title:
The relation between photospheric supergranular flows and magnetic flux
  emergence

abstract:
  A recent study carried out on high sensitivity SUNRISE/IMAX data has reported
about the existence of areas of limited flux emergence in the quiet Sun. By
exploiting an independent and longer (4 hours) data set acquired by HINODE/SOT,
we further investigate these regions by analysing their spatial distribution
and relation with the supergranular flow. Our findings, while confirming the
presence of these calm areas, also show that the rate of emergence of small
magnetic elements is largely suppressed at the locations where the divergence
of the supergranular plasma flows is positive. This means that the dead calm
areas previously reported in literature are not randomly distributed over the
solar photosphere but they are linked to the supergranular cells themselves.
These results are discussed in the framework of the recent literature.


title:
Analytical Perspective for Photonic Bound States in the Continuum in
  Photonic Crystal Slabs

abstract:
  We investigate the formation of photonic bound states in the continuum (BICs)
in photonic crystal slabs from an analytical perspective. Unlike the stationary
at-$\Gamma$ BICs which origin from the geometric symmetry, the tunable
off-$\Gamma$ BICs are due to the weighted destructive via-the-continuum
interference in the vicinity of accidental symmetry when the majority of the
radiation is pre-canceled. The symmetric compatible nature of the off-$\Gamma$
BICs leads to a trapping of light that can be tuned through continuously
varying the wavevector. With the analytical approach, we explain a reported
experiment and predict the existence of a new BIC at an unrevealed symmetry.


title: Exact Kink Solitons in Skyrme Crystals

abstract:
  We present an explicit integration of the kink soliton equation obtained in a
recent interesting study of the classical Skyrme model where the field
configurations are of a generalized hedgehog form which is of a domain-wall
type. We also show that in such a reduced one-dimensional setting the
first-order and second-order equations are equivalent. Consequently, in such a
context, all finite-energy solitons are BPS type and precisely known.


title:
Integral motives, relative Krull-Schmidt principle, and Maranda-type
  theorems

abstract:
  In the present article we investigate properties of the category of the
integral Grothendieck-Chow motives over a field. We discuss the Krull-Schmidt
principle for integral motives, provide a complete list of the generalized
Severi-Brauer varieties with indecomposable integral motive, and exploit a
relation between the category of motives of twisted flag varieties and integral
$p$-adic representations of finite groups.


title: Note On The Maximal Primes Gaps

abstract:
  This note presents a result on the maximal prime gap of the form p_(n+1) -
p_n <= C(log p_n)^(1+e), where C > 0 is a constant, for any arbitrarily small
real number e > 0, and all sufficiently large integer n > n_0. Equivalently,
the result shows that any short interval [x, x + y], y => C(log x)^(1+e),
contains prime numbers for all sufficiently large real numbers x => x_0
unconditionally. An application demonstrates that a prime p => x > 2 can be
determined in deterministic polynomial time O(log(x)^8).


title:
Automatic recognition and tagging of topologically different regimes in
  dynamical systems

abstract:
  Complex systems are commonly modeled using nonlinear dynamical systems. These
models are often high-dimensional and chaotic. An important goal in studying
physical systems through the lens of mathematical models is to determine when
the system undergoes changes in qualitative behavior. A detailed description of
the dynamics can be difficult or impossible to obtain for high-dimensional and
chaotic systems. Therefore, a more sensible goal is to recognize and mark
transitions of a system between qualitatively different regimes of behavior. In
practice, one is interested in developing techniques for detection of such
transitions from sparse observations, possibly contaminated by noise. In this
paper we develop a framework to accurately tag different regimes of complex
systems based on topological features. In particular, our framework works with
a high degree of success in picking out a cyclically orbiting regime from a
stationary equilibrium regime in high-dimensional stochastic dynamical systems.

categories: cs.CG cs.LG math.DS nlin.CD physics.data-an


title: A Protocol for Generating Random Elements with their Probabilities

abstract:
  We give an AM protocol that allows the verifier to sample elements x from a
probability distribution P, which is held by the prover. If the prover is
honest, the verifier outputs (x, P(x)) with probability close to P(x). In case
the prover is dishonest, one may hope for the following guarantee: if the
verifier outputs (x, p), then the probability that the verifier outputs x is
close to p. Simple examples show that this cannot be achieved. Instead, we show
that the following weaker condition holds (in a well defined sense) on average:
If (x, p) is output, then p is an upper bound on the probability that x is
output. Our protocol yields a new transformation to turn interactive proofs
where the verifier uses private random coins into proofs with public coins. The
verifier has better running time compared to the well-known Goldwasser-Sipser
transformation (STOC, 1986). For constant-round protocols, we only lose an
arbitrarily small constant in soundness and completeness, while our public-coin
verifier calls the private-coin verifier only once.


title: Quantum groups and functional relations for higher rank

abstract:
  A detailed construction of the universal integrability objects related to the
integrable systems associated with the quantum group $\mathrm U_q(\mathcal
L(\mathfrak{sl}_3))$ is given. The full proof of the functional relations in
the form independent of the representation of the quantum group on the quantum
space is presented. The case of the general gradation and general twisting is
treated. The specialization of the universal functional relations to the case
when the quantum space is the state space of a discrete spin chain is
described.


title: Semiovals in PG(2,8) and PG(2,9)

abstract:
  The classification of all semiovals and blocking semiovals in
$\mathrm{PG}(2,8)$ and in $\mathrm{PG}(2,9)$ of size less than $17$ is
determined. Also, some information on the stabilizer groups and the
intersection sizes with lines is given.


title:
Chemistry and structure of homoepitaxial SrTiO$_3$ films and their
  influence on oxide-heterostructure interfaces

abstract:
  The properties of single-crystal SrTiO$_{3}$ substrates and homoepitaxial
SrTiO$_{3}$ films grown by pulsed laser deposition have been compared, in order
to understand the loss of interfacial conductivity when more than a critical
thickness of nominally homoepitaxial SrTiO$_{3}$ is inserted between a
LaAlO$_{3}$ film and a SrTiO$_{3}$ substrate. In particular, the chemical
composition and the structure of homoepitaxial SrTiO$_{3}$ investigated by
low-energy ion-scattering and surface x-ray diffraction, show that for
insulating heterointerfaces, a Sr-excess is present between the LaAlO$_{3}$ and
homoepitaxial SrTiO$_{3}$. Furthermore, an increase in the out-of-plane lattice
constant is observed in LaAlO$_{3}$, indicating that the conductivity both with
and without insertion of SrTiO$_{3}$ thin film originates from a Zener
breakdown associated with the polar catastrophe. When more than a critical
thickness of homoepitaxial SrTiO$_{3}$ is inserted between LaAlO$_3$ and
SrTiO$_3$, the electrons transferred by the electronic reconstruction are
trapped by the formation of a Sr-rich secondary phase and Sr-vacancies. The
migration of Sr towards the surface of homoepitaxial STO and accompanying loss
of interfacial conductivity can be delayed by reducing the Sr-content in the
PLD target.


title: Local limit theorems for multiplicative free convolutions

abstract:
  This paper describes the quality of convergence to an infinitely divisible
law relative to free multiplicative convolution. We show that convergence in
distribution for products of identically distributed and infinitesimal free
random variables implies superconvergence of their probability densities to the
density of the limit law. Superconvergence to the marginal law of free
multiplicative Brownian motion at a specified time is also studied. In the
unitary case, the superconvergence to free Brownian motion and that to the Haar
measure are shown to be uniform over the entire unit circle, implying further a
free entropic limit theorem and a universality result for unitary free L\'{e}vy
processes. Finally, the method of proofs on the positive half-line gives rise
to a new multiplicative Boolean to free Bercovici-Pata bijection.


title: Scalable numerical approach for the steady-state ab initio laser theory

abstract:
  We present an efficient and flexible method for solving the non-linear lasing
equations of the steady-state ab initio laser theory. Our strategy is to solve
the underlying system of partial differential equations directly, without the
need of setting up a parametrized basis of constant flux states. We validate
this approach in one-dimensional as well as in cylindrical systems, and
demonstrate its scalability to full-vector three-dimensional calculations in
photonic-crystal slabs. Our method paves the way for efficient and accurate
simulations of lasing structures which were previously inaccessible.


title:
Femtosecond 240-keV electron pulses from direct laser acceleration in a
  low-density gas

abstract:
  We propose a simple laser-driven electron acceleration scheme based on
tightly focused radially polarized laser pulses for the production of
femtosecond electron bunches with energies in the few-hundreds-of-keV range. In
this method, the electrons are accelerated forward in the focal volume by the
longitudinal electric field component of the laser pulse. Three-dimensional
test-particle and particle-in-cell simulations reveal the feasibility of
generating well-collimated electron bunches with an energy spread of 5% and a
temporal duration of the order of 1 fs. These results offer a route towards
unprecedented time resolution in ultrafast electron diffraction experiments.


title: A New View on Worst-Case to Average-Case Reductions for NP Problems

abstract:
  We study the result by Bogdanov and Trevisan (FOCS, 2003), who show that
under reasonable assumptions, there is no non-adaptive worst-case to
average-case reduction that bases the average-case hardness of an NP-problem on
the worst-case complexity of an NP-complete problem. We replace the hiding and
the heavy samples protocol in [BT03] by employing the histogram verification
protocol of Haitner, Mahmoody and Xiao (CCC, 2010), which proves to be very
useful in this context. Once the histogram is verified, our hiding protocol is
directly public-coin, whereas the intuition behind the original protocol
inherently relies on private coins.


title:
A singular M-matrix perturbed by a nonnegative rank one matrix has
  positive principal minors; is it D-stable?

abstract:
  The positive stability and D-stability of singular M-matrices, perturbed by
(non-trivial) nonnegative rank one perturbations, is investigated. In special
cases positive stability or D-stability can be established. In full generality
this is not the case, as illustrated by a counterexample. However, matrices of
the mentioned form are shown to be P-matrices.


title: Massless modes and abelian gauge fields in multi-band superconductors

abstract:
  In $N$-band superconductors, the $U(1)^N$ phase invariance is spontaneously
broken. We propose a model for $N$-band superconductors where the phase
differences between gaps are represented by abelian gauge fields. This model
corresponds to an $SU(N)$ gauge theory with the abelian projection. We show
that there are massless modes as well as massive modes when the number of gaps
$N$ is greater than 3. There are $N-3$ massless modes and two massive modes
near a minimum of the Josephson potential when $N$ bands are equivalent and
Josephson couplings are frustrated. The global symmetry $U(1)^{N-1}$ is broken
down by the Josephson term to $U(1)^{N-3}$. A non-trivial configuration of the
gauge field, that is, a monopole singularity of the gauge field results in a
fractional quantum-flux vortex. The fractional quantum-flux vortex corresponds
to a monopole in superconductors.


title: A product formula for the TASEP on a ring

abstract:
  For a random permutation sampled from the stationary distribution of the
TASEP on a ring, we show that, conditioned on the event that the first entries
are strictly larger than the last entries, the order of the first entries is
independent of the order of the last entries. The proof uses multi-line queues
as defined by Ferrari and Martin, and the theorem has an enumerative
combinatorial interpretation in that setting.
  Finally, we present a conjecture for the case where the small and large
entries are not separated.


title: New generalizations of BCI, BCK and Hilbert algebras

abstract:
  We introduce more generalizations of BCI, BCK and of Hilbert algebras, with
proper examples, and show the hierarchies existing between all these algebras,
old and new ones. Namely, we found thirty one new generalizations of BCI and
BCK algebras and twenty generalizations of Hilbert algebras.


title:
The inhomogeneous invariance quantum group of q-deformed boson algebra
  with continuous parameters

abstract:
  We present a q-deformed boson algebra using continuous momentum parameters
and investigate its inhomogeneous invariance quantum group.


title: On the hardness of classically simulating the one clean qubit model

abstract:
  Deterministic quantum computation with one quantum bit (DQC1) is a model of
quantum computing where the input restricted to containing a single qubit in a
pure state and with all other qubits in a completely-mixed state, with only a
single qubit measurement at the end of the computation [E. Knill and R.
Laflamme, Phys. Rev. Lett. {\bf81}, 5672 (1998)]. While it is known that DQC1
can efficiently solve several problems for which no known classical efficient
algorithms exist, the question of whether DQC1 is really more powerful than
classical computation remains open. In this paper, we introduce a slightly
modified version of DQC1, which we call DQC1$_k$, where $k$ output qubits are
measured, and show that DQC1$_k$ cannot be classically efficiently simulated
for any $k\geq3$ unless the polynomial hierarchy collapses at the third level.

categories: quant-ph cond-mat.stat-mech cond-mat.str-el cs.CC


title: On the operation of X-ray polarimeters with a large field of view

abstract:
  The measurement of the linear polarization is one of the hot topics of High
Energy Astrophysics. Gas detectors based on photoelectric effect have paved the
way for the design of sensitive instruments and mission proposals based on them
have been presented in the last few years in the energy range from about 2 keV
to a few tens of keV. As well, a number of polarimeters based on Compton
scattering are approved or discussed for launch on-board balloons or space
satellites at higher energies. These instruments are typically dedicated to
pointed observations with narrow field of view telescopes or collimators, but
there are also projects aimed at the polarimetry of bright transient sources,
like Soft Gamma Repeaters or the prompt emission of Gamma Ray Bursts. Given the
erratic appearance of such events in the sky, these polarimeters have a large
field of view to catch a reasonable number of them and, as a result, photons
may impinge on the detector off-axis. This changes dramatically the response of
the instrument to polarization, regardless if photoabsorption or Compton
scattering is involved. Instead of the simple cosine square dependency expected
for polarized photons which are incident on-axis, the response is never purely
cosinusoidal and a systematic modulation appears also for unpolarized
radiation. We investigate the origin of these differences and present an
analytic treatment which proves that actually such systematic effects are the
natural consequence of how current instruments operate. Our analysis provides
the expected response of photoelectric or Compton polarimeters to photons
impinging with any inclination and state of polarization.


title:
Random Distances Associated with Arbitrary Triangles: A Systematic
  Approach between Two Random Points

abstract:
  It has been known that the distribution of the random distances between two
uniformly distributed points within a convex polygon can be obtained based on
its chord length distribution (CLD). In this report, we first verify the
existing known CLD for arbitrary triangles, and then derive and verify the
distance distribution between two uniformly distributed points within an
arbitrary triangle by simulation. Furthermore, a decomposition and recursion
approach is applied to obtain the random point distance distribution between
two arbitrary triangles sharing a side. As a case study, the explicit
distribution functions are derived when two congruent isosceles triangles with
the acute angle equal to $\frac{\pi}{6}$ form a rhombus or a concave 4-gon.


title:
Diffusion coefficients from signal fluctuations: Influence of molecular
  shape and rotational diffusion

abstract:
  Analysis of signal fluctuations of a locally fixed probe, caused by molecules
diffusing under the probe, can be used to determine diffusion coefficients.
Theoretical treatments so far have been limited to point-like particles or to
molecules with circle-like shapes. Here we extend these treatments to molecules
with rectangle-like shapes, for which also rotational diffusion needs to be
taken into account. Focusing on the distribution of peak widths in the signal,
we show how translational as well as rotational diffusion coefficients can be
determined. We address also the question, how the distribution of interpeak
time intervals and autocorrelation function can be employed for determining
diffusion coefficients. Our approach is validated against kinetic Monte Carlo
simulations.


title: Regularizations of non-euclidean polygons

abstract:
  We are interested in easy geometric transformations which regularize
n-polygons in the non-euclidean plane. A transformation is called easy if it
can be easily implemented into an algorithm. This article is motivated by
preceding work on geometric transformations on euclidean polygons and possible
applications for non-euclidean meshes.


title: Data Structures for Task-based Priority Scheduling

abstract:
  Many task-parallel applications can benefit from attempting to execute tasks
in a specific order, as for instance indicated by priorities associated with
the tasks. We present three lock-free data structures for priority scheduling
with different trade-offs on scalability and ordering guarantees. First we
propose a basic extension to work-stealing that provides good scalability, but
cannot provide any guarantees for task-ordering in-between threads. Next, we
present a centralized priority data structure based on $k$-fifo queues, which
provides strong (but still relaxed with regard to a sequential specification)
guarantees. The parameter $k$ allows to dynamically configure the trade-off
between scalability and the required ordering guarantee. Third, and finally, we
combine both data structures into a hybrid, $k$-priority data structure, which
provides scalability similar to the work-stealing based approach for larger
$k$, while giving strong ordering guarantees for smaller $k$. We argue for
using the hybrid data structure as the best compromise for generic,
priority-based task-scheduling.
  We analyze the behavior and trade-offs of our data structures in the context
of a simple parallelization of Dijkstra's single-source shortest path
algorithm. Our theoretical analysis and simulations show that both the
centralized and the hybrid $k$-priority based data structures can give strong
guarantees on the useful work performed by the parallel Dijkstra algorithm. We
support our results with experimental evidence on an 80-core Intel Xeon system.


title: Improved integrality gap upper bounds for TSP with distances one and two

abstract:
  We study the structure of solutions to linear programming formulations for
the traveling salesperson problem (TSP).
  We perform a detailed analysis of the support of the subtour elimination
linear programming relaxation, which leads to algorithms that find 2-matchings
with few components in polynomial time. The number of components directly leads
to integrality gap upper bounds for the TSP with distances one and two, for
both undirected and directed graphs.
  Our main results concern the subtour elimination relaxation with one
additional cutting plane inequality:
  - For undirected instances we obtain an integrality gap upper bound of 5/4
without any further restrictions, of 7/6 if the optimal LP solution is
half-integral.
  - For instances of order n where the fractional LP value has a cost of n, we
obtain a tight integrality gap upper bound of 10/9 if there is an optimal
solution with subcubic support graph. The latter property that the graph is
subcubic is implied if the solution is a basic solution in the fractional
2-matching polytope.
  - For directed instances we obtain an integrality gap upper bound of 3/2, and
of 4/3 if given an optimal 1/2-integral solution. In the case of undirected
graphs, we can avoid to add the cutting plane inequality if we accept slightly
increased values. For the tight result, the cutting plane is not required.
  Additionally, we show that relying on the structure of the support is not an
artefact of our algorithm, but is necessary under standard complexity-theoretic
assumptions: we show that finding improved solutions via local search is
W[1]-hard for k-edge change neighborhoods even for the TSP with distances one
and two, which strengthens a result of D\'aniel Marx.


title:
High-order post-Newtonian contributions to the two-body gravitational
  interaction potential from analytical gravitational self-force calculations

abstract:
  We extend the analytical determination of the main radial potential
describing (within the effective one-body formalism) the gravitational
interaction of two bodies beyond the 4th post-Newtonian approximation recently
obtained by us. This extension is done to linear order in the mass ratio by
applying analytical gravitational self-force theory (for a particle in circular
orbit around a Schwarzschild black hole) to Detweiler's gauge-invariant
redshift variable. By using the version of black hole perturbation theory
developed by Mano, Suzuki and Takasugi, we have pushed the analytical
determination of the (linear in mass ratio) radial potential to the 6th
post-Newtonian order (passing through 5 and 5.5 post-Newtonian terms). In
principle, our analytical method can be extended to arbitrarily high
post-Newtonian orders.


title: Light Chargino Effects onto H -> gamma gamma in the MSSM

abstract:
  We analyse the implications of light charginos on the Higgs boson signal
strength via gluon-gluon fusion and di-photon decay in the Minimal
Supersymmetric Standard Model (MSSM) at the Large Hadron Collider (LHC). We
show that enhancements are possible with a rate up to 25%. We also prove that
they are possible for a high scale constrained version of the MSSM with
non-universal Higgs and gaugino masses. In contrast, effects due to light
charged Higgs bosons, that we also have investigated, are generically
negligible in the \gamma\gamma decay, though they may affect the b \bar b rate,
hence the total width.


title: Large Neutrino Magnetic Dipole Moments in MSSM Extensions

abstract:
  An analysis of the Dirac neutrino magnetic moment with standard model
interactions gives $\mu_\nu\sim 3 \times 10^{-19} \mu_B (m_\nu/1 eV)$. The
observation of a significantly larger magnetic moment will provide a clear
signal of new physics beyond the standard model. The current experimental
limits on the neutrino magnetic moments are orders of magnitude larger than the
prediction with the standard model interactions and thus its test appears out
of reach. Here we give an analysis of the Dirac neutrino magnetic moments
within the framework of a minimal supersymmetric standard model extension with
a vectorlike lepton generation. Specifically we compute the moments arising
from the exchange of W and the charged leptons in the loop, as well as from the
exchange of charginos, charged sleptons and charged mirror sleptons. It is
shown that the neutrino moment in this case can be several orders of magnitude
larger than the one with standard model like interactions, lying close to and
below the current experimental upper limits and should be accessible in
improved future experiment. A correlated prediction of the heaviest neutrino
lifetimes from radiative decays to the lighter neutrinos via exchange of
charginos and sleptons in the loops is also made. The predicted lifetimes are
several orders of magnitudes smaller than the one with the standard model
interactions and also lie close to the current experimental limits from
analyses using the cosmic background neutrino data.


title:
An Application of Answer Set Programming to the Field of Second Language
  Acquisition

abstract:
  This paper explores the contributions of Answer Set Programming (ASP) to the
study of an established theory from the field of Second Language Acquisition:
Input Processing. The theory describes default strategies that learners of a
second language use in extracting meaning out of a text, based on their
knowledge of the second language and their background knowledge about the
world. We formalized this theory in ASP, and as a result we were able to
determine opportunities for refining its natural language description, as well
as directions for future theory development. We applied our model to automating
the prediction of how learners of English would interpret sentences containing
the passive voice. We present a system, PIas, that uses these predictions to
assist language instructors in designing teaching materials. To appear in
Theory and Practice of Logic Programming (TPLP).


title:
A novel terahertz time-domain spectroscopic endoscope based on a single
  photoconductive antenna chip

abstract:
  The common terahertz time-domain spectroscopy (THz-TDS) based on
photoconductive antenna (PCA) needs two separate PCA chips. One PCA works as an
emitter, and the other works as a receiver. For a reflection-type measurement,
the technique called 'attenuated total reflection' usually is needed to enhance
the reflection sensitivity. These make the system bulk and complicated for the
reflection-type measurement. In this paper, we propose a novel THz-TDS
endoscope that is specifically designed for reflection-type measurement. This
THz-TDS endoscope is benefited from an integrated photoconductive antenna (we
call it iPCA), which integrates the emitter and receiver on a single antenna
chip. Therefore, the dimension of the endoscope can be shrunk as much as
possible for practical usage. We present the design and working principle of
this THz-TDS endoscope in details. It may open a promising way for the THz-TDS
application in biomedical fields.


title:
Strong ferromagnetism at the surface of an antiferromagnet caused by
  buried magnetic moments

abstract:
  Carrying a large, pure spin magnetic moment of 7 $\mu$bohr/atom in the
half-filled 4f shell, divalent europium is an outstanding element for
assembling novel magnetic devices in which a two-dimensional electron gas
(2DEG) is polarized due to exchange interaction with an underlying
magnetically-active Eu layer, even in the absence of a magnetic field. A
natural example for such geometry is the intermetallic layered material
EuRh$_2$Si$_2$, in which magnetically active layers of Eu are well separated
from each other by non-magnetic Si-Rh-Si trilayers. Applying angle-resolved
photoelectron spectroscopy (ARPES) to this system, we discovered a large spin
splitting of a Shockley-type surface state formed by itinerant electrons of the
Si-Rh-Si surface related trilayer. ARPES shows that the splitting sets in below
approx. 32.5K and quickly saturates to around 150meV upon cooling.
Interestingly, this temperature is substantially higher than the order
temperature of the Eu 4f moments (approx. 24.5K) in the bulk. Our results
clearly show that the magnetic exchange interaction between the surface state
and the buried 4f moments in the 4th subsurface layer is the driving force for
the formation of itinerant ferromagnetism at the surface. We demonstrate that
the observed spin splitting of the surface state, reflecting properties of
2DEG, is easily controlled by temperature. Such a splitting may also be induced
into states of functional surface layers deposited onto the surface of
EuRh$_2$Si$_2$ or similarly ordered magnetic materials with metallic or
semiconducting properties.


title: Parabolic equations with exponential nonlinearity and measure data

abstract:
  Let $\Omega$ be a bounded domain in ${\mathbb R}^N$ and $T>0$. We study the
problem \begin{equation} (P)\left\{ \begin{array}{lll} u_t - \Delta u \pm g(u)
&= \mu \quad &\text{in } Q_T:=\Omega \times (0,T) \\ \phantom{------,} u&=0
&\text{on } \partial \Omega \times (0,T)\\ \phantom{----,} u(.,0) &=\omega
&\text{in } \Omega. \end{array} \right. \end{equation} where $\mu$ and $\omega$
are bounded Radon measures in $Q_T$ and $\Omega$ respectively and $g(u) \sim
e^{a |u|^q} $ with $a>0$ and $q \geq 1$. We provide a sufficient condition in
terms of fractional maximal potentials of $\mu$ and $\omega$ for solving (P).


title: On the convergence to $0$ of $m_n \xi $ mod $1$

abstract:
  We show that for any irrational number $\a$ and a sequence of integers
$\{m_l\}_{l\in \N}$ such that $\displaystyle{\lim_{l\to \infty} \norm{m_l \a} =
0}$, there exists a continuous measure $\mu$ on the circle such that
$\displaystyle{\lim_{l\to \infty} \int_\T \norm{m_l \th} d\mu(\th) = 0}$. This
implies that any rigidity sequence of any ergodic transformation is a rigidity
sequence for some weakly mixing dynamical system.
  On the other hand, we show that for any $\a \in \R - \Q$, there exists a
sequence of integers $\{m_l\}_{l\in \N}$ such that $\norm{m_l \a} \to 0$ and
$m_l \theta [1]$ is dense on the circle if and only if $\th \notin \Q \a+\Q$.


title: Mixing and transport by ciliary carpets: a numerical study

abstract:
  We use a 3D computational model to study the fluid transport and mixing due
to the beating of an infinite array of cilia. In accord with recent
experiments, we observe two distinct regions: a fluid transport region above
the cilia and a fluid mixing region below the cilia tip. The metachronal wave
due to phase differences between neighboring cilia is known to enhance the
fluid transport above the ciliary tip. In this work, we show that the
metachronal wave also enhances the mixing rates in the sub-ciliary region,
often simultaneously with the flow rate enhancement. Our results suggest that
this simultaneous enhancement in transport and mixing is due to an enhancement
in shear flow. As the flow above the cilia increases, shear rate in the fluid
increases and such shear enhances stretching, which is an essential ingredient
for mixing. Estimates of the mixing time scale indicate that, compared to
diffusion, the mixing due to the cilia beat may be significant and sometimes
dominates chemical diffusion.


title: Superexchange blockade in triple quantum dots

abstract:
  We propose the interaction of two electrons in a triple quantum dot as a
minimal system to control long range superexchange transitions. These are
probed by transport spectroscopy. Narrow resonances appear indicating the
transfer of charge from one side of the sample to the other with the central
one being occupied only virtually. We predict that two different intermediate
states establish the two arms of a one dimensional interferometer.
Configurations of destructive interference of the two superexchage trajectories
totally block the current through the system. We emphasize the role of spin
correlations giving rise to lifetime-enhanced resonances.


title:
Strong neutrino cooling by cycles of electron capture and $\beta^-$
  decay in neutron star crusts

abstract:
  The temperature in the crust of an accreting neutron star, which comprises
its outermost kilometer, is set by heating from nuclear reactions at large
densities, neutrino cooling, and heat transport from the interior. The heated
crust has been thought to affect observable phenomena at shallower depths, such
as thermonuclear bursts in the accreted envelope. Here we report that cycles of
electron capture and its inverse, $\beta^-$ decay, involving neutron-rich
nuclei at a typical depth of about 150 m, cool the outer neutron star crust by
emitting neutrinos while also thermally decoupling the surface layers from the
deeper crust. This Urca mechanism has been studied in the context of white
dwarfs and Type Ia supernovae, but hitherto was not considered in neutron
stars, because previous models computed the crust reactions using a
zero-temperature approximation and assumed that only a single nuclear species
was present at any given depth. This thermal decoupling means that X-ray bursts
and other surface phenomena are largely independent of the strength of deep
crustal heating. The unexpectedly short recurrence times, of the order of
years, observed for very energetic thermonuclear superbursts are therefore not
an indicator of a hot crust, but may point instead to an unknown local heating
mechanism near the neutron star surface.


title: Ulrich sheaves and higher-rank Brill-Noether theory

abstract:
  An Ulrich sheaf on an embedded projective variety is a normalized
arithmetically Cohen-Macaulay sheaf with the maximum possible number of
independent sections. Ulrich sheaves are important in the theory of Chow forms,
Boij-Soderberg theory, generalized Clifford algebras, and for an approach to
Lech's conjecture in commutative algebra. In this note, we give a reduction of
the construction of Ulrich sheaves on a projective variety X to the
construction of an Ulrich sheaf for a finite map of curves, which is in turn
equivalent to a higher-rank Brill-Noether problem for any of a certain class of
curves on X. Then we show that existence of an Ulrich sheaf for a finite map of
curves implies sharp numerical constraints involving the degree of the map and
the ramification divisor.


title: Measuring entanglement of photons produced by a pulsed source

abstract:
  A pulsed source of entangled photons is desirable for some applications. Yet,
such a source has intrinsic problems arising from the simultaneous arrival of
the signal and noise photons to the detectors. These problems are analyzed and
practical methods to calculate the number of accidental (or spurious)
coincidences are described in detail, and experimentally checked, for the
different regimes of interest. The results are useful not only to measure
entanglement, but to all the situations where extracting the number of valid
coincidences from noisy data is required. As an example of the use of those
methods, we present the time-resolved measurement of the Concurrence of the
field produced by spontaneous parametric down conversion with pump pulses of
duration in the ns-range at a repetition of kHz. The predicted discontinuous
evolution of the entanglement at the edges of the pump pulse is observed.


title: Analysis of polarity

abstract:
  We develop a differential theory for the polarity transform parallel to that
for the Legendre transform, which is applicable when the functions studied are
"geometric convex", namely convex, non-negative and vanish at the origin. This
analysis may be used to solve a family of first order equations reminiscent of
Hamilton--Jacobi and conservation law equations, as well as some second order
Monge-Ampere type equations. A special case of the latter, that we refer to as
the homogeneous polar Monge--Ampere equation, gives rise to a canonical method
of interpolating between convex functions.


title:
A new method of construction of all sets of mutually unbiased bases for
  two-qubit systems

abstract:
  Mutually unbiased bases are an important tool in many applications of quantum
information theory. We present a new algorithm for finding the mutually
unbiased bases for two-qubit systems. We derive a system of four equations in
the Galois field GF(4) and show that the solutions of this system are
sufficient for obtaining the most general set of mutually unbiased bases.
Further, our algorithm is applied to an example and we show that there are
three possible solutions of the system of four equations, each solution leading
to a different set of mutually unbiased bases.


title: Solvability of linear differential systems in the Liouvillian sense

abstract:
  The paper concerns the solvability by quadratures of linear differential
systems, which is one of the questions of differential Galois theory. We
consider systems with regular singular points as well as those with
(non-resonant) irregular ones and propose some criteria of solvability for
systems whose (formal) exponents are sufficiently small.


title:
A Discontinuous Galerkin - Front Tracking Scheme and its Optimal$^2$
  Error Estimation

abstract:
  In [11] and [5], an error estimate of optimal convergence rates and optimal
error propagation (optimal^2) was given for the Runge-Kutta discontinuous
Galerkin (RKDG) method solving the scalar nonlinear conservation laws in the
case of smooth solutions. This manuscript generalizes the problem to the case
of a piecewise smooth solution containing one fully developed shock. A front
tracking technique is incorporated in the RKDG scheme to produce a numerical
solution with a truly high order error. The numerical smoothness approach of
[11] is generalized to this particular case of a discontinuous solution.


title: The $m$-Cover Posets and Their Applications

abstract:
  In this article we introduce the $m$-cover poset of an arbitrary bounded
poset $\mathcal{P}$, which is a certain subposet of the $m$-fold direct product
of $\mathcal{P}$ with itself. Its ground set consists of multichains of
$\mathcal{P}$ that contain at most three different elements, one of which has
to be the least element of $\mathcal{P}$, and the other two elements have to
form a cover relation in $\mathcal{P}$. We study the $m$-cover poset from a
structural and topological point of view. In particular, we characterize the
posets whose $m$-cover poset is a lattice for all $m>0$, and we characterize
the special cases, where these lattices are EL-shellable, left-modular, or
trim. Subsequently, we investigate the $m$-cover poset of the Tamari lattice
$\mathcal{T}_{n}$, and we show that the smallest lattice that contains the
$m$-cover poset of $\mathcal{T}_{n}$ is isomorphic to the $m$-Tamari lattice
$\mathcal{T}_{n}^{(m)}$ introduced by Bergeron and Pr\'eville-Ratelle. We
conclude this article with a conjectural desription of an explicit realization
of $\mathcal{T}_{n}^{(m)}$ in terms of $m$-tuples of Dyck paths.


title: A quenched large deviation principle in a continuous scenario

abstract:
  We prove the analogue for continuous space-time of the quenched LDP derived
in Birkner, Greven and den Hollander (2010) for discrete space-time. In
particular, we consider a random environment given by Brownian increments, cut
into pieces according to an independent continuous-time renewal process. We
look at the empirical process obtained by recording both the length of and the
increments in the successive pieces. For the case where the renewal time
distribution has a Lebesgue density with a polynomial tail, we derive the
quenched LDP for the empirical process, i.e., the LDP conditional on a typical
environment. The rate function is a sum of two specific relative entropies, one
for the pieces and one for the concatenation of the pieces. We also obtain a
quenched LDP when the tail decays faster than algebraic. The proof uses
coarse-graining and truncation arguments, involving various approximations of
specific relative entropies that are not quite standard.
  In a companion paper we show how the quenched LDP and the techniques
developed in the present paper can be applied to obtain a variational
characterisation of the free energy and the phase transition line for the
Brownian copolymer near a selective interface.


title:
Herschel SPIRE-FTS Observations of Excited CO and [CI] in the Antennae
  (NGC 4038/39): Warm and Cold Molecular Gas

abstract:
  We present Herschel SPIRE-FTS observations of the Antennae (NGC 4038/39), a
well studied, nearby ($22$ Mpc) ongoing merger between two gas rich spiral
galaxies. We detect 5 CO transitions ($J=4-3$ to $J=8-7$), both [CI]
transitions and the [NII]$205\mu m$ transition across the entire system, which
we supplement with ground based observations of the CO $J=1-0$, $J=2-1$ and
$J=3-2$ transitions, and Herschel PACS observations of [CII] and [OI]$63\mu m$.
Using the CO and [CI] transitions, we perform both a LTE analysis of [CI], and
a non-LTE radiative transfer analysis of CO and [CI] using the radiative
transfer code RADEX along with a Bayesian likelihood analysis. We find that
there are two components to the molecular gas: a cold ($T_{kin}\sim 10-30$ K)
and a warm ($T_{kin} \gtrsim 100$ K) component. By comparing the warm gas mass
to previously observed values, we determine a CO abundance in the warm gas of
$x_{CO} \sim 5\times 10^{-5}$. If the CO abundance is the same in the warm and
cold gas phases, this abundance corresponds to a CO $J=1-0$ luminosity-to-mass
conversion factor of $\alpha_{CO} \sim 7 \ M_{\odot}{pc^{-2} \ (K \ km \
s^{-1})^{-1}}$ in the cold component, similar to the value for normal spiral
galaxies. We estimate the cooling from H$_2$, [CII], CO and [OI]$63\mu m$ to be
$\sim 0.01 L_{\odot}/M_{\odot}$. We compare PDR models to the ratio of the flux
of various CO transitions, along with the ratio of the CO flux to the
far-infrared flux in NGC 4038, NGC 4039 and the overlap region. We find that
the densities recovered from our non-LTE analysis are consistent with a
background far-ultraviolet field of strength $G_0\sim 1000$. Finally, we find
that a combination of turbulent heating, due to the ongoing merger, and
supernova and stellar winds are sufficient to heat the molecular gas.


title:
Precise Calculation of the Dilepton Invariant-Mass Spectrum and the
  Decay Rate in $B^\pm \to \pi^\pm \mu^+ \mu^-$ in the SM

abstract:
  We present a precise calculation of the dilepton invariant-mass spectrum and
the decay rate for $B^\pm \to \pi^\pm \ell^+ \ell^-$ ($\ell^\pm = e^\pm,
\mu^\pm $) in the Standard Model (SM) based on the effective Hamiltonian
approach for the $b \to d \ell^+ \ell^-$ transitions. With the Wilson
coefficients already known in the next-to-next-to-leading logarithmic (NNLL)
accuracy, the remaining theoretical uncertainty in the short-distance
contribution resides in the form factors $f_+ (q^2)$, $f_0 (q^2)$ and $f_T
(q^2)$. Of these, $f_+ (q^2)$ is well measured in the charged-current
semileptonic decays $B \to \pi \ell \nu_\ell$ and we use the $B$-factory data
to parametrize it. The corresponding form factors for the $B \to K$ transitions
have been calculated in the Lattice-QCD approach for large-$q^2$ and
extrapolated to the entire $q^2$-region using the so-called $z$-expansion.
Using an $SU(3)_F$-breaking Ansatz, we calculate the $B \to \pi$ tensor form
factor, which is consistent with the recently reported lattice $B \to \pi$
analysis obtained at large~$q^2$. The prediction for the total branching
fraction ${\cal B} (B^\pm \to \pi^\pm \mu^+ \mu^-) = (1.88 ^{+0.32}_{-0.21})
\times 10^{-8}$ is in good agreement with the experimental value obtained by
the LHCb Collaboration. In the low $q^2$-region, heavy-quark symmetry (HQS)
relates the three form factors with each other. Accounting for the
leading-order symmetry-breaking effects, and using data from the
charged-current process $B \to \pi \ell \nu_\ell$ to determine $f_+ (q^2)$, we
calculate the dilepton invariant-mass distribution in the low $q^2$-region in
the $B^\pm \to \pi^\pm \ell^+ \ell^-$ decay. This provides a model-independent
and precise calculation of the partial branching ratio for this decay.


title: Cosmological Perturbations Across an S-brane

abstract:
  Space-filling S-branes can mediate a transition between a contracting and an
expanding universe in the Einstein frame. Following up on previous work that
uncovered such bouncing solutions in the context of weakly coupled thermal
configurations of a certain class of type II superstrings, we set up here the
formalism in which we can study the evolution of metric fluctuations across
such an S-brane. Our work shows that the specific nature of the S-brane, which
is sourced by non-trivial massless thermal string states and appears when the
universe reaches a maximal critical temperature, allows for a scale invariant
spectrum of curvature fluctuations to manifest at late times via a stringy
realization of the matter bounce scenario. The finite energy density at the
transition from contraction to expansion provides calculational control over
the propagation of the curvature perturbations through the bounce, furnishing a
working proof of concept that such a stringy universe can result in viable late
time cosmology.


title:
Comptonization in ultra-strong magnetic fields: numerical solution of
  the radiative transfer problem

abstract:
  We consider the radiative transfer problem in a plane-parallel slab of
thermal electrons in the presence of an overcritical magnetic field. Under such
conditions, the magnetic field behaves as a birefringent medium for the
propagating photons, and the electromagnetic radiation is split into two
polarization modes, ordinary and extraordinary, having different
cross-sections. When the optical depth of the slab is large, the ordinary-mode
photons are strongly Comptonized and the photon field is dominated by an
isotropic component. The radiative transfer problem in strong magnetic fields
presents many mathematical issues and analytical or numerical solutions can be
obtained only under some given approximations. We investigate this problem both
from the analytical and numerical point of view, providing a test of the
previous analytical estimates and extending these results introducing numerical
techniques. We consider the case of low temperature blackbody photons
propagating in a sub-relativistic temperature plasma, which allows us to deal
with a semi Fokker-Planck approximation of the radiative transfer equation. We
report the numerical solution obtained for eigenvalues and eigenfunctions of
the space operator, and the emerging Comptonization spectrum of the
ordinary-mode photons for any eigenvalue of the space equation and for energies
significantly less than the cyclotron energy, which is of the order of MeV for
the intensity of the magnetic field here considered. We derived the specific
intensity of the ordinary photons, under the approximation of large angle and
large optical depth. These assumptions allow the equation to be treated using a
diffusion-like approximation.


title: Connectivity maintenance by robotic Mobile Ad-hoc NETwork

abstract:
  The problem of maintaining a wireless communication link between a fixed base
station and an autonomous agent by means of a team of mobile robots is
addressed in this work. Such problem can be of interest for search and rescue
missions in post disaster scenario where the autonomous agent can be used for
remote monitoring and first hand knowledge of the aftermath, while the mobile
robots can be used to provide the agent the possibility to dynamically send its
collected information to an external base station. To study the problem, a
distributed multi-robot system with wifi communication capabilities has been
developed and used to implement a Mobile Ad-hoc NETwork (MANET) to guarantee
the required multi-hop communication. None of the robots of the team possess
the knowledge of agent's movement, neither they hold a pre-assigned position in
the ad-hoc network but they adapt with respect to the dynamic environmental
situations. This adaptation only requires the robots to have the knowledge of
their position and the possibility to exchange such information with their
one-hop neighbours. Robots' motion is achieved by implementing a behavioural
control, namely the Null-Space based Behavioural control, embedding the
collective mission to achieve the required self-configuration. Validation of
the approach is performed by means of demanding experimental tests involving
five ground mobile robots capable of self localization and dynamic obstacle
avoidance.


title:
Point contact spectroscopy in Fe-based superconductors: recent
  advancements and future challenges

abstract:
  Iron-based superconductors (FeSC) present an unprecedented variety of
features both in the superconducting and in the normal state. Different
families differ in the value of the critical temperature, in the shape of the
Fermi surface, in the existence or absence of quasi-nesting conditions, in the
range of doping in which the antiferromagnetic (AFM) and the superconducting
phase coexist and in the structure of the order parameter in the reciprocal
space, and so on. In this paper the most important results of point-contact
spectroscopy (PCS) in Fe-based superconductors are reviewed, and the most
recent advances are described with the aim to discuss the future perspectives
and challenges of this spectroscopic technique in the characterization of the
superconducting properties of these complex compounds. One of the main
challenges, faced so far only by a few researchers in the PCS field, is to
fully explore the phase diagram of these materials, as a function of doping or
pressure, to understand the interplay between superconductivity and magnetism,
the effect of intrinsic or extrinsic inhomogeneities, the role of spin
fluctuations (SFs) in the pairing, the symmetry and the structure of the order
parameter(s).


title: Free-energy bounds for hierarchical spin models

abstract:
  In this paper we study two non-mean-field spin models built on a hierarchical
lattice: The hierarchical Edward-Anderson model (HEA) of a spin glass, and
Dyson's hierarchical model (DHM) of a ferromagnet. For the HEA, we prove the
existence of the thermodynamic limit of the free energy and the
replica-symmetry-breaking (RSB) free-energy bounds previously derived for the
Sherrington-Kirkpatrick model of a spin glass. These RSB mean-field bounds are
exact only if the order-parameter fluctuations (OPF) vanish: Given that such
fluctuations are not negligible in non-mean-field models, we develop a novel
strategy to tackle part of OPF in hierarchical models. The method is based on
absorbing part of OPF of a block of spins into an effective Hamiltonian of the
underlying spin blocks. We illustrate this method for DHM and show that,
compared to the mean-field bound for the free energy, it provides a tighter
non-mean-field bound, with a critical temperature closer to the exact one. To
extend this method to the HEA model, a suitable generalization of Griffith's
correlation inequalities for Ising ferromagnets is needed: Since correlation
inequalities for spin glasses are still an open topic, we leave the extension
of this method to hierarchical spin glasses as a future perspective.


title: Modified Paouris inequality

abstract:
  The Paouris inequality gives the large deviation estimate for Euclidean norms
of log-concave vectors. We present a modified version of it and show how the
new inequality may be applied to derive tail estimates of l_r-norms and suprema
of norms of coordinate projections of isotropic log-concave vectors.


title:
Mr. Moo's First RPG: Rules, Discussion and the Instructional
  Implications of Collective Intelligence on the Open Web

abstract:
  For a moment, imagine an active online learning community of writers,
artists, and designers, many spending more than eight hours a week composing
projects. In this community, young people, primarily between the ages of 18-26,
regularly critique, facilitate, and support each other in their composition
activities. They are motivated to participate by their shared interest and
affinity for their creative work. In the age of Wikipedia, this might not seem
particularly novel, but what I am actually describing is an online discussion
board, RPGmakerVX.net. Elsewhere, I have presented a general outline of the
kinds of individuals involved in this community and the way that the site as a
whole functions as an open learning environment (Owens, 2010). In this essay, I
present a case study of one participant in this community. His user name is Mr.
Moo, and at the time I interviewed him, he was a 19 year old college student
from Calgary, Canada. When he created his first role-playing game, Prelude of
Identity, he was eighteen. After providing a conceptual context for this case
study in work on collective intelligence, I draw out the relationship between
the technical system of the discussion boards and the creative process of
engaging with peers in the production of a video game. I suggest that the
discussion board rules and interaction enable a dialogue around composition
that ultimately leaves Mr. Moo with a valuable learning experience while also
producing a role-playing game. Thinking about this system from the perspective
of collective intelligence enables us to use these kinds of interest-driven,
online affinity communities as tools in an open education tool kit for
educators in more formal learning environments. Ultimately, discussion boards
in gaming communities, both the technical and social systems they represent,
could be thought of as instructional tools.


title:
Some possible numbers of edge coverings of a bipartite graph or shortest
  paths with fixed ends in a space of compact sets in $R^n$

abstract:
  In this paper we provide a method of finding possible numbers of shortest
paths between two points in a space of compact sets in Euclidean space with
Hausdorff distance. We also prove that there cannot be some of the numbers of
shortest paths, thus expanding previous works [1][2]


title:
Description of the isotope chain $^{180-196}$Pt within some solvable
  approaches

abstract:
  Energies of the ground, $\beta$ and $\gamma$ bands as well as the associated
B(E2) values are determined for each even-even isotope of the $^{180-196}$Pt
chain by the exact solutions of some differential equations which approximate
the generalized Bohr-Mottelson Hamiltonian. The emerging approaches are called
the Sextic and Spheroidal Approach (SSA), the Sextic and Mathieu Approach
(SMA), the Infinite Square Well and Spheroidal Approach (ISWSA) and the
Infinite Square Well and Mathieu Approach (ISWMA), respectively. While the
first three methods were formulated in some earlier papers of the present
authors, ISWMA is an inedited approach of this work. Numerical results are
compared with those obtained with the so called X(5) and Z(5) models. A contour
plot for the probability density as function of the intrinsic dynamic
deformations is given for a few states of the three considered bands with the
aim of evidencing the shape evolution along the isotope chain and pointing out
possible shape coexistence.


title:
On Dealing with Censored Largest Observations under Weighted Least
  Squares

abstract:
  When observations are subject to right censoring, weighted least squares with
appropriate weights (to adjust for censoring) is sometimes used for parameter
estimation. With Stute's weighted least squares method, when the largest
observation is censored ($Y_{(n)}^+$), it is natural to apply the
redistribution to the right algorithm of Efron (1967). However, Efron's
redistribution algorithm can lead to bias and inefficiency in estimation. This
study explains the issues clearly and proposes some alternative ways of
treating $Y_{(n)}^+$. The first four proposed approaches are based on the well
known Buckley--James (1979) method of imputation with the Efron's tail
correction and the last approach is indirectly based on a general mean
imputation technique in literature. All the new schemes use penalized weighted
least squares optimized by quadratic programming implemented with the
accelerated failure time models. Furthermore, two novel additional imputation
approaches are proposed to impute the tail tied censored observations that are
often found in survival analysis with heavy censoring. Several simulation
studies and real data analysis demonstrated that the proposed approaches
generally outperform Efron's redistribution approach and lead to considerably
smaller mean squared error and bias estimates.


title:
Exact time-dependent density-functional potentials for strongly
  correlated tunneling electrons

abstract:
  By propagating the many-body Schr\"odinger equation, we determine the exact
time-dependent Kohn-Sham potential for a system of strongly correlated
electrons which undergo field-induced tunneling. Numerous features are entirely
absent from the approximations commonly used in time-dependent
density-functional theory. The self-interaction correction is strong and time
dependent, owing to electron localization, and prominent dynamic spatial
potential steps arise from minima in the charge density, as modified by the
Coulomb interaction experienced by the partially tunneled electron.


title: Gapless superconductivity and string theory

abstract:
  Coexistence of superconducting and normal components in nanowires at currents
below the critical (a "mixed" state) would have important consequences for the
nature and range of potential applications of these systems. For clean samples,
it represents a genuine interaction effect, not seen in the mean-field theory.
Here we consider properties of such a state in the gravity dual of a strongly
coupled superconductor constructed from D3 and D5 branes. We find numerically
uniform gapless solutions containing both components but argue that they are
unstable against phase separation, as their free energies are not convex. We
speculate on the possible nature of the resulting non-uniform sate ("emulsion")
and draw analogies between that state and the familiar mixed state of a type II
superconductor in a magnetic field.


title:
Tunneling-assisted optical information storage with lattice polariton
  solitons in cavity-QED arrays

abstract:
  Considering two-level media in the array of weakly coupled nano-cavities, we
reveal a variety of dynamical regimes, such as diffusion, self-trapping,
soliton, and breathers for the wave-packets in the presence of photon tunneling
processes between the next-nearest cavities. We focus our attention on the low
branch (LB) bright polariton soliton formation, due to the two-body
polariton-polariton scattering processes. When detuning frequency is
manipulated adiabatically, the low-branch lattice polariton localized states,
i.e., that are solitons and breathers evolving between photon-like and
matter-like states, are shown to act as carriers for spatially distributed
storage and retrieval of optical information.


title: Congruences and prime-perspectivities in finite lattices

abstract:
  IIn a finite lattice, a congruence spreads from a prime interval to another
by a sequence of congruence-perspectivities through \emph{intervals of
arbitrary size}, by a 1955 result of J. Jakub\'ik.
  In this note, I introduce the concept of \emph{prime-perspectivity} and prove
the Prime-projectivity Lemma: a congruence spreads from a prime interval to
another by a sequence of prime-perspectivities through \emph{prime ntervals}.
  A planar semimodular lattice is \emph{slim} if it contains no $\mathsf{M}_3$
sublattice. I introduce the Swing Lemma, a very strong version of the
Prime-projectivity Lemma for slim, planar, semimodular lattices.


title: Enumeration of Grothendieck's dessins and KP hierarchy

abstract:
  Branched covers of the complex projective line ramified over $0,1$ and
$\infty$ (Grothendieck's {\em dessins d'enfant}) of fixed genus and degree are
effectively enumerated. More precisely, branched covers of a given ramification
profile over $\infty$ and given numbers of preimages of $0$ and $1$ are
considered. The generating function for the numbers of such covers is shown to
satisfy a PDE that determines it uniquely modulo a simple initial condition.
Moreover, this generating function satisfies an infinite system of PDE's called
the KP (Kadomtsev-Petviashvili) hierarchy. A specification of this generating
function for certain values of parameters generates the numbers of {\em
dessins} of given genus and degree, thus providing a fast algorithm for
computing these numbers.


title: A Key Set Cipher for Wireless Sensor Networks

abstract:
  This paper proposes the use of sets of keys, together with corresponding
identifiers, for use in wireless sensor networks and similar
resource-constrained applications. A specific cryptographic scheme described in
the paper is based on the use of a family of self-inverting matrices derived
from the number theoretic Hilbert transform in conjunction with the Blom's
scheme. In a randomized version of this scheme, the users change their
published IDs at will but the parties can still reach agreement on the key by
using individual scaling factors. The random protocol increases the security of
the system.


title: Equivariant Torsion and Base Change

abstract:
  What is the true order of growth of torsion in the cohomology of an
arithmetic group? Let $D$ be a quaternion over an imaginary quadratic field
$F.$ Let $E/F$ be a cyclic Galois extension with $\mathrm{Gal}(E/F) = \langle
\sigma \rangle.$ We prove lower bounds for "the Lefschetz number of $\sigma$
acting on torsion cohomology" of certain Galois-stable arithmetic subgroups of
$D_E^\times.$ For these same subgroups, we unconditionally prove a
would-be-numerical consequence of the existence of a hypothetical base change
map for torsion cohomology.


title:
Model of hydrogen atom for twisted acceleration-enlarged Newton-Hooke
  space-times

abstract:
  We define the model of hydrogen atom for twist-deformed acceleration-enlarged
Newton-Hooke space-time. Further, using time-dependent perturbation theory, we
find in first step of iteration procedure the solution of corresponding
Schroedinger equation as well as the probability of transition between two
different energy-eigenstates.


title:
Chaotic behavior of three interacting vortices in a confined
  Bose-Einstein condensate

abstract:
  Motivated by recent experimental works, we investigate a system of vortex
dynamics in an atomic Bose-Einstein condensate (BEC), consisting of three
vortices, two of which have the same charge. These vortices are modeled as a
system of point particles which possesses a Hamiltonian structure. This tripole
system constitutes a prototypical model of vortices in BECs exhibiting chaos.
By using the angular momentum integral of motion we reduce the study of the
system to the investigation of a two degree of freedom Hamiltonian model and
acquire quantitative results about its chaotic behavior. Our investigation tool
is the construction of scan maps by using the Smaller ALignment Index (SALI) as
a chaos indicator. Applying this approach to a large number of initial
conditions we manage to accurately and efficiently measure the extent of chaos
in the model and its dependence on physically important parameters like the
energy and the angular momentum of the system.


title: The Equivariant Cheeger-M\"uller Theorem on Locally Symmetric Spaces

abstract:
  In this paper, we provide a concrete interpretation of equivariant
Reidemeister torsion and demonstrate that Bismut-Zhang's equivariant
Cheeger-M\"{u}ller theorem simplifies considerably when applied to locally
symmetric spaces. In a companion paper, this allows us to extend recent results
on torsion cohomology growth and torsion cohomology comparison for arithmetic
locally symmetric spaces an equivariant setting.


title:
Time-Switching Uplink Network-Coded Cooperative Communication with
  Downlink Energy Transfer

abstract:
  In this work, we consider a multiuser cooperative wireless network where the
energy-constrained sources have independent information to transmit to a common
destination, which is assumed to be externally powered and responsible for
transferring energy wirelessly to the sources. The source nodes may cooperate,
under either decode-and-forward or network coding-based protocols. Taking into
account the fact that the energy harvested by the source nodes is a function of
the fading realization of inter-user channels and user-destination channels, we
obtain a closed-form approximation for the system outage probability, as well
as an approximation for the optimal energy transfer period that minimizes such
outage probability. It is also shown that, even though the achievable diversity
order is reduced due to wireless energy transfer process, it is very close to
the one achieved for a network without energy constraints. Numerical results
are also presented to validate the theoretical results.


title:
Blue Straggler Star Populations in Globular Clusters: I. Dynamical
  Properties of Blue Straggler Stars in NGC 3201, NGC 6218 and $\omega$
  Centauri

abstract:
  We present the first dynamical study of Blue Straggler Stars (BSSs) in three
Galactic globular clusters, NGC\,3201, NGC\,5139 ($\omega$Cen), and NGC\,6218,
based on medium-resolution spectroscopy (R 10000) obtained with IMACS. Our BSS
candidate selection technique uses HST/ACS and ESO/WFI photometric data out to
$>\!4.5\,r_c$. We use radial velocity measurements to discard non-members and
achieve a success rate of $\sim93\%$, which yields a sample of 116 confirmed
BSSs. Using the penalized pixel fitting method (pPXF) we measure the $v\sin(i)$
values of the sample BSSs and find their distribution functions peaked at slow
velocities with a long tail towards fast velocities in each globular cluster.
We find that the BSSs in NGC\,3201 and NGC\,6218 which show $v\sin(i)\!>\!50$
km s$^{-1}$ are all found in the central cluster regions, inside a projected
$2\,r_c$, of their parent clusters. We find a similar result in $\omega$Cen for
BSSs with $v\sin(i)\!>\!70$ km s$^{-1}$ which are all, except for two,
concentrated inside $2\,r_c$. In all globular clusters we find rapidly rotating
BSSs that have relatively high differential radial velocities which likely put
them on hyperbolic orbits, suggestive of strong dynamical interactions in the
past. We estimate that all the observed rapidly rotating BSSs are likely to
form in their central cluster regions no longer than $\sim\!300$ Myr ago. Using
dereddened $V\!-\!I$ colors of our photometric selection we show that blue BSSs
in $\omega$Cen with $(V-I)_0$<0.25 mag show a significantly increased
$v\sin(i)$ dispersion compared with their red counterparts and all other BSSs
in our sample, therefore strongly implying that fast rotating BSSs in
$\omega$Cen are preferentially bluer, i.e. more massive. This may indicate that
this particular blue BSS population was formed in an unique formation event
and/or through an unique mechanism.


title:
Decoding in Hyperbolic Spaces: LDPC Codes With Linear Rate and Efficient
  Error Correction

abstract:
  We analyze the four dimensional toric code in a hyperbolic space and show
that it has a classical error correction procedure which runs in almost linear
time and can be parallelized to almost constant time, giving an example of a
quantum LDPC code with linear rate and efficient error correction.


title:
Weinberg's Higgs portal confronting recent LUX and LHC results together
  with upper limits on B^+ and K^+ decay into invisibles

abstract:
  We discuss a number of experimental constraints on Weinberg's Higgs portal
model. In this framework, the standard model (SM) particle spectrum is extended
to include one complex scalar field S and one Dirac fermion \psi. These new
fields are singlets under the SM gauge group and are charged under a global
U(1) symmetry. Breaking of this U(1) symmetry results in a massless Goldstone
boson \alpha and a massive CP-even scalar r, and splits the Dirac fermion into
two new mass-eigenstates \psi_\pm, corresponding to Majorana fermions. The
interest on such a minimal SM extension is twofold. On the one hand, if the
Goldstone bosons are in thermal equilibrium with SM particles until the era of
muon annihilation their contribution to the effective number of neutrino
species can explain the hints from cosmological observations of extra
relativistic degrees of freedom at the epoch of last scattering. On the other
hand, the lightest Majorana fermion \psi_- provides a plausible dark matter
candidate. Mixing of r with the Higgs doublet \phi is characterized by the mass
of hidden scalar m_h and the mixing angle \theta. We constrain this parameter
space using a variety of experimental data, including heavy meson decays with
missing energy, the invisible Higgs width, and direct dark matter searches. We
show that different experimental results compress the allowed parameter space
in complementary ways, covering a large range of \psi_- masses (5 GeV \alt m_-
\alt 100 GeV). Though current results narrow the parameter space significantly
(for the mass range of interest, \theta \alt 10^{-3} to 10^{-4}), there is
still room for discovery (\alpha decoupling at the muon annihilation era
requires \theta \agt 10^{-5} to 10^{-4}). In the near future, measurements from
ATLAS, CMS, LHCb, NA62, XENON1T, LUX, and CDMSlite will probe nearly the full
parameter space.


title: High magnetic field evolution of ferroelectricity in CuCrO2

abstract:
  CuCrO2 offers insights into the different types of spiral magnetic orderings
that can form spontaneously due to frustration in triangular-lattice
antiferromagnets. We explore the magnetic phase diagram up to 65 T along all
the principle axes, and also use electric polarization to probe changes in the
spiral order at high magnetic fields. It is known that at zero magnetic field a
proper-screw spiral of the Cr S = 3/2 spins forms that in turn induces electric
polarization with six possible orientations ab-plane. Applied magnetic fields
in the (hard) ab-plane have been shown to induce a transition to cycloidal
spiral magnetic order above 5.3 T in those domains that have spins
perpendicular to the applied magnetic field. We show that the cycloidal order
remains unchanged all the way up to 65 T, which is one quarter of the
extrapolated saturation magnetization. On the other hand for magnetic fields
along the (easy) c-axis, we observe a transition in the electric polarization
near 45 T, and it is followed by a series of steps and/or oscillations in the
electric polarization. The data is consistent with the a
proper-screw-to-cycloidal transition that is pushed from 5.3 to 45 T by
easy-axis anisotropy, and is in turn followed by stretching of the magnetic
spiral through commensurate and incommensurate wave vectors. This work also
highlights the ability of the magnetically-induced electric polarization to
probe complex magnetic orders in regimes of phase space that are difficult to
reach with neutron diffraction.


title: On the approximability of covering points by lines and related problems

abstract:
  Given a set $P$ of $n$ points in the plane, {\sc Covering Points by Lines} is
the problem of finding a minimum-cardinality set $\L$ of lines such that every
point $p \in P$ is incident to some line $\ell \in \L$. As a geometric variant
of {\sc Set Cover}, {\sc Covering Points by Lines} is still NP-hard. Moreover,
it has been proved to be APX-hard, and hence does not admit any polynomial-time
approximation scheme unless P $=$ NP\@. In contrast to the small constant
approximation lower bound implied by APX-hardness, the current best
approximation ratio for {\sc Covering Points by Lines} is still $O(\log n)$,
namely the ratio achieved by the greedy algorithm for {\sc Set Cover}.
  In this paper, we give a lower bound of $\Omega(\log n)$ on the approximation
ratio of the greedy algorithm for {\sc Covering Points by Lines}. We also study
several related problems including {\sc Maximum Point Coverage by Lines}, {\sc
Minimum-Link Covering Tour}, {\sc Minimum-Link Spanning Tour}, and {\sc
Min-Max-Turn Hamiltonian Tour}. We show that all these problems are either
APX-hard or at least NP-hard. In particular, our proof of APX-hardness of {\sc
Min-Max-Turn Hamiltonian Tour} sheds light on the difficulty of {\sc
Bounded-Turn-Minimum-Length Hamiltonian Tour}, a problem proposed by Aggarwal
et al.\ at SODA 1997.


title:
The influence of local majority opinions on the dynamics of the Sznajd
  model

abstract:
  In this work we study a Sznajd-like opinion dynamics on a square lattice of
linear size $L$. For this purpose, we consider that each agent has a convincing
power $C$, that is a time-dependent quantity. Each high convincing power group
of four agents sharing the same opinion may convince its neighbors to follow
the group opinion, which induces an increase of the group's convincing power.
In addition, we have considered that a group with a local majority opinion (3
up/1 down spins or 1 up/3 down spins) can persuade the agents neighboring the
group with probability $p$, since the group's convincing power is high enough.
The two mechanisms (convincing powers and probability $p$) lead to an increase
of the competition among the opinions, which avoids dictatorship (full
consensus, all spins parallel) for a wide range of model's parameters, and
favors the occurrence of democratic states (partial order, the majority of
spins pointing in one direction). We have found that the relaxation times of
the model follow log-normal distributions, and that the average relaxation time
$\tau$ grows with system size as $\tau \sim L^{5/2}$, independent of $p$. We
also discuss the occurrence of the usual phase transition of the Sznajd model.


title:
A state vector algebra for algorithmic implementation of second-order
  logic

abstract:
  We present a mathematical framework for mapping second-order logic relations
onto a simple state vector algebra. Using this algebra, basic theorems of set
theory can be proven in an algorithmic way, hence by an expert system. We
illustrate the use of the algebra with simple examples and show that, in
principle, all theorems of basic set theory can be recovered in an elementary
way. The developed technique can be used for an automated theorem proving in
the 1st and 2nd order logic.


title: Abstract Interpretation of Temporal Concurrent Constraint Programs

abstract:
  Timed Concurrent Constraint Programming (tcc) is a declarative model for
concurrency offering a logic for specifying reactive systems, i.e. systems that
continuously interact with the environment. The universal tcc formalism (utcc)
is an extension of tcc with the ability to express mobility. Here mobility is
understood as communication of private names as typically done for mobile
systems and security protocols. In this paper we consider the denotational
semantics for tcc, and we extend it to a "collecting" semantics for utcc based
on closure operators over sequences of constraints. Relying on this semantics,
we formalize a general framework for data flow analyses of tcc and utcc
programs by abstract interpretation techniques. The concrete and abstract
semantics we propose are compositional, thus allowing us to reduce the
complexity of data flow analyses. We show that our method is sound and
parametric with respect to the abstract domain. Thus, different analyses can be
performed by instantiating the framework. We illustrate how it is possible to
reuse abstract domains previously defined for logic programming to perform, for
instance, a groundness analysis for tcc programs. We show the applicability of
this analysis in the context of reactive systems. Furthermore, we make also use
of the abstract semantics to exhibit a secrecy flaw in a security protocol. We
also show how it is possible to make an analysis which may show that tcc
programs are suspension free. This can be useful for several purposes, such as
for optimizing compilation or for debugging.


title:
Hyperviscosity and statistical equilibria of Euler turbulence on the
  torus and the sphere

abstract:
  Coherent structures such as jets and vortices appear in two-dimensional (2D)
turbulence. To gain insight into both numerical simulation and equilibrium
statistical mechanical descriptions of 2D Euler flows, the Euler equation with
added hyperviscosity is integrated forward in time on the square torus and on
the sphere. Coherent structures that form are compared against a hierarchy of
truncated Miller-Robert-Sommeria equilibria. The energy-circulation-enstrophy
MRS-2 description produces a complete condensation of energy to the largest
scales, and in the absence of rotation correctly predicts the number and
polarity of coherent vortices. Perturbative imposition of the quartic Casimir
constraint improves agreement with numerical simulation by sharpening the cores
and transferring some energy to smaller-scale modes. MRS-2 cannot explain
qualitative changes due to rotation, but descriptions that conserve higher
Casimirs beyond enstrophy have the potential to do so. The result is in
agreement with the somewhat paradoxical observation that hyperviscosity helps
to remedy the non-conservation of the third and higher Casimirs in numerical
simulation. For a rotating sphere, numerical simulation also demonstrates that
coherent structures found at late times depend on initial conditions, limiting
the usefulness of statistical mechanics.


title: Gaussian curvature in codimension > 1

abstract:
  The Gaussian curvature $K$ is a fundamental geometric quantity discovered by
Gauss in the case of surfaces embedded in $\mathbb{R}^3$. One can naturally
extend the definition of the Gaussian curvature to arbitrary submanifolds of
$\mathbb{R}^k$ so that the extrinsic interpretation of $K$, the Theorema
Egregium and the Gauss-Bonnet Theorem still hold. We give a concise exposition
of these classical facts.


title: Peres Lattices and chaos in the Dicke model

abstract:
  Peres lattices are employed as a visual method to identify the presence of
chaos in different regions of the energy spectra in the Dicke model. The
coexistence of regular and chaotic regions can be clearly observed for certain
energy regions, even if the coupling constant is smaller than the critical
value to reach superradiance. It also exhibits the presence of two
Excited-State Quantum Phase Transitions, a static and a dynamic one. The
diagonalization is performed in a extended bosonic coherent basis which enable
us to reach a large number of excited states with good numerical convergence.


title:
A method for importance sampling through Markov chain Monte Carlo with
  post sampling variational estimate

abstract:
  We propose a method to efficiently integrate truncated probability densities.
The method uses Markov chain Monte Carlo method to sample from a probability
density matching the function being integrated. The required normalisation or
equivalently the result is obtained by constructing a function with known
integral, through non-parametric kernel density estimation and variational
procedure. The method is demonstrated with numerical case studies. Possible
enhancements to the method and limitations are discussed.


title:
Single Particle Transport in Two-dimensional Heterojunction Interlayer
  Tunneling Field Effect Transistor

abstract:
  The single particle tunneling in a vertical stack consisting of monolayers of
two-dimensional semiconductors is studied theoretically and its application to
a novel Two-dimensional Heterojunction Interlayer Tunneling Field Effect
Transistor (Thin-TFET) is proposed and described. The tunneling current is
calculated by using a formalism based on the Bardeen's transfer Hamiltonian,
and including a semi-classical treatment of scattering and energy broadening
effects. The misalignment between the two 2D materials is also studied and
found to influence the magnitude of the tunneling current, but have a modest
impact on its gate voltage dependence. Our simulation results suggest that the
Thin-TFETs can achieve very steep subthreshold swing, whose lower limit is
ultimately set by the band tails in the energy gaps of the 2D materials
produced by energy broadening. The Thin-TFET is thus very promising as a low
voltage, low energy solid state electronic switch.


title: Hamiltonian Characterization for Dipolar Coupled Spin Systems

abstract:
  Measuring the Hamiltonian of dipolar coupled spin systems is usually a
difficult task due to the high complexity of their spectra. Currently,
molecules with unknown geometrical structure and low symmetry are extremely
tedious or impossible to analyze by sheer spectral fitting. We present a novel
method that addresses the problem of spectral analysis, and report experimental
results of extracting, by spectral fitting, the parameters of an oriented
6-spin system with very low symmetry in structure, without using a priori
knowledge or assumptions on the molecular geometry or order parameters. The
advantages of our method are achieved with the use of a new spectral analysis
algorithm - NAFONS (Non-Assigned Frequency Optimization of NMR Spectra), and by
the use of simplified spectra obtained by transition selective pulses. This new
method goes beyond the limit of spectral analysis for dipolar coupled spin
systems and is helpful for related fields, such as quantum computation and
molecular structure analysis.


title: Induced Superconductivity in the Quantum Spin Hall Edge

abstract:
  Topological insulators are a newly discovered phase of matter characterized
by a gapped bulk surrounded by novel conducting boundary states. Since their
theoretical discovery, these materials have encouraged intense efforts to study
their properties and capabilities. Among the most striking results of this
activity are proposals to engineer a new variety of superconductor at the
surfaces of topological insulators. These topological superconductors would be
capable of supporting localized Majorana fermions, particles whose braiding
properties have been proposed as the basis of a fault-tolerant quantum
computer. Despite the clear theoretical motivation, a conclusive realization of
topological superconductivity remains an outstanding experimental goal. Here we
present measurements of superconductivity induced in two-dimensional
HgTe/HgCdTe quantum wells, a material which becomes a quantum spin Hall
insulator when the well width exceeds d_{C}=6.3 nm. In wells that are 7.5 nm
wide, we find that supercurrents are confined to the one-dimensional sample
edges as the bulk density is depleted. However, when the well width is
decreased to 4.5 nm the edge supercurrents cannot be distinguished from those
in the bulk. These results provide evidence for superconductivity induced in
the helical edges of the quantum spin Hall effect, a promising step toward the
demonstration of one-dimensional topological superconductivity. Our results
also provide a direct measurement of the widths of these edge channels, which
range from 180 nm to 408 nm.


title:
Modelling of the dielectric properties of trabecular bone samples at
  microwave frequency

abstract:
  In this paper the dielectric properties of human trabecular bone are
evaluated under physiological condition in the microwave range. Assuming a two
components medium, simulation and experimental data are presented and
discussed. A special experimental setup is developed in order to deal with
inhomogeneous samples. Simulation data are obtained using finite difference
time domain from a realistic sample. The bone mineral density of the samples
are also measured. The simulation and experimental results of the present study
suggest that there is a negative relation between bone volume fraction (BV/TV)
and permittivity (conductivity): the higher the BV/TV the lower the
permittivity (conductivity). This is in agreement with the recently published
in vivo data. Keywords: Bone dielectric properties, Microwave tomography,
Finite difference time domain.


title: Hot Core, Outflows and Magnetic Fields in W43-MM1 (G30.79 FIR 10)

abstract:
  We present submillimeter spectral line and dust continuum polarization
observations of a remarkable hot core and multiple outflows in the high-mass
star-forming region W43-MM1 (G30.79 FIR 10), obtained using the Submillimeter
Array (SMA). A temperature of $\sim$ 400 K is estimated for the hot-core using
CH$_3$CN (J=19-18) lines, with detections of 11 K-ladder components. The high
temperature and the mass estimates for the outflows indicate high-mass
star-formation. The continuum polarization pattern shows an ordered
distribution, and its orientation over the main outflow appears aligned to the
outflow. The derived magnetic field indicates slightly super-critical
conditions. While the magnetic and outflow energies are comparable, the B-field
orientation appears to have changed from parsec scales to $\sim$ 0.1 pc scales
during the core/star-formation process.


title:
Descent and the Koszul duality for locally constant factorization
  algebras

abstract:
  Generalizing Jacob Lurie's idea on the relation between the Verdier duality
and the iterated loop space theory, we study the Koszul duality for locally
constant factorization algebras. We formulate an analogue of Lurie's
"nonabelian Poincare duality" theorem (which is closely related to earlier
results of Graeme Segal, of Dusa McDuff, and of Paolo Salvatore) in a symmetric
monoidal stable infinity category carefully, using John Francis' notion of
excision. Its proof is done by first studying the Koszul duality for
E_n-algebras in detail. As a consequence, we obtain a Verdier type equivalence
for factorization algebras by a Koszul duality construction.
  At a foundational level, we study descent properties of Lurie's topological
chiral homology. We prove that this homology theory satisfies descent for a
factorizing cover, as defined by Kevin Costello and Owen Gwilliam. We also
obtain a generalization of Lurie's approach to this homology theory, which
leads to a product formula for the infinity category of factorization algebras,
and its twisted generalization.


title: Vortex Rings in a Trap

abstract:
  We present a simple Hamiltonian description of the dynamics of a quantized
vortex ring in a trapped superfluid, compare this description with dynamical
simulations, and characterize the dependence of the dynamics of the shape of
the trap.


title: The s-cobordism theorem seen as a particular case of Latour's theorem

abstract:
  We show how Latour's theorem can be understood as a natural generalization of
the $ s $-cobordism theorem for cohomology classes $ u\in H^1(M;\mathbb{R}) $.
The $ s $-cobordism theorem becomes a special degenerate case when $ u=0 $.


title: An SIR Graph Growth Model for the Epidemics of Communicable Diseases

abstract:
  It is the main purpose of this paper to introduce a graph-valued stochastic
process in order to model the spread of a communicable infectious disease. The
major novelty of the SIR model we promote lies in the fact that the social
network on which the epidemics is taking place is not specified in advance but
evolves through time, accounting for the temporal evolution of the interactions
involving infective individuals. Without assuming the existence of a fixed
underlying network model, the stochastic process introduced describes, in a
flexible and realistic manner, epidemic spread in non-uniformly mixing and
possibly heterogeneous populations. It is shown how to fit such a
(parametrised) model by means of Approximate Bayesian Computation methods based
on graph-valued statistics. The concepts and statistical methods described in
this paper are finally applied to a real epidemic dataset, related to the
spread of HIV in Cuba in presence of a contact tracing system, which permits
one to reconstruct partly the evolution of the graph of sexual partners
diagnosed HIV positive between 1986 and 2006.


title:
An introduction to finite type invariants of knots and 3-manifolds
  defined by counting graph configurations

abstract:
  These introductory lectures show how to define finite type invariants of
links and 3-manifolds by counting graph configurations in 3-manifolds,
following ideas of Witten and Kontsevich. The linking number is the simplest
finite type invariant for 2-component links. It is defined in many equivalent
ways in the first section. As an important example, we present it as the
algebraic intersection of a torus and a 4-chain called a propagator in a
configuration space. In the second section, we introduce the simplest finite
type 3-manifold invariant, which is the Casson invariant (or the
Theta-invariant) of integer homology 3-spheres. It is defined as the algebraic
intersection of three propagators in the same two-point configuration space. In
the third section, we explain the general notion of finite type invariants and
introduce relevant spaces of Feynman Jacobi diagrams. In Sections 4 and 5, we
sketch an original construction based on configuration space integrals of
universal finite type invariants for links in rational homology 3-spheres and
we state open problems. Our construction generalizes the known constructions
for links in the ambient space, and it makes them more flexible. In Section 6,
we present the needed properties of parallelizations of 3-manifolds and
associated Pontrjagin classes, in details.


title: Structure of distributions generated by the scenery flow

abstract:
  We expand the ergodic theory developed by Furstenberg and Hochman on
dynamical systems that are obtained from magnifications of measures. We prove
that any fractal distribution in the sense of Hochman is generated by a
uniformly scaling measure, which provides a converse to a regularity theorem on
the structure of distributions generated by the scenery flow. We further show
that the collection of fractal distributions is closed under the weak topology
and, moreover, is a Poulsen simplex, that is, extremal points are dense. We
apply these to show that a Baire generic measure is as far as possible from
being uniformly scaling: at almost all points, it has all fractal distributions
as tangent distributions.


title: Sobolev and Hardy-Littlewood-Sobolev inequalities

abstract:
  This paper is devoted to improvements of Sobolev and Onofri inequalities. The
additional terms involve the dual counterparts, i.e. Hardy-Littlewood-Sobolev
type inequalities. The Onofri inequality is achieved as a limit case of Sobolev
type inequalities. Then we focus our attention on the constants in our improved
Sobolev inequalities, that can be estimated by completion of the square
methods. Our estimates rely on nonlinear flows and spectral problems based on a
linearization around optimal Aubin-Talenti functions.


title: On Landau's function g(n)

abstract:
  Let $S_n$ be the symmetric group of $n$ letters; Landau considered the
function $g(n)$ defined as the maximal order of an element of $S_n$. This
function is non-decreasing. Let us define the sequence $n_1=1, n_2=2, n_3=3,
n_4=4,n_5=5,n_6=7, ...,n_k$ such that $g(n_k) > g(n_k -1)$. It is known that
$lim sup n_{k+1}-n_k =infinity$. Here it is shown that $lim inf n_{k+1}-n_k is
finite.


title: A New Modular Division Algorithm and Applications

abstract:
  The present paper proposes a new parallel algorithm for the modular division
$u/v\bmod \beta^s$, where $u,\; v,\; \beta$ and $s$ are positive integers
$(\beta\ge 2)$. The algorithm combines the classical add-and-shift
multiplication scheme with a new propagation carry technique. This "Pen and
Paper Inverse" ({\em PPI}) algorithm, is better suited for systolic
parallelization in a "least-significant digit first" pipelined manner. Although
it is equivalent to Jebelean's modular division algorithm~\cite{jeb2} in terms
of performance (time complexity, work, efficiency), the linear parallelization
of the {\em PPI} algorithm improves on the latter when the input size is large.
The parallelized versions of the {\em PPI} algorithm leads to various
applications, such as the exact division and the digit modulus operation (dmod)
of two long integers. It is also applied to the determination of the periods of
rational numbers as well as their $p$-adic expansion in any radix $\beta \ge
2$.


title: The Number of Open Paths in Oriented Percolation

abstract:
  We study the number $N\_n$ of open paths of length $n$ in supercritical
oriented percolation on $\Zd \times \N$, with $d \ge 1$. We prove that on the
percolation event $\{\inf N\_n\textgreater{}0\}$, $N\_n^{1/n}$ almost surely
converges to a positive deterministic constant. We also study the existence of
directional limits. The proof relies on the introduction of adapted sequences
of regenerating times, on subadditive arguments and on the properties of the
coupled zone in supercritical oriented percolation.


title:
Cubic surfaces violating the Hasse principle are Zariski dense in the
  moduli scheme

abstract:
  We construct new examples of cubic surfaces, for which the Hasse principle
fails. Thereby, we show that, over every number field, the counterexamples to
the Hasse principle are Zariski dense in the moduli scheme of non-singular
cubic surfaces.


title: Precision calculation of the quartet-channel p-d scattering length

abstract:
  We present a fully perturbative calculation of the quartet-channel
proton--deuteron scattering length up to next-to-next-to-leading order in
pionless effective field theory. We use a framework that consistently extracts
the Coulomb-modified effective range function for a screened Coulomb potential
in momentum space and allows for a clear linear extrapolation back to the
physical limit without screening. Our result of (10.9 +/- 0.4) fm agrees with
older experimental determinations of this quantity but deviates from
potential-model calculations and a more recent result from Black et al., which
find larger values around 14 fm. As a possible resolution to this discrepancy,
we discuss the scheme dependence of Coulomb subtractions in a three-body
system.


title:
Backing off from Infinity: Performance Bounds via Concentration of
  Spectral Measure for Random MIMO Channels

abstract:
  The performance analysis of random vector channels, particularly
multiple-input-multiple-output (MIMO) channels, has largely been established in
the asymptotic regime of large channel dimensions, due to the analytical
intractability of characterizing the exact distribution of the objective
performance metrics. This paper exposes a new non-asymptotic framework that
allows the characterization of many canonical MIMO system performance metrics
to within a narrow interval under moderate-to-large channel dimensionality,
provided that these metrics can be expressed as a separable function of the
singular values of the matrix. The effectiveness of our framework is
illustrated through two canonical examples. Specifically, we characterize the
mutual information and power offset of random MIMO channels, as well as the
minimum mean squared estimation error of MIMO channel inputs from the channel
outputs. Our results lead to simple, informative, and reasonably accurate
control of various performance metrics in the finite-dimensional regime, as
corroborated by the numerical simulations. Our analysis framework is
established via the concentration of spectral measure phenomenon for random
matrices uncovered by Guionnet and Zeitouni, which arises in a variety of
random matrix ensembles irrespective of the precise distributions of the matrix
entries.


title:
A Galois connection between classical and intuitionistic logics. I:
  Syntax

abstract:
  In a 1985 commentary to his collected works, Kolmogorov remarked that his
1932 paper "was written in hope that with time, the logic of solution of
problems [i.e., intuitionistic logic] will become a permanent part of a
[standard] course of logic. A unified logical apparatus was intended to be
created, which would deal with objects of two types - propositions and
problems." We construct such a formal system QHC, which is a conservative
extension of both the intuitionistic predicate calculus QH and the classical
predicate calculus QC.
  The only new connectives ? and ! of QHC induce a Galois connection (i.e., a
pair of adjoint functors) between the Lindenbaum posets (i.e. the underlying
posets of the Lindenbaum algebras) of QH and QC. Kolmogorov's double negation
translation of propositions into problems extends to a retraction of QHC onto
QH; whereas Goedel's provability translation of problems into modal
propositions extends to a retraction of QHC onto its QC+(?!) fragment,
identified with the modal logic QS4. The QH+(!?) fragment is an intuitionistic
modal logic, whose modality !? is a strict lax modality in the sense of Aczel -
and thus resembles the squash/bracket operation in intuitionistic type
theories.
  The axioms of QHC attempt to give a fuller formalization (with respect to the
axioms of intuitionistic logic) to the two best known contentual
interpretations of intiuitionistic logic: Kolmogorov's problem interpretation
(incorporating standard refinements by Heyting and Kreisel) and the proof
interpretation by Orlov and Heyting (as clarified by G\"odel). While these two
interpretations are often conflated, from the viewpoint of the axioms of QHC
neither of them reduces to the other one, although they do overlap.


title: Lensed Type Ia Supernovae as Probes of Cluster Mass Models

abstract:
  Using three magnified Type Ia supernovae (SNe Ia) detected behind CLASH
clusters, we perform a first pilot study to see whether standardizable candles
can be used to calibrate cluster mass maps created from strong lensing
observations. Such calibrations will be crucial when next generation HST
cluster surveys (e.g. FRONTIER) provide magnification maps that will, in turn,
form the basis for the exploration of the high redshift Universe. We classify
SNe using combined photometric and spectroscopic observations, finding two of
the three to be clearly of type SN Ia and the third probable. The SNe exhibit
significant amplification, up to a factor of 1.7 at $\sim5\sigma$ significance
(SN-L2). We conducted this as a blind study to avoid fine tuning of parameters,
finding a mean amplification difference between SNe and the cluster lensing
models of $0.09 \pm 0.09^{stat} \pm 0.05^{sys}$ mag. This impressive agreement
suggests no tension between cluster mass models and high redshift standardized
SNe Ia. However, the measured statistical dispersion of $\sigma_{\mu}=0.21$ mag
appeared large compared to the dispersion expected based on statistical
uncertainties ($0.14$). Further work with the supernova and cluster lensing
models, post unblinding, reduced the measured dispersion to
$\sigma_{\mu}=0.12$. An explicit choice should thus be made as to whether SNe
are used unblinded to improve the model, or blinded to test the model. As the
lensed SN samples grow larger, this technique will allow improved constraints
on assumptions regarding e.g. the structure of the dark matter halo.