title: Perturbations of the Dirichlet Problem and Error Bounds

abstract:
  The Dirichlet problem on a bounded planar domain is more readily understood
and solved for the Laplace operator than it is for a Schrodinger operator. When
the potential function is small, we might hope to approximate the solution to
the Schrodinger equation with the solution to the Laplace equation. In this
vein we develop a series expansion for the solution and give explicit bounds on
the error terms when truncating the series. We also examine a handful of
examples and derive similar results for the Green function and
Dirichlet-to-Neumann map.


title:
Spectral parameter power series for polynomial pencils of
  Sturm-Liouville operators and Zakharov-Shabat systems

abstract:
  A spectral parameter power series (SPPS) representation for solutions of
Sturm-Liouville equations of the form
$$(pu')'+qu=u\sum_{k=1}^{N}\lambda^{k}r_{k}$$ is obtained. It allows one to
write a general solution of the equation as a power series in terms of the
spectral parameter $\lambda$. The coefficients of the series are given in terms
of recursive integrals involving a particular solution of the equation
$(pu_{0}')'+qu_{0}=0$. The convenient form of the solution provides an
efficient numerical method for solving corresponding initial value, boundary
value and spectral problems.
  A special case of the considered Sturm-Liouville equation arises in relation
with the Zakharov-Shabat system. We derive an SPPS representation for its
general solution and consider other applications as the one-dimensional Dirac
system and the equation describing a damped string. Several numerical examples
illustrate the efficiency and the accuracy of the numerical method based on the
SPPS representations which besides its natural advantages like the simplicity
in implementation and accuracy is applicable to the problems admitting complex
coefficients, spectral parameter dependent boundary conditions and complex
spectrum.


title: Topological phase transition in a discrete quasicrystal

abstract:
  We investigate a two-dimensional tiling model. Even though the degrees of
freedom in this model are discrete, it has a hidden continuous global symmetry
in the infinite lattice limit, whose corresponding Goldstone modes are the
quasicrystalline phasonic degrees of freedom. We show that due to this
continuous symmetry, and despite the apparent discrete nature of the model, a
topological phase transition from a quasi-long-range ordered to a disordered
phase occurs at a finite temperature, driven by vortex proliferation. We argue
that some of the results are universal properties of two-dimensional systems
whose ground state is a quasicrystalline state.


title: Efficient and accurate simulation of dynamic dielectric objects

abstract:
  Electrostatic interactions between dielectric objects are complex and of a
many-body nature, owing to induced surface bound charge. We present a
collection of techniques to simulate dynamical dielectric objects. We calculate
the surface bound charge from a matrix equation using the Generalized Minimal
Residue method (GMRES). Empirically, we find that GMRES converges very quickly.
Indeed, our detailed analysis suggests that the relevant matrix has a very
compact spectrum for all non-degenerate dielectric geometries. Each GMRES
iteration can be evaluated using a fast Ewald solver with cost that scales
linearly or near-linearly in the number of surface charge elements. We analyze
several previously proposed methods for calculating the bound charge, and show
that our approach compares favorably.


title:
Firewalls and flat mirrors: An alternative to the AMPS experiment which
  evades the Harlow-Hayden obstacle

abstract:
  If quantum gravity does not lead to a breakdown of predictability, then
Almheiri, Marolf, Polchinski and Sully (AMPS) have argued that an observer
falling into a black hole can perform an experiment which verifies a violation
of entanglement monogamy - that late time Hawking radiation is maximally
entangled with early time Hawking radiation and also with infalling radiation -
something impossible in quantum field theory. However, as pointed out by Hayden
and Harlow, this experiment is infeasible, as the time required to perform the
experiment is almost certainly longer than the lifetime of the black hole. Here
we propose an alternative firewall experiment which could actually be performed
within the black hole's lifetime. The alternative experiment involves forming
an entangled black hole in which the unscrambling of information is precomputed
on a quantum memory prior to the creation of the black hole and without acting
on the matter which forms the black hole or emerges from it. This would allow
an observer near a black hole to signal faster than light. As another
application of our precomputing strategy, we show how one can produce entangled
black holes which acts like ``flat mirrors'', in the sense that information
comes out almost instantly (as in the Hayden-Preskill scenario), but also
emerge unscrambled, so that it can actually be observed instantly as well.
Finally, we prove that a black hole in thermal equilibrium with its own
radiation, is uncorrelated with this radiation.


title: A conjectured class of scale-invariant distances on inner product spaces

abstract:
  Let $V$ be an inner product space, and $x, y \in V$; the conjecture is made
that, for any $p \in [1, \infty]$, the function $d_p(x, y):=\|x-y\|/(\|x\|^p+
\|y\|^p)^{1/p}$ is a distance on $V$.


title:
The Bannai-Ito algebra and a superintegrable system with reflections on
  the 2-sphere

abstract:
  A quantum superintegrable model with reflections on the 2-sphere is
introduced. Its two algebraically independent constants of motion generate a
central extension of the Bannai--Ito algebra. The Schrodinger equation
separates in spherical coordinates and its exact solutions are presented. It is
further observed that the Hamiltonian of the system arises in the addition of
three representations of the sl_{-1}(2) algebra (the dynamical algebra of the
one-dimensional parabosonic oscillator). The contraction from the two-sphere to
the Euclidean plane yields the Dunkl oscillator in two dimensions and its
Schwinger-Dunkl symmetry algebra sd(2).


title:
Additional Constructions to Solve the Generalized Russian Cards Problem
  using Combinatorial Designs

abstract:
  In the generalized Russian cards problem, we have a card deck $X$ of $n$
cards and three participants, Alice, Bob, and Cathy, dealt $a$, $b$, and $c$
cards, respectively. Once the cards are dealt, Alice and Bob wish to privately
communicate their hands to each other via public announcements, without the
advantage of a shared secret or public key infrastructure. Cathy should remain
ignorant of all but her own cards after Alice and Bob have made their
announcements. Notions for Cathy's ignorance in the literature range from Cathy
not learning the fate of any individual card with certainty (weak $1$-security)
to not gaining any probabilistic advantage in guessing the fate of some set of
$\delta$ cards (perfect $\delta$-security). As we demonstrate, the generalized
Russian cards problem has close ties to the field of combinatorial designs, on
which we rely heavily, particularly for perfect security notions. Our main
result establishes an equivalence between perfectly $\delta$-secure strategies
and $(c+\delta)$-designs on $n$ points with block size $a$, when announcements
are chosen uniformly at random from the set of possible announcements. We also
provide construction methods and example solutions, including a construction
that yields perfect $1$-security against Cathy when $c=2$. We leverage a known
combinatorial design to construct a strategy with $a=8$, $b=13$, and $c=3$ that
is perfectly $2$-secure. Finally, we consider a variant of the problem that
yields solutions that are easy to construct and optimal with respect to both
the number of announcements and level of security achieved. Moreover, this is
the first method obtaining weak $\delta$-security that allows Alice to hold an
arbitrary number of cards and Cathy to hold a set of $c = \lfloor
\frac{a-\delta}{2} \rfloor$ cards. Alternatively, the construction yields
solutions for arbitrary $\delta$, $c$ and any $a \geq \delta + 2c$.


title:
What is the minimal model of magnetic interactions in Fe-based
  superconductors?

abstract:
  Using noncollinear first-principles calculations we perform a systematic
study of the magnetic order in several families of ferropnictides. We find a
fairly universal energy dependence on the magnetization order in all cases. Our
results confirm that a simple Heisenberg model fails to account for the energy
dependence of the magnetization in couple of ways: first a biquadratic term is
present in all cases and second the magnetic moment softens depending on the
orientation. We also find that hole doping substantially reduces the
biquadratic contribution, although the antiferromagnetic stripe state remains
stable within the whole range of doping concentrations, and thus the reported
lack of the orthorhombicity in Na-doped BaFe$_2$As$_2$ is probably due to
factors other than a sign reversal of the biquadratic term. Finally, we
discovered that even with the biquadratic term, there is a limit to the
accuracy of mapping the density functional theory energetics onto
Heisenberg-type models, independent of the range of the model.


title: Evolution of Accreting Binary Systems on the Spin-up Line

abstract:
  The measured characteristics of binary pulsars provide valuable insights into
the evolution of these systems. We study the aspects of binary evolution
particularly relevant to binary Millisecond Pulsars (MSPs), and the formation
of close binaries involving degenerate stars through a spin-evolution diagram
(spin-up line). For this task, we use a wide variety of binaries, including
those with compact components that observed in different energy bands, which we
analyze them according to the spin-up line. Their formation and evolution over
timescales of binary evolution models are investigated in order to grab any
constraint on their evolution, and to estimate the masses of neutron stars with
different mass-transfer histories.


title:
New Algorithm and Phase Diagram of Noncommutative Phi**4 on the Fuzzy
  Sphere

abstract:
  We propose a new algorithm for simulating noncommutative phi-four theory on
the fuzzy sphere based on, i) coupling the scalar field to a U(1) gauge field,
in such a way that in the commutative limit N\longrightarrow \infty, the two
modes decouple and we are left with pure scalar phi-four on the sphere, and ii)
diagonalizing the scalar field by means of a U(N) unitary matrix, and then
integrating out the unitary group from the partition function. The number of
degrees of freedom in the scalar sector reduces, therefore, from N^2 to the N
eigenvalues of the scalar field, whereas the dynamics of the U(1) gauge field,
is given by D=3 Yang-Mills matrix model with a Myers term. As an application,
the phase diagram, including the triple point, of noncommutative phi-four
theory on the fuzzy sphere, is reconstructed with small values of N up to N=10,
and large numbers of statistics.

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


title:
Stochastic ODEs and stochastic linear PDEs with critical drift:
  regularity, duality and uniqueness

abstract:
  In this paper linear stochastic transport and continuity equations with drift
in critical $L^{p}$ spaces are considered. In this situation noise prevents
shocks for the transport equation and singularities in the density for the
continuity equation, starting from smooth initial conditions. Specifically, we
first prove a result of Sobolev regularity of solutions, which is false for the
corresponding deterministic equation. The technique needed to reach the
critical case is new and based on parabolic equations satisfied by moments of
first derivatives of the solution, opposite to previous works based on
stochastic flows. The approach extends to higher order derivatives under more
regularity of the drift term. By a duality approach, these regularity results
are then applied to prove uniqueness of weak solutions to linear stochastic
continuity and transport equations and certain well-posedness results for the
associated stochastic differential equation (sDE) (roughly speaking, existence
and uniqueness of flows and their $C^\alpha$ regularity, strong uniqueness for
the sDE when the initial datum has diffuse law). Finally, we show two types of
examples: on the one hand, we present well-posed sDEs, when the corresponding
ODEs are ill-posed, and on the other hand, we give a counterexample in the
supercritical case.


title: Images of edge current in InAs/GaSb quantum wells

abstract:
  Quantum spin Hall devices with edges much longer than several microns do not
display ballistic transport: that is, their measured conductances are much less
than $e^2/h$ per edge. We imaged edge currents in InAs/GaSb quantum wells with
long edges and determined an effective edge resistance. Surprisingly, although
the effective edge resistance is much greater than $h/e^2$, it is independent
of temperature up to 30 K within experimental resolution. Known candidate
scattering mechanisms do not explain our observation of an effective edge
resistance that is large yet temperature-independent.


title:
An Explicit Conjectured Determinant Evaluation Whose Proof Would Make Me
  Happy (and the OEIS richer)

abstract:
  I conjecture a certain explicit determinant evaluation, whose proof would
imply the solution of certain enumeration problem that I have been working on,
and that I find interesting. I am pledging \$500 to the OEIS Foundation (in
honor of the prover!) for a proof, and \$50 (in honor of the disprover)


title:
Proposta di nuovi strumenti per comprendere come funziona la cognizione
  (Novel tools to understand how cognition works)

abstract:
  I think that the main reason why we do not understand the general principles
of how knowledge works (and probably also the reason why we have not yet
designed and built efficient machines capable of artificial intelligence), is
not the excessive complexity of cognitive phenomena, but the lack of the
conceptual and methodological tools to properly address the problem. It is like
trying to build up Physics without the concept of number, or to understand the
origin of species without including the mechanism of natural selection. In this
paper I propose some new conceptual and methodological tools, which seem to
offer a real opportunity to understand the logic of cognitive processes. I
propose a new method to properly treat the concepts of structure and schema,
and to perform on them operations of structural analysis. These operations
allow to move straightforwardly from concrete to more abstract representations.
With these tools I will suggest a definition for the concept of rule, of
regularity and of emergent phenomena. From the analysis of some important
aspects of the rules, I suggest to distinguish them in operational and
associative rules. I propose that associative rules assume a dominant role in
cognition. I also propose a definition for the concept of problem. At the end I
will briefly illustrate a possible general model for cognitive systems.


title:
Global Regularity vs. Finite-Time Singularities: Some Paradigms on the
  Effect of Boundary Conditions and Certain Perturbations

abstract:
  In light of the question of finite-time blow-up vs. global well-posedness of
solutions to problems involving nonlinear partial differential equations, we
provide several cautionary examples which indicate that modifications to the
boundary conditions or to the nonlinearity of the equations can effect whether
the equations develop finite-time singularities. In particular, we aim to
underscore the idea that in analytical and computational investigations of the
blow-up of three-dimensional Euler and Navier-Stokes equations, the boundary
conditions may need to be taken into greater account. We also examine a
perturbation of the nonlinearity by dropping the advection term in the
evolution of the derivative of the solutions to the viscous Burgers equation,
which leads to the development of singularities not present in the original
equation, and indicates that there is a regularizing mechanism in part of the
nonlinearity. This simple analytical example corroborates recent computational
observations in the singularity formation of fluid equations.


title:
An Updated Version of the Unified Radio Catalog: A Multi-Wavelength
  Radio and Optical Catalog of Quasars and Radio Galaxies

abstract:
  We present an updated version of the Kimball & Ivezic (2008) radio catalog
using updated radio and optical data, and new low-frequency radio data. The
catalog, containing millions of radio sources, was created by consolidating
large-area radio and optical surveys GB6 (6cm), FIRST (20cm), NVSS (20cm),
WENSS (92cm), VLSSr (4m), and SDSS DR9 (optical). The region where all surveys
overlap covers 3269 square degrees in the North Galactic Cap, and contains
>160,000 20-cm sources, with about 12,000 detected in all five radio surveys
and over one-third detected optically. Combining parameters from the sky
surveys allows easy and efficient classification by radio and optical
morphology and radio spectral index. The catalog is available at
http://www.aoc.nrao.edu/~akimball/radiocat.shtml .


title:
On Darboux transformations for the derivative nonlinear Schr\"odinger
  equation

abstract:
  We consider Darboux transformations for the derivative nonlinear
Schr\"odinger equation. A new theorem for Darboux transformations of operators
with no derivative term are presented and proved. The solution is expressed in
quasideterminant forms. Additionally, the parabolic and soliton solutions of
the derivative nonlinear Schr\"odinger equation are given as explicit examples.


title:
Some criteria to check if a projective hypersurfaces is smooth or
  singular

abstract:
  In this paper we present some properties for projective hypersurfaces, smooth
and singular, to be criteria for identification. To make the decision with
these criteria, we have included procedures written in Singular language.


title: Dynamical magnetic charges and linear magnetoelectricity

abstract:
  Magnetoelectric (ME) materials are of fundamental interest and have been
investigated for their broad potential for technological applications. The
search for, and eventually the theoretical design of, materials with large ME
couplings present challenging issues. First-principles methods have only
recently been developed to calculate the full ME response tensor $\alpha$
including both electronic and ionic (i.e., lattice-mediated) contributions. The
latter is proportional to both the Born dynamical electric charge $Z^{\rm e}$
and its analogue, the dynamical magnetic charge $Z^{\rm m}$. Here we present a
theoretical study of the magnetic charge $Z^{\rm m}$ and the mechanisms that
could enhance it. Using first-principles density-functional methods, we
calculate the atomic $Z^{\rm m}$ tensors in $\rm{Cr_2O_3}$, a prototypical
magnetoelectric, and in KITPite, a fictitious material that has previously been
reported to show a strong ME response arising from exchange striction effects.
Our results confirm that in $\rm{Cr_2O_3}$, the $Z^{\rm m}$ values and
resulting ME responses arise only from spin-orbit coupling (SOC) and are
therefore rather weak. In KITPite, by contrast, the exchange striction acting
on the non-collinear spin structure induces much $Z^{\rm m}$ values that
persist even when SOC is completely absent.


title:
Complex magnetic behavior of the sawtooth Fe chains in
  Rb$_{2}$Fe$_{2}$O(AsO$_{4}$)$_{2}$

abstract:
  Results of magnetic field and temperature dependent neutron diffraction and
magnetization measurements on oxy-arsenate Rb$_{2}$Fe$_{2}$O(AsO$_{4}$)$_{2}$
are reported. The crystal structure of this compound contains
pseudo-one-dimensional [Fe$_{2}$O$_{6}$]$^\infty$ sawtooth-like chains, formed
by corner sharing isosceles triangles of $Fe^{3+}$ ions occupying two
nonequivalent crystallographic sites. The chains extend infinitely along the
crystallographic $b$-axis and are structurally confined from one another via
diamagnetic (AsO$_{4}$)$^{3-}$ units along the $a$-axis, and Rb$^+$ cations
along the $c$-axis direction. Neutron diffraction measurements indicate the
onset of a long range antiferromagnetic order below approximately 25 K. The
magnetic structure consists of ferrimagnetic chains which are
antiferromagnetically coupled with each other. Within each chain, one of the
two Fe sites carries a moment which lies along the \emph{b}-axis, while the
second site bears a canted moment in the opposite direction. Externally applied
magnetic field induces a transition to a ferrimagnetic state, in which the
coupling between the sawtooth chains becomes ferromagnetic. Magnetization
measurements performed on optically-aligned single crystals reveal evidence for
an uncompensated magnetization at low magnetic fields that could emerge from to
a phase-segregated state with ferrimagnetic inclusions or from
antiferromagnetic domain walls. The observed magnetic states and the
competition between them is expected to arise from strongly frustrated
interactions within the sawtooth chains and relatively weak coupling between
them.


title: Two-photon dynamics in coherent Rydberg atomic ensemble

abstract:
  We study the interaction of two photons in a Rydberg atomic ensemble under
the condition of electromagnetically induced transparency, combining a
semi-classical approach for pulse propagation and a complete quantum treatment
for quantum state evolution. We find that the blockade regime is not suitable
for implementing photon-photon cross-phase modulation due to pulse absorption
and dispersion. However, approximately ideal cross-phase modulation can be
realized based on relatively weak interactions, with counter-propagating and
transversely separated pulses.


title: On polygon numbers of circle graphs and distance hereditary graphs

abstract:
  Circle graphs are intersection graphs of chords in a circle and $k$-polygon
graphs are intersection graphs of chords in a convex $k$-sided polygon where
each chord has its endpoints on distinct sides. The $k$-polygon graphs, for $k
\ge 2$, form an infinite chain of graph classes, each of which contains the
class of permutation graphs. The union of all of those graph classes is the
class of circle graphs. The polygon number $\gp(G)$ of a circle graph $G$ is
the minimum $k$ such that $G$ is a $k$-polygon graph. Given a circle graph $G$
and an integer $k$, determining whether $\gp(G) \le k$ is NP-complete, while
the problem is solvable in polynomial time for fixed $k$.
  In this paper, we show that $\gp(G)$ is always at least as large as the
asteroidal number of $G$, and equal to the asteroidal number of $G$ when $G$ is
a connected distance hereditary graph that is not a clique. This implies that
the classes of distance hereditary permutation graphs and distance hereditary
AT-free graphs are the same, and we give a forbidden subgraph characterization
of that class. We also establish the following upper bounds: $\gp(G)$ is at
most the clique cover number of $G$ if $G$ is not a clique, at most 1 plus the
independence number of $G$, and at most $\lceil n/2 \rceil$ where $n \ge 3$ is
the number of vertices of $G$. Our results lead to linear time algorithms for
finding the minimum number of corners that must be added to a given circle
representation to produce a polygon representation, and for finding the
asteroidal number of a distance hereditary graph, both of which are
improvements over previous algorithms for those problems.


title:
Optical phase-noise dynamics of Titanium:sapphire optical frequency
  combs

abstract:
  Stabilized optical frequency combs (OFC) can have remarkable levels of
coherence across their broad spectral bandwidth. We study the scaling of the
optical noise across hundreds of nanometers of optical spectra. We measure the
residual phase noise between two OFC's (having offset frequencies $f^{(1)}_0 $
and $f^{(2)}_0$) referenced to a common cavity-stabilized narrow linewidth CW
laser. Their relative offset frequency $ \Delta f_0 = f^{(2)}_0 - f^{(1)}_0 $,
which appears across their entire spectra, provides a convenient measure of the
phase noise. By comparing $\Delta f_0$ at different spectral regions, we
demonstrate that the observed scaling of the residual phase noise is in very
good agreement with the noise predicted from the standard frequency comb
equation.


title: Classical entanglement in polarization metrology

abstract:
  Quantum approaches relying on entangled photons have been recently proposed
to increase the efficiency of optical measurements. We demonstrate here that,
surprisingly, the use of classical light with entangled degrees of freedom can
also bring outstanding advantages over conventional measurements in
polarization metrology. Specifically, we show that radially polarized beams of
light allow to perform real-time single-shot Mueller matrix polarimetry. Our
results also indicate that quantum optical procedures requiring entanglement
without nonlocality can be actually achieved in classical optics regime.


title:
Limits on Stellar Companions to Exoplanet Host Stars With Eccentric
  Planets

abstract:
  Though there are now many hundreds of confirmed exoplanets known, the
binarity of exoplanet host stars is not well understood. This is particularly
true of host stars which harbor a giant planet in a highly eccentric orbit
since these are more likely to have had a dramatic dynamical history which
transferred angular momentum to the planet. Here we present observations of
four exoplanet host stars which utilize the excellent resolving power of the
Differential Speckle Survey Instrument (DSSI) on the Gemini North telescope.
Two of the stars are giants and two are dwarfs. Each star is host to a giant
planet with an orbital eccentricity > 0.5 and whose radial velocity data
contain a trend in the residuals to the Keplerian orbit fit. These observations
rule out stellar companions 4-8 magnitudes fainter than the host star at
passbands of 692nm and 880nm. The resolution and field-of-view of the
instrument result in exclusion radii of 0.05-1.4 arcsecs which excludes stellar
companions within several AU of the host star in most cases. We further provide
new radial velocities for the HD 4203 system which confirm that the linear
trend previously observed in the residuals is due to an additional planet.
These results place dynamical constraints on the source of the planet's
eccentricities, constraints on additional planetary companions, and informs the
known distribution of multiplicity amongst exoplanet host stars.


title:
A Round-Robin Protocol for Distributed Estimation with $H_\infty$
  Consensus

abstract:
  The paper considers a distributed robust estimation problem over a network
with directed topology involving continuous time observers. While measurements
are available to the observers continuously, the nodes interact according to a
Round-Robin rule, at discrete time instances. The results of the paper are
sufficient conditions which guarantee a suboptimal $H_\infty$ level of
consensus between observers with sampled interconnections.


title:
Glassy Chimeras could be blind to quantum speedup: Designing better
  benchmarks for quantum annealing machines

abstract:
  Recently, a programmable quantum annealing machine has been built that
minimizes the cost function of hard optimization problems by adiabatically
quenching quantum fluctuations. Tests performed by different research teams
have shown that, indeed, the machine seems to exploit quantum effects. However
experiments on a class of random-bond instances have not yet demonstrated an
advantage over classical optimization algorithms on traditional computer
hardware. Here we present evidence as to why this might be the case. These
engineered quantum annealing machines effectively operate coupled to a
decohering thermal bath. Therefore, we study the finite-temperature critical
behavior of the standard benchmark problem used to assess the computational
capabilities of these complex machines. We simulate both random-bond Ising
models and spin glasses with bimodal and Gaussian disorder on the D-Wave
Chimera topology. Our results show that while the worst-case complexity of
finding a ground state of an Ising spin glass on the Chimera graph is not
polynomial, the finite-temperature phase space is likely rather simple: Spin
glasses on Chimera have only a zero-temperature transition. This means that
benchmarking optimization methods using spin glasses on the Chimera graph might
not be the best benchmark problems to test quantum speedup. We propose
alternative benchmarks by embedding potentially harder problems on the Chimera
topology. Finally, we also study the (reentrant) disorder-temperature phase
diagram of the random-bond Ising model on the Chimera graph and show that a
finite-temperature ferromagnetic phase is stable up to 19.85(15)%
antiferromagnetic bonds. Beyond this threshold the system only displays a
zero-temperature spin-glass phase. Our results therefore show that a careful
design of the hardware architecture and benchmark problems is key when building
quantum annealing machines.


title: Higher-twist contributions to neutrino-production of pions

abstract:
  In this paper we estimate the size of twist-3 corrections to the deeply
virtual meson production in neutrino interactions due to the chiral odd
transversity Generalized Parton Distribution (GPD). We conclude that in
contrast to pion electroproduction, in neutrino-induced reactions these
corrections are small. This happens due to large contribution of unpolarized
GPDs H, E to the leading-twist amplitude in neutrinoproduction. We provide a
computational code, which can be used for evaluation of the cross-sections
accounting for these twist-3 corrections with various GPD models. Our results
are particularly relevant for analyses of the pion and kaon production in the
Minerva experiment at FERMILAB.


title:
Black holes and fundamental fields in Numerical Relativity: initial data
  construction and evolution of bound states

abstract:
  Fundamental fields are a natural outcome in cosmology and particle physics
and might therefore serve as a proxy for more complex interactions. The
equivalence principle implies that all forms of matter gravitate, and one
therefore expects relevant, universal imprints of new physics in strong field
gravity, such as that encountered close to black holes. Fundamental fields in
the vicinities of supermassive black holes give rise to extremely long-lived,
or even unstable, configurations which slowly extract angular momentum from the
black hole or simply evolve non-linearly over long timescales, with important
implications for particle physics and gravitational-wave physics. Here, we
perform a fully non-linear study of scalar-field condensates around rotating
black holes. We provide novel ways to specify initial data for the
Einstein-Klein-Gordon system, with potential applications in a variety of
scenarios. Our numerical results confirm the existence of long-lived bar-modes
which act as lighthouses for gravitational wave emission: the scalar field
condenses outside the black hole geometry and acts as a constant frequency
gravitational-wave source for very long timescales. This effect could turn out
to be a potential signature of beyond standard model physics and also a
promising source of gravitational waves for future gravitational wave
detectors.


title: Optimal Demand Response Using Device Based Reinforcement Learning

abstract:
  Demand response (DR) for residential and small commercial buildings is
estimated to account for as much as 65% of the total energy savings potential
of DR, and previous work shows that a fully automated Energy Management System
(EMS) is a necessary prerequisite to DR in these areas. In this paper, we
propose a novel EMS formulation for DR problems in these sectors. Specifically,
we formulate a fully automated EMS's rescheduling problem as a reinforcement
learning (RL) problem, and argue that this RL problem can be approximately
solved by decomposing it over device clusters. Compared with existing
formulations, our new formulation (1) does not require explicitly modeling the
user's dissatisfaction on job rescheduling, (2) enables the EMS to
self-initiate jobs, (3) allows the user to initiate more flexible requests and
(4) has a computational complexity linear in the number of devices. We also
demonstrate the simulation results of applying Q-learning, one of the most
popular and classical RL algorithms, to a representative example.


title:
Optical nanofiber integrated into an optical tweezers for particle
  manipulation and in-situ fiber probing

abstract:
  Precise control of particle positioning is desirable in many optical
propulsion and sorting applications. Here, we develop an integrated platform
for particle manipulation consisting of a combined optical nanofiber and
optical tweezers system. Individual silica microspheres were introduced to the
nanofiber at arbitrary points using the optical tweezers, thereby producing
pronounced dips in the fiber transmission. We show that such consistent and
reversible transmission modulations depend on both particle and fiber diameter,
and may be used as a reference point for in-situ nanofiber or particle size
measurement. Therefore we combine SEM size measurements with nanofiber
transmission data to provide calibration for particle-based fiber assessment.
We also demonstrate how the optical tweezers can be used to create a particle
jet to feed a supply of microspheres to the nanofiber surface, forming a
particle conveyor belt. This integrated optical platform provides a method for
selective evanescent field manipulation of micron-sized particles and
facilitates studies of optical binding and light-particle interaction dynamics.


title:
Updating Neighbour Cell List via Crowdsourced User Reports: a Framework
  for Measuring Time Performance

abstract:
  In this paper we introduce the idea of estimating local topology in wireless
networks by means of crowdsourced user reports. In this approach each user
periodically reports to the serving basestation information about the set of
neighbouring basestations observed by the user. We show that, by mapping the
local topological structure of the network onto states of increasing knowledge,
a crisp mathematical framework can be obtained, which allows in turn for the
use of a variety of user mobility models. Using a simplified mobility model we
show how obtain useful upper bounds on the expected time for a basestation to
gain full knowledge of its local neighbourhood, answering the fundamental
question about which classes of network deployments can effectively benefit
from a crowdsourcing approach.


title: Probing neutron-skin thickness with total reaction cross sections

abstract:
  We analyze total reaction cross sections, $\sigma_R$, for exploring their
sensitivity to the neutron-skin thickness of nuclei. We cover 91 nuclei of O,
Ne, Mg, Si, S, Ca, and Ni isotopes. The cross sections are calculated in the
Glauber theory using the density distributions obtained with the
Skyrme-Hartree-Fock method in 3-dimensional coordinate space. Defining a
reaction radius, $a_R=\sqrt{\sigma_R/\pi}$, to characterize the nuclear size
and target (proton or $^{12}$C) dependence, we find an empirical formula for
expressing $a_R$ with the point matter radius and the skin thickness, and
assess two practical ways of determining the skin thickness from proton-nucleus
$\sigma_R$ values measured at different energies or from $\sigma_R$ values
measured for different targets.


title: A Simple Direct Proof of Billingsley's Theorem

abstract:
  Billingsley's theorem (1972) asserts that the Poisson--Dirichlet process is
the limit, as $n \to \infty$, of the process giving the relative log sizes of
the largest prime factor, the second largest, and so on, of a random integer
chosen uniformly from 1 to $n$. In this paper we give a new proof that directly
exploits Dickman's asymptotic formula for the number of such integers with no
prime factor larger than $n^{1/u}$, namely $\Psi(n,n^{1/u}) \sim n \rho(u)$, to
derive the limiting joint density functions of the finite-dimensional
projections of the log prime factor processes. Our main technical tool is a new
criterion for the convergence in distribution of non-lattice discrete random
variables to continuous random variables.


title:
Many faces of the Landau gauge gluon propagator at zero and finite
  temperature: positivity violation, spectral density and mass scales

abstract:
  We address several aspects of gluon propagation at zero and finite
temperature. In particular, we study the violation of spectral positivity, we
discuss a method to extract the K\"all\'{e}n-Lehmann spectral density of a
particle (be it elementary or bound state) propagator and apply it to compute
gluon spectral densities from lattice data. Furthermore, we also consider the
interpretation of the Landau gauge gluon propagator at finite temperature as a
massive type bosonic propagator.


title: Extensions of Billingsley's Theorem via Multi-Intensities

abstract:
  Let $p_1 \ge p_2 \ge \dots$ be the prime factors of a random integer chosen
uniformly from $1$ to $n$, and let $$ \frac{\log p_1}{\log n}, \frac{\log
p_2}{\log n}, \dots $$ be the sequence of scaled log factors. Billingsley's
Theorem (1972), in its modern formulation, asserts that the limiting process,
as $n \to \infty$, is the Poisson-Dirichlet process with parameter $\theta =1$.
  In this paper we give a new proof, inspired by the 1993 proof by Donnelly and
Grimmett, and extend the result to factorizations of elements of normed
arithmetic semigroups satisfying certain growth conditions, for which the
limiting Poisson-Dirichlet process need not have $\theta =1$. We also establish
Poisson-Dirichlet limits, with $\theta \ne 1$, for ordinary integers
conditional on the number of prime factors deviating from the usual value $\log
\log n$.
  At the core of our argument is a purely probabilistic lemma giving a new
criterion for convergence in distribution to a Poisson-Dirichlet process, from
which the number-theoretic applications follow as straightforward corollaries.
The lemma uses ingredients similar to those employed by Donnelly and Grimmett,
but reorganized so as to allow subsequent number theory input to be processed
as rapidly as possible.
  A by-product of this work is a new characterization of Poisson-Dirichlet
processes in terms of multi-intensities.


title:
Poisson--Dirichlet Limit Theorems in Combinatorial Applications via
  Multi-Intensities

abstract:
  We present new, exceptionally efficient proofs of Poisson--Dirichlet limit
theorems for the scaled sizes of irreducible components of random elements in
the classic combinatorial contexts of arbitrary assemblies, multisets, and
selections, when the components generating functions satisfy certain standard
hypotheses. The proofs exploit a new criterion for Poisson--Dirichlet limits,
originally designed for rapid proofs of Billingsley's theorem on the scaled
sizes of log prime factors of random integers (and some new generalizations).
  Unexpectedly, the technique applies in the present combinatorial setting as
well, giving, perhaps, a long sought-after unifying point of view. The proofs
depend also on formulas of Arratia and Tavar{\'e} for the mixed moments of
counts of components of various sizes, as well as formulas of Flajolet and
Soria for the asymptotics of generating function coefficients.


title: Dynamics of hyperbolic iwips

abstract:
  We present two proofs of the fact, originally due to Reiner Martin, that any
fully irreducible hyperbolic element of $Out(F_N)$ acts on the projectivized
space of geodesic currents $\mathbb{P}Curr(F_N)$ with uniform north-south
dynamics. The first proof, using purely train-track methods, provides an
elaborated and corrected version of Reiner Martin's original approach. The
second proof uses the geometric intersection form of Kapovich and Lustig and
relies on unique ergodicity results from symbolic dynamics.


title: The Continuity of Images by Transmission Imaging Revisited

abstract:
  Transmission imaging, as an important imaging technique widely used in
astronomy, medical diagnosis, and biology science, has been shown in [49] quite
different from reflection imaging used in our everyday life. Understanding the
structures of images (the prior information) is important for designing,
testing, and choosing image processing methods, and good image processing
methods are helpful for further uses of the image data, e.g., increasing the
accuracy of the object reconstruction methods in transmission imaging
applications. In reflection imaging, the images are usually modeled as
discontinuous functions and even piecewise constant functions. In transmission
imaging, it was shown very recently in [49] that almost all images are
continuous functions. However, the author in [49] considered only the case of
parallel beam geometry and used some too strong assumptions in the proof, which
exclude some common cases such as cylindrical objects. In this paper, we
consider more general beam geometries and simplify the assumptions by using
totally different techniques. In particular, we will prove that almost all
images in transmission imaging with both parallel and divergent beam geometries
(two most typical beam geometries) are continuous functions, under much weaker
assumptions than those in [49], which admit almost all practical cases.
Besides, taking into accounts our analysis, we compare two image processing
methods for Poisson noise (which is the most significant noise in transmission
imaging) removal. Numerical experiments will be provided to demonstrate our
analysis.


title: Price Competition in Online Combinatorial Markets

abstract:
  We consider a single buyer with a combinatorial preference that would like to
purchase related products and services from different vendors, where each
vendor supplies exactly one product. We study the general case where subsets of
products can be substitutes as well as complementary and analyze the game that
is induced on the vendors, where a vendor's strategy is the price that he asks
for his product. This model generalizes both Bertrand competition (where
vendors are perfect substitutes) and Nash bargaining (where they are perfect
complements), and captures a wide variety of scenarios that can appear in
complex crowd sourcing or in automatic pricing of related products.
  We study the equilibria of such games and show that a pure efficient
equilibrium always exists. In the case of submodular buyer preferences we fully
characterize the set of pure Nash equilibria, essentially showing uniqueness.
For the even more restricted "substitutes" buyer preferences we also prove
uniqueness over {\em mixed} equilibria. Finally we begin the exploration of
natural generalizations of our setting such as when services have costs, when
there are multiple buyers or uncertainty about the the buyer's valuation, and
when a single vendor supplies multiple products.


title:
Beyond One-Step-Ahead Forecasting: Evaluation of Alternative
  Multi-Step-Ahead Forecasting Models for Crude Oil Prices

abstract:
  An accurate prediction of crude oil prices over long future horizons is
challenging and of great interest to governments, enterprises, and investors.
This paper proposes a revised hybrid model built upon empirical mode
decomposition (EMD) based on the feed-forward neural network (FNN) modeling
framework incorporating the slope-based method (SBM), which is capable of
capturing the complex dynamic of crude oil prices. Three commonly used
multi-step-ahead prediction strategies proposed in the literature, including
iterated strategy, direct strategy, and MIMO (multiple-input multiple-output)
strategy, are examined and compared, and practical considerations for the
selection of a prediction strategy for multi-step-ahead forecasting relating to
crude oil prices are identified. The weekly data from the WTI (West Texas
Intermediate) crude oil spot price are used to compare the performance of the
alternative models under the EMD-SBM-FNN modeling framework with selected
counterparts. The quantitative and comprehensive assessments are performed on
the basis of prediction accuracy and computational cost. The results obtained
in this study indicate that the proposed EMD-SBM-FNN model using the MIMO
strategy is the best in terms of prediction accuracy with accredited
computational load.


title:
From the Biot-Savart Law to Ampere's Magnetic Circuital Law via
  Synthetic Differential Geometry

abstract:
  It is well known in classical electrodynamics that the magnetic field given
by a current loop and the electric field caused by the corresponding dipoles in
sheets are very similar, as far as we are far away from the loop, which enables
us to deduce Ampere's magnetic circuital law from the Biot-Savart law easily.
The principal objective in this paper is to show that synthetic differential
geometry, in which nilpotent infinitesimals are in abundance, furnishes out a
natural framework for the exquisite formulation and its demonstration. This
similitude in heaven enables us to transit from the Biot-Savart law to Ampere's
magnetic circuital law like a shot on earth.


title:
A test of the millisecond magnetar central engine model of GRBs with
  Swift data

abstract:
  A rapidly spinning, strongly magnetized neutron star (magnetar) has been
proposed as one possible candidate of the central engine of gamma-ray bursts
(GRBs). We systematically analyze the Swift/XRT light curves of long GRBs
detected before 2013 August, and characterize them into four categories based
on how likely they may harbor a magnetar central engine: Gold, Silver,
Aluminum, and Non-magnetar. We also independently analyze the data of short
GRBs with a putative magnetar central engine. We then perform a statistical
study of various properties of the magnetar samples and the non-magnetar
sample, and investigate whether the data are consistent with the hypothesis
that there exist two types of central engines. By deriving the physical
parameters of the putative magnetars, we find that the observations of the Gold
and Silver samples are generally consistent with the predictions of the
magnetar model. For a reasonable beaming factor for long GRBs, the derived
magnetar surface magnetic field $B_p$ and initial spin period $P_0$ fall into
the reasonable range. Magnetar winds in short GRBs, on the other hand, are
consistent with being isotropic. No GRB in the magnetar sample has a
beam-corrected total energy exceeding the maximum energy budget defined by the
initial spin energy of the magnetar, while some non-magnetar GRBs do violate
such a limit. With beaming correction, on average the non-magnetar sample is
more energetic and luminous than the magnetar samples. Our analysis hints that
millisecond magnetars are likely operating in a good fraction, but probably not
all, GRBs.


title: Chemical abundance analysis of the old, rich open cluster Trumpler 20

abstract:
  Trumpler 20 is an open cluster located at low Galactic longitude, just beyond
the great Carina spiral arm, and whose metallicity and fundamental parameters
were very poorly known until now. As it is most likely a rare example of an
old, rich open cluster -- possibly a twin of NGC 7789 -- it is useful to
characterize it. To this end, we determine here the abundance of several
elements and their ratios in a sample of stars in the clump of Trumpler 20. The
primary goal is to measure Trumpler 20 metallicity, so far very poorly
constrained, and revise the cluster's fundamental parameters. We present
high-resolution spectroscopy of eight clump stars. Based on their radial
velocities, we identify six bona fide cluster members, and for five of them
(the sixth being a fast rotator) we perform a detailed abundance analysis.
  We find that Trumpler 20 is slightly more metal-rich than the Sun, having
[Fe/H]=+0.09$\pm$0.10. The abundance ratios of alpha-elements are generally
solar. In line with recent studies of clusters as old as Trumpler 20, Ba is
overabundant compared to the Sun. Our analysis of the iron-peak elements (Cr
and Ni) does not reveal anything anomalous. Based on these results, we
re-estimate the cluster age to be 1.5$^{+0.2}_{-0.1}$ Gyr. Its distance to the
Galactic centre turns out to be 7.3 kpc. With this distance and metallicity,
Trumpler 20 fits fairly well in the metallicity gradient for the galactic inner
disc. With this new study, the characterization of Trumpler~20 is now on much
more solid ground. Further studies should focus on the estimate of the binary
fraction and on its main sequence membership.


title: Nonlinear Elasticity of Flow-Stabilized Solids

abstract:
  Thermal fluctuations, geometric exclusion, and external driving all govern
the mechanical response of dense particulate suspensions. Here, we measure the
stress-strain response of quasi-two-dimensional flow-stabilized microsphere
heaps in a regime in which all three effects are present using a microfluidic
device. We observe that the elastic modulus and the mean interparticle
separation of the heaps are tunable via the confining stress provided by the
fluid flow. Furthermore, the measured stress-strain curves exhibit a universal
nonlinear shape which can be predicted from a thermal van der Waals equation of
state with excluded volume. This analysis indicates that many-body interactions
contribute a significant fraction of the stress supported by the heap.


title:
Four-ball genus bounds and a refinement of the Ozsvath-Szabo
  tau-invariant

abstract:
  Based on work of Rasmussen, we construct a concordance invariant associated
to the knot Floer complex, and exhibit examples in which this invariant gives
arbitrarily better bounds on the 4-ball genus than the Ozsvath-Szabo tau
invariant.


title:
Internal energy density of the critical three-state Potts model on the
  kagome lattice

abstract:
  It has been conjectured that the internal energy density of the Potts model
on a semi-infinite strip with a width $L$ does not have any finite-size
corrections at the critical point $K=K_c$. By factorizing the transfer matrix
for the kagome lattice with larger widths, we have found that this conjecture
is not correct in that the internal energy density slightly varies with $L$ at
the critical point. From this size dependence of the internal energy density,
we obtain an upper bound as $K_c < 1.0565615$, which is close to a recent
estimate $K_c^{\rm JS} = 1.0565600(7)$ by Jacobsen and Scullard
[arXiv:1204.0622]. We also obtain a lower bound as $K_c > 1.0560$ by
calculating the correlation length along the strips.


title: Commutator subgroup of the Hecke group $G_5$ is not congruence

abstract:
  We prove that the power subgroup $G_5^5$ and the commutator subgroup $G_5'$
of the Hecke group $G_5$ are not congruence.


title: Universal statistics of the knockout tournament

abstract:
  We study statistics of the knockout tournament, where only the winner of a
fixture progresses to the next. We assign a real number called competitiveness
to each contestant and find that the resulting distribution of prize money
follows a power law with an exponent close to unity if the competitiveness is a
stable quantity and a decisive factor to win a match. Otherwise, the
distribution is found narrow. The existing observation of power law
distributions in various kinds of real sports tournaments therefore suggests
that the rules of those games are constructed in such a way that it is possible
to understand the games in terms of the contestants' inherent characteristics
of competitiveness.


title: Surface pole bracket polynomials of virtual knots and twisted knots

abstract:
  Dye and Kauffman defined surface bracket polynomials for virtual links by use
of surface states, and found a relationship between the surface states and the
minimal genus of a surface in which a virtual link diagram is realized. They
and Miyazawa independently defined a multivariable polynomial invariant of
virtual links. This invariant is deeply related to the surface states. In this
paper, we introduce the notion of surface pole bracket polynomials for link
diagrams in closed surfaces, as a generalization of surface bracket polynomials
by Dye and Kauffman. The polynomials induce the invariant of twisted links
defined by the author before as a generalization of Dye, Kauffman and
Miyazawa's polynomial invariant. Furthermore we discuss a relationship between
curves in surface pole states and variables of the polynomial invariant.


title: Forking and dividing in Henson graphs

abstract:
  For $n\geq 3$, define $T_n$ to be the theory of the generic $K_n$-free graph,
where $K_n$ is the complete graph on $n$ vertices. We prove a graph theoretic
characterization of dividing in $T_n$, and use it to show that forking and
dividing are the same for complete types. We then give an example of a forking
and nondividing formula. Altogether, $T_n$ provides a counterexample to a
recent question of Chernikov and Kaplan.


title: Generalized stretched ideals and Sally Conjecture

abstract:
  We introduce the concept of $j$-stretched ideals in a Noetherian local ring.
This notion generalizes to arbitrary ideals the classical notion of stretched
$\mathfrak{m}$-primary ideals of Sally and Rossi-Valla, as well as the concept
of ideals of minimal and almost minimal $j$-multiplicity introduced by
Polini-Xie. One of our main theorems states that, for a $j$-stretched ideal,
the associated graded ring is Cohen-Macaulay if and only if two classical
invariants of the ideal, the reduction number and the index of nilpotency, are
equal. Our second main theorem, presenting numerical conditions which ensure
the almost Cohen-Macaulayness of the associated graded ring of a $j$-stretched
ideal, provides a generalized version of Sally's conjecture. This work, which
also holds for modules, unifies the approaches of Rossi-Valla and Polini-Xie
and generalizes simultaneously results on the Cohen-Macaulayness or almost
Cohen-Macaulayness of the associated graded module by several authors,
including Sally, Rossi-Valla, Wang, Elias, Corso-Polini-Vaz Pinto, Huckaba,
Marley and Polini-Xie.


title:
From building blocks of proteins to drugs: A quantum chemical study on
  structure-property relationships of phenylalanine, tyrosine and dopa

abstract:
  Density functional theory and ab initio methods have been employed to address
the impacts of hydroxyl (OH) group substitutions on the physico-chemical
properties of levodopa (or L-dopa) against the natural amino acids,
phenylalanine and tyrosine. L-dopa, which is an important therapeutic drug for
Parkinson's disease, shares structural homology with the amino acids, whose
structures differ only by OH substitutions in their phenyl side chains. It is
revealed that the backbone geometries of the aromatic molecules do not show
apparent OH-dependent differences; however, their other molecular-level
properties, such as molecular dipole moment, electronic properties and
aromaticity, change significantly. The core binding energy spectra indicate
that the atom sites that undergo modifications exhibit large energy shifts, so
as to accommodate the changes in the intra-molecular chemical environment of
the molecules. The binding energies of the modified C 1s sites in the molecules
shift as much as 1.8 eV, whereas the electronic changes in their O 1s spectra
happen in the higher energy region (ca. 536 eV). The valence spectra provide
enhanced insights on the reactivity and chemical properties of the aromatic
molecules. The impacts of OH moieties on the valence spectra are predominantly
focussed in the energy band<16 eV, where the frontier molecular orbitals
display much reorganization and energy shifts from the amino acids to L-dopa.
Of the three molecules, L-dopa also has the least HOMO-LUMO energy gap, which
can readily explain its proactivity as a drug compound. Furthermore, the
nuclear independent chemical shift calculations suggest that L-dopa also has
more aromaticity features than those of the amino acids. The OH groups,
therefore, play a more prominent role in shaping the physico-chemical
properties of L-dopa, which significantly improve its drug potency.


title: The security deposit for finitely repeated Prisoner's dilemma

abstract:
  Under the assumption of complete rationality, Nash equilibrium is the only
reasonable strategy (set) of the finitely repeated prisoner's dilemma. In fact,
some strategies only slightly deviate from the so-called rationality, and the
corresponding payoff may much better than that of Nash equilibrium. This
article points out, even under the rational assumptions, the players have
reason to seek a mutually beneficial agreement (Pareto dominated compare to
Nash equilibrium) and a weak and optional constraints, so that the agreement
can be successfully implemented. If the constraint does not harm the interests
of the participants, or the adversely affects of the constraint are negligible,
then the finitely repeated prisoner's dilemma becomes a bargaining problem
issues on the strategy sequences and the problem to seek the constraints. The
quantification of the constraints, the so-called security deposit in this
paper, is nearly a concept of distance from an agreement (a strategy set) to
the complete rationality.


title: Quantum curves

abstract:
  One says that a pair (P,Q) of ordinary differential operators specify a
quantum curve if [P,Q]=const. If a pair of difference operators (K,L) obey the
relation KL=const LK we say that they specify a discrete quantum curve. This
terminology is prompted by well known results about commuting differential and
difference operators, relating pairs of such operators with pairs of
meromorphic functions on algebraic curves obeying some conditions. The goal of
this paper is to study the moduli spaces of quantum curves. We will show how to
quantize a pair of commuting differential or difference operators (i.e. to
construct the corresponding quantum curve or discrete quantum curve). The
KP-hierarchy acts on the moduli space of quantum curves; we prove that
similarly the discrete KP-hierarchy acts on the moduli space of discrete
quantum curves.


title:
Optimal quantum control of multi-mode couplings between trapped ion
  qubits for scalable entanglement

abstract:
  We demonstrate high fidelity entangling quantum gates within a chain of five
trapped ion qubits by optimally shaping optical fields that couple to multiple
collective modes of motion. We individually address qubits with segmented
optical pulses to construct multipartite entangled states in a programmable
way. This approach enables both high fidelity and fast quantum gates that can
be scaled to larger qubit registers for quantum computation and simulation.


title: The abstract Hodge-Dirac operator and its stable discretization

abstract:
  This paper adapts the techniques of finite element exterior calculus to study
and discretize the abstract Hodge-Dirac operator, which is a square root of the
abstract Hodge-Laplace operator considered by Arnold, Falk, and Winther [Bull.
Amer. Math. Soc. 47 (2010), 281-354]. Dirac-type operators are central to the
field of Clifford analysis, where recently there has been considerable interest
in their discretization. We prove a priori stability and convergence estimates,
and show that several of the results in finite element exterior calculus can be
recovered as corollaries of these new estimates.


title:
Discrete-Time Output-Feedback Robust Repetitive Control for a Class of
  Nonlinear Systems by Additive State Decomposition

abstract:
  The discrete-time robust repetitive control (RC, or repetitive controller,
also designated RC) problem for nonlinear systems is both challenging and
practical. This paper proposes a discrete-time output-feedback RC design for a
class of systems subject to measurable nonlinearities to track reference
robustly with respect to the period variation. The design relies on additive
state decomposition, by which the output-feedback RC problem is decomposed into
an output-feedback RC problem for a linear time-invariant system and a
state-feedback stabilization problem for a nonlinear system. Thanks to the
decomposition, existing controller design methods in both the frequency domain
and time domain can be employed to make the robustness and discretization for a
nonlinear system tractable. To demonstrate the effectiveness, an illustrative
example is given.


title: Density Functional Theory for Plasmon-Assisted Superconductivity

abstract:
  We review the recent progress in the density functional theory for
superconductors (SCDFT). Motivated by the long-studied plasmon mechanism of
superconductivity, we have constructed an exchange-correlation kernel entering
the SCDFT gap equation which includes the plasmon effect. For the case of
lithium under high pressures, we show that the plasmon effect substantially
enhances the transition temperature (Tc) by cooperating with the conventional
phonon mechanism and results in a better agreement between the theoretical and
experimentally observed Tc. Our present formalism will be a first step to
density functional theory for unconventional superconductors.


title:
General multicomponent Yajima-Oikawa system: Painlev\'e analysis,
  soliton solutions, and energy-sharing collisions

abstract:
  We consider the multicomponent Yajima-Oikawa (YO) system and show that the
two-component YO system can be derived in a physical setting of three-coupled
nonlinear Schr\"odinger (3-CNLS) type system by the asymptotic reduction
method. The derivation is further generalized to multicomponent case. This set
of equations describes the dynamics of nonlinear resonant interaction between
one-dimensional long-wave and multiple short-waves. The Painlev\'e analysis of
the general multicomponent YO system shows that the underlying set of evolution
equations is integrable for arbitrary nonlinearity coefficients which will
result in three different sets of equations corresponding to positive, negative
and mixed nonlinearity coefficients. We obtain general bright $N$-soliton
solution of multicomponent YO system in the Gram determinant form by using
Hirota's bilinearization method and explicitly analyze the one- and two-soliton
solutions of the multicomponent YO system for the above mentioned three choices
of nonlinearity coefficients. We also point out that the 3-CNLS system admits
special asymptotic solitons of bright, dark, anti-dark and grey types, when the
long-wave--short-wave resonance takes place. The short-wave component solitons
undergo two types of energy sharing collisions. The solitons appearing in the
long-wave component always exhibit elastic collision whereas that of short-wave
components exhibit standard elastic collisions only for specific choice of
parameters. We have also investigated the collision dynamics of asymptotic
solitons in the original 3-CNLS system. For completeness, we explore the
three-soliton interaction and demonstrate the pair-wise nature of collision and
unravel fascinating state restoration property.


title: A New Causal Ideal Internal Dynamics Generator

abstract:
  The design of ideal internal dynamics (IID) generators, namely solving IID,
is a fundamental problem, which is a key step to handle the nonminimum-phase
output tracking problem. In this paper, for a class of unstable matrix
differential equations, a new causal dynamic IID generator is proposed, whose
parameters are partly chosen via H_2/H_inf optimization. Compared with existing
similar generators, it is applicable to matrix differential equations with
singular system matrices and is easily extended to slowly time-varying matrix
differential equations without extra computation.


title:
Propagation and neutrino oscillations in the base of a highly magnetized
  gamma-ray burst fireball flow

abstract:
  Neutrons play an important role in the dynamics of gamma-ray bursts. The
presence of neutrons in the baryon-loaded fireball is expected. If the neutrons
abundance is comparable to that of protons, important features may be observed
such as quasi-thermal multi-GeV neutrinos in coincidence with a subphotospheric
$\gamma$-ray emission, nucleosynthesis at later times and rebrightening of the
afterglow emission. Additionally, thermal MeV neutrinos are created by
electron-positron annihilation, electron (positron) capture on protons
(neutrons) and nucleonic bremsstrahlung. Although MeV neutrinos are difficult
to detect, quasi-thermal GeV neutrinos are expected in km$^3$ detectors and/or
DeepCore+IceCube. In this paper, we show that neutrino oscillations have
outstanding implications for the dynamics of the fireball evolution and also
that they can be detected through their flavor ratio on Earth. For that we
derive the resonance and charged-neutrality conditions as well as the neutrino
self-energy and effective potential up to order $m_W^{-4}$ at strong, moderate
and weak magnetic field approximation to constrain the dynamics of the
fireball. We found important implications: i) resonant oscillations are
suppressed for high baryon densities as well as neutrons abundance larger than
that of protons and ii) the effect of magnetic field is to decrease the
proton-to-neutron ratio aside from the number of multi-GeV neutrinos expected
in DeepCore detector. Also we estimate the GeV neutrino flavor ratios along the
jet and on Earth.


title: HATS-5b: A Transiting hot-Saturn from the HATSouth Survey

abstract:
  We report the discovery of HATS-5b, a transiting hot-Saturn orbiting a G type
star, by the HAT-South survey. HATS-5b has a mass of Mp=0.24 Mj, radius of
Rp=0.91 Rj, and transits its host star with a period of P=4.7634d. The radius
of HATS-5b is consistent with both theoretical and empirical models. The host
star has a V band magnitude of 12.6, mass of 0.94 Msun, and radius of 0.87
Rsun. The relatively high scale height of HATS-5b, and the bright,
photometrically quiet host star, make this planet a favourable target for
future transmission spectroscopy follow-up observations. We reexamine the
correlations in radius, equilibrium temperature, and metallicity of the
close-in gas-giants, and find hot Jupiter-mass planets to exhibit the strongest
dependence between radius and equilibrium temperature. We find no significant
dependence in radius and metallicity for the close-in gas-giant population.


title:
Quotient cohomology of certain 1- and 2-dimensional substitution tiling
  spaces

abstract:
  The quotient cohomology of tiling spaces is a topological invariant that
relates a tiling space to one of its factors, viewed as topological dynamical
systems. In particular, it is a relative version of the tiling cohomology that
distinguishes factors of tiling spaces. In this work, the quotient cohomologies
within certain families of substitution tiling spaces in 1 and 2 dimensions are
determined. Specifically, the quotient cohomologies for the family of the
generalised Thue-Morse sequences and generalised chair tilings are presented.


title: Detecting CMB modulations and non-Gaussianities from power multipoles

abstract:
  By decomposing the CMB temperature fluctuations \emph{squared} into spherical
harmonics, we can define the \emph{CMB power multipoles} as the fundamental
observables to quantify any generic modulations in the CMB. This allows for
simple direct measurements for the CMB modulations, and also indirect
measurements for the CMB trispectrum, which fully determines the CMB
modulations in a statistically isotropic universe. The CMB power multipoles can
reach the theoretical accuracies higher than the current constraints from
Planck observations. The theoretical accuracy for the dipole modulation,
$A\sim0.0015$, receives $\sim 10$ times improvement; higher $l$ modulations
have even higher accuracies. This calls for practical observational studies of
its possible improvements on the CMB modulation and non-Gaussianity
constraints.


title: Green tea induced gold nanostar synthesis mediated by Ag(I) ions

abstract:
  We report a synthesis of tea components conjugated gold nanostars (AuNSs)
with strong near infrared absorption by reducing an aqueous solution of
chloroauric acid trihydrate via green tea in association with Ag(I) ions. Green
tea acts as a reducing agent by providing electrons for the gold (III)
reduction as well as a stabilizing agent by conjugating some of its components
on the surfaces of AuNSs. Moreover, the Ag(I) ions play an important role in
mediating the branched growth of the resultant AuNSs by inducing anisotropic
growth on the surfaces of initially formed spherical gold nanoparticles.


title:
Strongly fluctuating fermionic superfluid in attractive \pi-flux Hubbard
  model

abstract:
  Ultracold atoms in optical lattice provides a platform to realize the
superfluid (SF) state, a quantum order with paired charge-neutral fermions. In
this paper, we studied SF state in the twodimensional attractive Hubbard model
with pi-flux on each plaquette. The SF state in the pi-flux lattice model
suffers very strong quantum fluctuations and the ground state becomes a
possible quantum phase liquid state. In this phase, there exists the Cooper
pairing together with a finite energy gap for the atoms, but no long range SF
phase coherence exists at zero temperature. In addition, we discussed the
properties of the SF vortices.


title: Multiple resource demands and viability in multiplex networks

abstract:
  Many complex systems demand manifold resources to be supplied from distinct
channels to function properly, i.e, water, gas, and electricity for a city.
Here, we study a model for viability of such systems demanding more than one
type of vital resources produced and distributed by resource nodes in multiplex
networks. We found a rich variety of behaviors such as discontinuity,
bistability, and hysteresis in the fraction of viable nodes with respect to the
density of networks and the fraction of resource nodes. Our result suggests
that viability in multiplex networks is not only exposed to the risk of abrupt
collapse but also suffers excessive complication in recovery.


title: Log del Pezzo surfaces with large volumes

abstract:
  We classify all of the log del Pezzo surfaces $S$ of index $a$ such that the
volume $(-K_S^2)$ is larger than or equal to $2a$.


title:
A singular integral approach to the maximal L^p regularity of parabolic
  equations

abstract:
  Here we describe a simple and fundamental approach to the maximal L^p
regularity of parabolic equations, which only uses the concept of singular
integrals of Volterra type. Knowledge of analytic semigroups, R-boundedness or
H^\infty-functional calculus are not required.


title:
An Approximate Dynamic Programming Algorithm for Monotone Value
  Functions

abstract:
  Many sequential decision problems can be formulated as Markov Decision
Processes (MDPs) where the optimal value function (or cost-to-go function) can
be shown to satisfy a monotone structure in some or all of its dimensions. When
the state space becomes large, traditional techniques, such as the backward
dynamic programming algorithm (i.e., backward induction or value iteration),
may no longer be effective in finding a solution within a reasonable time
frame, and thus we are forced to consider other approaches, such as approximate
dynamic programming (ADP). We propose a provably convergent ADP algorithm
called Monotone-ADP that exploits the monotonicity of the value functions in
order to increase the rate of convergence. In this paper, we describe a general
finite-horizon problem setting where the optimal value function is monotone,
present a convergence proof for Monotone-ADP under various technical
assumptions, and show numerical results for three application domains: optimal
stopping, energy storage/allocation, and glycemic control for diabetes
patients. The empirical results indicate that by taking advantage of
monotonicity, we can attain high quality solutions within a relatively small
number of iterations, using up to two orders of magnitude less computation than
is needed to compute the optimal solution exactly.


title:
Laser-induced instabilities in liquid crystal cells with a
  photosensitive substrate

abstract:
  Liquid crystal layers sandwiched between a reference plate and a
photosensitive substrate were investigated. We focused on the reverse geometry,
where the cell was illuminated by a laser beam from the reference side. In
planar cells instabilities occurred, static and dynamic ones, depending on the
angle between the laser polarization and the director orientation on the
reference plate. In cells where the molecules were aligned along the normal of
the reference plate, dynamic pattern was observed at all angles of
polarization. A simple model based on a photo-induced surface torque gives
account of the findings. Light scattering studies revealed some basic
properties of the instabilities.


title: Light-induced instabilities in photo-oriented liquid crystal cells

abstract:
  In a planar liquid crystal sample sandwiched between a photosensitive and a
reference plate instabilities occurred, when the cell was illuminated from the
reference side. The instabilities were induced both by polarized white light
source and monochromatic laser beams. Static and dynamic regimes were found;
for laser irradiation dynamic instability was found only in a range of
polarization directions. A model, developed for monochromatic excitation,
predicts that at certain thicknesses dynamic instability is forbidden.
Experiments on a wedge-like cell confirmed this conclusion.


title: Experimental study of the two-body spin-orbit force

abstract:
  Energies and spectroscopic factors of the first $7/2^-$, $3/2^-$, $1/2^-$ and
$5/2^-$ states in the $^{35}$Si$_{21}$ nucleus were determined by means of the
(d,p) transfer reaction in inverse kinematics at GANIL using the MUST2 and
EXOGAM detectors. By comparing the spectroscopic information on the $^{35}$Si
and $^{37}$S isotones, a reduction of the $p_{3/2} - p_{1/2}$ spin-orbit
splitting by about 25% is proposed, while the $f_{7/2} -f_{5/2}$ spin-orbit
splitting seems to remain constant. These features, derived after having
unfolded nuclear correlations using shell model calculations, have been
attributed to the properties of the 2-body spin-orbit interaction, the
amplitude of which is derived for the first time in an atomic nucleus. The
present results, remarkably well reproduced by using several realistic
nucleon-nucleon forces, provide a unique touchstone for the modeling of the
spin-orbit interaction in atomic nuclei.


title: Generalized universal series

abstract:
  We unify the recently developed abstract theories of universal series and
extended universal series to include sums of the form $\sum_{k=0}^n a_k
x_{n,k}$ for given sequences of vectors $(x_{n,k})_{n\geq k\geq 0}$ in a
topological vector space X. The algebraic and topological genericity as well as
the spaceability are discussed. Then we provide various examples of such
generalized universal series which do not proceed from the classical theory. In
particular, we build universal series involving Bernstein's polynomials, we
obtain a universal series version of MacLane's Theorem, and we extend a result
of Tsirivas concerning universal Taylor series on simply connected domains,
exploiting Bernstein- Walsh quantitative approximation theorem.


title: Higher bottom and bottom-strange mesons

abstract:
  Motivated by the recent observation of the orbital excitation $B(5970)$ by
CDF collaboration, we have performed a systematical study of the mass spectrum
and strong decay patterns of the higher $B$ and $B_s$ mesons. Hopefully the
present investigation may provide valuable clues to further experimental
exploration of these intriguing excited heavy mesons.


title: The Merrifield-Simmons conjecture also holds for parity graphs

abstract:
  The Merrifield-Simmons conjectures states a relation between the distance of
vertices in a simple graph $G$ and the number of independent sets, denoted as
$\sigma(G)$, in vertex-deleted subgraphs. Namely, that the sign of the term
$\sigma(G_{-u}) \cdot \sigma(G_{-v}) - \sigma(G) \cdot \sigma(G_{-u-v})$ only
depends on the parity of the distance of $u$ and $v$ in $G$. We prove this
statement in the case of parity graphs and give some evidence that this result
may not be further generalized to other classes of graphs.


title:
Triggering jet-driven explosions of core-collapse supernovae by
  accretion from convective regions

abstract:
  We find that convective regions of collapsing massive stellar cores possess
sufficient stochastic angular momentum to form intermittent accretion disks
around the newly born neutron star (NS) or black hole (BH), as required by the
jittering-jets model for core-collapse supernova (CCSN) explosions. To reach
this conclusion we derive an approximate expression for stochastic specific
angular momentum in convection layers of stars, and using the mixing-length
theory apply it to four stellar models at core-collapse epoch. In all models,
evolved using the stellar evolution code MESA, the convective helium layer has
sufficient angular momentum to form an accretion disk. The mass available for
disk formation around the NS or BH is 0.1-1.2Mo; stochastic accretion of this
mass can form intermittent accretion disks that launch jets powerful enough to
explode the star according to the jittering-jets model. Our results imply that
even if no explosion occurs after accretion of the inner ~2-5Mo of the core
onto the NS or BH (the mass depends on the stellar model), accretion of outer
layers of the core will eventually lead to an energetic supernova explosion.


title: Primary Cyclic Matrices in Irreducible Matrix Subalgebras

abstract:
  Primary Cyclic matrices were used (but not named) by Holt and Rees in their
version of Parker's MEAT-AXE algorithm to test irreducibility of finite matrix
groups and algebras. They are matrices $X$ with at least one cyclic component
in the primary decomposition of the underlying vector space as an $X$-module.
Let $\operatorname{M}(c,q^b)$ be an irreducible subalgebra of
$\operatorname{M}(n,q)$, where $n=bc >c$. We prove a generalisation of the
Kung-Stong Cycle Index, and use it to obtain a lower bound for the proportion
of primary cyclic matrices in $\operatorname{M}(c,q^b)$. This extends work of
Glasby and the second author on the case $b=1$.


title: Hawking radiation from rotating AdS black holes in conformal gravity

abstract:
  We extend to study Hawking radiation via tunneling in conformal gravity. We
adopt Parikh-Wilczek's semi-classical tunneling method and the method of
complex-path integral to investigate Hawking radiation from new rotating AdS
black holes in conformal gravity. In this paper, the research on Hawking
radiation from the rotating black holes is done in a general system, not
limited in dragging coordinate systems any longer. Moreover, there existed some
shortcomings in the previous derivation of geodesic equations. Different from
the massless case, they used a different approach to derive the geodesic
equation of the massive particles. Even the treatment was inconsistent with the
variation principle of action. To remedy the shortcoming, we improve treatment
to deduce the geodesic equations of massive and massless particles in a unified
and self-consistent way. In addition, we also recover the Hawking temperature
resorting to the complex-path integral method.


title:
Single photons in an imperfect array of beam-splitters: Interplay
  between percolation, backscattering and transient localization

abstract:
  Photons in optical networks can be used in multi-path interferometry and
various quantum information processing and communication protocols. Large
networks, however, are often not free from defects, which can appear randomly
between the lattice sites and are caused either by production faults or
deliberate introduction. In this work we present numerical simulations of the
behaviour of a single photon injected into a regular lattice of beam-splitting
components in the presence of defects that cause perfect backward reflections.
We find that the photon dynamics is quickly dominated by the backscattering
processes, and a small fraction of reflectors in the paths of the
beam-splitting array strongly affects the percolation probability of the
photon. We carefully examine such systems and show an interesting interplay
between the probabilities of percolation, backscattering and temporary
localization. We also discuss the sensitivity of these probabilities to lattice
size, timescale, injection point, fraction of reflectors and boundary
conditions.


title:
X-Ray Afterglow Plateaus of Long Gamma-Ray Bursts: Further Evidence for
  Millisecond Magnetars

abstract:
  Many long-duration gamma-ray bursts (GRBs) were observed by {\it Swift}/XRT
to have plateaus in their X-ray afterglow light curves. This plateau phase has
been argued to be evidence for long-lasting activity of magnetar
(ultra-strongly magnetized neutron stars) central engines. However, the
emission efficiency of such magnetars in X-rays is still unknown. Here we
collect 24 long GRB X-ray afterglows showing plateaus followed by steep decays.
We extend the well-known relationship between the X-ray luminosity
${L_{\mathrm{X}}}$ and spin-down luminosity $L_{\mathrm{sd}}$ of pulsars to
magnetar central engines, and find that the initial rotation period $P_{0}$
ranges from 1 ms to 10 ms and that the dipole magnetic field $B$ is centered
around $10^{15}$ G. These constraints not only favor the suggestion that the
central engines of some long GRBs are very likely to be rapidly rotating
magnetars but also indicate that the magnetar plateau emission efficiency in
X-rays is close to 100%.


title: Optimal Bounds for Integrals with Respect to Copulas and Applications

abstract:
  We consider the integration of two-dimensional, piecewise constant functions
with respect to copulas. By drawing a connection to linear assignment problems,
we can give optimal upper and lower bounds for such integrals and construct the
copulas for which these bounds are attained. Furthermore, we show how our
approach can be extended in order to approximate extremal values in very
general situations. Finally, we apply our approximation technique to problems
in financial mathematics and uniform distribution theory, such as the
model-independent pricing of first-to-default swaps.


title: On multichannel film dosimetry with channel-independent perturbations

abstract:
  Purpose: Different multichannel methods for film dosimetry have been proposed
in the literature. Two of them are the weighted mean method and the method put
forth by Micke et al and Mayer et al. The purpose of this work was to compare
their results and to develop a generalized channel-independent perturbations
framework in which both methods enter as special cases.
  Methods: Four models of channel-independent perturbations were compared:
weighted mean, Micke-Mayer method, uniform distribution and truncated normal
distribution. A closed-form formula to calculate film doses and the associated
Type B uncertainty for all four models was deduced. To evaluate the models,
film dose distributions were compared with planned and measured dose
distributions. At the same time, several elements of the dosimetry process were
compared: film type EBT2 versus EBT3, different waiting-time windows,
reflection mode versus transmission mode scanning, and planned versus measured
dose distribution for film calibration and for gamma-index analysis. The
methods and the models described in this study are publicly accessible through
IRISEU. Alpha 1.1 (http://www.iriseu.com). IRISEU. is a cloud computing web
application for calibration and dosimetry of radiochromic films.
  Results: The truncated normal distribution model provided the best agreement
between film and reference doses, both for calibration and gamma-index
verification, and proved itself superior to both the weighted mean model, which
neglects correlations between the channels, and the Micke-Mayer model, whose
accuracy depends on the properties of the sensitometric curves.
  Conclusions: The truncated normal distribution model of channel-independent
perturbations was found superior to the other three models under comparison and
we propose its use for multichannel dosimetry.


title: Fundamental Limits of Detection in the Far Infrared

abstract:
  We study the fundamental limits of detection for astrophysical observations
in the far infrared. Understanding these fundamental limits is critical to the
planning and analysis of experiments in this region. We specifically
characterize the difficulties associated with observing in the 0.1-10 THz
(30-3000 \mu m) regime including extraterrestrial, atmospheric, and optical
emission. We present signal, noise, and integration time models for selected
terrestrial, aircraft, balloon, and space missions. While ground based
telescopes offer the great advantage of aperture size, and hence angular
resolution, they suffer from the relatively low transmission and high radiance
of the atmosphere, particularly for wavelengths less than 500 \mu m. Space
telescopes are the inverse; they are limited by a small aperture, while an
airborne telescope is constrained by both. Balloon-borne telescopes provide an
option over much of the band. A quantitative understanding of this is critical
in comparing the sensitivity of various experiments and in planning the next
generation of missions. As representative sources we use the luminous far-IR
dusty galaxies NGC 958 and Mrk 231, but the same formalism can be applied to
any source. In this paper we focus on continuum emission but a future paper
will focus on line emission.


title: Fast nonparametric clustering of structured time-series

abstract:
  In this publication, we combine two Bayesian non-parametric models: the
Gaussian Process (GP) and the Dirichlet Process (DP). Our innovation in the GP
model is to introduce a variation on the GP prior which enables us to model
structured time-series data, i.e. data containing groups where we wish to model
inter- and intra-group variability. Our innovation in the DP model is an
implementation of a new fast collapsed variational inference procedure which
enables us to optimize our variationala pproximation significantly faster than
standard VB approaches. In a biological time series application we show how our
model better captures salient features of the data, leading to better
consistency with existing biological classifications, while the associated
inference algorithm provides a twofold speed-up over EM-based variational
inference.


title: Loop groups, Clusters, Dimers and Integrable systems

abstract:
  We describe a class of integrable systems on Poisson submanifolds of the
affine Poisson-Lie groups $\widehat{PGL}(N)$, which can be enumerated by
cyclically irreducible elements the co-extended affine Weyl groups
$(\widehat{W}\times \widehat{W})^\sharp$. Their phase spaces admit cluster
coordinates, whereas the integrals of motion are cluster functions. We show,
that this class of integrable systems coincides with the constructed by
Goncharov and Kenyon out of dimer models on a two-dimensional torus and
classified by the Newton polygons. We construct the correspondence between the
Weyl group elements and polygons, demonstrating that each particular integrable
model admits infinitely many realisations on the Poisson-Lie groups. We also
discuss the particular examples, including the relativistic Toda chains and the
Schwartz-Ovsienko-Tabachnikov pentagram map.


title: Algebras with only finitely many subalgebras

abstract:
  Let R be a commutative ring. A not necessarily commutative R-algebra A is
called futile if it has only finitely many R-subalgebras. In this article we
relate the notion of futility to familiar properties of rings and modules. We
do this by first reducing to the case where A is commutative. Then we refine
the description of commutative futile algebras from Dobbs, Picavet and
Picavet-L'hermite.


title:
An algorithm for deciding the number of clusters and validation using
  simulated data with application to exploring crop population structure

abstract:
  A first step in exploring population structure in crop plants and other
organisms is to define the number of subpopulations that exist for a given data
set. The genetic marker data sets being generated have become increasingly
large over time and commonly are of the high-dimension, low sample size (HDLSS)
situation. An algorithm for deciding the number of clusters is proposed, and is
validated on simulated data sets varying in both the level of structure and the
number of clusters covering the range of variation observed empirically. The
algorithm was then tested on six empirical data sets across three small grain
species. The algorithm uses bootstrapping, three methods of clustering, and
defines the optimum number of clusters based on a common criterion, the
Hubert's gamma statistic. Validation on simulated sets coupled with testing on
empirical sets suggests that the algorithm can be used for a wide variety of
genetic data sets.


title: Plates with incompatible prestrain

abstract:
  We study the effective elastic behavior of incompatibly prestrained plates,
where the prestrain is independent of thickness as well as uniform through the
thickness. We model such plates as three-dimensional elastic bodies with a
prescribed pointwise stress-free state characterized by a Riemannian metric $G$
with the above properties, and seek the limiting behavior as the thickness goes
to zero.
  Our results extand the prior analysis in M. Lewicka, M. R. Pakzad ESAIM
Control Optim. Calc. Var. 17 (2011), no. 4. We first establish that the
$\Gamma$-limit is a Kirchhoff type bending. Further, we show that the minimum
energy configuration contains non-trivial Kirchhoff type bending -- i.e., the
scaling of the three-dimensional energy is of the order of the cube of the
plate thickness -- if and only if the Riemann curvatures $R^3_{112}, R^3_{221}$
and $ R_{1212}$ of $G$ do not identically vanish. We demonstrate through
examples, the existence of a new regime where the three above curvatures of $G$
vanish (while the mid-plane of the plate may or may not be flat), but the
limiting configuration still has energy that is of the order of F\"oppl - von
K\'arm\'an plates. Finally, we apply these results to a model of nematic glass,
including a characterization of the condition when the metric is immersible,
for $G=\mbox{Id}_3 +\gamma\vec n\otimes \vec n$ given in terms of the
inhomogeneous unit director field distribution $\vec n\in\mathbb{R}^3$.


title:
Computation of the "Enrichment" of a Value Functions of an Optimization
  Problem on Cumulated Transaction-Costs through a Generalized Lax-Hopf Formula

abstract:
  The Lax-Hopf formula simplifies the value function of an intertemporal
optimization (infinite dimensional) problem associated with a convex
transaction-cost function which depends only on the transactions (velocities)
of a commodity evolution: it states that the value function is equal to the
marginal fonction of a finite dimensional problem with respect to durations and
average ransactions, much simpler to solve. The average velocity of the value
function on a investment temporal window is regarded as an enrichment,
proportional to the profit and inversely proportional to the investment
duration. At optimum, the Lax-Hopf formula implies that the enrichment is equal
to the cost of the average transaction on the investment temporal window. In
this study, we generalize the Lax-Hopf formula when the transaction-cost
function depends also on time and commodity, for reducing the infinite
dimensional problem to a finite dimensional problem. For that purpose, we
introduce the moderated ansaction-cost function which depends only on the
duration and on a commodity. Here again, the generalized Lax-Hopf formula
reduces the computation of the value function to the marginal fonction of an
optimization problem on durations and commodities involving the moderated
transaction cost function. At optimum, the enrichment of the value function is
still equal to the moderated transition cost-function of average transaction.


title:
Big denominators and analytic normal forms with an appendix by M.
  Zhitomirskii

abstract:
  We study the {\it regular} action of an analytic pseudo-group of
transformations on the space of germs of various analytic objects of local
analysis and local differential geometry. We fix a homogeneous object $F_0$ and
we are interested in an analytic normal form for the whole affine space $\{F_0
+ h.o.t.\}$. We prove that if the cohomological operator defined by $F_0$ has
the big denominators property and if a formal normal form is well chosen then
this formal normal form holds in analytic category. We also define big
denominators in systems of nonlinear PDEs and prove a theorem on local analytic
solvability of systems of nonlinear PDEs with big denominators. %This theorem,
which a priori has nothing to do with local classification problems,generalizes
the theorem on analytic normal forms. Moreover, we prove that if the
denominators grow "relatively fast", but not fast enough to satisfy the big
denominator property, then we have a normal form, respectively local
solvability of PDEs, in a formal Gevrey category. We illustrate our theorems by
explanation of known results and by new results in the problems of local
classification of singularities of vector fields, non-isolated singularities of
functions, tuples of germs of vector fields, local Riemannian metrics and
conformal structures.


title:
Fe impurity induced ion-nanopatterning: atomistic simulations using a
  new force field for FeSi

abstract:
  The ion-bombardment induced nanopatterning of Si(001) has been simulated by
atomistic simulations with and without Fe impurity. The surface contamination
has been simulated by using a new force field developed for FeSi. This is a
fitted bond order potential (BOP) given for Si and for Fe by Albe et al. This
BOP formula has been optimized simultaneously for FeSi, Si and for Fe. Using
this new force field we are able to follow the ion-beam assisted deposition for
Si in the presence of Fe contamination in the surface region. As an overall
result, we get an unexpectedly rich variety of nanopatterns formed by the
reorganization of the crater rims of the individual ion impacts. The previously
thought simple atomistically roughened surfaces show unprecedented landscapes
and topography with nanoscale features. The characteristic size of the units of
the pattern is in the range of a few nms. Typical of the occurred pattern is
the network of interconnected elongated adatom islands. We also see the
self-organization of this pattern upon ion-bombardments. At $50^{\circ}$ impact
angle we get a nanoporous surface (sponge-like) both for Fe-contaminated and
Fe-free simulations. At $70^{\circ}$ of impact (grazing angle of incidence) the
pattern resembles to that of elongated atomic chains (adatom islands) along the
ion impact direction. This latter pattern could be understood as a prepattern
state towards rippling. At lower angles ($30^{\circ}$) nanoholes rule the
landsdcape. The obtained pattern corresponds to low fluence experiments which
are used to consider as simple roughening without showing any sing of
patterning.


title: The effective cone of the moduli space of sheaves on the plane

abstract:
  We compute the cone of effective divisors on any moduli space of semistable
sheaves on the plane. The computation hinges on finding a good resolution of a
general stable sheaf. This resolution is determined by Bridgeland stability and
arises from a well-chosen Beilinson spectral sequence. The existence of a good
choice of spectral sequence depends on remarkable number-theoretic properties
of the slopes of exceptional bundles.


title: About the mass of certain second order elliptic operators

abstract:
  Let $(M,g)$ be a closed Riemannian manifold of dimension $n \geq 3$ and let
$f\in C^{\infty}(M)$, such that the operator $P_f:= \Delta_g+f$ is positive. If
$g$ is flat near some point $p$ and $f$ vanishes around $p$, we can define the
mass of $P_f$ as the constant term in the expansion of the Green function of
$P_f$ at $p$. In this paper, we establish many results on the mass of such
operators. In particular, if $f:= \frac{n-2}{4(n-1)} \scal_g$, i.e. if $P_f$ is
the Yamabe operator, we show the following result: assume that there exists a
closed simply connected non-spin manifold $M$ such that the mass is
non-negative for every metric $g$ as above on $M$, then the mass is
non-negative for every such metric on every closed manifold of the same
dimension as $M$.


title:
On the determination of the spin and disc truncation of accreting black
  holes using X-ray reflection

abstract:
  We discuss the application of simple relativistically-blurred X-ray
reflection models to the determination of the spin and the inner radius of the
disc in accreting black holes. Observationally, the nature of the corona is
uncertain a priori, but a robust determination of the inner disk radius can be
made when the disc emissivity index is tightly constrained. When the inner disc
is well illuminated, the black hole spin can also be determined. Using
reflection modelling derived from ray tracing, we show that robust
determination of disc truncation requires that the location of the coronal
source is quasi-static and at a height and radius less than the truncation
radius of the disc. Robust spin measurements require that at least part of the
corona lies less than about 10 gravitational radii above the black hole in
order that the innermost regions, including the innermost stable circular
orbit, are well illuminated. The width of the blurring kernel (e.g., the iron
line) has a strong dependence on coronal height. These limitations may be
particularly applicable at low Eddington fractions (e.g. the low/hard state,
and low-luminosity AGN) where the height of the corona may be relatively large,
or outflowing, and tied to jet production.


title: Smooth Gevrey normal forms of vector fields near a fixed point

abstract:
  We study germs of smooth vector fields in a neighborhood of a fixed point
having an hyperbolic linear part at this point. It is well known that the
"small divisors" are invisible either for the smooth linearization or normal
form problem. We prove that this is completely different in the smooth Gevrey
category. We prove that a germ of smooth $\al$-Gevrey vector field with an
hyperbolic linear part admits a smooth $\be$-Gevrey transformation to a smooth
$\be$-Gevrey normal form. The Gevrey order $\be$ depends on the rate of
accumulation to $0$ of the small divisors. We show that a formally linearizable
Gevrey smooth germ with the linear part satisfies Brjuno's small divisors
condition can be linearized in the same Gevrey class.