title:
Coherent photoproductions of $J/\Psi$ and $\Upsilon$ mesons in pp and
  PbPb ultraperipheral collisions from dynamical gluon distribution

abstract:
  We present calculations of coherent photoproduction of vector mesons
($J/\Psi$ and $\Upsilon$) with leading-order parton distribution functions to
check new kinds of corrections of the DGLAP equations and nuclear
modifications. The input gluon distribution of the proton is the dynamical
parton model from the DGLAP equations with GLR-MQ-ZRS (Gribov-Levin-Ryskin,
Mueller-Qiu, Zhu-Ruan-Shen) modifications. From comparison between several
other gluon distribution models, we find that the dynamical gluon distribution
fits with the results of meson photoproduction experiments in the high energy
region. The calculation of the differential cross sections using dynamical and
other gluon distributions is compared with the experimental data from the HERA,
ZEUS and LHCb Collaborations. Although there is little data for the rapidity
distribution of vector meson photoproduction near zero rapidity, the dynamical
gluon distribution works well with the data in the large rapidity region.


title: Model-based generation of natural language specifications

abstract:
  Application of formal models provides many benefits for the software and
system development, however, the learning curve of formal languages could be a
critical factor for an industrial project. Thus, a natural language
specification that reflects all the aspects of the formal model might help to
understand the model and be especially useful for the stakeholders who do not
know the corresponding formal language. Moreover, an automated generation of
the documentation from the model would replace manual updates of the
documentation for the cases the model is modified. This paper presents an
ongoing work on generating natural language specifications from formal models.
Our goal is to generate documentation in English from the basic modelling
artefacts, such as data types, state machines, and architectural components. To
allow further formal analysis of the generated specification, we restrict
English to its subset, Attempto Controlled English.


title: Unitification of Weakly p.q.-Baer *-Rings

abstract:
  In this paper, we introduce a concept of weakly principally quasi-Baer
*-rings in terms of central cover. We prove that a *-rings is a principally
quasi-Baer *-rings if and only if it is weakly principally quasi-Baer *-rings
with unity. A partial solution to the problem similar to unitification problem
raised by S. K. Berberian is obtained.


title: "Boring formal methods" or "Sherlock Holmes deduction methods"?

abstract:
  This paper provides an overview of common challenges in teaching of logic and
formal methods to Computer Science and IT students. We discuss our experiences
from the course IN3050: Applied Logic in Engineering, introduced as a "logic
for everybody" elective course at at TU Munich, Germany, to engage pupils
studying Computer Science, IT and engineering subjects on Bachelor and Master
levels. Our goal was to overcome the bias that logic and formal methods are not
only very complicated but also very boring to study and to apply. In this
paper, we present the core structure of the course, provide examples of
exercises and evaluate the course based on the students' surveys.


title:
Propagation property and its application to inverse scattering for
  fractional powers of the negative Laplacian

abstract:
  Enss (1983) proved a propagation estimate for the usual free Schroedinger
operator that turned out later to be very useful for inverse scattering in the
work of Enss--Weder (1995). Since then, this method has been called the
Enss--Weder time-dependent method. We study the same type of propagation
estimate for the fractional powers of the negative Laplacian and, as with the
Enss--Weder method, we apply our estimate to inverse scattering. We find that
the high-velocity limit of the scattering operator uniquely determines the
short-range interactions.


title: Throughput-Optimal Load Balancing for Intra Datacenter Networks

abstract:
  Traffic load-balancing in datacenters alleviates hot spots and improves
network utilization. In this paper, a stable in-network load-balancing
algorithm is developed in the setting of software-defined networking. A control
plane configures a data plane over successive intervals of time. While the
MaxWeight algorithm can be applied in this setting and offers certain
throughput optimality properties, its bang-bang control structure rewards
single flows on each interval and prohibits link-capacity sharing. This paper
develops a new algorithm that is throughput-optimal and allows link-capacity
sharing, leading to low queue occupancy. The algorithm deliberately imitates
weighted fair queueing, which provides fairness and graceful interaction with
TCP traffic. Inspired by insights from the analysis, a heuristic improvement is
also developed to operate with practical switches and TCP flows. Simulations
from a network simulator shows that the algorithm outperforms the widely-used
equal-cost multipath (ECMP) technique.


title:
Test of source selection for constructing a more stable and uniform
  celestial reference frame

abstract:
  We aim to evaluate the possibility of improving the ICRS realization starting
from the ICRF2 catalogue by investigating the coordinate time series of radio
sources observed by VLBI between 1979 and 2016. Sources with long observational
history are selected as the candidates and the least squares fits with special
handling of the weights are performed to derive the linear drifts of the source
coordinates. Then the sources are sorted based on the normalized linear drift
(i) over the whole sky and (ii) in four homolographic areas divided by
declinations. The axial stability of the reference system and sky distribution
defined by the selected sources are evaluated, which are acted as the criterion
for the final source lists. With our improved source selection scheme, two
groups of sources are proposed and considered suitable for defining a more
stable and homogeneous celestial reference system compared to the current
ICRF2. The number of sources in the final lists are 323 and 294, respectively,
and the global rotation of the axes derived from apparent motion of the sources
are about two times better than the ICRF2.


title: Spatio-temporal Models for Formal Analysis and Property-based Testing

abstract:
  This paper presents our ongoing work on spatio-temporal models for formal
analysis and property-based testing. Our proposed framework aims at reducing
the impedance mismatch between formal methods and practitioners. We introduce a
set of formal methods and explain their interplay and benefits in terms of
usability.


title: Noncommutative enhancements of contractions

abstract:
  Given a contraction of a variety X to a base Y, we enhance the locus in Y
over which the contraction is not an isomorphism with a certain sheaf of
noncommutative rings D, under mild assumptions which hold in the case of (1)
crepant partial resolutions admitting a tilting bundle with trivial summand,
and (2) all contractions with fibre dimension at most one. In all cases, this
produces a global invariant. In the crepant setting, we then apply this to
study derived autoequivalences of X. We work generally, dropping many of the
usual restrictions, and so both extend and unify existing approaches. In full
generality we construct a new endofunctor of the derived category of X by
twisting over D, and then, under appropriate restrictions on singularities,
give conditions for when it is an autoequivalence. We show that these
conditions hold automatically when the non-isomorphism locus in Y has
codimension 3 or more, which covers determinantal flops, and we also control
the conditions when the non-isomorphism locus has codimension 2, which covers
3-fold divisor-to-curve contractions.


title:
Symplectic and antiplectic waves in an array of beating cilia attached
  to a closed body

abstract:
  By taking into account the hydrodynamic interactions in a one dimensional
array of model cilia attached to a no-slip cylinderical surface, we investigate
their synchronized motion. We show, how does the emergence of metachronal waves
depend on the initial state of the system and investigate the conditions under
which, the formation of symplectic and antiplectic waves are possible.


title: Cluster-Wise Ratio Tests for Fast Camera Localization

abstract:
  Feature point matching for camera localization suffers from scalability
problems. Even when feature descriptors associated with 3D scene points are
locally unique, as coverage grows, similar or repeated features become
increasingly common. As a result, the standard distance ratio-test used to
identify reliable image feature points is overly restrictive and rejects many
good candidate matches. We propose a simple coarse-to-fine strategy that uses
conservative approximations to robust local ratio-tests that can be computed
efficiently using global approximate k-nearest neighbor search. We treat these
forward matches as votes in camera pose space and use them to prioritize
back-matching within candidate camera pose clusters, exploiting feature
co-visibility captured by clustering the 3D model camera pose graph. This
approach achieves state-of-the-art camera localization results on a variety of
popular benchmarks, outperforming several methods that use more complicated
data structures and that make more restrictive assumptions on camera pose. We
also carry out diagnostic analyses on a difficult test dataset containing
globally repetitive structure that suggest our approach successfully adapts to
the challenges of large-scale image localization.


title: Grothendieck duality and Q-Gorenstein morphisms

abstract:
  The notions of $\mathbb Q$-Gorenstein scheme and of $\mathbb Q$-Gorenstein
morphism are introduced for locally Noetherian schemes by dualizing complexes
and (relative) canonical sheaves. These cover all the previously known notions
of $\mathbb Q$-Gorenstein algebraic variety and of $\mathbb Q$-Gorenstein
deformation satisfying Koll\'ar condition, over a field. By studies on relative
$\mathbf S_{2}$-condition and base change properties, valuable results are
proved for $\mathbb Q$-Gorenstein morphisms, which include infinitesimal
criterion, valuative criterion, $\mathbb Q$-Gorenstein refinement, and so
forth.


title: Fleet Size and Mix Split-Delivery Vehicle Routing

abstract:
  In the classic Vehicle Routing Problem (VRP) a fleet of of vehicles has to
visit a set of customers while minimising the operations' costs. We study a
rich variant of the VRP featuring split deliveries, an heterogeneous fleet, and
vehicle-commodity incompatibility constraints. Our goal is twofold: define the
cheapest routing and the most adequate fleet.
  To do so, we split the problem into two interdependent components: a fleet
design component and a routing component. First, we define two Mixed Integer
Programming (MIP) formulations for each component. Then we discuss several
improvements in the form of valid cuts and symmetry breaking constraints.
  The main contribution of this paper is a comparison of the four resulting
models for this Rich VRP. We highlight their strengths and weaknesses with
extensive experiments.
  Finally, we explore a lightweight integration with Constraint Programming
(CP). We use a fast CP model which gives good solutions and use the solution to
warm-start our models.


title:
7-dimensional ${\cal N}=2$ Consistent Truncations using $\mathrm{SL}(5)$
  Exceptional Field Theory

abstract:
  We show how to construct seven-dimensional half-maximally supersymmetric
consistent truncations of 11-/10-dimensional SUGRA using $\mathrm{SL}(5)$
exceptional field theory. Such truncations are defined on generalised
$\mathrm{SU}(2)$-structure manifolds and give rise to seven-dimensional
half-maximal gauged supergravities coupled to $n$ vector multiplets and thus
with scalar coset space $\mathbb{R}^+ \times
\mathrm{O}(3,n)/\mathrm{O}(3)\times\mathrm{O}(n)$. The consistency conditions
for the truncation can be written in terms of the generalised Lie derivative
and take a simple geometric form. We show that after imposing certain "doublet"
and "closure" conditions, the embedding tensor of the gauged supergravity is
given by the intrinsic torsion of generalised $\mathrm{SU}(2)$-connections and
automatically satisfies the linear constraint of seven-dimensional half-maximal
gauged supergravities, as well as the quadratic constraint when the section
condition is satisfied.


title:
Design and Evaluation of Alternate Enumeration Techniques for Subset Sum
  Problem

abstract:
  The subset sum problem, also referred as SSP, is a NP-Hard computational
problem. SSP has its applications in broad domains like cryptography, number
theory, operation research and complexity theory. The most famous algorithm for
solving SSP is Backtracking Algorithm which has exponential time complexity.
Therefore, our goal is to design and develop better alternate enumeration
techniques for faster generation of SSP solutions. Given the set of first n
natural numbers which is denoted by Xn and a target sum S, we propose various
alternate enumeration techniques which find all the subsets of Xn that add up
to sum S.
  In this paper, we present the mathematics behind this exponential problem. We
analyze the distribution of power set of Xn and present formulas which show
definite patterns and relations among these subsets. We introduce three major
distributions for power set of Xn: Sum Distribution, Length-Sum Distribution
and Element Distribution. These distributions are prepossessing procedures for
various alternate enumeration techniques for solving SSP. We propose novel
algorithms: Subset Generation using Sum Distribution, Subset Generation using
Length-Sum Distribution, Basic Bucket Algorithm, Maximum and Minimum Frequency
Driven Bucket Algorithms and Local Search using Maximal and Minimal Subsets for
enumerating SSP.
  We compare the performance of these approaches against the traditional
backtracking algorithm. The efficiency and effectiveness of these algorithms
are presented with the help of these experimental results. Furthermore, we
studied the over solution set of subsets generated by various algorithms to get
the complete solution for subset sum problem. Finally, we present a conjecture
about upper bound on the number of subsets that has to be enumerated to get all
solutions for Subset Sum Problem.


title: Tree Matchings

abstract:
  An $(s,t)$-matching in a bipartite graph $G=(U,V,E)$ is a subset of the edges
$F$ such that each component of $G[F]$ is a tree with at most $t$ edges and
each vertex in $U$ has $s$ neighbours in $G[H]$. We give sharp conditions for a
bipartite graph to contain an $(s,t)$-matching. As a special case, we prove a
conjecture of Bonacina, Galesi, Huynh and Wollan \cite{CNF}.


title:
Dust formation and mass loss around intermediate-mass AGB stars with
  initial metallicity $Z_{\rm ini} \leq 10^{-4}$ in the early Universe I:
  Effect of surface opacity on the stellar evolution and dust-driven wind

abstract:
  Dust formation and resulting mass loss around Asymptotic Giant Branch (AGB)
stars with initial metallicity in the range of $0 \leq Z_{\rm ini} \leq
10^{-4}$ and initial mass $2\leq M_{\rm ini}/M_{\odot} \leq 5$ are explored by
the hydrodynamical calculations of dust-driven wind (DDW) along the AGB
evolutionary tracks. We employ the MESA code to simulate the evolution of
stars, assuming an empirical mass-loss rate in the post-main sequence phase,
and considering the three types of low-temperature opacities (scaled-solar,
CO-enhanced, and CNO-enhanced opacities) to elucidate the effect on the stellar
evolution and the DDW. We find that the treatment of low-temperature opacity
strongly affects the dust formation and resulting DDW; in the carbon-rich AGB
phase, the maximum $\dot{M}$ of $M_{\rm ini} \geq$ 3 $M_{\odot}$ star with the
CO-enhanced opacity is at least one order of magnitude smaller than that with
the CNO-enhanced opacity. A wide range of stellar parameters being covered, a
necessary condition for driving efficient DDW with $\dot{M} \ge 10^{-6}$
$M_{\odot}$ yr$^{-1}$ is expressed as the effective temperature $T_{\rm eff}
\lesssim 3850$ K and $\log(\delta_{\rm C}L/\kappa_{\rm R} M) \gtrsim 10.43\log
T_{\rm eff}-32.33 $ with the carbon excess $\delta_{\rm C}$ defined as
$\epsilon_{\rm C} - \epsilon_{\rm O}$ and the Rosseland mean opacity
$\kappa_{\rm R}$ in units of cm$^2$g$^{-1}$ in the surface layer, and the
stellar mass (luminosity) $M$ $(L)$ in solar units. The derived fitting
formulae of gas and dust mass-loss rates in terms of input stellar parameters
could be useful for investigating the dust yield from AGB stars in the early
Universe being consistent with the stellar evolution calculations.


title: Optimal Approximate Polytope Membership

abstract:
  In the polytope membership problem, a convex polytope $K$ in $R^d$ is given,
and the objective is to preprocess $K$ into a data structure so that, given a
query point $q \in R^d$, it is possible to determine efficiently whether $q \in
K$. We consider this problem in an approximate setting and assume that $d$ is a
constant. Given an approximation parameter $\varepsilon > 0$, the query can be
answered either way if the distance from $q$ to $K$'s boundary is at most
$\varepsilon$ times $K$'s diameter. Previous solutions to the problem were on
the form of a space-time trade-off, where logarithmic query time demands
$O(1/\varepsilon^{d-1})$ storage, whereas storage $O(1/\varepsilon^{(d-1)/2})$
admits roughly $O(1/\varepsilon^{(d-1)/8})$ query time. In this paper, we
present a data structure that achieves logarithmic query time with storage of
only $O(1/\varepsilon^{(d-1)/2})$, which matches the worst-case lower bound on
the complexity of any $\varepsilon$-approximating polytope. Our data structure
is based on a new technique, a hierarchy of ellipsoids defined as
approximations to Macbeath regions.
  As an application, we obtain major improvements to approximate Euclidean
nearest neighbor searching. Notably, the storage needed to answer
$\varepsilon$-approximate nearest neighbor queries for a set of $n$ points in
$O(\log \frac{n}{\varepsilon})$ time is reduced to $O(n/\varepsilon^{d/2})$.
This halves the exponent in the $\varepsilon$-dependency of the existing space
bound of roughly $O(n/\varepsilon^d)$, which has stood for 15 years (Har-Peled,
2001).


title:
Deep Neural Networks for No-Reference and Full-Reference Image Quality
  Assessment

abstract:
  We present a deep neural network-based approach to image quality assessment
(IQA). The network is trained end-to-end and comprises ten convolutional layers
and five pooling layers for feature extraction, and two fully connected layers
for regression, which makes it significantly deeper than related IQA models.
Unique features of the proposed architecture are that: 1) with slight
adaptations it can be used in a no-reference (NR) as well as in a
full-reference (FR) IQA setting and 2) it allows for joint learning of local
quality and local weights, i.e., relative importance of local quality to the
global quality estimate, in an unified framework. Our approach is purely
data-driven and does not rely on hand-crafted features or other types of prior
domain knowledge about the human visual system or image statistics. We evaluate
the proposed approach on the LIVE, CISQ, and TID2013 databases as well as the
LIVE In the wild image quality challenge database and show superior performance
to state-of-the-art NR and FR IQA methods. Finally, cross-database evaluation
shows a high ability to generalize between different databases, indicating a
high robustness of the learned features.


title: Moments of Hardy's function over short intervals

abstract:
  Let as usual $Z(t) = \zeta(1/2+it)\chi^{-1/2}(1/2+it)$ denote Hardy's
function, where $\zeta(s) = \chi(s)\zeta(1-s)$. Assuming the Riemann hypothesis
upper and lower bounds for some integrals involving $Z(t)$ and $Z'(t)$ are
proved. It is also proved that $$ H(\log T)^{k^2} \ll_{k,\alpha}
\sum_{T<\gamma\le T+H}\max_{\gamma\le \tau_\gamma\le \gamma^+} |\zeta(1/2 +
i\tau_\gamma)|^{2k} \ll_{k,\alpha} H(\log T)^{k^2}. $$ Here $k>1$ is a fixed
integer, $\gamma, \gamma^+$ denote ordinates of consecutive complex zeros of
$\zeta(s)$ and $T^\alpha \le H \le T$, where $\alpha$ is a fixed constant such
that $0<\alpha \le 1$. This sharpens and generalizes a result of M.B.
Milinovich.


title: Nuclear spin relaxation in n-GaAs: from insulating to metallic regime

abstract:
  Nuclear spin relaxation is studied in n-GaAs thick layers and microcavity
samples with different electron densities. We reveal that both in metallic
samples where electrons are free and mobile, and in insulating samples, where
electrons are localized, nuclear spin relaxation is strongly enhanced at low
magnetic field. The origin of this effect could reside in the quadrupole
interaction between nuclei and fluctuating electron charges, that has been
proposed to drive nuclear spin dynamics at low magnetic fields in the
insulating samples. The characteristic values of these magnetic fields are
given by dipole-dipole interaction between nuclei in bulk samples, and are
greatly enhanced in microcavities, presumably due to additional strain,
inherent to micro and nanostructures.


title:
A family of degenerate elliptic operators: maximum principle and its
  consequences

abstract:
  In this paper we investigate the validity and the consequences of the maximum
principle for degenerate elliptic operators whose higher order term is the sum
of "k" eigenvalues of the Hessian. In particular we shed some light on some
very unusual phenomena due to the degeneracy of the operator. We prove moreover
Lipschitz regularity results and boundary estimates for problems in convex
domains which are intersections of ball of same radius. We prove also that
smooth bounded strictly convex domains are part of this class. As a consequence
we obtain the existence of solutions of the Dirichlet problem and of principal
eigenfunctions.


title: Computing arbitrary Lagrangian Eulerian maps for evolving surfaces

abstract:
  The good mesh quality of an evolving discretized surface or domain is often
compromised during time evolution. In recent years this phenomena have been
overcome in a couple of ways, one of them uses arbitrary Lagrangian Eulerian
maps. However, the numerical computation of such maps, without a priori
knowledge, still remained elusive. An algorithm is proposed here to numerically
compute an arbitrary Lagrangian Eulerian map, which helps to preserve the mesh
properties over time. The algorithm is based on finding an equilibrium state of
a mechanical system of springs, which is determined by the connectivity of the
nodes in the mesh. We present various numerical experiments illustrating the
good properties of the algorithm.


title: On the irreducibility of multivariate polynomials

abstract:
  Let (K, v) be a henselian valued field of arbitrary rank. In this paper, we
give an irreducibility criterion for multivariate polynomials over K using
valuation theory.


title:
Fermi Surface Reconstruction in the Electron-doped Cuprate
  Pr(2-x)CexCuO4

abstract:
  We report extensive resistivity, Hall, and magnetoresistance measurements on
thin films of the electron-doped cuprate \PCCO~(PCCO), as a function of doping,
temperature and magnetic field. The doping dependence of the resistivity and
Hall number at low temperatures are characteristic of a system near a quantum
phase transition or a Fermi Surface Reconstruction (FSR) point. The spin
magnetoresistance drops to zero near the critical point. The data presented in
this paper were compiled during the 2004-2007 period but were never published
in this comprehensive form. Because of the recent interest in very similar
results now being found in the normal state of hole-doped cuprates, we believe
the results of our older, mostly unpublished, work will be of interest to the
present community of cuprate researchers. In particular, Fig.11 shows the large
change in Hall number at the FSR point in \PCCO, similar to that found recently
in YBCO and LSCO (See ref[1] and [2]). Also, Fig.6 illustrates how the
resistivity upturn is affected by the FSR. The cause of the resistivity upturn
has been attributed to the loss of carriers at doping below the FSR in the
hole-doped cuprates (see Ref. 3), however, this scenario does not explain the
data for PCCO. The upturn in n-doped cuprates is more-likely due to a
combination of carrier decrease and a change in the scattering rate below the
FSR (see also Ref. 4). The change in spin scattering below the FSR is
illustrated by Fig.18 in this paper. Chen et al. [5] have developed a model
based on spin scattering that is able to explain qualitatively the resistivity
upturn in all the cuprates.


title:
A Unified Method of Detecting Core-Periphery Structure and Community
  Structure in Networks

abstract:
  Core-periphery structure and community structure are two typical meso-scale
structures in complex networks. Though the community detection has been
extensively investigated from different perspectives, the definition and the
detection of core-periphery structure have not received much attention.
Furthermore, the detection problems of the core-periphery and community
structure were separately investigated. In this paper, we develop a unified
framework to simultaneously detect core-periphery structure and community
structure in complex networks. Moreover, there are several extra advantages of
our algorithm: our method can detect not only single but also multiple pairs of
core-periphery structures; the overlapping nodes belonging to different
communities can be identified; different scales of core-periphery structures
can be detected by adjusting the size of core. The good performance of the
method has been validated on synthetic and real complex networks. So we provide
a basic framework to detect the two typical meso-scale structures:
core-periphery structure and community structure.


title:
Intraband memory function and memory-function conductivity formula in
  doped graphene

abstract:
  The generalized self-consistent field method is used to describe intraband
relaxation processes in a general multiband electronic system with presumably
weak residual electron-electron interactions. The resulting memory-function
conductivity formula is shown to have the same structure as the result of a
more accurate approach based on the quantum kinetic equation. The results are
applied to heavily doped and lightly doped graphene. It is shown that the
scattering of conduction electron by phonons leads to the redistribution of the
intraband conductivity spectral weight over a wide frequency range, however, in
a way consistent with the partial transverse conductivity sum rule. The present
form of the intraband memory function is found to describe correctly the
scattering by quantum fluctuations of the lattice, at variance with the
semiclassical Boltzmann transport equations, where this scattering channel is
absent. This is shown to be of fundamental importance in quantitative
understanding of the reflectivity data measured in lightly doped graphene as
well as in different low-dimensional strongly correlated electronic systems,
such as the cuprate superconductors.


title: Supercharacters of queer Lie superalgebras

abstract:
  Let $\mathfrak g=\mathfrak g_{\bar 0}\oplus\mathfrak g_{\bar 1}$ be the queer
Lie superalgebra and let $L$ be a finite-dimensional non-trivial irreducible
$\mathfrak g$-module. Restricting the $\mathfrak g$-action on $L$ to $\mathfrak
g_{\bar 0}$, we show that the space of $\mathfrak g_{\bar 0}$-invariants
$L^{\mathfrak g_{\bar 0}}$ is trivial. As a consequence we establish a
conjecture first formulated by Gorelik, Grantcharov and Mazorchuk on the
triviality of the supercharacter of irreducible $\mathfrak g$-modules in the
case when the modules are finite dimensional.


title: Detecting Byzantine Attacks for Gaussian Two-Way Relay System

abstract:
  This paper focuses on Byzantine attack detection for Gaussian two-way relay
network. In this network, two source nodes communicate with each other with the
help of an amplify-and-forward relay which may perform Byzantine attacks by
forwarding altered symbols to the sources. For simple investigating the
detectability of attacks conducted in Gaussian channels, we focus on the MA
channel of the network, while assuming the BC channel is noiseless. Upon such
model, we propose a attack detection scheme implemented in the sources.
Specifically, we consider a open wireless propagation environment that allows
the symbols, forwarded by the relay, to go through a continuous channel and
arrive to the sources. With the observations of the source, we develop a
detection scheme for the source by comparing the joint empirical distribution
of its received and transmitted signals with the known channel statistics. The
main contribution of this paper is to prove that if and only if the Gaussian
relay network satisfies a non-manipulable channel condition, the proposed
detection scheme can detect arbitrary attacks that allows the stochastic
distributions of altered symbols to vary arbitrarily and depend on each other.
No pre-shared secret or secret transmission is needed for the detection.
Furthermore, we also prove that for the considered Gaussian two-way relay
networks, the non-manipulable channel condition is always satisfied. This
result indicates that arbitrary attacks conducted in MA Gaussian channels are
detectable by only using observations, while providing a base for attack
detection in more general Gaussian networks.


title: Critical exponents of induced Dirichlet forms on self-similar sets

abstract:
  In a previous paper [arXiv:1604.05440], we studied certain random walks on
the hyperbolic graphs $X$ associated with the self-similar sets $K$, and showed
that the discrete energy ${\mathcal E}_X$ on $X$ has an induced energy form
${\mathcal E}_K$ on $K$ that is a Gagliardo-type integral. The domain of
${\mathcal E}_K$ is a Besov space $\Lambda^{\alpha, \beta/2}_{2,2}$ where
$\alpha$ is the Hausdorff dimension of $K$ and $\beta$ is a parameter
determined by the "return ratio" of the random walk. In this paper, we study
the functional relationship of ${\mathcal E}_X$ and ${\mathcal E}_K$. In
particular, we investigate the critical exponents of the $\beta$ in the domain
$\Lambda^{\alpha, \beta/2}_{2,2}$ in order for ${\mathcal E}_K$ to be a regular
Dirichlet form. We provide some criteria to determine the critical exponents
through the effective resistance of the random walk on $X$, and make use of
certain electrical network techniques to calculate the exponents for some
concrete examples.


title:
Fulde-Ferrell-Larkin-Ovchinnikov pairing states between $s$- and
  $p$-orbital fermions

abstract:
  We study pairing states in an largely imbalanced two-component Fermi gas
loaded in an anisotropic two-dimensional optical lattice, where the spin up and
spin down fermions filled to the $s$- and $p_x$-orbital bands, respectively. We
show that due to the relative inversion of band structures of the $s$ and $p_x$
orbitals, the system favors pairing between two fermions on the same side of
the Brillouin zone, leading to a large stable regime for states with finite
center-of-mass momentum, i.e., the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)
state. In particular, when the two Fermi surfaces are close in momentum space,
a nesting effect stabilizes a special kind of $\pi$-FFLO phase with spatial
modulation of $\pi$ along the easily tunneled $x$-direction. We map out the
zero temperature phase diagrams within mean-field approach for various aspect
ratio within the two-dimensional plane, and calculate the
Berezinskii-Kosterlitz-Thouless (BKT) transition temperatures $T_{\rm BKT}$ for
different phases.


title: Linear Response Theory: A Modern Analytic-Algebraic Approach

abstract:
  Linear response theory is a tool with which one can study systems that are
driven out of equilibrium by external perturbations. This monograph presents a
thoroughly modern framework to make linear response theory rigorous for a wide
array of systems, that is suitable for novel applications such as periodic and
random light conductors not yet covered in the literature. Our
analytic-algebraic approach, based on von Neumann algebras and associated
non-commutative $L^p$-spaces, can deal with discrete and continuous models
alike, and include effects of disorder. First, we explain the mathematical
setting, give a complete list of our hypotheses and state the main results,
which include Kubo and Kubo-Streda formulas. To make our book accessible to a
wide audience, we spend Chapters 3 and 4 explaining the mathematical
underpinnings such as non-commutative $L^p$- and Sobolev spaces, and
generalized commutators. Furthermore, we show how to construct a von Neumann
algebras from a topological dynamical system and a 2-cocycle, a procedure which
applies to discrete and continuous quantum systems. We dedicate Chapters 5 and
6 to the proofs of our main results. We close the book by sketching a novel
application, linear response theory for periodic and random light conductors.
This monograph is aimed at advanced students in mathematical physics and
researchers.


title: Memristor Threshold Logic: An Overview to Challenges and Applications

abstract:
  Once referred to as the missing circuit component, memristor has come long
way across to be recognized and taken as important to future circuit designs.
The memristor due to its ability to memorize the state, switch between
different resistance level, smaller size and low leakage currents makes it
useful for a wide range of intelligent memory and computing applications. This
overview paper highlights broadly provides the uses of memristor in the
implementation of cognitive cells for different imaging and pattern matching
applications.


title: An irreducibility criterion for integer polynomials

abstract:
  Let $f(x) = \sum\limits _{i=0}^{n} a_i x^i $ be a polynomial with
coefficients from the ring $\mathbb{Z}$ of integers satisfying either $(i)$ $0
< a_0 \leq a_{1} \leq \cdots \leq a_{k-1} < a_{k} < a_{k+1} \leq \cdots \leq
a_n$ for some $k$, $0 \leq k \leq n-1$; or $(ii)$ $|a_n| > |a_{n-1}| + \cdots +
|a_{0}|$ with $a_0 \neq 0$. In this paper, it is proved that if $|a_n|$ or
$|f(m)|$ is a prime number for some integer $m$ with $|m|\geq 2 $ then the
polynomial $f(x)$ is irreducible over $\mathbb{Z}$.


title:
Odd-petal states and persistent flows in spin-orbit-coupled
  Bose-Einstein condensates

abstract:
  We study the phase diagram of a Rashba spin-orbit-coupled Bose-Einstein
condensate confined in a two-dimensional toroidal trap. In the immiscible
regime we find an azimuthally periodic density distribution, with the
periodicity highly tuneable as a function of the spin-orbit coupling strength
and which favours an odd number of petals in each component. This allows for a
wide range of states that can be created. We further show that in the miscible
regime, both components possess states with persistent flows with a unit
winding number difference between them and with the absolute values of these
winding numbers depending on the spin-orbit coupling strength. All features of
the odd-petal and the persistent flow states can be explained using a simple
but effective model.


title: Turbulent channel flow of a dense binary mixture of rigid particles

abstract:
  We study turbulent channel flow of a binary mixture of finite-size
neutrally-buoyant rigid particles by means of interface-resolved direct
numerical simulations. We fix the bulk Reynolds number and total solid volume
fraction, $Re_b = 5600$ and $\Phi=20\%$, and vary the relative fraction of
small and large particles. The binary mixture consists of particles of two
different sizes, $2h/d_l=20$ and $2h/d_s=30$ where $h$ is the half channel
height and $d_l$ and $d_s$ the diameter of the large and small particles. While
the particulate flow statistics exhibit a significant alteration of the mean
velocity profile and turbulent fluctuations with respect to the unladen flow,
the differences between the mono-disperse and bi-disperse cases are small.
However, we observe a clear segregation of small particles at the wall in
binary mixtures, which affects the dynamics of the near wall region and thus
the overall drag. This results in a higher drag in suspensions with a larger
amount of large particles. As regards bi-disperse effects on the particle
dynamics, a non-monotonic variation of the particle dispersion in the spanwise
(homogeneous) direction is observed when increasing the percentage of
small/large particles. Finally, we note that particles of the same size tend to
cluster more at contact whereas the dynamics of the large particles gives
highest collision kernels due to a higher approaching speed.


title: Quantum Friction in Arbitrarily Directed Motion

abstract:
  Quantum friction, the electromagnetic fluctuation-induced frictional force
decelerating an atom which moves past a macroscopic dielectric body, has so far
eluded experimental evidence despite more than three decades of theoretical
studies. Inspired by the recent finding that dynamical corrections to such an
atom's internal dynamics are enhanced by one order of magnitude for vertical
motion -- compared to the paradigmatic setup of parallel motion -- we
generalize quantum friction calculations to arbitrary angles between the atom's
direction of motion and the surface in front of which it moves. Motivated by
the disagreement between quantum friction calculations based on Markovian
quantum master equations and time-dependent perturbation theory, we carry out
our derivations of the quantum frictional force for arbitrary angles employing
both methods and compare them.


title:
Pairwise mode entanglement in Schwinger production of
  particle-antiparticle pairs in an electric field

abstract:
  Quantum entanglement is the characteristic quantum correlation. Here we use
this concept to analyze the quantum entanglement generated by Schwinger
production of particle-antiparticle pairs in an electric field, as well as the
change of mode entanglement as a consequence of the electric field effect on an
entangled pair of particles. The system is partitioned by using momentum modes.
Various kinds of pairwise mode entanglement are calculated as functions of the
electric field. Both constant and pulsed electric fields are considered. The
use of entanglement exposes information beyond that in particle number
distributions.


title:
Statistical mechanics of unsupervised feature learning in a restricted
  Boltzmann machine with binary synapses

abstract:
  Revealing hidden features in unlabeled data is called unsupervised feature
learning, which plays an important role in pretraining a deep neural network.
Here we provide a statistical mechanics analysis of the unsupervised learning
in a restricted Boltzmann machine with binary synapses. A message passing
equation to infer the hidden feature is derived, and furthermore, variants of
this equation are analyzed. A statistical analysis by replica theory describes
the thermodynamic properties of the model. Our analysis confirms an entropy
crisis preceding the non-convergence of the message passing equation,
suggesting a discontinuous phase transition as a key characteristic of the
restricted Boltzmann machine. Continuous phase transition is also confirmed
depending on the embedded feature strength in the data. The mean-field result
under the replica symmetric assumption agrees with that obtained by running
message passing algorithms on single instances of finite sizes. Interestingly,
in an approximate Hopfield model, the entropy crisis is absent, and a
continuous phase transition is observed instead. We also develop an iterative
equation to infer the hyper-parameter (temperature) hidden in the data, which
in physics corresponds to iteratively imposing Nishimori condition. Our study
provides insights towards understanding the thermodynamic properties of the
restricted Boltzmann machine learning, and moreover important theoretical basis
to build simplified deep networks.

categories: cs.LG cond-mat.dis-nn cond-mat.stat-mech cs.NE q-bio.NC


title: Biological signaling by interfacial sound pulses. A physics approach

abstract:
  Biological signaling is imagined as a combination of activation and
transport. The former is triggered by local molecular interactions and the
latter is the result of molecular diffusion. However, other fundamental
physical principles of communication have yet to be addressed. We have recently
shown, that lipid interfaces allow for the excitation and propagation of sound
pulses. Here we demonstrate, that these reversible perturbations can control
the activity of membrane embedded enzymes without the necessity of molecular
transport. They therefore allow for the rapid communication between distant
biological entities (e.g. receptor and enzyme) at the speed of sound, which is
here in the order of 1 m/s within the membrane. The mechanism reported provides
a new physical framework for biological signaling.


title:
Tropical Vorticity Forcing and Superrotation in the Spherical Shallow
  Water Equations

abstract:
  The response of the nonlinear shallow water equations (SWE) on a sphere to
tropical vorticity forcing is examined with an emphasis on momentum fluxes and
the emergence of a superrotating (SR) state. Fixing the radiative damping and
momentum drag timescales to be of the order of a few days, a state of SR is
shown to emerge under steady large-scale and random small-scale vorticity
forcing. In the first example, the stationary response to a pair of equal and
oppositely signed vortices placed on the equator is considered. Here, the
equatorial flux budget is dominated by the eddy fluxes and these drive the
system into a state of SR. Eventually, the flux associated with the momentum
drag increases to balance the eddy fluxes, resulting in a steady state with a
SR jet at the equator. The initial value problem with these twin vortices also
exhibits SR driven by eddy fluxes. Curiously, this transient solution
spontaneously propagates westward and continually circumnavigates the globe. It
is worth emphasizing that this SR state does not rely on any particular form of
dissipation at large scales, and is in fact observed even in the absence of any
large-scale damping mechanism. In the second example, a random small-scale
vorticity forcing is applied across the tropics. The statistically steady state
obtained is fairly turbulent in nature, but here too, the eddy fluxes dominate,
and the system exhibits SR. It is important to note that in both these cases,
the direct forcing of the zonal mean zonal flow is zero by construction, and
the eddy fluxes at the equator are responsible for its eastward acceleration.
Further, in both these examples, the rotational part of the flow dominates the
momentum fluxes as well as the stationary zonal mean zonal flow itself.
Arguments based on the nature of potential vorticity and enstrophy are put
forth to shed some light on these results.


title: Weighted Matrix Completion and Recovery with Prior Subspace Information

abstract:
  An incoherent low-rank matrix can be efficiently reconstructed after
observing a few of its entries at random, and then solving a convex program
that minimizes the nuclear norm. In many applications, in addition to these
entries, potentially valuable prior knowledge about the column and row spaces
of the matrix is also available to the practitioner. In this paper, we
incorporate this prior knowledge in matrix completion---by minimizing a
weighted nuclear norm---and precisely quantify any improvements. In particular,
we find in theory that reliable prior knowledge reduces the sample complexity
of matrix completion by a logarithmic factor, and the observed improvement in
numerical simulations is considerably more magnified. We also present similar
results for the closely related problem of matrix recovery from generic linear
measurements.


title: On the power domination number of de Bruijn and Kautz digraphs

abstract:
  Let $G=(V,A)$ be a directed graph without parallel arcs, and let $S\subseteq
V$ be a set of vertices. Let the sequence $S=S_0\subseteq S_1\subseteq
S_2\subseteq\cdots$ be defined as follows: $S_1$ is obtained from $S_0$ by
adding all out-neighbors of vertices in $S_0$. For $k\geqslant 2$, $S_k$ is
obtained from $S_{k-1}$ by adding all vertices $w$ such that for some vertex
$v\in S_{k-1}$, $w$ is the unique out-neighbor of $v$ in $V\setminus S_{k-1}$.
We set $M(S)=S_0\cup S_1\cup\cdots$, and call $S$ a \emph{power dominating set}
for $G$ if $M(S)=V(G)$. The minimum cardinality of such a set is called the
\emph{power domination number} of $G$. In this paper, we determine the power
domination numbers of de Bruijn and Kautz digraphs.


title:
Geometric explanation of anomalous finite-size scaling in high
  dimensions

abstract:
  We give an intuitive geometric explanation for the apparent breakdown of
standard finite-size scaling in systems with periodic boundaries above the
upper critical dimension. The Ising model and self-avoiding walk are simulated
on five-dimensional hypercubic lattices with free and periodic boundary
conditions, by using geometric representations and recently introduced
Markov-chain Monte Carlo algorithms. We show that previously observed anomalous
behaviour for correlation functions, measured on the standard Euclidean scale,
can be removed by defining correlation functions on a scale which correctly
accounts for windings.


title:
Multipoint Green's functions in 1+1 dimensional integrable quantum field
  theories

abstract:
  We calculate the multipoint Green functions in 1+1 dimensional integrable
quantum field theories. We use the crossing formula for general models and
calculate the 3 and 4 point functions taking in to account only the lower
nontrivial intermediate states contributions. Then we apply the general results
to the examples of the scaling $Z_{2}$ Ising model, sinh-Gordon model and
$Z_{3}$ scaling Ising model. We demonstrate this calculations explicitly. The
results can be applied to physical phenomena as for example to the Raman
scattering.


title:
On thermodynamics of viscoelastic rate type fluids with temperature
  dependent material coefficients

abstract:
  We derive a class of thermodynamically consistent variants of
Maxwell/Oldroyd-B type models for viscoelastic fluids. In particular, we study
the models that allow one to consider temperature dependent material
coefficients. This naturally calls for the formulation of a temperature
evolution equation that would accompany the evolution equations for the
mechanical quantities. The evolution equation for the temperature is explicitly
formulated, and it is shown to be consistent with the laws of thermodynamics
and the evolution equations for the mechanical quantities. The temperature
evolution equation contains terms that are ignored or even not thought of in
most of the works dealing with this class of fluids. The impact of the
additional terms in the temperature evolution equation on the flow dynamics is
documented by the solution of simple initial/boundary value problems.


title: Deep Stereo Matching with Dense CRF Priors

abstract:
  Stereo reconstruction from rectified images has recently been revisited
within the context of deep learning. Using a deep Convolutional Neural Network
to obtain patch-wise matching cost volumes has resulted in state of the art
stereo reconstruction on classic datasets like Middlebury and Kitti. By
introducing this cost into a classical stereo pipeline, the final results are
improved dramatically over non-learning based cost models. However these
pipelines typically include hand engineered post processing steps to
effectively regularize and clean the result. Here, we show that it is possible
to take a more holistic approach by training a fully end-to-end network which
directly includes regularization in the form of a densely connected Conditional
Random Field (CRF) that acts as a prior on inter-pixel interactions. We
demonstrate that our approach on both synthetic and real world datasets
outperforms an alternative end-to-end network and compares favorably to more
hand engineered approaches.


title: The stability of relativistic stars and the role of the adiabatic index

abstract:
  We study the stability of three analytical solutions of the Einstein's field
equations for spheres of fluid. These solutions are suitable to describe
compact objects including white dwarfs, neutron stars and supermassive stars
and they have been extensively employed in the literature. We re-examine the
range of stability of the Tolman VII solution, we focus on the stability of the
Buchdahl solution which is under contradiction in the literature and we examine
the stability of the Nariai IV solution. We found that all the mentioned
solutions are stable in an extensive range of the compactness parameter. We
also concentrate on the effect of the adiabatic index on the instability
condition. We found that the critical adiabatic index, depends linearly on the
ratio of central pressure over central energy density $P_c/{\cal E}_c$, up to
high values of the compactness. Finally, we examine the possibility to impose
constraints, via the adiabatic index, on realistic equations of state in order
to ensure stable configurations of compact objects.


title: Scaling Properties of Polycrystalline Graphene: A Review

abstract:
  We present an overview of the electrical, mechanical, and thermal properties
of polycrystalline graphene. Most global properties of this material, such as
the charge mobility, thermal conductivity, or Young's modulus, are sensitive to
its microstructure, for instance the grain size and the presence of line or
point defects. Both the local and global features of polycrystalline graphene
have been investigated by a variety of simulations and experimental
measurements. In this review, we summarize the properties of polycrystalline
graphene, and by establishing a perspective on how the microstructure impacts
its large-scale physical properties, we aim to provide guidance for further
optimization and improvement of applications based on this material, such as
flexible and wearable electronics, and high-frequency or spintronic devices.


title: Focusing in Orthologic

abstract:
  We propose new sequent calculus systems for orthologic (also known as minimal
quantum logic) which satisfy the cut elimination property. The first one is a
simple system relying on the involutive status of negation. The second one
incorporates the notion of focusing (coming from linear logic) to add
constraints on proofs and to optimise proof search. We demonstrate how to take
benefits from the new systems in automatic proof search for orthologic.


title: Breakdown of Fermi liquid theory in topological multi-Weyl semimetals

abstract:
  Fermi liquid theory works very well in most normal metals, but is found
violated in many strongly correlated electron systems, such as cuprate and
heavy-fermion superconductors. A widely accepted criterion is that, the Fermi
liquid theory is valid when the interaction-induced fermion damping rate
approaches zero more rapidly than the energy. Otherwise, it is invalid. Here,
we demonstrate that this criterion breaks down in topological double-and
triple-Weyl semimetals. Renormalization group analysis reveals that, although
the damping rate of double- and triple-Weyl fermions induced by the Coulomb
interaction approaches zero more rapidly than the energy, the quasiparticle
residue vanishes and the Fermi liquid theory is invalid. This behavior
indicates a weaker-than-marginal violation of the Fermi liquid theory. Such an
unconventional non-Fermi liquid state originates from the special dispersion of
double- and triple-Weyl fermions, and is qualitatively different from all the
other Fermi-liquid and non-Fermi-liquid states. The predicted properties of the
fermion damping rate and the spectral function can be probed by the
angle-resolved photoemission spectroscopy. The density of states, specific
heat, and conductivities are also calculated and analyzed after incorporating
the corrections induced by the Coulomb interaction.


title: The BMS Bootstrap

abstract:
  We initiate a study of the bootstrap programme for field theories with BMS
symmetry. Specifically, we look at two-dimensional field theories with BMS3
symmetry and, using highest weight representations, we construct the BMS
bootstrap equation by formulating the notion of crossing symmetry in the
four-point functions of these field theories. In the limit of large central
charges, we find analytic expressions for the BMS blocks that are the basic
ingredients for the solution of the bootstrap equation. This constitutes, to
the best of our knowledge, the first example of the formulation and significant
steps towards the solution of a bootstrap equation in a theory which is not a
relativistic conformal field theory.


title: Generalized Artin-Mumford curves over finite fields

abstract:
  Let $\mathbb{F}_q$ be the finite field of order $q=p^h$ with $p>2$ prime and
$h>1$, and let $\mathbb{F}_{\bar{q}}$ be a subfield of $\mathbb{F}_q$. From any
two $\bar{q}$-linearized polynomials $L_1,L_2 \in \overline{\mathbb{F}}_q[T]$
of degree $q$, we construct an ordinary curve $\mathcal{X}_{(L_1,L_2)}$ of
genus $(q-1)^2$ which is a generalized Artin-Schreier cover of the projective
line $\mathbb{P}^1$. The automorphism group of $\mathcal{X}_{(L_1,L_2)}$ over
the algebraic closure $\overline{\mathbb{F}}_q$ of $\mathbb{F}_q$ contains a
semidirect product $\Sigma \rtimes \Gamma$ of an elementary abelian $p$-group
$\Sigma$ of order $q^2$ by a cyclic group $\Gamma$ of order $\bar{q}-1$. We
show that for $L_1 \neq L_2$, $\Sigma \rtimes \Gamma$ is the full automorphism
group ${\rm Aut}(\mathcal{X}_{(L_1,L_2)})$ over $\overline{\mathbb{F}}_q$; for
$L_1=L_2$ there exists an extra involution and ${\rm
Aut}(\mathcal{X}_{(L_1,L_1)})=\Sigma \rtimes \Delta$ with a dihedral group
$\Delta$ of order $2(\bar{q}-1)$ containing $\Gamma$. Two different choices of
the pair $\{L_1,L_2\}$ may produce birationally isomorphic curves, even for
$L_1=L_2$. We prove that any curve of genus $(q-1)^2$ whose
$\overline{\mathbb{F}}_q$-automorphism group contains an elementary abelian
subgroup of order $q^2$ is birationally equivalent to $\mathcal{X}_{(L_1,
L_2)}$ for some separable $\bar{q}$-linearized polynomials $L_1,L_2$ of degree
$q$. We produce an analogous characterization in the special case $L_1=L_2$.
This extends a result on the Artin-Mumford curves, due to Arakelian and
Korchm\'aros.


title: Right-angled Artin groups and full subgraphs of graphs

abstract:
  For a finite graph $\Gamma$, let $G(\Gamma)$ be the right-angled Artin group
defined by the complement graph of $\Gamma$. We show that, for any linear
forest $\Lambda$ and any finite graph $\Gamma$, $G(\Lambda)$ can be embedded
into $G(\Gamma)$ if and only if $\Lambda$ can be realised as a full subgraph of
$\Gamma$. We also prove that if we drop the assumption that $\Lambda$ is a
linear forest, then the above assertion does not hold, namely, for any finite
graph $\Lambda$, which is not a linear forest, there exists a finite graph
$\Gamma$ such that $G(\Lambda)$ can be embedded into $G(\Gamma)$, though
$\Lambda$ cannot be embedded into $\Gamma$ as a full subgraph.


title: Moduli spaces, indecomposable objects and potentials over a finite field

abstract:
  Given a linear category over a finite field such that the moduli space of its
objects is a smooth Artin stack (and some additional conditions) we give
formulas for an exponential sum over the set of absolutely indecomposable
objects and a stacky sum over the set of all objects of the category,
respectively, in terms of the geometry of the cotangent bundle on the moduli
stack. The first formula was inspired by the work of Hausel, Letellier, and
Rodriguez-Villegas. It provides a new approach for counting absolutely
indecomposable quiver representations, vector bundles with parabolic structure
on a projective curve, and irreducible etale local systems (via a result of
Deligne). Our second formula resembles formulas appearing in the theory of
Donaldson-Thomas invariants.


title:
Do we really need to catch them all? A new User-guided Social Media
  Crawling method

abstract:
  With the growing use of popular social media services like Facebook and
Twitter it is challenging to collect all content from the networks without
access to the core infrastructure or paying for it. Thus, if all content cannot
be collected one must consider which data are of most importance. In this work
we present a novel User-guided Social Media Crawling method (USMC) that is able
to collect data from social media, utilizing the wisdom of the crowd to decide
the order in which user generated content should be collected to cover as many
user interactions as possible. USMC is validated by crawling 160 public
Facebook pages, containing content from 368 million users including 1.3 billion
interactions, and it is compared with two other crawling methods. The results
show that it is possible to cover approximately 75% of the interactions on a
Facebook page by sampling just 20% of its posts, and at the same time reduce
the crawling time by 53%. In addition, the social network constructed from the
20% sample contains more than 75% of the users and edges compared to the social
network created from all posts, and it has similar degree distribution.


title:
A review of geometric, topological and graph theory apparatuses for the
  modeling and analysis of biomolecular data

abstract:
  Geometric, topological and graph theory modeling and analysis of biomolecules
are of essential importance in the conceptualization of molecular structure,
function, dynamics, and transport. On the one hand, geometric modeling provides
molecular surface and structural representation, and offers the basis for
molecular visualization, which is crucial for the understanding of molecular
structure and interactions. On the other hand, it bridges the gap between
molecular structural data and theoretical/mathematical models. Topological
analysis and modeling give rise to atomic critical points and connectivity, and
shed light on the intrinsic topological invariants such as independent
components (atoms), rings (pockets) and cavities. Graph theory analyzes
biomolecular interactions and reveals biomolecular structure-function
relationship. In this paper, we review certain geometric, topological and graph
theory apparatuses for biomolecular data modeling and analysis. These
apparatuses are categorized into discrete and continuous ones. For discrete
approaches, graph theory, Gaussian network model, anisotropic network model,
normal mode analysis, quasi-harmonic analysis, flexibility and rigidity index,
molecular nonlinear dynamics, spectral graph theory, and persistent homology
are discussed. For continuous mathematical tools, we present discrete to
continuum mapping, high dimensional persistent homology, biomolecular geometric
modeling, differential geometry theory of surfaces, curvature evaluation,
variational derivation of minimal molecular surfaces, atoms in molecule theory
and quantum chemical topology. Four new approaches, including analytical
minimal molecular surface, Hessian matrix eigenvalue map, curvature map and
virtual particle model, are introduced for the first time to bridge the gaps in
biomolecular modeling and analysis.


title:
Fine structure of the spectra of the Kondo lattice model: two-site
  cellular DMFT study

abstract:
  We study the antiferromagnetic and the paramagnetic Kondo insulator phases of
the Kondo lattice model on the cubic lattice at half-filling using the cellular
dynamical mean-field theory (CDMFT) with numerical renormalization group (NRG)
as the impurity solver, focusing on the fine details of the spectral function
and self-energy. We find that the non-local correlations increase the gap in
both the antiferromagnetic and the Kondo insulator phase and shrink the extent
of the antiferromagnetic phase in the phase diagram but do not alter any
properties qualitatively. The agreement between the numerical CDMFT results and
those within a simple hybridization picture, which adequately describes the
overall band structure of the system but neglects all effects on the
inelastic-scattering processes, is similar to that of the single-site DMFT
results; there are deviations that are responsible for the additional fine
structure, in particular for the asymmetric spectral resonances or dips that
become more pronounced in the strong-coupling regime close to the
antiferromagnet-paramagnetic quantum phase transition. These features appear
broader in the CDMFT mostly due to numerical artifacts linked to more
aggressive state truncation required in the NRG.


title:
Dynamical scaling for underdamped strain order parameters quenched below
  first-order phase transitions

abstract:
  In the conceptual framework of phase ordering after temperature quenches
below transition, we consider the underdamped Bales-Gooding-type 'momentum
conserving' dynamics of a 2D martensitic structural transition from a
square-to-rectangle unit cell. The one-component or $N_{\rm OP} =1$ order
parameter is one of the physical strains, and the Landau free energy has a
triple well, describing a first-order transition. We numerically study the
evolution of the strain-strain correlation, and find that it exhibits dynamical
scaling, with a coarsening length $L(t) \sim t^{\alpha}$. We find at
intermediate and long times that the coarsening exponent sequentially takes on
respective values close to $\alpha=2/3$ and $\alpha=1/2$. For deep quenches,
the coarsening can be arrested at long times, with $\alpha \simeq 0$. These
exponents are also found in 3D. To understand such behaviour, we insert a
dynamical-scaling ansatz into the correlation function dynamics to give, at a
dominant scaled separation, a nonlinear kinetics of the curvature $g (t) \equiv
1/ L(t)$. The curvature solutions have time windows of power-law decays $g \sim
1/t^\alpha$, with exponent values $\alpha$ matching simulations, and manifestly
independent of spatial dimension. Applying this curvature-kinetics method to
mass-conserving Cahn-Hilliard dynamics for a double-well Landau potential in a
scalar $N_{\rm OP}=1$ order parameter yields exponents $\alpha = 1/4$ and $1/3$
for intermediate and long times. For vector order parameters with $N_{\rm OP}
\geq 2$, the exponents are $\alpha = 1/4$ only, consistent with previous work.
The curvature kinetics method could be useful in extracting coarsening
exponents for other phase-ordering dynamics.


title: Geometry of Special Galileon

abstract:
  Theory known as Special Galileon has recently attracted considerable interest
due to its peculiar properties. It has been shown that it represents an
extremal member of the set of effective field theories with enhanced soft
limit. This property makes its tree-level S-matrix fully on-shell
reconstructible and representable by means of the Cachazo-He-Yuan
representation. The enhanced soft limit is a consequence of new hidden symmetry
of the Special Galileon action, however, until now, the origin of this peculiar
symmetry has remained unclear. In this paper we interpret this symmetry as a
special transformation of the coset space $GAL(D,1)/SO(1,D-1)$ and show, that
there exists a three-parametric family of invariant Galileon actions. The
latter family is closed under duality which appears as a natural generalization
of the above mentioned symmetry. We also present a geometric construction of
the Special Galileon action using $D$-dimensional brane propagating in
$2D$-dimensional flat pseudo-riemannian space. Within such framework, the
Special Galileon symmetry emerges as an $U(1,D-1)$ symmetry of the target
space, which can be treated as a $D$-dimensional K\"ahler manifold. Such a
treatment allows for classification of the higher order invariant Lagrangians
needed as counterterms on the quantum level. We also briefly comment on
relation between such higher order Lagrangians and the Lagrangians invariant
with respect to the polynomial shift symmetry.


title:
SALT observations of the Chromospheric Activity of Transiting Planet
  Hosts: Mass Loss and Star Planet Interactions

abstract:
  We measured the chromospheric activity of the four hot Jupiter hosts WASP-43,
WASP-51/HAT-P-30, WASP-72 & WASP-103 to search for anomalous values caused by
the close-in companions. The Mount Wilson Ca II H&K S-index was calculated for
each star using observations taken with the Robert Stobie Spectrograph at the
Southern African Large Telescope. The activity level of WASP-43 is anomalously
high relative to its age and falls among the highest values of all known main
sequence stars. We found marginal evidence that the activity of WASP-103 is
also higher than expected from the system age. We suggest that for WASP-43 and
WASP-103 star-planet interactions (SPI) may enhance the Ca II H&K core
emission. The activity levels of WASP-51/HAT-P-30 and WASP-72 are anomalously
low, with the latter falling below the basal envelope for both main sequence
and evolved stars. This can be attributed to circumstellar absorption due to
planetary mass loss, though absorption in the ISM may contribute. A quarter of
known short period planet hosts exhibit anomalously low activity levels,
including systems with hot Jupiters and low mass companions. Since SPI can
elevate and absorption can suppress the observed chromospheric activity of
stars with close-in planets, their Ca II H&K activity levels are an unreliable
age indicator. Systems where the activity is depressed by absorption from
planetary mass loss are key targets for examining planet compositions through
transmission spectroscopy.


title:
Instabilities and spin-up behaviour of a rotating magnetic field driven
  flow in a rectangular cavity

abstract:
  This study presents numerical simulations and experiments considering the
flow of an electrically conducting fluid inside a cube driven by a rotating
magnetic field (RMF). The investigations are focused on the spin-up, where a
liquid metal (GaInSn) is suddenly exposed to an azimuthal body force generated
by the RMF, and the subsequent flow development. The numerical simulations rely
on a semi-analytical expression for the induced electromagnetic force density
in an electrically conducting medium inside a cuboid container with insulating
walls. Velocity distributions in two perpendicular planes are measured using a
novel dual-plane, two-component ultrasound array Doppler velocimeter (UADV)
with continuous data streaming, enabling long term measurements for
investigating transient flows. This approach allows to identify the main
emerging flow modes during the transition from a stable to unstable flow
regimes with exponentially growing velocity oscillations using the Proper
Orthogonal Decomposition (POD) method.
  Characteristic frequencies in the oscillating flow regimes are determined in
the super critical range above the critical magnetic Taylor number $Ta_c
\approx 1.26 \times 10^5$, where the transition from the steady double vortex
structure of the secondary flow to an unstable regime with exponentially
growing oscillations is detected.
  The mean flow structures and the temporal evolution of the flow predicted by
the numerical simulations and observed in experiments are in very good
agreement.


title:
Rational torus-equivariant stable homotopy IV: thick tensor ideals and
  the Balmer spectrum for finite spectra

abstract:
  We classify thick tensor ideals of finite objects in the category of rational
torus-equivariant spectra, showing that they are completely determined by
geometric isotropy. This is essentially equivalent to showing that the Balmer
spectrum is the set of closed subgroups under cotoral inclusion. Corresponding
statements are deduced for toral spectra for general groups.


title: Complemented subspaces of homogeneous polynomials

abstract:
  Let $\mathcal{P}_{K} (^{n}E; F)$ (resp. $\mathcal{P}_{w} (^{n}E; F)$) the
subspace of all $P\in \mathcal{P}(^{n}E; F)$ which are compact (resp. weakly
continuous on bounded sets). We show that if $\mathcal{P}_{K} (^{n}E; F)$
contains an isomorphic copy of $c_{0}$, then $\mathcal{P}_{K} (^{n}E; F)$ is
not complemented in $\mathcal{P}(^{n}E; F)$. Likewise we show that if
$\mathcal{P}_{w} (^{n}E; F)$ contains an isomorphic copy of $c_{0}$, then
$\mathcal{P}_{w}(^{n}E; F)$ is not complemented in $\mathcal{P}(^{n}E; F)$.


title: Force on slowly moving variable electric or magnetic dipoles in vacuo

abstract:
  The force on electric and magnetic dipoles moving in vacuo is discussed in
the general case of time-variable non-uniform fields and time-variable dipole
moments, to first order in v/c and neglecting radiation reaction. Emphasis is
given to the symmetry between electric and magnetic dipoles, justifying in
general Amp\`ere's equivalence principle, and showing that the difference
between gilbertian and amperian dipoles (in vacuo) is only a question of
interpretation. The expression for the force can be expressed in a variety of
different forms, and each term of each form is susceptible of specific physical
interpretations. Terms not described in the literature are pointed out. A
possible experiment for verifying the (dual-Lorentz) force of an electric field
on a magnetic current (and then "hidden momentum") is proposed.


title:
Listen and Translate: A Proof of Concept for End-to-End Speech-to-Text
  Translation

abstract:
  This paper proposes a first attempt to build an end-to-end speech-to-text
translation system, which does not use source language transcription during
learning or decoding. We propose a model for direct speech-to-text translation,
which gives promising results on a small French-English synthetic corpus.
Relaxing the need for source language transcription would drastically change
the data collection methodology in speech translation, especially in
under-resourced scenarios. For instance, in the former project DARPA TRANSTAC
(speech translation from spoken Arabic dialects), a large effort was devoted to
the collection of speech transcripts (and a prerequisite to obtain transcripts
was often a detailed transcription guide for languages with little standardized
spelling). Now, if end-to-end approaches for speech-to-text translation are
successful, one might consider collecting data by asking bilingual speakers to
directly utter speech in the source language from target language text
utterances. Such an approach has the advantage to be applicable to any
unwritten (source) language.


title:
A distinct magnetic property of the inner penumbral boundary. II.
  Formation of a penumbra at the expense of a pore

abstract:
  We recently presented evidence that stable umbra-penumbra boundaries are
characterised by a distinct canonical value of the vertical component of the
magnetic field, $B^{\rm stable}_{\rm ver}$. In order to trigger the formation
of a penumbra, large inclinations in the magnetic field are necessary. In
sunspots, the penumbra develops and establishes by colonising both umbral areas
and granulation, that is, penumbral magneto-convection takes over in umbral
regions with $B_{\rm ver} < B^{\rm stable}_{\rm ver}$, as well as in granular
convective areas. Eventually, a stable umbra-penumbra boundary settles at
$B^{\rm stable}_{\rm ver}$. Here, we aim to study the development of a penumbra
initiated at the boundary of a pore, where the penumbra colonises the entire
pore ultimately. We have used Hinode/SOT G-band images to study the evolution
of the penumbra. Hinode/SOT spectropolarimetric data were used to infer the
magnetic field properties in the studied region. The penumbra forms at the
boundary of a pore located close to the polarity inversion line of NOAA\,10960.
As the penumbral bright grains protrude into the pore, the magnetic flux in the
forming penumbra increases at the expense of the pore magnetic flux.
Consequently, the pore disappears completely giving rise to an orphan penumbra.
At all times, the vertical component of the magnetic field in the pore is
smaller than $B^{\rm stable}_{\rm ver} \approx 1.8$~kG. Our findings are in an
agreement with the need of $B^{\rm stable}_{\rm ver}$ for establishing a stable
umbra-penumbra boundary: while $B_{\rm ver}$ in the pore is smaller than
$B^{\rm stable}_{\rm ver}$, the protrusion of penumbral grains into the pore
area is not blocked, a stable pore-penumbra boundary does not establish, and
the pore is fully overtaken by the penumbral magneto-convective mode. This
scenario could also be one of the mechanisms giving rise to orphan penumbrae.


abstract:
  Scarce data is a major challenge to scaling robot learning to truly complex
tasks, as we need to generalize locally learned policies over different
"contexts". Bayesian optimization approaches to contextual policy search (CPS)
offer data-efficient policy learning that generalize over a context space. We
propose to improve data-efficiency by factoring typically considered contexts
into two components: target-type contexts that correspond to a desired outcome
of the learned behavior, e.g. target position for throwing a ball; and
environment type contexts that correspond to some state of the environment,
e.g. initial ball position or wind speed. Our key observation is that
experience can be directly generalized over target-type contexts. Based on that
we introduce Factored Contextual Policy Search with Bayesian Optimization for
both passive and active learning settings. Preliminary results show faster
policy generalization on a simulated toy problem. A full paper extension is
available at arXiv:1904.11761


title: Formulas of Szeg\H{o} type for the periodic Schr\"odinger operator

abstract:
  We prove asymptotic formulas of Szeg\H{o} type for the periodic Schr\"odinger
operator $H=-\frac{d^2}{dx^2}+V$ in dimension one. Admitting fairly general
functions $h$ with $h(0)=0$, we study the trace of the operator
$h(\chi_{(-\alpha,\alpha)}\chi_{(-\infty,\mu)}(H)\chi_{(-\alpha,\alpha)})$ and
link its subleading behaviour as $\alpha\to\infty$ to the position of the
spectral parameter $\mu$ relative to the spectrum of $H$.


title: Deterministic Indexing for Packed Strings

abstract:
  Given a string $S$ of length $n$, the classic string indexing problem is to
preprocess $S$ into a compact data structure that supports efficient subsequent
pattern queries. In the \emph{deterministic} variant the goal is to solve the
string indexing problem without any randomization (at preprocessing time or
query time). In the \emph{packed} variant the strings are stored with several
character in a single word, giving us the opportunity to read multiple
characters simultaneously. Our main result is a new string index in the
deterministic \emph{and} packed setting. Given a packed string $S$ of length
$n$ over an alphabet $\sigma$, we show how to preprocess $S$ in $O(n)$
(deterministic) time and space $O(n)$ such that given a packed pattern string
of length $m$ we can support queries in (deterministic) time $O\left(m/\alpha +
\log m + \log \log \sigma\right), $ where $\alpha = w / \log \sigma$ is the
number of characters packed in a word of size $w = \Theta(\log n)$. Our query
time is always at least as good as the previous best known bounds and whenever
several characters are packed in a word, i.e., $\log \sigma \ll w$, the query
times are faster.


title: FoCUS: Fourier-based Coded Ultrasound

abstract:
  Modern imaging systems typically use single-carrier short pulses for
transducer excitation. Coded signals together with pulse compression are
successfully used in radar and communication to increase the amount of
transmitted energy. Previous research verified significant improvement in SNR
and imaging depth for ultrasound imaging with coded signals. Since pulse
compression needs to be applied at each transducer element, the implementation
of coded excitation (CE) in array imaging is computationally complex. Applying
pulse compression on the beamformer output reduces the computational load but
also degrades both the axial and lateral point spread function (PSF)
compromising image quality. In this work we present an approach for efficient
implementation of pulse compression by integrating it into frequency domain
beamforming. This method leads to significant reduction in the amount of
computations without affecting axial resolution. The lateral resolution is
dictated by the factor of savings in computational load. We verify the
performance of our method on a Verasonics imaging system and compare the
resulting images to time-domain processing. We show that up to 77 fold
reduction in computational complexity can be achieved in a typical imaging
setups. The efficient implementation makes CE a feasible approach in array
imaging paving the way to enhanced SNR as well as improved imaging depth and
frame-rate.


title:
Mass transport of adsorbates near a discontinuous structural phase
  transition

abstract:
  We study the mass transport dynamics of an adsorbed layer near a
discontinuous incommensurate striped-honeycomb phase transition via numerical
simulations of a coarse-grained model focusing on the motion of domain walls
rather than individual atoms. Following an initial step profile created in the
incommensurate striped phase, an intermediate hexagonal incommensurate phase
nucleates and grows, leading to a bifurcation into two sharp profiles
propagating in opposite directions as opposed to broad profiles induced by
atomic diffusive motion. Our results are in agreement with recent numerical
simulations of a microscopic model as well as experimental observations for the
Pb/Si(111) adsorbate system.


title:
Numerical Realization of Bethe Rapidities in cold quenched systems by
  Feynman-Kac path integral method

abstract:
  We apply Quantum Monte Carlo technique to analyze the non equlibrium state of
a trapped 1d Bose gas just after the quenching of the confining potential. As a
matter of fact we solve the time dependent Schroedinger equation for the system
of one-dimensional bosons interacting via delta potential in an infinite square
well (namely Lieb-Liniger model) using Feynman-Kac path integral Monte Carlo
technique. These 1d systems are extremely interesting and worth investigating
in the context of non-equilibrium dynamics of interacting many body systems.
Even though the systems can be realized experimentally and are exactly solvable
by Bethe Ansatz, the diffusion Monte Carlo is proven to be more efficient in
most circumstances than other mean value techniques as the numerical method can
incorporate the finite interaction very easily. Using N particle ground state
wavefunction for one-dimensional hard core bosons in a harmonic trap, we
develop an algorithm to calculate density. We also observe the change in the
density distribution by changing the length of the hard wall box. After an
increase in the box length, we still get a self-similar density distribution.


title:
Complexity of Single-Swap Heuristics for Metric Facility Location and
  Related Problem

abstract:
  Metric facility location and $K$-means are well-known problems of
combinatorial optimization. Both admit a fairly simple heuristic called
single-swap, which adds, drops or swaps open facilities until it reaches a
local optimum. For both problems, it is known that this algorithm produces a
solution that is at most a constant factor worse than the respective global
optimum. In this paper, we show that single-swap applied to the weighted metric
uncapacitated facility location and weighted discrete $K$-means problem is
tightly PLS-complete and hence has exponential worst-case running time.


title:
Analytical approach to the multiband filter synthesis and comparison to
  other approaches

abstract:
  A novel analytical approach to the synthesis of electrical (e.g. analogue,
digital or microwave) filters is proposed. This approach allows to obtain
lowest possible degree filters with given involved specification including e.g.
many pass and stop bands, narrow transition bands, high attenuation at the stop
bands and low magnitude oscillations at the pass bands. Comparison to other
existing approaches is given.


title:
Inequalities for the Casorati curvatures of real hypersurfaces in some
  Grassmannians

abstract:
  In this paper we obtain two types of optimal inequalities consisting of the
normalized scalar curvature and the generalized normalized $\delta$-Casorati
curvatures for real hypersurfaces of complex two-plane Grassmannians and
complex hyperbolic two-plane Grassmannians. We also find the conditions on
which the equalities hold.


title: On the Bonsall cone spectral radius and the approximate point spectrum

abstract:
  We study the Bonsall cone spectral radius and the approximate point spectrum
of (in general non-linear) positively homogeneous, bounded and supremum
preserving maps, defined on a max-cone in a given normed vector lattice. We
prove that the Bonsall cone spectral radius of such maps is always included in
its approximate point spectrum. Moreover, the approximate point spectrum always
contains a (possibly trivial) interval. Our results apply to a large class of
(nonlinear) max-type operators.
  We also generalize a known result that the spectral radius of a positive
(linear) operator on a Banach lattice is contained in the approximate point
spectrum. Under additional generalized compactness type assumptions our results
imply Krein-Rutman type results.


title: Video Ladder Networks

abstract:
  We present the Video Ladder Network (VLN) for efficiently generating future
video frames. VLN is a neural encoder-decoder model augmented at all layers by
both recurrent and feedforward lateral connections. At each layer, these
connections form a lateral recurrent residual block, where the feedforward
connection represents a skip connection and the recurrent connection represents
the residual. Thanks to the recurrent connections, the decoder can exploit
temporal summaries generated from all layers of the encoder. This way, the top
layer is relieved from the pressure of modeling lower-level spatial and
temporal details. Furthermore, we extend the basic version of VLN to
incorporate ResNet-style residual blocks in the encoder and decoder, which help
improving the prediction results. VLN is trained in self-supervised regime on
the Moving MNIST dataset, achieving competitive results while having very
simple structure and providing fast inference.


title:
Mostow's Fibration for canonical embeddings of compact homogeneous CR
  manifolds

abstract:
  We define a class of compact homogeneous CR manifolds which are bases of
Mostow fibrations having total spaces equal to their canonical complex
realizations and Hermitian fibers. This is used to establish isomorphisms
between their tangential Cauchy-Riemann cohomology groups and the corresponding
Dolbeault cohomology groups of the embeddings.


title: Weak amenability for dynamical systems

abstract:
  Using the recently developed notion of a Herz--Schur multiplier of a
C*-dynamical system we introduce weak amenability of C*- and W*-dynamical
systems. As a special case we recover Haagerup's characterisation of weak
amenability of a discrete group. We also consider a generalisation of the
Fourier algebra to crossed products and study its multipliers.


title:
Profile of solutions for nonlocal equations with critical and
  supercritical nonlinearities

abstract:
  We study the fractional laplacian problem (-\Delta)^s u &=& u^p -\epsilon u^q
\quad\text{in }\quad \Omega, u &\in& H^s(\Omega)\cap L^{q+1}(\Omega),u &>&0
\quad\text{in }\quad \Omega, u&=&0 \quad\text{in}\quad
\mathbb{R}^N\setminus\Omega, where $s\in(0,1)$, $q>p\geq \frac{N+2s}{N-2s}$ and
$\epsilon>0$ is a parameter. Here $\Omega\subseteq\mathbb{R}^N$ is a bounded
star-shaped domain with smooth boundary and $N> 2 s$. We establish existence of
a variational positive solution $u_{\epsilon}$ and characterize the asymptotic
behaviour of $u_{\epsilon}$ as $\epsilon\to 0$. When $p=\frac{N+2s}{N-2s}$, we
describe how the solution $u_{\epsilon}$ concentrates and blows up at a
interior point of the domain. Furthermore, we prove the local uniqueness of
solution of the above problem when $\Omega$ is a convex symmetric domain of
$\mathbb{R}^N$ with $N>4s$ and $p=\frac{N+2s}{N-2s}$.


title:
A Maximal Extension of the Best-Known Bounds for the
  Furstenberg-S\'ark\"ozy Theorem

abstract:
  We show that if $h\in \mathbb{Z}[x]$ is a polynomial of degree $k \geq 2$
such that $h(\mathbb{N})$ contains a multiple of $q$ for every $q\in
\mathbb{N}$, known as an $\textit{intersective polynomial}$, then any subset of
$\{1,2,\dots,N\}$ with no nonzero differences of the form $h(n)$ for
$n\in\mathbb{N}$ has density at most a constant depending on $h$ and $c$ times
$(\log N)^{-c\log\log\log\log N}$, for any $c<(\log((k^2+k)/2))^{-1}$. Bounds
of this type were previously known only for monomials and intersective
quadratics, and this is currently the best-known bound for the original
Furstenberg-S\'ark\"ozy Theorem, i.e. $h(n)=n^2$. The intersective condition is
necessary to force any density decay for polynomial difference-free sets, and
in that sense our result is the maximal extension of this particular
quantitative estimate. Further, we show that if $g,h\in \mathbb{Z}[x]$ are
intersective, then any set lacking nonzero differences of the form $g(m)+h(n)$
for $m,n\in \mathbb{N}$ has density at most $\exp(-c(\log N)^{\mu})$, where
$c=c(g,h)>0$, $\mu=\mu(\text{deg}(g),\text{deg}(h))>0$, and $\mu(2,2)=1/2$. We
also include a brief discussion of sums of three or more polynomials in the
final section.


title:
A necessary and sufficient condition for a matrix equilibrium state to
  be mixing

abstract:
  Since the 1970s there has been a rich theory of equilibrium states over shift
spaces associated to H\"older-continuous real-valued potentials. The
construction of equilibrium states associated to matrix-valued potentials is
much more recent, with a complete description of such equilibrium states being
achieved in 2011 by D.-J. Feng and A. K\"aenm\"aki. In a recent article the
author investigated the ergodic-theoretic properties of these matrix
equilibrium states, attempting in particular to give necessary and sufficient
conditions for mixing, positive entropy, and the property of being a Bernoulli
measure with respect to the natural partition, in terms of the algebraic
properties of the semigroup generated by the matrices. Necessary and sufficient
conditions were successfully established for the latter two properties but only
a sufficient condition for mixing was given. The purpose of this note is to
complete that investigation by giving a necessary and sufficient condition for
a matrix equilibrium state to be mixing.


title: Computing tropical varieties over fields with valuation

abstract:
  We show how tropical varieties of ideals I over a field K with non-trivial
valuation can be traced back to tropical varieties of ideals in R[[t]][x] over
some dense subring R in its ring of integers. Moreover, for homogeneous ideals,
we present algorithms on how the latter can be computed in finite time,
provided that generators are polynomial in t. While doing so, we also comment
on the computation of the Groebner polytope structure and p-adic Groebner bases
using our framework. All algorithms solely rely on existing standard basis
techniques.


title: Logarithmic convexity of fixed points of stochastic kernel operators

abstract:
  In this article we prove results on logaritmic convexity of fixed points of
stochastic kernel operators. These results are expected to play a key role in
the economic application to strategic market games.


title: Relics in galaxy clusters at high radio frequencies

abstract:
  We observed three radio relics in galaxy clusters and one radio relic
candidate at 4.85 and 8.35 GHz in total emission and linearly polarized
emission with the Effelsberg 100-m telescope and one radio relic candidate in
X-rays with the Chandra telescope. The radio spectra of the integrated emission
below 8.35 GHz can be well fitted by single power laws for all four relics. The
flat spectra (spectral indices of 0.9 and 1.0) for the "Sausage" relic in
cluster CIZA J2242+53 and the "Toothbrush" relic in cluster 1RXS 06+42 indicate
that models describing the origin of relics have to include effects beyond the
assumptions of diffuse shock acceleration. The spectra of the radio relics in
ZwCl 0008+52 and in Abell 1612 are steep, as expected from weak shocks (Mach
number $\approx 2.4$). We find polarization degrees of more than 50 % in the
two prominent Mpc-sized radio relics, the Sausage and the Toothbrush. The high
degree of polarization indicates that the magnetic field vectors are almost
perfectly aligned along the relic structure. The polarization degrees
correspond to Mach numbers of $>2.2$. Polarized emission is also detected in
the radio relics in ZwCl 0008+52 and, for the first time, in Abell 1612. Abell
1612 shows a complex X-ray surface brightness distribution, indicating a recent
major merger. No Faraday depolarization is detected between 4.85 GHz and 8.35
GHz, except for one component of the Toothbrush relic. Faraday depolarization
between 1.38 GHz and 8.35 GHz varies with distance from the center of the host
cluster 1RXS 06+42, which can be explained by a decrease in electron density
and/or in strength of a turbulent magnetic field. Faraday rotation measures
show large-scale gradients along the relics, which cannot be explained by
variations in the Milky Way foreground. Large-scale regular fields appear to be
present in intergalactic space around galaxy clusters.


title:
Bounds on the joint and generalized spectral radius of Hadamard
  geometric mean of bounded sets of positive kernel operators

abstract:
  Let $\Psi _1, \ldots \Psi _m$ be bounded sets of positive kernel operators on
a Banach function space $L$. We prove that for the generalized spectral radius
$\rho$ and the joint spectral radius $\hat{\rho}$ the inequalities $$\rho
\left(\Psi _1 ^{\left( \frac{1}{m} \right)} \circ \cdots \circ \Psi _m ^{\left(
\frac{1}{m} \right)} \right) \le \rho (\Psi _1 \Psi _2 \cdots \Psi _m)
^{\frac{1}{m}},$$ $$\hat{\rho} \left(\Psi _1 ^{\left( \frac{1}{m} \right)}
\circ \cdots \circ \Psi _m ^{\left( \frac{1}{m} \right)} \right) \le \hat{\rho}
(\Psi _1 \Psi _2 \cdots \Psi _m) ^{\frac{1}{m}}$$ hold, where $\Psi _1 ^{\left(
\frac{1}{m} \right)} \circ \cdots \circ \Psi _m ^{\left( \frac{1}{m} \right)}$
denotes the Hadamard (Schur) geometric mean of the sets $\Psi _1, \ldots , \Psi
_m$.


title:
The unramified inverse Galois problem and cohomology rings of totally
  imaginary number fields

abstract:
  We employ methods from homotopy theory to define new obstructions to
solutions of embedding problems. By using these novel obstructions we study
embedding problems with non-solvable kernel. We apply these obstructions to
study the unramified inverse Galois problem. That is, we show that our methods
can be used to determine that certain groups cannot be realized as the Galois
groups of unramified extensions of certain number fields. To demonstrate the
power of our methods, we give an infinite family of totally imaginary quadratic
number fields such that $\text{Aut}(\text{PSL}(2,q^2))$ for $q$ an odd prime
power, cannot be realized as an unramified Galois group over $K,$ but its
maximal solvable quotient can. To prove this result, we determine the ring
structure of the \'etale cohomology ring $H^*(\text{Spec
}\mathcal{O}_K;\mathbb{Z}/ 2\mathbb{Z})$ where $\mathcal{O}_K$ is the ring of
integers of an arbitrary totally imaginary number field $K.$


title:
Inequalities on the spectral radius, operator norm and numerical radius
  of Hadamard weighted geometric mean of positive kernel operators

abstract:
  Recently, several authors have proved inequalities on the spectral radius
$\rho$, operator norm $\|\cdot\|$ and numerical radius of Hadamard products and
ordinary products of non-negative matrices that define operators on sequence
spaces, or of Hadamard geometric mean and ordinary products of positive kernel
operators on Banach function spaces. In the present article we generalize and
refine several of these results. In particular, we show that for a Hadamard
geometric mean $A ^{\left( \frac{1}{2} \right)} \circ B ^{\left( \frac{1}{2}
\right)}$ of positive kernel operators $A$ and $B$ on a Banach function space
$L$, we have $$ \rho \left(A^{(\frac{1}{2})} \circ B^{(\frac{1}{2})} \right)
\le \rho \left((AB)^{(\frac{1}{2})} \circ
(BA)^{(\frac{1}{2})}\right)^{\frac{1}{2}} \le \rho (AB)^{\frac{1}{2}}.$$ In the
special case $L=L^2(X, \mu)$ we also prove that $$\|A^{(\frac{1}{2})} \circ
B^{(\frac{1}{2})} \| \le \rho \left ( (A^* B ) ^{(\frac{1}{2})}\circ (B ^*
A)^{(\frac{1}{2})}\right)^{\frac{1}{2}} \le \rho (A^* B )^{\frac{1}{2}}.$$


title:
Convergence analysis of the mimetic finite difference method for
  elliptic problems with staggered discretization of the diffusion coefficients

abstract:
  We study the convergence of the new family of mimetic finite difference
schemes for linear diffusion problems recently proposed in [38]. In contrast to
the conventional approach, the diffusion coefficient enters both the primary
mimetic operator, i.e., the discrete divergence, and the inner product in the
space of gradients. The diffusion coefficient is therefore evaluated on
different mesh locations, i.e., inside mesh cells and on mesh faces. Such a
staggered discretization may provide the exibility necessary for future
development of efficient numerical schemes for nonlinear problems, especially
for problems with degenerate coefficients. These new mimetic schemes preserve
symmetry and positive-definiteness of the continuum problem, which allow us to
use efficient algebraic solvers such as the preconditioned Conjugate Gradient
method. We show that these schemes are inf-sup stable and establish a priori
error estimates for the approximation of the scalar and vector solution fields.
Numerical examples confirm the convergence analysis and the effectiveness of
the method in providing accurate approximations.


title:
Unraveling the Salvinia paradox: design principles for submerged
  superhydrophobicity

abstract:
  The complex structure of the Salvinia molesta is investigated via rare event
molecular dynamics simulations. Results show that a hydrophilic/hydrophobic
patterning together with a re-entrant geometry control the free energy barriers
for bubble nucleation and for the Cassie-Wenzel transition. This natural
paradigm is translated into simple macroscopic design criteria for engineering
robust superhydrophobicity in submerged applications.


title:
Measuring field-normalized impact of papers on specific societal groups:
  An altmetrics study based on Mendeley data

abstract:
  Bibliometrics is successful in measuring impact, because the target is
clearly defined: the publishing scientist who is still active and working.
Thus, citations are a target-oriented metric which measures impact on science.
In contrast, societal impact measurements based on altmetrics are as a rule
intended to measure impact in a broad sense on all areas of society (e.g.
science, culture, politics, and economics). This tendency is especially
reflected in the efforts to design composite indicators (e.g. the Altmetric
attention score). We deem appropriate that not only the impact measurement
using citations is target-oriented (citations measure the impact of papers on
scientists), but also the measurement of impact using altmetrics. Impact
measurements only make sense, if the target group - the recipient of academic
papers - is clearly defined. Thus, we extend in this study the field-normalized
reader impact indicator proposed by us in an earlier study, which is based on
Mendeley data (the mean normalized reader score, MNRS), to a target-oriented
field-normalized impact indicator (e.g., MNRS_ED measures reader impact on the
sector of educational donation, i.e., teaching). This indicator can show - as
demonstrated in empirical examples - the ability of journals, countries, and
academic institutions to publish papers which are below or above the average
impact of papers on a specific sector in society (e.g., the educational or
teaching sector). For example, the method allows to measure the impact of
scientific papers on students - controlling for the field in which the papers
have been published and their publication year.


title: Wetting and cavitation pathways on nanodecorated surfaces

abstract:
  In this contribution we study wetting and nucleation of vapor bubbles on
nanodecorated surfaces via free energy molecular dynamics simulations. The
results shed light on the stability of superhydrophobicity in submerged
surfaces with nanoscale corrugations. The re-entrant geometry of the cavities
under investigation is capable of sustaining a confined vapor phase within the
surface roughness (Cassie state) both for hydrophobic and hydrophilic
combinations of liquid and solid. The atomistic system is of nanometric size;
on this scale thermally activated events can play an important role ultimately
determining the lifetime of the Cassie state. Such superhydrophobic state can
break down by full wetting of the texture at large pressures (Cassie-Wenzel
transition) or by nucleating a vapor bubble at negative pressures (cavitation).
Specialized rare event techniques show that several pathways for wetting and
cavitation are possible, due to the complex surface geometry. The related free
energy barriers are of the order of 100 k_B T and vary with pressure. The
atomistic results are found to be in semi-quantitative accord with macroscopic
capillarity theory. However, the latter is not capable of capturing the density
fluctuations, which determine the destabilization of the confined liquid phase
at negative pressures (liquid spinodal).


title: Slightly subcritical hypercube percolation

abstract:
  We study bond percolation on the hypercube $\{0,1\}^m$ in the slightly
subcritical regime where $p = p_c (1-\varepsilon_m)$ and $\varepsilon_m = o(1)$
but $\varepsilon_m \gg 2^{-m/3}$ and study the clusters of largest volume and
diameter. We establish that with high probability the largest component has
cardinality $\Theta\left(\varepsilon_m^{-2} \log(\varepsilon_m^3 2^m)\right)$,
that the maximal diameter of all clusters is $(1+o(1)) \varepsilon_m^{-1}
\log(\varepsilon_m^3 2^m)$, and that the maximal mixing time of all clusters is
$\Theta\left(\varepsilon_m^{-3} \log^2(\varepsilon_m^3 2^m)\right)$.
  These results hold in different levels of generality, and in particular, some
of the estimates hold for various classes of graphs such as high-dimensional
tori, expanders of high degree and girth, products of complete graphs, and
infinite lattices in high dimensions.