativistic charged particles is built. LCCSA possesses
Lorentz invariance as well as long-term numerical accuracy and stability, due
to the preservation of discrete symplectic structure and Lorentz symmetry of
the system. For situations with time-dependent electromagnetic fields, which is
difficult to handle in traditional construction procedures of symplectic
algorithms, LCCSA provides a perfect explicit canonical symplectic solution by
implementing the discretization in 4-spacetime. We also show that LCCSA has
built-in energy-based adaptive time steps, which can optimize the computation
performance when the Lorentz factor varies.


title:
Scale-free unique continuation estimates and Logvinenko-Sereda Theorems
  on the torus

abstract:
  We study uncertainty principles for function classes on the torus. The
classes are defined in terms of spectral subspaces of the energy or the
momentum, respectively. In our main theorems, the support of the Fourier
transform of the considered functions is allowed to be supported in a (finite
number of) parallelepipeds. The estimates we obtain do not depend on the size
of the torus and the position of the parallelepipeds, but only on their size
and number, and the density and scale of the observability set. Our results are
on the one hand closely related to unique continuation for linear combinations
of eigenfunctions (aka spectral inequalities) which can be obtained by Carleman
estimates, on the other hand to observability estimates for the time-dependent
Schroedinger and for the heat equation, and finally to the Logvinenko & Sereda
theorem. In fact, they are based on the methods developed by Kovrijkine to
refine and generalize the results of Logvinenko & Sereda and Kacnel'son.
Furthermore, relying on completely different techniques associated with the
time-dependent Schroedinger equation, we prove a companion theorem where the
energy of the considered functions is allowed to be in a spectral subspace of a
Schroedinger operator.


title:
Efficient unitary designs with nearly time-independent Hamiltonian
  dynamics

abstract:
  We provide new constructions of unitary $t$-designs for general $t$ on one
qudit and $N$ qubits, and propose a design Hamiltonian, a random Hamiltonian of
which dynamics always forms a unitary design after a threshold time, as a basic
framework to investigate randomising time evolution in quantum many-body
systems. The new constructions are based on recently proposed schemes of
repeating random unitaires diagonal in mutually unbiased bases. We first show
that, if a pair of the bases satisfies a certain condition, the process on one
qudit approximately forms a unitary $t$-design after $O(t)$ repetitions. We
then construct quantum circuits on $N$ qubits that achieve unitary $t$-designs
for $t = o(N^{1/2})$ using $O(t N^2)$ gates, improving the previous result
using $O(t^{10}N^2)$ gates in terms of $t$. Based on these results, we present
a design Hamiltonian with periodically changing two-local spin-glass-type
interactions, leading to fast and relatively natural realisations of unitary
designs in complex many-body systems.


title:
Competing turbulent cascades and eddy-wave interactions in shallow water
  equilibria

abstract:
  In recent work, Renaud, Venaille, and Bouchet (RVB) revisit the equilibrium
statistical mechanics theory of the shallow water equations, within a
microcanonical approach, focusing on a more careful treatment of the energy
partition between inertial gravity wave and eddy motions in the equilibrium
state, and deriving joint probability distributions for the corresponding
dynamical degrees of freedom. The authors derive a Liouville theorem that
determines the underlying phase space statistical measure, but then, through
some physical arguments, actually compute the equilibrium statistics using a
measure that \emph{violates} this theorem. Here, using a more convenient, but
essentially equivalent, grand canonical approach, the full statistical theory
consistent with the Liouville theorem is derived. The results reveal several
significant differences from the previous results: (1) The microscale wave
motions lead to a strongly fluctuating thermodynamics, including long-ranged
correlations, in contrast to the mean-field-like behavior found by RVB. The
final effective model is equivalent to that of an elastic membrane with a
nonlinear wave-renormalized surface tension. (2) Even when a mean field
approximation is made, a rather more complex joint probability distribution is
revealed. Alternative physical arguments fully support the consistency of the
results. Of course, the true fluid final steady state relies on dissipative
processes not included in the shallow water equations, such as wave breaking
and viscous effects, but it is argued that the current theory provides a more
mathematically consistent starting point for future work aimed at assessing
their impacts.


title:
Strength and scales of itinerant spin fluctuations in 3d paramagnetic
  metals

abstract:
  The full spin density fluctuations (SDF) spectra in 3d paramagnetic metals
are analyzed from first principles using the linear response technique. Using
the calculated complete wavevector and energy dependence of the dynamic spin
susceptibility, we obtain the most important, but elusive, characteristic of
SDF in solids: on-site spin correlator (SC). We demonstrate that the SDF have a
mixed character consisting of interacting collective and single-particle
excitations of similar strength spreading continuously over the entire
Brillouin zone and a wide energy range up to femtosecond time scales. These
excitations cannot be adiabatically separated and their intrinsically
multiscale nature should be always taken into account for a proper description
of metallic systems. Overall, in all studied systems, despite the lack of local
moment, we found a very large SC resulting in an effective fluctuating moment
of the order of several Bohr magnetons.


title: Spin effects in the pion holographic light-front wavefunction

abstract:
  We account for dynamical spin effects in the holographic light-front
wavefunction of the pion in order to predict its mean charge radius, decay
constant, spacelike electromagnetic form factor, twist-2 Distribution Amplitude
and the photon-to-pion transition form factor. Using a universal fundamental
AdS/QCD scale of 523 MeV and a constituent quark mass of 330 MeV, we find a
remarkable improvement in describing all observables.


title:
Photothermal optomechanics in superfluid helium coupled to a fiber-based
  cavity

abstract:
  Presented in this paper are measurements of an optomechanical device in which
various acoustic modes of a sample of superfluid helium couple to a fiber-based
optical cavity. In contrast with recent work on the paraxial acoustic mode
confined by the cavity mirrors, we focus specifically on the acoustic modes
associated with the helium surrounding the cavity. This paper provides a
framework for understanding how the acoustic modes depend on device geometry.
The acoustic modes are observed using the technique of optomechanically induced
transparency/amplification. The optomechanical coupling to these modes is found
to be predominantly photothermal.