title: Bias-Reduction in Variational Regularization

abstract:
  The aim of this paper is to introduce and study a two-step debiasing method
for variational regularization. After solving the standard variational problem,
the key idea is to add a consecutive debiasing step minimizing the data
fidelity on an appropriate set, the so-called model manifold. The latter is
defined by Bregman distances or infimal convolutions thereof, using the
(uniquely defined) subgradient appearing in the optimality condition of the
variational method. For particular settings, such as anisotropic $\ell^1$ and
TV-type regularization, previously used debiasing techniques are shown to be
special cases. The proposed approach is however easily applicable to a wider
range of regularizations. The two-step debiasing is shown to be well-defined
and to optimally reduce bias in a certain setting.
  In addition to visual and PSNR-based evaluations, different notions of bias
and variance decompositions are investigated in numerical studies. The
improvements offered by the proposed scheme are demonstrated and its
performance is shown to be comparable to optimal results obtained with Bregman
iterations.


title:
Detached eddy simulation of shock unsteadiness in an over-expanded
  planar nozzle

abstract:
  This work investigates the self-excited shock wave oscillations in a
three-dimensional planar over-expanded nozzle turbulent flow by means of
Detached Eddy Simulations. Time resolved wall pressure measurements are used as
primary diagnostics. The statistical analysis reveals that the shock
unsteadiness has common features in terms of the root mean square of the
pressure fluctuations with other classical shock wave/boundary layer
interactions, like compression ramps and incident shocks on a flat plate. The
Fourier transform and the continuous wavelet transform are used to conduct the
spectral analysis. The results of the former indicate that the pressure in the
shock region is characterized by a broad low-frequency content, without any
resonant tone. The wavelet analysis, which is well suited to study non
stationary process, reveals that the pressure signal is characterized by an
amplitude and a frequency modulation in time.


title: Legendre-type relations for generalized complete elliptic integrals

abstract:
  Legendre's relation for the complete elliptic integrals of the first and
second kinds is generalized. The proof depends on an application of the
generalized trigonometric functions and is alternative to the proof for
Elliott's identity.


title:
Decoupling of the re-parametrization degree of freedom and a generalized
  probability in quantum cosmology

abstract:
  The high degree of symmetry renders the dynamics of cosmological as well as
some black hole spacetimes describable by a system of finite degrees of
freedom. These systems are generally known as minisuperspace models. One of
their important key features is the invariance of the corresponding reduced
actions under reparametrizations of the independent variable, a fact that can
be seen as the remnant of the general covariance of the full theory. In the
case of a system of $n$ degrees of freedom, described by a Lagrangian quadratic
in velocities, one can use the lapse by either gauge fixing it or letting it be
defined by the constraint and subsequently substitute into the rest of the
equations. In the first case, the system is solvable for $n$ accelerations and
the constraint becomes a restriction among constants. In the second case, the
system can only be solved for $n-1$ accelerations and the "gauge" freedom is
transferred to the choice of one of the scalar degrees of freedom. In this
paper, we take the second path and express all $n-1$ scalar degrees of freedom
in terms of the remaining one, say $q$. By considering these $n-1$ degrees of
freedom as arbitrary but given functions of $q$, we manage to extract a two
dimensional pure gauge system consisting of the lapse $N$ and the arbitrary
$q$: in a way, we decouple the reparametrization invariance from the rest of
the equations of motion. The solution of the corresponding quantum two
dimensional system is used for the definition of a generalized probability for
every configuration $f^i (q)$, be it classical or not. The main result is that,
interestingly enough, this probability attains its extrema on the classical
solution of the initial $n$-dimensional system.


title: Recycled Pulsars: Spins, Masses and Ages

abstract:
  Recycled pulsars are mainly characterized by their spin periods, B-fields and
masses. All these quantities are affected by previous interactions with a
companion star in a binary system. Therefore, we can use these quantities as
fossil records and learn about binary evolution. Here, I briefly review the
distribution of these observed quantities and summarize our current
understanding of the pulsar recycling process.


title:
Production of the $X_b$ in $\Upsilon(5S, 6S)\to \gamma X_b$ radiative
  decays

abstract:
  In this work, we investigate the production of $X_b$ in the process
$\Upsilon(5S,6S)\to \gamma X_b$, where $X_b$ is assumed to be the counterpart
of $X(3872)$ in the bottomonium sector as a $B {\bar B}^*$ molecular state. We
use the effective Lagrangian based on the heavy quark symmetry to explore the
rescattering mechanism and calculate their production ratios. Our results have
shown that the production ratios for the $\Upsilon(5S,6S) \to \gamma X_b$ are
orders of $10^{-5}$ with reasonable cutoff parameter range $\alpha \simeq 2\sim
3$. The sizeable production ratios may be accessible at the future experiments
like forthcoming BelleII, which will provide important clues to the inner
structures of the exotic state $X_b$.


title: Average Shortest Path Length of Graphs of Diameter 3

abstract:
  A network topology with low average shortest path length (ASPL) provides
efficient data transmission while the number of nodes and the number of links
incident to each node are often limited due to physical constraints. In this
paper, we consider the construction of low ASPL graphs under these constraints
by using stochastic local search (SLS) algorithms. Since the ASPL cannot be
calculated efficiently, the ASPL is not suitable for the evaluation function of
SLS algorithms. We first derive an equality and bounds for the ASPL of graphs
of diameter 3. Then, we propose use the simpliest upper bound represented by
the number of triangles and squares in the graph as an evaluation function for
graphs of diameter 3. We show that the proposed evaluation function can be
evaluated in O(1) time as the number of nodes and the maximum degree tend to
infinity by using some data tables. By using the simulated annealing with the
proposed evaluation function, we construct low ASPL regular graphs of diameter
3 with 10 000 nodes.


title:
Planck intermediate results. XLV. Radio spectra of northern
  extragalactic radio sources

abstract:
  Continuum spectra covering centimetre to submillimetre wavelengths are
presented for a northern sample of 104 extragalactic radio sources, mainly
active galactic nuclei, based on four-epoch Planck data. The nine Planck
frequencies, from 30 to 857 GHz, are complemented by a set of simultaneous
ground-based radio observations between 1.1 and 37 GHz. The single-survey
Planck data confirm that the flattest high-frequency radio spectral indices are
close to zero, indicating that the original accelerated electron energy
spectrum is much harder than commonly thought, with power-law index around 1.5
instead of the canonical 2.5. The radio spectra peak at high frequencies and
exhibit a variety of shapes. For a small set of low-z sources, we find a
spectral upturn at high frequencies, indicating the presence of intrinsic cold
dust. Variability can generally be approximated by achromatic variations, while
sources with clear signatures of evolving shocks appear to be limited to the
strongest outbursts.


title:
Large effects of subtle electronic correlations on the energetics of
  vacancies in alpha-Fe

abstract:
  We study the effect of electronic Coulomb correlations on the vacancy
formation energy in paramagnetic alpha-Fe within ab initio dynamical mean-field
theory. The calculated value for the formation energy is substantially lower
than in standard density-functional calculations and in excellent agreement
with experiment. The reduction is caused by an enhancement of electronic
correlations at the nearest neighbors of the vacancy. This effect is explained
by subtle changes in the corresponding spectral function of the d-electrons.
The local lattice relaxations around the vacancy are substantially increased by
many-body effects.


title: Toward a Boundary Regional Control Problem for Boolean Cellular Automata

abstract:
  An important question to be addressed regarding system control on a time
interval $[0, T]$ is whether some particular target state in the configuration
space is reachable from a given initial state. When the target of interest
refers only to a portion of the spatial domain, we speak about regional
analysis. Cellular Automata (CA) approach have been recently promoted for the
study of control problems on spatially extended systems for which the classical
approaches cannot be used. An interesting problem concerns the situation where
the subregion of interest is not interior to the domain but a portion of its
boundary. In this paper we address the problem of regional controllability of
cellular automata via boundary actions, i.e., we investigate the
characteristics of a cellular automaton so that it can be controlled inside a
given region only acting on the value of sites at its boundaries.


title:
Revisiting the Majority Problem: Average-Case Analysis with Arbitrarily
  Many Colours

abstract:
  The majority problem is a special case of the heavy hitters problem. Given a
collection of coloured balls, the task is to identify the majority colour or
state that no such colour exists. Whilst the special case of two-colours has
been well studied, the average-case performance for arbitrarily many colours
has not. In this paper, we present heuristic analysis of the average-case
performance of three deterministic algorithms that appear in the literature. We
empirically validate our analysis with large scale simulations.


title:
Robust Active Perception via Data-association aware Belief Space
  planning

abstract:
  We develop a belief space planning (BSP) approach that advances the state of
the art by incorporating reasoning about data association (DA) within planning,
while considering additional sources of uncertainty. Existing BSP approaches
typically assume data association is given and perfect, an assumption that can
be harder to justify while operating, in the presence of localization
uncertainty, in ambiguous and perceptually aliased environments. In contrast,
our data association aware belief space planning (DA-BSP) approach explicitly
reasons about DA within belief evolution, and as such can better accommodate
these challenging real world scenarios. In particular, we show that due to
perceptual aliasing, the posterior belief becomes a mixture of probability
distribution functions, and design cost functions that measure the expected
level of ambiguity and posterior uncertainty. Using these and standard costs
(e.g.~control penalty, distance to goal) within the objective function, yields
a general framework that reliably represents action impact, and in particular,
capable of active disambiguation. Our approach is thus applicable to robust
active perception and autonomous navigation in perceptually aliased
environments. We demonstrate key aspects in basic and realistic simulations.


title:
Ginzburg - Landau Expansion in BCS - BEC Crossover Region of Disordered
  Attractive Hubbard Model

abstract:
  We have studied disorder effects on the coefficients of Ginzburg - Landau
(GL) expansion for attractive Hubbard model within the generalized DMFT+Sigma
approximation for the wide region of the values of attractive potential U -
from the weak-coupling limit, where superconductivity is described by BCS
model, towards the strong coupling, where superconducting transition is related
to Bose - Einstein condensation (BEC) of compact Cooper pairs. For the case of
semi-elliptic initial density of states disorder influence on the coefficients
A and B before the square and the fourth power of the order parameter is
universal for at all values of electronic correlations and is related only to
the widening of the initial conduction band (density of states) by disorder.
Similar universal behavior is valid for superconducting critical temperature
T_c (the generalized Anderson theorem) and specific heat discontinuity at the
transition. This universality is absent for the coefficient C before the
gradient term, which in accordance with the standard theory of "dirty"
superconductors is strongly suppressed by disorder in the weak-coupling region,
but can slightly grow in BCS - BEC crossover region, becoming almost
independent of disorder in the strong coupling region. This leads to rather
weak disorder dependence of the penetration depth and coherence length, as well
as the slope of the upper critical magnetic field at T_c, in BCS - BEC
crossover and strong coupling regions.


title:
Exclusive diffractive production of $\pi^{+}\pi^{-}\pi^{+}\pi^{-}$ via
  the intermediate $\sigma\sigma$ and $\rho\rho$ states in proton-proton
  collisions within tensor pomeron approach

abstract:
  We present first predictions of the cross sections and differential
distributions for the central exclusive reaction $pp \to pp \pi^{+} \pi^{-}
\pi^{+} \pi^{-}$ being studied at RHIC and LHC. The amplitudes for the
processes are formulated in terms of the tensor pomeron and tensor $f_{2 R}$
reggeon exchanges with the vertices respecting the standard crossing and
charge-conjugation relations of Quantum Field Theory. The $\sigma \sigma$ and
$\rho \rho$ contributions to the $\pi^{+} \pi^{-} \pi^{+} \pi^{-}$ final state
are considered focussing on their specificities. The correct inclusion of the
pomeron spin structure seems crucial for the considered sequential mechanisms
in particular for the $\rho\rho$ contribution which is treated here for the
first time. The mechanism considered gives a significant contribution to the
$pp \to pp \pi^{+} \pi^{-} \pi^{+} \pi^{-}$ reaction. We adjust parameters of
our model to the CERN-ISR experimental data and present several predictions for
the STAR, ALICE, ATLAS and CMS experiments. A measurable cross section of order
of a few $\mu b$ is obtained including the experimental cuts relevant for the
LHC experiments. We show the influence of the experimental cuts on the
integrated cross section and on various differential distributions.


title:
On the Calculation of the Incomplete MGF with Applications to Wireless
  Communications

abstract:
  The incomplete moment generating function (IMGF) has paramount relevance in
communication theory, since it appears in a plethora of scenarios when
analyzing the performance of communication systems. We here present a general
method for calculating the IMGF of any arbitrary fading distribution. Then, we
provide exact closed-form expressions for the IMGF of the very general
{\kappa}-{\mu} shadowed fading model, which includes the popular
{\kappa}-{\mu}, {\eta}-{\mu}, Rician shadowed and other classical models as
particular cases. We illustrate the practical applicability of this result by
analyzing several scenarios of interest in wireless communications: (1)
Physical layer security in the presence of an eavesdropper, (2) Outage
probability analysis with interference and background noise, (3) Channel
capacity with side information at the transmitter and the receiver, and (4)
Average bit-error rate with adaptive modulation, when the fading on the desired
link can be modeled by any of the aforementioned distributions.


title: Quantum Wells in Photovoltaic Cells

abstract:
  The fundamental efficiency limit of a single bandgap solar cell is about 31%
at one sun with a bandgap of about Eg = 1.35 eV (1), determined by the
trade-off of maximising current with a smaller bandgap and voltage with a
larger bandgap. Multiple bandgaps can be introduced to absorb the broad solar
spectrum more efficiently. This can be realised in multi- junction cells, for
example, where two or more cells are stacked on top of each other either
mechanically or monolithically connected by a tunnel junction. An alternative
or complementary (see section 1.4) approach is the quantum well cell (QWC).


title:
Search for heavy long-lived charged $R$-hadrons with the ATLAS detector
  in 3.2 fb$^{-1}$ of proton--proton collision data at $\sqrt{s} = 13$ TeV

abstract:
  A search for heavy long-lived charged $R$-hadrons is reported using a data
sample corresponding to 3.2$^{-1}$ of proton--proton collisions at $\sqrt{s} =
13$ TeV collected by the ATLAS experiment at the Large Hadron Collider at CERN.
The search is based on observables related to large ionisation losses and slow
propagation velocities, which are signatures of heavy charged particles
travelling significantly slower than the speed of light. No significant
deviations from the expected background are observed. Upper limits at 95%
confidence level are provided on the production cross section of long-lived
$R$-hadrons in the mass range from 600 GeV to 2000 GeV and gluino, bottom and
top squark masses are excluded up to 1580 GeV, 805 GeV and 890 GeV,
respectively.


title: Tracing dark energy with quasars

abstract:
  The nature of dark energy, driving the accelerated expansion of the Universe,
is one of the most important issues in modern astrophysics. In order to
understand this phenomenon, we need precise astrophysical probes of the
universal expansion spanning wide redshift ranges. Quasars have recently
emerged as such a probe, thanks to their high intrinsic luminosities and, most
importantly, our ability to measure their luminosity distances independently of
redshifts. Here we report our ongoing work on observational reverberation
mapping using the time delay of the Mg II line, performed with the South
African Large Telescope (SALT).


title: Crofton Formulae for Tensor-Valued Curvature Measures

abstract:
  The tensorial curvature measures are tensor-valued generalizations of the
curvature measures of convex bodies. We prove a set of Crofton formulae for
such tensorial curvature measures. These formulae express the integral mean of
the tensorial curvature measures of the intersection of a given convex body
with a uniform affine $k$-flat in terms of linear combinations of tensorial
curvature measures of the given convex body. Here we first focus on the case
where the tensorial curvature measures of the intersection of the given body
with an affine flat is defined with respect to the affine flat as its ambient
space. From these formulae we then deduce some new and also recover known
special cases. In particular, we substantially simplify some of the constants
that were obained in previous work on Minkowski tensors. In a second step, we
explain how the results can be extended to the case where the tensorial
curvature measure of the intersection of the given body with an affine flat is
determined with respect to the ambient Euclidean space.


title:
Determining Curie temperature of (Ga,Mn)As samples based on electrical
  transport measurements: low Curie temperature case

abstract:
  In this paper we show that the widely accepted method of the determination of
Curie temperature (TC) in (Ga,Mn)As samples, based on the position of the peak
in the temperature derivative of the resistivity,completely fails in the case
of non-metallic and low-TC unannealed samples. In this case we propose an
alternative method, also based on electric transport measurements, which
exploits temperature dependence of the second derivative of the resistivity
upon magnetic field.


title:
Reduced fusion systems over $p$-groups with abelian subgroup of index
  $p$: II

abstract:
  Let $p$ be an odd prime, and let $S$ be a $p$-group with a unique elementary
abelian subgroup $A$ of index $p$. We classify the simple fusion systems over
all such groups $S$ in which $A$ is essential. The resulting list, which
depends on the classification of finite simple groups, includes a large variety
of new, exotic simple fusion systems.


title: Combinatorial Optimization of Work Distribution on Heterogeneous Systems

abstract:
  We describe an approach that uses combinatorial optimization and machine
learning to share the work between the host and device of heterogeneous
computing systems such that the overall application execution time is
minimized. We propose to use combinatorial optimization to search for the
optimal system configuration in the given parameter space (such as, the number
of threads, thread affinity, work distribution for the host and device). For
each system configuration that is suggested by combinatorial optimization, we
use machine learning for evaluation of the system performance. We evaluate our
approach experimentally using a heterogeneous platform that comprises two
12-core Intel Xeon E5 CPUs and an Intel Xeon Phi 7120P co-processor with 61
cores. Using our approach we are able to find a near-optimal system
configuration by performing only about 5% of all possible experiments.


title:
Distributed Beam Scheduling for Multi-RAT Coexistence in mm-Wave 5G
  Networks

abstract:
  Millimetre-wave communication (licensed or unlicensed) is envisaged to be an
important part of the fifth generation (5G) multi-RAT ecosystem. In this paper,
we consider the spectrum bands shared by 5G cellular base stations and some
existing networks, such as WiGig. Sharing the same band among such multiple
radio access technologies (RATs) is very challenging due to the lack of
centralized coordination and demands novel and efficient interference
mitigation and coexistence mechanisms to reduce the mutual interference. To
address this important challenge, we propose in this paper a novel multi-RAT
coexistence mechanism where neighbouring 5G and WiGig base stations, each
serving their own associated UEs, schedule their beam configurations in a
distributed manner such that their own utility function, e.g. spectral
efficiency, is maximized. We formulate the problem as a combinatorial
optimization problem and show via simulations that our proposed distributed
algorithms yield a comparable spectral efficiency for the entire networks as
that using an exhaustive search, which requires global coordination among
coexisting RATs and also has a much higher algorithmic complexity.


title:
Triangles as basis to detect communities: an application to Twitter's
  network

abstract:
  Nowadays, the interest given by the scientific community to the investigation
of the data generated by social networks is increasing as much as the
exponential increasing of social network data. The data structure complexity is
one among the snags, which slowdown their understanding. On the other hand,
community detection in social networks helps the analyzers to reveal the
structure and the underlying semantic within communities. In this paper we
propose an interactive visualization approach relying on our application
NLCOMS, which uses synchronous and related views for graph and community
visualization. Additionally, we present our algorithm for community detection
in networks. A computation study is conducted on instances generated with the
LFR [9]-[10] benchmark. Finally, in order to assess our approach on real-world
data, we consider the data of the ANR-Info-RSN project. The latter addresses
community detection in Twitter.


title: Fe doped Magnetic Nanodiamonds made by Ion Implantation

abstract:
  Here we present a simple physical method to produce magnetic nanodiamonds
(NDs) using high dose Fe ion-implantation. The Fe atoms are distributed inside
the NDs without affecting their crystal structure. So the NDs can be still
functionalized through surface modification for targeted chemotherapy and the
added magnetic property will make the NDs suitable for localized thermal
treatment for cancer cells without the toxicity from the Fe atoms being
directly in contact with the living tissue.


title: Method for Determining AGN Accretion Phase in Field Galaxies

abstract:
  Recent observations of AGN activity in massive galaxies (log Mstar / Msun >
10.4) show that: 1) at z < 1, AGN-hosting galaxies do not show enhanced merger
signatures compared to normal galaxies, 2) also at z < 1, most AGNs are hosted
by quiescent galaxies; and 3) at z > 1, percentage of AGNs in star forming
galaxies increases and becomes comparable to AGN percentage in quiescent
galaxies at z ~ 2. How can major mergers explain AGN activity in massive
quiescent galaxies which have no merger features and no star formation to
indicate recent galaxy merger? By matching merger events in a cosmological
N-body simulation to the observed AGN incidence probability in the COSMOS
survey, we show that major merger triggered AGN activity is consistent with the
observations. By distinguishing between "peak" AGNs (recently merger triggered
and hosted by star forming galaxies) and "faded" AGNs (merger triggered a long
time ago and now residing in quiescent galaxies), we show that the AGN
occupation fraction in star forming and quiescent galaxies simply follows the
evolution of the galaxy merger rate. Since the galaxy merger rate drops
dramatically at z < 1, the only AGNs left to be observed are the ones triggered
by old mergers and are now in the declining phase of their nuclear activity,
hosted by quiescent galaxies. As we go toward higher redshifts the galaxy
merger rate increases and the percentages of "peak" AGNs and "faded" AGNs
become comparable.


title:
The stochastic heat equation, 2D Toda equations and dynamics for the
  multilayer process

abstract:
  We show that solutions of the stochastic heat equation driven by space-time
white noise, although not smooth, meaningfully solve the two-dimensional Toda
equations. Then by extending our arguments we show the time evolution of the
multilayer process introduced by O'Connell and Warren is conjugate to a flow
induced by the stochastic heat equation. In particular this establishes a
Markov property conjectured by O'Connell and Warren. It also defines, for the
first time, the multilayer process started from a general initial condition.


title:
Characterizing Relative Frame Definability in Team Semantics via the
  Universal Modality

abstract:
  Let ML(U^+) denote the fragment of modal logic extended with the universal
modality in which the universal modality occurs only positively. We
characterize the relative definability of ML(U^+) relative to finite transitive
frames in the spirit of the well-known Goldblatt-Thomason theorem. We show that
a class F of Kripke frames is definable in ML(U^+) relative to finite
transitive frames if and only if F is closed under taking generated subframes
and bounded morphic images. In addition, we study modal definability in
team-based logics. We study (extended) modal dependence logic, (extended) modal
inclusion logic, and modal team logic. With respect to global model
definability we obtain a trichotomy and with respect to frame definability a
dichotomy. As a corollary we obtain relative Goldblatt--Thomason -style
theorems for each of the logics listed above.


title: Comments on the slope function

abstract:
  The exact slope function was first proposed in $SL(2)$ sector and generalized
to $SU(2)$ sector later. In this note, we consider the slope function in
$SU(1|1)$ sector of ${\cal N}=4$ SYM. We derive the quantity through the method
invented by N. Gromov and discuss about its validity. Further, we give comments
on the slope function in deformed SYM.


title: Sources of The Slow Solar wind During the Solar Cycle 23/24 Minimum

abstract:
  We investigate the characteristics and the sources of the slow (< 450 km/s)
solar wind during the four years (2006-2009) of low solar activity between
Solar Cycles 23 and 24. We use a comprehensive set of in-situ observations in
the near-Earth solar wind (Wind and ACE) and remove the periods when
large-scale interplanetary coronal mass ejections were present. The
investigated period features significant variations in the global coronal
structure, including the frequent presence of low-latitude active regions in
2006-2007, long-lived low- and mid-latitude coronal holes in 2006 - mid-2008
and mostly the quiet Sun in 2009. We examine both Carrington Rotation averages
of selected solar plasma, charge state and compositional parameters and
distributions of these parameters related to Quiet Sun, Active Region Sun and
the Coronal Hole Sun. While some of the investigated parameters (e.g., speed,
the C^{+6}/C^{+4} and He/H ratio) show clear variations over our study period
and with solar wind source type, some (Fe/O) exhibit very little changes. Our
results highlight the difficulty in distinguishing between the slow solar wind
sources based on the inspection of the solar wind conditions.


title: Advanced-Retarded Differential Equations in Quantum Photonic Systems

abstract:
  We propose the realization of photonic circuits whose dynamics is governed by
advanced-retarded differential equations. Beyond their mathematical interest,
these photonic configurations enable the implementation of quantum feedback and
feedforward without requiring any intermediate measurement. We show how this
protocol can be applied to implement interesting delay effects in the quantum
regime, as well as in the classical limit. Our results elucidate the potential
of the protocol as a promising route towards integrated quantum control systems
on a chip.


title: New nonbinary code bounds based on divisibility arguments

abstract:
  For $q,n,d \in \mathbb{N}$, let $A_q(n,d)$ be the maximum size of a code $C
\subseteq [q]^n$ with minimum distance at least $d$. We give a divisibility
argument resulting in the new upper bounds $A_5(8,6) \leq 65$, $A_4(11,8)\leq
60$ and $A_3(16,11) \leq 29$. These in turn imply the new upper bounds
$A_5(9,6) \leq 325$, $A_5(10,6) \leq 1625$, $A_5(11,6) \leq 8125$ and
$A_4(12,8) \leq 240$. Furthermore, we prove that for $\mu,q \in \mathbb{N}$,
there is a 1-1-correspondence between symmetric $(\mu,q)$-nets (which are
certain designs) and codes $C \subseteq [q]^{\mu q}$ of size $\mu q^2$ with
minimum distance at least $\mu q - \mu$. We derive the new upper bounds
$A_4(9,6) \leq 120$ and $A_4(10,6) \leq 480$ from these `symmetric net' codes.


title:
Label-Free Nanoscopy with Contact Microlenses: Super-Resolution
  Mechanisms and Limitations

abstract:
  Despite all the success with developing super-resolution imaging techniques,
the Abbe limit poses a severe fundamental restriction on the resolution of
far-field imaging systems based on diffraction of light. Imaging with contact
microlenses, such as microspheres or microfibers, can increase the resolution
by a factor of two beyond the Abbe limit. The theoretical mechanisms of these
methods are debated in the literature. In this work, we focus on the recently
expressed idea that optical coupling between closely spaced nanoscale objects
can lead to the formation of the modes that drastically impact the imaging
properties. These coupling effects emerge in nanoplasmonic or nanocavity
clusters, photonic molecules, or various arrays under resonant excitation
conditions. The coherent nature of imaging processes is key to understanding
their physical mechanisms. We used a cluster of point dipoles, as a simple
model system, to study and compare the consequences of coherent and incoherent
imaging. Using finite difference time domain modeling, we show that the
coherent images are full of artefacts. The out-of-phase oscillations produce
zero-intensity points that can be observed with practically unlimited
resolution (determined by the noise). We showed that depending on the phase
distribution, the nanoplasmonic cluster can appear with the arbitrary shape,
and such images were obtained experimentally.


title: Quasistationary solutions of scalar fields around accreting black holes

abstract:
  Massive scalar fields can form long-lived configurations around black holes.
These configurations, dubbed quasi-bound states, have been studied both in the
linear and nonlinear regimes. In this paper we show that quasi-bound states can
form in a dynamical scenario in which the mass of the black hole grows
significantly due to the capture of infalling matter. We solve the Klein-Gordon
equation numerically in spherical symmetry, mimicking the evolution of the
spacetime through a sequence of analytic Schwarzschild black hole solutions of
increasing mass. It is found that the frequency of oscillation of the
quasi-bound states decreases as the mass of the black hole increases. In
addition, accretion leads to a significative increase of the exponential decay
of the scalar field energy due to the presence of terms of order higher than
linear in the exponent. We compare the black hole mass growth rates used in our
study with estimates from observational surveys and extrapolate our results to
values of the scalar field masses consistent with models that propose scalar
fields as dark matter in the universe. We show that even for unrealistically
large mass accretion rates, quasi-bound states around accreting black holes can
survive for cosmological timescales. Our results provide further support to the
intriguing possibility of the existence of dark matter halos based on
(ultra-light) scalar fields surrounding supermassive black holes in galactic
centers.


title:
Magnetostructural coupling, magnetic ordering and cobalt spin
  reorientation in metallic Pr0.50Sr0.50CoO3 cobaltite

abstract:
  In half-doped Pr0.50A0.50CoO3 metallic perovskites, the spin-lattice coupling
brings about distinct magnetostructural transitions for A=Ca and A=Sr at
temperatures close to 100 K. However, the ground magnetic properties of
Pr0.50Sr0.50CoO3 (PSCO) strongly differ from Pr0.50Ca0.50CoO3 ones, where a
partial Pr3+ to Pr4+ valence shift and Co spin transition makes the system
insulating below the transition. This work investigates and describes the
relationship between the Imma-to-I4/mcm symmetry change [Padilla-Pantoja et al,
Inorg. Chem. 53, 12297 (2014)] and the original magnetic behavior of PSCO
versus temperature and external magnetic fields. The FM1 and FM2 ferromagnetic
phases, above and below the magnetostructural transition (TS1=120 K) have been
investigated. The FM2 phase of PSCO is composed of [100] FM domains, with
magnetic symmetry Im'm'a (mz=0). The magnetic space group of the FM1 phase is
Fm'm'm (with mx=my). Neutron data analyses in combination with magnetometry and
earlier reports results agrees with a reorientation of the magnetization axis
by 45 deg within the a-b plane across the transition, in which the system
retains its metallic character. The presence below TS1 of conjugated magnetic
domains, both of Fm'm'm symmetry but having perpendicular spin orientations
along the diagonals in the xy-plane of the tetragonal unit cell, is at the
origin of the anomalies observed in the macroscopic magnetization. A relatively
small field m0H > 30 mT is able to reorient the magnetization within the a-b
plane, whereas a higher field (m0H,[H//z] >1.2 T at 2K) is necessary to align
the Co moments perpendicular to a-b plane. Such a spin reorientation, in which
the orbital and spin components of the Co moment rotate joined by 45deg, was
not observed with other lanthanides different to praseodymium.


title:
For Noble Gases, Energy is Positive for the Gas Phase, Negative for the
  Liquid Phase

abstract:
  We found from experimental data that for noble gases and H$_2$, the energy is
positive for the gas phase, and negative for the liquid, possibly except the
small vicinity of the critical point, about $(1- T/T_c) \le 0.005$. The line
$E=E_c$, in the supercritical region is found to lie close to the Widom line,
where $E_c$ is the critical energy.


title: Resonance interaction of two dipoles in optically active surroundings

abstract:
  We study the resonance interaction between two quantum electric dipoles
immersed in optically active surroundings. Quantum electrodynamics is employed
to deal with dipole-vacuum interaction. Our results show that the optical
activity of surroundings will not change the single atom behaviors while it can
change the collective behaviors of the two dipoles, as well as greatly affect
the dipole-dipole resonance interaction. Especially, if the orientations of two
dipoles are orthogonal and respectively perpendicular to the interdipole axis,
the interdipole resonance interaction can be established with the help of
optically active surroundings while there is no resonance interaction in
vacuum.


title:
Envelope Words and Return Words Sequences in the Period-doubling
  Sequence

abstract:
  We consider the infinite one-sided sequence generated by the period-doubling
substitution $\sigma(a,b)=(ab,aa)$, denoted by $\mathbb{D}$. Since $\mathbb{D}$
is uniformly recurrent, each factor $\omega$ appears infinite many times in the
sequence, which is arranged as $\omega_p$ $(p\ge 1)$. Let $r_p(\omega)$ be the
$p$-th return word over $\omega$. The main result is: for each factor $\omega$,
the sequence $\{r_p(\omega)\}_{p\geq1}$ is $\Theta_1$ or $\Theta_2$, which are
substitutive sequences and determined completely in this paper.


title:
Simulations of solitonic core mergers in ultra-light axion dark matter
  cosmologies

abstract:
  Using three-dimensional simulations, we study the dynamics and final
structure of merging solitonic cores predicted to form in ultra-light axion
dark matter halos. The classical, Newtonian equations of motion of a
self-gravitating scalar field are described by the Schr\"odinger-Poisson
equations. We investigate mergers of ground state (boson star) configurations
with varying mass ratios, relative phases, orbital angular momenta and initial
separation with the primary goal to understand the mass loss of the emerging
core by gravitational cooling. Previous results showing that the final density
profiles have solitonic cores and NFW-like tails are confirmed. In binary
mergers, the final core mass does not depend on initial phase difference or
angular momentum and only depends on mass ratio, total initial mass, and total
energy of the system. For non-zero angular momenta, the otherwise spherical
cores become rotating ellipsoids. The results for mergers of multiple cores are
qualitatively identical.


title: Edge-fault-tolerant edge-bipancyclicity of balanced hypercubes

abstract:
  The balanced hypercube, $BH_n$, is a variant of hypercube $Q_n$. R.X. Hao et
al. $(2014)$ \cite{R.X.Hao} showed that there exists a fault-free Hamiltonian
path between any two adjacent vertices in $BH_n$ with $(2n-2)$ faulty edges.
D.Q. Cheng et al. $(2015)$ \cite{Dongqincheng2} proved that $BH_n$ is
$6$-edge-bipancyclic after $(2n-3)$ faulty edges occur for all $n\ge2$. In this
paper, we improve these two results by demonstrating that $BH_n$ is
$6$-edge-bipancyclic even when there exist $(2n-2)$ faulty edges for all
$n\ge2$. Our result is optimal with respect to the maximum number of tolerated
edge faults.


title:
Comparing Single Molecule Tracking and correlative approaches: an
  application to the datasets recently presented in Nature Methods by Chenuard
  et al

abstract:
  Recent efforts to survey the numerous softwares available to perform single
molecule tracking (SMT) highlighted a significant dependence of the outcomes on
the specific method used, and the limitation encountered by most techniques to
capture fast movements in a crowded environment. Other approaches to identify
the mode and rapidity of motion of fluorescently labeled biomolecules, that do
not relay on the localization and linking of the images of isolated single
molecules are, however, available.This direct comparison shows that correlative
imaging analysis approaches complement effectively current SMT methods in
circumstances when, due to either the density of the sample, the low signal to
noise ratio or molecular blinking, trajectory linking does not allow to capture
long-range or fast motion.


title:
On a neutral particle with a magnetic quadrupole moment in a uniform
  effective magnetic field

abstract:
  Quantum effects on a Landau-type system associated with a moving atom with a
magnetic quadrupole moment subject to confining potentials are analysed. It is
shown that the spectrum of energy of the Landau-type system can be modified,
where the degeneracy of the energy levels can be broken. In three particular
cases, it is shown that the analogue of the cyclotron frequency is modified,
and the possible values of this angular frequency of the system are determined
by the quantum numbers associated with the radial modes and the angular
momentum and by the parameters associated with confining potentials in order
that bound states solutions can be achieved.


title:
Evaluation of the Convolution Sums $\underset{\substack{
  {(l,m)\in\mathbb{N}_{0}^{2}} {\alpha\,l+\beta\,m=n} }
  }{\sum}\sigma(l)\sigma(m)$, where $\alpha\beta=44,52$

abstract:
  The convolution sum, $\underset{\substack{ {(l,m)\in\mathbb{N}_{0}^{2}}
{\alpha\,l+\beta\,m=n} } }{\sum}\sigma(l)\sigma(m)$, where $\alpha\beta=44,52$,
is evaluated for all natural numbers $n$. We then use these convolution sums to
determine formulae for the number of representations of a natural number by the
octonary quadratic forms $a\,(x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2})+
b\,(x_{5}^{2} + x_{6}^{2} + x_{7}^{2} + x_{8}^{2})$, where $(a,b)=
(1,11),(1,13)$.


title:
Reciprocity Calibration for Massive MIMO: Proposal, Modeling and
  Validation

abstract:
  This paper presents a mutual coupling based calibration method for
time-division-duplex massive MIMO systems, which enables downlink precoding
based on uplink channel estimates. The entire calibration procedure is carried
out solely at the base station (BS) side by sounding all BS antenna pairs. An
Expectation-Maximization (EM) algorithm is derived, which processes the
measured channels in order to estimate calibration coefficients. The EM
algorithm outperforms current state-of-the-art narrow-band calibration schemes
in a mean squared error (MSE) and sum-rate capacity sense. Like its
predecessors, the EM algorithm is general in the sense that it is not only
suitable to calibrate a co-located massive MIMO BS, but also very suitable for
calibrating multiple BSs in distributed MIMO systems.
  The proposed method is validated with experimental evidence obtained from a
massive MIMO testbed. In addition, we address the estimated narrow-band
calibration coefficients as a stochastic process across frequency, and study
the subspace of this process based on measurement data. With the insights of
this study, we propose an estimator which exploits the structure of the process
in order to reduce the calibration error across frequency. A model for the
calibration error is also proposed based on the asymptotic properties of the
estimator, and is validated with measurement results.


title:
Automatic quality evaluation and (semi-) automatic improvement of OCR
  models for historical printings

abstract:
  Good OCR results for historical printings rely on the availability of
recognition models trained on diplomatic transcriptions as ground truth, which
is both a scarce resource and time-consuming to generate. Instead of having to
train a separate model for each historical typeface, we propose a strategy to
start from models trained on a combined set of available transcriptions in a
variety of fonts. These \emph{mixed models} result in character accuracy rates
over 90\% on a test set of printings from the same period of time, but without
any representation in the training data, demonstrating the possibility to
overcome the typography barrier by generalizing from a few typefaces to a
larger set of (similar) fonts in use over a period of time. The output of these
mixed models is then used as a baseline to be further improved by both fully
automatic methods and semi-automatic methods involving a minimal amount of
manual transcriptions. In order to evaluate the recognition quality of each
model in a series of models generated during the training process in the
absence of any ground truth, we introduce two readily observable quantities
that correlate well with true accuracy. These quantities are \emph{mean
character confidence C} (as given by the OCR engine OCRopus) and \emph{mean
token lexicality L} (a distance measure of OCR tokens from modern wordforms
taking historical spelling patterns into account, which can be calculated for
any OCR engine). Whereas the fully automatic method is able to improve upon the
result of a mixed model by only 1-2 percentage points, already 100-200
hand-corrected lines lead to much better OCR results with character error rates
of only a few percent. This procedure minimizes the amount of ground truth
production and does not depend on the previous construction of a specific
typographic model.


title:
CLEAR: Covariant LEAst-square Re-fitting with applications to image
  restoration

abstract:
  In this paper, we propose a new framework to remove parts of the systematic
errors affecting popular restoration algorithms, with a special focus for image
processing tasks. Generalizing ideas that emerged for $\ell_1$ regularization,
we develop an approach re-fitting the results of standard methods towards the
input data. Total variation regularizations and non-local means are special
cases of interest. We identify important covariant information that should be
preserved by the re-fitting method, and emphasize the importance of preserving
the Jacobian (w.r.t. the observed signal) of the original estimator. Then, we
provide an approach that has a "twicing" flavor and allows re-fitting the
restored signal by adding back a local affine transformation of the residual
term. We illustrate the benefits of our method on numerical simulations for
image restoration tasks.


title:
Admissible Banach function spaces for linear dynamics with nonuniform
  behavior on the half-line

abstract:
  For nonuniform exponentially bounded evolution families on the half-line we
introduce a class of Banach function spaces on which we define nonuniform
evolution semigroups. We completely characterize nonuniform exponential
stability in terms of invertibility of the corresponding generators. We
emphasize that in particular our results apply to all linear differential
equations with bounded operator and finite Lyapunov exponent.


title: Duality invariance in Fayet-Iliopoulos gauged supergravity

abstract:
  We propose a geometric method to study the residual symmetries in $N=2$,
$d=4$ $\text{U}(1)$ Fayet-Iliopoulos (FI) gauged supergravity. It essentially
involves the stabilization of the symplectic vector of gauge couplings (FI
parameters) under the action of the U-duality symmetry of the ungauged theory.
In particular we are interested in those transformations that act non-trivially
on the solutions and produce scalar hair and dyonic black holes from a given
seed. We illustrate the procedure for finding this group in general and then
show how it works in some specific models. For the prepotential $F=-iX^0X^1$,
we use our method to add one more parameter to the rotating Chow-Comp\`ere
solution, representing scalar hair.


title: Modules over cluster-tilted algebras that do not lie on local slices

abstract:
  We characterize the indecomposable transjective modules over an arbitrary
cluster-tilted algebra that do not lie on a local slice, and we provide a sharp
upper bound for the number of (isoclasses of) these modules.


title: On logarithmic coefficients of some close-to-convex functions

abstract:
  The logarithmic coefficients $\gamma_n$ of an analytic and univalent function
$f$ in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$ with the
normalization $f(0)=0=f'(0)-1$ is defined by $\log \frac{f(z)}{z}=
2\sum_{n=1}^{\infty} \gamma_n z^n$. Recently, D.K. Thomas [On the logarithmic
coefficients of close to convex functions, {\it Proc. Amer. Math. Soc.} {\bf
144} (2016), 1681--1687] proved that $|\gamma_3|\le \frac{7}{12}$ for functions
in a subclass of close-to-convex functions (with argument $0$) and claimed that
the estimate is sharp by providing a form of a extremal function. In the
present paper, we pointed out that such extremal functions do not exist and the
estimate is not sharp by providing a much more improved bound for the whole
class of close-to-convex functions (with argument $0$). We also determine a
sharp upper bound of $|\gamma_3|$ for close-to-convex functions (with argument
$0$) with respect to the Koebe function.


title: Radiative neutrino models in light of diphoton signals

abstract:
  Viable explanations of a hinted 750 GeV scalar resonance may be sought within
the extensions of the SM Higgs sector aimed at generating neutrino masses at
the loop level. We confront a compatibility with the 750 GeV diphoton excess
for two recent models which do not need to impose ad hoc symmetry to forbid the
tree-level masses: a one-loop mass model providing the H(750) candidate within
its real triplet scalar representation and a three-loop mass model providing it
within its two Higgs doublets. Besides accounting for the 750 GeV resonance, we
demonstrate that these complementary neutrino-mass scenarios have different
testable predictions for the LHC which should show up soon as more data is
accumulated during the ongoing 13 TeV run.


title: Network Valuation in Financial Systems

abstract:
  We introduce a general model for the balance-sheet consistent valuation of
interbank claims within an interconnected financial system. Our model
represents an extension of clearing models of interdependent liabilities to
account for the presence of uncertainty on banks' external assets. At the same
time, it also provides a natural extension of classic structural credit risk
models to the case of an interconnected system. We characterize the existence
and uniqueness of a valuation that maximises individual and total equity values
for all banks. We apply our model to the assessment of systemic risk, and in
particular for the case of stress-testing. Further, we provide a fixed-point
algorithm to carry out the network valuation and the conditions for its
convergence.


title:
Coupling and competition between ferroelectricity, magnetism, strain and
  oxygen vacancies in AMnO3 perovskites

abstract:
  We use first-principles calculations based on density functional theory to
investigate the interplay between oxygen vacancies, A-site cation size /
tolerance factor, epitaxial strain, ferroelectricity and magnetism in the
perovskite manganite series, AMnO3 (A=Ca2+, Sr2+, Ba2+). We find that, as
expected, increasing the volume through either chemical pressure or tensile
strain generally lowers the formation energy of neutral oxygen vacancies
consistent with their established tendency to expand the lattice. Increased
volume also favors polar distortions, both because competing rotations of the
oxygen octahedra are suppressed and because coulomb repulsion associated with
cation off-centering is reduced. Interestingly, the presence of ferroelectric
polarization favors ferromagnetic over antiferromagnetic ordering due to
suppressed antiferromagnetic superexchange as the polar distortion bends the
Mn-O-Mn bond angles away from the optimal 180deg. Intriguingly, we find that
polar distortions compete with the formation of oxygen vacancies, which have a
higher formation energy in the polar phases; conversely the presence of oxygen
vacancies suppresses the onset of polarization. In contrast, oxygen vacancy
formation energies are lower for ferromagnetic than antiferromagnetic orderings
of the same structure type. Our findings suggest a rich and complex phase
diagram, in which defect chemistry, polarization, structure and magnetism can
be modified using chemical potential, strain, and electric or magnetic fields.


title: A Burau-Alexander 2-functor on tangles

abstract:
  We construct a weak 2-functor from the bicategory of oriented tangles to a
bicategory of Lagrangian cospans. This functor simultaneously extends the Burau
representation of the braid groups, its generalization to tangles due to Turaev
and the first-named author, and the Alexander module of 1 and 2-dimensional
links.


title:
On goodness-of-fit tests for parametric hypotheses in perturbed
  dynamical systems using a minimum distance estimator

abstract:
  We consider the problem of the construction of the Goodness-of-Fit test in
the case of continuous time observations of a diffusion process with small
noise. The null hypothesis is parametric and we use a minimum distance
estimator of the unknown parameter. We propose an asymptotically distribution
free test for this model.


title:
Energy Conservation and Coupling Error Reduction in Non-Iterative
  Co-Simulations

abstract:
  When simulators are energetically coupled in a co-simulation, residual
energies alter the total energy of the full coupled system. This distorts the
system dynamics, lowers the quality of the results, and can lead to
instability. By using power bonds to realize simulator coupling, the
Energy-Conservation-based Co-Simulation method (ECCO) [Sadjina et al. 2016]
exploits these concepts to define non-iterative global error estimation and
adaptive step size control relying on coupling variable data alone. Following
similar argumentation, the Nearly Energy Preserving Coupling Element (NEPCE)
[Benedikt et al. 2013] uses corrections to the simulator inputs to
approximately ensure energy conservation. Here, we discuss a modification to
NEPCE for when direct feed-through is present in one of the coupled simulators.
We further demonstrate how accuracy and efficiency in non-iterative
co-simulations are substantially enhanced when combining NEPCE with ECCO's
adaptive step size controller. A quarter car model with linear and nonlinear
damping characteristics serves as a co-simulation benchmark, and we observe
reductions of the coupling errors of up to 98% utilizing the concepts discussed
here.


title:
Learning from Non-Stationary Stream Data in Multiobjective Evolutionary
  Algorithm

abstract:
  Evolutionary algorithms (EAs) have been well acknowledged as a promising
paradigm for solving optimisation problems with multiple conflicting objectives
in the sense that they are able to locate a set of diverse approximations of
Pareto optimal solutions in a single run. EAs drive the search for approximated
solutions through maintaining a diverse population of solutions and by
recombining promising solutions selected from the population. Combining machine
learning techniques has shown great potentials since the intrinsic structure of
the Pareto optimal solutions of an multiobjective optimisation problem can be
learned and used to guide for effective recombination. However, existing
multiobjective EAs (MOEAs) based on structure learning spend too much
computational resources on learning. To address this problem, we propose to use
an online learning scheme. Based on the fact that offsprings along evolution
are streamy, dependent and non-stationary (which implies that the intrinsic
structure, if any, is temporal and scale-variant), an online agglomerative
clustering algorithm is applied to adaptively discover the intrinsic structure
of the Pareto optimal solution set; and to guide effective offspring
recombination. Experimental results have shown significant improvement over
five state-of-the-art MOEAs on a set of well-known benchmark problems with
complicated Pareto sets and complex Pareto fronts.


title: Non-convex balls in the Teichm\"uller metric

abstract:
  We prove that the Teichm\"uller space of surfaces of genus $\mathbf{g}$ with
$\mathbf{p}$ punctures contains balls which are not convex in the Teichm\"uller
metric whenever $3\mathbf{g}-3+\mathbf{p} > 1$.


title:
Realistic model for a fifth force explaining anomaly in ${^8Be^*} \to
  {^8Be} \;{e^+e^-}$ Decay

abstract:
  A $6.8\,\sigma$ anomaly has been reported in the opening angle and invariant
mass distributions of $e^+e^-$ pairs produced in ${^8Be}$ nuclear transitions.
It has been shown that a protophobic fifth force mediated by a
$17\,\textrm{MeV}$ gauge boson $X$ with pure vector current interactions can
explain the data through the decay of an excited state to the ground state,
${^8Be^*} \to {^8Be}\, X$, and then the followed saturating decay $X \to
e^+e^-$. In this work we propose a renormalizable model to realize this fifth
force. Although axial-vector current interactions also exist in our model,
their contributions cancel out in the iso-scalar interaction for ${^8Be^*} \to
{^8Be} \,X$. Within the allowed parameter space, this model can alleviate the
$(g-2)_\mu$ anomaly problem and can be probed by the LHCb experiment. Several
other implications are discussed.


title: Asynchronous simulation of Boolean networks by monotone Boolean networks

abstract:
  We prove that the fully asynchronous dynamics of a Boolean network
$f:\{0,1\}^n\to\{0,1\}^n$ without negative loop can be simulated, in a very
specific way, by a monotone Boolean network with $2n$ components. We then use
this result to prove that, for every even $n$, there exists a monotone Boolean
network $f:\{0,1\}^n\to\{0,1\}^n$, an initial configuration $x$ and a fixed
point $y$ of $f$ such that: (i) $y$ can be reached from $x$ with a fully
asynchronous updating strategy, and (ii) all such strategies contains at least
$2^{\frac{n}{2}}$ updates. This contrasts with the following known property: if
$f:\{0,1\}^n\to\{0,1\}^n$ is monotone, then, for every initial configuration
$x$, there exists a fixed point $y$ such that $y$ can be reached from $x$ with
a fully asynchronous strategy that contains at most $n$ updates.


title: Partial $W^{2,p}$ regularity for optimal transport maps

abstract:
  We prove that, in the optimal transportation problem with general costs and
positive continuous densities, the potential function is always of class
$W^{2,p}_{loc}$ for any $p \geq 1$ outside of a closed singular set of measure
zero. We also establish global $W^{2,p}$ estimates when the cost is a small
perturbation of the quadratic cost. The latter result is new even when the cost
is exactly the quadratic cost.


title: Deep Reinforcement Learning Discovers Internal Models

abstract:
  Deep Reinforcement Learning (DRL) is a trending field of research, showing
great promise in challenging problems such as playing Atari, solving Go and
controlling robots. While DRL agents perform well in practice we are still
lacking the tools to analayze their performance. In this work we present the
Semi-Aggregated MDP (SAMDP) model. A model best suited to describe policies
exhibiting both spatial and temporal hierarchies. We describe its advantages
for analyzing trained policies over other modeling approaches, and show that
under the right state representation, like that of DQN agents, SAMDP can help
to identify skills. We detail the automatic process of creating it from
recorded trajectories, up to presenting it on t-SNE maps. We explain how to
evaluate its fitness and show surprising results indicating high compatibility
with the policy at hand. We conclude by showing how using the SAMDP model, an
extra performance gain can be squeezed from the agent.


title:
Haldane linearisation done right: Solving the nonlinear recombination
  equation the easy way

abstract:
  The nonlinear recombination equation from population genetics has a long
history and is notoriously difficult to solve, both in continuous and in
discrete time. This is particularly so if one aims at full generality, thus
also including degenerate parameter cases. Due to recent progress for the
continuous time case via the identification of an underlying stochastic
fragmentation process, it became clear that a direct general solution at the
level of the corresponding ODE itself should also be possible. This paper shows
how to do it, and how to extend the approach to the discrete-time case as well.


title: Contact matrix in dilute quantum systems

abstract:
  Contact has been well established as an important quantity to govern dilute
quantum systems, in which the pairwise correlation at short distance traces a
broad range of thermodynamic properties. So far, studies have been focusing on
contact in individual angular momentum channels. Here, we point out that, to
have a complete description of the pairwise correlation in a general dilute
quantum systems, contact should be defined as a matrix. Whereas the diagonal
terms of such matrix include contact of all partial wave scatterings, the
off-diagonal terms, which elude previous studies in the literature,
characterise the coherence of the asymptotic pairwise wavefunction in the
angular momentum space and determine important thermodynamic quantities
including the momentum distribution. Contact matrix allows physicists to access
unexplored connections between short-range correlations and macroscopic quantum
phenomena. As an example, we show the direct connection between contact matrix
and order parameters of a superfluid with mixed partial waves.


title: HARQ and AMC: Friends or Foes?

abstract:
  To ensure reliable communication in randomly varying and error-prone
channels, wireless systems use adaptive modulation and coding (AMC) as well as
hybrid ARQ (HARQ). In order to elucidate their compatibility and interaction,
we compare the throughput provided by AMC, HARQ, and their combination
(AMC-HARQ) under two operational conditions: in slow- and fast block-fading
channels. Considering both, incremental redundancy HARQ (HARQ-IR) and
repetition redundancy HARQ (HARQ-RR) we optimize the rate-decision regions for
AMC/HARQ and compare them in terms of attainable throughput. Under a fairly
general model of the channel variation and the decoding functions, we conclude
that i) adding HARQ on top of AMC may be counterproductive in the high average
signal- to-noise ratio regime for fast fading channels, and ii) HARQ is useful
for slow fading channels, but it provides moderate throughput gains. We provide
explanations for these results which allow us to propose paths to improve
AMC-HARQ systems.


title:
Coexistence of Weyl Physics and Planar Defects in Semimetals TaP and
  TaAs

abstract:
  We report a structural study of the Weyl semimetals TaAs and TaP, utilizing
diffraction and imaging techniques, where we show that they contain a high
density of defects, leading to non-stoichiometric single crystals of both
semimetals. Despite the observed defects and non-stoichiometry on samples grown
using techniques already reported in the literature, de Haas-van Alphen
measurements on TaP reveal quantum oscillations and a high carrier mobility, an
indication that the crystals are of quality comparable to those reported
elsewhere. Electronic structure calculations on TaAs reveal that the position
of the Weyl points relative to the Fermi level shift with the introduction of
vacancies and stacking faults. In the case of vacancies the Fermi surface
becomes considerably altered, while the effect of stacking faults on the
electronic structure is to allow the Weyl pockets to remain close to the Fermi
surface. The observation of quantum oscillations in a non-stoichiometric
crystal and the persistence of Weyl fermion pockets near the Fermi surface in a
crystal with stacking faults point to the robustness of these quantum phenomena
in these materials.


title: Incentivized Campaigning in Social Networks

abstract:
  Campaigners, advertisers and activists are increasingly turning to social
recommendation mechanisms, provided by social media, for promoting their
products, services, brands and even ideas. However, many times, such social
network based campaigns perform poorly in practice because the intensity of the
recommendations drastically reduces beyond a few hops from the source. A
natural strategy for maintaining the intensity is to provide incentives. In
this paper, we address the problem of minimizing the cost incurred by the
campaigner for incentivizing a fraction of individuals in the social network,
while ensuring that the campaign message reaches a given expected fraction of
individuals. We also address the dual problem of maximizing the campaign
penetration for a resource constrained campaigner. To help us understand and
solve the above mentioned problems, we use percolation theory to formally state
them as optimization problems. These problems are not amenable to traditional
approaches because of a fixed point equation that needs to be solved
numerically. However, we use results from reliability theory to establish some
key properties of the fixed point, which in turn enables us to solve these
problems using algorithms that are linearithmic in maximum node degree.
Furthermore, we evaluate the efficacy of the analytical solution by performing
simulations on real world networks.


title:
Partial redistribution in 3D non-LTE radiative transfer in solar
  atmosphere models

abstract:
  Resonance spectral lines such as H I Ly {\alpha}, Mg II h&k, and Ca II H&K
that form in the solar chromosphere are influenced by the effects of 3D
radiative transfer as well as partial redistribution (PRD). So far no one has
modeled these lines including both effects simultaneously owing to the high
computing demands of existing algorithms. Such modeling is however
indispensable for accurate diagnostics of the chromosphere. We present a
computationally tractable method to treat PRD scattering in 3D model
atmospheres using a 3D non-LTE radiative transfer code. To make the method
memory-friendly, we use the hybrid approximation of Leenaarts et al. (2012) for
the redistribution integral. To make it fast, we use linear interpolation on
equidistant frequency grids. We verify our algorithm against computations with
the RH code and analyze it for stability, convergence, and usefulness of
acceleration using model atoms of Mg II with the h&k lines and H I with the Ly
{\alpha} line treated in PRD. A typical 3D PRD solution can be obtained in a
model atmosphere with $252 \times 252 \times 496$ coordinate points in 50
000--200 000 CPU hours, which is a factor ten slower than computations assuming
complete redistribution. We illustrate the importance of the joint action of
PRD and 3D effects for the Mg II h&k lines for disk-center intensities as well
as the center-to-limb variation. The proposed method allows simulating PRD
lines in time series of radiation-MHD models in order to interpret observations
of chromospheric lines at high spatial resolution.


title: Hysteresis of nanocylinders with Dzyaloshinskii-Moriya interaction

abstract:
  The potential for application of magnetic skyrmions in high density storage
devices provides a strong drive to investigate and exploit their stability and
manipulability. Through a three-dimensional micromagnetic hysteresis study, we
investigate the question of existence of skyrmions in cylindrical
nanostructures of variable thickness. We quantify the applied field and
thickness dependence of skyrmion states, and show that these states can be
accessed through relevant practical hysteresis loop measurement protocols. As
skyrmionic states have yet to be observed experimentally in confined
helimagnetic geometries, our work opens prospects for developing viable
hysteresis process-based methodologies to access and observe skyrmionic states.


title: Adaptive Cross-Packet HARQ

abstract:
  In this work, we investigate a coding strategy devised to increase the
throughput in hybrid ARQ (HARQ) transmission over block fading channel. In our
approach, the transmitter jointly encodes a variable number of bits for each
round of HARQ. The parameters (rates) of this joint coding can vary and may be
based on the negative acknowledgment (NACK) provided by the receiver or, on the
past (outdated) information about the channel states. These new degrees of
freedom allow us to improve the match between the codebook and the channel
states experienced by the receiver. The results indicate that significant gains
can be obtained using the proposed coding strategy, particularly notable when
the conventional HARQ fails to offer throughput improvement even if the number
of transmission rounds is increased. The new cross-packet HARQ is also
implemented using turbo codes where we show that the theoretically predicted
throughput gains materialize in practice, and we discuss the implementation
challenges.


title: Reconstructing a Bounded-Degree Directed Tree Using Path Queries

abstract:
  We present a randomized algorithm for reconstructing directed rooted trees of
$n$ nodes and node degree at most $d$, by asking at most $O(dn\log^2 n)$ path
queries. Each path query takes as input an origin node and a target node, and
answers whether there is a directed path from the origin to the target.
Regarding lower bounds, we show that any randomized algorithm requires at least
$\Omega(n\log n)$ queries, while any deterministic algorithm requires at least
$\Omega(dn)$ queries. Additionally, we present a $O(dn\log^3 n)$ randomized
algorithm for noisy queries, and a $O(dn\log^2 n)$ randomized algorithm for
additive queries on weighted trees.


title: A Complete Characterization of Determinantal Quadratic Polynomials

abstract:
  The problem of expressing a multivariate polynomial as the determinant of a
monic (definite) symmetric or Hermitian linear matrix polynomial (LMP) has
drawn a huge amount of attention due to its connection with optimization
problems. In this paper we provide a necessary and sufficient condition for the
existence of \textit{monic Hermitian determinantal representation} as well as
\textit{monic symmetric determinantal representation} of size $2$ for a given
quadratic polynomial. Further we propose a method to construct such a monic
determinantal representtaion (MDR) of size $2$ if it exists. It is known that a
quadratic polynomial $f(\x)=\x^{T}A\x+b^{T}\x+1$ has a symmetric MDR of size
$n+1$ if $A$ is \textit{negative semidefinite}. We prove that if a quadratic
polynomial $f(\x)$ with $A$ which is not negative semidefinite has an MDR of
size greater than $2$, then it has an MDR of size $2$ too. We also characterize
quadratic polynomials which exhibit diagonal MDRs.


title: Regularity of the level set flow

abstract:
  We showed earlier that the level set function of a monotonic advancing front
is twice differentiable everywhere with bounded second derivative. We show here
that the second derivative is continuous if and only if the flow has a single
singular time where it becomes extinct and the singular set consists of a
closed $C^1$ manifold with cylindrical singularities.


title:
Characterization of Three High Efficiency and Blue Sensitive Silicon
  Photomultipliers

abstract:
  We report about the optical and electrical characterization of three high
efficiency and blue sensitive Silicon photomultipliers from FBK, Hamamatsu, and
SensL. Key features of the tested devices when operated at 90% breakdown
probability are peak photon detection efficiencies between 40% and 55%,
temperature dependencies of gain and PDE that are less than 1%/$^{\circ}$C,
dark rates of $\sim$50\,kHz/mm$^{2}$ at room temperature, afterpulsing of about
2%, and direct optical crosstalk between 6% and 20%. The characteristics of all
three devices impressively demonstrate how the Silicon-photomultiplier
technology has improved over the past ten years. It is further demonstrated how
the voltage and temperature characteristics of a number of quantities can be
parameterized on the basis of physical models. The models provide a deeper
understanding of the device characteristics over a wide bias and temperature
range. They also serve as examples how producers could provide the
characteristics of their SiPMs to users. A standardized parameterization of
SiPMs would enable users to find the optimal SiPM for their application and the
operating point of SiPMs without having to perform measurements thus
significantly reducing design and development cycles.


title:
Origin and evolution of two-component debris discs and an application to
  the q$^1$ Eridani system

abstract:
  Many debris discs reveal a two-component structure, with an outer Kuiper-belt
analogue and a warm inner component whose origin is still a matter of debate.
One possibility is that warm emission stems from an "asteroid belt" closer in
to the star. We consider a scenario in which a set of giant planets is formed
in an initially extended planetesimal disc. These planets carve a broad gap
around their orbits, splitting up the disc into the outer and the inner belts.
After the gas dispersal, both belts undergo collisional evolution in a
steady-state regime. This scenario is explored with detailed collisional
simulations involving realistic physics to describe a long-term collisional
depletion of the two-component disc. We find that the inner disc may be able to
retain larger amounts of material at older ages than thought before on the
basis of simplified analytic models. We show that the proposed scenario is
consistent with a suite of thermal emission and scattered light observational
data for a bright two-temperature debris disc around a nearby solar-type star
q$^1$ Eridani. This implies a Solar System-like architecture of the system,
with an outer massive "Kuiper belt", an inner "asteroid belt", and a few
Neptune- to Jupiter-mass planets in between.


title: A Framework for Optimal Matching for Causal Inference

abstract:
  We propose a novel framework for matching estimators for causal effect from
observational data that is based on minimizing the dual norm of estimation
error when expressed as an operator. We show that many popular matching
estimators can be expressed as optimal in this framework, including
nearest-neighbor matching, coarsened exact matching, and mean-matched sampling.
This reveals their motivation and aptness as structural priors formulated by
embedding the effect in a particular functional space. This also gives rise to
a range of new, kernel-based matching estimators that arise when one embeds the
effect in a reproducing kernel Hilbert space. Depending on the case, these
estimators can be found using either quadratic optimization or integer
optimization. We show that estimators based on universal kernels are
universally consistent without model specification. In empirical results using
both synthetic and real data, the new, kernel-based estimators outperform all
standard causal estimators in estimation error.


title: On the Astrid asteroid family

abstract:
  Among asteroid families, the Astrid family is peculiar because of its unusual
inclination distribution. Objects at $a\simeq$~2.764 au are quite dispersed in
this orbital element, giving the family a "crab-like" appearance. Recent works
showed that this feature is caused by the interaction of the family with the
$s-s_C$ nodal secular resonance with Ceres, that spreads the inclination of
asteroids near its separatrix. As a consequence, the currently observed
distribution of the $v_W$ component of terminal ejection velocities obtained
from inverting Gauss equation is quite leptokurtic, since this parameter mostly
depends on the asteroids inclination. The peculiar orbital configuration of the
Astrid family can be used to set constraints on key parameters describing the
strength of the Yarkovsky force, such as the bulk and surface density and the
thermal conductivity of surface material. By simulating various fictitious
families with different values of these parameters, and by demanding that the
current value of the kurtosis of the distribution in $v_W$ be reached over the
estimated lifetime of the family, we obtained that the thermal conductivity of
Astrid family members should be $\simeq$ 0.001 W/m/K, and that the surface and
bulk density should be higher than 1000 kg/m$^{3}$. Monte Carlo methods
simulating Yarkovsky and stochastic YORP evolution of the Astrid family show
its age to be $T$ = 140$\pm$30 Myr old, in good agreement with estimates from
other groups. Its terminal ejection velocity parameter is in the range $V_{EJ}=
5^{+17}_{-5}$~m/s.] Values of $V_{EJ}$ larger than 25 m/s are excluded from
constraints from the current inclination distribution.


title: Formation of the G-ring arc

abstract:
  Since 2004, the images obtained by Cassini spacecraft's on-board cameras have
revealed the existence of several small satellites in the Saturn system. Some
of these small satellites are embedded in arcs of particles. While these
satellites and their arcs are known to be in corotation resonances with Mimas,
their origin remains unknown. This work investigates one possible process for
capturing bodies into a corotation resonance, which involves raising the
eccentricity of a perturbing body. Therefore, through numerical simulations and
analytical studies, we show a scenario that the excitation of Mimas'
eccentricity could capture particles in a corotation resonance and given a
possible explanation for the origin for the arcs.


title: The Picard group of motivic A(1)

abstract:
  We show that the Picard group $Pic(A(1))$ of the stable category of modules
over $\mathbb{C}$-motivic $A(1)$ is isomorphic to $\mathbb{Z}^4$. By
comparison, the Picard group of classical $A(1)$ is $\mathbb{Z}^2 \oplus
\mathbb{Z}/2$. One extra copy of $\mathbb{Z}$ arises from the motivic
bigrading. The joker is a well-known exotic element of order $2$ in the Picard
group of classical $A(1)$. The $\mathbb{C}$-motivic joker has infinite order.


title:
Polarimetry of comets 67P/Churyumov-Gerasimenko, 74P/Smirnova-Chernykh,
  and 152P/Helin-Lawrence

abstract:
  Aims. Polarimetric characteristics of comets at large heliocentric distances
is a relatively unexplored area; we extend the idea by adding and analysing the
data for three Jupiter family comets (JFCs).
  Methods. With the FORS2 instrument of the ESO VLT, we performed
quasi-simultaneous photometry and polarimetry of three active JFCs
67P/Churyumov-Gerasimenko, 74P/Smirnova-Chernykh, and 152P/Helin-Lawrence.
  Results. We obtained in total 23 polarimetric measurements at different
epochs, covering a phase-angle range ~1 -16 degrees and heliocentric distances
from 3 to 4.6 au. From our observations we obtained both colour and
polarimetric maps to look for structures in the comae and tails of the comets.
  Conclusions. 74P/Smirnova-Chernykh and 152P/Helin-Lawrence exhibit enough
activity at large heliocentric distances to be detectable in polarimetric
measurements. Polarimetric and colour maps indicate no evidence of dust
particle


title: Detailed study of the microwave emission of the supernova remnant 3C 396

abstract:
  We have observed the supernova remnant 3C~396 in the microwave region using
the Parkes 64-m telescope. Observations have been made at 8.4 GHz, 13.5 GHz,
and 18.6 GHz and in polarisation at 21.5 GHz. We have used data from several
other observatories, including previously unpublished observations performed by
the Green Bank Telescope at 31.2 GHz, to investigate the nature of the
microwave emission of 3C 396. Results show a spectral energy distribution
dominated by a single component power law emission with $\alpha=(-0.364 \pm
0.017)$. Data do not favour the presence of anomalous microwave emission coming
from the source. Polarised emission at 21.5 GHz is consistent with
synchrotron-dominated emission. We present microwave maps and correlate them
with infrared (IR) maps in order to characterise the interplay between thermal
dust and microwave emission. IR vs. microwave TT plots reveal poor correlation
between mid-infrared and microwave emission from the core of the source. On the
other hand, a correlation is detected in the tail emission of the outer shell
of 3C 396, which could be ascribed to Galactic contamination.


title:
Asymptotic Theory of Channeling in the Field of an Atomic Chain and an
  Atomic Plane

abstract:
  A rigorous theory of diffraction scattering from extended objects is
proposed. The present theory is based on a multiple asymptotic expansion of an
integral equation for the exact wave function in terms of the large parameters
of the problem, which are the range of the potential and the momentum
components of the incident particle. For small angles of incidence the density
of positively charged particles on the axis of a chain is always lower than
unit y and the density of negatively charged particles has a maximum for
certain strength of the potential which can exceed considerably unity. The
conditions of validity of the proposed approach are obtained.


title: Effective Chabauty for symmetric powers of curves

abstract:
  Faltings' theorem states that curves of genus $g \geq 2$ have finitely many
rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one
obtains an upper bound on the number of rational points, but this bound is too
large to be used in any reasonable sense. In 1985, Coleman showed that
Chabauty's method, which works when the Mordell-Weil rank of the Jacobian of
the curve is smaller than $g$, can be used to give a good effective bound on
the number of rational points of curves of genus $g > 1$. We draw ideas from
nonarchimedean geometry to show that we can also give an effective bound on the
number of rational points outside of the special set of $d$-th symmetric power
of $X$, where $X$ is a curve of genus $g > d$, when the Mordell-Weil rank of
the Jacobian of the curve is at most $g-d$ and the curve further satisfies
certain rigid analytic conditions.


title: A Goldilocks principle for modeling radial velocity noise

abstract:
  The doppler measurements of stars are diluted and distorted by stellar
activity noise. Different choices of noise models and statistical methods have
led to much controversy in the confirmation of exoplanet candidates obtained
through analysing radial velocity data. To quantify the limitation of various
models and methods, we compare different noise models and signal detection
criteria for various simulated and real data sets in the Bayesian framework.
According to our analyses, the white noise model tend to interpret noise as
signal, leading to false positives. On the other hand, the red noise models are
likely to interprete signal as noise, resulting in false negatives. We find
that the Bayesian information criterion combined with a Bayes factor threshold
of 150 can efficiently rule out false positives and confirm true detections. We
further propose a Goldilocks principle aimed at modeling radial velocity noise
to avoid too many false positives and too many false negatives. We propose that
the noise model with RHK-dependent jitter is used in combination with the
moving average model to detect planetary signals for M dwarfs. Our work may
also shed light on the noise modeling for hotter stars, and provide a valid
approach for finding similar principles in other disciplines.


title: On Properties of Differential Inclusions with Prox-regular Sets

abstract:
  In this paper, some regularity properties of solutions of the following
differential inclusion \begin{equation}\nonumber \left\{ \begin{array}{l}
\dot{x}(t) \in f\big(x(t)\big) -N_{C}\big(x(t)\big)\; {\rm a.e.} \; t \in
[0,+\infty), x(0) = x_0\in C, \end{array}\right. \end{equation} are analyzed
where $f: H\to H$ is Lipschitz continuous and $C$ is closed, uniformly
prox-regular subset of a Hilbet space $H$. Here $N_{C}(\cdot)$ denotes the
proximal normal cone of $C$. This work can be considered as an improvement of
[Hantoute-Mazade 2013] since these properties are established without the
additional tangential condition at each point in $C$.


title:
LP-Based Robust Algorithms for Noisy Minor-Free and Bounded Treewidth
  Graphs

abstract:
  We give a general approach for solving optimization problems on noisy minor
free graphs, where a \delta-fraction of edges and vertices are adversarially
corrupted. The noisy setting was first considered by Magen and Moharrami and
they gave a (1 + \delta)-estimation algorithm for the independent set problem.
Later, Chan and Har-Peled designed a local search algorithm that finds a (1 +
O(\delta))-approximate independent set. However, nothing was known regarding
other problems in the noisy setting. Our main contribution is a general
LP-based framework that yields a (1 + O(\delta log m log log m))-approximation
algorithm for noisy MAX-k-CSPs on m clauses.


title:
Tuning of Near- and Far-Field Properties of All-dielectric Dimer
  Nanoantennas via Ultrafast Electron-Hole Plasma Photoexcitation

abstract:
  Achievement of all-optical ultrafast signal modulation and routing by a
low-loss nanodevice is a crucial step towards an ultracompact optical chip with
high performance. Here, we propose a specifically designed silicon dimer
nanoantenna, which is tunable via photoexcitation of dense electron-hole plasma
with ultrafast relaxation rate. Basing on this concept, we demonstrate the
effect of beam steering up to 20 degrees via simple variation of incident
intensity, being suitable for ultrafast light routing in an optical chip. The
effect is demonstrated both in the visible and near-IR spectral regions for
silicon and germanium based nanoantennas. We also reveal the effect of
electron-hole plasma photoexcitation on local density of states (LDOS) in the
dimer gap and find that the orientation averaged LDOS can be altered by 50\%,
whereas modification of the projected LDOS can be even more dramatic: almost
500\% for transverse dipole orientation. Moreover, our analytical model sheds
light on transient dynamics of the studied nonlinear nanoantennas, yielding all
temporal characteristics of the proposed ultrafast nanodevice. The proposed
concept paves the ways to creation of low-loss, ultrafast, and compact devices
for optical signal modulation and routing.


title: High-speed real-time single-pixel microscopy based on Fourier sampling

abstract:
  Single-pixel cameras based on the concepts of compressed sensing (CS)
leverage the inherent structure of images to retrieve them with far fewer
measurements and operate efficiently over a significantly broader spectral
range than conventional silicon-based cameras. Recently, photonic time-stretch
(PTS) technique facilitates the emergence of high-speed single-pixel cameras. A
significant breakthrough in imaging speed of single-pixel cameras enables
observation of fast dynamic phenomena. However, according to CS theory, image
reconstruction is an iterative process that consumes enormous amounts of
computational time and cannot be performed in real time. To address this
challenge, we propose a novel single-pixel imaging technique that can produce
high-quality images through rapid acquisition of their effective spatial
Fourier spectrum. We employ phase-shifting sinusoidal structured illumination
instead of random illumination for spectrum acquisition and apply inverse
Fourier transform to the obtained spectrum for image restoration. We evaluate
the performance of our prototype system by recognizing quick response (QR)
codes and flow cytometric screening of cells. A frame rate of 625 kHz and a
compression ratio of 10% are experimentally demonstrated in accordance with the
recognition rate of the QR code. An imaging flow cytometer enabling
high-content screening with an unprecedented throughput of 100,000 cells/s is
also demonstrated. For real-time imaging applications, the proposed
single-pixel microscope can significantly reduce the time required for image
reconstruction by two orders of magnitude, which can be widely applied in
industrial quality control and label-free biomedical imaging.


title:
Assessing and tuning brain decoders: cross-validation, caveats, and
  guidelines

abstract:
  Decoding, ie prediction from brain images or signals, calls for empirical
evaluation of its predictive power. Such evaluation is achieved via
cross-validation, a method also used to tune decoders' hyper-parameters. This
paper is a review on cross-validation procedures for decoding in neuroimaging.
It includes a didactic overview of the relevant theoretical considerations.
Practical aspects are highlighted with an extensive empirical study of the
common decoders in within-and across-subject predictions, on multiple datasets
--anatomical and functional MRI and MEG-- and simulations. Theory and
experiments outline that the popular " leave-one-out " strategy leads to
unstable and biased estimates, and a repeated random splits method should be
preferred. Experiments outline the large error bars of cross-validation in
neuroimaging settings: typical confidence intervals of 10%. Nested
cross-validation can tune decoders' parameters while avoiding circularity bias.
However we find that it can be more favorable to use sane defaults, in
particular for non-sparse decoders.


title:
Verification of the helioseismic Fourier-Legendre analysis for
  meridional flow measurements

abstract:
  Measuring the Sun's internal meridional flow is one of the key issues of
helioseismology. Using the Fourier-Legendre analysis is a technique for
addressing this problem. We validate this technique with the help of artificial
helioseismic data. The analysed data set was obtained by numerically simulating
the effect of the meridional flow on the seismic wave field in the full volume
of the Sun. In this way, a 51.2-hour long time series was generated. The
resulting surface velocity field is then analyzed in various settings: Two
$360^\circ \times 90^\circ$ halfspheres, two $120^\circ \times 60^\circ$
patches on the front and farside of the Sun (North and South, respectively) and
two $120^\circ \times 60^\circ$ patches on the northern and southern frontside
only. We compare two possible measurement setups: observations from Earth and
from an additional spacecraft on the solar farside, and observations from Earth
only, in which case the full information of the global solar oscillation wave
field was available. We find that, with decreasing observing area, the
accessible depth range decreases: the $360^\circ \times 90^\circ$ view allows
us to probe the meridional flow almost to the bottom of the convection zone,
while the $120^\circ \times 60^\circ$ view means only the outer layers can be
probed. These results confirm the validity of the Fourier-Legendre analysis
technique for helioseismology of the meridional flow. Furthermore these flows
are of special interest for missions like Solar Orbiter that promises to
complement standard helioseismic measurements from the solar nearside with
farside observations.


title: A new asymmetric generalisation of the t-distribution

abstract:
  A 6-parameter fat-tailed distribution is proposed that generalises the
t-distribution and allows asymmetry of scale and also of tail power, whilst
avoiding the discontinuity of the second derivative of the split-t (AST)
distribution. With the sixth parameter set to unity and no asymmetry, the
distribution reduces to a t-distribution, but with the sixth parameter reduced,
fatter tails than those of the t-distribution are allowed (the tails start
earlier) and the distribution generalises Johnson's $S_U$ distribution. Data
fitting is illustrated with examples.


title:
Multiple imputation of missing covariate values in multilevel models
  with random slopes: A cautionary note

abstract:
  Multiple imputation (MI) has become one of the main procedures used to treat
missing data, but the guidelines from the methodological literature are not
easily transferred to multilevel research. For models including random slopes,
proper MI can be difficult, especially when the covariate values are partially
missing. In the present article, we discuss applications of MI in multilevel
random-coefficient models, theoretical challenges posed by slope variation, and
the current limitations of standard MI software. Our findings from three
simulation studies suggest that (a) MI is able to recover most parameters, but
is currently not well suited to capture slope variation entirely when covariate
values are missing; (b) MI offers reasonable estimates for most parameters,
even in smaller samples or when its assumptions are not met; and (c) listwise
deletion can be an alternative worth considering when preserving the slope
variance is particularly important.


title: Spectral theory for structured perturbations of linear operators

abstract:
  We characterize the spectrum (and its parts) of operators which can be
represented as G=A+BC for a simpler operator A and a structured perturbation
BC. The interest in this kind of perturbations is motivated, e.g., by
perturbations of the domain of an operator A but also arises in the theory of
closed-loop systems in control theory. In many cases our results yield the
spectral values of G as zeros of a "characteristic equation".


title: On a geometric inequality related to fractional integration

abstract:
  In this paper we consider a new kind of inequality related to fractional
integration, motivated by Gressman's paper. Based on it we investigate its
multilinear analogue inequalities. Combining with the Gressman's work on
multilinear integral, we establish this new kind of geometric inequalities with
bilinear form and multilinear form in more general settings. Moreover, in some
cases we also find the best constants and optimisers for these geometric
inequalities on Euclidean spaces with Lebesgue measure settings with $L^p$
bounds.


title:
Stationary Schr\"odinger equation in the semi-classical limit: numerical
  coupling of oscillatory and evanescent regions

abstract:
  This paper is concerned with a 1D Schr\"odinger scattering problem involving
both oscillatory and evanescent regimes, separated by jump discontinuities in
the potential function, to avoid "turning points". We derive a non-overlapping
domain decomposition method to split the original problem into sub-problems on
these regions, both for the continuous and afterwards for the discrete problem.
Further, a hybrid WKB-based numerical method is designed for its efficient and
accurate solution in the semi-classical limit: a WKB-marching method for the
oscillatory regions and a FEM with WKB-basis functions in the evanescent
regions. We provide a complete error analysis of this hybrid method and
illustrate our convergence results by numerical tests.


title: On some determinant and matrix inequalities with a geometrical flavour

abstract:
  In this paper we study some determinant inequalities and matrix inequalities
which have a geometrical flavour. We first examine some inequalities which
place work of Macbeath [13] in a more general setting and also relate to recent
work of Gressman [8]. In particular, we establish optimisers for these
determinant inequalities. We then use these inequalities to establish our main
theorem which gives a geometric inequality of matrix type which improves and
extends some inequalities of Christ in [5].


title: Cost Effective Campaigning in Social Networks

abstract:
  Campaigners are increasingly using online social networking platforms for
promoting products, ideas and information. A popular method of promoting a
product or even an idea is incentivizing individuals to evangelize the idea
vigorously by providing them with referral rewards in the form of discounts,
cash backs, or social recognition. Due to budget constraints on scarce
resources such as money and manpower, it may not be possible to provide
incentives for the entire population, and hence incentives need to be allocated
judiciously to appropriate individuals for ensuring the highest possible
outreach size. We aim to do the same by formulating and solving an optimization
problem using percolation theory. In particular, we compute the set of
individuals that are provided incentives for minimizing the expected cost while
ensuring a given outreach size. We also solve the problem of computing the set
of individuals to be incentivized for maximizing the outreach size for given
cost budget. The optimization problem turns out to be non trivial; it involves
quantities that need to be computed by numerically solving a fixed point
equation. Our primary contribution is, that for a fairly general cost
structure, we show that the optimization problems can be solved by solving a
simple linear program. We believe that our approach of using percolation theory
to formulate an optimization problem is the first of its kind.


title: Weighted Online Problems with Advice

abstract:
  Recently, the first online complexity class, AOC, was introduced. The class
consists of many online problems where each request must be either accepted or
rejected, and the aim is to either minimize or maximize the number of accepted
requests, while maintaining a feasible solution. All AOC-complete problems
(including Independent Set, Vertex Cover, Dominating Set, and Set Cover) have
essentially the same advice complexity. In this paper, we study weighted
versions of problems in AOC, i.e., each request comes with a weight and the aim
is to either minimize or maximize the total weight of the accepted requests. In
contrast to the unweighted versions, we show that there is a significant
difference in the advice complexity of complete minimization and maximization
problems. We also show that our algorithmic techniques for dealing with
weighted requests can be extended to work for non-complete AOC problems such as
maximum matching (giving better results than what follow from the general AOC
results) and even non-AOC problems such as scheduling.


title: Singular inflation from Born-Infeld-f(R) gravity

abstract:
  Accelerating dynamics from Born-Infeld-$f(R)$ gravity are studied in a
simplified conformal approach without matter. Explicit unification of inflation
with late-time acceleration is realized within this singular inflation
approach, which is similar to Odintsov-Oikonomou singular $f(R)$ inflation. Our
model turns out to be consistent with the latest release of Planck data.


title:
Inertial displacement of a domain wall excited by ultra-short circularly
  polarized laser pulses

abstract:
  Domain wall motion driven by ultra-short laser pulses is a prerequisite for
envisaged low-power spintronics combining storage of information in magneto
electronic devices with high speed and long distance transmission of
information encoded in circularly polarized light. Here we demonstrate the
conversion of the circular polarization of incident femtosecond laser pulses
into inertial displacement of a domain wall in a ferromagnetic semiconductor.
In our study we combine electrical measurements and magneto-optical imaging of
the domain wall displacement with micromagnetic simulations. The optical spin
transfer torque acts over a picosecond recombination time of the spin polarized
photo-carriers which only leads to a deformation of the internal domain wall
structure. We show that subsequent depinning and micro-meter distance
displacement without an applied magnetic field or any other external stimuli
can only occur due to the inertia of the domain wall.