title:
Enhanced sensing of molecular optical activity with plasmonic nanohole
  arrays

abstract:
  Prospects of using metal hole arrays for the enhanced optical detection of
molecular chirality in nanosize volumes are investigated. Light transmission
through the holes filled with an optically active material is modeled and the
activity enhancement by more than an order of magnitude is demonstrated. The
spatial resolution of the chirality detection is shown to be of a few tens of
nanometers. From comparing the effect in arrays of cylindrical holes and holes
of complex chiral shape, it is concluded that the detection sensitivity is
determined by the plasmonic near field enhancement. The intrinsic chirality of
the arrays due to their shape appears to be less important.


title: Turbulence: does energy cascade exist?

abstract:
  To answer the question whether a cascade of energy exists or not in
turbulence, we propose a set of correlation functions able to test if there is
an irreversible transfert of energy, step by step, from large to small
structures. These tests are applied to real Eulerian data of a turbulent
velocity flow, taken in the wind grid tunnel of Modane, and also to a prototype
model equation for wave turbulence. First we demonstrate the irreversible
character of the flow by using multi-time correlation function at a given point
of space. Moreover the unexpected behavior of the test function leads us to
connect irreversibility and finite time singularities (intermittency). Secondly
we show that turbulent cascade exists, and is a dynamical process, by using a
test function depending on time and frequency. The cascade shows up only in the
inertial domain where the kinetic energy is transferred more rapidly (on
average) from the wavenumber $k_{1}$ to $k_{2}$ than from $k_{1}$ to $k'_{2}$
larger than $k_{2}$.


title: Stability of infinite time blow up for the Patlak Keller Segel system

abstract:
  We consider the parabolic-elliptic Patlak-Keller-Segel (PKS) model of
chemotactic aggregation in two space dimensions which describes the aggregation
of bacteria under chemo-taxis. When the mass is equal to $8\pi$ and the second
moment is finite (the doubly critical case), we give a precise description of
the dynamic as time goes to infinity and extract the limiting profile and
speed. The proof shows that this dynamic is stable under perturbations.


title:
Energy Efficient Restoring of Barrier Coverage in Wireless Sensor
  Networks Using Limited Mobility Sensors

abstract:
  In Wireless Sensor Networks, sensors are used for tracking objects,
monitoring health and observing a region/territory for different environmental
parameters. Coverage problem in sensor network ensures quality of monitoring a
given region. Depending on applications different measures of coverage are
there. Barrier coverage is a type of coverage, which ensures all paths that
cross the boundary of a region intersect at least one sensor's sensing region.
The goal of the sensors is to detect intruders as they cross the boundary or as
they penetrate a protected area. The sensors are dependent on their battery
life. Restoring barrier coverage on sensor failure using mobile sensors with
minimum total displacement is the primary objective of this paper. A
centralized barrier coverage restoring scheme is proposed to increase the
robustness of the network. We formulate restoring barrier coverage as bipartite
matching problem. A distributed restoring of barrier coverage algorithm is also
proposed, which restores it by first finding existing alternate barrier. If
alternate barrier is not found, an alternate barrier is reconstructed by
shifting existing sensors in a cascaded manner. Detailed simulation results are
shown to evaluate the performance of our algorithms.


title:
Orbital driven impurity spin effect on the magnetic order of quasi-three
  dimensional cupric oxide

abstract:
  Density functional calculations are performed to study the magnetic order of
the severely distorted square planar cupric oxide (CuO) and local spin disorder
in it in the presence of the transition metal impurities M (= Cr, Mn, Fe, Co
and Ni). The distortion in the crystal structure, arisen to reduce the band
energy by minimizing the covalent interaction, creates two crisscrossing zigzag
spin-1/2 chains. From the spin dimer analysis we find that while the spin chain
along [10$\bar 1$] has strong Heisenberg type antiferromagnetic coupling (J ~
127 meV), along [101] it exhibits weak, but robust, ferromagnetic coupling (J ~
9 meV) mediated by reminiscent p-d covalent interactions. The impurity effect
on the magnetic ordering is independent of M and purely orbital driven. If the
given spin-state of M is such that the d$_{x^2-y^2}$ orbital is spin-polarized,
then the original long-range ordering is maintained. However, if d$_{x^2-y^2}$
orbital is unoccupied, the absence of corresponding covalent interaction breaks
the weak ferromagnetic coupling and a spin-flip takes place at the impurity
site leading to breakdown of the long range magnetic ordering.


title:
Asymmetric propagation using enhanced self-demodulation in a chirped
  phononic crystal

abstract:
  Asymmetric propagation of acoustic waves is theoretically reported in a
chirped phononic crystal made of the combination of two different nonlinear
solids. The dispersion of the system is spatially dependent and allows the
rainbow trapping inside the structure. Nonlinearity is used to activate the
self-demodulation effect, which is enhanced due to the particular dispersion
characteristics of the system. The main feature of the device is that
integrates the nonlinear and the filtering effects in a single propagating
medium. The performed numerical study reveals an efficient generation of the
demodulated wave, up to 15\% in terms of the pressure amplitude, as well as
strong attenuation for undesired frequency components above the cut-off
frequency. The obtained energy rectification ratio is in the order of $10^4$
for the whole range of amplitudes employed in this work, indicating the
robustness of the asymmetry and non-reciprocity of the proposed device for a
wide operational range.


title:
Quantified-Self 2.0: Using Context-Aware Services for Promoting Gradual
  Behaviour Change

abstract:
  The recent development of smartphone and wearable sensor technologies enable
general public to carry self-tracking tasks more easily. Much work has been
devoted to life data collection and visualisation to help people with better
self-understanding. We believe that although (awareness/knowledge discovery is
an important aspect of personal informatics, knowledge maintenance is more, or
at least equally, important. In this paper, we propose a proactive approach
that uses the knowledge mined from people's activity data to nudge them towards
a good lifestyle (better knowledge maintenance). For demonstration purpose, a
trial study was designed and implemented for good sleep maintenance. In the
study, we first use smartphones as activity trackers to collect various
features in a non-intrusive manner. We then use those data to learn users'
activity patterns, including daily step amount, app usages, bedding time,
wake-up time and sleep duration. Subsequently, we analyse correlations that may
have the positive or negative impact on users' sleep qualities and finally we
designed and implemented three proactive services that are able to generate
customised advice in the "right" context to nudge users towards a better
lifestyle. The experiments results are positive showing that with the use of
the proposed services 1. daily step amount have been increased by 3.03% on
average in a 10 days study and 2. sleep durations are increased by 7% for two
subjects.


title: Source Accountability with Domain-brokered Privacy

abstract:
  In an ideal network, every packet would be attributable to its sender, while
host identities and transmitted content would remain private. Designing such a
network is challenging because source accountability and communication privacy
are typically viewed as conflicting properties. In this paper, we propose an
architecture that guarantees source accountability and privacy-preserving
communication by enlisting ISPs as accountability agents and privacy brokers.
While ISPs can link every packet in their network to their customers, customer
identity remains unknown to the rest of the Internet. In our architecture,
network communication is based on Ephemeral Identifiers
(EphIDs)---cryptographic tokens that can be linked to a source only by the
source's ISP. We demonstrate that EphIDs can be generated and processed
efficiently, and we analyze the practical considerations for deployment.


title:
Deep Learning the Quantum Phase Transitions in Random Two-Dimensional
  Electron Systems

abstract:
  Random electron systems show rich phases such as Anderson insulator,
diffusive metal, quantum and anomalous quantum Hall insulator, Weyl semimetal,
as well as strong/weak topological insulators. Eigenfunctions of each matter
phase have specific features, but due to the random nature of systems, judging
the matter phase from eigenfunctions is difficult. Here we propose the deep
learning algorithm to capture the features of eigenfunctions.
Localization-delocalization transition as well as disordered Chern
insulator-Anderson insulator transition is discussed.


title:
The role of substrates and environment in piezoresponse force
  microscopy: A case study with regular glass slides

abstract:
  Piezoresponse force microscopy (PFM) is a powerful tool for probing
nanometer-scale ferroelectric and piezoelectric properties. Hysteretic
switching of the phase and amplitude of the PFM response are believed to be the
hallmark of ferroelectric and piezoelectric behavior respectively. However, the
application of PFM is limited by the fact that similar hysteretic effects may
also arise from mechanisms not related to ferroelectricity or piezoelectricity.
In this paper we report our studies on regular glass slides that show
ferroelectric-like signal without being ferroelectric and frequently used as a
substrate in PFM experiments. We demonstrate how the substrates and other
environmental factors like relative humidity and experimental conditions may
influence the PFM results on novel materials.


title: Adiabatic Regularization for Gauge Field and the Conformal Anomaly

abstract:
  We construct the adiabatic regularization method for a $U(1)$ gauge field in
a conformally flat spacetime by quantizing in the canonical formalism the gauge
fixed $U(1)$ theory with mass terms for the gauge fields and the ghost fields.
We show that the adiabatic expansion for the mode functions and the adiabatic
vacuum can be defined in a similar way using WKB-type solutions as the scalar
fields. As an application of the adiabatic method, we compute the trace of the
energy momentum tensor and reproduces the known result for the conformal
anomaly obtained by the other regularization methods. The availability of the
adiabatic expansion scheme for gauge field allows one to study the
renormalization of the de-Sitter space maximal superconformal Yang-Mills theory
using the adiabatic regularization method.


title: Can Evolutionary Sampling Improve Bagged Ensembles?

abstract:
  Perturb and Combine (P&C) group of methods generate multiple versions of the
predictor by perturbing the training set or construction and then combining
them into a single predictor (Breiman, 1996b). The motive is to improve the
accuracy in unstable classification and regression methods. One of the most
well known method in this group is Bagging. Arcing or Adaptive Resampling and
Combining methods like AdaBoost are smarter variants of P&C methods. In this
extended abstract, we lay the groundwork for a new family of methods under the
P&C umbrella, known as Evolutionary Sampling (ES). We employ Evolutionary
algorithms to suggest smarter sampling in both the feature space (sub-spaces)
as well as training samples. We discuss multiple fitness functions to assess
ensembles and empirically compare our performance against randomized sampling
of training data and feature sub-spaces.


title: Quantum Black Hole Entropy and Localization in Supergravity

abstract:
  In this thesis, we examine in detail the notion of black hole entropy in
Quantum Field Theories, with a specific focus on supersymmetric black holes and
the perturbative and non-perturbative quantum corrections to the classical
area-law of Bekenstein-Hawking. To examine such corrections, we employ the
formalism of Sen's Quantum Entropy Function where the complete quantum entropy
of a supersymmetric black hole in theories of supergravity is defined as a
path-integral in the near-horizon region of the black hole. Evaluation of this
path-integral can then be conducted exactly using localization computation
techniques. Due to the exactness of the localization argument, the results
obtained in this manner are therefore formally expected to re-sum all
perturbative and non-perturbative corrections to the classical area-law, and
thus connect to string-theoretic predictions. We investigate such connections
in detail for specific supersymmetric black holes in the hopes of strengthening
a Boltzmann-type interpretation of their thermodynamic entropy as arising from
the degeneracies of the microscopic gravitational constituents (the D-branes).
We find that this picture holds very precisely for two types of black holes
preserving four real supercharges in both four-dimensional $\mathcal{N}=8$ and
$\mathcal{N}=4$ string theories and supergravities. From a broader point of
view, such results can be interpreted as providing important examples where
supergravity theories encode the complete low-energy dynamics of string
theories and provide a consistent effective picture. Some interesting
connections to the mathematical theory of modular forms and mock modular forms
are also exhibited.


title: A Multiplication Formula for the Modified Caldero Chapoton Map

abstract:
  A frieze in the modern sense is a map from the set of objects of a
triangulated category $\mathsf{C}$ to some ring. A frieze $X$ is characterised
by the property that if $\tau x\rightarrow y\rightarrow x$ is an
Auslander-Reiten triangle in $\mathsf{C}$, then $X(\tau x)X(x)-X(y)=1$. The
canonical example of a frieze is the (original) Caldero-Chapoton map, which
send objects of cluster categories to elements of cluster algebras. \par In
\cite{friezes1} and \cite{friezes2}, the notion of generalised friezes is
introduced. A generalised frieze $X'$ has the more general property that
$X'(\tau x)X'(x)-X'(y)\in\{0,1\}$. The canonical example of a generalised
frieze is the modified Caldero-Chapoton map, also introduced in \cite{friezes1}
and \cite{friezes2}. \par Here, we develop and add to the results in
\cite{friezes2}. We define Condition F for two maps $\alpha$ and $\beta$ in the
modified Calero-Chapoton map, and in the case when $\mathsf{C}$ is
2-Calabi-Yau, we show that it is sufficient to replace a more technical
"frieze-like" condition from \cite{friezes2}. We also prove a multiplication
formula for the modified Caldero-Chapoton map, which significantly simplifies
its computation in practice.


title: On the Modeling of Musical Solos as Complex Networks

abstract:
  Notes in a musical piece are building blocks employed in non-random ways to
create melodies. It is the "interaction" among a limited amount of notes that
allows constructing the variety of musical compositions that have been written
in centuries and within different cultures. Networks are a modeling tool that
is commonly employed to represent a set of entities interacting in some way.
Thus, notes composing a melody can be seen as nodes of a network that are
connected whenever these are played in sequence. The outcome of such a process
results in a directed graph. By using complex network theory, some main metrics
of musical graphs can be measured, which characterize the related musical
pieces. In this paper, we define a framework to represent melodies as networks.
Then, we provide an analysis on a set of guitar solos performed by main
musicians. Results of this study indicate that the presented model can have an
impact on audio and multimedia applications such as music classification,
identification, e-learning, automatic music generation, multimedia
entertainment.


title: Signatures of shape phase transitions in odd-mass nuclei

abstract:
  Quantum phase transitions between competing ground-state shapes of atomic
nuclei with an odd number of protons or neutrons are investigated in a
microscopic framework based on nuclear energy density functional theory and the
particle-plus-boson-core coupling scheme. The boson-core Hamiltonian, as well
as the single-particle energies and occupation probabilities of the unpaired
nucleon, are completely determined by constrained self-consistent mean-field
calculations for a specific choice of the energy density functional and paring
interaction, and only the strength parameters of the particle-core coupling are
adjusted to reproduce selected spectroscopic properties of the odd-mass system.
We apply this method to odd-A Eu and Sm isotopes with neutron number $N \approx
90$, and explore the influence of the single unpaired fermion on the occurrence
of a shape phase transition. Collective wave functions of low-energy states are
used to compute quantities that can be related to quantum order parameters:
deformations, excitation energies, E2 transition rates and separation energies,
and their evolution with the control parameter (neutron number) is analysed.


title:
A new kernel-based approach to system identification with quantized
  output data

abstract:
  In this paper we introduce a novel method for linear system identification
with quantized output data. We model the impulse response as a zero-mean
Gaussian process whose covariance (kernel) is given by the recently proposed
stable spline kernel, which encodes information on regularity and exponential
stability. This serves as a starting point to cast our system identification
problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods
to provide an estimate of the system. In particular, we design two methods
based on the so-called Gibbs sampler that allow also to estimate the kernel
hyperparameters by marginal likelihood maximization via the
expectation-maximization method. Numerical simulations show the effectiveness
of the proposed scheme, as compared to the state-of-the-art kernel-based
methods when these are employed in system identification with quantized data.


title:
D-optimal design of b-values for accurate intra-voxel incoherent motion
  imaging

abstract:
  The aim of this paper is to optimally design the set of b-values for
diffusion weighted MRI with the aim of accurate estimation of intra- voxel
incoherent motion (IVIM) parameters (f perfusion fraction, Ds slow diffusion,
Df fast diffusion) according to the model developed by Le Bihan. Previous
studies have addressed the design in a Monte Carlo fash- ion. Due to huge
computation times, this approach is feasible only for a limited number of
values of the parameters (local design): however, as the parameters of a
specific exam are not known a priori, it would be desirable to optimise
b-values over a region of parameters. In order to overcome this issue, we
propose to use a D-optimal design approach. The optimal combination of b-values
can be chosen from a candidate set of predefined values taken from the
literature. Our study has two key results: first, the optimal design does not
depend on perfusion fraction: this allow to perform a search over a 2D
parameter space instead of 3D; second, as an exhaustive search over all
possible designs would still be time consuming, we proposed an algorithm to
find an approximate solution can be found very quickly.


title:
Generation of basis vectors for magnetic structures and displacement
  modes

abstract:
  Increasing attention is being focussed on the use of symmetry-adapted
functions to describe magnetic structures, structural distortions, and
incommensurate crystallography. Though the calculation of such functions is
well developed, significant difficulties can arise, such as the generation of
too many or too few basis functions to minimally span the linear vector space.
We present an elegant solution to these difficulties using the concept of basis
sets, and discuss previous work in this area using this concept. Further, we
highlight the significance of unitary irreducible representations in this
method, and provide the first validation that the irreducible representations
of the crystallographic space groups tabulated by Kovalev are unitary


title: Constructive curves in non-Euclidean planes

abstract:
  In this paper we overview the theory of conics and roulettes in four
non-Euclidean planes. We collect the literature about these classical concepts,
from the eighteenth century to the present, including papers available only on
arXiv. The comparison of the four non-Euclidean planes, in terms of the known
results on conics and roulettes, reflects only the very subjective view of the
author.


title:
Direct illumination calibration of telescopes at the quantum precision
  limit

abstract:
  The electronic response of a telescope under direct illumination by a
point-like light source is based on photon counting. With the data obtained
using the SNDICE light source and the Megacam camera on the CFHT telescope, we
show that the ultimate precision is only limited by the photon statistical
fluctuation, which is below 1 ppm. A key feature of the analysis is the
incorporation of diffuse light that interferes with specularly reflected light
in the transmission model to explain the observed diffraction patterns. The
effect of diffuse light, usually hidden conveniently in the Strehl ratio for an
object at infinity, is characterized with a precision of 10 ppm. In particular,
the spatial frequency representation provides some strong physical constraints
and a practical monitoring of the roughness of various optical surfaces.


title: A Study of the H-dibaryon in Holographic QCD

abstract:
  We study the H-dibaryon (uuddss) in holographic QCD for the first time.
Holographic QCD is derived from a QCD-equivalent D-brane system
($S^1$-compactified D4/D8/$\overline{\rm D8}$) in the superstring theory via
the gauge/gravity correspondence. In holographic QCD, all baryons appear as
topological chiral solitons of Nambu-Goldstone bosons and (axial) vector
mesons. In this framework, the H-dibaryon can be described as an SO(3)-type
hedgehog state. We present the formalism of the H-dibaryon in holographic QCD,
and perform the calculation to investigate its properties in the chiral limit.


title:
A network theoretic study of ecological connectivity in Western
  Himalayas

abstract:
  Network theoretic approach has been used to model and study the flow of
ecological information, growth and connectivity on landscape level of
anemochory plant species Abied pindrow, Betula utilis and Taxus wallichiana in
the Western Himalaya region. A network is formally defined and derived for seed
dispersion model of aforementioned species where vertices represent habitat
patches which are connected by an edge if the distance between the patches is
less than a threshold distance. We define centrality of a network and
computationally identify the habitat patches that are central to the process of
seed dispersion to occur across the network. We find that the network of
habitat patches is a scale free network and at the same time it also displays
small world property characterized by high clustering and low average shortest
path length. Due to high clustering, the spread of species is locally even as
seed disperse mutually among the member vertices of a cluster. Also since every
vertex is only a short number of steps away from every other vertex, the
species rapidly covers all the habitat patches in the component. Also due to
presence of hubs in the network the spread of species is greatly boosted
whenever the species establish and thrive in a hub patch and disperse to
adjacent patches. However, the network is not modular due to geographical
constraints, and is is negatively assortative as the high degree vertices are
connected to vertices of low degree.


title:
Iterated matched products of finite braces and simplicity; new solutions
  of the Yang-Baxter equation

abstract:
  Braces were introduced by Rump as a promising tool in the study of the
set-theoretic solutions of the Yang-Baxter equation. It has been recently
proved that, given a left brace $B$, one can construct explicitly all the
non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation
such that the associated permutation group is isomorphic, as a left brace, to
$B$. It is hence of fundamental importance to describe all simple objects in
the class of finite left braces. In this paper we focus on the matched product
decompositions of an arbitrary finite left brace. This is used to construct new
families of finite simple left braces.


title: Smoothing effects for the filtration equation with different powers

abstract:
  We study the nonlinear diffusion equation $ u_t=\Delta\phi(u) $ on general
Euclidean domains, with homogeneous Neumann boundary conditions. We assume that
$ \phi^\prime(u) $ is bounded from below by $ |u|^{m_1-1} $ for small $ |u| $
and by $ |u|^{m_2-1} $ for large $|u|$, the two exponents $ m_1,m_2 $ being
possibly different and larger than one. The equality case corresponds to the
well-known porous medium equation. We establish sharp short- and long-time $
L^{q_0} $-$ L^\infty $ smoothing estimates: similar issues have widely been
investigated in the literature in the last few years, but the Neumann problem
with different powers had not been addressed yet. This work extends some
previous results in many directions.


title: Nonsymbolic Text Representation

abstract:
  We introduce the first generic text representation model that is completely
nonsymbolic, i.e., it does not require the availability of a segmentation or
tokenization method that attempts to identify words or other symbolic units in
text. This applies to training the parameters of the model on a training corpus
as well as to applying it when computing the representation of a new text. We
show that our model performs better than prior work on an information
extraction and a text denoising task.


title:
Engineering Diffusivity and Operating Voltage in Lithium Iron Phosphate
  through Transition Metal Doping

abstract:
  Density functional calculations are carried out to understand and tailor the
electrochemical profile diffusivity, band gap and open circuit voltage of
transition metal doped olivine phosphate $LiFe_{1-x}M_{x}PO_{4}$ (M = V, Cr,
Mn, Co and Ni). Diffusion and hence the ionic conductivity is studied by
calculating the activation barrier, $V_{act}$, experienced by the diffusing
$Li^{+}$ ion. We show that the effect of dopants on diffusion is both site
dependent and short ranged and thereby it paves ways for microscopic control of
ionic conductivity via selective dopants in this olivine phosphates. Dopants
with lower valence electrons (LVE) compared to Fe repel the $Li^{+}$ ion to
facilitate its outward diffusion, whereas higher valence electron (HVE) dopants
attracts the $Li^{+}$ ion to facilitate the inward diffusion. From the
electronic structure calculation we establish that irrespective of the dopant
M, except Mn, the band gap is reduced since the M-$d$ states always lie within
the pure band gap. Atomically localized $d$ states of HVE dopants lie above the
Fermi energy and that of LVE lie below it. Half-filled Mn-$d$ states undergo
large spin-exchange split to bury the dopant states in valence and conduction
bands of the pristine system and in turn the band gap remains unchanged in
$LiFe_{1-x}Mn_{x}PO_{4}$. Baring Mn, the open circuit voltage increases with
HVE dopants and decreases with LVE dopants.


title: Superprocesses on ultradistributions

abstract:
  Stochastic solutions provide new rigorous results for nonlinear PDE's and,
through its local non-grid nature, are a natural tool for parallel computation.
There are two different approaches for the construction of stochastic
solutions: McKean's and superprocesses. In favour of superprocesses is the fact
that they handle arbitrary boundary conditions. However, when restricted to
measures, superprocesses can only be used to generate solutions for a limited
class of nonlinear PDE's. A new class of superprocesses, namely superprocesses
on ultradistributions, is proposed to extend the stochastic solution approach
to a wider class of PDE's.


title:
Two-particle correlations in azimuthal angle and pseudorapidity in
  inelastic p+p interactions at the CERN Super Proton Synchrotron

abstract:
  Results on two-particle $\Delta\eta\Delta\phi$ correlations in inelastic p+p
interactions at 20, 31, 40, 80, and 158~GeV/c are presented. The measurements
were performed using the large acceptance NA61/SHINE hadron spectrometer at the
CERN Super Proton Synchrotron. The data show structures which can be attributed
mainly to effects of resonance decays, momentum conservation, and quantum
statistics. The results are compared with the EPOS and UrQMD models.


title:
Improved Direct Measurement of the 64.5 keV Resonance Strength in the
  17O(p,a)14N Reaction at LUNA

abstract:
  The $^{17}$O(p,$\alpha$)$^{14}$N reaction plays a key role in various
astrophysical scenarios, from asymptotic giant branch stars to classical novae.
It affects the synthesis of rare isotopes such as $^{17}$O and $^{18}$F, which
can provide constraints on astrophysical models. A new direct determination of
the $E_{\rm R}~=~64.5$~keV resonance strength performed at the Laboratory for
Underground Nuclear Astrophysics accelerator has led to the most accurate value
to date, $\omega\gamma = 10.0 \pm 1.4_{\rm stat} \pm 0.7_{\rm syst}$~neV,
thanks to a significant background reduction underground and generally improved
experimental conditions. The (bare) proton partial width of the corresponding
state at $E_{\rm x} = 5672$~keV in $^{18}$F is $\Gamma_{\rm p} = 35 \pm 5_{\rm
stat} \pm 3_{\rm syst}$~neV. This width is about a factor of 2 higher than
previously estimated thus leading to a factor of 2 increase in the
$^{17}$O(p,$\alpha$)$^{14}$N reaction rate at astrophysical temperatures
relevant to shell hydrogen-burning in red giant and asymptotic giant branch
stars. The new rate implies lower $^{17}$O/$^{16}$O ratios, with important
implications on the interpretation of astrophysical observables from these
stars.


title: Ultrafast Voltage Sampling using Single-Electron Wavepackets

abstract:
  We demonstrate an ultrafast voltage sampling technique using a stream of
electron wavepackets. Electrons are emitted from a single-electron pump and
travel through electron waveguides towards a detector potential barrier. Our
electrons sample an instantaneous voltage on the gate upon arrival at the
detector barrier. Fast sampling is achieved by minimising the duration that the
electrons interact with the barrier, which can be made as small as a few
picoseconds. The value of the instantaneous voltage can be determined by
varying the gate voltage to match the barrier height to the electron energy,
which is used as a stable reference. The test waveform can be reconstructed by
shifting the electron arrival time against it. We argue that this method has
scope to increase the bandwidth of voltage sampling to 100 GHz and beyond.


title:
Weighted composition operators on spaces of analytic functions on the
  complex half-plane

abstract:
  In this paper we will show how the boundedness condition for the weighted
composition operators on a class of spaces of analytic functions on the open
right complex half-plane called Zen spaces (which include the Hardy spaces and
weighted Bergman spaces) can be stated in terms of Carleson measures and
Bergman kernels. In Hilbertian setting we will also show how the norms of
\emph{causal} weighted composition operators on these spaces are related to
each other and use it to show that an \emph{(unweighted) composition operator}
$C_\varphi$ is bounded on a Zen space if and only if $\varphi$ has a finite
angular derivative at infinity. Finally, we will show that there is no compact
composition operator on Zen spaces.


title: Lecture notes on infinity-properads

abstract:
  These are notes for three lectures on higher properads given at a program at
the mathematical institute MATRIX in Australia in June 2016. The first lecture
covers the case of operads, and provides a brief introduction to the
Moerdijk-Weiss theory of dendroidal sets. The second lecture extends the
discussion to properads and our work with Donald Yau on graphical sets. These
two lectures conclude with models for higher (pr)operads given by an inner horn
filling condition. Finally, in the last lecture, we explore some properties of
the graphical category and use them to give a Segal-type model for higher
properads.


title: Uniformity norms, their weaker versions, and applications

abstract:
  We show that, under some mild hypotheses, the Gowers uniformity norms (both
in the additive and in the hypergraph setting) are essentially equivalent to
certain weaker norms which are easier to understand. We present two
applications of this equivalence: a variant of the Koopman--von Neumann
decomposition, and a proof of the relative inverse theorem for the Gowers
$U^s[N]$-norm using a norm-type pseudorandomness condition.


title: Non-Wieferich primes in number fields and ABC conjecture

abstract:
  Let $K/\mathbb{Q}$ be an algebraic number field of class number one and
$\mathcal{O}_K$ be its ring of integers. We show that there are infinitely many
non-Wieferich primes with respect to certain units in $\mathcal{O}_K$ under the
assumption of the \textit{abc} conjecture for number fields.


title: Quantum dilute droplets of dipolar bosons at finite temperature

abstract:
  We systematically study the properties of dipolar Bose gases with two- and
three-body contact interactions at finite temperature using the
Hartree-Fock-Bogoliubov-Popov approximation. In uniform case, we obtain an
exciting new extension of the seminal Lee-Huang-Yang corrected equation of
state that depends explicitly on the thermal fluctuations and on the coupling
constant of the three-body interaction. We investigate, on the other hand, the
effects of thermal fluctuations on the occurrence and stability of a droplet
state in a Bose-Einstein condensate with strong dipole-dipole interactions. We
find that at finite temperature, the droplet phase appears as a narrow peak
surrounded by a broader thermal halo. We show that the number of particles
inside the droplet decays with increasing temperature.


title: Floquet theory of radical pairs in radiofrequency magnetic fields

abstract:
  We present a new method for calculating the product yield of a radical pair
recombination reaction in the presence of a weak time-dependent magnetic field.
This method successfully circumvents the computational difficulties presented
by a direct solution of the Liouville-von Neumann equation for a long-lived
radical pair containing many hyperfine-coupled nuclear spins. Using a modified
formulation of Floquet theory, treating the time-dependent magnetic field as a
perturbation, and exploiting the slow radical pair recombination, we show that
one can obtain a good approximation to the product yield by considering only
nearly-degenerate sub-spaces of the Floquet space. Within a significant
parameter range, the resulting method is found to give product yields in good
agreement with exact quantum mechanical results for a variety of simple model
radical pairs. Moreover it is considerably more efficient than the exact
calculation, and it can be applied to radical pairs containing significantly
more nuclear spins. This promises to open the door to realistic theoretical
investigations of the effect of radiofrequency electromagnetic radiation on the
photochemically induced radical pair recombination reactions in the avian
retina which are believed to be responsible for the magnetic compass sense of
migratory birds.


title: Atomic disintegrations for partially hyperbolic diffeomorphisms

abstract:
  Shub & Wilkinson and Ruelle & Wilkinson studied a class of volume preserving
diffeomorphisms on the three dimensional torus that are stably ergodic. The
diffeomorphisms are partially hyperbolic and admit an invariant central
foliation of circles. The foliation is not absolutely continuous, in fact,
Ruelle & Wilkinson established that the disintegration of volume along central
leaves is atomic. We show that in such a class of volume preserving
diffeomorphisms the disintegration of volume along central leaves is a single
delta measure. We also formulate a general result for conservative three
dimensional skew product like diffeomorphisms on circle bundles, providing
conditions for delta measures as disintegrations of the smooth invariant
measure.


title: A DIY Ultrasonic Signal Generator for Sound Experiments

abstract:
  Many physics departments around the world have electronic and mechanical
workshops attached to them. The job of these workshops is to design and build
experimental setups and instruments for research and the training of
undergraduate students.
  However, in developing countries such as Sudan the lack of qualified
technicians and adequately equipped workshops hampered efforts by these
departments to supplement their laboratories with home built equipment. The
only other option is to buy needed equipment and experimental setups from
specialized manufactures. The latter option is not feasible the departments in
developing countries where funding for education and research is scarce and
very limited as equipments from these manufactures are typically too expensive.
  In the past couple of years and with the advancement in prototyping tools
like Arduino, and microcontroller development boards, more friendly programming
languages, 3D printers, desktop CNC machines and easy to use CAD/CAM softwares
the need for highly qualified technicians and expensive workshop equipment was
then relaxed \cite{nature-flypi}. The availability of such affordable, and
relatively easy to use tools had the effect of increasing the number of
teachers and researchers willing to develop their own experimental
setups\cite{polis-flypi}.
  During the past year and motivated by the need to equip our laboratories with
new setups we established a small workshop at the Department of Physics for
developing experimental setups to be used in our undergraduate laboratories.
The ultrasonic signal generator we are describing here is one such equipment.


title: Pooling Hybrid Representations for Web Structured Data Annotation

abstract:
  Automatically identifying data types of web structured data is a key step in
the process of web data integration. Web structured data is usually associated
with entities or objects in a particular domain. In this paper, we aim to map
attributes of an entity in a given domain to pre-specified classes of
attributes in the same domain based on their values. To perform this task, we
propose a hybrid deep learning network that relies on the format of the
attributes' values. It does so without any pre-processing or using pre-defined
hand-crafted features. The hybrid network combines sequence-based neural
networks, namely convolutional neural networks (CNN) and recurrent neural
networks (RNN), to learn the sequence structure of attributes' values. The CNN
captures short-distance dependencies in these sequences through a sliding
window approach, and the RNN captures long-distance dependencies by storing
information of previous characters. These networks create different vector
representations of the input sequence which are combined using a pooling layer.
This layer applies a specific operation on these vectors in order to capture
their most useful patterns for the task. Finally, on top of the pooling layer,
a softmax function predicts the label of a given attribute value. We evaluate
our strategy in four different web domains. The results show that the pooling
network outperforms previous approaches, which use some kind of input
pre-processing, in all domains.


title:
One-Trial Correction of Legacy AI Systems and Stochastic Separation
  Theorems

abstract:
  We consider the problem of efficient "on the fly" tuning of existing, or {\it
legacy}, Artificial Intelligence (AI) systems. The legacy AI systems are
allowed to be of arbitrary class, albeit the data they are using for computing
interim or final decision responses should posses an underlying structure of a
high-dimensional topological real vector space. The tuning method that we
propose enables dealing with errors without the need to re-train the system.
Instead of re-training a simple cascade of perceptron nodes is added to the
legacy system. The added cascade modulates the AI legacy system's decisions. If
applied repeatedly, the process results in a network of modulating rules
"dressing up" and improving performance of existing AI systems. Mathematical
rationale behind the method is based on the fundamental property of measure
concentration in high dimensional spaces. The method is illustrated with an
example of fine-tuning a deep convolutional network that has been pre-trained
to detect pedestrians in images.


title:
Rotational Dynamics and Star Formation in the Nearby Dwarf Galaxy NGC
  5238

abstract:
  We present new HI spectral line images of the nearby low-mass galaxy NGC
5238, acquired with the Karl G. Jansky Very Large Array (VLA). Located at a
distance of 4.51+/-0.04 Mpc, NGC 5238 is an actively star-forming galaxy with
widespread H-alpha and UV continuum emission. The source is included in many
ongoing and recent nearby galaxy surveys, but until this work the spatially
resolved qualities of its neutral interstellar medium have remained unstudied.
Our HI images resolve the disk on physical scales of ~400 pc, allowing us to
undertake a detailed comparative study of the gaseous and stellar components.
The HI disk is asymmetric in the outer regions, and the areas of high HI mass
surface density display a crescent-shaped morphology that is slightly offset
from the center of the stellar populations. The HI column density exceeds 10^21
cm^-2 in much of the disk. We quantify the degree of co-spatiality of dense HI
gas and sites of ongoing star formation as traced by far-UV and H-alpha
emission. The neutral gas kinematics are complex; using a spatially-resolved
position-velocity analysis, we infer a rotational velocity of 31+/-5 km/s. We
place NGC 5238 on the baryonic Tully-Fisher relation and contextualize the
system amongst other low-mass galaxies.


title:
Integrable differential systems of topological type and reconstruction
  by the topological recursion

abstract:
  Starting from a $d\times d$ rational Lax pair system of the form $\hbar
\partial_x \Psi= L\Psi$ and $\hbar \partial_t \Psi=R\Psi$ we prove that, under
certain assumptions (genus $0$ spectral curve and additional conditions on $R$
and $L$), the system satisfies the "topological type property". A consequence
is that the formal $\hbar$-WKB expansion of its determinantal correlators,
satisfy the topological recursion. This applies in particular to all $(p,q)$
minimal models reductions of the KP hierarchy, or to the six Painlev\'e
systems.


title:
Quantum metrology of spatial deformation using arrays of classical and
  quantum light emitters

abstract:
  We introduce spatial deformations to an array of light sources and study how
the estimation precision of the interspacing distance, d, changes with the
sources of light used. The quantum Fisher information (QFI) is used as the
figure of merit in this work to quantify the amount of information we have on
the estimation parameter. We derive the generator of translations, G, in d due
to an arbitrary homogeneous deformation applied to the array. We show how the
variance of the generator can be used to easily consider how different
deformations and light sources can effect the estimation precision. The single
parameter estimation problem is applied to the array and we report on the
optimal state that maximises the QFI for d. Contrary to what may have been
expected, the higher average mode occupancies of the classical states performs
better in estimating d when compared with single photon emitters (SPEs). The
optimal entangled state is constructed from the eigenvectors of the generator
and found to outperform all these states. We also find the existence of
multiple optimal estimators for the measurement of d. Our results find
applications in evaluating stresses and strains, fracture prevention in
materials expressing great sensitivities to deformations, and selecting
frequency distinguished quantum sources from an array of reference sources.


title:
Synthesis, structure and magnetism of the new $S=\frac{1}{2}$ kagome
  magnet NH$_4$Cu$_{2.5}$V$_2$O$_7$(OH)$_2$.H$_2$O

abstract:
  The study of quantum spin-liquid states (QSL) with lattice dimension $>1$ has
proven an enduring problem in solid state physics. Key candidate materials are
the $S=\frac{1}{2}$ kagome magnets due to their ability to host quantum
fluctuations within the high degeneracy of their frustrated geometries. Studies
of an increasing library of known $S=\frac{1}{2}$ kagome magnetic materials has
challenged our understanding of the possible QSL states, for example, the
recent discovery of a chiral spin-liquid ground state in kapellasite showed
that even magnets with ferromagnetic nearest-neighbour exchange are not
necessarily trivial and that QSL states beyond the superposition of simple
singlet are possible.
  Here, we outline the synthesis, structure and preliminary magnetic
characterisation of a candidate QSL material, the $S=\frac{1}{2}$ kagome magnet
NH$_4$Cu$_{2.5}$V$_2$O$_7$(OH)$_2$.H$_2$O. The crystal structure of
NH$_4$Cu$_{2.5}$V$_2$O$_7$(OH)$_2$.H$_2$O has the 3-fold symmetry of a
geometrically `perfect' kagome lattice while the magnetism shows a competition
between ferromagnetic and antiferromagnetic characters reminiscent of
kapellasite.


title: Extremums of Entropy Production and Second Law in Rayleigh Gas

abstract:
  From the previously obtained solutions of the Fokker - Planck equation for
Rayleigh gas (small impurity of heavy particles in a thermostat of light
particles) with sources and without them, the entropy production was
calculated. In a system without source (isolated system) shown that it holds
theorem of Prigogine, and in a system with sources (open system) implementation
of the principle of Ziegler (MEPP) depends on the relaxation direction. In an
open system entropy production is compensate by a negative production of
entropy, i.e. by a negentropy production. The algebraic sum of entropy and
negentropy productions is called the generalized entropy production. From the
balance of entropy and negentropy productions in an open system formulated a
possible variation of the second law for open systems in a form: "At the
relaxation of an open system to a nonequilibrium steady state, a generalized
entropy production decreases in absolute value and equal to zero in a
nonequilibrium steady state." Keywords: Fokker-Planck equation, Prigogine
theorem, principle of maximum entropy production, the second law, negentropy.


title: Vertical magnetic field gradient in the photospheric layers of sunspots

abstract:
  We investigate the vertical gradient of the magnetic field of sunspots in the
photospheric layer. Independent observations were obtained with the SOT/SP
onboard the Hinode spacecraft and with the TIP-2 mounted at the VTT. We apply
state-of-the-art inversion techniques to both data sets to retrieve the
magnetic field and the corresponding vertical gradient. In the sunspot
penumbrae we detected patches of negative vertical gradients of the magnetic
field strength, i.e.,the magnetic field strength decreases with optical depth
in the photosphere. The negative gradient patches are located in the inner and
partly in the middle penumbrae in both data sets. From the SOT/SP observations,
we found that the negative gradient patches are restricted mainly to the deep
photospheric layers and are concentrated near the edges of the penumbral
filaments. MHD simulations also show negative gradients in the inner penumbrae,
also at the locations of filaments. Both in the observations and simulation
negative gradients of the magnetic field vs. optical depth dominate at some
radial distances in the penumbra. The negative gradient with respect to optical
depth in the inner penumbrae persists even after averaging in the azimuthal
direction, both in the observations and, to a lesser extent, also in MHD
simulations. We interpret the observed localized presence of the negative
vertical gradient of the magnetic field strength in the observations as a
consequence of stronger field from spines expanding with height and closing
above the weaker field inter-spines. The presence of the negative gradients
with respect to optical depth after azimuthal averaging can be explained by two
different mechanisms: the high corrugation of equal optical depth surfaces and
the cancellation of polarized signal due to the presence of unresolved opposite
polarity patches in the deeper layers of the penumbra.


title: Cosmic Sculpture: A new way to visualise the Cosmic Microwave Background

abstract:
  3D printing presents an attractive alternative to visual representation of
physical datasets such as astronomical images that can be used for research,
outreach or teaching purposes, and is especially relevant to people with a
visual disability. We here report the use of 3D printing technology to produce
a representation of the all-sky Cosmic Microwave Background (CMB) intensity
anisotropy maps produced by the Planck mission. The success of this work in
representing key features of the CMB is discussed as is the potential of this
approach for representing other astrophysical data sets. 3D printing such
datasets represents a highly complementary approach to the usual 2D projections
used in teaching and outreach work, and can also form the basis of
undergraduate projects. The CAD files used to produce the models discussed in
this paper are made available.


title: A Survey of Symbolic Execution Techniques

abstract:
  Many security and software testing applications require checking whether
certain properties of a program hold for any possible usage scenario. For
instance, a tool for identifying software vulnerabilities may need to rule out
the existence of any backdoor to bypass a program's authentication. One
approach would be to test the program using different, possibly random inputs.
As the backdoor may only be hit for very specific program workloads, automated
exploration of the space of possible inputs is of the essence. Symbolic
execution provides an elegant solution to the problem, by systematically
exploring many possible execution paths at the same time without necessarily
requiring concrete inputs. Rather than taking on fully specified input values,
the technique abstractly represents them as symbols, resorting to constraint
solvers to construct actual instances that would cause property violations.
Symbolic execution has been incubated in dozens of tools developed over the
last four decades, leading to major practical breakthroughs in a number of
prominent software reliability applications. The goal of this survey is to
provide an overview of the main ideas, challenges, and solutions developed in
the area, distilling them for a broad audience.
  The present survey has been accepted for publication at ACM Computing
Surveys. If you are considering citing this survey, we would appreciate if you
could use the following BibTeX entry: http://goo.gl/Hf5Fvc


title: Bourgain-Brezis Estimates on Symmetric Spaces of Non-compact Type

abstract:
  Let M be a globally Riemannian symmetric space. We prove a duality estimate
between pairings of vector fields with divergence zero and and in L^1 with
vector fields in a critical Sobolev space on M. As a consequence we get a sharp
Calderon-Zygmund estimate for solutions to Poisson's equation on M, where the
right side data is manufactured from divergence free vector fields which are in
L^1. Such a result was proved earlier by Jean Bourgain and Haim Brezis on
Euclidean space.


title:
Non-perturbative guiding center and stochastic gyrocenter
  transformations: gyro-phase is the Kaluza-Klein 5^th dimension also for
  reconciling General Relativity with Quantum Mechanics

abstract:
  The non perturbative guiding center transformation is extended to the
relativistic regime and takes into account electromagnetic fluctuations. The
main solutions are obtained in covariant form: the gyrating particle and the
guiding particle solutions, both in gyro-kinetic as in MHD orderings. Moreover,
the presence of a gravitational field is also considered. The way to introduce
the gravitational field is original and based on the Einstein conjecture on the
feasibility to extend the general relativity theory to include electromagnetism
by geometry, if applied to the extended phase space. In gyro-kinetic theory,
some interesting novelties appear in a natural way, such as the exactness of
the conservation of a magnetic moment, or the fact that the gyro-phase is
treated as the non observable fifth dimension of the \emph{Kaluza-Klein} model.
Electrodynamic becomes non local, without the inconsistency of self-energy.
Finally, the gyrocenter transformation is considered in the presence of
stochastic e.m. fluctuations for explaining quantum behaviors via Nelson's
approach. The gyrocenter law of motion is the \emph{Schr\"odinger} equation.


title: On the Weighted Quartet Consensus problem

abstract:
  In phylogenetics, the consensus problem consists in summarizing a set of
phylogenetic trees that all classify the same set of species into a single
tree. Several definitions of consensus exist in the literature; in this paper
we focus on the Weighted Quartet Consensus problem, a problem with unknown
complexity status so far. Here we prove that the Weighted Quartet Consensus
problem is NP-hard and we give a 1/2-factor approximation for this problem.
During the process, we propose a derandomization procedure of a previously
known randomized 1/3-factor approximation. We also investigate the
fixed-parameter tractability of this problem.


title: Establishing binarity amongst Galactic RV Tauri stars with a disc

abstract:
  This study is a contribution in comprehending the role of binarity upon late
stages of stellar evolution. We determine the binary status of six Galactic RV
Tauri stars, namely DY Ori, EP Lyr, HP Lyr, IRAS 17038-4815, IRAS 09144-4933
and TW Cam, which are surrounded by a dusty disc. We also place them on the HR
diagram, thereby establishing their evolutionary nature. All the six Galactic
RV Tauri stars included in this study are binaries with orbital periods ranging
between $\sim$ 650 and 1700 days and with eccentricities between 0.2 and 0.6.
The mass functions range between 0.08 to 0.55 M$_\odot$ which points to an
unevolved low mass companion. In the photometric time series we detect a
long-term variation on the time-scale of the orbital period for IRAS
17038-4815, IRAS 09144-4933 and TW Cam. Our derived stellar luminosities
obtained from a calibrated PLC relation indicates that all except DY Ori and EP
Lyr, are post-AGB stars. DY Ori and EP Lyr are likely examples of the recently
discovered dusty post-RGB stars. The orbital parameters strongly suggest that
the evolution of these stars was interrupted by a strong phase of binary
interaction during or even prior to the AGB. The observed eccentricities and
long orbital periods among these stars provides a challenge to the standard
theory of binary evolution.


title: Visco-Energetic solutions to one-dimensional rate-independent problems

abstract:
  Visco-Energetic solutions of rate-independent systems are obtained by solving
a modified time Incremental Minimization Scheme, where at each step the
dissipation is reinforced by a viscous correction, typically a quadratic
perturbation of the dissipation distance. Like Energetic and Balanced Viscosity
solutions, they provide a variational characterization of rate-independent
evolutions, with an accurate description of their jump behaviour. In the
present paper we study Visco-Energetic solutions in the one-dimensional case
and we obtain a full characterization for a broad class of energy functionals.
In particular, we prove that they exhibit a sort of intermediate behaviour
between Energetic and Balanced Viscosity solutions, which can be finely tuned
according to the choice of the viscous correction.


title:
The uncertainty of parton distribution functions due to physical
  observables in a global analysis

abstract:
  The recent measurement of the differential $ \gamma+c $-jet cross section,
performed at the Tevatron collider in Run II by the D0 collaboration, is
studied in a next-to-leading order (NLO) global QCD analysis to assess its
impact on the proton parton distribution functions (PDFs). We show that these
data lead to a significant change on the gluon and charm quark distributions.
We demonstrate also that there is an inconsistency between the new high
precision HERA I+II combined data and Tevatron measurement. Moreover, in this
study we investigate the impact of older EMC measurements of charm structure
function $F_{c}^{2}$ on the PDFs and compare the results with those gaining
from the analysis of Tevatron data. We show that both of them have a same
impact on PDFs, and thus can be recognized as same evidences for inefficiency
of perturbative QCD in dealing with the charm production in some kinematic
regions.


title:
Unbound states in $^{12}$C populated by $\gamma$-decay of the
  $(J^{\pi},T) = (2^+,1)$ 16.11 MeV state

abstract:
  The reaction $^{11}\textrm{B}+p$ has been used to populate the $(J^\pi,T) =
(2^+,1)$ state at an excitation energy of 16.11 MeV in $^{12}$C. $\gamma$-decay
to unbound states in $^{12}$C are identified from analysis of the decay of the
populated daughter states. Due to a new technique, $\gamma$-decay to the 10.8
MeV 1$^-$ state is observed for the first time, and transitions to the 9.64 MeV
(3$^-$) and 12.71 MeV (1$^+$) are confirmed. Unresolved transitions to natural
parity strength at 10 MeV and 11.5-13 MeV are also observed. For all
transitions partial widths are deduced


title: Random Cyclic Quadrilaterals

abstract:
  The circumcircle of a planar convex polygon P is a circle C that passes
through all vertices of P. If such a C exists, then P is said to be cyclic. Fix
C to have unit radius. While any two angles of a uniform cyclic triangle are
negatively correlated, any two sides are independent. In contrast, for a
uniform cyclic quadrilateral, any two sides are negatively correlated, whereas
any two adjacent angles are uncorrelated yet dependent.


title: Ergodic averages with prime divisor weights in $L^{1}$

abstract:
  We show that $ { \omega }(n)$ and $ { \Omega }(n)$, the number of distinct
prime factors of $n$ and the number of distinct prime factors of $n$ counted
according to multiplicity are good weighting functions for the pointwise
ergodic theorem in $L^{1}$. That is, if $g$ denotes one of these functions and
$S_{g,K}=\sum_{n\leq K}g(n)$ then for every ergodic dynamical system $(X, { {
\cal A } },\mu, { \tau })$ and every $f\in L^{1}(X)$ $$\lim_{K\to { \infty }}
\frac{1}{S_{g,K}}\sum_{n=1}^{K} g(n)f( { \tau }^{n}x)=\int_{X}fd\mu \text{ for
$\mu$ a.e. }x\in X. $$
  This answers a question raised by C. Cuny and M. Weber who showed this result
for $L^{p}$, $p>1$.


title: Transport of measures on networks

abstract:
  In this paper we formulate a theory of measure-valued linear transport
equations on networks. The building block of our approach is the
initial/boundary-value problem for the measure-valued linear transport equation
on a bounded interval, which is the prototype of an arc of the network. For
this problem we give an explicit representation formula of the solution, which
also considers the total mass flowing out of the interval. Then we construct
the global solution on the network by gluing all the measure-valued solutions
on the arcs by means of appropriate distribution rules at the vertexes. The
measure-valued approach makes our framework suitable to deal with multiscale
flows on networks, with the microscopic and macroscopic phases represented by
Lebesgue-singular and Lebesgue-absolutely continuous measures, respectively, in
time and space.


title:
Mott transition in the A15 phase of Cs$_{3} $C$_{60}$: absence of
  pseudogap and charge order

abstract:
  We present a detailed NMR study of the insulator to metal transition induced
by an applied pressure $p$ in the A15 phase of Cs$_{3}$C$_{60}$. We evidence
that the insulating antiferromagnetic (AF) and superconducting (SC) phases only
coexist in a narrow $p$ range. At fixed $p$, in the metallic state above the SC
transition $T_c$, the $^{133}$Cs and $^{13}$C NMR spin lattice relaxation data
are seemingly governed by a pseudogap like feature. We prove that this feature,
also seen in the $^{133}$Cs NMR shift data is rather a signature of the Mott
transition, which broadens and smears out progressively for increasing $(p,T)$.
The analysis of the variation of the quadrupole splitting $\nu _{Q}$ of the
$^{133}$Cs NMR spectrum precludes any cell symmetry change at the Mott
transition and only monitors a weak variation of lattice parameter. These
results open an opportunity to consider theoretically the Mott transition in a
multiorbital three dimensional system well beyond its critical point.


title: The parabolic Anderson model on the hypercube

abstract:
  We consider the parabolic Anderson model $\frac{\partial}{\partial t}
v_n=\kappa\Delta_n v_n + \xi_n v_n$ on the $n$-dimensional hypercube
$\{-1,+1\}^n$ with random i.i.d. potential $\xi_n$. We parametrize time by
volume and study $v_n$ at the location of the $k$-th largest potential,
$x_{k,2^n}$. Our main result is that, for a certain class of potential
distributions, the solution exhibits a phase transition: for short time scales
$v_n(t_n,x_{k,2^n})$ behaves like a system without diffusion and grows as
$\exp\big\{(\xi_n(x_{k,2^n}) - \kappa)t_n\big\}$, whereas, for long time scales
the growth is dictated by the principle eigenvalue and the corresponding
eigenfunction of the operator $\kappa \Delta_n+\xi_n$, for which we give
precise asymptotics. Moreover, the transition time depends only on the
difference $\xi_n(x_{1,2^n})-\xi_n(x_{k,2^n})$.
  One of our main motivations in this article is to investigate the
mutation-selection model of population genetics on a random fitness landscape,
which is given by the ratio of $v_n$ to its total mass, with $\xi_n$
corresponding to the fitness landscape. We show that the phase transition of
the solution translates to the mutation-selection model as follows: a
population initially concentrated at $x_{k,2^n}$ moves completely to
$x_{1,2^n}$ on time scales where the transition of growth rates happens. The
class of potentials we consider involves the Random Energy Model (REM) of
statistical physics which is studied as one of the main examples of a random
fitness landscape.


title:
Quantitative results for Bruck iterations of demicontinuous
  pseudocontractions

abstract:
  Our first result is a rate of metastability in the sense of Tao for Bruck's
iteration scheme for demicontinuous pseudocontractions in Hilbert space,
extracted from Bruck's original proof. This result generalizes earlier work in
the ongoing program of proof mining from Lipschitzian to demicontinuous
pseudocontractions. Our second main result is a metastable version of
asymptotic regularity under the additional assumption that the underlying
operator is norm-to-norm uniformly continuous on bounded subsets. These results
(and their intermediate versions given in this paper) provide a thorough
quantitative analysis of Bruck's iteration scheme for pseudocontractions in
Hilbert space.


title:
Symplectic structure perturbations and continuity of symplectic
  invariants

abstract:
  This paper studies how symplectic invariants created from Hamiltonian Floer
theory change under the perturbations of symplectic structures, not necessarily
in the same cohomology class. These symplectic invariants include spectral
invariants, boundary depth, and (partial) symplectic quasi-states. This paper
can split into two parts. In the first part, we prove some energy estimations
that control the shifts of symplectic action functionals. These directly imply
positive conclusions on the continuity of spectral invariants and boundary
depth, in some important cases including any symplectic surface $\Sigma_{g
\geq1}$ and any closed symplectic manifold $M$ with $\dim_{\mathcal K} H^2(M;
\mathcal K) = 1$. This follows by applications on some rigidity of the subsets
of a symplectic manifold in terms of heaviness and superheaviness, as well as
on the continuity property of some symplectic capacities. In the second part,
we generalize the construction in the first part to any closed symplectic
manifold. In particular, to deal with the change of Novikov rings from
symplectic structure perturbations, we construct a family of variant Floer
chain complexes over a common Novikov-type ring. In this set-up, we define a
new family of spectral invariants called $t$-spectral invariants, and prove
that they are upper semicontinuous under the symplectic structure
perturbations. This implies a quasi-isometric embedding from $(\mathbb
R^{\infty}, |-|_{\infty})$ to $({\widetilde {\rm Ham}}(M, \omega), |-|_{\rm
Hofer})$ under some dynamical assumption, imitating a result from Usher.


title: Quantitative Strong Convergence for the Hybrid Steepest Descent Method

abstract:
  We provide new complexity information for the convergence of the Hybrid
Steepest Descent Method for solving the Variational Inequality Problem for a
strict contraction on Hilbert space over a closed convex set C given either as
the fixed point set of a single nonexpansive mapping or the intersection of the
fixed point sets of a finite family of nonexpansive mappings. More precisely,
we give metastability rates in the sense of Tao for those cases. The results in
this paper were extracted from a proof due to Yamada using proof-mining
techniques, and provide a thorough quantitative analysis of the Hybrid Steepest
Descent Method.


title:
Extrapolation-Based Implicit-Explicit Peer Methods with Optimised
  Stability Regions

abstract:
  In this paper we investigate a new class of implicit-explicit (IMEX) two-step
methods of Peer type for systems of ordinary differential equations with both
non-stiff and stiff parts included in the source term. An extrapolation
approach based on already computed stage values is applied to construct IMEX
methods with favourable stability properties. Optimised IMEX-Peer methods of
order p = 2, 3, 4, are given as result of a search algorithm carefully designed
to balance the size of the stability regions and the extrapolation errors.
Numerical experiments and a comparison to other implicit-explicit methods are
included.


title: Relativistic perfect fluids in local thermal equilibrium

abstract:
  Every evolution of a fluid is uniquely described by an energy tensor. But the
converse is not true: an energy tensor may describe the evolution of different
fluids. The problem of determining them is called here the {\em inverse
problem}. This problem may admit unphysical or non-deterministic solutions.
This paper is devoted to solve the inverse problem for perfect energy tensors
in the class of perfect fluids evolving in local thermal equilibrium (l.t.e.).
The starting point is a previous result (Coll and Ferrando in J Math Phys 30:
2918-2922, 1989) showing that thermodynamic fluids evolving in l.t.e. admit a
purely hydrodynamic characterization. This characterization allows solving this
inverse problem in a very compact form. The paradigmatic case of perfect energy
tensors representing the evolution of ideal gases is studied in detail and some
applications and examples are outlined.


title:
Semi-supervised Learning with Sparse Autoencoders in Phone
  Classification

abstract:
  We propose the application of a semi-supervised learning method to improve
the performance of acoustic modelling for automatic speech recognition based on
deep neural net- works. As opposed to unsupervised initialisation followed by
supervised fine tuning, our method takes advantage of both unlabelled and
labelled data simultaneously through mini- batch stochastic gradient descent.
We tested the method with varying proportions of labelled vs unlabelled
observations in frame-based phoneme classification on the TIMIT database. Our
experiments show that the method outperforms standard supervised training for
an equal amount of labelled data and provides competitive error rates compared
to state-of-the-art graph-based semi-supervised learning techniques.


title: Black hole and Hawking radiation by type-II Weyl fermions

abstract:
  The type-II Weyl and type-II Dirac fermions may emerge behind the event
horizon of black holes. Correspondingly the black hole can be simulated by
creation of the region with overtilted Weyl or Dirac cones. The filling of the
electronic states inside the "black hole" is accompanied by Hawking radiation.
The Hawking temperature in the Weyl semimetals can reach the room temperature,
if the black hole region is sufficiently small, and thus the effective gravity
at the horizon is large.


title: Parisian Ruin Probability Of An Integrated Gaussian Risk Model

abstract:
  In this paper we investigate the Parisian ruin probability for an integrated
Gaussian process. Under certain assumptions, we find the Parisian ruin
probability and the classical ruin probability are on the log-scale
asymptotically the same. Moreover, for any small interval required by the risk
process staying below level zero, the Parisian ruin probability and the
classical one are the same also in the premise asymptotic behavior.
Furthermore, we derive an approximation of the conditional ruin time.


title: Determining the First Order Character of La(Fe,Mn,Si)13

abstract:
  Definitive determination of first order character of the magnetocaloric
magnetic transition remains elusive. Here we use a microcalorimetry technique
in two modes of operation to determine the contributions to entropy change from
latent heat and heat capacity separately in an engineered set of La(Fe, Mn,
Si)13 samples. We compare the properties extracted by this method with those
determined using magnetometry and propose a model independent parameter that
would allow the degree of first order character to be defined across different
families of materials. The microcalorimetry method is sufficiently sensitive to
allow observation of an additional peak feature in the low field heat capacity
associated with the presence of Mn in these samples. The feature is of magnetic
origin but is insensitive to magnetic field, explicable in terms of
inhomogeneous occupancy of Mn within the lattice resulting in antiferromagnetic
ordered Mn clusters.


title: A New Reference Chemical Composition for TMC-1

abstract:
  Recent detections of complex organic molecules in dark clouds have rekindled
interest in the astrochemical modeling of these environments. Because of its
relative closeness and rich molecular complexity, TMC-1 has been extensively
observed to study the chemical processes taking place in dark clouds. We use
local thermodynamical equilibrium radiative transfer modeling coupled with a
Bayesian statistical method which takes into account outliers to analyze the
data from the Nobeyama spectral survey of TMC-1 between 8 and 50 GHz. We
compute the abundance relative to molecular hydrogen of 57 molecules, including
19 isotopologues in TMC-1 along with their associated uncertainty. The new
results are in general agreement with previous abundance determination from
Ohishi & Kaifu and the values reported in the review from Agundez & Wakelam.
However, in some cases, large opacity and low signal to noise effects allow
only upper or lower limits to be derived, respectively.


title: Linearity defect of the residue field of short local rings

abstract:
  Let $(R,\m,k)$ be a Noetherian local ring with maximal ideal $\m$ and residue
field $k$. The linearity defect of a finitely generated $R$-module $M$, which
is denoted $\ld_R(M)$, is a numerical measure of how far $M$ is from having
linear resolution. We study the linearity defect of the residue field. We give
a positive answer to the question raised by Herzog and Iyengar of whether
$\ld_R(k)<\infty$ implies $\ld_R(k)=0$, in the case when $\m^4=0$.


title: Exact solution of matricial $\Phi^3_2$ quantum field theory

abstract:
  We apply a recently developed method to exactly solve the $\Phi^3$ matrix
model with covariance of a two-dimensional theory, also known as regularised
Kontsevich model. Its correlation functions collectively describe graphs on a
multi-punctured 2-sphere. We show how Ward-Takahashi identities and
Schwinger-Dyson equations lead in a special large-$\mathcal{N}$ limit to
integral equations that we solve exactly for all correlation functions.
Remarkably, these functions are analytic in the $\Phi^3$ coupling constant,
although bounds on individual graphs justify only Borel summability.
  The solved model arises from noncommutative field theory in a special limit
of strong deformation parameter. The limit defines ordinary 2D Schwinger
functions which, however, do not satisfy reflection positivity.


title: Video Pixel Networks

abstract:
  We propose a probabilistic video model, the Video Pixel Network (VPN), that
estimates the discrete joint distribution of the raw pixel values in a video.
The model and the neural architecture reflect the time, space and color
structure of video tensors and encode it as a four-dimensional dependency
chain. The VPN approaches the best possible performance on the Moving MNIST
benchmark, a leap over the previous state of the art, and the generated videos
show only minor deviations from the ground truth. The VPN also produces
detailed samples on the action-conditional Robotic Pushing benchmark and
generalizes to the motion of novel objects.


title:
Activation cross sections of proton induced nuclear reactions on
  palladium up to 80 MeV

abstract:
  Activation cross sections of proton induced nuclear reactions on palladium
were measured up to 80 MeV by using the stacked foil irradiation technique and
gamma ray spectrometry. The beam intensity, the incident energy and the energy
degradation were controlled by a method based on flux constancy via
normalization to the excitation functions of monitor reactions measured in
parallel. Excitation functions for direct and cumulative cross-sections were
measured for the production of ${}^{104m,104g,105}$${}^{g,106m,110m}$Ag,
${}^{100,101}$Pd, ${}^{99m,99g,100,}$${}^{101m}$${}^{,101g,102m,102g,105}$Rh
and ${}^{103,}$${}^{97}$Ru radioisotopes. The cross section data were compared
with the theoretical predictions of TENDL-2014 and -2015 libraries. For
practical applications thick target yields were derived from the measured
excitation functions. Application in the field of medical radionuclide
production is shortly discussed.


title: Path Integral Guided Policy Search

abstract:
  We present a policy search method for learning complex feedback control
policies that map from high-dimensional sensory inputs to motor torques, for
manipulation tasks with discontinuous contact dynamics. We build on a prior
technique called guided policy search (GPS), which iteratively optimizes a set
of local policies for specific instances of a task, and uses these to train a
complex, high-dimensional global policy that generalizes across task instances.
We extend GPS in the following ways: (1) we propose the use of a model-free
local optimizer based on path integral stochastic optimal control (PI2), which
enables us to learn local policies for tasks with highly discontinuous contact
dynamics; and (2) we enable GPS to train on a new set of task instances in
every iteration by using on-policy sampling: this increases the diversity of
the instances that the policy is trained on, and is crucial for achieving good
generalization. We show that these contributions enable us to learn deep neural
network policies that can directly perform torque control from visual input. We
validate the method on a challenging door opening task and a pick-and-place
task, and we demonstrate that our approach substantially outperforms the prior
LQR-based local policy optimizer on these tasks. Furthermore, we show that
on-policy sampling significantly increases the generalization ability of these
policies.


title:
Potential Energy Landscape of the Apparent First-Order Phase Transition
  between Low-Density and High-Density Amorphous Ice

abstract:
  The potential energy landscape (PEL) formalism is a valuable approach within
statistical mechanics for describing supercooled liquids and glasses. Here we
use the PEL formalism and computer simulations to study the pressure-induced
transformations between low-density amorphous ice (LDA) and high-density
amorphous ice (HDA) at different temperatures. We employ the ST2 water model
for which the LDA-HDA transformations are remarkably sharp, similar to what is
observed in experiments, and reminiscent of a first-order phase transition. Our
results are consistent with the view that LDA and HDA configurations are
associated with two distinct regions (megabasins) of the PEL that are separated
by a potential energy barrier. At higher temperature, we find that low-density
liquid (LDL) configurations are located in the same megabasin as LDA, and that
high-density liquid (HDL) configurations are located in the same megabasin as
HDA. We show that the pressure-induced LDL-HDL and LDA-HDA transformations
occur along paths that interconnect these two megabasins, but that the path
followed by the liquid is different than the path followed by the amorphous
solid. At higher pressure, we also study the liquid-to-ice-VII first-order
phase transition, and find that the behavior of the PEL properties across this
transition are qualitatively similar to the changes found during the LDA-HDA
transformation. This similarity supports the interpretation that the LDA-HDA
transformation is a first-order-like phase transition between
out-of-equilibrium states.


title:
A $q$-boson representation of Zamolodchikov-Faddeev algebra for
  stochastic $R$ matrix of $U_q(A^{(1)}_n)$

abstract:
  We construct a $q$-boson representation of the Zamolodchikov-Faddeev algebra
whose structure function is given by the stochastic $R$ matrix of
$U_q(A^{(1)}_n)$ introduced recently. The representation involves quantum
dilogarithm type infinite products in the $n(n-1)/2$-fold tensor product of
$q$-bosons. It leads to a matrix product formula of the stationary
probabilities in the $U_q(A_n^{(1)})$-zero range process on a one-dimensional
periodic lattice.


title: Cellular Automata and Finite Groups

abstract:
  For a finite group $G$ and a finite set $A$, we study various algebraic
aspects of cellular automata over the configuration space $A^G$. In this
situation, the set $\text{CA}(G;A)$ of all cellular automata over $A^G$ is a
finite monoid whose basic algebraic properties had remained unknown. First, we
investigate the structure of the group of units $\text{ICA}(G;A)$ of
$\text{CA}(G;A)$. We obtain a decomposition of $\text{ICA}(G;A)$ into a direct
product of wreath products of groups that depends on the numbers $\alpha_{[H]}$
of periodic configurations for conjugacy classes $[H]$ of subgroups of $G$. We
show how the numbers $\alpha_{[H]}$ may be computed using the M\"obius function
of the subgroup lattice of $G$, and we use this to improve the lower bound
recently found by Gao, Jackson and Seward on the number of aperiodic
configurations of $A^G$. Furthermore, we study generating sets of
$\text{CA}(G;A)$; in particular, we prove that $\text{CA}(G;A)$ cannot be
generated by cellular automata with small memory set, and, when all subgroups
of $G$ are normal, we determine the relative rank of $\text{ICA}(G;A)$ on
$\text{CA}(G;A)$, i.e. the minimal size of a set $V \subseteq \text{CA}(G;A)$
such that $\text{CA}(G;A) = \langle \text{ICA}(G;A) \cup V \rangle$.


title:
Inertia and universality of avalanche statistics: The case of slowly
  deformed amorphous solids

abstract:
  By means of a finite elements technique we solve numerically the dynamics of
an amorphous solid under deformation in the quasistatic driving limit. We study
the noise statistics of the stress-strain signal in the steady state plastic
flow, focusing on systems with low internal dissipation. We analyze the
distributions of avalanche sizes and durations and the density of shear
transformations when varying the damping strength. In contrast to avalanches in
the overdamped case, dominated by the yielding point universal exponents,
inertial avalanches are controlled by a non-universal damping dependent
feedback mechanism; eventually turning negligible the role of correlations.
Still, some general properties of avalanches persist and new scaling relations
can be proposed.


title:
Spin dipole nuclear matrix elements for double beta decay nuclei by
  charge-exchange reactions

abstract:
  Spin dipole (SD) strengths for double beta-decay (DBD) nuclei were studied
experimentally for the first time by using measured cross sections of (3He,t)
charge exchange reactions (CERs). Then SD nuclear matrix elements (NMEs) for
low-lying 2- states were derived from the experimental SD strengths by
referring to the experimental GT (Gamow-Teller) and F (Fermi) strengths. They
are consistent with the empirical SD NMEs based on the quasi-particle model
with the empirical effective SD coupling constant. The CERs are used to
evaluate the SD NME, which is associated with one of the major components of
the neutrino-less DBD NME.


title:
On extreme transient events from rotating black holes and their
  gravitational wave emission

abstract:
  The super-luminous object ASASSN-15lh (SN2015L) is an extreme event with a
total energy $E_{rad}\simeq 1.1\times 10^{52}$ erg in black body radiation on
par with its kinetic energy $E_k$ in ejecta and a late time plateau in the UV,
that defies a nuclear origin. It likely presents a new explosion mechanism for
hydrogen-deprived supernovae. With no radio emission and no H-rich environment
we propose to identify $E_{rad}$ with dissipation of a baryon-poor outflow in
the optically thick remnant stellar envelope produced by a central engine. By
negligible time scales of light crossing and radiative cooling of the envelope,
SN2015L's light curve closely tracks the evolution of this engine. We here
model its light curve by the evolution of black hole spin, during angular
momentum loss in Alv\'en waves to matter at the Inner Most Stable Circular
Orbit (ISCO). The duration is determined by $\sigma=M_T/M$ of the torus mass
$M_T$ around the black hole of mass $M$: $\sigma\sim 10^{-7}$ and $\sigma\sim
10^{-2}$ for SN2015L and, respectively, a long GRB. The observed
electromagnetic radiation herein represents a minor output of the rotational
energy $E_{rot}$ of the black hole, while most is radiated unseen in
gravitational radiation. This model explains the high-mass slow-spin binary
progenitor of GWB150914, as the remnant of two CC-SNe in an intra-day binary of
two massive stars. This model rigorously predicts a change in magnitude $\Delta
m\simeq 1.15$ in the light curve post-peak, in agreement with the light curve
of SN2015L with no fine-tuning.


title:
Modelling Quantum Mechanical Processes by Processes Energy Distribution
  of Inner Oscillations of a Nanoparticle in the Phase Space

abstract:
  We consider the problem of computing energy distribution of inner harmonic
oscillations of a nanoparticle in its phase space, when the particle moves in a
medium in heat equilibrium under certain temperature. It is assumed that the
particle obeys the Brownian motion under the action of the medium and the force
field given by a potential function. In the present paper we provide and study
an equation describing the problem, generalizing the Klein--Kramers equation.
It is shown that for large value of medium resistance, the process of energy
distribution of inner harmonic oscillations of the nanoparticle is represented
as the composition of a rapid transition process and a slow process. After the
rapid transition process, the system goes to a quasi-stationary state. The slow
process is approximately described by the standard Schrodinger equation used
for description ofquantum processes. Thus, the process being studied can serve
as a model of quantum processes.


title:
Quantum Thermodynamics and Quantum Entanglement Entropies in an
  Expanding Universe

abstract:
  We investigate an asymptotically spatially flat Robertson-Walker spacetime
from two different perspectives. First, using von Neumann entropy, we evaluate
the entanglement generation due to the encoded information in spacetime. Then,
we work out the entropy of particle creation based on the quantum
thermodynamics of the scalar field on the underlying spacetime. We show that
the general behavior of both entropies are the same. Therefore, the
entanglement can be applied to the customary quantum thermodynamics of the
universe. Also, using these entropies, we can recover some information about
the parameters of spacetime.


title: Near-Field Thermal Energy Conversion by Tunneling to a Waveguide

abstract:
  Energy is a vital resource and hence there is a continuous strive to improve
upon existing technologies and to find new ones that address that basic need.
The conversion of thermal energy is the primary method of generating electrical
energy from a broad range of sources, for example fossil fuels, solar thermal,
geothermal, and nuclear energy. A common need in all cases is the ability to
efficiently extract the generated electromagnetic and thermal energy and to
convert it to electricity. The current methods of thermal energy extraction are
based on heat engines, thermoelectric and thermophotovoltaic conversion
systems. In this report a method based on the direct extraction of
Electromagnetic energy from the thermal near-field through tunneling and
subsequent waveguiding, is presented.


title:
Comment on 'Reasonable fermionic quantum information theories require
  relativity'

abstract:
  In [N. Friis, New J. Phys. 18, 033014 (2016)] the non-relativistic
description of fermions is considered and in particular the role of the parity
superselection rule in relation to the characterization of entanglement. An
argument based on the spin-statistics connection is presented as a physical
motivation for the parity superselection rule. Since the spin statistics
connection was derived in the context of relativistic quantum mechanics it is
argued that the inclusion of the parity superselection rule is motivated by
Lorentz invariance. Based on this it is further argued that fermionic Quantum
Information theory and the theory of special relativity are conceptually
inseparable. In this comment a different, and well known, motivation for the
parity superselection rule is given that does not rely on arguments from
relativistic quantum mechanics, but instead uses the assumptions that the laws
of physics are the same for different observers and the no-signalling
principle.


title:
K-theory of semi-linear endomorphisms via the Riemann-Hilbert
  correspondence

abstract:
  Grayson, developing ideas of Quillen, has made computations of the K-theory
of "semi-linear endomorphisms". In the present text we develop a technique to
compute these groups in the case of Frobenius semi-linear actions. The main
idea is to interpret the semi-linear modules as crystals and use a positive
characteristic version of the Riemann-Hilbert correspondence. We also compute
the K-theory of the category of etale constructible p-torsion sheaves.


title: A half-normal distribution scheme for generating functions

abstract:
  We present a general theorem on the structure of bivariate generating
functions which gives sufficient conditions such that the limiting probability
distribution is a half-normal distribution. If $X$ is a normally distributed
random variable with zero mean, then $|X|$ obeys a half-normal distribution. In
the second part, we apply our result to prove three natural appearances in the
domain of lattice paths: the number of returns to zero, the height, and the
sign changes are under zero drift distributed according to a half-normal
distribution. This extends known results to a general step set. Finally, our
result also gives a new proof of Banach's matchbox problem.


title:
The Gamma renewal process as an output of the diffusion leaky
  integrate-and-fire neuronal model

abstract:
  Statistical properties of spike trains as well as other neurophysiological
data suggest a number of mathematical models of neurons. These models range
from entirely descriptive ones to those deduced from the properties of the real
neurons. One of them, the diffusion leaky integrate-and-fire neuronal model,
which is based on the Ornstein-Uhlenbeck stochastic process that is restricted
by an absorbing barrier, can describe a wide range of neuronal activity in
terms of its parameters. These parameters are readily associated with known
physiological mechanisms. The other model is descriptive, Gamma renewal
process, and its parameters only reflect the observed experimental data or
assumed theoretical properties. Both of these commonly used models are related
here. We show under which conditions the Gamma model is an output from the
diffusion Ornstein-Uhlenbeck model. In some cases we can see that the Gamma
distribution is unrealistic to be achieved for the employed parameters of the
Ornstein-Uhlenbeck process.


title: Bow shock nebulae of hot massive stars in a magnetized medium

abstract:
  A significant fraction of OB-type, main-sequence massive stars are classified
as runaway and move supersonically through the interstellar medium (ISM). Their
strong stellar winds interact with their surroundings where the typical
strength of the local ISM magnetic field is about 3.5-7 micro-G, which can
result in the formation of bow shock nebulae. We investigate the effects of
such magnetic fields, aligned with the motion of the flow, on the formation and
emission properties of these circumstellar structures. Our axisymmetric,
magneto-hydrodynamical simulations with optically-thin radiative cooling,
heating and anisotropic thermal conduction show that the presence of the
background ISM magnetic field affects the projected optical emission our bow
shocks at Ha and [OIII] lambda 5007 which become fainter by about 1-2 orders of
magnitude, respectively. Radiative transfer calculations against dust opacity
indicate that the magnetic field slightly diminishes their projected infrared
emission and that our bow shocks emit brightly at 60 micron. This may explain
why the bow shocks generated by ionizing runaway massive stars are often
difficult to identify. Finally, we discuss our results in the context of the
bow shock of Zeta Ophiuchi and we support the interpretation of its imperfect
morphology as an evidence of the presence of an ISM magnetic field not aligned
with the motion of its driving star.


title: Nouvelles conditions pour l'inexistence des nombres parfaits impairs

abstract:
  We will show the two following results: If there existe an odd perfect number
$n$ of prime decomposition $n=p_1^{\alpha_1} \ldots p_k^{\alpha_k}q^\beta$,
where the $\alpha_i$ are even, the $\beta$ are odd and $q \equiv 5 \mod 8$.
Then there is at least one $p_i$, $1 \leq i \leq k$ that is not a square in
$\mathbb{Z}/q\mathbb{Z}$. More precisely there is an odd number of $p_i$ that
are not squares in $\mathbb{Z}/q\mathbb{Z}$. If there exist an odd perfect
number $n$ of prime decomposition $n=p_1^{\alpha_1} \ldots
p_k^{\alpha_k}q^\beta$, where the $\alpha_i$ are even, the $\beta$ are odd and
$p_{k+1} \equiv {1\mod 8}$. Then at least one $p_i$, $1 \leq i \leq k+1$ is a
non zero square in at least one $\mathbb{Z}/{p_j}\mathbb{Z}$, $1 \leq j \leq
k+1$. Contains an appendix of known results.
  -----
  Un nombre, $n$, est dit parfait s'il est \'egal \`a la somme de ses diviseurs
propres plus 1. Par exemple $6=1+2+3$. Dans ce document, les deux propositions
suivantes seront d\'emontr\'ees: S'il existe un nombre parfait impair, $n$, de
d\'ecomposition en nombre premier $n=p_1^{\alpha_1} \ldots
p_k^{\alpha_k}q^\beta$, o\`u les $ \alpha_i$ sont pairs, $\beta$ est impair et
$q \equiv 5 \mod 8$. Alors, au moins un $p_i$, $1 \leq i \leq k$ n'est pas un
carr\'e dans $\mathbb{Z}/q\mathbb{Z}$. Plus pr\'ecis\'ement un nombre impair de
$p_i$ ne sont pas des carr\'es dans $\mathbb{Z}/q\mathbb{Z}$. S'il existe un
nombre parfait impair, $n$, de d\'ecomposition en nombre premier
$n=p_1^{\alpha_1} \ldots p_k^{\alpha_k}q^\beta$, o\`u les $\alpha_i$ sont
pairs, $\beta$ est impair et $p_{k+1} \equiv {1\mod 8}$. Alors au moins un
$p_i$, $1 \leq i \leq k+1$ est un carr\'e non nul dans au moins un $\mathbb{Z}
/ {p_j}\mathbb{Z}$, $1 \leq j \leq k+1$. Contiens une annexe contenant les
r\'esultats d\'ej\`a connus et des preuves que j'en ai faites.


title:
Various 3x3 Nonnegative Matrices with Prescribed Eigenvalues and
  Diagonal Entries

abstract:
  In this paper, we answer the various forms of nonnegative inverse eigenvalue
problems with prescribed diagonal entries for order three: real or complex
general matrices, symmetric stochastic matrices, and real or complex doubly
stochastic matrices. We include the known cases, the symmetric matrices and
real or complex stochastic matrices, to compare the other results and for
completeness. In addition, for a given list of eigenvalues, we compute the
exact range for the largest value of the diagonal entries of the various
nonnegative matrices.


title:
Quark-flavour violating Higgs decays to charm and bottom pairs in the
  MSSM

abstract:
  We calculate the decay width of $h^0 \to b \bar{b}$ in the Minimal
Supersymmetric Standard Model (MSSM) with quark-flavour violation (QFV) at full
one-loop level. The effect of $\tilde{c}-\tilde{t}$ mixing and
$\tilde{s}-\tilde{b}$ mixing is studied taking into account the constraints
from the B-meson data. We discuss and compare in detail the decays $h^0 \to c
\bar{c}$ and $h^0 \to b \bar{b}$ within the framework of the perturbative mass
insertion technique using the Flavour Expansion Theorem. The deviation of both
decay widths from the Standard Model results can be quite large. While in $h^0
\to c \bar{c}$ it is almost entirely due to the flavour violating part of the
MSSM, in $h^0 \to b \bar{b}$ it is mainly due to the flavour conserving part.
Nevertheless, $\Gamma(h^0 \to b \bar{b})$ can fluctuate up to $\sim 7\%$ due to
QFV chargino exchange with large $\tilde{c}-\tilde{t}$ mixing. due to QFV
chargino exchange with large $\tilde{c}-\tilde{t}$ mixing.


title: Criteria for universality of quantum gates

abstract:
  We consider the problem of deciding if a set of quantum one-qudit gates
$\mathcal{S}=\{U_1,\ldots,U_n\}$ is universal. We provide the compact form
criteria leading to a simple algorithm that allows deciding universality of any
given set of gates in a finite number of steps. Moreover, for a non-universal
$\mathcal{S}$ our criteria indicate what type of gates can be added to
$\mathcal{S}$ to turn it into a universal set.


title:
Enceladus's and Dione's floating ice shells supported by minimum stress
  isostasy

abstract:
  Enceladus's gravity and shape have been explained in terms of a thick
isostatic ice shell floating on a global ocean, in contradiction of the thin
shell implied by librations. Here we propose a new isostatic model minimizing
crustal deviatoric stress, and demonstrate that gravity and shape data predict
a $\rm{38\pm4\,km}$-thick ocean beneath a $\rm{23\pm4\,km}$-thick shell
agreeing with -- but independent of -- libration data. Isostatic and tidal
stresses are comparable in magnitude. South polar crust is only $7\pm4\rm\,km$
thick, facilitating the opening of water conduits and enhancing tidal
dissipation through stress concentration. Enceladus's resonant companion,
Dione, is in a similar state of minimum stress isostasy. Its gravity and shape
can be explained in terms of a $\rm{99\pm23\,km}$-thick isostatic shell
overlying a $\rm{65\pm30\,km}$-thick global ocean, thus providing the first
clear evidence for a present-day ocean within Dione.


title: Origins and Impacts of High-Density Symmetry Energy

abstract:
  What is nuclear symmetry energy? Why is it important? What do we know about
it? Why is it so uncertain especially at high densities? Can the total symmetry
energy or its kinetic part be negative? What are the effects of three-body
and/or tensor force on symmetry energy? How can we probe the density dependence
of nuclear symmetry energy with terrestrial nuclear experiments? What
observables of heavy-ion reactions are sensitive to the high-density behavior
of nuclear symmetry energy? How does the symmetry energy affect properties of
neutron stars, gravitational waves and our understanding about the nature of
strong-field gravity? In this lecture, we try to answer these questions as best
as we can based on some of our recent work and/or understanding of research
done by others. This note summarizes the main points of the lecture.


title: Thermal spikes induced sublimation of carbon nanotubes

abstract:
  We report and provide justification for the consistently observed four
experimental facts of the mass spectrometric data of carbon cluster emission
from the low-energy Cs irradiated single-walled carbon nanotubes . Firstly, the
diatomic carbon C(2) is the most abundant sputtered species for Cs+ in the
energy range 0.2 keV to 2.0 keV. Secondly, monatomic carbon C(1) is emitted
with the least sputtering yield. Thirdly, at low cesium energies i the emitted
species are C(2), C(3) and C(4). Lastly, as the irradiating Cs+ energy
increases, the normalized yield of atomic carbon monotonically increases while
clusters show gradual decrease and saturation. Sputtering of clusters is proved
here to be due to thermal spikes. Binary collision cascade theory does not
explain cluster sputtering. A statistical thermal model is developed to explain
the experimentally observed data. The probability of a cluster C(x) to be
emitted is shown to be proportional to that for the creation of an x-member
vacancy with formation energy E at temperature T as {exp(E/kT)+1}^(-1). The
energies of formation of single and double vacancies from DFT calculations and
the ratio of normalized experimental yields have been used to estimate spike
temperature. We show that by invoking thermal spikes, cluster emission from,
and the multiple vacancy generation in, the Cs+-irradiated SWCNTs can be
explained. We also suggest modifications to Monte Carlo type calculations of
sputtering.