title: Closed form expression for the Goos-Haenchen lateral displacement

abstract:
  The Artmann formula provides an accurate determination of the Goos-Haenchen
lateral displacement in terms of the light wavelength, refractive index and
incidence angle. In the total reflection region, this formula is widely used in
the literature and confirmed by experiments. Nevertheless, for incidence at
critical angle, it tends to infinity and numerical calculations are needed to
reproduce the experimental data. In this paper, we overcome the divergence
problem at critical angle and find, for Gaussian beams, a closed formula in
terms of modified Bessel functions of the first kind. The formula is in
excellent agreement with numerical calculations and reproduces, for incidence
angles greater than critical ones, the Artmann formula. The closed form also
allows one to understand how the breaking of symmetry in the angular
distribution is responsible for the difference between measurements done by
considering the maximum and the mean value of the beam intensity. The results
obtained in this study clearly show the Goos-Haenchen lateral displacement
dependence on the angular distribution shape of the incoming beam. Finally, we
also present a brief comparison with experimental data and other analytical
formulas found in the literature.


title: Using Hadoop for Large Scale Analysis on Twitter: A Technical Report

abstract:
  Sentiment analysis (or opinion mining) on Twitter data has attracted much
attention recently. One of the system's key features, is the immediacy in
communication with other users in an easy, user-friendly and fast way.
Consequently, people tend to express their feelings freely, which makes Twitter
an ideal source for accumulating a vast amount of opinions towards a wide
diversity of topics. This amount of information offers huge potential and can
be harnessed to receive the sentiment tendency towards these topics. However,
since none can invest an infinite amount of time to read through these tweets,
an automated decision making approach is necessary. Nevertheless, most existing
solutions are limited in centralized environments only. Thus, they can only
process at most a few thousand tweets. Such a sample, is not representative to
define the sentiment polarity towards a topic due to the massive number of
tweets published daily. In this paper, we go one step further and develop a
novel method for sentiment learning in the MapReduce framework. Our algorithm
exploits the hashtags and emoticons inside a tweet, as sentiment labels, and
proceeds to a classification procedure of diverse sentiment types in a parallel
and distributed manner. Moreover, we utilize Bloom filters to compact the
storage size of intermediate data and boost the performance of our algorithm.
Through an extensive experimental evaluation, we prove that our solution is
efficient, robust and scalable and confirm the quality of our sentiment
identification.


title: Stokesian swimming of a sphere at low Reynolds number

abstract:
  Explicit expressions are derived for the matrices determining the mean
translational and rotational swimming velocities and the mean rate of
dissipation for Stokesian swimming at low Reynolds number of a distorting
sphere in a viscous incompressible fluid. As an application an efficient
helical propeller-type stroke is found and its properties are calculated.


title: Tensor products of f-algebras

abstract:
  We construct the tensor product for f-algebras, including proving a universal
property for it, and investigate how it preserves algebraic properties of the
factors.


title:
A consistent and unified picture for critical phenomena of $f(R)$ AdS
  black holes

abstract:
  A consistent and unified picture for critical phenomena of charged AdS black
holes in $f(R)$ gravity is drawn in this paper. Firstly, we investigate the
phase transition in canonical ensemble. We derive the explicit solutions
corresponding to the divergence of $C_Q$. The two solutions merge into one when
the condition $Q_c=\sqrt{\frac{-1}{3R_0}}$ is satisfied. The curve of specific
heat for $Q<Q_c$ has two divergent points and can be divided into three
regions. Both the large radius region and the small radius region are
thermodynamically stable with positive specific heat while the medium radius
region is unstable with negative specific heat. However, when $Q>Q_c$, the
specific heat is always positive, implying the black holes are locally stable
and no phase transition will take place. Secondly, both the $T-r_+$ curve and
$T-S$ curve $f(R)$ AdS black holes are investigated and they exhibit Van der
Vaals like behavior as the $P-v$ curve in the former research. Critical
physical quantities are obtained and they are consistent with those derived
from the specific heat analysis. We carry out numerical check of Maxwell equal
area law for the cases $Q=0.2Q_c, 0.4Q_c, 0.6Q_c, 0.8Q_c$. The relative errors
are amazingly small and can be negligible. So the Maxwell equal area law holds
for $T-S$ curve of $f(R)$ black holes. Thirdly, we establish
geometrothermodynamics for $f(R)$ AdS black hole to examine the phase
structure. It is shown that the Legendre invariant scalar curvature
$\mathfrak{R}$ would diverge exactly where the specific heat diverges. To
summarize, the above three perspectives are consistent with each other, thus
providing a unified picture which deepens the understanding of critical
phenomena of $f(R)$ AdS black holes.


title:
Probabilistic Trace and Poisson Summation Formulae on Locally Compact
  Abelian Groups

abstract:
  We investigate convolution semigroups of probability measures with continuous
densities on locally compact abelian groups, which have a discrete subgroup
such that the factor group is compact. Two interesting examples of the quotient
structure are the $d$--dimensional torus, and the ad\`{e}lic circle. Our main
result is to show that the Poisson summation formula for the density can be
interpreted as a probabilistic trace formula, linking values of the density on
the factor group to the trace of the associated semigroup on $L^{2}$-space. The
Gaussian is a very important example. For rotationally invariant
$\alpha$-stable densities, the trace formula is valid, but we cannot verify the
Poisson summation formula. To prepare to study semistable laws on the
ad\`{e}les, we first investigate these on the $p$--adics, where we show they
have continuous densities which may be represented as series expansions. We use
these laws to construct a convolution semigroup on the ad\`{e}les whose
densities fail to satisfy the probabilistic trace formula.


title: The definable (p,q)-theorem for distal theories

abstract:
  Answering a special case of a question of Chernikov and Simon, we show that
any non-dividing formula over a model M in a distal NIP theory is a member of a
consistent definable family, definable over M.


title:
A computationally efficient nonparametric approach for changepoint
  detection

abstract:
  In this paper we build on an approach proposed by Zou et al. (2014) for
nonpara- metric changepoint detection. This approach defines the best
segmentation for a data set as the one which minimises a penalised cost
function, with the cost function defined in term of minus a non-parametric
log-likelihood for data within each segment. Min- imising this cost function is
possible using dynamic programming, but their algorithm had a computational
cost that is cubic in the length of the data set. To speed up computation, Zou
et al. (2014) resorted to a screening procedure which means that the estimated
segmentation is no longer guaranteed to be the global minimum of the cost
function. We show that the screening procedure adversely affects the accuracy
of the changepoint detection method, and show how a faster dynamic programming
algorithm, Pruned Exact Linear Time, PELT (Killick et al., 2012), can be used
to find the optimal segmentation with a computational cost that can be close to
linear in the amount of data. PELT requires a penalty to avoid
under/over-fitting the model which can have a detrimental effect on the quality
of the detected changepoints. To overcome this issue we use a relatively new
method, Changepoints Over a Range of PenaltieS (CROPS) (Haynes et al., 2015),
which finds all of the optimal segmentations for multiple penalty values over a
continuous range. We apply our method to detect changes in heart rate during
physical activity.


title:
Learning scale-variant and scale-invariant features for deep image
  classification

abstract:
  Convolutional Neural Networks (CNNs) require large image corpora to be
trained on classification tasks. The variation in image resolutions, sizes of
objects and patterns depicted, and image scales, hampers CNN training and
performance, because the task-relevant information varies over spatial scales.
Previous work attempting to deal with such scale variations focused on
encouraging scale-invariant CNN representations. However, scale-invariant
representations are incomplete representations of images, because images
contain scale-variant information as well. This paper addresses the combined
development of scale-invariant and scale-variant representations. We propose a
multi- scale CNN method to encourage the recognition of both types of features
and evaluate it on a challenging image classification task involving
task-relevant characteristics at multiple scales. The results show that our
multi-scale CNN outperforms single-scale CNN. This leads to the conclusion that
encouraging the combined development of a scale-invariant and scale-variant
representation in CNNs is beneficial to image recognition performance.


title:
Crystallisation of soft matter under confinement at interfaces and in
  wedges

abstract:
  The surface freezing and surface melting transitions exhibited by a model
two-dimensional soft matter system is studied. The behaviour when confined
within a wedge is also considered. The system consists of particles interacting
via a soft purely repulsive pair potential. Density functional theory (DFT) is
used to calculate density profiles and thermodynamic quantities. The external
potential due to the confining walls is modelled via a hard-wall with an
additional repulsive Yukawa potential. The surface phase behaviour depends on
the range and strength of this repulsion: When the repulsion strength is weak,
the wall promotes freezing at the surface of the wall. The thickness of this
frozen layer grows logarithmically as the bulk liquid-solid phase coexistence
is approached. Our mean-field DFT predicts that this crystalline layer at the
wall must be nucleated (i.e. there is a free energy barrier) and its formation
is necessarily a first-order transition, referred to as `prefreezing', by
analogy with the prewetting transition. However, in contrast to the latter,
prefreezing cannot terminate in a critical point, since the phase transition
involves a change in symmetry. If the wall-fluid interaction is sufficiently
long ranged and the repulsion is strong enough, surface melting can instead
occur. Then the interface between the wall and the bulk crystalline solid
becomes wet by the liquid phase as the chemical potential is decreased towards
the value at liquid-solid coexistence. It is observed that the finite thickness
fluid film at the wall has a broken translational symmetry due to its proximity
to the bulk crystal and so the nucleation of the wetting film can be either
first-order or continuous. Our mean-field theory predicts that for certain wall
potentials there is a premelting critical point analogous to the surface
critical point for the prewetting transition. In a wedge...


title: Seeded excitation avalanches in off-resonantly driven Rydberg gases

abstract:
  We report an experimental investigation of the facilitated excitation
dynamics in off-resonantly driven Rydberg gases by separating the initial
off-resonant excitation phase from the facilitation phase, in which successive
facilitation events lead to excitation avalanches. We achieve this by creating
a controlled number of initial seed excitations. Greater insight into the
avalanche mechanism is obtained from an analysis of the full counting
distributions. We also present simple mathematical models and numerical
simulations of the excitation avalanches that agree well with our experimental
results.


title: A network-based rating system and its resistance to bribery

abstract:
  We study a rating system in which a set of individuals (e.g., the customers
of a restaurant) evaluate a given service (e.g, the restaurant), with their
aggregated opinion determining the probability of all individuals to use the
service and thus its generated revenue. We explicitly model the influence
relation by a social network, with individuals being influenced by the
evaluation of their trusted peers. On top of that we allow a malicious service
provider (e.g., the restaurant owner) to bribe some individuals, i.e., to
invest a part of his or her expected income to modify their opinion, therefore
influencing his or her final gain. We analyse the effect of bribing strategies
under various constraints, and we show under what conditions the system is
bribery-proof, i.e., no bribing strategy yields a strictly positive expected
gain to the service provider.


title:
The role of atmospheric greenhouse gases, orbital parameters, and
  southern ocean gateways: an idealized model study

abstract:
  A set of idealized experiments are performed to analyze the competing effects
of declining atmospheric CO2 concentrations, the opening of an ocean gateway,
and varying orbital parameters. These forcing mechanisms, which influence the
global mean climate state, may have played a role for triggering climate
transitions of the past (for example during the Eocene-Oligocene climate
transition and the build-up of the Antarctic Ice Sheet). Sensitivity
simulations with a coupled atmosphere-ocean general circulation model are
conducted to test these three forcings and their roles for the global climate.
The simulations are carried out under idealized conditions to focus on the
essentials. The combination of all three forcings triggers a climate transition
which resembles the onset of the Antarctic glaciation. In particular, the
temperatures in the southern high latitudes decrease and snow accumulates
constantly. Moreover, the relative importance of each possible forcing is
explored. All three of the mechanisms (atmospheric CO2 decrease, opening of the
ocean gateways, and changing orbital parameters) cool the climate of the
southern polar continent. The change induced by the orbital parameters depends
strongly on the magnitude of the change in obliquity.


title:
Detrending Moving Average Algorithm: Frequency Response and Scaling
  Performances

abstract:
  The Detrending Moving Average (DMA) algorithm has been widely used in its
several variants for characterizing long-range correlations of random signals
and sets (one-dimensional sequences or high-dimensional arrays) either over
time or space. In this paper, mainly based on analytical arguments, the scaling
performances of the centered DMA, including higher-order ones, are investigated
by means of a continuous time approximation and a frequency response approach.
Our results are also confirmed by numerical tests. The study is carried out for
higher-order DMA operating with moving average polynomials of different degree.
In particular, detrending power degree, frequency response, asymptotic scaling,
upper limit of the detectable scaling exponent and finite scale range behavior
will be discussed.


title:
User Collusion Avoidance Scheme for Privacy-Preserving Decentralized
  Key-Policy Attribute-Based Encryption -- Full Version

abstract:
  Recent trend towards cloud computing paradigm, smart devices and 4G wireless
technologies has enabled seamless data sharing among users. Cloud computing
environment is distributed and untrusted, hence data owners have to encrypt
their data to enforce data confidentiality. The data confidentiality in a
distributed environment can be achieved by using attribute-based encryption
technique. Decentralized attribute-based encryption technique is a variant of
multiple authority based attribute-based encryption whereby any attribute
authority can independently join and leave the system without collaborating
with the existing attribute authorities. In this paper, we propose a
privacy-preserving decentralized key-policy attribute-based encryption scheme.
The scheme preserves the user privacy when users interact with multiple
authorities to obtain decryption keys while mitigating the well-known user
collusion security vulnerability. We showed that our scheme relies on
decisional bilinear Diffie-Hellman standard complexity assumption in contrast
to the previous nonstandard complexity assumptions such as $q-$decisional
Diffie-Hellman inversion.


title: Hidden Regular Variation under Full and Strong Asymptotic Dependence

abstract:
  Data exhibiting heavy-tails in one or more dimensions is often studied using
the framework of regular variation. In a multivariate setting this requires
identifying specific forms of dependence in the data; this means identifying
that the data tends to concentrate along particular directions and does not
cover the full space. This is observed in various data sets from finance,
insurance, network traffic, social networks, etc. In this paper we discuss the
notions of full and strong asymptotic dependence for bivariate data along with
the idea of hidden regular variation in these cases. In a risk analysis
setting, this leads to improved risk estimation accuracy when regular methods
provide a zero estimate of risk. Analyses of both real and simulated data sets
illustrate concepts of generation and detection of such models.


title:
Achievability of Quantum Regime in Optomechanics of Electromagnetically
  Levitated Nanoparticles: Inclusion of Gradient Force Fluctuations

abstract:
  Counterintuitively, experiments show that an electromagnetically levitated
particle escapes from its trap when the ambient pressure is reduced below a
certain level even if the particle's motion is cooled by a resonator-based or
feedback-based mechanism. Here, we theoretically show that the ambient pressure
must be kept well above a critical value arising from gradient force
fluctuations (viz., fluctuations in part of the EM force whose Hamiltonian is
quadratic in the position of the particle). Also, we consider other force
fluctuations, and determine whether different realizations of feedback cooling
are able to reach the ground state. In some realizations, the cooling rate must
be kept well below a critical value arising from feedback-induced gradient
force fluctuations.


title: Square and Delta reflection

abstract:
  Starting from infinitely many supercompact cardinals, we force a model of ZFC
where $\aleph_{\omega^2+1}$ satisfies simultaneously a strong principle of
reflection, called $\Delta$-reflection, and a version of the square principle,
denoted $\square(\aleph_{\omega^2+1}).$ Thus we show that $\aleph_{\omega^2+1}$
can satisfy simultaneously a strong reflection principle and an anti-reflection
principle.


title:
Quantifying synergistic information using intermediate stochastic
  variables

abstract:
  Quantifying synergy among stochastic variables is an important open problem
in information theory. Information synergy occurs when multiple sources
together predict an outcome variable better than the sum of single-source
predictions. It is an essential phenomenon in biology such as in neuronal
networks and cellular regulatory processes, where different information flows
integrate to produce a single response, but also in social cooperation
processes as well as in statistical inference tasks in machine learning. Here
we propose a metric of synergistic entropy and synergistic information from
first principles. The proposed measure relies on so-called synergistic random
variables (SRVs) which are constructed to have zero mutual information about
individual source variables but non-zero mutual information about the complete
set of source variables. We prove several basic and desired properties of our
measure, including bounds and additivity properties. In addition, we prove
several important consequences of our measure, including the fact that
different types of synergistic information may co-exist between the same sets
of variables. A numerical implementation is provided, which we use to
demonstrate that synergy is associated with resilience to noise. Our measure
may be a marked step forward in the study of multivariate information theory
and its numerous applications.


title: The model of the black hole enclosed in dust. The flat space case

abstract:
  In this work the model is constructed to describe the black hole enclosed in
the dust cosmological background in case of zero spatial curvature. This model
is based on our exact solution of the class of LTB inhomogeneous solutions. We
considered the properties of the model and built the R-T-structure of the
resulting space-time. It was shown that central region includes the
Schwarzchild-like black hole. We derived the equations of motion of the test
particle from the point of view of the observer comoving with cosmological
expansion. We found analytical expressions for observable orbital and radial
velocities of the particle and plotted the surface profile of the total
velocity in this case. In comoving coordinate frame it is impossible to study
the questions concerning the black hole horizon but one can observe the local
motion of the particles influenced by the cosmological expansion.


title: Majorana modes meet fractional fermions in one dimension

abstract:
  Majorana modes and fractional fermions are two types of edge zero modes
appearing separately in topological superconductors and dimerized chains. Here
we reveal how to harvest both types of edge modes simultaneously in an exotic
chain. Such modes are naturally spin-charge separated, and are protected by the
inversion and spin-parity symmetries. We construct a lattice model to
illustrate the nature of these edge modes, utilizing fermionic functional
renormalization group, mean-field theory and bosonization. We also elucidate
that the four-fold degenerate ground states with edge-spinons in the Haldane
phase of spin-$1$ chain may be reinterpreted as our spin-charge separated edge
modes in an equivalent spin-$1/2$ fermionic model.


title: Slender-ribbon theory

abstract:
  Ribbons are long narrow strips possessing three distinct material length
scales (thickness, width, and length) which allow them to produce unique shapes
unobtainable by wires or filaments. For example when a ribbon has half a twist
and is bent into a circle it produces a M\"obius strip. Significant effort has
gone into determining the structural shapes of ribbons but less is know about
their behavior in viscous fluids. In this paper we determine, asymptotically,
the leading-order hydrodynamic behavior of a slender ribbon in Stokes flows.
The derivation, reminiscent of slender-body theory for filaments, assumes that
the length of the ribbon is much larger than its width, which itself is much
larger than its thickness. The final result is an integral equation for the
force density on a mathematical ruled surface, termed the ribbon plane, located
inside the ribbon. A numerical implementation of our derivation shows good
agreement with the known hydrodynamics of long flat ellipsoids, and
successfully captures the swimming behavior of artificial microscopic swimmers
recently explored experimentally. We also study the asymptotic behavior of a
ribbon bent into a helix, that of a twisted ellipsoid, and we investigate how
accurately the hydrodynamics of a ribbon can be effectively captured by that of
a slender filament. Our asymptotic results provide the fundamental framework
necessary to predict the behavior of slender ribbons at low Reynolds numbers in
a variety of biological and engineering problems.


title:
Frequentistic approximations to Bayesian prevision of exchangeable
  random elements

abstract:
  Given a sequence \xi_1, \xi_2,... of X-valued, exchangeable random elements,
let q(\xi^(n)) and p_m(\xi^(n)) stand for posterior and predictive
distribution, respectively, given \xi^(n) = (\xi_1,..., \xi_n). We provide an
upper bound for limsup b_n d_[[X]](q(\xi^(n)), \delta_\empiricn) and limsup b_n
d_[X^m](p_m(\xi^(n)), \empiricn^m), where \empiricn is the empirical measure,
b_n is a suitable sequence of positive numbers increasing to +\infty, d_[[X]]
and d_[X^m] denote distinguished weak probability distances on [[X]] and [X^m],
respectively, with the proviso that [S] denotes the space of all probability
measures on S. A characteristic feature of our work is that the aforesaid
bounds are established under the law of the \xi_n's, unlike the more common
literature on Bayesian consistency, where they are studied with respect to
product measures (p_0)^\infty, as p_0 varies among the admissible
determinations of a random probability measure.


title: On random partitions induced by random maps

abstract:
  The lattice of the set partitions of $[n]$ ordered by refinement is studied.
Given a map $\phi: [n] \rightarrow [n]$, by taking preimages of elements we
construct a partition of $[n]$. Suppose $t$ partitions $p_1,p_2,\dots,p_t$ are
chosen independently according to the uniform measure on the set of mappings
$[n]\rightarrow [n]$. The probability that the coarsest refinement of all
$p_i$'s is the finest partitions $\{\{1\},\dots,\{n\}\}$ is shown to approach
$1$ for any $t\geq 3$ and $e^{-1/2}$ for $t=2$. The probability that the finest
coarsening of all $p_i$'s is the one-block partition is shown to approach 1 if
$t(n)-\log{n}\rightarrow \infty$ and $0$ if $t(n)-\log{n}\rightarrow -\infty$.
The size of the maximal block of the finest coarsening of all $p_i$'s for a
fixed $t$ is also studied.


title:
On the parameter identifiability problem in Agent Based economical
  models

abstract:
  Identifiability of parameters is a fundamental prerequisite for model
identification. It concerns uniqueness of the model parameters determined from
experimental or simulated observations. This dissertation specifically deals
with structural or a priori identifiability: whether or not parameters can be
identified from a given model structure and experimental measurements. We
briefly present the identifiability problem in linear and non linear dynamical
model. We compare DSGE and Agent Based model (ABM) in terms of identifiability
of the structural parameters and we finally discuss limits and perspective of
numerical protocols to test global identifiability in case of ergodic and
markovian economical systems.


title: Computability of the (co)homology of cyclic monoids

abstract: Leech's (co)homology groups of finite cyclic monoids are computed.


title: Probing Compositeness with the CMS $eejj$ & $eej$ Data

abstract:
  Quark-lepton compositeness is a well-known beyond the Standard Model (SM)
scenario with heavy exotic particles like leptoquarks (LQs) and leptogluons
(LGs) etc. These particles can couple to leptons and jets simultaneously. In
this letter, we use the recent CMS scalar LQ search data in the $eejj$ and
$eej$ channels to probe this scenario. We recast the data in terms of a color
octet partner of the SM electron (or a first generation spin-1/2 LG) that
couples to an electron and a gluon via a dimension five operator suppressed by
the quark-lepton compositeness scale ($\Lambda$). By combining different
production processes of the color octet electron ($e_8$) at the LHC, we use the
CMS 8TeV data to obtain a simultaneous bound on $\Lambda$ and the mass of the
$e_8$ ($M_{e_8}$). We also study the reach of the 13 TeV LHC to discover the
$e_8$ and interpret the required luminosity in terms of $M_{e_8}$ and
$\Lambda$.


title: Left fibrations and homotopy colimits II

abstract:
  For a small simplicial category A, we prove that the homotopy colimit functor
from the category of simplicial diagrams on A to the category of simplicial
sets over the homotopy-coherent nerve of A provides a left Quillen equivalence
between the projective model structure on the former category and the covariant
model structure on the latter. We compare this Quillen equivalence to the
straightening-unstraightening equivalence previously established by Lurie,
where the left adjoint goes in the opposite direction. The existence of left
Quillen functors in both directions considerably simplifies the proof that
these constructions provide Quillen equivalences. The results of this paper
generalize those of part I, where A was an ordinary category. The proofs for a
simplicial category are more involved and can be read independently.


title:
Robust Exponential Attractors for Coleman--Gurtin Equations with Dynamic
  Boundary Conditions Possessing Memory

abstract:
  The well-posedness of a generalized Coleman--Gurtin equation equipped with
dynamic boundary conditions with memory was recently established by the author
with C.G. Gal. In this article we report advances concerning the asymptotic
behavior and stability of this heat transfer model. For the model under
consideration, we obtain a family of exponential attractors that is
robust/H\"older continuous with respect to a perturbation parameter occurring
in a singularly perturbed memory kernel. We show that the basin of attraction
of these exponential attractors is the entire phase space. The existence of
(finite dimensional) global attractors follows. The results are obtained by
assuming the nonlinear terms defined on the interior of the domain and on the
boundary satisfy standard dissipation assumptions. Also, we work under a
crucial assumption that dictates the memory response in the interior of the
domain matches that on the boundary.


title: Charge dynamics of the antiferromagnetically ordered Mott insulator

abstract:
  We study the charge dynamics of the half-filled Hubbard model on the square
lattice at zero temperature. We employ a slave-fermion formulation in which the
charge degrees of freedom are represented by fermionic holons and doublons and
the bosonic spin degrees of freedom are assumed to be described by the
antiferromagnetic Heisenberg model. The ground state has long-ranged magnetic
(N\'eel) order and its Mott-insulating characteristics are the consequence of
holon-doublon bound-state formation. Within this framework, we calculate the
average double occupancy, the electron density of states, and the spectral
function in the self-consistent Born approximation. The lower and upper Hubbard
bands are reproduced, there is spectral-weight transfer into a coherent
quasiparticle band at their lower edges, and the Mott gap, associated with
holon-doublon binding, is renormalized due to the interactions of the holons
and doublons with the magnons. We compute the zeros of the Green function at
the chemical potential to discuss the Luttinger volume and show that the poles
of the self-energy reflect the underlying quasiparticle dispersion with a
spin-renormalized hopping parameter. Optical conductivity results relate the
optical gap to the Mott gap of the insulating system. We conclude that a
self-consistent treatment of the spin fluctuation effects on the charge degrees
of freedom captures all the essential physics of the antiferromagnetic
Mott-Hubbard insulator.


title:
A stable, single-photon emitter in a thin organic crystal for
  application to quantum-photonic devices

abstract:
  Single organic molecules offer great promise as bright, reliable sources of
identical single photons on demand, capable of integration into solid-state
devices. It has been proposed that such molecules in a crystalline organic
matrix might be placed close to an optical waveguide for this purpose, but so
far there have been no demonstrations of sufficiently thin crystals, with a
controlled concentration of suitable dopant molecules. Here we present a method
for growing very thin anthracene crystals from super-saturated vapour, which
produces crystals of extreme flatness and controlled thickness. We show how
this crystal can be doped with a widely adjustable concentration of
dibenzoterrylene (DBT) molecules and we examine the optical properties of these
molecules to demonstrate their suitability as quantum emitters in nanophotonic
devices. Our measurements show that the molecules are available in the crystal
as single quantum emitters, with a well-defined polarisation relative to the
crystal axes, making them amenable to alignment with optical nanostructures. We
find that the radiative lifetime and saturation intensity vary little within
the crystal and are not in any way compromised by the unusual matrix
environment. We show that a large fraction of these emitters are able to
deliver more than $10^{12}$ photons without photo-bleaching, making them
suitable for real applications.


title:
Explorations on anisotropic regularisation of dynamic inverse problems
  by bilevel optimisation

abstract:
  We explore anisotropic regularisation methods in the spirit of [Holler &
Kunisch, 14]. Based on ground truth data, we propose a bilevel optimisation
strategy to compute the optimal regularisation parameters of such a model for
the application of video denoising. The optimisation poses a challenge in
itself, as the dependency on one of the regularisation parameters is non-linear
such that the standard existence and convergence theory does not apply.
Moreover, we analyse numerical results of the proposed parameter learning
strategy based on three exemplary video sequences and discuss the impact of
these results on the actual modelling of dynamic inverse problems.


title:
Attractors for Damped Semilinear Wave Equations with Singularly
  Perturbed Acoustic Boundary Conditions

abstract:
  Under consideration is the damped semilinear wave equation \[
u_{tt}+u_t-\Delta u+u+f(u)=0 \] in a bounded domain $\Omega$ in $\mathbb{R}^3$
subject to an acoustic boundary condition with a singular perturbation, which
we term "massless acoustic perturbation," \[ \ep\delta_{tt}+\delta_t+\delta =
-u_t\quad\text{for}\quad \ep\in[0,1]. \] By adapting earlier work by S.
Frigeri, we prove the existence of a family of global attractors for each
$\ep\in[0,1]$. We also establish the optimal regularity for the global
attractors, as well as the existence of an exponential attractor, for each
$\ep\in[0,1].$ The later result insures the global attractors possess finite
(fractal) dimension, however, we cannot yet guarantee that this dimension is
independent of the perturbation parameter $\ep.$ The family of global
attractors are upper-semicontinuous with respect to the perturbation parameter
$\ep$, a result which follows by an application of a new abstract result also
contained in this article. Finally, we show that it is possible to obtain the
global attractors using weaker assumptions on the nonlinear term $f$, however,
in that case, the optimal regularity, the finite dimensionality, and the
upper-semicontinuity of the global attractors does not necessarily hold.


title: Quantum optical dipole radiation fields

abstract:
  We introduce quantum optical dipole radiation fields defined in terms of
photon creation and annihilation operators. These fields are identified through
their spatial dependence, as the components of the total fields that survive
infinitely far from the dipole source. We use these radiation fields to
perturbatively evaluate the electromagnetic radiated energy-flux of the excited
dipole. Our results indicate that the standard interpretation of a bare atom
surrounded by a localised virtual photon cloud, is difficult to sustain,
because the radiated energy-flux surviving infinitely far from the source
contains virtual contributions. It follows that there is a clear distinction to
be made between a radiative photon defined in terms of the radiation fields,
and a real photon, whose identification depends on whether or not a given
process conserves the free energy. This free energy is represented by the
difference between the total dipole-field Hamiltonian and its interaction
component.


title:
Acceleration toward polarization singularity inspired by relativistic
  ExB drift

abstract:
  The relativistic trajectory of a charged particle driven by the Lorentz force
is different from the classical one, by velocity-dependent relativistic
acceleration term. Here we show that the evolution of optical polarization
states near the polarization singularity can be described in analogy to the
relativistic dynamics of charged particles. A phase transition in parity-time
symmetric potentials is then interpreted in terms of the competition between
electric and magnetic 'pseudo'-fields applied to polarization states. Based on
this Lorentz pseudo-force representation, we reveal that zero Lorentz
pseudo-force is the origin of recently reported strong polarization convergence
to the singular state at the exceptional point. We also demonstrate the
deterministic design of achiral and directional eigenstates at the exceptional
point, allowing an anomalous linear polarizer which operates orthogonal to
forward and backward waves. Our results linking parity-time symmetry and
relativistic electrodynamics show that previous PT-symmetric potentials for the
polarization singularity with a chiral eigenstate are the subset of optical
potentials for the ExB "polarization" drift.


title:
Fractal behavior of multivariate operator-self-similar stable random
  fields

abstract:
  We investigate the sample path regularity of multivariate
operator-self-similar stable random fields with values in $\mathbb{R}^m$ given
by a harmonizable representation. Such fields were introduced in [25] as a
generalization of both operator-self-similar stochastic processes and operator
scaling random fields and satisfy the scaling property $\{X(c^E t) : t \in
\mathbb{R}^d \} \stackrel{\rm d}{=} \{c^D X(t) : t \in \mathbb{R}^d \}$, where
$E$ is a real $d \times d$ matrix and $D$ is a real $m \times m$ matrix. This
paper provides the first results concerning sample path properties of such
fields, including both $E$ and $D$ different from identity matrices. In
particular, this solves an open problem in [25].


title:
Limit theorems for number of edges in the generalized random graphs with
  random vertex weights

abstract:
  We get central limit type theorems for the total number of edges in the
generalized random graphs with random vertex weights under different moment
conditions on distributions of the weights.


title: Excess B-modes extracted from the Planck polarization maps

abstract:
  One of the main obstacles for extracting the Cosmic Microwave Background
(CMB) from mm/submm observations is the pollution from the main Galactic
components: synchrotron, free-free and thermal dust emission. The feasibility
of using simple neural networks to extract CMB has been demonstrated on both
temperature and polarization data obtained by the WMAP satellite. The main goal
of this paper is to demonstrate the feasibility of neural networks for
extracting the CMB signal from the Planck polarization data with high
precision. Both auto-correlation and cross-correlation power spectra within a
mask covering about 63 percent of the sky have been used together with a 'high
pass filter' in order to minimize the influence of the remaining systematic
errors in the Planck Q and U maps. Using the Planck 2015 released polarization
maps, a BB power spectrum have been extracted by \textit{Multilayer Perceptron}
neural networks. This spectrum contains a bright feature with signal to noise
ratios $\simeq$ 4.5 within 200 $\leq$ l $\leq$ 250. The spectrum is
significantly brighter than the BICEP2 2015 spectrum, with a spectral behaviour
quite different from the 'canonical' models (weak lensing plus B-modes spectra
with different tensor to scalar ratios). The feasibility of the neural network
to remove the residual systematics from the available Planck polarization data
to a high level has been demonstrated.


title: Cooperative Spin Caloritronic Devices

abstract:
  We report a concept of thermoelectric devices, cooperative spin caloritronics
device (CSCD), where cooperation between two or more energy channels such as
spin, charge and heat currents can significantly enhance energy efficiency of
spin caloritronic devices. We derive the figure of merit and the maximum
efficiency due to cooperative effect in analytic forms for a CSCD. Cooperative
effects significantly improve the figure of merit and the maximum efficiency in
spin caloritronic systems with multiply couplings effects. Several examples of
CSCDs, including electrical and thermal current induced DW motion,
spin-thermoelectric power generator and spin-thermoelectric cooling/heating,
are studied to illustrate the usefulness of the cooperative effect. We compare
the efficiency of CSCD with several recently proposed spin caloritronic
devices. Our scheme provides a novel route to seek high performance materials
and structures for future spin caloritronic devices.


title: Constructing Dominating Sets in Circulant Graphs

abstract:
  We give an efficient construction of a reasonably small dominating set in a
circulant graph on $n$ notes and $k$ distinct chord lengths. This result is
based on bounds on some double exponential sums. .


title: Dynamical stability of extended teleparallel gravity

abstract:
  We discuss modified teleparallel gravity with function $f(T,T_G)$ in the
action, where function depend on two arguments: torsion scalar $T$ and analogue
of Gauss-Bonnet invariant $T_G$. In contradistinction to usual teleparallel
gravity $f(T)$, this theory contains higher derivative terms, which may produce
different instabilities. We discuss Minkowski stability problem in such kind of
theories and explicitly demonstrate that for stability must be $f_T(0,0)<0$,
$f_{T_GT_G}>0$. We apply these restrictions for the few types of functions
discussed by the early authors.


title: NIKEL_AMC: Readout electronics for the NIKA2 experiment

abstract:
  The New Iram Kid Arrays-2 (NIKA2) instrument has recently been installed at
the IRAM 30 m telescope. NIKA2 is a state-of-art instrument dedicated to
mm-wave astronomy using microwave kinetic inductance detectors (KID) as
sensors. The three arrays installed in the camera, two at 1.25 mm and one at
2.05 mm, feature a total of 3300 KIDs. To instrument these large array of
detectors, a specifically designed electronics, composed of 20 readout boards
and hosted in three microTCA crates, has been developed. The implemented
solution and the achieved performances are presented in this paper. We find
that multiplexing factors of up to 400 detectors per board can be achieved with
homogeneous performance across boards in real observing conditions, and a
factor of more than 3 decrease in volume with respect to previous generations.


title:
A Scaling Relation in Inhomogeneous Cosmology with k-essence scalar
  fields

abstract:
  We obtain a scaling relation for spherically symmetric k-essence scalar
fields $\phi(r,t)$ for an inhomogeneous cosmology with the Lemaitre-Tolman-
Bondi (LTB) metric. We show that this scaling relation reduces to the known
relation for a homogeneous cosmology when the LTB metric reduces to the
Friedmann-Lemaitre-Robertson-Walker (FLRW) metric under certain identifications
of the metric functions. A k-essence lagrangian is set up and the
Euler-Lagrangian equations solved assuming $\phi(r,t)=\phi_{1}(r) +
\phi_{2}(t)$. The solutions enable the LBT metric functions to be related to
the fields. The LTB inhomogeneous universe exhibits late time accelerated
expansion i.e.cosmic acceleration driven by negative pressure.


title:
Characterization of the potential smoothness of one-dimensional Dirac
  operator subject to general boundary conditions and its Riesz basis property

abstract:
  The one-dimensional Dirac operator with periodic potential $V=\begin{pmatrix}
0 & \mathcal{P}(x) \\ \mathcal{Q}(x) & 0 \end{pmatrix}$, where
$\mathcal{P},\mathcal{Q}\in L^2([0,\pi])$ subject to periodic, antiperiodic or
a general strictly regular boundary condition $(bc)$ has discrete spectrums. It
is known that, for large enough $|n|$ in the disc centered at $n$ of radius
1/4, the operator has exactly two (periodic if $n$ is even or antiperiodic if
$n$ is odd) eigenvalues $\lambda_n^+$ and $\lambda_n^-$ (counted according to
multiplicity) and one eigenvalue $\mu_n^{bc}$ corresponding to the boundary
condition $(bc)$. We prove that the smoothness of the potential could be
characterized by the decay rate of the sequence $|\delta_n^{bc}|+|\gamma_n|$,
where $\delta_n^{bc}=\mu_n^{bc}-\lambda_n^+$ and
$\gamma_n=\lambda_n^+-\lambda_n^-.$ Furthermore, it is shown that the Dirac
operator with periodic or antiperiodic boundary condition has the Riesz basis
property if and only if $\sup\limits_{\gamma_n\neq0}
\frac{|\delta_n^{bc}|}{|\gamma_n|}$ is finite.


title: Aspects of Stability of Hairy Black Holes

abstract:
  We analyze spherical and odd-parity linear perturbations of hairy black holes
with a minimally coupled scalar field.


title: Central tetrads and quantum spacetimes

abstract:
  In this paper, we perform a parallel analysis to the model proposed in [25].
By considering the central co-tetrad (instead of the central metric), we
investigate the modifications in the gravitational metrics coming from the
noncommutative spacetime of the $\kappa$-Minkowski type in four dimensions. The
differential calculus corresponding to a class of Jordanian
$\kappa$-deformations provides metrics, which lead either to cosmological
constant or spatial curvature type solutions of non-vacuum Einstein equations.
Among vacuum solutions, we find pp-wave type.


title:
An application of a functional inequality to quasi-invariance in
  infinite dimensions

abstract:
  One way to interpret smoothness of a measure in infinite dimensions is
quasi-invariance of the measure under a class of transformations. Usually such
settings lack a reference measure such as the Lebesgue or Haar measure, and
therefore we can not use smoothness of a density with respect to such a
measure. We describe how a functional inequality can be used to prove
quasi-invariance results in several settings. In particular, this gives a
different proof of the classical Cameron-Martin (Girsanov) theorem for an
abstract Wiener space. In addition, we revisit several more geometric examples,
even though the main abstract result concerns quasi-invariance of a measure
under a group action on a measure space.


title: Dynamics of infinite classical anharmonic crystals

abstract:
  We consider an unbounded lattice and at each point of this lattice an
anharmonic oscillator, that interacts with its first neighborhoods via a pair
potential $V$ and is subjected to a restoring force of potential $U$. We assume
that $U$ and $V$ are even nonnegative polynomials of degree $2\sigma_1$ and
$2\sigma_2$. We study the time evolution of this system, with a control of the
growth in time of the local energy, and we give a nontrivial bound on the
velocity of propagation of a perturbation. This is an extension to the case
$\sigma_1 < 2\sigma_2-1$ of some already known results obtained for $\sigma_1
\geq 2\sigma_2-1$.


title: How proofs are prepared at Camelot

abstract:
  We study a design framework for robust, independently verifiable, and
workload-balanced distributed algorithms working on a common input. An
algorithm based on the framework is essentially a distributed encoding
procedure for a Reed--Solomon code, which enables (a) robustness against
byzantine failures with intrinsic error-correction and identification of failed
nodes, and (b) independent randomized verification to check the entire
computation for correctness, which takes essentially no more resources than
each node individually contributes to the computation. The framework builds on
recent Merlin--Arthur proofs of batch evaluation of Williams~[{\em Electron.\
Colloq.\ Comput.\ Complexity}, Report TR16-002, January 2016] with the
observation that {\em Merlin's magic is not needed} for batch evaluation---mere
Knights can prepare the proof, in parallel, and with intrinsic
error-correction.
  The contribution of this paper is to show that in many cases the verifiable
batch evaluation framework admits algorithms that match in total resource
consumption the best known sequential algorithm for solving the problem. As our
main result, we show that the $k$-cliques in an $n$-vertex graph can be counted
{\em and} verified in per-node $O(n^{(\omega+\epsilon)k/6})$ time and space on
$O(n^{(\omega+\epsilon)k/6})$ compute nodes, for any constant $\epsilon>0$ and
positive integer $k$ divisible by $6$, where $2\leq\omega<2.3728639$ is the
exponent of matrix multiplication. This matches in total running time the best
known sequential algorithm, due to Ne{\v{s}}et{\v{r}}il and Poljak [{\em
Comment.~Math.~Univ.~Carolin.}~26 (1985) 415--419], and considerably improves
its space usage and parallelizability. Further results include novel algorithms
for counting triangles in sparse graphs, computing the chromatic polynomial of
a graph, and computing the Tutte polynomial of a graph.


title:
B-spline parameterization of spatial response in a monolithic
  scintillation camera

abstract:
  A framework for parameterization of the light response functions (LRFs) in a
scintillation camera is presented. It is based on approximation of the measured
or simulated photosensor response with weighted sums of uniform cubic B-splines
or their tensor products. The LRFs represented in this way are smooth,
computationally inexpensive to evaluate and require much less computer memory
than non-parametric alternatives. The parameters are found in a straightforward
way by the linear least squares method. Several techniques that allow to reduce
the storage and processing power requirements were developed. A software
library for fitting simulated and measured light response with spline functions
was developed and integrated into an open source software package ANTS2
designed for simulation and data processing for Anger camera type detectors.


title:
On the local Langlands correspondence for quasi-split even orthogonal
  groups

abstract:
  In this paper, we highlight and state precisely the local Langlands
correspondence for quasi-split O_{2n} established by Arthur. We give two
applications: Prasad's conjecture and Gross--Prasad conjecture for O_{n}. Also,
we discuss the Arthur conjecture for O_{2n}, and establish the Arthur
multiplicity formula for O_{2n}.


title: The b-continuity of graphs with large girth

abstract:
  A b-coloring of the vertices of a graph is a proper coloring where each color
class contains a vertex which is adjacent to each other color class. The
b-chromatic number of $G$ is the maximum integer $b(G)$ for which $G$ has a
b-coloring with $b(G)$ colors. A graph $G$ is b-continuous if $G$ has a
b-coloring with $k$ colors, for every integer $k$ in the interval
$[\chi(G),b(G)]$. It is known that not all graphs are b-continuous. In this
article, we show that if $G$ has girth at least 10, then $G$ is b-continuous.


title:
Local Theta correspondence of Tempered Representations and Langlands
  parameters

abstract:
  In this paper, we give an explicit determination of the theta lifting for
symplectic-orthogonal and unitary dual pairs over a nonarchimedean field $F$ of
characteristic $0$. We determine when theta lifts of tempered representations
are nonzero, and determine the theta lifts in terms of the local Langlands
correspondence.


title: On the shadow problem for domains in the Euclidean spaces

abstract:
  In the present work, the problem about shadow, generalized on domains of
space $\mathbb{R}^n$, $n\le 3$, is investigated. Here the shadow problem means
to find the minimal number of balls satisfying some conditions an such that
every line passing through the given point intersects at least one ball of the
collection. It is proved that to generate the shadow at every given point of
any domain of the space $\mathbb{R}^3$ ($\mathbb{R}^2$) with collection of
mutually non-overlapping closed or open balls which do not hold the point and
with centers on the boundary of the domain, it is sufficient to have four
balls.


title:
Expansion-maximization-compression algorithm with spherical harmonics
  for single particle imaging with X-ray lasers

abstract:
  In 3D single particle imaging with X-ray free-electron lasers, particle
orientation is not recorded during measurement but is instead recovered as a
necessary step in the reconstruction of a 3D image from the diffraction data.
Here we use harmonic analysis on the sphere to cleanly separate the angu- lar
and radial degrees of freedom of this problem, providing new opportunities to
efficiently use data and computational resources. We develop the
Expansion-Maximization-Compression algorithm into a shell-by-shell approach and
implement an angular bandwidth limit that can be gradually raised during the
reconstruction. We study the minimum number of patterns and minimum rotation
sampling required for a desired angular and radial resolution. These extensions
provide new av- enues to improve computational efficiency and speed of
convergence, which are critically important considering the very large datasets
expected from experiment.


title: Henri Poincar\'e and his "model" of hyperbolic geometry

abstract:
  The aim of the talk is to trace how and when Henri Poincar\'e used
non-Euclidean geometries (NEG) in his mathematical and philosophical works,
with a particular attention to the genesis and the description of his model. We
begin by a short presentation of the context of NEG in France around the
1870-80s. Then we expound from several sources the introduction and use of NEG
in Poincar\'e's work about Fuchsian functions and we stress on the analogy
between elliptic functions and fuchsian functions.


title: Division and Slope Factorization of p-Adic Polynomials

abstract:
  We study two important operations on polynomials defined over complete
discrete valuation fields: Euclidean division and factorization. In particular,
we design a simple and efficient algorithm for computing slope factorizations,
based on Newton iteration. One of its main features is that we avoid working
with fractional exponents. We pay particular attention to stability, and
analyze the behavior of the algorithm using several precision models.


title: Inverse Inequality Estimates with Symbolic Computation

abstract:
  In the convergence analysis of numerical methods for solving partial
differential equations (such as finite element methods) one arrives at certain
generalized eigenvalue problems, whose maximal eigenvalues need to be estimated
as accurately as possible. We apply symbolic computation methods to the
situation of square elements and are able to improve the previously known upper
bound, given in "p- and hp-finite element methods" (Schwab, 1998), by a factor
of 8. More precisely, we try to evaluate the corresponding determinant using
the holonomic ansatz, which is a powerful tool for dealing with determinants,
proposed by Zeilberger in 2007. However, it turns out that this method does not
succeed on the problem at hand. As a solution we present a variation of the
original holonomic ansatz that is applicable to a larger class of determinants,
including the one we are dealing with here. We obtain an explicit closed form
for the determinant, whose special form enables us to derive new and tight
upper resp. lower bounds on the maximal eigenvalue, as well as its asymptotic
behaviour.


title: On the K-stability of Fano varieties and anticanonical divisors

abstract:
  We apply a recent theorem of Li and the first author to give some criteria
for the K-stability of Fano varieties in terms of anticanonical Q-divisors.
First, we propose a condition in terms of certain anticanonical Q-divisors of
given Fano variety, which we conjecture to be equivalent to the K-stability. We
prove that it is at least sufficient condition and also relate to the
Berman-Gibbs stability. We also give another algebraic proof of the K-stability
of Fano varieties which satisfy Tian's alpha invariants condition.


title: On the interplay between embedded graphs and delta-matroids

abstract:
  The mutually enriching relationship between graphs and matroids has motivated
discoveries in both fields. In this paper, we exploit the similar relationship
between embedded graphs and delta-matroids. There are well-known connections
between geometric duals of plane graphs and duals of matroids. We obtain
analogous connections for various types of duality in the literature for graphs
in surfaces of higher genus and delta-matroids. Using this interplay, we
establish a rough structure theorem for delta-matroids that are twists of
matroids, we translate Petrie duality on ribbon graphs to loop complementation
on delta-matroids, and we prove that ribbon graph polynomials, such as the
Penrose polynomial, the characteristic polynomial, and the transition
polynomial, are in fact delta-matroidal. We also express the Penrose polynomial
as a sum of characteristic polynomials.


title: On an explicit lower bound for the star discrepancy in three dimensions

abstract:
  Following a result of D.~Bylik and M.T.~Lacey from 2008 it is known that
there exists an absolute constant $\eta>0$ such that the (unnormalized)
$L^{\infty}$-norm of the three-dimensional discrepancy function, i.e, the
(unnormalized) star discrepancy $D^{\ast}_N$, is bounded from below by
$D_{N}^{\ast}\geq c (\log N)^{1+\eta}$, for all $N\in\mathbb{N}$ sufficiently
large, where $c>0$ is some constant independent of $N$. This paper builds upon
their methods to verify that the above result holds with
$\eta<1/(32+4\sqrt{41})\approx 0.017357\ldots$


title:
An SLC-type $e^{+}e^{-}/\gamma\gamma$ facility at a Future Circular
  Collider

abstract:
  It is proposed to place the arcs of an SLC-type facility inside the tunnel of
a Future Circular Collider (FCC). Accelerated by a linear accelerator (linac),
electron and positron beams would traverse the bending arcs in opposite
directions and collide at centre-of-mass energies considerably exceeding those
attainable at circular $e^{+}e^{-}$ colliders. The proposed SLC-type facility
would have the same luminosity as a conventional two-linac $e^{+}e^{-}$
collider. Using an optical free-electron laser, the facility could be converted
into a $\gamma\gamma$ collider. A superconducting L-band linac at the proposed
facility may form a part of the injector chain for a 100-TeV proton collider in
the FCC tunnel. The whole accelerator complex would serve as a source of
$e^{+}e^{-}$, $\gamma\gamma$, $pp$ and $ep$ interactions. The L-band linac
could also be used to produce high-intensity neutrino, kaon and muon beams for
fixed-target experiments, as well as X-ray free-electron laser (XFEL) photons
for applications in material science and medicine.


title:
Continuity of the Feynman-Kac formula for a generalized parabolic
  equation

abstract:
  It is well-known since the work of Pardoux and Peng [12] that Backward
Stochastic Differential Equations provide probabilistic formulae for the
solution of (systems of) second order elliptic and parabolic equations, thus
providing an extension of the Feynman-Kac formula to semilinear PDEs, see also
Pardoux and Rascanu [14]. This method was applied to the class of PDEs with a
nonlinear Neumann boundary condition first by Pardoux and Zhang [15]. However,
the proof of continuity of the extended Feynman-Kac formula with respect to x
(resp. to (t,x)) is not correct in that paper. Here we consider a more general
situation, where both the equation and the boundary condition involve the
(possibly multivalued) gradient of a convex function. We prove the required
continuity. The result for the class of equations studied in [15] is a
Corollary of our main results.


title: Self-avoiding walks adsorbed at a surface and subject to a force

abstract:
  We consider self-avoiding walks terminally attached to an impenetrable
surface at which they can adsorb. We call the vertices farthest away from this
plane the top vertices and we consider applying a force at the plane containing
the top vertices. This force can be directed away from the adsorbing surface or
towards it. In both cases we prove that the free energy (in the thermodynamic
limit) is identical to the free energy when the force is applied at the last
vertex. This means that the criterion determining the critical force -
temperature curve is identical for the two ways in which the force is applied
and the response to pushing the walk is also the same in the two cases.


title: A note on the path integral representation for Majorana fermions

abstract:
  Majorana fermions are currently of huge interest in the context of
nanoscience and condensed matter physics. Different to usual fermions, Majorana
fermions have the property that the particle is its own anti-particle thus,
they must be described by real fields. Mathematically, this property makes
nontrivial the quantization of the problem due, for instance, to the absence of
a Wick-like theorem. In view of the present interest on the subject, it is
important to develop different theoretical approaches in order to study
problems where Majorana fermions are involved. In this note we show that
Majorana fermions can be studied in the context of field theories for
constrained systems. Using the Faddeev-Jackiw formalism for quantum field
theories with constraints, we derived the path integral representation for
Majorana fermions. In order to show the validity of the path integral we apply
it to an exactly solvable problem. This application also shows that it is
rather simple to perform systematic calculations on the basis of the present
framework.


title:
An Entropy Stable Discontinuous Galerkin Finite-Element Moment Method
  for the Boltzmann Equation

abstract:
  This paper presents a numerical approximation technique for the Boltzmann
equation based on a moment system approximation in velocity dependence and a
discontinuous Galerkin finite-element approximation in position dependence. The
closure relation for the moment systems derives from minimization of a suitable
{\phi}-divergence. This divergence-based closure yields a hierarchy of
tractable symmetric hyperbolic moment systems that retain the fundamental
structural properties of the Boltzmann equation. The resulting combined
discontinuous Galerkin moment method corresponds to a Galerkin approximation of
the Boltzmann equation in renormalized form. We present a new class of
numerical flux functions, based on the underlying renormalized Boltzmann
equation, that ensure entropy dissipation of the approximation scheme.
Numerical results are presented for a one-dimensional test case.

categories: physics.comp-ph math-ph math.MP physics.flu-dyn


title: A new model of the microwave polarized sky for CMB experiments

abstract:
  We present a new model of the microwave sky in polarization that can be used
to simulate data from CMB polarization experiments. We exploit the most recent
results from the Planck satellite to provide an accurate description of the
diffuse polarized foreground synchrotron and thermal dust emission. Our model
can include the two mentioned foregrounds, and also a constructed template of
Anomalous Microwave Emission (AME). Several options for the frequency
dependence of the foregrounds can be easily selected, to reflect our
uncertainties and to test the impact of different assumptions. Small angular
scale features can be added to the foreground templates to simulate
high-resolution observations. We present tests of the model outputs to show the
excellent agreement with Planck and WMAP data. We determine the range within
which the foreground spectral indices can be varied to be consistent with the
current data. We also show forecasts for a high-sensitivity, high-resolution
full-sky experiment such as the Cosmic ORigin Explorer (COrE). Our model is
released as a python script that is quick and easy to use, available at
\url{http://www.jb.man.ac.uk/~chervias}.


title:
Quantum non-equilibrium dynamics of Rydberg gases in the presence of
  dephasing noise of different strengths

abstract:
  In the presence of strong dephasing noise the dynamics of Rydberg gases
becomes effectively classical, due to the rapid decay of quantum superpositions
between atomic levels. Recently a great deal of attention has been devoted to
the stochastic dynamics that emerges in that limit, revealing several
interesting features, including kinetically-constrained glassy behaviour,
self-similarity and aggregation effects. However, the non-equilibrium physics
of these systems, in particular in the regime where coherent and dissipative
processes contribute on equal footing, is yet far from being understood. To
explore this we study the dynamics of a small one-dimensional Rydberg lattice
gas subject to dephasing noise by numerically integrating the quantum Master
equation. We interpolate between the coherent and the strongly dephased regime
by defining a generalised concept of a blockade length. We find indications
that the main features observed in the strongly dissipative limit persist when
the dissipation is not strong enough to annihilate quantum coherences at the
dynamically relevant time scales. These features include the existence of a
time-dependent Rydberg blockade radius, and a growth of the density of
excitations which is compatible with the power-law behaviour expected in the
classical limit.


title:
A Numerical Model for Accretion in Intermediate Polars with Dipolar
  Magnetic Fields

abstract:
  A three-dimensional numerical model for an accretion process investigation in
the magnetosphere of a white dwarf in magnetic cataclysmic variables is
developed. The model assumes that the white dwarf has a dipole magnetic field
with its symmetry axis inclined to the rotation axis. The model is based on the
equations of modified MHD, that describe the mean flow parameters in the wave
MHD turbulence. Diffusion of the magnetic field and radiative heating and
cooling are taken into account. The suitability of the model is confirmed by
modeling the accretion in a typical intermediate polar. The computations show
that a magnetosphere forms around the accretor, with the accretion occurring
via columns. The accretion columns have a curtain-like shape, and arc-shaped
zones of energy release form on the surface of the white dwarf in the magnetic
poles area as a result of the matter infall.


title:
Analytic approximation of energy resolution in cascaded gaseous
  detectors

abstract:
  An approximate formula has been derived for gain fluctuations in cascaded
gaseous detectors such as GEM-s, based on the assumption that the charge
collection, avalanche formation and extraction steps are independent cascaded
processes. In order to test the approximation experimentally, a setup involving
a standard GEM layer has been constructed to measure the energy resolution for
5.9 keV gamma particles. The formula reasonably traces both the charge
collection as well as the extraction process dependence of the energy
resolution. Such analytic approximation for gain fluctuations can be applied to
multi-GEM detectors where it aids the interpretation of measurements as well as
simulations.


title:
Equation of state of imbalanced cold matter from chiral perturbation
  theory

abstract:
  We study the thermodynamic properties of matter at vanishing temperature for
non-extreme values of the isospin chemical potential and of the strange quark
chemical potential. From the leading order pressure obtained by maximizing the
static chiral Lagrangian density we derive a simple expression for the equation
of state in the pion condensed phase and in the kaon condensed phase. We find
an analytical expression for the maximum of the ratio between the energy
density and the Stefan-Boltzmann energy density as well as for the isospin
chemical potential at the peak both in good agreement with lattice simulations
of quantum chromodynamics. We speculate on the location of the crossover from
the Bose-Einstein condensate state to the Bardeen-Cooper-Schrieffer state by a
simple analysis of the thermodynamic properties of the system. For $\mu_I
\gtrsim 2 m_\pi$ the leading order chiral perturbation theory breaks down; as
an example it underestimates the energy density of the system and leads to a
wrong asymptotic behavior.

categories: hep-ph astro-ph.HE cond-mat.quant-gas hep-lat


title: Quantum Dot-Ring Nanostructure - a Comparison of Different Approaches

abstract:
  It has been recently shown that a nanostructure composed of a quantum dot
surrounded by a quantum ring possesses a set of very unique characteristics
that make it a good candidate for future nanoelectronic devices. Its main
advantage is the ability to easily tune transport properties on demand by so
called "wave function engineering". In practice, the distribution of the
electron wave function in the nanostructure can be controlled by, e.g.,
electrical gating. In order to predict some particular properties of the system
one has to know the exact wave functions for different shapes of the confining
potential that defines the structure.
  In this paper we compare three different methods that can be used to
determine the energy spectrum, electron wave functions and transport properties
of the system under investigation. In the first approach we utilize the
cylindrical symmetry of the confining potential and solve only the radial part
of the Schrodinger equation; in the second approach we discretize the
Schrodinger equation in two dimensions and find the eigenstates with the help
of the Lanczos method; in the third approach we use package Kwant to solve a
tight-binding approximation of the original system. To study the transport
properties in all these approaches we calculate microscopically the strength of
the coupling between the nanosystem and leads. In the first two approaches we
use the Bardeen method, in the third one calculations are performed with the
help of package Kwant.


title: Classical and quantum cosmology of Born-Infeld type models

abstract:
  We discuss Born-Infeld type fields (tachyon fields) in classical and quantum
cosmology. We first partly review and partly extend the discussion of the
classical solutions and focus in particular on the occurrence of singularities.
For quantization, we employ geometrodynamics. In the case of constant
potential, we discuss both Wheeler-DeWitt quantization and reduced
quantization. We are able to give various solutions and discuss their
asymptotics. For the case of general potential, we transform the Wheeler-DeWitt
equation to a form where it leads to a difference equation. Such a difference
equation was previously found in the quantization of black holes. We give
explicit results for the cases of constant potential and inverse squared
potential and point out special features possessed by solutions of the
difference equation.


title:
A temperature condensation trend in the debris-disk binary system Zet2
  Ret

abstract:
  We explore condensation temperature Tc trends in the unique binary system
Zet1 Ret - Zet2 Ret, to determine whether there is a depletion of refractories,
which could be related to the planet formation process. The star Zet2 Ret hosts
a debris disk which was detected by an IR excess and confirmed by direct
imaging and numerical simulations, while Zet1 Ret does not present IR excess
nor planets. We carried out a high-precision abundance determination in both
components of the binary system via a line-by-line, strictly differential
approach. The stellar parameters Teff , log g, [Fe/H] and vturb were determined
by imposing differential ionization and excitation equilibrium of Fe I and Fe
II lines, with an updated version of the program FUNDPAR. The star Zet1 Ret
resulted slightly more metal rich than Zet2 Ret by 0.02 dex. In the
differential calculation of Zet1 Ret using Zet2 Ret as reference, the
abundances of the refractory elements resulted higher than the volatile
elements, and the trend of the refractory elements with Tc showed a positive
slope. These facts together show a lack of refractory elements in Zet2 Ret (a
debris-disk host) relative to Zet1 Ret. The Tc trend would be in agreement with
the proposed signature of planet formation (Melendez et al. 2009) rather than
possible Galactic Chemical Evolution or age effects, which are largely
diminished here. Then, following the interpretation of Melendez et al. (2009),
we propose an scenario in which the refractory elements depleted in Zet2 Ret
are possibly locked-up in the rocky material that orbits this star and produce
the debris disk observed around this object. We estimated a lower limit of
Mrock = 3 Me for the rocky mass of depleted material, which is compatible with
a rough estimation of 3-50 Me of a debris disk mass around a solar-type star
(Krivov et al. 2008). (abridged)


title:
A continuum among logarithmic, linear, and exponential functions, and
  its potential to improve generalization in neural networks

abstract:
  We present the soft exponential activation function for artificial neural
networks that continuously interpolates between logarithmic, linear, and
exponential functions. This activation function is simple, differentiable, and
parameterized so that it can be trained as the rest of the network is trained.
We hypothesize that soft exponential has the potential to improve neural
network learning, as it can exactly calculate many natural operations that
typical neural networks can only approximate, including addition,
multiplication, inner product, distance, polynomials, and sinusoids.


title: Extending the velocity-dependent one-scale model for domain walls

abstract:
  We report on an extensive study of the evolution of domain wall networks in
Friedmann-Lema\^{\i}tre-Robertson-Walker universes by means of the largest
currently available field-theory simulations. These simulations were done in
$4096^3$ boxes and for a range of different fixed expansion rates, as well as
for the transition between the radiation and matter eras. A detailed comparison
with the velocity-dependent one-scale (VOS) model shows that this cannot
accurately reproduce the results of the entire range of simulated regimes if
one assumes that the phenomenological energy loss and momentum parameters are
constants. We therefore discuss how a more accurate modeling of these
parameters can be done, specifically by introducing an additional mechanism of
energy loss (scalar radiation, which is particularly relevant for regimes with
relatively little damping) and a modified momentum parameter which is a
function of velocity (in analogy to what was previously done for cosmic
strings). We finally show that this extended model, appropriately calibrated,
provides an accurate fit to our simulations.


title:
Biclustering Readings and Manuscripts via Non-negative Matrix
  Factorization, with Application to the Text of Jude

abstract:
  The text-critical practice of grouping witnesses into families or texttypes
often faces two obstacles: Contamination in the manuscript tradition, and
co-dependence in identifying characteristic readings and manuscripts. We
introduce non-negative matrix factorization (NMF) as a simple, unsupervised,
and efficient way to cluster large numbers of manuscripts and readings
simultaneously while summarizing contamination using an easy-to-interpret
mixture model. We apply this method to an extensive collation of the New
Testament epistle of Jude and show that the resulting clusters correspond to
human-identified textual families from existing research.


title: A microscopic nuclear collective rotation-vibration model: 2D submodel

abstract:
  We develop in this article a microscopic version of the successful
phenomenological hydrodynamic Bohr-Davydov-Faessler-Greiner (BDFG) model for
the collective rotation-vibration motion of a deformed nucleus. The model
derivation is not limited to small oscillation amplitudes. The model
generalizes the author's previous model to include interaction between
collective oscillations in each pair of spatial directions, and to remove many
of the previous-model approximations. To derive the model, the nuclear
Schrodinger equation is canonically transformed to collective coordinates and
then linearized using a constrained variational method. The associated
transformation constraints are imposed on the wavefunction and not on the
particle co-ordinates. This approach yields four self-consistent, time-reversal
invariant, cranking-type Schrodinger equations for the rotation-vibration and
intrinsic motions, and a self-consistency equation. To facilitate comparison
with the BDFG model, simplify the solution of the equations, and gain physical
insight, we restrict in this article the collective oscillations to only two
space dimensions. For harmonic oscillator mean-field potentials, the equations
are then solved in closed forms and applied to the ground-state rotational
bands in some even-even light and rare-earth nuclei. The computed ground-state
rotational band excitation energy, quadrupole moment and electric quadrupole
transition probabilities are found to agree favourably with measured data and
the results from mean-field, Sp(3,R), and SU(3) models.


title:
On the large time behaviour of the solution of an SDE driven by a
  Poisson Point Process

abstract:
  We study a stochastic differential equation driven by a Poisson point
process, which models continuous changes in a population's environment, as well
as the stochastic fixation of beneficial mutations that might compensate for
this change. The fixation probability of a given mutation increases as the
phenotypic lag X_t between the population and the optimum grows larger, and
successful mutations are assumed to fix instantaneously (leading to an adaptive
jump). Our main result is that the process is transient (i.e., continued
adaptation is impossible) if the rate of environmental change v exceeds a
parameter m, which can be interpreted as the rate of adaptation in case every
beneficial mutation gets fixed with probability 1. If v < m, the process is
positive recurrent, while in the limiting case m=v, null recurrence or
transience depends upon additional technical conditions. We show how our
results can be extended to the case of a time varying rate of environmental
change.


title:
Phase diagram of Model C in the parametric space of order parameter and
  space dimensions

abstract:
  The scaling behavior of model C describing the dynamical behaviour of the
$n$-component nonconserved order parameter coupled statically to a scalar
conserved density is considered in $d$-dimensional space. Conditions for the
realization of different types of scaling regimes in the $(n,d)$ plane are
studied within the field-theoretical renormalization group approach. Borders
separating these regions are calculated on the base of high-order RG functions
using $\epsilon$-expansions as well as by fixed dimension $d$ approach with
resummation.


title: On The Construction of Capacity-Achieving Lattice Gaussian Codes

abstract:
  In this paper, we propose a new approach to proving results regarding channel
coding schemes based on construction-A lattices for the Additive White Gaussian
Noise (AWGN) channel that yields new characterizations of the code construction
parameters, i.e., the primes and dimensions of the codes, as functions of the
block-length. The approach we take introduces an averaging argument that
explicitly involves the considered parameters. This averaging argument is
applied to a generalized Loeliger ensemble to provide a more practical proof of
the existence of AWGN-good lattices, and to characterize suitable parameters
for the lattice Gaussian coding scheme proposed by Ling and Belfiore.


title: Geometry of infinite planar maps with high degrees

abstract:
  We study the geometry of infinite random Boltzmann planar maps with vertices
of high degree. These correspond to the duals of the Boltzmann maps associated
to a critical weight sequence $(q_{k})_{ k \geq 0}$ for the faces with
polynomial decay $k^{-a}$ with $a \in ( 3/2, 5/2)$ which have been studied by
Le Gall & Miermont as well as by Borot, Bouttier & Guitter. We show the
existence of a phase transition for the geometry of these maps at $a = 2$. In
the dilute phase corresponding to $a \in (2, 5/2)$ we prove that the volume of
the ball of radius $r$ (for the graph distance) is of order $r^{\mathsf{d}}$
with $\mathsf{d}= (a-1/2)/(a-2)$, and we provide distributional scaling limits
for the volume and perimeter process. In the dense phase corresponding to $a
\in (3/2,2)$ the volume of the ball of radius $r$ is exponential in $r$. We
also study the first-passage percolation (FPP) distance with exponential edge
weights and show in particular that in the dense phase the FPP distance between
the origin and infinity is finite. The latter implies in addition that the
random lattices in the dense phase are transient. The proofs rely on the recent
peeling process introduced in arXiv:1506.01590 and use ideas of arXiv:1412.5509
in the dilute phase.


title: Effect of Data Sharing on Private Cache Design in Chip Multiprocessors

abstract:
  In multithreaded applications with high degree of data sharing, the miss rate
of private cache is shown to exhibit a compulsory miss component. It manifests
because at least some of the shared data originates from other cores and can
only be accessed in a shared cache. The compulsory component does not change
with the private cache size, causing its miss rate to diminish slower as the
cache size grows. As a result, the peak performance of a Chip Multiprocessor
(CMP) for workloads with high degree of data sharing is achieved with a smaller
private cache, compared to workloads with no data sharing. The CMP performance
can be improved by reassigning some of the constrained area or power resource
from private cache to core. Alternatively, the area or power budget of a CMP
can be reduced without a performance hit.


title: Nambu-Jona-Lasinio Theory and Dynamical Breaking of Supersymmetry

abstract:
  A recently proposed new mechanism of D-term triggered dynamical supersymmetry
breaking is reviewed. Supersymmetry is dynamically broken by nonvanishing
D-term vacuum expectation value, which is realized as a nontrivial solution of
the gap equation in the self-consistent approximation as in the case of
Nambu-Jona-Lasinio model and BCS superconductivity.


title:
Cosmological constrains on fast transition Unified Dark Energy/Matter
  models

abstract:
  We explore the observational adequacy of a class of Unified Dark
Energy/Matter (UDE/M) models with a fast transition. Our constraints are set
using a combination of geometric probes, some low redshift ones, and some high
redshift ones (CMB related included). The transition is phenomenologically
modeled by two different transition functions corresponding to a fast and to an
ultra-fast transition respectively. We find that the key parameters governing
the transition can be well constrained, and from the statistical point of view
it follows that the models cannot be discarded when compared to $\Lambda$CDM.
We find the intriguing result that standard/input parameters such as $\Omega_m$
and $\Omega_b$ are far better constrained than in $\Lambda$CDM, and this is the
case for the derived/output parameter measuring the deceleration value at
present, $q_0$.


title:
Radiative heat transfer between nanoparticles: shape dependence and
  three-body effect

abstract:
  We study the effect of particles shape on the radiative heat transfer in a
three-body system. It is found that the radiative heat flux between two
nanoparticles in a three body system can be tuned by the shape of the third
particle. In particular, we show that the heat flux is very sensitive to the
particle shapes and slight mismatches of shapes results in either enhanced or
suppressed heat flux.


title:
Super Yang-Mills and theta-exact Seiberg-Witten map: Absence of
  quadratic noncommutative IR divergences

abstract:
  We compute the one-loop 1PI contributions to all the propagators of the
noncommutative N=1, 2, 4 super Yang-Mills (SYM) U(1) theories defined by the
means of the theta-exact Seiberg-Witten (SW) map in the Wess-Zumino gauge. Then
we extract the UV divergent contributions and the noncommutative IR
divergences. We show that all the quadratic noncommutative IR divergences add
up to zero in each propagator.


title:
Symplectically invariant flow equations for N=2, D=4 gauged supergravity
  with hypermultiplets

abstract:
  We consider N=2 supergravity in four dimensions, coupled to an arbitrary
number of vector- and hypermultiplets, where abelian isometries of the
quaternionic hyperscalar target manifold are gauged. Using a static and
spherically or hyperbolically symmetric ansatz for the fields, a
one-dimensional effective action is derived whose variation yields all the
equations of motion. By imposing a sort of Dirac charge quantization condition,
one can express the complete scalar potential in terms of a superpotential and
write the action as a sum of squares. This leads to first-order flow equations,
that imply the second-order equations of motion. The first-order flow turns out
to be driven by Hamilton's characteristic function in the Hamilton-Jacobi
formalism, and contains among other contributions the superpotential of the
scalars. We then include also magnetic gaugings and generalize the flow
equations to a symplectically covariant form. Moreover, by rotating the charges
in an appropriate way, an alternative set of non-BPS first-order equations is
obtained that corresponds to a different squaring of the action. Finally, we
use our results to derive the attractor equations for near-horizon geometries
of extremal black holes.


title:
Towards the multivariate simplotope spline: continuity conditions in a
  class of mixed simplotopic grids

abstract:
  Smooth joins of simplex Bernstein-B\'ezier polynomials have been studied
extensively in the past. In this paper a new method is proposed to define
continuity conditions for tensor-product Bernstein polynomials on a class of
mixed grids that meets certain out-of-facet parallelism criteria. The
conditions are derived by first defining a simplex around the simplotopic bases
of the tensor-product polynomials. Then the continuity conditions in the
multivariate simplex spline defined on the resulting simplices, are adapted to
hold for the tensor-product polynomials. The two- and three-dimensional results
agree with the results found in the literature. It is expected that the method
can be employed in more general grids.


title:
The Galactic O-Star Spectroscopic Survey (GOSSS). III. 142 additional
  O-type systems

abstract:
  This is the third installment of GOSSS, a massive spectroscopic survey of
Galactic O stars, based on new homogeneous, high signal-to-noise ratio, R~2500
digital observations selected from the Galactic O-Star Catalog (GOSC). In this
paper we present 142 additional stellar systems with O stars from both
hemispheres, bringing the total of O-type systems published within the project
to 590. Among the new objects there are 20 new O stars. We also identify 11 new
double-lined spectroscopic binaries (SB2s), of which 6 are of O+O type and 5 of
O+B type, and an additional new tripled-lined spectroscopic binary (SB3) of
O+O+B type. We also revise some of the previous GOSSS classifications, present
some egregious examples of stars erroneously classified as O-type in the past,
introduce the use of luminosity class IV at spectral types O4-O5.5, and adapt
the classification scheme to the work of Arias et al. (2016).


title: Perfect (super) edge-magic crowns

abstract:
  In this paper we continue the study of the valences for (super) edge-magic
labelings of crowns $C_{m}\odot \overline K_{n}$ and we prove that the crowns
are perfect (super) edge-magic when $m=pq$ where $p$ and $q$ are different odd
primes. We also provide a lower bound for the number of different valences of
$C_{m}\odot \overline K_{n}$, in terms of the prime factors of $m$.


title:
Vortex clustering and universal scaling laws in two-dimensional quantum
  turbulence

abstract:
  We investigate numerically the statistics of quantized vortices in
two-dimensional quantum turbulence using the Gross-Pitaevskii equation. We find
that a universal $-5/3$ scaling law in the turbulent energy spectrum is
intimately connected with the vortex statistics, such as number fluctuations
and vortex velocity, which is also characterized by a similar scaling behavior.
The $-5/3$ scaling law appearing in the power spectrum of vortex number
fluctuations is consistent with the scenario of passive advection of isolated
vortices by a turbulent superfluid velocity generated by like-signed vortex
clusters. The velocity probability distribution of clustered vortices is also
sensitive to spatial configurations, and exhibits a power-law tail distribution
with a $-5/3$ exponent.


title: Quantum properties of a binary bosonic mixture in a double well

abstract:
  This work contains a detailed analysis of the properties of the ground state
of a two-component two-sites Bose-Hubbard model, which captures the physics of
a binary mixture of Bose-Einstein condensates trapped in a double-well
potential. The atom-atom interactions within each species and among the two
species are taken as variable parameters while the hopping terms are kept
fixed. To characterize the ground state we use observables such as the
imbalance of population and its quantum uncertainty. The quantum many-body
correlations present in the system are further quantified by studying the
degree of condensation of each species, the entanglement between the two sites
and the entanglement between the two species. The latter is measured by means
of the Schmidt gap, the von Neumann entropy or the purity obtained after
tracing out a part of the system. A number of relevant states are identified,
e.g. Schr\"odinger catlike many-body states, in which the outcome of the
population imbalance of both components is completely correlated, and other
states with even larger von Neumann entropy which have a large spread in Fock
space.


title:
Nonequilibrium thermodynamics in the strong coupling and non-Markovian
  regime based on a reaction coordinate mapping

abstract:
  We propose a method to study the thermodynamic behaviour of small systems
beyond the weak coupling and Markovian approximation, which is different in
spirit from conventional approaches. The idea is to redefine the system and
environment such that the effective, redefined system is again coupled weakly
to Markovian residual baths and thus, allows to derive a consistent
thermodynamic framework for this new system-environment partition. To achieve
this goal we make use of the reaction coordinate mapping, which is a general
method in the sense that it can be applied to an arbitrary (quantum or
classical and even time-dependent) system coupled linearly to an arbitrary
number of harmonic oscillator reservoirs. The core of the method relies on an
appropriate identification of a part of the environment (the reaction
coordinate), which is subsequently included as a part of the system. We
demonstrate the power of this concept by showing that non-Markovian effects can
significantly enhance the steady state efficiency of a three-level-maser heat
engine, even in the regime of weak system-bath coupling. Furthermore, we show
for a single electron transistor coupled to vibrations that our method allows
one to justify master equations derived in a polaron transformed reference
frame.


title: KAM for quasi-linear forced hamiltonian NLS

abstract:
  In this paper we prove the existence of quasi-periodic, small-amplitude,
solutions for quasi-linear Hamiltonian perturbations of the non-linear
Schroedinger equation on the torus in presence of a quasi-periodic forcing. In
particular we prove that such solutions are linearly stable. The proof is based
on a Nash-Moser implicit function theorem and on a reducibility result on the
linearized operator in a neighborhood of zero. The proof of the reducibility
relies on changes of coordinates such as diffeomorphisms of the torus,
pseudo-differential operators and a KAM-reducibility arguments. Due to the
multiplicity of the eigenvalues we obtain a block-diagonalization.


title: Plurality Consensus via Shuffling: Lessons Learned from Load Balancing

abstract:
  We consider \emph{plurality consensus} in a network of $n$ nodes. Initially,
each node has one of $k$ opinions. The nodes execute a (randomized) distributed
protocol to agree on the plurality opinion (the opinion initially supported by
the most nodes). Nodes in such networks are often quite cheap and simple, and
hence one seeks protocols that are not only fast but also simple and space
efficient. Typically, protocols depend heavily on the employed communication
mechanism, which ranges from sequential (only one pair of nodes communicates at
any time) to fully parallel (all nodes communicate with all their neighbors at
once) communication and everything in-between.
  We propose a framework to design protocols for a multitude of communication
mechanisms. We introduce protocols that solve the plurality consensus problem
and are with probability 1-o(1) both time and space efficient. Our protocols
are based on an interesting relationship between plurality consensus and
distributed load balancing. This relationship allows us to design protocols
that generalize the state of the art for a large range of problem parameters.
In particular, we obtain the same bounds as the recent result of Alistarh et
al. (who consider only two opinions on a clique) using a much simpler protocol
that generalizes naturally to general graphs and multiple opinions.


title: Symmetric Derivations on Kahler Modules

abstract:
  In this paper, we define generalized symmetric derivations on K\"{a}hler
modules. We give the relationships between the projective dimensions of
$\Omega^{(1)}(R/k)$ and $\Omega^{(2)}(R/k)$ by using the symmetric
derivation.We then give some interesting results by using this definition and
related to K\"{a}hler modules and symmetric derivations.


title: Discovering correlated fermions using quantum Monte Carlo

abstract:
  It has become increasingly feasible to use quantum Monte Carlo (QMC) methods
to study correlated fermion systems for realistic Hamiltonians. We give a
summary of these techniques targeted at researchers in the field of correlated
electrons, focusing on the fundamentals, capabilities, and current status of
this technique. The QMC methods often offer the highest accuracy solutions
available for systems in the continuum, and, since they address the many-body
problem directly, the simulations can be analyzed to obtain insight into the
nature of correlated quantum behavior.


title: A Probabilistic Modeling Approach to Hearing Loss Compensation

abstract:
  Hearing Aid (HA) algorithms need to be tuned ("fitted") to match the
impairment of each specific patient. The lack of a fundamental HA fitting
theory is a strong contributing factor to an unsatisfying sound experience for
about 20% of hearing aid patients. This paper proposes a probabilistic modeling
approach to the design of HA algorithms. The proposed method relies on a
generative probabilistic model for the hearing loss problem and provides for
automated inference of the corresponding (1) signal processing algorithm, (2)
the fitting solution as well as a principled (3) performance evaluation metric.
All three tasks are realized as message passing algorithms in a factor graph
representation of the generative model, which in principle allows for fast
implementation on hearing aid or mobile device hardware. The methods are
theoretically worked out and simulated with a custom-built factor graph toolbox
for a specific hearing loss model.


title: C-planarity of Embedded Cyclic c-Graphs

abstract:
  We show that c-planarity is solvable in quadratic time for flat clustered
graphs with three clusters if the combinatorial embedding of the underlying
graph is fixed. In simpler graph-theoretical terms our result can be viewed as
follows. Given a graph $G$ with the vertex set partitioned into three parts
embedded on a 2-sphere, our algorithm decides if we can augment $G$ by adding
edges without creating an edge-crossing so that in the resulting spherical
graph the vertices of each part induce a connected sub-graph. We proceed by a
reduction to the problem of testing the existence of a perfect matching in
planar bipartite graphs. We formulate our result in a slightly more general
setting of cyclic clustered graphs, i.e., the simple graph obtained by
contracting each cluster, where we disregard loops and multi-edges, is a cycle.


title:
Bayesian prediction for physical models with application to the
  optimization of the synthesis of pharmaceutical products using chemical
  kinetics

abstract:
  Quality control in industrial processes is increasingly making use of prior
scientific knowledge, often encoded in physical models that require numerical
approximation. Statistical prediction, and subsequent optimization, is key to
ensuring the process output meets a specification target. However, the
numerical expense of approximating the models poses computational challenges to
the identification of combinations of the process factors where there is
confidence in the quality of the response. Recent work in Bayesian computation
and statistical approximation (emulation) of expensive computational models is
exploited to develop a novel strategy for optimizing the posterior probability
of a process meeting specification. The ensuing methodology is motivated by,
and demonstrated on, a chemical synthesis process to manufacture a
pharmaceutical product, within which an initial set of substances evolve
according to chemical reactions, under certain process conditions, into a
series of new substances. One of these substances is a target pharmaceutical
product and two are unwanted by-products. The aim is to determine the
combinations of process conditions and amounts of initial substances that
maximize the probability of obtaining sufficient target pharmaceutical product
whilst ensuring unwanted by-products do not exceed a given level. The
relationship between the factors and amounts of substances of interest is
theoretically described by the solution to a system of ordinary differential
equations incorporating temperature dependence. Using data from a small
experiment, it is shown how the methodology can approximate the multivariate
posterior predictive distribution of the pharmaceutical target and by-products,
and therefore identify suitable operating values. Materials to replicate the
analysis can be found at www.github.com/amo105/chemicalkinetics.