title: READ-EVAL-PRINT in Parallel and Asynchronous Proof-checking

abstract:
  The LCF tradition of interactive theorem proving, which was started by Milner
in the 1970-ies, appears to be tied to the classic READ-EVAL-PRINT-LOOP of
sequential and synchronous evaluation of prover commands. We break up this loop
and retrofit the read-eval-print phases into a model of parallel and
asynchronous proof processing. Thus we explain some key concepts of the
Isabelle/Scala approach to prover interaction and integration, and the
Isabelle/jEdit Prover IDE as front-end technology. We hope to open up the
scientific discussion about non-trivial interaction models for ITP systems
again, and help getting other old-school proof assistants on a similar track.


title:
Theorema 2.0: A Graphical User Interface for a Mathematical Assistant
  System

abstract:
  Theorema 2.0 stands for a re-design including a complete re-implementation of
the Theorema system, which was originally designed, developed, and implemented
by Bruno Buchberger and his Theorema group at RISC. In this paper, we present
the first prototype of a graphical user interface (GUI) for the new system. It
heavily relies on powerful interactive capabilities introduced in recent
releases of the underlying Mathematica system, most importantly the possibility
of having dynamic objects connected to interface elements like sliders, menus,
check-boxes, radio-buttons and the like. All these features are fully
integrated into the Mathematica programming environment and allow the
implementation of a modern user interface.


title:
Partial regularity result of elliptic systems with Dini continuous
  coefficients and $q$-growth

abstract:
  We establish partial regularity result for vector-valued solutions to second
order elliptic system in divergence form. The coefficients safisfies Dini
condition respect to $(x,u)$ with growth order lager than 2. We prove
$C^1$-regularity of the solutions outside of singular set.


title:
Dipole anisotropy in sky brightness and source count distribution in
  radio NVSS data

abstract:
  We study the dipole anisotropy in number counts and flux density weighted
number counts {or sky brightness} in the NRAO VLA Sky Survey (NVSS) data. The
dipole anisotropy is expected due to our local motion with respect to the CMBR
rest frame. We analyse data with an improved fit to the number density, n(S),
as a function of the flux density S, which allows deviation from a pure power
law behaviour. We also impose more stringent cuts to remove the contribution
due to clustering dipole. In agreement with earlier results, we find that the
amplitude of anisotropy is significantly larger in comparison to the prediction
based on CMBR measurements. The extracted speed is found to be roughly 3 times
the speed corresponding to CMBR. The significance of deviation is smaller,
roughly 2 sigma, in comparison to earlier estimates. For the cut, S>30 mJy, the
speed is found to be $1110\pm370$ Km/s using the source count analysis. The
direction of the dipole anisotropy is found to be approximately in agreement
with CMBR. We find that the results are relatively insensitive to the lower as
well as upper limit imposed on the flux density. Our results suggest that the
Universe is intrinsically anisotropic with the axis of anisotropy axis pointing
roughly towards the CMBR dipole direction. Finally we present a method which
may allow an independent extraction of the local speed and an intrinsic dipole
anisotropy, provided a larger data set becomes available in future.


title: Effect of Quantum correlation on Perfect K pair Quantum Network Coding

abstract:
  We find a protocol transmitting K quantum states crossly in the quantum
networks with K pair sender-receiver and one bottleneck channels only with
sharing quantum correlations between senders. In these networks senders want to
multi cast perfect quantum states to receivers. Perfect send on the quantum
networks is impossible just using some additional resources like quantum
correlation. This protocol has been used maximum entangled states and Quantum
Discord which is best indicator of the quantum nature of the correlation to
sharing between senders. At first, to send perfect K states in quantum network
applied some maximum entanglement states to teleport quantum states, Enistein -
Podolsky - Rosen (EPR) states as simple and two qubit states and Grrenberger-
Horne - Zeilinger (GHZ) states and W states as kinds of three qubit states.
Then reached that there is no difference between sharing these maximum
entanglement states and must send same amount of classical bits in bottleneck
channel. In the second part of this paper of sharing Quantum Correlation
(quantum discord) perfect send of two quantum states is possible in the
Butterfly network with fidelity equal one.


title:
Orthogonal Matching Pursuit with Thresholding and its Application in
  Compressive Sensing

abstract:
  Greed is good. However, the tighter you squeeze, the less you have. In this
paper, a less greedy algorithm for sparse signal reconstruction in compressive
sensing, named orthogonal matching pursuit with thresholding is studied. Using
the global 2-coherence , which provides a "bridge" between the well known
mutual coherence and the restricted isometry constant, the performance of
orthogonal matching pursuit with thresholding is analyzed and more general
results for sparse signal reconstruction are obtained. It is also shown that
given the same assumption on the coherence index and the restricted isometry
constant as required for orthogonal matching pursuit, the thresholding
variation gives exactly the same reconstruction performance with significantly
less complexity.


title:
Proposal for High-harmonic EEHG Lasing at Shanghai Deep Ultra-Violet
  Free-electron Laser

abstract:
  The echo-enabled harmonic generation (EEHG) free-electron laser (FEL) has
been already demonstrated at lower harmonics and the first lasing at third
harmonic also has been achieved at Shanghai deep ultra-violet FEL (SDUV-FEL).
While the great advantage of much higher harmonic up-conversion efficiency of
EEHG over other seeded FELs only shows evidently at much higher harmonics. In
this paper, we investigate the possibility of EEHG lasing at 10-th harmonic of
the seed laser at SDUV-FEL, both physical designs and numerical simulations
have been studied carefully. Two proposals of EEHG at 10-th harmonic have been
studied respectively, i.e. with the seed lasers of the same color and two
difference colors, the simulation results indicate that both approaches could
be the candidate for EEHG lasing at 10-th harmonic at SDUV-FEL, meanwhile the
coherent synchrotron radiation does not affect the performance of EEHG-FEL but
only slightly shifts the central radiation frequency.


title: Quasar-Galaxy Clustering through Projected Galaxy Counts at z=0.6-1.2

abstract:
  We investigate the spatial clustering of galaxies around quasars at redshifts
from 0.6 to 1.2 using the photometric data from Sloan Digital Sky Survey (SDSS)
Stripe 82. The quasar and galaxy cross-correlation functions are measured
through the projected galaxy number density n(r_p) on scales $0.05<r_p<20 h^-1
Mpc around quasars for a sample of 2300 quasars from Schneider et al. (2007).
We detect strong clustering signals at all redshifts, and find that the
clustering amplitude increases significantly with redshift. We examine the
dependence of the quasar-galaxy clustering on quasar and galaxy properties and
find that the clustering amplitude is significantly larger for quasars with
more massive black holes, or with bluer colors, while the dependence on quasar
luminosity is absent. We also show that quasars have a stronger correlation
amplitude with blue galaxies than with red galaxies. We finally discuss the
implication of our finding.


title:
Rates of convergence of the Adaptive LASSO estimators to the Oracle
  distribution and higher order refinements by the bootstrap

abstract:
  Zou [J. Amer. Statist. Assoc. 101 (2006) 1418-1429] proposed the Adaptive
LASSO (ALASSO) method for simultaneous variable selection and estimation of the
regression parameters, and established its oracle property. In this paper, we
investigate the rate of convergence of the ALASSO estimator to the oracle
distribution when the dimension of the regression parameters may grow to
infinity with the sample size. It is shown that the rate critically depends on
the choices of the penalty parameter and the initial estimator, among other
factors, and that confidence intervals (CIs) based on the oracle limit law
often have poor coverage accuracy. As an alternative, we consider the residual
bootstrap method for the ALASSO estimators that has been recently shown to be
consistent; cf. Chatterjee and Lahiri [J. Amer. Statist. Assoc. 106 (2011a)
608-625]. We show that the bootstrap applied to a suitable studentized version
of the ALASSO estimator achieves second-order correctness, even when the
dimension of the regression parameters is unbounded. Results from a moderately
large simulation study show marked improvement in coverage accuracy for the
bootstrap CIs over the oracle based CIs.


title: Vision-based macroscopic pedestrian models

abstract:
  We propose a hierarchy of kinetic and macroscopic models for a system
consisting of a large number of interacting pedestrians. The basic interaction
rules are derived from earlier work where the dangerousness level of an
interaction with another pedestrian is measured in terms of the derivative of
the bearing angle (angle between the walking direction and the line connecting
the two subjects) and of the time-to-interaction (time before reaching the
closest distance between the two subjects). A mean-field kinetic model is
derived. Then, three different macroscopic continuum models are proposed. The
first two ones rely on two different closure assumptions of the kinetic model,
respectively based on a monokinetic and a von Mises-Fisher distribution. The
third one is derived through a hydrodynamic limit. In each case, we discuss the
relevance of the model for practical simulations of pedestrian crowds.


title: B-tests: Low Variance Kernel Two-Sample Tests

abstract:
  A family of maximum mean discrepancy (MMD) kernel two-sample tests is
introduced. Members of the test family are called Block-tests or B-tests, since
the test statistic is an average over MMDs computed on subsets of the samples.
The choice of block size allows control over the tradeoff between test power
and computation time. In this respect, the $B$-test family combines favorable
properties of previously proposed MMD two-sample tests: B-tests are more
powerful than a linear time test where blocks are just pairs of samples, yet
they are more computationally efficient than a quadratic time test where a
single large block incorporating all the samples is used to compute a
U-statistic. A further important advantage of the B-tests is their
asymptotically Normal null distribution: this is by contrast with the
U-statistic, which is degenerate under the null hypothesis, and for which
estimates of the null distribution are computationally demanding. Recent
results on kernel selection for hypothesis testing transfer seamlessly to the
B-tests, yielding a means to optimize test power via kernel choice.


title:
Revisiting Co-Processing for Hash Joins on the Coupled CPU-GPU
  Architecture

abstract:
  Query co-processing on graphics processors (GPUs) has become an effective
means to improve the performance of main memory databases. However, the
relatively low bandwidth and high latency of the PCI-e bus are usually
bottleneck issues for co-processing. Recently, coupled CPU-GPU architectures
have received a lot of attention, e.g. AMD APUs with the CPU and the GPU
integrated into a single chip. That opens up new opportunities for optimizing
query co-processing. In this paper, we experimentally revisit hash joins, one
of the most important join algorithms for main memory databases, on a coupled
CPU-GPU architecture. Particularly, we study the fine-grained co-processing
mechanisms on hash joins with and without partitioning. The co-processing
outlines an interesting design space. We extend existing cost models to
automatically guide decisions on the design space. Our experimental results on
a recent AMD APU show that (1) the coupled architecture enables fine-grained
co-processing and cache reuses, which are inefficient on discrete CPU-GPU
architectures; (2) the cost model can automatically guide the design and tuning
knobs in the design space; (3) fine-grained co-processing achieves up to 53%,
35% and 28% performance improvement over CPU-only, GPU-only and conventional
CPU-GPU co-processing, respectively. We believe that the insights and
implications from this study are initial yet important for further research on
query co-processing on coupled CPU-GPU architectures.


title: Existential 0-definability of henselian valuation rings

abstract:
  Recently, Anscombe and Koenigsmann gave an existential 0-definition of the
ring of formal power series F[[t]] in its quotient field in the case where F is
finite. We extend their method in several directions to give general
definability results for henselian valued fields with finite or
pseudo-algebraically closed residue fields.


title: The Donaldson-Futaki invariant for sequences of test configurations

abstract:
  In this note, given a polarized algebraic manifold $(X,L)$, we define the
Donaldson-Futaki invariant for a sequence of test configurations for $(X,L)$
with exponents tending to infinity. This then allows us to define a strong
version of K-stability or K-semistability for $(X,L)$. In particular, $(X,L)$
will be shown to be K-semistable in this strong sense if the polarization class
$c_1(L)$ admits a constant scalar curvature Kaehler metric.


title: Strongly Coupled Models with a Higgs-like Boson

abstract:
  Considering the one-loop calculation of the oblique S and T parameters, we
have presented a study of the viability of strongly-coupled scenarios of
electroweak symmetry breaking with a light Higgs-like boson. The calculation
has been done by using an effective Lagrangian, being short-distance
constraints and dispersive relations the main ingredients of the estimation.
Contrary to a widely spread believe, we have demonstrated that strongly coupled
electroweak models with massive resonances are not in conflict with
experimental constraints on these parameters and the recently observed
Higgs-like resonance. So there is room for these models, but they are
stringently constrained. The vector and axial-vector states should be heavy
enough (with masses above the TeV scale), the mass splitting between them is
highly preferred to be small and the Higgs-like scalar should have a WW
coupling close to the Standard Model one. It is important to stress that these
conclusions do not depend critically on the inclusion of the second Weinberg
sum rule.


title: Strong K-stability and asymptotic Chow-stability

abstract:
  For a polarized algebraic manifold $(X,L)$, let $T$ be an algebraic torus in
the group of all holomorphic automorphisms of $X$. Then strong relative
K-stability will be shown to imply asymptotic relative Chow-stability. In
particular, by taking $T$ to be trivial, we see that asymptotic Chow-stability
follows from strong K-stability.


title: Modal Analysis with Compressive Measurements

abstract:
  Structural Health Monitoring (SHM) systems are critical for monitoring aging
infrastructure (such as buildings or bridges) in a cost-effective manner. Such
systems typically involve collections of battery-operated wireless sensors that
sample vibration data over time. After the data is transmitted to a central
node, modal analysis can be used to detect damage in the structure. In this
paper, we propose and study three frameworks for Compressive Sensing (CS) in
SHM systems; these methods are intended to minimize power consumption by
allowing the data to be sampled and/or transmitted more efficiently. At the
central node, all of these frameworks involve a very simple technique for
estimating the structure's mode shapes without requiring a traditional CS
reconstruction of the vibration signals; all that is needed is to compute a
simple Singular Value Decomposition. We provide theoretical justification
(including measurement bounds) for each of these techniques based on the
equations of motion describing a simplified Multiple-Degree-Of-Freedom (MDOF)
system, and we support our proposed techniques using simulations based on
synthetic and real data.


title: Optimal Locally Repairable Linear Codes

abstract:
  Linear erasure codes with local repairability are desirable for distributed
data storage systems. An [n, k, d] code having all-symbol (r,
\delta})-locality, denoted as (r, {\delta})a, is considered optimal if it also
meets the minimum Hamming distance bound. The existing results on the existence
and the construction of optimal (r, {\delta})a codes are limited to only the
special case of {\delta} = 2, and to only two small regions within this special
case, namely, m = 0 or m >= (v+{\delta}-1) > ({\delta}-1), where m = n mod
(r+{\delta}-1) and v = k mod r. This paper investigates the existence
conditions and presents deterministic constructive algorithms for optimal (r,
{\delta})a codes with general r and {\delta}. First, a structure theorem is
derived for general optimal (r, {\delta})a codes which helps illuminate some of
their structure properties. Next, the entire problem space with arbitrary n, k,
r and {\delta} is divided into eight different cases (regions) with regard to
the specific relations of these parameters. For two cases, it is rigorously
proved that no optimal (r, {\delta})a could exist. For four other cases the
optimal (r, {\delta})a codes are shown to exist, deterministic constructions
are proposed and the lower bound on the required field size for these
algorithms to work is provided. Our new constructive algorithms not only cover
more cases, but for the same cases where previous algorithms exist, the new
constructions require a considerably smaller field, which translates to
potentially lower computational complexity. Our findings substantially enriches
the knowledge on (r, {\delta})a codes, leaving only two cases in which the
existence of optimal codes are yet to be determined.


title:
Moment bounds and mean squared prediction errors of long-memory time
  series

abstract:
  A moment bound for the normalized conditional-sum-of-squares (CSS) estimate
of a general autoregressive fractionally integrated moving average (ARFIMA)
model with an arbitrary unknown memory parameter is derived in this paper. To
achieve this goal, a uniform moment bound for the inverse of the normalized
objective function is established. An important application of these results is
to establish asymptotic expressions for the one-step and multi-step mean
squared prediction errors (MSPE) of the CSS predictor. These asymptotic
expressions not only explicitly demonstrate how the multi-step MSPE of the CSS
predictor manifests with the model complexity and the dependent structure, but
also offer means to compare the performance of the CSS predictor with the least
squares (LS) predictor for integrated autoregressive models. It turns out that
the CSS predictor can gain substantial advantage over the LS predictor when the
integration order is high. Numerical findings are also conducted to illustrate
the theoretical results.


title:
Effects of the non-uniform initial environment and the guide field on
  the plasmoid instability

abstract:
  Effects of non-uniform initial mass density and temperature on the plasmoid
instability are studied via 2.5-dimensional resistive magnetohydrodynamic(MHD)
simulations. Our results indicate that the development of the plasmoid
instability is apparently prevented when the initial plasma density at the
center of the current sheet is higher than that in the upstream region. As a
result, the higher the plasma density at the center and the lower the plasma
$\beta$ in the upstream region, the higher the critical Lundquist number needed
for triggering secondary instabilities. When $\beta =0.2$, the critical
Lundquist number is higher than $10^4$. For the same Lundquist number, the
magnetic reconnection rate is lower for the lower plasma $\beta$ case.
Oppositely, when the initial mass density is uniform and the Lundquist number
is low, the magnetic reconnection rate turns out to be higher for the lower
plasma $\beta$ case. For the high Lundquist number case ($>10^4$) with uniform
initial mass density, the magnetic reconnection is not affected by the initial
plasma $\beta$ and the temperature distribution. Our results indicate that the
guide field has a limited impact on the plasmoid instability in resistive MHD.


title: Astronomical orientations in sanctuaries of Daunia

abstract:
  Prehistoric sanctuaries of Daunia date back several thousand years. During
the Neolithic and Bronze Age the farmers in that region dug hypogea and holes
whose characteristics suggest a ritual use. In the present note we summarize
the results of the astronomical analysis of the orientation of the row holes in
three different sites, and we point out the possible use of the setting of the
stars of Centaurus. An interesting archaeological confirmation of an
archaeoastronomical prediction is also reported.


title:
Studies on the hollow states of atomic lithium by a density functional
  approach

abstract:
  Density functional calculations are performed for twelve $2l2l'$n$l"$
(n$\geq$2) triply excited hollow resonance series of Li, {\em viz.,} 2s$^2$ns
$^2$S$^e$, 2s$^2$np $^2$P$^o$, 2s$^2$nd $^2$D$^e$, 2p$^2$ns
$^2$D$^e$,$^4$P$^e$, 2s2pns $^4$P$^o$, 2s2pnp $^4$D$^e$, 2p$^2$np
$^2$F$^o$,$^4$D$^o$, 2p$^2$nd $^2$G$^e$, $^4$F$^e$ and 2s2pnd $^4$F$^o$,
covering a total of about 270 low-, moderately high- and high-lying states,
with n as high as up to 25. The work-function-based exchange potential and the
nonlinear gradient plus Laplacian included Lee-Yang-Parr correlation energy
functional is used. The relevant Kohn-Sham-type equation is solved numerically
using the generalized pseudospectral method offering nonuniform, optimal
spatial discretization to obtain the orbitals and densities. Except for the one
state, the discrepancy in the calculated state energies remains well within
0.98%, whereas the excitation energies deviate by 0.02--0.58% compared to the
available experimental and other theoretical results. Additionally companion
calculations are also presented for the 37 $3l3l'$n$l"$ (n$\geq$3) doubly
hollow states (seven are n=3 intrashell type) of Li with both K and L shells
empty (up to n=6) in the photon energy range 175.63--180.51 eV, with varying
symmetries and multiplicities. Our calculation shows good agreement with the
recent literature data for the only two such doubly hollow states reported so
far, {\em viz.,} 3s$^2$3p $^2$P$^o$ and 3s3p$^2$ $^4$P$^e$. The resonance
series are found to be inextricably entangled to each other, leading to
complicated behavior in their positions. Many new states are reported here for
the first time. This provides a simple, efficient and general scheme for the
accurate calculation of these and other multiply excited Rydberg series of
many-electron atomic systems within density functional theory.


title:
Mathematical modeling of fluorescence diffuse optical imaging of cell
  membrane potential changes

abstract:
  The aim of this paper is to provide a mathematical model for spatial
distribution of membrane electrical potential changes by fluorescence diffuse
optical tomography. We derive the resolving power of the imaging method in the
presence of measurement noise. The proposed mathematical model can be used for
cell membrane tracking with the resolution of the optical microscope.


title: Parameters of Chelyabinsk and Tunguska Objects and their Explosion Modes

abstract:
  This paper describes briefly a mathematical model that relates the parameters
of celestial bodies motion in the spheres of activity of the Sun and the Earth
with mass-energy characteristics of these celestial bodies and their explosion
modes during destruction in the Earth atmosphere, that in turn are linked with
phenomena observed on the underlying surface. This model was used to calculate
the characteristics of the objects which are causes of Chelyabinsk and Tunguska
incidents. Thus, the basic data characterizing these two outstanding phenomena
were obtained with using a regular physical-mathematical procedure without any
speculative hypotheses and/or assumptions.


title: The Calderon projection over C* algebras

abstract:
  We construct the Calderon projection on the space of Cauchy datas for a
twisted Dirac operator in the Mischenko--Fomenko pseudodifferential calculus
for operators acting on bundles of finitely generated $C^*$--Hilbert modules on
a compact manifold with boundary. In particular an invertible double is
constructed generalizing the classical result.


title: Stochastic Theory of Dust-Grain Charging in Low-Pressure Plasmas

abstract:
  Charging of dust grains in low-pressure plasmas is reviewed critically. A
theory based on the Fokker-Planck equation and orbital motion limited
approximation is proposed. The theory predicts that dust grains can acquire a
positive charge in low-pressure electropositive plasmas having a sufficiently
high plasma potential, in agreement with experimental observations. It is also
shown that variations in the plasma potential (electron temperature) can lead
to spatial regions in which grains have opposite charges.


title: Spectral modelling of the Alpha Virginis (Spica) binary system

abstract:
  Context: The technique of matching synthetic spectra computed with
theoretical stellar atmosphere models to the observations is widely used in
deriving fundamental parameters of massive stars. When applied to binaries,
however, these models generally neglect the interaction effects present in
these systems Aims: The aim of this paper is to explore the uncertainties in
binary stellar parameters that are derived from single-star models Methods:
Synthetic spectra that include the tidal perturbations and irradiation effects
are computed for the binary system alpha Virginis (Spica) using our
recently-developed CoMBiSpeC model. The synthetic spectra are compared to
S/N~2000 observations and optimum values of Teff and log(g) are derived.
Results: The binary interactions have only a small effect on the strength of
the photospheric absorption lines in Spica (<2% for the primary and <4% for the
secondary). These differences are comparable to the uncertainties inherent to
the process of matching synthetic spectra to the observations and thus the
derived values of Teff and log(g) are unaffected by the binary perturbations.
On the other hand, the interactions do produce significant phase-dependent line
profile variations in the primary star, leading to systematic distortions in
the shape of its radial velocity curve. Migrating sub-features ("bumps") are
predicted by our model to be present in the same photospheric lines as
observed, and their appearance does not require any a priori assumptions
regarding non-radial pulsation modes. Matching the strength of lines in which
the most prominent "bumps" occur requires synthetic spectra computed with
larger "microturbulence" than that required by other lines.


title:
Theoretical estimation of density profile of semiflexible polymers
  adsorbed on a surface and thermodynamic glass transition scenario by means of
  the Bethe-Peierls approximation

abstract:
  We develop a theory describing density profile of the semi-flexible polymers
absorbed onto a planar surface. The theoretical analysis consists of two parts.
As a first part, we calculate a density profile of the adsorbed polymers by
developing an extension of the Bethe-Peierls approximation to the case of
nonhomogeneous systems. This approach relies on the combination of the single
chain adsorption theory and the lattice version of the self-consistent field
theory. Semi-flexibility of a chain is described by incorporating a finite
coordination number of the lattice into the consideration, in the spirit of the
previous Silberberg approach. The developed lattice theory incorporates the
interaction between nearest-neighbor pairs of segments and finite chain length.
The theory is completely mapped into the Scheutjens-Fleer theory in the limit
of infinite coordination number. As a second part of the developed approach, we
calculate the configurational entropy to investigate how the density structure
of the semi-flexible polymers near the surface relates to possible reduction of
glass transition temperature near nonabsorbing surface and enhancement near the
strongly attractive surface.


title:
Regularity of solutions to quantum master equations: A stochastic
  approach

abstract:
  Applying probabilistic techniques we study regularity properties of quantum
master equations (QMEs) in the Lindblad form with unbounded coefficients; a
density operator is regular if, roughly speaking, it describes a quantum state
with finite energy. Using the linear stochastic Schr\"{o}dinger equation we
deduce that solutions of QMEs preserve the regularity of the initial states
under a general nonexplosion condition. To this end, we develop the
probabilistic representation of QMEs, and we prove the uniqueness of solutions
for adjoint quantum master equations. By means of the nonlinear stochastic
Schr\"{o}dinger equation, we obtain the existence of regular stationary
solutions for QMEs, under a Lyapunov-type condition.


title: Injectivity of the composition operators of \'etale mappings

abstract:
  We consider the semigroup of \'etale polynomial mappings
$\mathbb{C}^2\rightarrow\mathbb{C}^2$ where the binary operation is
composition. We prove that both the right and the left composition operators on
this semigroup are injective. This is in contrast to the situation in the
semigroup of the entire functions $\mathbb{C}\rightarrow\mathbb{C}$ which are
locally injective, where the left composition operator is not injective. Our
interest in the injectivity (of the left composition operator) results from a
new approach to deal with the two dimensional Jacobian Conjecture. In this
approach we construct a fractal like structure on the above (first) semigroup
in order to use it to settle the conjecture (in preparation). Injectivity is
crucial for that construction.


title: Hamiltonian Formalism of Bimetric Gravity In Vierbein Formulation

abstract:
  This paper is devoted to the Hamiltonian analysis of bimetric gravity in
vierbein formulation. We identify all constraints and determine their nature.
We also show an existence of additional constraint so that the scalar mode can
be eliminated.


title: Extended rotating disks around post-AGB stars

abstract:
  There is a group of binary post-AGB stars that show a conspicuous NIR excess,
usually assumed to arise from hot dust in very compact possibly rotating disks.
These stars are surrounded by significantly fainter nebulae than the
"standard", well studied protoplanetary and planetary nebulae (PPNe, PNe).
  We present high-sensitivity mm-wave observations of CO lines in 24 objects of
this type. CO emission is detected in most observed sources and the line
profiles show that the emissions very probably come from disks in rotation. We
derive typical values of the disk mass between 1e-3 and 1e-2 Mo, about two
orders of magnitude smaller than the (total) masses of "standard" PPNe. The
high-detection rate (upper limits being in fact not very significant) clearly
confirm that the NIR excess of these stars arises from compact disks in
rotation, very probably the inner parts of those found here. Low-velocity
outflows are also found in about eight objects, with moderate expansion
velocities of ~ 10 km/s, to be compared with the velocities of about 100 km/s
often found in "standard" PPNe. Except for two sources with complex profiles,
the outflowing gas in our objects represents a minor nebular component. Our
simple estimates of the disk typical sizes yields values ~ 0.5 - 1 arcsec, i.e.
between 5e15 and 3e16 cm. Estimates of the linear momenta carried by the
outflows, which can only be performed in a few well studied objects, also yield
moderate values, compared with the linear momenta that can be released by the
stellar radiation pressure (contrary, again, to the case of the very massive
and fast bipolar outflows in "standard" PPNe, that are strongly overluminous).
The mass and dynamics of nebulae around various classes of post-AGB stars
differ very significantly, and we can expect the formation of PNe with very
different properties.


title: Expected number of massive galaxy relics in the present-day Universe

abstract:
  The number of present-day massive galaxies that has survived untouched since
their formation at high-z is an important observational constraint to the
hierarchical galaxy formation models. Using three different semianalytical
models based on the Millenium simulation, we quantify the expected fraction and
number densities of the massive galaxies form at z>2 which have evolved in
stellar mass less than 10% and 30%. We find that only a small fraction of the
massive galaxies already form at z~2 have remained almost unaltered since their
formation (<2% with Delta_M*/M*<0.1 and <8% with Delta_M*/M*<0.3). These
fractions correspond to the following number densities of massive relics in the
present-day Universe: ~1.2x10^-6 Mpc^-3 for Delta_M*/M*<0.1 and ~5.7x10^-6
Mpc^-3 for Delta_M*/M*<0.3. The observed number of relic candidates found in
the nearby Universe is today pretty uncertain (with uncertainties up to a
factor of ~100) preventing to establish a firm conclusion about the goodness of
current theoretical expectations to predict such important number.


title: Compatibility waves drive crystal growth on patterned substrates

abstract:
  We explore the crystallization in a colloidal monolayer on a structured
template starting from a few-particle nucleus. The competition between the
substrate structure and that of the growing crystal induces a new crystal
growth scenario. Unlike with the crystal growth in the bulk where a
well-defined and connected crystal-fluid interface grows into the fluid, we
identify a mechanism where a "compatibility wave" of the prescribed nucleus
with the underlying substrate structure dictates the growth direction and
efficiency. The growth process is strongly anisotropic and proceeds via
transient island formation in front of an initial solid-fluid interface. We
demonstrate the validity of this compatibility wave concept for a large class
of substrate structures including a square-lattice and a quasicrystalline
pattern. Dynamical density functional theory which provides a microscopic
approach to the crystallization process is employed for colloidal hard spheres.
Our predictions can be verified in experiments on confined colloids and also
bear consequences for molecular crystal growth on structured substrates.


title:
Blowup of smooth solutions for general 2-D quasilinear wave equations
  with small initial data

abstract:
  For the 2-D quasilinear wave equation $\displaystyle
\sum_{i,j=0}^2g_{ij}(\nabla u)\partial_{ij}u=0$ with coefficients independent
of the solution $u$, a blowup result for small data solutions has been
established in [1,2] provided that the null condition does not hold and a
generic nondegeneracy condition on the initial data is fulfilled. In this
paper, we are concerned with the more general 2-D quasilinear wave equation
$\displaystyle \sum_{i,j=0}^2g_{ij}(u, \nabla u)\partial_{ij}u=0$ with
coefficients that depend simultaneously on $u$ and $\nabla u$. When the null
condition does not hold and a suitable nondegeneracy condition on the initial
data is satisfied, we show that smooth small data solutions blow up in finite
time. Furthermore, we derive an explicit expression for the lifespan and
establish the blowup mechanism.


title: Scattering amplitudes for high-energy factorization

abstract:
  A prescription is presented to construct manifestly gauge invariant
tree-level scattering amplitudes with one or two off-shell initial-state gluons
for processes with arbitrary particles in the final state, which allows for
calculations that are efficient and easy to automate. These scattering
amplitudes are relevant for factorization schemes beyond collinear
factorization that allow the gluons entering the partonic cross section to have
non-vanishing transversal momentum components.


title: PDE estimates for multi-dimensional KPZ equation

abstract:
  We study in this series of articles the Kardar-Parisi-Zhang (KPZ) equation $$
\partial_t h(t,x)=\nu\Delta h(t,x)+\lambda V(|\nabla h(t,x)|) +\sqrt{D}\,
\eta(t,x), \qquad x\in{\mathbb{R}}^d $$ in $d\ge 1$ dimensions. The forcing
term $\eta$ in the right-hand side is a regularized white noise. The deposition
rate $V$ is assumed to be isotropic and convex. Assuming $V(0)\ge 0$, one finds
$V(|\nabla h|)\ltimes |\nabla h|^2$ for small gradients, yielding the equation
which is most commonly used in the literature.
  The present article is dedicated to existence results and PDE estimates for
the solution. Our results extend in a non-trivial way those previously obtained
for the noiseless equation. We prove in particular a comparison principle for
sub- and supersolutions of the KPZ equation in new functional spaces containing
unbounded functions, implying existence and uniqueness. These new functional
spaces made up of functions with "locally bounded averages", generically called
${\cal W}$-spaces thereafter, and which may be of interest for the study of
parabolic equations in general, allow local or pointwise estimates. The
comparison to the linear heat equation through a Cole-Hopf transform is an
essential ingredient in the proofs, and our results are accordingly valid only
for a function $V$ with at most quadratic growth at infinity.


title: Hadamard matrices modulo 5

abstract:
  In this paper we introduce modular symmetric designs and use them to study
the existence of Hadamard matrices modulo 5. We prove that there exist
5-modular Hadamard matrices of order n if and only if n != 3, 7 (mod 10) or n
!= 6, 11. In particular, this solves the 5-modular version of the Hadamard
conjecture.


title:
Star Formation in the First Galaxies - II: Clustered Star Formation and
  the Influence of Metal Line Cooling

abstract:
  Population III stars are believed to have been more massive than typical
stars today and to have formed in relative isolation. The thermodynamic impact
of metals is expected to induce a transition leading to clustered, low-mass
Population II star formation. In this work, we present results from three
cosmological simulations, only differing in gas metallicity, that focus on the
impact of metal fine-structure line cooling on the formation of stellar
clusters in a high-redshift atomic cooling halo. Introduction of sink particles
allows us to follow the process of gas hydrodynamics and accretion onto cluster
stars for 4 Myr corresponding to multiple local free-fall times. At
metallicities at least $10^{-3}\, Z_{\odot}$, gas is able to reach the CMB
temperature floor and fragment pervasively resulting in a stellar cluster of
size $\sim1$ pc and total mass $\sim1000\, M_{\odot}$. The masses of individual
sink particles vary, but are typically $\sim100\, M_{\odot}$, consistent with
the Jeans mass when gas cools to the CMB temperature, though some solar mass
fragments are also produced. At the low metallicity of $10^{-4}\, Z_{\odot}$,
fragmentation is completely suppressed on scales greater than 0.01 pc and total
stellar mass is lower by a factor of 3 than in the higher metallicity
simulations. The sink particle accretion rates, and thus their masses, are
determined by the mass of the gravitationally unstable gas cloud and the
prolonged gas accretion over many Myr. The simulations thus exhibit features of
both monolithic collapse and competitive accretion. Even considering possible
dust induced fragmentation that would occur at higher densities, the formation
of a bona fide stellar cluster seems to require metal line cooling and
metallicities of at least $10^{-3}\, Z_{\odot}$.


title:
On the connections between symmetries and conservation rules of
  dynamical systems

abstract:
  The strict connection between Lie point-symmetries of a dynamical system and
its constants of motion is discussed and emphasized, through old and new
results. It is shown in particular how the knowledge of a symmetry of a
dynamical system can allow to obtain conserved quantities which are invariant
under the symmetry. In the case of Hamiltonian dynamical systems it is shown
that, if the system admits a symmetry of "weaker" type (specifically, a
\lambda\ or a \Lambda-symmetry), then the generating function of the symmetry
is not a conserved quantity, but the deviation from the exact conservation is
"controlled" in a well defined way. Several examples illustrate the various
aspects.


title:
Half-filled orbital and unconventional geometry of a common dopant in
  Si(001)

abstract:
  The determining factor of the bulk properties of doped Si is the column
rather than the row in the periodic table from which the dopants are drawn. It
is unknown whether the basic properties of dopants at surfaces and interfaces,
steadily growing in importance as microelectronic devices shrink, are also
solely governed by their column of origin. The common light impurity P replaces
individual Si atoms and maintains the integrity of the dimer superstructure of
the Si(001) surface, but loses its valence electrons to surface states. Here we
report that isolated heavy dopants are entirely different: Bi atoms form pairs
with Si vacancies, retain their electrons and have highly localized,
half-filled orbitals.


title:
CAST solar axion search with 3^He buffer gas: Closing the hot dark
  matter gap

abstract:
  The CERN Axion Solar Telescope (CAST) has finished its search for solar
axions with 3^He buffer gas, covering the search range 0.64 eV < m_a <1.17 eV.
This closes the gap to the cosmological hot dark matter limit and actually
overlaps with it. From the absence of excess X-rays when the magnet was
pointing to the Sun we set a typical upper limit on the axion-photon coupling
of g_ag < 3.3 x 10^{-10} GeV^{-1} at 95% CL, with the exact value depending on
the pressure setting. Future direct solar axion searches will focus on
increasing the sensitivity to smaller values of g_a, for example by the
currently discussed next generation helioscope IAXO.


title: Generalized notions of symmetry of ODE's and reduction procedures

abstract:
  This paper describes the notion of \sigma -symmetry, which extends the one of
\lambda-symmetry, and its application to reduction procedures of systems of
ordinary differential equations and of dynamical systems as well. We also
consider orbital symmetries, which give rise to a different form of reduction
of dynamical systems. Finally, we discuss how dynamical systems can be
transformed into higher-order ordinary differential equations, and how these
symmetry properties of the dynamical systems can be transferred into reduction
properties of the corresponding ordinary differential equations. Many examples
illustrate the various situations.


title: On tilted Giraud subcategories

abstract:
  Firstly we provide a technique to move torsion pairs in abelian categories
via adjoint functors and in particular through Giraud subcategories. We apply
this point in order to develop a correspondence between Giraud subcategories of
an abelian category $C$ and those of its tilt $H(C)$ i.e., the heart of a
t-structure on $D(C)$ induced by a torsion pair.


title: Energetics and efficiency of a molecular motor model

abstract:
  The energetics and efficiency of a linear molecular motor model proposed by
Mogilner et al. (Phys. Lett. 237, 297 (1998)) is analyzed from an analytical
point of view. The model which is based on protein friction with a track is
described by coupled Langevin equations for the motion in combination with
coupled master equations for the ATP hydrolysis. Here the energetics and
efficiency of the motor is addressed using a many body scheme with focus on the
efficiency at maximum power (EMP). It is found that the EMP is reduced from
about 10 pct in a heuristic description of the motor to about 1 per mille when
incorporating the full motor dynamics, owing to the strong dissipation
associated with the motor action.


title:
Strong colorings yield kappa-bounded spaces with discretely untouchable
  points

abstract:
  It is well-known that every non-isolated point in a compact Hausdorff space
is the accumulation point of a discrete subset. Answering a question raised by
Z. Szentmiklossy and the first author, we show that this statement fails for
countably compact regular spaces, and even for omega-bounded regular spaces. In
fact, there are kappa-bounded counterexamples for every infinite cardinal
kappa. The proof makes essential use of the so-called 'strong colorings' that
were invented by the second author.


title: Self-consistent approach for Bose-condensed atoms in optical lattices

abstract:
  Bose atoms in optical lattices are considered at low temperatures and weak
interactions, when Bose-Einstein condensate is formed. A self-consistent
approach, based on the use of a representative statistical ensemble, is
employed, ensuring a gapless spectrum of collective excitations and the
validity of conservation laws. In order to show that the approach is applicable
to both weak and tight binding, the problem is treated in the Bloch as well as
in the Wannier representations. Both these ways result in similar expressions
that are compared for the self-consistent Hartree-Fock-Bogolubov approximation.
A convenient general formula for the superfluid fraction of atoms in an optical
lattice is derived.


title:
Critical behaviour of the O(n)-$\phi^{4}$ model with an antisymmetric
  order parameter

abstract:
  Critical behaviour of the O(n)-symmetric $\phi^{4}$-model with an
antisymmetric tensor order parameter is studied by means of the field-theoretic
renormalization group (RG) in the leading order of the
$\varepsilon=4-d$-expansion (one-loop approximation). For $n=2$ and 3 the model
is equivalent to the scalar and the O(3)-symmetric vector models, for $n\ge4$
it involves two independent interaction terms and two coupling constants. It is
shown that for $n>4$ the RG equations have no infrared (IR) attractive fixed
points and their solutions (RG flows) leave the stability region of the model.
This means that fluctuations of the order parameter change the nature of the
phase transition from the second-order type (suggested by the mean-field
theory) to the first-order one. For $n=4$, the IR attractive fixed point exists
and the IR behaviour is non-universal: if the coupling constants belong to the
basin of attraction for the IR point, the phase transition is of the second
order and the IR critical scaling regime realizes. The corresponding critical
exponents $\nu$ and $\eta$ are presented in the order $\varepsilon$ and
$\varepsilon^{2}$, respectively. Otherwise the RG flows pass outside the
stability region and the first-order transition takes place.


title: Lieb-Robinson bounds for spin-boson lattice models and trapped ions

abstract:
  We derive a Lieb-Robinson bound for the propagation of spin correlations in a
model of spins interacting through a bosonic lattice field, which satisfies
itself a Lieb-Robinson bound in the absence of spin-boson couplings. We apply
these bounds to a system of trapped ions, and find that the propagation of spin
correlations, as mediated by the phonons of the ion crystal, can be faster than
the regimes currently explored in experiments. We propose a scheme to test the
bounds by measuring retarded correlation functions via the crystal
fluorescence.

categories: quant-ph cond-mat.mes-hall cond-mat.quant-gas math-ph math.MP


title: On the embeddings of the Riemann sphere with nonnegative normal bundles

abstract:
  We describe the (complex) quaternionic geometry encoded by the embeddings of
the Riemann sphere, with nonnegative normal bundles.


title:
Hierarchical Bipartition Routing for delivery guarantee in sparse
  wireless ad hoc sensor networks with obstacles

abstract:
  We introduce and evaluate a very simple landmark-based network partition
technique called Hierarchical Bipartition Routing (HBR) to support routing with
delivery guarantee in wireless ad hoc sensor networks. It is a simple routing
protocol that can easily be combined with any other greedy routing algorithm to
obtain delivery guarantee. The efficiency of HBR increases if the network is
sparse and contains obstacles. The space necessary to store the additional
routing information at a node u is on average not larger than the size
necessary to store the IDs of the neighbors of u. The amount of work to setup
the complete data structure is on average proportional to flooding the entire
network log(n) times, where n is the total number of sensor nodes. We evaluate
the performance of HBR in combination with two simple energy-aware geographic
greedy routing algorithms based on physical coordinates and virtual
coordinates, respectively. Our simulations show that the difference between
using HBR and a weighted shortest path to escape a dead-end is only a few
percent in typical cases.


title:
Noncommutative reciprocity laws on algebraic surfaces: a case of tame
  ramification

abstract:
  We prove non-commutative reciprocity laws on an algebraic surface defined
over a perfect field. These reciprocity laws claim the splittings of some
central extensions of globally constructed groups over some subgroups
constructed by points or projective curves on a surface. For a two-dimensional
local field with a finite last residue field the constructed local central
extension is isomorphic to a central extension which comes from the case of
tame ramification of the Abelian two-dimensional local Langlands correspondence
suggested by M. Kapranov.


title: Equitable $(d,m)$-edge designs

abstract:
  The paper addresses design of experiments for classifying the input factors
of a multi-variate function into negligible, linear and other
(non-linear/interaction) factors. We give constructive procedures for
completing the definition of the clustered designs proposed Morris 1991, that
become defined for arbitrary number of input factors and desired clusters'
multiplicity. Our work is based on a representation of subgraphs of the
hyper-cube by polynomials that allows the formal verification of the designs'
properties. Ability to generate these designs in a systematic manner opens new
perspectives for the characterisation of the behaviour of the function's
derivatives over the input space that may offer increased discrimination.


title:
On Quasi-Modular Forms, Almost Holomorphic Modular Forms, and the
  Vector-Valued Modular Forms of Shimura

abstract:
  We extend the relation between quasi-modular forms and modular forms to a
wider class of functions. We then relate both forms to vector-valued modular
forms with symmetric power representations, and prove a general structure
theorem for these vector-valued forms.


title:
Using Clustering to extract Personality Information from socio economic
  data

abstract:
  It has become apparent that models that have been applied widely in
economics, including Machine Learning techniques and Data Mining methods,
should take into consideration principles that derive from the theories of
Personality Psychology in order to discover more comprehensive knowledge
regarding complicated economic behaviours. In this work, we present a method to
extract Behavioural Groups by using simple clustering techniques that can
potentially reveal aspects of the Personalities for their members. We believe
that this is very important because the psychological information regarding the
Personalities of individuals is limited in real world applications and because
it can become a useful tool in improving the traditional models of Knowledge
Economy.


title: Geography of Gorenstein stable log surfaces

abstract:
  We study the geography of Gorenstein stable log surfaces and prove two
inequalities for their invariants: the stable Noether inequality and the
$P_2$-inequality.
  By constructing examples we show that all invariants are realised except
possibly some cases where the inequalities become equalities.


title:
High resolution coherent population trapping on a single hole spin in a
  semiconductor

abstract:
  We report high resolution coherent population trapping on a single hole spin
in a semiconductor quantum dot. The absorption dip signifying the formation of
a dark state exhibits an atomic physics-like dip width of just 10 MHz. We
observe fluctuations in the absolute frequency of the absorption dip, evidence
of very slow spin dephasing. We identify this process as charge noise by,
first, demonstrating that the hole spin g-factor in this configuration
(in-plane magnetic field) is strongly dependent on the vertical electric field,
and second, by characterizing the charge noise through its effects on the
optical transition frequency. An important conclusion is that charge noise is
an important hole spin dephasing process.


title:
Variance in System Dynamics and Agent Based Modelling Using the SIR
  Model of Infectious Disease

abstract:
  Classical deterministic simulations of epidemiological processes, such as
those based on System Dynamics, produce a single result based on a fixed set of
input parameters with no variance between simulations. Input parameters are
subsequently modified on these simulations using Monte-Carlo methods, to
understand how changes in the input parameters affect the spread of results for
the simulation. Agent Based simulations are able to produce different output
results on each run based on knowledge of the local interactions of the
underlying agents and without making any changes to the input parameters. In
this paper we compare the influence and effect of variation within these two
distinct simulation paradigms and show that the Agent Based simulation of the
epidemiological SIR (Susceptible, Infectious, and Recovered) model is more
effective at capturing the natural variation within SIR compared to an
equivalent model using System Dynamics with Monte-Carlo simulation. To
demonstrate this effect, the SIR model is implemented using both System
Dynamics (with Monte-Carlo simulation) and Agent Based Modelling based on
previously published empirical data.


title: Updated constraints from the PLANCK experiment on modified gravity

abstract:
  A modification of the action of the general relativity produces a different
pattern for the growth of the cosmic structures below a certain length-scale
leaving an imprint on the cosmic microwave background (CMB) anisotropies. We
re-examine the upper limits on the length-scale parameter B0 of f (R) models
using the recent data from the Planck satellite experiment. We also investigate
the combined constraints obtained when including the Hubble Space Telescope H0
measurement and the baryon acoustic oscillations measurements from the SDSS,
WiggleZ and BOSS surveys.


title:
The contribution of secondary eclipses as astrophysical false positives
  to exoplanet transit surveys

abstract:
  We investigate in this paper the astrophysical false-positive configuration
in exoplanet-transit surveys that involves eclipsing binaries and giant planets
which present only a secondary eclipse, as seen from the Earth. To test how an
eclipsing binary configuration can mimic a planetary transit, we generate
synthetic light curve of three examples of secondary-only eclipsing binary
systems that we fit with a circular planetary model. Then, to evaluate its
occurrence we model a population of binaries in double and triple system based
on binary statistics and occurrence. We find that 0.061% +/- 0.017% of
main-sequence binary stars are secondary-only eclipsing binaries mimicking a
planetary transit candidate down to the size of the Earth. We then evaluate the
occurrence that an occulting-only giant planet can mimic an Earth-like planet
or even smaller planet. We find that 0.009% +/- 0.002% of stars harbor a giant
planet that present only the secondary transit. Occulting-only giant planets
mimic planets smaller than the Earth that are in the scope of space missions
like Kepler and PLATO. We estimate that up to 43.1 +/- 5.6 Kepler Objects of
Interest can be mimicked by this new configuration of false positives,
re-evaluating the global false-positive rate of the Kepler mission from 9.4%
+/- 0.9% to 11.3% +/- 1.1%. We note however that this new false-positive
scenario occurs at relatively long orbital period compared with the median
period of Kepler candidates.


title: Imperative Programs as Proofs via Game Semantics

abstract:
  Game semantics extends the Curry-Howard isomorphism to a three-way
correspondence: proofs, programs, strategies. But the universe of strategies
goes beyond intuitionistic logics and lambda calculus, to capture stateful
programs. In this paper we describe a logical counterpart to this extension, in
which proofs denote such strategies. The system is expressive: it contains all
of the connectives of Intuitionistic Linear Logic, and first-order
quantification. Use of Laird's sequoid operator allows proofs with imperative
behaviour to be expressed. Thus, we can embed first-order Intuitionistic Linear
Logic into this system, Polarized Linear Logic, and an imperative total
programming language.
  The proof system has a tight connection with a simple game model, where games
are forests of plays. Formulas are modelled as games, and proofs as
history-sensitive winning strategies. We provide a strong full completeness
result with respect to this model: each finitary strategy is the denotation of
a unique analytic (cut-free) proof. Infinite strategies correspond to analytic
proofs that are infinitely deep. Thus, we can normalise proofs, via the
semantics.


title:
Energy spectrum and phase diagrams of two-sublattice hard-core boson
  model

abstract:
  The energy spectrum, spectral density and phase diagrams have been obtained
for two-sublattice hard-core boson model in frames of random phase
approximation approach. Reconstruction of boson spectrum at the change of
temperature, chemical potential and energy difference between local positions
in sublattices is studied. The phase diagrams illustrating the regions of
existence of a normal phase which can be close to Mott-insulator (MI) or
charge-density (CDW) phases as well as the phase with the Bose-Einstein
condensate (SF phase) are built.


title:
An algorithm for deciding the finiteness of the number of simple
  permutations in permutation classes

abstract:
  In this article, we describe an algorithm to determine whether a permutation
class C given by a finite basis B of excluded patterns contains a finite number
of simple permutations. This is a continuation of the work initiated in
[Brignall, Ruskuc, Vatter, Simple permutations: decidability and unavoidable
substructures, 2008], and shares several aspects with it. Like in this article,
the main difficulty is to decide whether C contains a finite number of proper
pin-permutations, and this decision problem is solved using automata theory.
Moreover, we use an encoding of proper pin-permutations by words over a finite
alphabet, introduced by Brignall et al. However, unlike in their article, our
construction of automata is fully algorithmic and efficient. It is based on the
study of pin-permutations in [Bassino, Bouvel, Rossin, Enumeration of
pin-permutations, 2011]. The complexity of the overall algorithm is O(n log n +
s^{2k}) where n denotes the sum of the sizes of permutations in the basis B, s
is the maximal size of a pin-permutation in B and k is the number of
pin-permutations in B.


title: The generalized 3-connectivity of Lexicographic product graphs

abstract:
  The generalized $k$-connectivity $\kappa_k(G)$ of a graph $G$, introduced by
Chartrand et al., is a natural and nice generalization of the concept of
(vertex-)connectivity. In this paper, we prove that for any two connected
graphs $G$ and $H$, $\kappa_3(G\circ H)\geq \kappa_3(G)|V(H)|$. We also give
upper bounds for $\kappa_3(G\Box H)$ and $\kappa_3(G\circ H)$. Moreover, all
the bounds are sharp.


title: Topological surface states of strained Mercury-Telluride probed by ARPES

abstract:
  The topological surface states of strained HgTe have been measured using
high-resolution ARPES measurements. The dispersion of surface states form a
Dirac cone, which origin is close to the top of the \ghh band: the top half of
the Dirac cone is inside the stress-gap while the bottom half lies within the
heavy hole bands and keeps a linear dispersion all the way to the X-point. The
circular dichroism of the photo-emitted electron intensity has also been
measured for all the bands.


title:
Alternating Projections and Douglas-Rachford for Sparse Affine
  Feasibility

abstract:
  The problem of finding a vector with the fewest nonzero elements that
satisfies an underdetermined system of linear equations is an NP-complete
problem that is typically solved numerically via convex heuristics or
nicely-behaved nonconvex relaxations. In this work we consider elementary
methods based on projections for solving a sparse feasibility problem without
employing convex heuristics. In a recent paper Bauschke, Luke, Phan and Wang
(2014) showed that, locally, the fundamental method of alternating projections
must converge linearly to a solution to the sparse feasibility problem with an
affine constraint. In this paper we apply different analytical tools that allow
us to show global linear convergence of alternating projections under familiar
constraint qualifications. These analytical tools can also be applied to other
algorithms. This is demonstrated with the prominent Douglas-Rachford algorithm
where we establish local linear convergence of this method applied to the
sparse affine feasibility problem.


title:
Bivariate Generating Functions for a Class of Linear Recurrences:
  General Structure

abstract:
  We consider Problem 6.94 posed in the book Concrete Mathematics by Graham,
Knuth, and Patashnik, and solve it by using bivariate exponential generating
functions. The family of recurrence relations considered in the problem
contains many cases of combinatorial interest for particular choices of the six
parameters that define it. We give a complete classification of the partial
differential equations satisfied by the exponential generating functions, and
solve them in all cases. We also show that the recurrence relations defining
the combinatorial numbers appearing in this problem display an interesting
degeneracy that we study in detail. Finally, we obtain for all cases the
corresponding univariate row generating polynomials.


title:
Order parameter of a three-dimensional Ising-like system in the simplest
  and higher non-Gaussian approximations

abstract:
  The application of the collective variables method to the study of the
behaviour of nonuniversal characteristics of the system in the critical region
is illustrated by an example of the order parameter. Explicit expressions for
the order parameter (the average spin moment) of a three-dimensional uniaxial
magnet are obtained in approximations of quartic and sextic non-Gaussian
fluctuation distributions (the \rho^4 and \rho^6 models, respectively), taking
into account confluent corrections. Some distinctive features appearing in the
process of calculating the order parameter on the basis of two successive
non-Gaussian approximations are indicated. The dependence of the average spin
moment of an Ising-like system on the temperature and microscopic parameters is
studied.


title:
Is there plenty of metal-poor stars with planets in the Galactic thick
  disk?

abstract:
  We performed an uniform spectroscopic analysis of 1111 FGK dwarfs observed as
part of the HARPS GTO planet search program. We applied a purely chemical
approach, based on [alpha/Fe] ratio, to distinguish the various stellar
components in the Galaxy. Apart from the well known Galactic thick and thin
disks, we separated an alpha-enhanced stellar family at super-solar
metallicities. The metal-rich high-alpha stars have orbits similar to the thin
disk stars, but they are similar to thick disk stars in terms of age. Our data
indicate that the incidence of stars with planets are greater among the
chemically separated thick disk stars with [Fe/H] < -0.3 dex than they are
among thin disk stars in the same [Fe/H] interval. Our results allow us to
suppose that a certain chemical composition, and not the Galactic birth place
of the stars, is the causative factor for that.


title: Universality classes and critical phenomena in confined liquid systems

abstract:
  It is well known that the similar universal behavior of infinite-size (bulk)
systems of different nature requires the same basic conditions: space
dimensionality; number components of order parameter; the type (short- or
long-range) of the intermolecular interaction; symmetry of the fluctuation part
of thermodynamical potential. Basic conditions of similar universal behavior of
confined systems needs the same supplementary conditions such as the number of
monolayers for a system confinement; low crossover dimensionality, i.e.,
geometric form of restricted volume; boundary conditions on limiting surfaces;
physical properties under consideration. This review paper is aimed at studying
all these conditions of similar universal behavior for diffusion processes in
confined liquid systems. Special attention was paid to the effects of spatial
dispersion and low crossover dimensionality. This allowed us to receive
receiving correct nonzero expressions for the diffusion coefficient at the
critical point and to take into account the specific geometric form of the
confined liquid volume. The problem of 3D \Leftrightarrow 2D dimensional
crossover was analyzed. To receive a smooth crossover for critical exponents,
the Kawasaki-like approach from the theory of mode coupling in critical
dynamics was proposed. This ensured a good agreement between data of computer
experiment and theoretical calculations of the size dependence of the critical
temperature T_{c}(H) of water in slitlike pores. The width of the quasi-elastic
scattering peak of slow neutrons near the structural phase transition in the
aquatic suspensions of plasmatic membranes (mesostructures with the typical
thickness up to 10 nm) was studied.


title: On the multifractal effects generated by monofractal signals

abstract:
  We study quantitatively the level of false multifractal signal one may
encounter while analyzing multifractal phenomena in time series within
multifractal detrended fluctuation analysis (MF-DFA). The investigated effect
appears as a result of finite length of used data series and is additionally
amplified by the long-term memory the data eventually may contain. We provide
the detailed quantitative description of such apparent multifractal background
signal as a threshold in spread of generalized Hurst exponent values $\Delta h$
or a threshold in the width of multifractal spectrum $\Delta \alpha$ below
which multifractal properties of the system are only apparent, i.e. do not
exist, despite $\Delta\alpha\neq0$ or $\Delta h\neq 0$. We find this effect
quite important for shorter or persistent series and we argue it is linear with
respect to autocorrelation exponent $\gamma$. Its strength decays according to
power law with respect to the length of time series. The influence of basic
linear and nonlinear transformations applied to initial data in finite time
series with various level of long memory is also investigated. This provides
additional set of semi-analytical results. The obtained formulas are
significant in any interdisciplinary application of multifractality, including
physics, financial data analysis or physiology, because they allow to separate
the 'true' multifractal phenomena from the apparent (artificial) multifractal
effects. They should be a helpful tool of the first choice to decide whether we
do in particular case with the signal with real multiscaling properties or not.


title: Full-text Support for Publish/Subscribe Ontology Systems

abstract:
  We envision a publish/subscribe ontology system that is able to index
millions of user subscriptions and filter them against ontology data that
arrive in a streaming fashion. In this work, we propose a SPARQL extension
appropriate for a publish/subscribe setting; our extension builds on the
natural semantic graph matching of the language and supports the creation of
full-text subscriptions. Subsequently, we propose a main-memory subscription
indexing algorithm which performs both semantic and full-text matching at low
complexity and minimal filtering time. Thus, when ontology data are published
matching subscriptions are identified and notifications are forwarded to users.


title: Smooth crossed products of Rieffel's deformations

abstract:
  Assume A is a Frechet algebra equipped with a smooth isometric action of a
vector group V, and consider Rieffel's deformation A_J of A. We construct an
explicit isomorphism between the smooth crossed products V\ltimes\A_J and
V\ltimes\A. When combined with the Elliott-Natsume-Nest isomorphism, this
immediately implies that the periodic cyclic cohomology is invariant under
deformation. Specializing to the case of smooth subalgebras of C*-algebras, we
also get a simple proof of equivalence of Rieffel's and Kasprzak's approaches
to deformation.


title:
The effects of rotation on the s-process nucleosynthesys in Asymptotic
  Giant Branch stars

abstract:
  In this paper we analyze the effects induced by rotation on low mass
Asymptotic Giant Branch stars. We compute two sets of models, M=2.0 Msun at
[Fe/H]=0 and M=1.5 Msun at [Fe/H]=-1.7, respectively, by adopting Main Sequence
rotation velocities in the range 0 - 120 km/s. At high metallicity, we find
that the Goldreich-Schubert-Fricke instability, active at the interface between
the convective envelope and the rapid rotating core, contaminates the
13C-pocket (the major neutron source) with 14N (the major neutron poison), thus
reducing the neutron flux available for the synthesis of heavy elements. As a
consequence, the yields of heavy-s elements (Ba, La, Nd, Sm) and, to a less
extent, those of light-s elements (Sr, Y, Zr) decrease with increasing rotation
velocities up to 60 km/s. However, for larger initial rotation velocities, the
production of light-s and, to a less extent, that of heavy-s begins again to
increase, due to mixing induced by meridional circulations. At low metallicity,
the effects of meridional circulations are important even at rather low
rotation velocity. The combined effect of Goldreich-Schubert-Fricke instability
and meridional circulations determines an increase of light-s and, to a less
extent, heavy-s elements, while lead is strongly reduced. For both
metallicities, the rotation-induced instabilities active during the interpulse
phase reduce the neutrons-to-seeds ratio, so that the spectroscopic indexes
[hs/ls] and [Pb/hs] decrease by increasing the initial rotation velocity. Our
analysis suggests that rotation could explain the spread in the s-process
indexes, as observed in s-process enriched stars at different metallicities.


title: OntoFM: A Personal Ontology-based File Manager for the Desktop

abstract:
  Personal ontologies have been proposed as a means to support the semantic
management of user information. Assuming that a personal ontology system is in
use, new tools have to be developed at user interface level to exploit the
enhanced capabilities offered by the system. In this work, we present an
ontology-based file manager that allows semantic searching on the user's
personal information space. The file manager exploits the ontology relations to
present files associated with specific concepts, proposes new related concepts
to users, and helps them explore the information space and locate the required
file.


title: Dynamics of a deformable active particle under shear flow

abstract:
  The motion of a deformable active particle in linear shear flow is explored
theoretically. Based on symmetry considerations, in two spatial dimensions, we
propose coupled nonlinear dynamical equations for the particle position,
velocity, deformation, and rotation. In our model, both, passive rotations
induced by the shear flow as well as active spinning motions, are taken into
account. Our equations reduce to known models in the two limits of vanishing
shear flow and vanishing particle deformability. For varied shear rate and
particle propulsion speed, we solve the equations numerically and obtain a
manifold of different dynamical modes including active straight motion,
periodic motions, motions on undulated cycloids, winding motions, as well as
quasi-periodic and chaotic motions induced at high shear rates. The types of
motion are distinguished by different characteristics in the real-space
trajectories and in the dynamical behavior of the particle orientation and its
deformation. Our predictions can be verified in experiments on self-propelled
droplets exposed to a linear shear flow.


title:
The stellar mass function, binary content and radial structure of the
  open cluster Praesepe derived from PPMXL and SDSS data

abstract:
  We have determined possible cluster members of the nearby open cluster
Praesepe (M44) based on J and K photometry and proper motions from the PPMXL
catalogue and z photometry from the Sloan Digital Sky Survey (SDSS). In total
we identified 893 possible cluster members down to a magnitude of J = 15.5 mag,
corresponding to a mass of about 0.15 Msun for an assumed cluster distance
modulus of (m-M)_0 = 6.30 mag (d ~ 182 pc), within a radius of 3.5{\deg} around
the cluster centre. We derive a new cluster centre for Praesepe
({\alpha}_centre = 8h 39m 37s, {\delta}_centre = 19{\deg} 35' 02"). We also
derive a total cluster mass of about 630 Msun and a 2D half-number and
half-mass radius of 4.25 pc and 3.90 pc respectively. The global mass function
(MF) of the cluster members shows evidence for a turnover around m = 0.65 Msun.
While more massive stars can be fit by a power-law {\xi}(m) ~ m^(-{\alpha})
with slope {\alpha} = 2.88 +/- 0.22, stars less massive than m = 0.65 Msun are
best fitted with {\alpha} = 0.85 +/- 0.10. In agreement with its large
dynamical age, we find that Praesepe is strongly mass segregated and that the
mass function slope for high mass stars steepens from a value of {\alpha} =
2.32 +/- 0.24 inside the half-mass radius to {\alpha} = 4.90 +/- 0.51 outside
the half-mass radius. We finally identify a significant population of binaries
and triples in the colour-magnitude diagram of Praesepe. Assuming non-random
pairing of the binary components, a binary fraction of about 35% for primaries
in the mass range 0.6 < m/Msun < 2.20 is required to explain the observed
number of binaries in the colour-magnitude diagram (CMD).


title: DA white dwarfs observed in LAMOST pilot survey

abstract:
  A total of $\sim640,000$ objects from LAMOST pilot survey have been publicly
released. In this work, we present a catalog of DA white dwarfs from the entire
pilot survey. We outline a new algorithm for the selection of white dwarfs by
fitting S\'ersic profiles to the Balmer H$\beta$, H$\gamma$ and H$\delta$ lines
of the spectra, and calculating the equivalent width of the CaII K line. 2964
candidates are selected by constraining the fitting parameters and the
equivalent width of CaII K line. All the spectra of candidates are visually
inspected. We identify 230 (59 of them are already in Villanova and SDSS WD
catalog) DA white dwarfs, 20 of which are DA white dwarfs with non-degenerate
companions. In addition, 128 candidates are classified as DA white
dwarf/subdwarfs, which means the classifications are ambiguous. The result is
consistent with the expected DA white dwarf number estimated based on the LEGUE
target selection algorithm.


title:
Measurement of the integrated luminosities of the data taken by BESIII
  at $\sqrt s=$ 3.650 and 3.773 GeV

abstract:
  Data sets were collected with the BESIII detector at the BEPCII collider at
the center-of-mass energy of $\sqrt s =$ 3.650 GeV during May 2009 and at
$\sqrt s=$ 3.773 GeV from January 2010 to May 2011. By analyzing the large
angle Bhabha scattering events, the integrated luminosities of the two data
sets are measured %at $\sqrt s=$ 3.650 and 3.773 GeV to be ($\rm
44.49\pm0.02\pm0.44$) $\rm pb^{-1}$ and ($\rm 2916.94\pm0.18\pm29.17$) $\rm
pb^{-1}$, respectively, where the first error is statistical and the second
error is systematic.


title:
Off-diagonal Bethe ansatz solutions of the anisotropic spin-1/2 chains
  with arbitrary boundary fields

abstract:
  The anisotropic spin-1/2 chains with arbitrary boundary fields are
diagonalized with the off-diagonal Bethe ansatz method. Based on the properties
of the R-matrix and the K-matrices, an operator product identity of the
transfer matrix is constructed at some special points of the spectral
parameter. Combining with the asymptotic behavior (for XXZ case) or the
quasi-periodicity properties (for XYZ case) of the transfer matrix, the
extended T-Q ansatzs and the corresponding Bethe ansatz equations are derived.

categories: cond-mat.stat-mech hep-th math-ph math.MP


title:
Transverse current current response of graphene at finite temperature,
  plasmons and absorption

abstract:
  We calculate the linear transverse current current response function for
graphene at finite temperature and chemical potential. Within the Random Phase
Approximation, we then discuss general aspects of transverse plasmons beyond
the local response such as their dependence on temperature and on the
surrounding dielectric media. We find, e.g., maximal confinement of this mode
for a homogeneous dielectric media with refractive index $n\simeq 40$.
Confinement can further be enhanced by placing the graphene sheet inside an
optical cavity, but there exists a critical width below which no transverse
mode can be sustained. For zero doping and finite temperature, there are no
well-defined transverse plasmonic excitations in contrast to the longitudinal
channel. We also discuss the absorption of electromagnetic radiation in single
and double-layer systems for $s$ and $p$ polarizations and point out that the
theoretical limit of 50% is reached for $s$-polarized light with incident angle
of $\theta\approx89^o$.


title:
Eigenvalue statistics as indicator of integrability of non-equilibrium
  density operators

abstract:
  We propose to quantify the complexity of non-equilibrium steady state density
operators, as well as of long-lived Liouvillian decay modes, in terms of level
spacing distribution of their spectra. Based on extensive numerical studies in
a variety of models, some solvable and some unsolved, we conjecture that
integrability of density operators (e.g., existence of an algebraic procedure
for their construction in finitely many steps) is signaled by a Poissonian
level statistics, whereas in the generic non-integrable cases one finds level
statistics of a Gaussian unitary ensemble of random matrices. Eigenvalue
statistics can therefore be used as an efficient tool to identify integrable
quantum non-equilibrium systems.


title: Quantum Probability assignment limited by relativistic causality

abstract:
  The quantum nonlocality is limited by relativistic causality, however, the
reason is not fully understood yet. The relativistic causality condition on
nonlocal correlations has been usually accepted as a prohibition of
faster-than-light signaling, called no-signaling condition. We propose another
causality condition from the observation that space-like separate events should
have no causal relationship. It is proved that the new condition is stronger
than no-signaling condition for a pair of binary devices. We derive the
standard probability assignment rule, so-called Born rule, on quantum
measurement, which determines the degree of quantum nonlocality, by using
relativistic causality constraint. This shows how the causality limits the
upper bound of quantum nonlocality through quantum probability assignment.


title: Universality versus nonuniversality in asymmetric fluid criticality

abstract:
  Critical phenomena in real fluids demonstrate a combination of universal
features caused by the divergence of long-range fluctuations of density and
nonuniversal (system-dependent) features associated with specific
intermolecular interactions. Asymptotically, all fluids belong to the
Ising-model class of universality. The asymptotic power laws for the
thermodynamic properties are described by two independent universal critical
exponents and by two independent nonuniversal critical amplitudes; other
critical amplitudes can be obtained by universal relations. The nonuniversal
critical parameters (critical temperature, pressure, and density) can be
absorbed in the property units. Nonasymptotic critical behavior of fluids can
be divided into two parts, symmetric ("Ising-like") and asymmetric
("fluid-like"). The symmetric nonasymptotic behavior contains a new universal
exponent (Wegner exponent) and the system-dependent crossover scale (Ginzburg
number) associated with the range of intermolecular interactions, while the
asymmetric features are generally described by an additional universal exponent
and by three nonasymptotic amplitudes associated with mixing of the physical
fields into the scaling fields.


title: Resolution Proof Transformation for Compression and Interpolation

abstract:
  Verification methods based on SAT, SMT, and Theorem Proving often rely on
proofs of unsatisfiability as a powerful tool to extract information in order
to reduce the overall effort. For example a proof may be traversed to identify
a minimal reason that led to unsatisfiability, for computing abstractions, or
for deriving Craig interpolants. In this paper we focus on two important
aspects that concern efficient handling of proofs of unsatisfiability:
compression and manipulation. First of all, since the proof size can be very
large in general (exponential in the size of the input problem), it is indeed
beneficial to adopt techniques to compress it for further processing. Secondly,
proofs can be manipulated as a flexible preprocessing step in preparation for
interpolant computation. Both these techniques are implemented in a framework
that makes use of local rewriting rules to transform the proofs. We show that a
careful use of the rules, combined with existing algorithms, can result in an
effective simplification of the original proofs. We have evaluated several
heuristics on a wide range of unsatisfiable problems deriving from SAT and SMT
test cases.


title: In-flight calibration and verification of the Planck-LFI instrument

abstract:
  In this paper we discuss the Planck-LFI in-flight calibration campaign. After
a brief overview of the ground test campaigns, we describe in detail the
calibration and performance verification (CPV) phase, carried out in space
during and just after the cool-down of LFI. We discuss in detail the
functionality verification, the tuning of the front-end and warm electronics,
the preliminary performance assessment and the thermal susceptibility tests.
The logic, sequence, goals and results of the in-flight tests are discussed.
All the calibration activities were successfully carried out and the instrument
response was comparable to the one observed on ground. For some channels the
in-flight tuning activity allowed us to improve significantly the noise
performance.


title: Liquid-gas phase transition at and below the critical point

abstract:
  This article is a continuation of our previous works (see Yukhnovskii I.R. et
al., J. Stat. Phys, 1995, 80, 405 and references therein), where we have
described the behavior of a simple system of interacting particles in the
region of temperatures at and about the critical point, T \geqslant T_{c}. Now
we present a description of the behavior of the system at the critical point
(T_{c}, \eta_{c}) and in the region below the critical point. The calculation
is carried out from the first principles. The expression for the grand
canonical partition function is brought to the functional integrals defined on
the set of collective variables. The Ising-like form is singled out. Below
T_{c}, when a gas-liquid system undergoes a phase transition of the first
order, i.e., boiling, a "jump" occurs from the "extreme" high probability gas
state to the "extreme" high probability liquid state, releasing or absorbing
the latent heat of the transition. The phase equilibria conditions are also
derived.


title: Composite and elementary nature of a resonance in the sigma model

abstract:
  We analyze the mixing nature of the low-lying scalar resonance consisting of
the pipi composite and the elementary particle within the sigma model. A method
to disentangle the mixing is formulated in the scattering theory with the
concept of the two-level problem. We investigate the composite and elementary
components of the sigma meson by changing a mixing parameter. We also study the
dependence of the results on model parameters such as the cut-off value and the
mass of the elementary sigma meson.


title:
Reaction and structure effects of light mass nuclei using Glauber model
  with relativistic and non relativistic simple effective interaction densities

abstract:
  We study the structural properties of some nuclei in the region of light mass
using simple effective interaction in the frame work of microscopic non
relativistic Hartree-Fock and relativistic mean field formalism. For the
reaction dynamics, well known Glauber model is used with the conjunctions of
the densities obtained from these formalism. We observe good agreement of
results by both the formalism in comparison to the experimental values. These
two different approaches seems to be equally capable to reproduce the ground
state properties of nuclei in this region. A careful study of reaction dynamics
suggest the superiority of relativistic mean field over the Hartree-Fock with
simple effective interaction densities. But good agreement of reaction cross
section is appeared with simple effective interaction density for halo nuclear
systems. The possibility of existence of bubble nuclei are also studied using
both the formalism.


title:
The Effect of Composition on the Evolution of Giant and
  Intermediate-Mass Planets

abstract:
  We model the evolution of planets with various masses and compositions. We
investigate the effects of the composition and its depth dependence on the
long-term evolution of the planets. The effects of opacity and stellar
irradiation are also considered. It is shown that the change in radius due to
various compositions can be significantly smaller than the change in radius
caused by the opacity. Irradiation also affects the planetary contraction but
is found to be less important than the opacity effects. We suggest that the
mass-radius relationship used for characterization of observed extrasolar
planets should be taken with great caution since different physical conditions
can result in very different mass-radius relationships.


title: Measurement of radiative tau decays at BaBar

abstract:
  We present a study for the measurement of of radiative decays, tau -> l gamma
nu nu, l=e, mu, and tau -> pi gamma nu using 500 fb-1 of electron-positron
annihilations recorded by the BaBar detector at the PEP-II asymmetric
B-factory.


title:
Periodic Strategies: A New Solution Concept and an Algorithm for
  NonTrivial Strategic Form Games

abstract:
  We introduce a new solution concept, called periodicity, for selecting
optimal strategies in strategic form games. This periodicity solution concept
yields new insight into non-trivial games. In mixed strategy strategic form
games, periodic solutions yield values for the utility function of each player
that are equal to the Nash equilibrium ones. In contrast to the Nash
strategies, here the payoffs of each player are robust against what the
opponent plays. Sometimes, periodicity strategies yield higher utilities, and
sometimes the Nash strategies do, but often the utilities of these two
strategies coincide. We formally define and study periodic strategies in two
player perfect information strategic form games with pure strategies and we
prove that every non-trivial finite game has at least one periodic strategy,
with non-trivial meaning non-degenerate payoffs. In some classes of games where
mixed strategies are used, we identify quantitative features. Particularly
interesting are the implications for collective action games, since there the
collective action strategy can be incorporated in a purely non-cooperative
context. Moreover, we address the periodicity issue when the players have a
continuum set of strategies available.


title:
Massively parallel solvers for elliptic PDEs in Numerical Weather- and
  Climate Prediction

abstract:
  The demand for substantial increases in the spatial resolution of global
weather- and climate- prediction models makes it necessary to use numerically
efficient and highly scalable algorithms to solve the equations of large scale
atmospheric fluid dynamics. For stability and efficiency reasons several of the
operational forecasting centres, in particular the Met Office and the ECMWF in
the UK, use semi-implicit semi-Lagrangian time stepping in the dynamical core
of the model. The additional burden with this approach is that a three
dimensional elliptic partial differential equation (PDE) for the pressure
correction has to be solved at every model time step and this often constitutes
a significant proportion of the time spent in the dynamical core. To run within
tight operational time scales the solver has to be parallelised and there seems
to be a (perceived) misconception that elliptic solvers do not scale to large
processor counts and hence implicit time stepping can not be used in very high
resolution global models. After reviewing several methods for solving the
elliptic PDE for the pressure correction and their application in atmospheric
models we demonstrate the performance and very good scalability of Krylov
subspace solvers and multigrid algorithms for a representative model equation
with more than $10^{10}$ unknowns on 65536 cores on HECToR, the UK's national
supercomputer. For this we tested and optimised solvers from two existing
numerical libraries (DUNE and hypre) and implemented both a Conjugate Gradient
solver and a geometric multigrid algorithm based on a tensor-product approach
which exploits the strong vertical anisotropy of the discretised equation. We
study both weak and strong scalability and compare the absolute solution times
for all methods; in contrast to one-level methods the multigrid solver is
robust with respect to parameter variations.


title:
Positive-energy D-bar method for acoustic tomography: a computational
  study

abstract:
  A new computational method for reconstructing a potential from the
Dirichlet-to-Neumann map at positive energy is developed. The method is based
on D-bar techniques and it works in absence of exceptional points -- in
particular, if the potential is small enough compared to the energy. Numerical
tests reveal exceptional points for perturbed, radial potentials.
Reconstructions for several potentials are computed using simulated
Dirichlet-to-Neumann maps with and without added noise. The new reconstruction
method is shown to work well for energy values between $10^{-5}$ and $5$,
smaller values giving better results.


title: The night sky brightness at Potsdam-Babelsberg

abstract:
  We analyze the results of a 2 years (2011--2012) time series of night sky
photometry performed at the Leibniz Institute for Astrophysics in Potsdam
(AIP). This observatory is located on top of a hill ("Babelsberg"), 22\,km to
the southwest of the center of Berlin. The measurements have been performed
with a Unihedron Sky Quality Meter. We find night sky brightness values ranging
from 16.5 to 20.3 mag$_{\rm SQM}$ arcsec$^{-2}$; the latter (best) value
corresponds to 4.7 times the natural zenithal night sky brightness. We discuss
the influence of clouds, of the Moon and other factors on the night sky
brightness. With respect to the influence of the Moon, it turns out that
Potsdam-Babelsberg, despite its proximity to Berlin, still shows a circalunar
periodicity of the night sky brightness, although it is much weaker than
naturally. The light-pollution-enhancing effect of clouds dominates the night
sky brightness by far. Overcast nights with light pollution (up to 16.5
mag$_{\rm SQM}$ arcsec$^{-2}$) are brighter than clear full moon nights
($\approx$ 18.5 mag$_{\rm SQM}$ arcsec$^{-2}$) in roughly the same proportion
as the latter compared to clear nights with light pollution (20.3 mag$_{\rm
SQM}$ arcsec$^{-2}$).


title: Exchangeable sequences driven by an absolutely continuous random measure

abstract:
  Let $S$ be a Polish space and $(X_n:n\geq1)$ an exchangeable sequence of
$S$-valued random variables. Let $\alpha_n(\cdot)=P(X_{n+1}\in \cdot\mid
X_1,\...,X_n)$ be the predictive measure and $\alpha$ a random probability
measure on $S$ such that
$\alpha_n\stackrel{\mathrm{weak}}{\longrightarrow}\alpha$ a.s. Two (related)
problems are addressed. One is to give conditions for $\alpha\ll\lambda$ a.s.,
where $\lambda$ is a (nonrandom) $\sigma$-finite Borel measure on $S$. Such
conditions should concern the finite dimensional distributions $\mathcal
{L}(X_1,\...,X_n)$, $n\geq1$, only. The other problem is to investigate whether
$\Vert\alp ha_n-\alpha\Vert\stackrel{\mathrm{a.s.}}{\longrightarrow}0$, where
$\Vert\cdot\Vert$ is total variation norm. Various results are obtained. Some
of them do not require exchangeability, but hold under the weaker assumption
that $(X_n)$ is conditionally identically distributed, in the sense of [Ann.
Probab. 32 (2004) 2029-2052].


title: Particle Acceleration And Emission Processes In Mrk 421

abstract:
  We investigate the X-ray and $\gamma$-ray flares of Mrk 421 on 2008 June 6-15
using the synchrotron self- Compton(SSC) model with electron acceleration, in
which an evident correlation between the X-ray and $\gamma$-ray bands appears,
while no significant correlation between the optical and X-ray band is
observed. We argue that the emission from Mrk 421 may originate from two
different components. One is the steady component from the outer region that is
mainly attributed to the optical band, in which the electrons are accelerated
by first-order Fermi acceleration mechanism. We use a steady electron spectrum
to produce the synchrotron self-Compton emission. The other is the variable
component from the inner region, in which the electrons are accelerated by the
stochastic acceleration process. We use the time-dependent SSC model to produce
the emission from the variable component. We suggest that the flares are due to
the hardening of the electron spectrum under the process of the stochastic
acceleration, which leads to the hardening of the observed spectrum in the
X-ray and $\gamma$-ray bands. Furthermore, we find that the energy densities of
electrons and magnetic fields are near equipartition in both jet regions.


title:
On the largest component in the subcritical regime of the Bohman-Frieze
  process

abstract:
  Kang, Perkins and Spencer showed that the size of the largest component of
the Bohman-Frieze process at a fixed time $t$ smaller than $t_c$, the critical
time for the process is $L_1(t)=\Omega(\log n/(t_c-t)^2)$ with high
probability. They also conjectured that this is the correct order, that is
$L_1(t)=O(\log n/(t_c-t)^2)$ with high probability for fixed $t$ smaller than
$t_c$. Using a different approach, Bhamidi, Budhiraja and Wang showed that
$L_1(t_n)=O((\log n)^4/(t_c-t_n)^2)$ with high probability for $t_n\leq
t_c-n^{-\gamma}$ where $\gamma\in(0,1/4)$. In this paper, we improve their
result by showing that for any fixed $\lambda>0$, $L_1(t_n)=O(\log
n/(t_c-t_n)^2)$ with high probability for $t_n\leq t_c-\lambda n^{-1/3}$. In
particular, this settles the conjecture of Kang, Perkins and Spencer. We also
prove some generalizations for general bounded size rules.


title:
On Fragments without Implications of both the Full Lambek Logic and some
  of its Substructural Extensions

abstract:
  In this paper we study some fragments without implications of the (Hilbert)
full Lambek logic $\mathbf{HFL}$ and also some fragments without implications
of some of the substructural extensions of that logic. To do this, we perform
an algebraic analysis of the Gentzen systems defined by the substructural
calculi $\FL_\sigma$. Such systems are extensions of the full Lambek calculus
$\FL$ with the rules codified by a subsequence, $\sigma$, of the sequence $e
w_l w_r c$; where $e$ stands for \emph{exchange}, $w_l$ for \emph{left
weakening}, $w_r$ for \emph{right weakening}, and $c$ for \emph{contraction}.
We prove that these Gentzen systems (in languages without implications) are
algebraizable by obtaining their equivalent algebraic semantics. All these
classes of algebras are varieties of pointed semilatticed monoids and they can
be embedded in their ideal completions. As a consequence of these results, we
reveal that the fragments of the Gentzen systems associated with the calculi
$\FL_\sigma$ are the restrictions of them to the sublanguages considered, and
we also reveal that in these languages, the fragments of the external systems
associated with $\FL[\sigma]$ are the external systems associated with the
restricted Gentzen systems (i.e., those obtained by restriction of
$\FL_\sigma]$ to the implication-less languages considered). We show that all
these external systems without implication have algebraic semantics but they
are not algebraizable (and are not even protoalgebraic). Results concerning
fragments without implication of intuitionistic logic without contraction were
already reported in Bou et al.(2006): On two fragments with negation and
without implication of the logic of residuated lattices. Archive for
Mathematical Logic 45(5) and in Adill\'on et al. (2007): On three
implication-less fragments of t-norm based fuzzy logics. Fuzzy Sets and Systems
158(23).


title:
Distance domination, guarding and vertex cover for maximal outerplanar
  graph

abstract:
  This paper discusses a distance guarding concept on triangulation graphs,
which can be associated with distance domination and distance vertex cover. We
show how these subjects are interconnected and provide tight bounds for any
n-vertex maximal outerplanar graph: the 2d-guarding number, g_{2d}(n) = n/5;
the 2d-distance domination number, gamma_{2d}(n) = n/5; and the 2d-distance
vertex cover number, beta_{2d}(n) = n/4.