title: On adaptive posterior concentration rates

abstract:
  We investigate the problem of deriving posterior concentration rates under
different loss functions in nonparametric Bayes. We first provide a lower bound
on posterior coverages of shrinking neighbourhoods that relates the metric or
loss under which the shrinking neighbourhood is considered, and an intrinsic
pre-metric linked to frequentist separation rates. In the Gaussian white noise
model, we construct feasible priors based on a spike and slab procedure
reminiscent of wavelet thresholding that achieve adaptive rates of contraction
under $L^2$ or $L^{\infty}$ metrics when the underlying parameter belongs to a
collection of H\"{o}lder balls and that moreover achieve our lower bound. We
analyse the consequences in terms of asymptotic behaviour of posterior credible
balls as well as frequentist minimax adaptive estimation. Our results are
appended with an upper bound for the contraction rate under an arbitrary loss
in a generic regular experiment. The upper bound is attained for certain sieve
priors and enables to extend our results to density estimation.


title:
Self-adjoint extensions and stochastic completeness of the
  Laplace-Beltrami operator on conic and anticonic surfaces

abstract:
  We study the evolution of the heat and of a free quantum particle (described
by the Schr\"odinger equation) on two-dimensional manifolds endowed with the
degenerate Riemannian metric $ds^2=dx^2+|x|^{-2\alpha}d\theta^2$, where $x\in
\mathbb R$, $\theta\in\mathbb T$ and the parameter $\alpha\in\mathbb R$. For
$\alpha\le-1$ this metric describes cone-like manifolds (for $\alpha=-1$ it is
a flat cone). For $\alpha=0$ it is a cylinder. For $\alpha\ge 1$ it is a
Grushin-like metric. We show that the Laplace-Beltrami operator $\Delta$ is
essentially self-adjoint if and only if $\alpha\notin(-3,1)$. In this case the
only self-adjoint extension is the Friedrichs extension $\Delta_F$, that does
not allow communication through the singular set $\{x=0\}$ both for the heat
and for a quantum particle. For $\alpha\in(-3,-1]$ we show that for the
Schr\"odinger equation only the average on $\theta$ of the wave function can
cross the singular set, while the solutions of the only Markovian extension of
the heat equation (which indeed is $\Delta_F$) cannot. For $\alpha\in(-1,1)$ we
prove that there exists a canonical self-adjoint extension $\Delta_B$, called
bridging extension, which is Markovian and allows the complete communication
through the singularity (both of the heat and of a quantum particle). Also, we
study the stochastic completeness (i.e., conservation of the $L^1$ norm for the
heat equation) of the Markovian extensions $\Delta_F$ and $\Delta_B$, proving
that $\Delta_F$ is stochastically complete at the singularity if and only if
$\alpha\le -1$, while $\Delta_B$ is always stochastically complete at the
singularity.


title:
Euler & Lagrange versus Heisenberg & Schroedinger: Dynamical Pictures
  in Classical and Quantum Mechanics

abstract:
  Using quantum-classical analogies, we find that dynamical pictures of quantum
mechanics have precise counterparts in classical mechanics. In particular, the
Eulerian and Lagrangian descriptions of fluid dynamics in classical mechanics
are the analogs of the Schroedinger and Heisenberg pictures in quantum
mechanics, respectively. Similarities between classical and quantum dynamical
pictures are explored within the framework of the Koopman-von Neumann
formalism. These allow for a natural definition of various dynamical pictures
in classical mechanics as well as the application of classical concepts to
quantum dynamics. As an illustration, we use the interaction picture to find
the classical evolution of an ensemble of particles of equal initial momenta
and arbitrary configuration density under the action of a constant force in one
dimension. As a second example, we discuss the extension of the ideas of
sensitivity to initial conditions and chaos in classical mechanics to quantum
mechanics.


title: Radiation fields on Schwarzschild spacetime

abstract:
  In this paper we define the radiation field for the wave equation on the
Schwarzschild black hole spacetime. In this context it has two components: the
rescaled restriction of the time derivative of a solution to null infinity and
to the event horizon. In the process, we establish some regularity properties
of solutions of the wave equation on the spacetime. In particular, we prove
that the regularity of the solution across the event horizon and across null
infinity is determined by the regularity and decay rate of the initial data at
the event horizon and at infinity. We also show that the radiation field is
unitary with respect to the conserved energy and prove support theorems for
each piece of the radiation field.


title: RKKY interaction induced by two-dimensional hole gases

abstract:
  We analytically compute the RKKY range function as induced by two-dimensional
(2D) hole gases. The bulk valence-band includes heavy-hole (HH) and light-hole
(LH) states and their dynamics is described by the Luttinger Hamiltonian which
we adopt as our framework. We show that even for situations where only the
lowest HH-like subband is occupied the resulting form of the RKKY function can
be very different as compared to the one of a 2D electron gas. The associated
spin susceptibility tensor has entries along the quantum-well directions and
perpendicular to it. Our formluae for the spin susceptibility tensor reveal the
crucial influence of HH-LH mixing which gives rise to large anisotropies both
among the in-plane components as well as among the in-plane components and the
component perpendicular to the quantum-well.


title:
Resolved Giant Molecular Clouds in Nearby Spiral Galaxies: Insights from
  the CANON CO (1-0) Survey

abstract:
  We resolve 182 individual giant molecular clouds (GMCs) larger than 2.5
$\times$ 10$^{5}$ \Msun in the inner disks of five large nearby spiral galaxies
(NGC 2403, NGC 3031, NGC 4736, NGC 4826, and NGC 6946) to create the largest
such sample of extragalactic GMCs within galaxies analogous to the Milky Way.
Using a conservatively chosen sample of GMCs most likely to adhere to the
virial assumption, we measure cloud sizes, velocity dispersions, and $^{12}$CO
(J=1-0) luminosities and calculate cloud virial masses. The average conversion
factor from CO flux to H$_{2}$ mass (or \xcons) for each galaxy is 1-2
\xcounits, all within a factor of two of the Milky Way disk value ($\sim$2
\xcounits). We find GMCs to be generally consistent within our errors between
the galaxies and with Milky Way disk GMCs; the intrinsic scatter between clouds
is of order a factor of two. Consistent with previous studies in the Local
Group, we find a linear relationship between cloud virial mass and CO
luminosity, supporting the assumption that the clouds in this GMC sample are
gravitationally bound. We do not detect a significant population of GMCs with
elevated velocity dispersions for their sizes, as has been detected in the
Galactic center. Though the range of metallicities probed in this study is
narrow, the average conversion factors of these galaxies will serve to anchor
the high metallicity end of metallicity-\xco trends measured using conversion
factors in resolved clouds; this has been previously possible primarily with
Milky Way measurements.


title: Ideal triangulations and geometric transitions

abstract:
  Thurston introduced a technique for finding and deforming three-dimensional
hyperbolic structures by gluing together ideal tetrahedra. We generalize this
technique to study families of geometric structures that transition from
hyperbolic to anti de Sitter (AdS) geometry. Our approach involves solving
Thurston's gluing equations over several different shape parameter algebras. In
the case of a punctured torus bundle with Anosov monodromy, we identify two
components of real solutions for which there are always nearby positively
oriented solutions over both the complex and pseudo-complex numbers. These
complex and pseudo-complex solutions define hyperbolic and AdS structures that,
after coordinate change in the projective model, may be arranged into one
continuous family of real projective structures. We also study the rigidity
properties of certain AdS structures with tachyon singularities.


title: Double Neutrino Production and Detection in Neutrino Detectors

abstract:
  Large, high-energy ($E>100$ GeV) cosmic neutrino telescopes are now quite
mature. IceCube, for example, observes about 50,000 well-reconstructed single
atmospheric neutrino events/year, with energies above 100 GeV. Although the
neutrino detection probability is small, current detectors are large enough so
that it is possible to detect two neutrinos from the same cosmic-ray
interaction. In this paper, we calculate the expected rate of double-neutrino
interactions from a single cosmic-ray air shower. The rate is small, about 0.07
events/year for a 1 km$^3$ detector like IceCube, with only a small dependence
on the assumed cosmic-ray composition and hadronic interaction model. For a
larger detector, like the proposed KM3Net, the rate is about 0.8 events/year, a
rate that should be easily observable. These double neutrino interactions are
the major irreducible background to searches of pairs of particles produced in
supersymmetric neutrino or cosmic-ray air-shower interactions. Other
standard-model backgrounds are considered, and found to be small.


title: The second laws of quantum thermodynamics

abstract:
  The second law of thermodynamics tells us which state transformations are so
statistically unlikely that they are effectively forbidden. Its original
formulation, due to Clausius, states that "Heat can never pass from a colder to
a warmer body without some other change, connected therewith, occurring at the
same time". The second law applies to systems composed of many particles
interacting; however, we are seeing that one can make sense of thermodynamics
in the regime where we only have a small number of particles interacting with a
heat bath. Is there a second law of thermodynamics in this regime? Here, we
find that for processes which are cyclic or very close to cyclic, the second
law for microscopic systems takes on a very different form than it does at the
macroscopic scale, imposing not just one constraint on what state
transformations are possible, but an entire family of constraints. In
particular, we find a family of free energies which generalise the traditional
one, and show that they can never increase. We further find that there are
three regimes which determine which family of second laws govern state
transitions, depending on how cyclic the process is. In one regime one can
cause an apparent violation of the usual second law, through a process of
embezzling work from a large system which remains arbitrarily close to its
original state. These second laws are not only relevant for small systems, but
also apply to individual macroscopic systems interacting via long-range
interactions, which only satisfy the ordinary second law on average. By making
precise the definition of thermal operations, the laws of thermodynamics take
on a simple form with the first law defining the class of thermal operations,
the zeroeth law emerging as a unique condition ensuring the theory is
nontrivial, and the remaining laws being a monotonicity property of our
generalised free energies.

categories: quant-ph cond-mat.stat-mech cs.IT math.IT


title: Open Gromov-Witten invariants and SYZ under local conifold transitions

abstract:
  For a local Calabi-Yau manifold which is a smoothing of toric Gorenstein
singularity, this paper computes the open Gromov-Witten invariants of a generic
fiber of the special Lagrangian fibration constructed by Gross and thereby
constructs its SYZ mirror. Moreover it derives a relation for the generating
function of open Gromov-Witten invariants of the local Calabi-Yau manifold and
that of its conifold transition.


title: Two-mode effective interaction in a double-well condensate

abstract:
  We investigate the origin of a disagreement between the two-mode model and
the exact Gross-Pitaevskii dynamics applied to double-well systems. In general
this model, even in its improved version, predicts a faster dynamics and
underestimates the critical population imbalance separating Josephson and
self-trapping regimes. We show that the source of this mismatch in the dynamics
lies in the value of the on-site interaction energy parameter. Using simplified
Thomas-Fermi densities, we find that the on-site energy parameter exhibits a
linear dependence on the population imbalance, which is also confirmed by
Gross-Pitaevskii simulations. When introducing this dependence in the two-mode
equations of motion, we obtain a reduced interaction energy parameter which
depends on the dimensionality of the system. The use of this new parameter
significantly heals the disagreement in the dynamics and also produces better
estimates of the critical imbalance.


title: Results from NA61/SHINE

abstract:
  In this paper we summarize recent results from NA61/SHINE relevant for heavy
ion physics, neutrino oscillations and the interpretation of air showers
induced by ultra-high energy cosmic rays.


title: Fractal multi-scale nature of solar/stellar magnetic field

abstract:
  An abstract mathematical concept of fractal organization of certain complex
objects received significant attention in astrophysics during last decades. The
concept evolved into a broad field including multi-fractality and
intermittency, percolation theory, self-organized criticality, theory of
catastrophes, etc. Such a strong mathematical and physical approach provide new
possibilities for exploring various aspects of astrophysics. In particular, in
the solar and stellar magnetism, multi-fractal properties of magnetized plasma
turned to be useful for understanding burst-like dynamics of energy release
events, conditions for turbulent dynamo action, nature of turbulent magnetic
diffusivity, and even the dual nature of solar dynamo. In this review, I will
briefly outline how the ideas of multi-fractality are used to explore the above
mentioned aspects of solar magnetism.


title:
The Explicit Sato-Tate Conjecture and Densities Pertaining to
  Lehmer-Type Questions

abstract:
  Let $f(z)=\sum_{n=1}^\infty a(n)q^n\in S^{\text{new}}_ k (\Gamma_0(N))$ be a
newform with squarefree level $N$ that does not have complex multiplication.
For a prime $p$, define $\theta_p\in[0,\pi]$ to be the angle for which
$a(p)=2p^{( k -1)/2}\cos \theta_p $. Let $I\subset[0,\pi]$ be a closed
subinterval, and let $d\mu_{ST}=\frac{2}{\pi}\sin^2\theta d\theta$ be the
Sato-Tate measure of $I$. Assuming that the symmetric power $L$-functions of
$f$ satisfy certain analytic properties (all of which follow from Langlands
functoriality and the Generalized Riemann Hypothesis), we prove that if $x$ is
sufficiently large, then \[ \left|\#\{p\leq x:\theta_p\in I\}
-\mu_{ST}(I)\int_2^x\frac{dt}{\log t}\right|\ll\frac{x^{3/4}\log(N k x)}{\log
x} \] with an implied constant of $3.34$. By letting $I$ be a short interval
centered at $\frac{\pi}{2}$ and counting the primes using a smooth cutoff, we
compute a lower bound for the density of positive integers $n$ for which
$a(n)\neq0$. In particular, if $\tau$ is the Ramanujan tau function, then under
the aforementioned hypotheses, we prove that \[
\lim_{x\to\infty}\frac{\#\{n\leq x:\tau(n)\neq0\}}{x}>1-1.54\times10^{-13}. \]
We also discuss the connection between the density of positive integers $n$ for
which $a(n)\neq0$ and the number of representations of $n$ by certain
positive-definite, integer-valued quadratic forms.


title:
The discovery of gluon-dominant system in heavy ion collisions ---- the
  large elliptic flow of direct photons

abstract:
  The discussion of the large elliptic flow of direct photons in Quark Matter
2014 has been reviewed. Then based on previous technique work, the physics
meaning related to the large elliptic flow of direct photons is invetigated in
this paper.


title: Electron Transport Through Ag-Silicene-Ag Junctions

abstract:
  For several years the electronic structure properties of the novel
two-dimensional system silicene have been studied extensively. Electron
transport across metal-silicence junctions, however, remains relatively
unexplored. To address this issue, we developed and implemented a theoretical
framework that utilizes the tight-binding Fisher-Lee relation to span
non-equilibrium Green's function (NEGF) techniques, the scattering method, and
semiclassical Boltzmann transport theory. Within this hybrid quantum-classical,
two-scale framework, we calculated transmission and reflection coefficients of
monolayer and bilayer Ag-silicene-Ag junctions using the NEGF method in
conjunction with density functional theory; derived and calculated the group
velocities; and computed resistance using the semi-classical Boltzmann
equation. We found that resistances of these junctions are $\sim${}$ 0.08 \fom$
for monolayer silicene junctions and $\sim${}$ 0.3 \fom$ for bilayer ones,
factors of $\sim$8 and $\sim$2, respectively, smaller than Sharvin resistances
estimated via the Landauer formalism.


title: Smoothness of subRiemannian isometries

abstract:
  We show that the group of isometries (i.e., distance-preserving
homeomorphisms) of an equiregular subRiemannian manifold is a
finite-dimensional Lie group of smooth transformations. The proof is based on a
new PDE argument, in the spirit of harmonic coordinates, establishing that in
an arbitrary subRiemannian manifold there exists an open dense subset where all
isometries are smooth.


title: Interpolation, Bridgeland stability and monomial schemes in the plane

abstract:
  Given a zero-dimensional scheme Z, the higher-rank interpolation problem asks
for the classification of slopes of vector bundles cohomologically orthogonal
to the ideal sheaf of Z. In this paper, we solve this problem for all
zero-dimensional monomial schemes in the projective plane. As a corollary, we
obtain detailed information on the stable base loci of divisors on the Hilbert
scheme of points on the plane. We prove the correspondence between walls in the
Bridgeland stability manifold and walls in the Mori chamber decomposition of
the effective cone conjectured by Arcara-Bertram-Coskun-Huizenga for monomial
schemes. We determine the Harder-Narasimhan filtration of ideal sheaves of
monomial schemes for suitable Bridgeland stability conditions and, as a
consequence, obtain a new resolution better suited for cohomology computations
than other standard resolutions such as the minimal free resolution.


title:
CPMD simulation of Cu2+ -- phenylalanine complex under micro-solvated
  environment

abstract:
  The study combines DFT calculations and CPMD simulations to investigate the
structures of phenylalanine-copper (II) ([Phe-Cu]2+) complexes and the
micro-solvation processes. ....It is found that the phenylalanine moiety
appears to be in the neutral form in isolated and mono-hydrated complexes, but
in the zwitterionic form in other hydrated complexes (with n no less than 2).
.... The present CPMD simulations reveal that the maximum coordination of Cu2+
in the presence of the Phe ligand does not exceed four: the oxygen atoms from
three water molecules and one carboxyl oxygen atom of Phe. Any excess water
molecules will migrate to the second solvation shell. Moreover a unique
structural motif is present in the lowest energy complexes, which is recognized
to be significant in stabilizing the structures of the complexes. .....


title: Single Dirac point and helical states in a one-dimensional system

abstract:
  Odd numbers of Dirac points and helical states can exist at edges (surfaces)
of two-dimensional (three-dimensional) topological insulators. In the bulk of a
one-dimensional lattice (not an edge) with time reversal symmetry, however, a
no-go theorem forbids the existence of an odd number of Dirac points or helical
states. Introducing a magnetic field can violate the time reversal condition
but would usually lift the degeneracy at the Dirac points. We find that a
spatially periodic magnetic field with zero mean value can induce a single
Dirac point in a one-dimensional system with spin-orbit coupling. A wealth of
new physics may emerge due to the existence of a single Dirac point and helical
states in the bulk of a one-dimensional lattice (rather than edge states). A
series of quantized numbers emerge due to the non-trivial topology of the 1D
helical states, including the doubled period of helical Bloch oscillations,
quantized conductance near the Dirac point, and 1/2-charge solitons at mass
kinks. Such a system can be realized in one-dimensional semiconductor systems
or in optical traps of atoms.


title:
A study of aliphatic amino acids using simulated vibrational circular
  dichroism and Raman optical activity spectra

abstract:
  Vibrational optical activity (VOA) spectra, such as vibrational circular
dichroism (VCD) and Raman optical activity (ROA) spectra, of aliphatic amino
acids are simulated using density functional theory (DFT) methods in both gas
phase (neutral form) and solution (zwitterionic form), together with their
respective infrared (IR) and Raman spectra of the amino acids. The DFT models,
which are validated by excellent agreements with the available experimental
Raman and ROA spectra of alanine in solution, are employed to study other
aliphatic amino acids. The inferred (IR) intensive region (below 2000 cm-1)
reveals the signature of alkyl side chains, whereas the Raman intensive region
(above 3000 cm-1) contains the information of the functional groups in the
amino acids. Furthermore, the chiral carbons of the amino acids (except for
glycine) dominate the VCD and ROA spectra in the gas phase, but the methyl
group vibrations produce stronger VCD and ROA signals in solution. The C-H
related asymmetric vibrations dominate the VOA spectra (i.e., VCD and ROA) >
3000 cm-1 reflecting the side chain structures of the amino acids. Finally the
carboxyl and the C(2)H modes of aliphatic amino acids, together with the side
chain vibrations, are very active in the VCD/IR and ROA/Raman spectra, which
makes such the vibrational spectroscopic methods a very attractive means to
study biomolecules.


title:
Broadband infrared and Raman probes of excited-state vibrational
  molecular dynamics; Simulation protocols based on loop diagram

abstract:
  Vibrational motions in electronically excited states can be observed by
either time and frequency resolved infrared absorption or by off resonant
stimulated Raman techniques. Multipoint correlation function expressions are
derived for both signals. Three representations for the signal which suggest
different simulation protocols are developed. These are based on the forward
and the backward propagation of the wavefunction, sum over state expansion
using an effective vibration Hamiltonian and a semiclassical treatment of a
bath. We show that the effective temporal ($\Delta t$) and spectral
($\Delta\omega$) resolution of the techniques is not controlled solely by
experimental knobs but also depends on the system dynamics being probed. The
Fourier uncertainty $\Delta\omega\Delta t>1$ is never violated.


title: Thermopower and the Mott formula for a Majorana edge state

abstract:
  We study the thermoelectric effect between a conducting lead and a Majorana
edge state. In the tunneling limit, we first use the Landuaer-Buttiker
formalism to derive the Mott formula relating the thermopower and the
differential conductance between a conducting lead and a superconductor. When
the tunneling takes place between a conducting lead and a Majorana edge state,
we show that a non-vanishing thermopower can exist. Combining measurements of
the differential conductance and the voltage difference induced by the
temperature difference between the conducting lead and the edge state, the Mott
formula provides a unique way to infer the temperature of the Majorana edge
state.


title: Vassiliev Invariants of Virtual Legendrian Knots

abstract:
  We introduce a theory of virtual Legendrian knots. A virtual Legendrian knot
is a cooriented wavefront on an oriented surface up to Legendrian isotopy of
its lift to the unit cotangent bundle and stabilization and destablization of
the surface away from the wavefront. We show that the groups of Vassiliev
invariants of virtual Legendrian knots and of virtual framed knots are
isomorphic. In particular, Vassiliev invariants cannot be used to distinguish
virtual Legendrian knots that are isotopic as virtual framed knots and have
equal virtual Maslov numbers.


title:
Chen's conjecture and epsilon-superbiharmonic submanifolds of Riemannian
  manifolds

abstract:
  B.-Y. Chen famously conjectured that every submanifold of Euclidean space
with harmonic mean curvature vector is minimal. In this note we establish a
much more general statement for a large class of submanifolds satisfying a
growth condition at infinity. We discuss in particular two popular competing
natural interpretations of the conjecture when the Euclidean background space
is replaced by an arbitrary Riemannian manifold. Introducing the notion of
epsilon-superbiharmonic submanifolds, which contains each of the previous
notions as special cases, we prove that epsilon-superbiharmonic submanifolds of
a complete Riemannian manifold which satisfy a growth condition at infinity are
minimal.


title: Diophantine and cohomological dimensions

abstract:
  We give explicit linear bounds on the p-cohomological dimension of a field in
terms of its Diophantine dimension. In particular, we show that for a field of
Diophantine dimension at most 4, the 3-cohomological dimension is less than or
equal to the Diophantine dimension.


title:
Hwang-Mok rigidity of cominuscule homogeneous varieties in positive
  characteristic

abstract:
  Jun-Muk Hwang and Ngaiming Mok have proved the rigidity of irreducible
Hermitian symmetric spaces of compact type under Kaehler degeneration. I adapt
their argument to the algebraic setting in positive characteristic, where
cominuscule homogeneous varieties serve as an analogue of Hermitian symmetric
spaces. The main result gives an explicit (computable in terms of Schubert
calculus) lower bound on the characteristic of the base field, guaranteeing
that a smooth projective family with cominuscule homogeneous generic fibre is
isotrivial. The bound depends only on the type of the generic fibre, and on the
degree of an invertible sheaf whose extension to the special fibre is very
ample. An important part of the proof is a characteristic-free analogue of
Hwang and Mok's extension theorem for maps of Fano varieties of Picard number
1, a result I believe to be interesting in its own right.


title:
Photonic Bound State in the Continuum for Strong Light-matter
  Interaction

abstract:
  The photonic bound state in the continuum (BIC) is discovered in a hybrid
photonic circuit with low refractive index waveguide on a high refractive index
thin membrane, where the optical dissipation is forbidden because of the
destructive interference of different leakage channels. Based on the photonic
BIC, the low mode area in a hybrid waveguide and high quality factor in a
microresonator can be applied to enhance the light-matter interaction. Taking
the fabrication-friendly polymer structure on diamond membrane as an example,
those excellent optical performances can exist in a wide range of structure
parameters with large fabrication tolerance and induce the strong coupling
between photon and nitrogen-vacancy center in the diamond for scalable quantum
information processors and networks. Such a fabrication-friendly structure with
photonic BIC is also very promising in laser, nonlinear optical and quantum
optical applications.


title:
Pathwise uniqueness of one-dimensional SDEs driven by one-sided stable
  processes

abstract:
  For $\alpha\in (0,1)$, we consider stochastic differential equations driven
by one-sided stable processes of order $\alpha$: \[dX_t= \phi(X_{t-})\ dZ_t.\]
We prove that pathwise uniqueness holds for this equation under the assumptions
that $\phi$ is continuous, non-decreasing and positive on $\R$. A
counterexample is given to show that the positivity of $\phi$ is crucial for
pathwise uniqueness to hold.


title: An Introduction to the Einstein Toolkit

abstract:
  We give an introduction to the Einstein Toolkit, a mature, open-source
computational infrastructure for numerical relativity based on the Cactus
Framework, for the target group of new users. This toolkit is composed of
several different modules, is developed by researchers from different
institutions throughout the world and is in active continuous development.
Documentation for the toolkit and its several modules is often scattered across
different locations, a difficulty new users may at times have to struggle with.
Scientific papers exist describing the toolkit and its methods in detail, but
they might be overwhelming at first. With these lecture notes we hope to
provide an initial overview for new users. We cover how to obtain, compile and
run the toolkit, and give an overview of some of the tools and modules provided
with it.


title: Removable sets for homogeneous linear PDE in Carnot groups

abstract:
  Let $\cL$ be a homogeneous left invariant differential operator on a Carnot
group. Assume that both $\cL$ and $\cL^t$ are hypoelliptic. We study the
removable sets for $\cL$-solutions. We give precise conditions in terms of the
Carnot--Carath\'eodory Hausdorff dimension for the removability for
$\cL$-solutions under several auxiliary integrability or regularity hypotheses.
In some cases, our criteria are sharp on the level of the relevant Hausdorff
measure. One of the main ingredients in our proof is the use of novel local
self similar tilings in Carnot groups.


title:
Lacerta I and Cassiopeia III: Two luminous and distant Andromeda
  satellite dwarf galaxies found in the 3{\pi} Pan-STARRS1 survey

abstract:
  We report the discovery of two new dwarf galaxies, Lacerta I/Andromeda XXXI
(Lac I/And XXXI) and Cassiopeia III/Andromeda XXXII (Cas III/And XXXII), in
stacked Pan-STARRS1 r_P1- and i_P1-band imaging data. Both are luminous systems
(M_V ~ -12) located at projected distances of 20.3{\deg} and 10.5{\deg} from
M31. Lac I and Cas III are likely satellites of the Andromeda galaxy with
heliocentric distances of 756^{+44}_{-28} kpc and 772^{+61}_{-56} kpc,
respectively, and corresponding M31-centric distances of 275+/-7 kpc and
144^{+6}_{-4} kpc . The brightest of recent Local Group member discoveries,
these two new dwarf galaxies owe their late discovery to their large sizes (r_h
= 4.2^{+0.4}_{-0.5} arcmin or 912^{+124}_{-93} pc for Lac I; r_h =
6.5^{+1.2}_{-1.0} arcmin or 1456+/-267 pc for Cas III), and consequently low
surface brightness (\mu_0 ~ 26.0 mag/arcsec^2), as well as to the lack of a
systematic survey of regions at large radii from M31, close to the Galactic
plane. This latter limitation is now alleviated by the 3{\pi} Pan-STARRS1
survey, which could lead to the discovery of other distant Andromeda satellite
dwarf galaxies.


title: Planck Constraints on Holographic Dark Energy

abstract:
  We perform a detailed investigation on the cosmological constraints on the
holographic dark energy (HDE) model by using the Planck data. HDE can provide a
good fit to Planck high-l (l>40) temperature power spectrum, while the
discrepancy at l=20-40 found in LCDM remains unsolved in HDE. The Planck data
alone can lead to strong and reliable constraint on the HDE parameter c. At 68%
CL, we get c=0.508+-0.207 with Planck+WP+lensing, favoring the present phantom
HDE at > 2sigma CL. Comparably, by using WMAP9 alone we cannot get interesting
constraint on c. By combining Planck+WP with the BAO measurements from
6dFGS+SDSS DR7(R)+BOSS DR9, the H0 measurement from HST, the SNLS3 and Union2.1
SNIa data sets, we get 68% CL constraints c=0.484+-0.070, 0.474+-0.049,
0.594+-0.051 and 0.642+-0.066. Constraints can be improved by 2%-15% if we
further add the Planck lensing data. Compared with the WMAP9 results, the
Planck results reduce the error by 30%-60%, and prefer a phantom-like HDE at
higher CL. We find no evident tension between Planck and BAO/HST. Especially,
the strong correlation between Omegam h^3 and dark energy parameters is helpful
in relieving the tension between Planck and HST. The residual
chi^2_{Planck+WP+HST}-chi^2_{Planck+WP} is 7.8 in LCDM, and is reduced to 1.0
or 0.3 if we switch dark energy to the w model or the holographic model. We
find SNLS3 is in tension with all other data sets; for Planck+WP, WMAP9 and
BAO+HST, the corresponding Delta chi^2 is 6.4, 3.5 and 4.1, respectively.
Comparably, Union2.1 is consistent with these data sets, but the combination
Union2.1+BAO+HST is in tension with Planck+WP+lensing, corresponding to a Delta
chi^2 8.6 (1.4% probability). Thus, it is not reasonable to perform an
all-combined (CMB+SNIa+BAO+HST) analysis for HDE when using the Planck data.
Our tightest self-consistent constraint is c=0.495+-0.039 obtained from
Planck+WP+BAO+HST+lensing.


title: A geometric approach to the Global Attractor Conjecture

abstract:
  This paper introduces the class of "strongly endotactic networks", a subclass
of the endotactic networks introduced by G. Craciun, F. Nazarov, and C. Pantea.
The main result states that the global attractor conjecture holds for
complex-balanced systems that are strongly endotactic: every trajectory with
positive initial condition converges to the unique positive equilibrium allowed
by conservation laws. This extends a recent result by D. F. Anderson for
systems where the reaction diagram has only one linkage class (connected
component). The results here are proved using differential inclusions, a
setting that includes power-law systems. The key ideas include a perspective on
reaction kinetics in terms of combinatorial geometry of reaction diagrams, a
projection argument that enables analysis of a given system in terms of systems
with lower dimension, and an extension of Birch's theorem, a well-known result
about intersections of affine subspaces with manifolds parameterized by
monomials.


title: Outflows from Evolved Stars: The Rapidly Changing Fingers of CRL618

abstract:
  Our ultimate goal is to probe the nature of the collimator of the outflows in
the pre PN CRL618. CRL618 is uniquely suited for this purpose owing to its
multiple, bright, and carefully studied finger-shaped outflows east and west of
its nucleus. We compare new HST images to images in the same filters observed
as much as 11 y previously to uncover large proper motions and surface
brightness changes in its multiple finger-shaped outflows. The expansion age of
the ensemble of fingers is close to 100y. We find strong brightness variations
at the fingertips during the past decade. Deep IR images reveal a multiple
ring- like structure of the surrounding medium into which the outflows
propagate and interact. Tightly constrained three-dimensional ("3D")
hydrodynamic models link the properties of the fingers to their possible
formation histories. We incorporate previously published complementary
information to discern whether each of the fingers of CRL618 are the results of
steady, collimated outflows or a brief ejection event that launched a set of
bullets about a century ago. Finally, we argue on various physical grounds that
fingers of CRL618 are likely to be the result of a spray of clumps ejected at
the nucleus of CRL618 since any mechanism that form a sustained set of
unaligned jets is unprecedented.


title: Backstepping Transformation of Input Delay Nonlinear Systems

abstract:
  We present here the details of a backstepping transformation aiming at
reformulating the dynamics of a nonlinear systems subject to unknown long input
delay in a form which is suitable for Lyapunov stability analysis. The control
law underlying this transformation is predictor-based, as often considered for
long delays. The proposed transformation follows recent results of the
literature, based on the representation of the constant actuator delay as a
transport Partial Differential Equation (PDE).


title:
A Supervised Neural Autoregressive Topic Model for Simultaneous Image
  Classification and Annotation

abstract:
  Topic modeling based on latent Dirichlet allocation (LDA) has been a
framework of choice to perform scene recognition and annotation. Recently, a
new type of topic model called the Document Neural Autoregressive Distribution
Estimator (DocNADE) was proposed and demonstrated state-of-the-art performance
for document modeling. In this work, we show how to successfully apply and
extend this model to the context of visual scene modeling. Specifically, we
propose SupDocNADE, a supervised extension of DocNADE, that increases the
discriminative power of the hidden topic features by incorporating label
information into the training objective of the model. We also describe how to
leverage information about the spatial position of the visual words and how to
embed additional image annotations, so as to simultaneously perform image
classification and annotation. We test our model on the Scene15, LabelMe and
UIUC-Sports datasets and show that it compares favorably to other topic models
such as the supervised variant of LDA.


title: Minimal Fine Tuning in Supersymmetric Higgs Inflation

abstract:
  We investigate characteristic features of realistic parameter choice for
primordial inflation with supersymmetric Higgs inflaton as an example of
particle physics inflation model. We discuss constraints from observational
results and analyze the degree of fine tuning needed to induce slow-roll
inflation for wide range of soft supersymmetry breaking scale. The observed
amplitude of density fluctuations implies that the minimal fine tuning for the
combined electroweak scale and inflaton flatness predicts the spectral index of
0.950--0.965, which includes the central value from observational data.


title:
Galaxy And Mass Assembly: Evolution of the Halpha luminosity function
  and star formation rate density up to z<0.35

abstract:
  Measurements of the low-z Halpha luminosity function have a large dispersion
in the local number density of sources, and correspondingly in the SFR density.
The possible causes for these discrepancies include limited volume sampling,
biases arising from survey sample selection, different methods of correcting
for dust obscuration and AGN contamination. The Galaxy And Mass Assembly (GAMA)
survey and Sloan Digital Sky Survey (SDSS) provide deep spectroscopic
observations over a wide sky area enabling detection of a large sample of
star-forming galaxies spanning 0.001<SFR(Halpha)<100 with which to robustly
measure the evolution of the SFR density in the low-z universe. The large
number of high SFR galaxies present in our sample allow an improved measurement
of the bright end of the luminosity function, indicating that the decrease in
number density of sources at bright luminosities is best described by a
Saunders functional form rather than the traditional Schechter function. This
result is consistent with other published luminosity functions in the FIR and
radio. For GAMA and SDSS we find the r-band apparent magnitude limit, combined
with the subsequent requirement for Halpha detection leads to an incompleteness
due to missing bright Halpha sources with faint r-band magnitudes.


title: Atom trapping in a bottle beam created by a diffractive optical element

abstract:
  A diffractive optical element (DOE) has been fabricated for creating blue
detuned atomic bottle beam traps. The DOE integrates several diffractive lenses
for trap creation and imaging of atomic fluorescence. We characterize the
performance of the DOE and demonstrate trapping of cold Cesium atoms inside a
bottle beam.


title:
Existence of a solution to a fluid-multi-layered-structure interaction
  problem

abstract:
  We study a nonlinear, unsteady, moving boundary, fluid-structure (FSI)
problem in which the structure is composed of two layers: a thin layer which is
in contact with the fluid, and a thick layer which sits on top of the thin
structural layer. The fluid flow, which is driven by the time-dependent dynamic
pressure data, is governed by the 2D Navier-Stokes equations for an
incompressible, viscous fluid, defined on a 2D cylinder. The elastodynamics of
the cylinder wall is governed by the 1D linear wave equation modeling the thin
structural layer, and by the 2D equations of linear elasticity modeling the
thick structural layer. The fluid and the structure, as well as the two
structural layers, are fully coupled via the kinematic and dynamic coupling
conditions describing continuity of velocity and balance of contact forces. The
thin structural layer acts as a fluid-structure interface with mass. The
resulting FSI problem is a nonlinear moving boundary problem of
parabolic-hyperbolic type. This problem is motivated by the flow of blood in
elastic arteries whose walls are composed of several layers, each with
different mechanical characteristics and thickness. We prove existence of a
weak solution to this nonlinear FSI problem as long as the cylinder radius is
greater than zero. The proof is based on a novel semi-discrete, operator
splitting numerical scheme, known as the kinematically coupled scheme. We
effectively prove convergence of that numerical scheme to a solution of the
nonlinear fluid-multi-layered-structure interaction problem. The spaces of weak
solutions presented in this manuscript reveal a striking new feature: the
presence of a thin fluid-structure interface with mass regularizes solutions of
the coupled problem.


title: A reduction technique for Generalised Riccati Difference Equations

abstract:
  This paper proposes a reduction technique for the generalised Riccati
difference equation arising in optimal control and optimal filtering. This
technique relies on a study on the generalised discrete algebraic Riccati
equation. In particular, an analysis on the eigen- structure of the
corresponding extended symplectic pencil enables to identify a subspace in
which all the solutions of the generalised discrete algebraic Riccati equation
are coin- cident. This subspace is the key to derive a decomposition technique
for the generalised Riccati difference equation that isolates its nilpotent
part, which becomes constant in a number of steps equal to the nilpotency index
of the closed-loop, from another part that can be computed by iterating a
reduced-order generalised Riccati difference equation.


title:
The generalised continuous algebraic Riccati equation and impulse-free
  continuous-time LQ optimal control

abstract:
  The purpose of this paper is to investigate the role that the continuous-time
generalised Riccati equation plays within the context of singular
linear-quadratic optimal control. This equation has been defined following the
analogy with the discrete-time generalised Riccati equation, but, differently
from the discrete case, to date the importance of this equation in the context
of optimal control is yet to be understood. This note addresses this point. We
show in particular that when the continuous-time generalised Riccati equation
admits a symmetric solution, the corresponding linear-quadratic (LQ) problem
admits an impulse-free optimal control.


title: Compact manifolds with positive $\Gamma_2$-curvature

abstract:
  The Schouten tensor \ $A$ \ of a Riemannian manifold \ $(M,g)$ provides
important scalar curvature invariants $\sigma_k$, that are the symmetric
functions on the eigenvalues of $A$, where, in particular, $\sigma_1$ \
coincides with the standard scalar curvature \ $\Scal(g)$. Our goal here is to
study compact manifolds with positive \ $\Gamma_2$-curvature, \ i.e., when
$\sigma_1(g)>0$ and $\sigma_2(g)>0$. In particular, we prove that a 3-connected
non-string manifold $M$ admits a positive$\Gamma_2$-curvature metric if and
only if it admits a positive scalar curvature metric. Also we show that any
finitely presented group $\pi$ can always be realised as the fundamental group
of a closed manifold of positive $\Gamma_2$-curvature and of arbitrary
dimension greater than or equal to six.


title: Quantum simulations of the early universe

abstract:
  A procedure is described whereby a linearly coupled spinor Bose condensate
can be used as a physically accessible quantum simulator of the early universe.
In particular, an experiment to generate an analog of an unstable vacuum in a
relativistic scalar field theory is proposed. This is related to quantum
theories of the inflationary phase of the early universe. There is an unstable
vacuum sector whose dynamics correspond to the quantum sine-Gordon equations in
one, two or three space dimensions. Numerical simulations of the expected
behavior are reported using a truncated Wigner phase-space method, giving
evidence for the dynamical formation of complex spatial clusters. Preliminary
results showing the dependence on coupling strength, condensate size and
dimensionality are obtained.


title:
Compensatory dynamics of fish recruitment illuminated by functional
  elasticities

abstract:
  Models of Stock Recruitment Relationships (SRRs) are often used to predict
fish population dynamics. Commonly used SRRs include the Ricker, Beverton-Holt,
and Cushing functional forms, which differ primarily by the degree of density
dependent effects (compensation). The degree of compensation determines whether
recruitment respectively decreases, saturates, or increases at high levels of
spawning stock biomass. In 1982 J.G. Shepherd united these dynamics into a
single model, where the degree of compensation is determined by a single
parameter, however the difficulty in relating this parameter to biological data
has limited its usefulness. Here we use a generalized modeling framework to
show that the degree of compensation can be related directly to the functional
elasticity of growth, which is a general quantity that measures the change in
recruitment relative to a change in biomass, irrespective of the specific SRR.
We show that the elasticity of growth can be calculated from short-term
fluctuations in fish biomass, is robust to observation error, and can be used
to determine general attributes of the SRR in both continuous time production
models, as well as discrete time age-structured models. This framework may be
particularly useful if fisheries time-series data are limited, and not
conducive to determining functional relationships using traditional methods of
statistical best-fit.


title:
Energy Efficient Transmission over Space Shift Keying Modulated MIMO
  Channels

abstract:
  Energy-efficient communication using a class of spatial modulation (SM) that
encodes the source information entirely in the antenna indices is considered in
this paper. The energy-efficient modulation design is formulated as a convex
optimization problem, where minimum achievable average symbol power consumption
is derived with rate, performance, and hardware constraints. The theoretical
result bounds any modulation scheme of this class, and encompasses the existing
space shift keying (SSK), generalized SSK (GSSK), and Hamming code-aided SSK
(HSSK) schemes as special cases. The theoretical optimum is achieved by the
proposed practical energy-efficient HSSK (EE-HSSK) scheme that incorporates a
novel use of the Hamming code and Huffman code techniques in the alphabet and
bit-mapping designs. Experimental studies demonstrate that EE-HSSK
significantly outperforms existing schemes in achieving near-optimal energy
efficiency. An analytical exposition of key properties of the existing GSSK
(including SSK) modulation that motivates a fundamental consideration for the
proposed energy-efficient modulation design is also provided.


title:
Quasi-Gasdynamic Approach for Numerical Solution of Magnetohydrodynamic
  Equations

abstract:
  We introduce an application of the Quasi-Gasdynamic method for a solution of
ideal magnetohydrodynamic equations in the modeling of compressible conductive
gas flows. A time-averaging procedure is applied for all physical parameters in
order to obtain the quasi-gas-dynamic system of equations for
magnetohydrodynamics. Evolution of all physical variables is presented in an
unsplit divergence form. Divergence-free evolution of the magnetic field is
provided by using a constrained transport method based on Stokes theorem.
Accuracy and convergence of this method are verified on a large set of standard
1D and 2D test cases.


title:
Two-dimensional arrays of superconducting and soft magnetic strips as dc
  magnetic metamaterials

abstract:
  We have theoretically investigated the magnetic response of two-dimensional
(2D) arrays of superconducting and soft magnetic strips, which are regarded as
models of dc magnetic metamaterials. The anisotropy of the macroscopic
permeabilities depends on whether the applied magnetic field is parallel to the
wide surface of the strips ($\mu_{\parallel}$) or perpendicular
($\mu_{\perp}$). For the 2D arrays of superconducting strips,
$0<\mu_{\perp}/\mu_0\ll \mu_{\parallel}/\mu_0\simeq 1$, whereas for the 2D
arrays of soft magnetic strips,
$\mu_{\parallel}/\mu_0\gg\mu_{\perp}/\mu_0\simeq 1$, where $\mu_0$ is the
vacuum permeability. We also demonstrate that strong anisotropy of the
macroscopic permeability can be obtained for hybrid arrays of superconducting
and soft magnetic strips, where $\mu_{\parallel}/\mu_0\gg 1\gg
\mu_{\perp}/\mu_0>0$.


title:
Effect of Genetic Variation in a Drosophila Model of Diabetes-Associated
  Misfolded Human Proinsulin

abstract:
  The identification and validation of gene-gene interactions is a major
challenge in human studies. Here, we explore an approach for studying epistasis
in humans using a Drosophila melanogaster model of neonatal diabetes mellitus.
Expression of mutant preproinsulin, hINSC96Y, in the eye imaginal disc mimics
the human disease activating conserved cell stress response pathways leading to
cell death and reduction in eye area. Dominant-acting variants in wild-derived
inbred lines from the Drosophila Genetics Reference Panel produce a continuous,
highly heritable, distribution of eye degeneration phenotypes. A genome-wide
association study (GWAS) in 154 sequenced lines identified 29 candidate SNPs in
16 loci with P < 10-5 including one SNP in an intron of the gene sulfateless
(sfl) which exceeded a conservative genome-wide significance threshold of P =
0.05 level (-log10 P > 7.62). RNAi knock-downs of sfl enhanced the eye
degeneration phenotype in a mutant-hINS-dependent manner. sfl encodes a protein
required for sulfation of the glycosaminoglycan, heparan sulfate. Two
additional genes in the heparan sulfate (HS) biosynthetic pathway (tout velu,
ttv and brother of tout velu, botv) also modified the eye phenotype, suggesting
a link between HS-modified proteins and cellular responses to misfolded
proteins. Finally, intronic variants marking the QTL were associated with
decreased sfl expression, a result consistent with that predicted by RNAi
studies. The ability to create a model of human genetic disease in the fly, map
a QTL by GWAS to a specific gene (and noncoding variant), validate its
contribution to disease with available genetic resources, and experimentally
link the variant to a molecular mechanism, demonstrate the many advantages
Drosophila holds in determining the genetic underpinnings of human disease.


title:
$B\to DK^*_{0,2}$ Decays: PQCD analysis to determine CP violation phase
  angle $\gamma$

abstract:
  $B^\pm \to (D^0, \bar D^0, D_{CP})K^{*\pm}_{0,2}$ decays are helpful in
determining the CP violation angle $\gamma$, and we analyze these decay
processes within the perturbative QCD approach based on $k_T$ factorization. We
found that the branching ratio of $B^-\to D^0 K^{*-}_0$ can reach the order of
$10^{-4}$, due to the enhancement of nonfactorizable contributions in
color-suppressed $D^0$-emission, while the branching ratio of $B^-\to \bar D^0
K^{*-}_0$ is of the order $10^{-5}$. The ratio of decay amplitudes is about 3
times larger than the one in the channel $B^\pm\to D K^\pm$. Large branching
ratios provide a good opportunity to observe $ B^\pm \to D K^{*\pm}_2$ on the
ongoing and forthcoming experimental facilities and consequently these channels
may be of valuable avail in reducing the errors in the CP violation phase angle
$\gamma$. We also explore the possible time-dependent CP asymmetries of $B_s$
decay into a scalar meson to determine the phase angle $\gamma$.


title:
Solvability of Naiver-Stokes equations in some rearrangement invariant
  spaces

abstract:
  We prove that the multidimensional dimensional initial value problem for the
Navier-Stokes equations is globally well-posed in the so-called Moment and
Grand Lebesgue Spaces (GLS), and give some a priory estimations for solution in
this spaces.


title: Non-classical features of Polarization Quasi-Probability Distribution

abstract:
  Polarization quasi-probability distribution (PQPD) is defined in the Stokes
space, and it enables the calculation of mean values and higher-order moments
for polarization observables using simple algebraic averaging. It can be
reconstructed with the help of polarization quantum tomography and provides a
full description of the polarization properties of quantum states of light.
  We show here that, due to its definition in terms of the discrete-valued
Stokes operators, polarization quasi-probability distribution has singularities
and takes negative values at integer values of the Stokes observables. However,
in experiments with `bright' many-photon states, the photon-number resolution
is typically smeared due to the technical limitations of contemporary
photodetectors. This results in a PQPD that is positive and regular even for
such strongly nonclassical states as single-photon seeded squeezed vacuum.
  This problem can be solved by `highlighting' the quantum state, that is, by
adding a strong coherent beam into the orthogonal polarization mode. This
procedure bridges polarization quantum tomography with the Wigner-function
tomography, while preserving the main advantage of the first one, namely,
immunity to the common phase fluctuations in the light path. Thus, it provides
a convenient method for the verification of bright nonclassical states of
light, such as squeezed Fock states.


title: Realization of stripes and slabs in two and three dimensions

abstract:
  We consider Ising models in two and three dimensions with nearest neighbor
ferromagnetic interactions and long range, power law decaying,
antiferromagnetic interactions. If the strength of the ferromagnetic coupling J
is larger than a critical value J_c, then the ground state is homogeneous and
ferromagnetic. As the critical value is approached from smaller values of J, it
is believed that the ground state consists of a periodic array of stripes (d=2)
or slabs (d=3), all of the same size and alternating magnetization. Here we
prove rigorously that the ground state energy per site converges to that of the
optimal periodic striped/slabbed state, in the limit that J tends to the
ferromagnetic transition point. While this theorem does not prove rigorously
that the ground state is precisely striped/slabbed, it does prove that in any
suitably large box the ground state is striped/slabbed with high probability.


title: Second Order PDEs with Dirichlet White Noise Boundary Condition

abstract:
  In this paper we study the Poisson and heat equations on bounded and
unbounded domains with smooth boundary with random Dirichlet boundary
conditions. The main novelty of this work is a convenient framework for the
analysis of such equations excited by the white in time and/or space noise on
the boundary. Our approach allows us to show the existence and uniqueness of
weak solutions in the space of distributions. Then we prove that the solutions
can be identified as smooth functions inside the domain, and finally the rate
of their blow up at the boundary is estimated. A large class of noises
including Wiener and fractional Wiener space time white noise, homogeneous
noise and L\'evy noise is considered.


title: Soliton resolution for equivariant wave maps to the sphere

abstract:
  We consider finite energy corotationnal wave maps with target manifold $\m
S^2$. We prove that for a sequence of times, they decompose as a sum of
decoupled harmonic maps in the light cone, and a smooth wave map (in the blow
case) or a linear scattering term (in the global case), up to an error which
tends to 0 in the energy space.


title:
The influence of the secondary electron induced asymmetry on the
  Electrical Asymmetry Effect in capacitively coupled plasmas

abstract:
  In geometrically symmetric capacitive radio-frequency plasmas driven by two
consecutive harmonics a dc self-bias can be generated as a function of the
phase shift between the driving frequencies via the Electrical Asymmetry Effect
(EAE). Recently the Secondary Electron Asymmetry Effect (SEAE) was discovered
(T. Lafleur, P. Chabert and J.P. Booth, J. Phys. D: Appl. Phys. 46 135201
(2013)): unequal secondary electron emission coefficients at both electrodes
were found to induce an asymmetry in single frequency capacitive plasmas. Here,
we investigate the simultaneous presence of both effects, i.e. a dual-frequency
plasma driven by two consecutive harmonics with different electrode materials.
We find, that the superposition of the EAE and the SEAE is non-linear, i.e. the
asymmetries generated by each individual effect do not simply add up. The
control ranges of the dc self-bias and the mean ion energy can be enlarged, if
both effects are combined.


title:
Influence of vacuum electric field on the stability of a plasma-vacuum
  interface

abstract:
  We study the free boundary problem for the plasma-vacuum interface in ideal
compressible magnetohydrodynamics. Unlike the classical statement, when the
vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, we do
not neglect the displacement current in the vacuum region and consider the
Maxwell equations for electric and magnetic fields. We show that a sufficiently
large vacuum electric field can make the planar interface violently unstable.
We find and analyze a sufficient condition on the vacuum electric field that
precludes violent instabilities. Under this condition satisfied at each point
of the unperturbed nonplanar plasma-vacuum interface, we prove the
well-posedness of the linearized problem in anisotropic weighted Sobolev
spaces.


title: Orbits of pairs in abelian groups

abstract:
  We compute the number of orbits of pairs in a finitely generated torsion
module (more generally, a module of bounded order) over a discrete valuation
ring. The answer is found to be a polynomial in the cardinality of the residue
field whose coefficients are integers which depend only on the elementary
divisors of the module, and not on the ring in question. The coefficients of
these polynomials are conjectured to be non-negative integers.


title: The Local Index Theorem

abstract:
  This article is based on author's talk at the International Conference
"Alexandroff Reading", Moscow 21 - 25 May, 2012. The material presented in
article is a programme intended to organise the ingredients of the index
formula. The first results results obtained in this project were announced at
the International Conference on Non-commutative Geometry, Trieste, November
2007. Progress obtained along the path of the project was reported at different
conferences in Crakovia (June 2011), "K-Theory, C*-Algebras and Index Theory
International Conference", Goettingen (November 2010) and Iasi (September
2011). The unifying idea behind our program is to localise K-theory and the
non-commutative geometry basic tools (Hochschild, cyclic homology and
co-homology, Connes-Karoubi Chern character) along the lines of
Alexander-Spanier co-homology and homology. The motivation for the realisation
of this programme is four-fold: -1) the classical Atiyah-Singer type index
formula is a global statement with local controle, -2) the non-localised
existing tools are not fine enough to capture sufficient information in the
case of Banach algebras, -3) one wants to make so that the Alexander-Spanier
(co)-homology becomes a natural ingredient of non-commutative geometry and -4)
the Alexander-Spanier co-homology, with respect to the existing non-commutative
geometry tools, has the advantage that it does need extra regularity beyond the
ordinary topology. Author's last reference publications represent parts of this
programme


title: A toy model of information retrieval system based on quantum probability

abstract:
  Recent numerical results show that non-Bayesian knowledge revision may be
helpful in search engine training and optimization. In order to demonstrate how
basic assumption about about the physical nature (and hence the observed
statistics) of retrieved documents can affect the performance of search engines
we suggest an idealized toy model with minimal number of parameters.


title:
Dipolar needles in the microcanonical ensemble: evidence of spontaneous
  magnetization and ergodicity breaking

abstract:
  We have studied needle shaped three-dimensional classical spin systems with
purely dipolar interactions in the microcanonical ensemble, using both
numerical simulations and analytical approximations. We have observed
spontaneous magnetization for different finite cubic lattices. The transition
from the paramagnetic to the ferromagnetic phase is shown to be first-order.
For two lattice types we have observed magnetization flips in the phase
transition region. In some cases, gaps in the accessible values of
magnetization appear, a signature of the ergodicity breaking found for systems
with long-range interactions. We analytically explain these effects by
performing a nontrivial mapping of the model Hamiltonian onto a one-dimensional
Ising model with competing antiferromagnetic nearest-neighbor and ferromagnetic
mean-field interactions. These results hint at performing experiments on
isolated dipolar needles in order to verify some of the exotic properties of
systems with long-range interactions in the microcanonical ensemble.


title: Heavy-to-light chromomagentic matrix element

abstract:
  We report the computation of the matrix element of the chromomagnetic
operator of the flavour changing neutral current (FCNC)-type between a $B$- or
$D$-meson state and a light hadron and off-shell photon. The computation is
carried out by using the method of light-cone sum rules (LCSR). It is found
that the matrix element exhibits a large strong phase for which we give a long
distance interpretation. The analytic structure of the correlation function in
use admits a complex anomalous threshold on the physical sheet, the meaning and
handling of which within the sum rule approach is discussed. We compare our
results to QCD factorisation for which spectator photon emission is end-point
divergent.


title:
Observation of a structure at 1.84 GeV/c$^2$ in the $3(\pi^+\pi^-)$ mass
  spectrum in $J/\psi\rightarrow \gamma 3(\pi^+\pi^-)$ decays

abstract:
  With a sample of 225.3 million $J/\psi$ events taken with the BESIII
detector, the decay $J/\psi\rightarrow \gamma 3(\pi^+\pi^-)$ is analyzed. A
structure at 1.84 GeV/c$^2$ is observed in the $3(\pi^+\pi^-)$ invariant mass
spectrum with a statistical significance of 7.6$\sigma$ . The mass and width
are measured to be $M=1842.2\pm 4.2^{+7.1}_{-2.6}$ MeV/c$^2$ and $\Gamma=83\pm
14 \pm 11$ MeV. The product branching fraction is determined to be
$B(J/\psi\rightarrow\gamma X(1840))\times B(X(1840)\rightarrow
3(\pi^+\pi^-))=(2.44\pm0.36^{+0.60}_{-0.74})\times 10^{-5}$. No $\eta^\prime$
signals are observed in the $3(\pi^+\pi^-)$ invariant mass spectrum, and the
upper limit of the branching fraction for the decay $\eta^\prime\rightarrow
3(\pi^+\pi^-)$ is set to be $3.1\times10^{-5}$ at a 90% confidence level.


title: Rigorous bounds for Renyi entropies of spherically symmetric potentials

abstract:
  The R\'enyi and Shannon entropies are information-theoretic measures which
have enabled to formulate the position-momentum uncertainty principle in a much
more adequate and stringent way than the (variance-based) Heisenberg-like
relation. Moreover, they are closely related to various energetic
density-functionals of quantum systems. Here we find sharp upper bounds to
these quantities in terms of the second order moment $\langle r^2\rangle$ for
general spherically symmetric potentials, which substantially improve previous
results of this type, by means of the R\'enyi maximization procedure with a
covariance constraint due to Costa, Hero and Vignat \cite{CosHer03}. The
contributions to these bounds coming from the radial and angular parts of the
physical wavefunctions are explicitly given.


title: Cone-volume measures of polytopes

abstract:
  The cone-volume measure of a polytope with centroid at the origin is proved
to satisfy the subspace concentration condition. As a consequence a conjectured
(a dozen years ago) fundamental sharp affine isoperimetric inequality for the
U-functional is completely established -- along with its equality conditions.


title:
Constraining the density dependence of symmetry energy from nuclear
  masses

abstract:
  Empirically determined values of the nuclear volume and surface symmetry
energy coefficients from nuclear masses are expressed in terms of density
distributions of nucleons in heavy nuclei in the local density approximation.
This is then used to extract the value of the symmetry energy slope parameter
$L$. The density distributions in both spherical and well deformed nuclei
calculated within microscopic framework with different energy density
functionals give $L = 59.0 \pm 13.0$ MeV. Application of the method also helps
in a precision determination of the neutron skin thickness of nuclei that are
difficult to measure accurately.


title: System error of project ETONN and EIAS

abstract:
  Detected a system error of the project ETONN&EIAS.NET, which consists in the
use of the developers EIAS.NET the Windows operating system in the software
EIAS.NET, which in accordance with the requirements of the specification for
the project EIAS.NET should provide information exchange in real time . It is
concluded that it is impossible to meet the requirement specification for the
project EIAS.NET about providing work ETONN/ETNaSP with the support of EIAS /
EIAS.NET in real time, providing the use of the Windows operating system in the
software EIAS.NET.


title: Domain wall and isocurvature perturbation problems in axion models

abstract:
  Axion models have two serious cosmological problems, domain wall and
isocurvature perturbation problems. In order to solve these problems we
investigate the Linde's model in which the field value of the Peccei-Quinn (PQ)
scalar is large during inflation. In this model the fluctuations of the PQ
field grow after inflation through the parametric resonance and stable axionic
strings may be produced, which results in the domain wall problem. We study
formation of axionic strings using lattice simulations. It is found that in
chaotic inflation the axion model is free from both the domain wall and the
isocurvature perturbation problems if the initial misalignment angle \theta_a
is smaller than O(10^{-2}). Furthermore, axions can also account for the dark
matter for the breaking scale v \simeq 10^{12-16} GeV and the Hubble parameter
during inflation H_{inf} \lesssim 10^{11-12} GeV in general inflation models.


title:
Combinatorial optimization problems with uncertain costs and the OWA
  criterion

abstract:
  In this paper a class of combinatorial optimization problems with uncertain
costs is discussed. The uncertainty is modeled by specifying a discrete
scenario set containing $K$ distinct cost scenarios. The Ordered Weighted
Averaging (OWA for short) aggregation operator is applied to choose a solution.
The well-known criteria such as: the maximum, minimum, average, Hurwicz and
median are special cases of OWA. By using OWA, the traditional min-max approach
to combinatorial optimization problems with uncertain costs, often regarded as
too conservative, can be generalized. The computational complexity and
approximability of the problem of minimizing OWA for the considered class of
problems are investigated and some new positive and negative results in this
area are provided. These results remain valid for many important problems, such
as network or resource allocation problems.


title: Regularities and symmetries in atomic structure and spectra

abstract:
  The use of statistical methods for the description of complex quantum systems
was primarily motivated by the failure of a line-by-line interpretation of
atomic spectra. Such methods reveal regularities and trends in the
distributions of levels and lines. In the past, much attention was paid to the
distribution of energy levels (Wigner surmise, random-matrix model...).
However, information about the distribution of the lines (energy and strength)
is lacking. Thirty years ago, Learner found empirically an unexpected law: the
logarithm of the number of lines whose intensities lie between 2^kI_0 and
2^{k+1}I_0, I_0 being a reference intensity and k an integer, is a decreasing
linear function of k. In the present work, the fractal nature of such an
intriguing regularity is outlined and a calculation of its fractal dimension is
proposed. Other peculiarities are also presented, such as the fact that the
distribution of line strengths follows Benford's law of anomalous numbers, the
existence of additional selection rules (PH coupling), the symmetry with
respect to a quarter of the subshell in the spin-adapted space (LL coupling)
and the odd-even staggering in the distribution of quantum numbers, pointed out
by Bauche and Coss\'e.


title:
Electronic origin of the orthorhombic Cmca structure in compressed
  elements and binary alloys

abstract:
  Formation of the complex structure with 16 atoms in the orthorhombic cell,
space group Cmca (Pearson symbol oC16) was experimentally found under high
pressure in the alkali elements (K, Rb, Cs) and polyvalent elements of groups
IV (Si, Ge) and V (Bi). Intermetallic phases with this structure form under
pressure in binary Bi-based alloys (Bi-Sn, Bi-In, Bi-Pb). Stability of the Cmca
- oC16 structure is analyzed within the nearly free-electron model in the frame
of Fermi sphere - Brillouin zone interaction. A Brillouin-Jones zone formed by
a group of strong diffraction reflections close to the Fermi sphere is the
reason for reduction of crystal energy and stabilization of the structure. This
zone corresponds well to the 4 valence electrons in Si and Ge and leads to
assume a spd-hybridization for Bi. To explain the stabilization of this
structure within the same model in alkali metals, that are monovalent at
ambient conditions, a possibility of an overlap of the core and valence band
electrons at strong compression is considered. The assumption of the increase
in the number of valence electrons helps to understand sequences of complex
structures in compressed alkali elements and unusual changes in their physical
properties such as electrical resistance and superconductivity.


title: Ultrafast graphene-based broadband THz detector

abstract:
  We present an ultrafast graphene-based detector, working in the THz range at
room temperature. A logarithmic-periodic antenna is coupled to a graphene flake
that is produced by exfoliation on SiO2. The detector was characterized with
the free-electron laser FELBE for wavelengths from 8 um to 220 um. The detector
rise time is 50 ps in the wavelength range from 30 um to 220 um.
Autocorrelation measurements exploiting the nonlinear photocurrent response at
high intensities reveal an intrinsic response time below 10 ps. This detector
has a high potential for characterizing temporal overlaps, e. g. in two-color
pump-probe experiments.


title: Spatial pattern of discrete and ultradiscrete Gray-Scott model

abstract:
  Ultradiscretization is a limiting procedure transforming a given difference
equation into a cellular automaton. In addition the cellular automaton
constructed by this procedure preserves the essential properties of the
original equation, such as the structure of exact solutions for integrable
equations. In this article, we propose a discretization and an
ultradiscretization of Gray-Scott model which is not an integrable system and
which gives various spatial patterns with appropriate initial data and
parameters. The resulting systems give a travelling pulse and a
self-replication pattern with appropriate initial data and parameters. The
ultradiscrete system is directly related to the elementary cellular automaton
Rule 90 which gives a Sierpinski gasket pattern. A $(2+1)$D ultradiscrete
Gray-Scott model that gives a ring pattern, a self-replication pattern and a
chaotic pattern, is also constructed.


title:
Nonnegative Tensor Factorization, Completely Positive Tensors and an
  Hierarchical Elimination Algorithm

abstract:
  Nonnegative tensor factorization has applications in statistics, computer
vision, exploratory multiway data analysis and blind source separation. A
symmetric nonnegative tensor, which has a symmetric nonnegative factorization,
is called a completely positive (CP) tensor. The H-eigenvalues of a CP tensor
are always nonnegative. When the order is even, the Z-eigenvalue of a CP tensor
are all nonnegative. When the order is odd, a Z-eigenvector associated with a
positive (negative) Z-eigenvalue of a CP tensor is always nonnegative
(nonpositive). The entries of a CP tensor obey some dominance properties. The
CP tensor cone and the copositive tensor cone of the same order are dual to
each other. We introduce strongly symmetric tensors and show that a symmetric
tensor has a symmetric binary decomposition if and only if it is strongly
symmetric. Then we show that a strongly symmetric, hierarchically dominated
nonnegative tensor is a CP tensor, and present a hierarchical elimination
algorithm for checking this. Numerical examples are also given.


title: A criterion of reducibility for a parallelohedron

abstract:
  A parallelohedron is called reducible, if it can be represented as a direct
product of two parallelohedra of lower dimension. In his Ph.D. thesis (2005)
the first author proved a criterion of reducibility of a parallelohedron in
terms of the Venkov graph. In December 2011 the second author presented a
slightly revised version of the original proof at the seminar "Discrete
Geometry and Geometry of Numbers" (Moscow State University). The present paper
follows that talk.


title:
Do radio magnetars J1550-5418 and J1622-4950 have gigahertz-peaked
  spectra?

abstract:
  We study the radio spectra of two magnetars PSR J1550-5418 and J1622-4950. We
argue that they are good candidates for the pulsars with gigahertz-peaked
spectra as their observed flux density decreases at frequencies below 7 GHz. We
suggest this behavior is due to the influence of pulsars' environments on the
radio waves. Both of the magnetars are associated with supernova remnants, thus
are surrounded by a hot, ionized gas, which can be responsible for the
free-free absorption of radio-waves. We conclude that the GPS feature of both
magnetars and typical pulsars are formed by similar processes in the
surrounding media, rather than by different radio-emission mechanisms. Thus,
the radio magnetars PSR J1550-5418 and J1622-4950 can be included in the class
of the gigahertz-peaked spectra pulsars.


title: Lord Kelvin's atmospheric electricity measurements

abstract:
  Lord Kelvin (William Thomson) made important contributions to the study of
atmospheric electricity during a brief but productive period from 1859-1861. By
1859 Kelvin had recognised the need for "incessant recording" of atmospheric
electrical parameters, and responded by inventing both the water-dropper
instrument for measuring the atmospheric Potential Gradient (PG), and
photographic data logging. The water-dropper was widely adopted internationally
and is still in use today. Following theoretical considerations of electric
field distortion by local topography, Kelvin developed a portable electrometer,
using it to investigate PG on the Scottish island of Arran. During these
environmental measurements, Kelvin may have unwittingly detected atmospheric PG
changes during solar activity in August/September 1859 associated with the
"Carrington event". Kelvin's atmospheric electricity work presents an early
representative study in quantitative environmental physics, through the
application of mathematical principles to an environmental problem, the design
and construction of bespoke instrumentation for real world measurements and the
limitations of the original theoretical view revealed by experimental work.


title: Deconfinement transition and Black Holes

abstract:
  In this paper we propose an effective description of the transition to
deconfinement in the vicinity of a black hole. For this we adapt the approach
that uses the dual quark condensate as order parameter for confinement,
originally introduced in the context of lattice QCD, to a strongly interacting
fermion effective field theory propagating on a curved background. We construct
numerically the dual condensate and determine approximately the region of the
deconfined phase. The present analysis suggests that quarks will be radiated
directly by Hawking emission, while hadrons will form at the boundary of the
deconfined region by "standard" nonperturbative QCD effects. This example
provides a nontrivial setup to discuss how gravity affects confinement.


title: Triangulated categories of motives in positive characteristic

abstract:
  This thesis presents a way to apply this theorem of Gabber to a large portion
of Voevodsky's work in order to lift the assumption that resolution of
singularities holds. This gives unconditional versions of many of his and
others' theorems provided we work Z[1/p] linearly, where p is the exponential
characteristic of the base field. One example of the many applications we give
is a partial answer to a 1980 conjecture of Weibel. Another is the removal of
the hypothesis of resolution of singularities from a result of Suslin that
compares Bloch's higher Chow groups and etale cohomology.
  Voevodsky's main tool in applying resolution of singularities is the cdh
topology. We enlarge it slightly in order to apply this theorem of Gabber,
presenting in this thesis a topology that we name the ldh topology, where l is
a prime. We compare the cdh and ldh topologies using the concept of a "presheaf
with traces", providing conditions under which the cdh and ldh sheafifications
of a presheaf agree, as well as its cdh and ldh cohomologies.
  As far as applying resolution of singularities to motives goes, Voevodsky's
most important theorem can be rephrased as a cdh descent condition, and we are
led to ask for conditions under which certain objects in the Morel-Voevodsky
stable homotopy category satisfy ldh descent. In order to compare cdh and ldh
descent, we generalise the notion of a "presheaf with traces" to the concept of
an "object with traces". We build on some results of Pelaez on the
functoriality of the slice filtration to show that this concept of an "object
with traces" interacts well enough with the slice filtration to provide the ldh
descent that we need.


title:
Optimal sub-Poissonian light generation from twin beams by photon-number
  resolving detectors

abstract:
  We generate nonclassical conditional states by exploiting the quantum
correlations of multi-mode twin-beam states endowed with a sizeable number of
photons. A strong relation between the sub-shot-noise correlations exhibited by
twin beams and the sub-Poissonian character of the conditional states is
experimentally revealed. It determines optimal conditions for sub-Poissonian
light generation.


title: Commutators and pronilpotent subgroups in profinite groups

abstract:
  Let G be a profinite group in which all pronilpotent subgroups generated by
commutators are periodic. We prove that G' is locally finite.


title:
Tight Upper and Lower Bounds to the Information Rate of the Phase Noise
  Channel

abstract:
  Numerical upper and lower bounds to the information rate transferred through
the additive white Gaussian noise channel affected by discrete-time
multiplicative autoregressive moving-average (ARMA) phase noise are proposed in
the paper. The state space of the ARMA model being multidimensional, the
problem cannot be approached by the conventional trellis-based methods that
assume a first-order model for phase noise and quantization of the phase space,
because the number of state of the trellis would be enormous. The proposed
lower and upper bounds are based on particle filtering and Kalman filtering.
Simulation results show that the upper and lower bounds are so close to each
other that we can claim of having numerically computed the actual information
rate of the multiplicative ARMA phase noise channel, at least in the cases
studied in the paper. Moreover, the lower bound, which is virtually
capacity-achieving, is obtained by demodulation of the incoming signal based on
a Kalman filter aided by past data. Thus we can claim of having found the
virtually optimal demodulator for the multiplicative phase noise channel, at
least for the cases considered in the paper.


title: On convergence to the Denjoy-Wolff point in the parabolic case

abstract:
  Based on dynamical behavior, all self-maps of the unit disk in the complex
plane can be classified as elliptic, hyperbolic or parabolic. The parabolic
case is the most complicated one and branches into two subcases - zero-step and
non-zero-step cases. In several dimensions, zero-step and non-zero step cases
can be defined for sequences of forward iterates, but it is not known yet if
the classification can be extended to parabolic maps of the ball. However, some
geometric properties of the forward iterates can be generalized to
higher-dimensional case.


title:
A phenomenological model for the description of rotating spokes in
  HiPIMS discharges

abstract:
  In the ionization region above circular planar magnetrons well defined
regions of high emissivity are observed, when the discharge is driven in the
HiPIMS regime. Once their mode is stabilized, these structures rotate in the E
x B direction with a constant rotation frequency in the hundreds of kHz range.
A phenomenological model of the phenomenon is developed, in the form of a
system of nonlinear coupled partial differential equations. The system is
solved analytically in a frame co-moving with the structure, and its solution
gives the neutral density and the plasma density once the electron density
shape is imposed. From the balance of the mechanisms of ionization, electron
loss and constant neutral refilling, a steady state configuration in the
rotating frame is achieved for the electron and neutral densities. Therefore,
the spoke experimentally observed can be sustained simply by the combination of
this highly reduced number of phenomena. Finally, a study of the sensitivity of
neutral and plasma densities to the physical parameters is also given.


title:
Variable selection for sparse Dirichlet-multinomial regression with an
  application to microbiome data analysis

abstract:
  With the development of next generation sequencing technology, researchers
have now been able to study the microbiome composition using direct sequencing,
whose output are bacterial taxa counts for each microbiome sample. One goal of
microbiome study is to associate the microbiome composition with environmental
covariates. We propose to model the taxa counts using a Dirichlet-multinomial
(DM) regression model in order to account for overdispersion of observed
counts. The DM regression model can be used for testing the association between
taxa composition and covariates using the likelihood ratio test. However, when
the number of covariates is large, multiple testing can lead to loss of power.
To address the high dimensionality of the problem, we develop a penalized
likelihood approach to estimate the regression parameters and to select the
variables by imposing a sparse group $\ell_1$ penalty to encourage both
group-level and within-group sparsity. Such a variable selection procedure can
lead to selection of the relevant covariates and their associated bacterial
taxa. An efficient block-coordinate descent algorithm is developed to solve the
optimization problem. We present extensive simulations to demonstrate that the
sparse DM regression can result in better identification of the
microbiome-associated covariates than models that ignore overdispersion or only
consider the proportions. We demonstrate the power of our method in an analysis
of a data set evaluating the effects of nutrient intake on human gut microbiome
composition. Our results have clearly shown that the nutrient intake is
strongly associated with the human gut microbiome.


title:
Polarization structure in the core of 1803+784: a signature of
  recollimation shocks?

abstract:
  The extragalactic radio source 1803+784 is a BL Lac object that shows rapid
variability and strong linear polarization. Very long baseline interferometry
observations reveal that the core possesses a distinctive structure in
polarized intensity with two maxima on axis and two minima symmetrically placed
on either side. The approximately radial pattern of electric field polarization
rods is reminiscent of the results obtained earlier by Cawthorne (2006) for
conical shocks, but, individually, these do not reproduce the main features of
the polarized intensity images. In numerical simulations and experiments, these
shocks occur in pairs and help to stabilize jets as they adjust to changes in
environment. Here, the polarization resulting from such structures is
investigated using an approximate, analytical approach, by making some simple
assumptions about the nature of the flow between two such shock waves. For
fairly small viewing angles, it is found that a reasonable representation of
the core polarization of 1803+784 can be obtained. The similarity between the
observed and model polarization supports the view that the core structure in
1803+784 represents a recollimation shock, and that such shock waves may be
responsible for the first disturbance and hence brightening of the quiescent
flow in astrophysical jets.


title: Linked Partitions and Permutation Tableaux

abstract:
  Linked partitions are introduced by Dykema in the study of transforms in free
probability theory, whereas permutation tableaux are introduced by
Steingr\'{i}msson and Williams in the study of totally positive Grassmannian
cells. Let $[n]=\{1,2,\ldots,n\}$. Let $L(n,k)$ denote the set of linked
partitions of $[n]$ with $k$ blocks, let $P(n,k)$ denote the set of
permutations of $[n]$ with $k$ descents, and let $T(n,k)$ denote the set of
permutation tableaux of length $n$ with $k$ rows. Steingr\'{i}msson and
Williams found a bijection between the set of permutation tableaux of length
$n$ with $k$ rows and the set of permutations of $[n]$ with $k$ weak
excedances. Corteel and Nadeau gave a bijection from the set of permutation
tableaux of length $n$ with $k$ columns to the set of permutations of $[n]$
with $k$ descents. In this paper, we establish a bijection between $L(n,k)$ and
$P(n,k-1)$ and a bijection between $L(n,k)$ and $T(n,k)$. Restricting the
latter bijection to noncrossing linked partitions, we find that the
corresponding permutation tableaux can be characterized by pattern avoidance.


title:
The Occulting Galaxy Pair UGC 3995; Dust properties from HST and CALIFA
  data

abstract:
  UGC 3995 is an interacting and occulting galaxy pair. UGC 3995B is a
foreground face-on spiral and UGC 3995A a bright background spiral with an AGN.
We present analysis of the dust in the disc of UGC 3995B based on archival
Hubble Space Telescope WFPC2 and PPAK IFU data from the CALIFA survey's first
data release.
  From the HST F606W image, we construct an extinction map by modeling the
isophotes of the background galaxy UGC 3995A and the resulting transmission
through UGC 3995B. This extinction map of UGC 3995B shows several distinct
spiral extinction features. The radial distribution of $A_V$ values declines
slowly with peaks corresponding to the spiral structures. The distribution of
$A_V$ values in the HST extinction map peaks near $A_V = 0.3-0.4$. Beyond this
point, the distribution of $A_V$ values drops like an exponential: $N(A_V) =
N_0 \times e^{(-A_V/0.5)}$. The 0.5 value is higher than typical for a spiral
galaxy. The outer arms may be tidally distended; the extinction in the
corresponding interarm regions is small to an unusually small radius.
  To analyse the PPAK IFU data, we take the ratio of a fibre spectrum in the
overlap region and the corresponding background fiber spectrum to construct an
extinction curve. We fit the Cardelli, Clayton and Mathis (CCM) curve to the
extinction curve of each fiber element in the overlap region. A map of the
extinction constructed from PPEX IFU data-cubes shows the same spiral structure
of the HST extinction map but the some differences in the distribution of the
normalization of the CCM fits ($A_V$). The inferred extinction slopes ($R_V$)
maps do not display any structure and a range of values partly due to the
sampling effects of the disc by fibers, sometimes due to bad fits, and possibly
partly due to some reprocessing of dust grains in the interacting disc.
(abridged)


title: A coercion-resistant protocol for conducting elections by telephone

abstract:
  We present a protocol that allows voters to phone in their votes. Our
protocol makes it expensive for a candidate and a voter to cooperate to prove
to the candidate who the voter voted for. When the electoral pool is large
enough, the cost to the candidate of manipulating sufficiently many votes to
have an influence on the election results becomes impossibly expensive. Hence,
the protocol provides candidates no incentive to attempt inducement or coercion
of voters, resulting in free and fair elections with the promise of cost
savings and higher voter turnout over traditional elections. One major
inadequacy with our suggested protocol is that we assume the existence of a
trusted election authority to count the votes.


title:
The formation of disc galaxies in high resolution moving-mesh
  cosmological simulations

abstract:
  We present cosmological hydrodynamical simulations of eight Milky Way-sized
haloes that have been previously studied with dark matter only in the Aquarius
project. For the first time, we employ the moving-mesh code AREPO in zoom
simulations combined with a comprehensive model for galaxy formation physics
designed for large0 cosmological simulations. Our simulations form in most of
the eight haloes strongly disc-dominated systems with realistic rotation
curves, close to exponential surface density profiles, a stellar-mass to
halo-mass ratio that matches expectations from abundance matching techniques,
and galaxy sizes and ages consistent with expectations from large galaxy
surveys in the local Universe. There is no evidence for any dark matter core
formation in our simulations, even so they include repeated baryonic outflows
by supernova-driven winds and black hole quasar feedback. For one of our
haloes, the object studied in the recent `Aquila' code comparison project, we
carried out a resolution study with our techniques, covering a dynamic range of
64 in mass resolution. Without any change in our feedback parameters, the final
galaxy properties are reassuringly similar, in contrast to other modelling
techniques used in the field that are inherently resolution dependent. This
success in producing realistic disc galaxies is reached, in the context of our
interstellar medium treatment, without resorting to a high density threshold
for star formation, a low star formation efficiency, or early stellar feedback,
factors deemed crucial for disc formation by other recent numerical studies.


title: \'Etale motives

abstract:
  We define a theory of etale motives over a noetherian scheme. This provides a
system of categories of complexes of motivic sheaves with integral coefficients
which is closed under the six operations of Grothendieck. The rational part of
these categories coincides with the triangulated categories of Beilinson
motives (and is thus strongly related to algebraic $K$-theory). We extend the
rigity theorem of Suslin and Voevodsky over a general base scheme. This can be
reformulated by saying that torsion etale motives essentially coincide with the
usual complexes of torsion etale sheaves (at least if we restrict ourselves to
torsion prime to the residue characteristics). As a consequence, we obtain the
expected results of absolute purity, of finiteness, and of Grothendieck duality
for etale motives with integral coefficients, by putting together their
counterparts for Beilinson motives and for torsion etale sheaves. Following
Thomason's insights, this also provides a conceptual and convenient
construction of the $\ell$-adic realization of motives, as the homotopy
$\ell$-completion functor.


title:
ADI splitting schemes for a fourth-order nonlinear partial differential
  equation from image processing

abstract:
  We present directional operator splitting schemes for the numerical solution
of a fourth-order, nonlinear partial differential evolution equation which
arises in image processing. This equation constitutes the $H^{-1}$-gradient
flow of the total variation and represents a prototype of higher-order
equations of similar type which are popular in imaging for denoising,
deblurring and inpainting problems. The efficient numerical solution of this
equation is very challenging due to the stiffness of most numerical schemes. We
show that the combination of directional splitting schemes with implicit
time-stepping provides a stable and computationally cheap numerical realisation
of the equation.


title:
Narrowing the gap on heritability of common disease by direct estimation
  in case-control GWAS

abstract:
  One of the major developments in recent years in the search for missing
heritability of human phenotypes is the adoption of linear mixed-effects models
(LMMs) to estimate heritability due to genetic variants which are not
significantly associated with the phenotype. A variant of the LMM approach has
been adapted to case-control studies and applied to many major diseases by Lee
et al. (2011), successfully accounting for a considerable portion of the
missing heritability. For example, for Crohn's disease their estimated
heritability was 22% compared to 50-60% from family studies. In this letter we
propose to estimate heritability of disease directly by regression of phenotype
similarities on genotype correlations, corrected to account for ascertainment.
We refer to this method as genetic correlation regression (GCR). Using GCR we
estimate the heritability of Crohn's disease at 34% using the same data. We
demonstrate through extensive simulation that our method yields unbiased
heritability estimates, which are consistently higher than LMM estimates.
Moreover, we develop a heuristic correction to LMM estimates, which can be
applied to published LMM results. Applying our heuristic correction increases
the estimated heritability of multiple sclerosis from 30% to 52.6%.


title: Composite or elementary? Probing the nature of the Higgs

abstract:
  I discuss consequences of electroweak symmetry breaking by strong dynamics,
assuming the existence of a light composite scalar appearing as a
pseudo-Goldstone boson of some global symmetry of the new strongly interacting
sector. In such a scenario, the composite scalar has properties very similar to
the Standard Model Higgs, but the existence of additional resonances with
different spins is also expected. Properties and phenomenology of lightest
spin-1 resonances are considered in a simple general effective Lagrangian
description. The question whether the effects of spin-1 resonances can be
observed at the LHC, shedding light on the nature of the Higgs boson, is
addressed.


title: Fine scales of decay of operator semigroups

abstract:
  Motivated by potential applications to partial differential equations, we
develop a theory of fine scales of decay rates for operator semigroups. The
theory contains, unifies, and extends several notable results in the literature
on decay of operator semigroups and yields a number of new ones. Its core is a
new operator-theoretical method of deriving rates of decay combining
ingredients from functional calculus, and complex, real and harmonic analysis.
It also leads to several results of independent interest.


title: Deformation equivalence of affine ruled surfaces

abstract:
  A smooth family $\varphi:\mathcal V\to S$ of surfaces will be called {\em
completable} if there is a logarithmic deformation $(\bar {\mathcal
V},{\mathcal D})$ over $S$ so that ${\mathcal V}=\bar{\mathcal V}\backslash
{\mathcal D}$. Two smooth surfaces $V$ and $V'$ are said to be deformations of
each other if there is a completable flat family ${\mathcal V}\to S$ of smooth
surfaces over a connected base so that $V$ and $V'$ are fibers over suitable
points $s,s'\in S$. This relation generates an equivalence relation called {\em
deformation equivalence}. In this paper we give a complete combinatorial
description of this relation in the case of affine ruled surfaces, which by
definition are surfaces that admit an affine ruling $V\to B$ over an affine
base with possibly degenerate fibers. In particular we construct complete
families of such affine ruled surfaces. In a few particular cases we can also
deduce the existence of a coarse moduli space.


title: Controlling Sub-nm Gaps in Plasmonic Dimers using Graphene

abstract:
  Graphene is used as the thinnest possible spacer between gold nanoparticles
and a gold substrate. This creates a robust, repeatable, and stable
sub-nanometre gap for massive plasmonic field enhancements. White light
spectroscopy of single 80 nm gold nanoparticles reveals plasmonic coupling
between the particle and its image within the gold substrate. While for a
single graphene layer, spectral doublets from coupled dimer modes are observed
shifted into the near infra-red, these disappear for increasing numbers of
layers. These doublets arise from plasmonic charge transfer, allowing the
direct optical measurement of out-of-plane conductivity in such layered
systems. Gating the graphene can thus directly produce plasmon tuning.


title: A primal-dual approach for a total variation Wasserstein flow

abstract:
  We consider a nonlinear fourth-order diffusion equation that arises in
denoising of image densities. We propose an implicit time-stepping scheme that
employs a primal-dual method for computing the subgradient of the total
variation seminorm. The constraint on the dual variable is relaxed by adding a
\emph{penalty term}, depending on a parameter that determines the weight of the
penalisation. The paper is furnished with some numerical examples showing the
denoising properties of the model considered.