title:
Bidirectional and efficient conversion between microwave and optical
  light

abstract:
  Converting low-frequency electrical signals into much higher frequency
optical signals has enabled modern communications networks to leverage both the
strengths of microfabricated electrical circuits and optical fiber
transmission, allowing information networks to grow in size and complexity. A
microwave-to-optical converter in a quantum information network could provide
similar gains by linking quantum processors via low-loss optical fibers and
enabling a large-scale quantum network. However, no current technology can
convert low-frequency microwave signals into high-frequency optical signals
while preserving their fragile quantum state. For this demanding application, a
converter must provide a near-unitary transformation between different
frequencies; that is, the ideal transformation is reversible, coherent, and
lossless. Here we demonstrate a converter that reversibly, coherently, and
efficiently links the microwave and optical portions of the electromagnetic
spectrum. We use our converter to transfer classical signals between microwave
and optical light with conversion efficiencies of ~10%, and achieve performance
sufficient to transfer quantum states if the device were further precooled from
its current 4 kelvin operating temperature to below 40 millikelvin. The
converter uses a mechanically compliant membrane to interface optical light
with superconducting microwave circuitry, and this unique combination of
technologies may provide a way to link distant nodes of a quantum information
network.


title: The Brownian Conga Line

abstract:
  We introduce a new model called the Brownian Conga Line. It is a random curve
evolving in time, generated when a particle performing a two dimensional
Gaussian random walk leads a long chain of particles connected to each other by
cohesive forces. We approximate the discrete Conga line in some sense by a
smooth random curve and subsequently study some properties of this smooth
curve. Some such properties include the different scales in which particles
show noticeable motion in different regions of the Conga line, distribution of
critical points, length, and distribution of loops.


title:
Axial Symmetric Kahler manifolds, the D-map of Inflaton Potentials and
  the Picard-Fuchs Equation

abstract:
  In this paper we provide a definition of the D-map, namely of the
mathematical construction implicitly utilized by supergravity that associates
an axial symmetric Kahler surface to every positive definite potential function
V(phi). The properties of the D-map are discussed in general. Then the D-map is
applied to the list of integrable cosmological potentials classified by us in a
previous publication with A. Sagnotti. Several interesting geometrical and
analytical properties of the manifolds in the image of this D-map are
discovered and illustrated. As a by-product of our analysis we demonstrate the
existence of (integrable) Starobinsky-like potentials that can be embedded into
supergravity. Some of them follow from constant curvature Kahler manifolds. In
the quest for a microscopic interpretation of inflaton dynamics we present the
Ariadne's thread provided by a new mathematical concept that we introduce under
the name of axial symmetric descendants of one dimensional special Kahler
manifolds. By means of this token we define a clearcut algorithm that to each
potential function V(phi) associates a unique 4th order Picard-Fuchs equation
of restricted type. Such an equation encodes information on the chiral ring of
a superconformal field theory to be sought for, unveiling in this way a
microscopic interpretation of the inflaton potential. We conjecture that the
physical mechanism at the basis of the transition from a special manifold to
its axial symmetric descendant is probably the construction of an Open String
descendant of a Closed String model.

categories: hep-th astro-ph.CO gr-qc hep-ph math-ph math.MP


title: Homoclinic points for convex billiards

abstract:
  In this paper we investigate some generic properties of a billiard system on
a convex table. We show that generically, every hyperbolic periodic point
admits some homoclinic orbit.


title: The cubic Dirac equation: Small initial data in $H^1(\mathbb{R}^3)$

abstract:
  We establish global well-posedness and scattering for the cubic Dirac
equation for small data in the critical space $H^1(\mathbb{R}^3)$. The main
ingredient is obtaining a sharp end-point Strichartz estimate for the
Klein-Gordon equation. In a classical sense this fails and it is related to the
failure of the endpoint Strichartz estimate for the wave equation in space
dimension three. In this paper, systems of coordinate frames are constructed in
which endpoint Strichartz estimates are recovered and energy estimates are
established.


title: Anomalous Topological Pumps and Fractional Josephson Effects

abstract:
  We discover novel topological pumps in the Josephson effects for
superconductors. The phase difference, which is odd under the chiral symmetry
defined by the product of time-reversal and particle-hole symmetries, acts as
an anomalous adiabatic parameter. These pumping cycles are different from those
in the "periodic table", and are characterized by $Z\times Z$ or $Z_2\times
Z_2$ strong invariants. We determine the general classifications in class AIII,
and those in class DIII with a single anomalous parameter. For the $Z_2\times
Z_2$ topological pump in class DIII, one $Z_2$ invariant describes the
coincidence of fermion parity and spin pumps whereas the other one reflects the
non-Abelian statistics of Majorana Kramers pairs, leading to three distinct
fractional Josephson effects.

categories: cond-mat.supr-con cond-mat.mes-hall cond-mat.str-el math-ph math.MP


title: An interesting $q$-series related to the 4-th symmetrized rank function

abstract:
  This paper presents the methods to utilizing the $s$-fold extension of
Bailey's lemma to obtain $spt$-type functions related to the symmetrized rank
function $\eta_{2k}(n).$ We provide the $k=2$ example, but clearly illustrate
how deep connections between higher-order spt functions exist for any integer
$k>1,$ and provide several directions for possible research. In particular, we
present why the function $spt_M^{*}(n),$ the total number of appearances of the
smallest parts of partitions where parts greater than the smallest plus $M$ do
not occur, is an $spt$ function that appears to have central importance.


title:
Green's function retrieval and fluctuations of cross density of states
  in multiple scattering media

abstract:
  In this article we derive the average and the variance of the
cross-correlation of a noise wavefield. The noise cross-correlation function
(NCF) is widely used to passively estimate the Green's function between two
probes and is proportional to the cross density of states (CDOS) in photonic
and plasmonic systems. We first explain from the ladder approximation how the
diffusion halo plays the role of secondary sources to reconstruct the mean
Green's function. We then show that fluctuations of NCF are governed by several
non-Gaussian correlations. An infinite-range NCF correlation dominates CDOS
fluctuations and proves that NCF is not a self averaging quantity with respect
to the plurality of noise sources. The link between these correlations and the
intensity ones is highlighted. These results are supported by numerical
simulations and are of importance for passive imaging applications and material
science.


title:
On the energy conservation electrostatic PIC/MC simulating: benchmark
  and application to the radio frequency discharges

abstract:
  We benchmark and analyze the error of energy conservation (EC) scheme for
Particle in cell/Monte-Carlo Couple (PIC/MCC) algorithms by a radio frequency
discharging simulation. The plasma heating behaviors and electron distributing
functions obtained by 1D simulation are analyzed. Both explicit and implicit
algorithms are checked. The results showed that the EC scheme can eliminated
the self-heating with wide grid spacing in both cases with a small reduction of
the accuracies. In typical parameters, the EC implicit scheme has higher
precision than EC explicit scheme.
  Some "numerical cooling" behaviors are observed and analyzed. Some other
error are analyzed also. The analysis showed
  EC implicit scheme can be used to qualitative estimation of some discharge
problems with much less computational resource costs without much loss of
accuracies.


title:
Hadron formation in semi-inclusive deep inelastic lepton-nucleus
  scattering

abstract:
  Hadron production in lepton-nucleus deep inelastic scattering is studied in a
model including quark energy loss and nuclear absorption. The leading-order
computations for hadron multiplicity ratios are presented and compared with the
selected HERMES experimental data with the quark hadronization occurring inside
the nucleus by means of the hadron formation time. It is shown that with
increase of the energy fraction carried by the hadron, the nuclear suppression
on hadron multiplicity ratio from nuclear absorption gets bigger. It is found
that when hadronization occurs inside the nucleus, the nuclear absorption is
the dominant mechanism causing a reduction of the hadron yield. The atomic mass
dependence of hadron attenuation for quark hadronization starting inside the
nucleus is confirmed theoretically and experimentally to be proportional to $
A^{1/3}$.


title: Topology of quantum discord

abstract:
  Quantum discord is an important measure of quantum correlations that can
serve as a resource for certain types of quantum information processing. \ Like
entanglement, discord is subject to destruction by external noise. The routes
by which this destruction can take place depends on the shape of the
hypersurface of zero discord $\mathcal{C}$ in the space of generalized Bloch
vectors. For 2 qubits, we show that with a few points subtracted, this
hypersurface is a simply-connected 9-dimensional manifold embedded in a
15-dimensional background space. \ We do this by constructing an explicit\
homeomorphism from a known manifold to the subtracted version of $\mathcal{C}
$. We also construct a coordinate map on $\mathcal{C}$ that can be used for
integration or other purposes. This topological characterization of $%
\mathcal{C}$ has important implications for the classification of the possible
time evolutions of discord in physical models. The classification for discord
contrasts sharply with the possible evolutions of entanglement.
  Using topological methods, we classify the possible joint evolutions of
entanglement and discord. There are 9 allowed categories: 6 categories for a
Markovian process and 3 categories for a non-Markovian process, respectively.
We illustrate these conclusions with an anisotropic XY spin model. All 9
categories can be obtained by adjusting parameters.


title: On asymptotic solutions of Friedmann equations

abstract:
  Our main aim is to apply the theory of regularly varying functions to the
asymptotical analysis at infinity of solutions of Friedmann cosmological
equations. A new constant $\Gamma$ is introduced related to the Friedmann
cosmological equations. Determining the values of $\Gamma$ we obtain the
asymptotical behavior of the solutions, i.e. of the expansion scale factor
$a(t)$ of a universe. The instance $\Gamma < 1/4$ is appropriate for both
cases, the spatially flat and open universe, and gives a sufficient and
necessary condition for the solutions to be regularly varying. This property of
Friedmann equations is formulated as the generalized power law principle. From
the theory of regular variation it follows that the solutions under usual
assumptions include a multiplicative term which is a slowly varying function.


title:
GPatt: Fast Multidimensional Pattern Extrapolation with Gaussian
  Processes

abstract:
  Gaussian processes are typically used for smoothing and interpolation on
small datasets. We introduce a new Bayesian nonparametric framework -- GPatt --
enabling automatic pattern extrapolation with Gaussian processes on large
multidimensional datasets. GPatt unifies and extends highly expressive kernels
and fast exact inference techniques. Without human intervention -- no hand
crafting of kernel features, and no sophisticated initialisation procedures --
we show that GPatt can solve large scale pattern extrapolation, inpainting, and
kernel discovery problems, including a problem with 383400 training points. We
find that GPatt significantly outperforms popular alternative scalable Gaussian
process methods in speed and accuracy. Moreover, we discover profound
differences between each of these methods, suggesting expressive kernels,
nonparametric representations, and exact inference are useful for modelling
large scale multidimensional patterns.


title:
Global classical solution of the Cauchy problem to 1D compressible
  Navier-Stokes equations with large initial data

abstract:
  In this paper, we prove that the 1D Cauchy problem of the compressible
Navier-Stokes equations admits a unique global classical solution $(\rho,\rm
u)$ if the viscosity $\mu(\rho)=1+\rho^{\beta}$ with $\beta\geq0$. The initial
data can be arbitrarily large and may contain vacuum.
  Some new weighted estimates of the density and velocity are obtained when
deriving higher order estimates of the solution.


title: Furrows in the wake of propagating d-cones

abstract:
  We investigate the formation dynamics of plastic creases in thin
elasto-plastic sheets. In contrast to the commonly accepted description of
crumpled thin sheets, which asserts that creases form only by elastic
interaction between two d-cones, the creases we study in this letter are
created by plastic deformations left in the wake of a single propagating
d-cone. Upon application of load, a d-cone initially remains stationary and
responds by deforming globally. However, above a critical load, the d-cone
undergoes a sharpening transition that focuses the stresses at its tip,
allowing it to propagate along the sheet, leaving a furrow-like scar in its
wake. Our results show that the dynamics of plastic defect creation are
important for predicting the final geometry and statistics of a defect network
in a crumpled thin sheet.


title: Ultrafast and Fault-Tolerant Quantum Communication across Long Distances

abstract:
  Quantum repeaters (QRs) provide a way of enabling long distance quantum
communication by establishing entangled qubits between remote locations. We
investigate a new approach to QRs in which quantum information can be
faithfully transmitted via a noisy channel without the use of long distance
teleportation, thus eliminating the need to establish remote entangled links.
Our approach makes use of small encoding blocks to fault-tolerantly correct
both operational and photon loss errors. We describe a way to optimize the
resource requirement for these QRs with the aim of the generation of a secure
key. Numerical calculations indicate that the number of quantum memory bits
required for our scheme has favorable poly-logarithmic scaling with the
distance across which the communication is desired.


title:
Bounds on the spectral radius of nonnegative matrices and applications
  in graph spectra

abstract:
  In this paper, we give upper and lower bounds for the spectral radius of a
nonnegative irreducible matrix and characterize the equality cases. These
bounds theoretically improve and generalize some known results of Duan et
al.[X. Duan, B. Zhou, Sharp bounds on the spectral radius of a nonnegative
matrix, Linear Algebra Appl. (2013),
http://dx.doi.org/10.1016/j.laa.2013.08.026]. Finally, applying these bounds to
various matrices associated with a graph, we obtain some new upper and lower
bounds on various spectral radiuses of graphs, which generalize and improve
some known results.


title: Theory of magneto-electric susceptibility in multiferroic chiral magnets

abstract:
  We present a theoretical examination of the magneto-electric response in the
recently discovered multiferroic insulator Cu$_2$OSeO$_3$. Combining Monte
Carlo simulation and Ginzburg-Landau analysis we predict the response in each
of the magnetic phases, including helical, conical, ferromagnetic and Skyrmion
crystal phases, both for thin film and bulk systems. A common feature for all
non-collinear phases is that the magneto-electric susceptibility increases
linearly with the applied magnetic field. Being both calculable and measurable,
the magneto-electric susceptibility can serve as a new powerful probe to detect
and investigate magnetic phases and phase transitions in multiferroic chiral
magnets in general.


title:
Combinatorial, piecewise-linear, and birational homomesy for products of
  two chains

abstract:
  This article illustrates the dynamical concept of $homomesy$ in three kinds
of dynamical systems -- combinatorial, piecewise-linear, and birational -- and
shows the relationship between these three settings. In particular, we show how
the rowmotion and promotion operations of Striker and Williams can be lifted to
(continuous) piecewise-linear operations on the order polytope of Stanley, and
then lifted to birational operations on the positive orthant in
$\mathbb{R}^{|P|}$ and indeed to a dense subset of $\mathbb{C}^{|P|}$. When the
poset $P$ is a product of a chain of length $a$ and a chain of length $b$,
these lifted operations have order $a+b$, and exhibit the homomesy phenomenon:
the time-averages of various quantities are the same in all orbits. One
important tool is a concrete realization of the conjugacy between rowmotion and
promotion found by Striker and Williams; this $recombination$ $map$ allows us
to use homomesy for promotion to deduce homomesy for rowmotion.
  NOTE: An earlier draft showed that Stanley's transfer map between the order
polytope and the chain polytope arises as the tropicalization of an analogous
map in the bilinear realm; in 2020 we removed this material for the sake of
brevity, especially after Joseph and Roby generalized our proof to the
noncommutative realm (see arXiv:1909.09658v3). Readers who nonetheless wish to
see our proof can find the September 2018 draft of this preprint through the
arXiv.


title: Remarks on level one conformal blocks divisors

abstract:
  We show that conformal blocks divisors of type B_r and D_r at level one are
effective sums of boundary divisors of $\bar{M}_{0,n}$. We also prove that the
conformal blocks divisor of type $B_r$ at level 1 with weights
(\omega_1,\dots,\omega_1) scales linearly with the level.


title:
New criteria for self-adjointness and its application to Dirac-Maxwell
  Hamiltonian

abstract:
  We present a new theorem concerning a sufficient condition for a symmetric
operator acting in a complex Hilbert space to be essentially self-adjoint. By
applying the theorem, we prove that the Dirac Maxwell Hamiltonian, which
describes a quantum system of a Dirac particle and a radiation field minimally
interacting with each other, is essentially self-adjoint. Our theorem covers
the case where the Dirac particle is in the Coulomb type potential.


title: New solutions with accelerated expansion in string theory

abstract:
  We present concrete solutions with accelerated expansion in string theory,
requiring a small, tractable list of stress energy sources. We explain how this
construction (and others in progress) evades previous no go theorems for simple
accelerating solutions. Our solutions respect an approximate scaling symmetry
and realize discrete sequences of values for the equation of state, including
one with an accumulation point at w=-1 and another accumulating near w=-1/3
from below. In another class of models, a density of defects generates scaling
solutions with accelerated expansion. We briefly discuss potential applications
to dark energy phenomenology, and to holography for cosmology.


title:
Compact difference schemes for the modified anomalous fractional
  sub-diffusion equation and the fractional diffusion-wave equation

abstract:
  In this paper, compact finite difference schemes for the modified anomalous
fractional sub-diffusion equation and fractional diffusion-wave equation are
studied. Schemes proposed previously can at most achieve temporal accuracy of
order which depends on the order of fractional derivatives in the equations and
is usually less than two. Based on the idea of weighted and shifted Grunwald
difference operator, we establish schemes with temporal and spatial accuracy
order equal to two and four respectively.


title: Charge States of Ions, and Mechanisms of Charge-Ordering Transitions

abstract:
  To gain insight into the mechanism of charge-ordering transitions, which
conventionally are pictured as a disproportionation of an ion M as 2M$^{n+}$
$\rightarrow$ M$^{(n+1)+}$ + M$^{(n-1)+}$, we (1) review and reconsider the
charge state (or oxidation number) picture itself, (2) introduce new results
for the putative charge ordering compound AgNiO$_2$ and the dual charge state
insulator AgO, and (3) analyze cationic occupations of actual (not formal)
charge, and work to reconcile the conundrums that arise. We establish that
several of the clearest cases of charge ordering transitions involve no
disproportion (no charge transfer between the cations, hence no charge
transfer), and that the experimental data used to support charge ordering can
be accounted for within density functional based calculations that contain no
charge transfer between cations. We propose that the charge state picture
retains meaning and importance, at least inn many cases, if one focuses on
Wannier functions rather than atomic orbitals. The challenge of modeling charge
ordering transitions with model Hamiltonians is discussed.


title: Sensitivity curves for searches for gravitational-wave backgrounds

abstract:
  We propose a graphical representation of detector sensitivity curves for
stochastic gravitational-wave backgrounds that takes into account the increase
in sensitivity that comes from integrating over frequency in addition to
integrating over time. This method is valid for backgrounds that have a
power-law spectrum in the analysis band. We call these graphs "power-law
integrated curves." For simplicity, we consider cross-correlation searches for
unpolarized and isotropic stochastic backgrounds using two or more detectors.
We apply our method to construct power-law integrated sensitivity curves for
second-generation ground-based detectors such as Advanced LIGO, space-based
detectors such as LISA and the Big Bang Observer, and timing residuals from a
pulsar timing array. The code used to produce these plots is available at
https://dcc.ligo.org/LIGO-P1300115/public for researchers interested in
constructing similar sensitivity curves.


title: A possible new phase in non-perturbatively gauge-fixed Yang-Mills theory

abstract:
  The standard expectation is that gauge fixing cannot alter the physics in the
physical sector of a Yang-Mills theory. Here we argue that this may not always
be true: in an SU(2) Yang-Mills theory in which the $SU(2)/U(1)$ coset is
non-perturbatively gauge fixed, we find that a new phase, with spontaneous
symmetry breaking and a Higgs-like mechanism, appears to be a possibility.


title: Precision metrology using weak measurements

abstract:
  Weak values and measurements have been proposed as means to achieve dramatic
enhancements in metrology based on the greatly increased range of possible
measurement outcomes. Unfortunately, the very large values of measurement
outcomes occur with highly suppressed probabilities. This raises three vital
questions in weak-measurement-based metrology, namely, (Q1) Does post-selection
enhance the measurement precision? (Q2) Does weak measurement offer better
precision than strong measurement? (Q3) Is it possible to beat the standard
quantum limit or to achieve the Heisenberg limit with weak measurement using
only classical resources? We analyse these questions for two prototypical, and
generic, measurement protocols and show that while the answers to the first two
questions are negative for both protocols, the answer to the last is
affirmative for measurements with phase-space interactions, and negative for
configuration space interactions. Our results, particularly the ability of weak
measurements to perform at par with strong measurements in some cases, are
instructive for the design of weak-measurement-based protocols for quantum
metrology.


title:
On the associated primes and the depth of the second power of squarefree
  monomial ideals

abstract:
  We present combinatorial characterizations for the associated primes of the
second power of squarefree monomial ideals and criteria for this power to have
positive depth or depth greater than one.


title:
Local asymptotic mixed normality property for nonsynchronously observed
  diffusion processes

abstract:
  We prove the local asymptotic mixed normality (LAMN) property for a family of
probability measures defined by parametrized diffusion processes with
nonsynchronous observations. We assume that observation times of processes are
independent of processes and we will study asymptotics when the maximum length
of observation intervals goes to zero in probability. We also prove that the
quasi-maximum likelihood estimator and the Bayes-type estimator proposed in
Ogihara and Yoshida (Stochastic Process. Appl. 124 (2014) 2954-3008) are
asymptotically efficient.


title: A record of atmospheric 210Pb accumulation in the industrial city

abstract:
  The deposition flux of total atmospheric 210Pb in the industrial city
Rostov-on-Don, Russia from 2002 to 2010 has been measured. The variations in
annual 210Pb deposition flux appear to be mainly correlated with the number of
rains and significant amount of anthropogenic 210Pb, polluted into the surface
layer of air in the home-heating period. The average 210Pb deposition is 1.75
mBq/m3. Several meteorological parameters which are strongly associated with
the fluctuations of concentrations of 210Pb are identified. These results are
useful to provide typical information on the atmosphere radioactivity in an
industrial city.


title: Can social microblogging be used to forecast intraday exchange rates?

abstract:
  The Efficient Market Hypothesis (EMH) is widely accepted to hold true under
certain assumptions. One of its implications is that the prediction of stock
prices at least in the short run cannot outperform the random walk model. Yet,
recently many studies stressing the psychological and social dimension of
financial behavior have challenged the validity of the EMH. Towards this aim,
over the last few years, internet-based communication platforms and search
engines have been used to extract early indicators of social and economic
trends. Here, we used Twitter's social networking platform to model and
forecast the EUR/USD exchange rate in a high-frequency intradaily trading
scale. Using time series and trading simulations analysis, we provide some
evidence that the information provided in social microblogging platforms such
as Twitter can in certain cases enhance the forecasting efficiency regarding
the very short (intradaily) forex.


title:
A New Kind of High-Order Multi-step Schemes for Forward Backward
  Stochastic Differential Equations

abstract:
  In this work, we concern with the high order numerical methods for coupled
forward-backward stochastic differential equations (FBSDEs). Based on the
FBSDEs theory, we derive two reference ordinary differential equations (ODEs)
from the backward SDE, which contain the conditional expectations and their
derivatives. Then, our high order multi-step schemes are obtained by carefully
approximating the derivatives and the conditional expectations in the reference
ODEs. Motivated by the local property of the generator of diffusion processes,
the Euler method is used to solve the forward SDE, however, it is noticed that
the numerical solution of the backward SDE is still of high order accuracy.
Such results are obviously promising: on one hand, the use of Euler method (for
the forward SDE) can dramatically simplifies the entire computational scheme,
and on the other hand, one might be only interested in the solution of the
backward SDE in many real applications such as option pricing. Several
numerical experiments are carried out to demonstrate the effectiveness of the
numerical method.


title:
The GRW flash theory: a relativistic quantum ontology of matter in
  space-time?

abstract:
  John Bell proposed an ontology for the GRW modification of quantum mechanics
in terms of flashes occurring at space-time points. The paper spells out the
motivation for this ontology, enquires into the status of the wave-function in
it, critically examines the claim of its being Lorentz-invariant and considers
whether it is a parsimonious, but nevertheless physically adequate ontology.


title: The imaginary Kapitza pendulum

abstract:
  We extend the theory of Kapitza stabilization within the complex domain, i.e.
for the case of an imaginary oscillating potential. At a high oscillation
frequency, the quasi-energy spectrum is found to be entirely real-valued,
however a substantial difference with respect to a real potential emerges, that
is the formation of a truly bound state instead of a resonance. The predictions
of the Kapitza averaging method and the transition from a complex to an
entirely real-valued quasi-energy spectrum at high frequencies are confirmed by
numerical simulations of the Schrodinger equation for an oscillating Gaussian
potential. An application and a physical implementation of the imaginary
Kapitza pendulum to the stability of optical resonators with variable
reflectivity is discussed.


title: Depleted Galaxy Cores and Dynamical Black Hole Masses

abstract:
  Shallow cores in bright, massive galaxies are commonly thought to be the
result of scouring of stars by mergers of binary supermassive black holes. Past
investigations have suggested correlations between the central black hole mass
and the stellar light or mass deficit in the core, using proxy measurements of
$M_{\rm BH}$ or stellar mass-to-light ratios ($\Upsilon$). Drawing on a wealth
of dynamical models which provide both $M_{\rm BH}$ and $\Upsilon$, we identify
cores in 23 galaxies, of which 20 have direct, reliable measurements of $M_{\rm
BH}$ and dynamical stellar mass-to-light ratios ($\Upsilon_{\star,{\rm dyn}}$).
These cores are identified and measured using Core-S\'ersic model fits to
surface brightness profiles which extend out to large radii (typically more
than the effective radius of the galaxy); for approximately one fourth of the
galaxies, the best fit includes an outer (\sersic) envelope component. We find
that the core radius is most strongly correlated with the black hole mass and
that it correlates better with total galaxy luminosity than it does with
velocity dispersion. The strong core-size-- $M_{\rm BH}$ correlation enables
estimation of black hole masses (in core galaxies) with an accuracy comparable
to the $M_{\rm BH}$--$\sigma$ relation (rms scatter of 0.30 dex in $\log M_{\rm
BH}$), without the need for spectroscopy. The light and mass deficits correlate
more strongly with galaxy velocity dispersion than they do with black hole
mass. Stellar mass deficits span a range of 0.2--39 \mbh, with almost all (87%)
being $< 10 \, M_{\rm BH}$; the median value is 2.2 $M_{\rm BH}$.


title: Newton slopes for Artin-Schreier-Witt towers

abstract:
  We fix a monic polynomial $f(x) \in \mathbb F_q[x]$ over a finite field and
consider the Artin-Schreier-Witt tower defined by $f(x)$; this is a tower of
curves $\cdots \to C_m \to C_{m-1} \to \cdots \to C_0 =\mathbb A^1$, with total
Galois group $\mathbb Z_p$. We study the Newton slopes of zeta functions of
this tower of curves. This reduces to the study of the Newton slopes of
L-functions associated to characters of the Galois group of this tower. We
prove that, when the conductor of the character is large enough, the Newton
slopes of the L-function form arithmetic progressions which are independent of
the conductor of the character. As a corollary, we obtain a result on the
behavior of the slopes of the eigencurve associated to the Artin-Schreier-Witt
tower, analogous to the result of Buzzard and Kilford.


title: Bloch Oscillations in the Optical Waveguide Array

abstract:
  The multiple scattering formalism is proposed describing the guided modes in
the optical waveguide array within the framework of macroscopic
electrodynamics. It is shown that, under sufficiently general assumptions, our
approach justifies the phenomenological model used widely to treat various
physical phenomena in the optical micro- and nano-structures. It is found that
the theory developed in this paper describes the real experiments in which the
the Bloch oscillations are observed. Surprisingly, not only qualitative but
also reasonably quantitative agreement is found.


title: s-Inversion Sequences and P-Partitions of Type B

abstract:
  Given a sequence $s=(s_1,s_2,\ldots)$ of positive integers, the inversion
sequences with respect to $s$, or $s$-inversion sequences, were introduced by
Savage and Schuster in their study of lecture hall polytopes. A sequence
$(e_1,e_2,\ldots,e_n)$ of nonnegative integers is called an $s$-inversion
sequence of length $n$ if $0\leq e_i < s_i$ for $1\leq i\leq n$. Let I(n) be
the set of $s$-inversion sequences of length $n$ for $s=(1,4,3,8,5,12,\ldots)$,
that is, $s_{2i}=4i$ and $s_{2i-1}=2i-1$ for $i\geq1$, and let $P_n$ be the set
of signed permutations on $\{1^2,2^2,\ldots,n^2\}$. Savage and Visontai
conjectured that when $n=2k$, the ascent number over $I_n$ is equidistributed
with the descent number over $P_k$. For a positive integer $n$, we use type $B$
$P$-partitions to give a characterization of signed permutations over which the
descent number is equidistributed with the ascent number over $I_n$. When $n$
is even, this confirms the conjecture of Savage and Visontai. Moreover, let
$I'_n$ be the set of $s$-inversion sequences of length $n$ for
$s=(2,2,6,4,10,6,\ldots)$, that is, $s_{2i}=2i$ and $s_{2i-1}=4i-2$ for
$i\geq1$. We find a set of signed permutations over which the descent number is
equidistributed with the ascent number over $I'_n$.


title:
Beauville-Bogomolov lattice for a singular symplectic variety of
  dimension 4

abstract:
  The Beauville-Bogomolov lattice is computed for a simplest singular
symplectic manifold of dimension 4, obtained as a partial desingularization of
the quotient $S^{[2]}/\iota$, where $S^{[2]}$ is the Hilbert square of a K3
surface $S$ and $\iota$ is a symplectic involution on it. This result applies,
in particular, to the singular symplectic manifolds of dimension 4, constructed
by Markushevich-Tikhomirov as compactifications of families of Prym varieties
of a linear system of curves on a K3 surface with an anti-symplectic
involution.


title:
Birational Mori fiber structures of Q-Fano 3-fold weighted complete
  intersections

abstract:
  In this paper we consider Q-Fano 3-fold weighted complete intersections of
codimension 2 in the 85 families listed in the Iano-Fletcher's list and
determine which cycle is a maximal center or not. For each maximal center, we
construct either a birational involution which untwists the maximal singularity
or a Sarkisov link centered at the cycle to an another explicitly described
Mori fiber space. As a consequence, 19 families are proved to be birationally
rigid and the remaining 66 families are proved to be birationally nonrigid.


title: Using cascade development universality for thin calorimeter

abstract:
  A method for measurement of energy of high-energy particles by a thin
calorimeter, is presented. The method is based on the correlation analysis of
dependence of number of secondary particles, $N_e$, at observation level and
the relation of number of particles, $dN$, at two levels, divided by an
absorber layer. It is shown, that use of correlation curves ($log N_e$ versus
$dN$) allows to reduce essentially errors of definition of energy of the
primary particle, which are connected with uncertainty of a primary nucleus and
with fluctuations in development of cascade process.


title:
Nowhere-zero 3-flows in graphs admitting solvable arc-transitive groups
  of automorphisms

abstract:
  Tutte's 3-flow conjecture asserts that every 4-edge-connected graph has a
nowhere-zero 3-flow. In this note we prove that every regular graph of valency
at least four admitting a solvable arc-transitive group of automorphisms admits
a nowhere-zero 3-flow.


title:
The role of the $\Delta(1232)$-resonance in covariant baryon chiral
  perturbation theory

abstract:
  We stress, on theoretical and phenomenological grounds, the importance of the
$\Delta(1232)$-resonance in a chiral effective field theory approach applied to
the study of $\pi N$ scattering. We show how its inclusion as a dynamical
degree of freedom allow us to obtain reliably valuable information from $\pi N$
scattering data.


title:
Hydrodynamical chemistry simulations of the SZ effect and the impacts
  from primordial non-Gaussianities

abstract:
  The impacts of Compton scattering of hot cosmic gas with the cosmic microwave
background radiation (Sunyaev-Zel'dovich effect, SZ) are consistently
quantified in Gaussian and non-Gaussian scenarios, by means of 3D numerical,
N-body, hydrodynamic simulations, including cooling, star formation, stellar
evolution and metal pollution (He, C, O, Si, Fe, S, Mg, etc.) from different
stellar phases, according to proper yields for individual metal species and
mass-dependent stellar lifetimes. Light cones are built through the simulation
outputs and samples of one hundred maps for the resulting temperature
fluctuations are derived for both Gaussian and non-Gaussian primordial
perturbations. From them, we estimate the possible changes due to early
non-Gaussianities on: SZ maps, probability distribution functions, angular
power spectra and corresponding bispectra. We find that the different growth of
structures in the different cases induces significant spectral distortions only
in models with large non-Gaussian parameters, $f_{\rm NL}$. In general, the
overall trends are covered by the non-linear, baryonic evolution, whose
feedback mechanisms tend to randomize the gas behaviour and homogenize its
statistical features, quite independently from the background matter
distribution. Deviations due to non-Gaussianity are almost undistinguishable
for $f_{\rm NL}\lesssim 100$, remaining always at few-per-cent level, within
the error bars of the Gaussian scenario. Rather extreme models with $f_{\rm
NL}\sim1000$ present more substantial deviations from the Gaussian case,
overcoming baryon contaminations and showing discrepancies up to a factor of a
few in the spectral properties.


title:
Birational Mori fiber structures of Q-Fano 3-fold weighted complete
  intersections, II

abstract:
  In this paper we study 14 families among 85 families of anticanonically
embedded Q-Fano threefolds weighted complete intersections of codimension 2 and
show that every quasismooth member is birationally birigid, that is, it is
birational to another Q-Fano threefold but not birational to any other Mori
fiber space.


title: Graded Limits of Minimal Affinizations in Type D

abstract:
  We study the graded limits of minimal affinizations over a quantum loop
algebra of type D in the regular case. We show that the graded limits are
isomorphic to multiple generalizations of Demazure modules, and also give their
defining relations. As a corollary we obtain a character formula for the
minimal affinizations in terms of Demazure operators, and a multiplicity
formula for a special class of the minimal affinizations.


title: Bishop and Laplacian comparison theorems on Sasakian manifolds

abstract:
  We prove a Bishop volume comparison theorem and a Laplacian comparison
theorem for a natural sub-Riemannian structure defined on Sasakian manifolds.
This generalizes the earlier work for the three dimensional case.


title:
Shortcuts to adiabatic passage for population transfer and maximum
  entanglement creation between two atoms in a cavity

abstract:
  We use the approach of "transitionless quantum driving" proposed by Berry to
construct shortcuts to the population transfer and the creation of maximal
entanglement between two $\Lambda $-type atoms based on the cavity quantum
electronic dynamics (CQED) system. An effective Hamiltonian is designed by
resorting to an auxiliary excited level, a classical driving field and an extra
cavity field mode to supplement or substitute the original reference
Hamiltonian, and steer the system evolution along its instantaneous eigenstates
in an arbitrarily short time, speeding up the rate of population transfer and
creation of maximal entanglement between the two atoms inside a cavity.
Numerical simulation demonstrates that our shortcuts' performance is robust
against the decoherences caused by atomic spontaneous emission and cavity
photon leakage.


title: The Absolute Calibration of the EUV Imaging Spectrometer on Hinode

abstract:
  We investigate the absolute calibration of the EUV Imaging Spectrometer (EIS)
on Hinode by comparing EIS full-disk mosaics with irradiance observations from
the EUV Variability Experiment (EVE) on the Solar Dynamics Observatory. We also
use ultra-deep (>10^5s) exposures of the quiet corona above the limb combined
with a simple differential emission measure model to establish new effective
area curves that incorporate information from the most recent atomic physics
calculations. We find that changes to the EIS instrument sensitivity are a
complex function of both time and wavelength. We find that the sensitivity is
decaying exponentially with time and that the decay constants vary with
wavelength. The EIS short wavelength channel shows significantly longer decay
times than the long wavelength channel.


title: Compatibility of state assignments and pooling of information

abstract:
  We say that two (or more) state assignments for one and the same quantum
system are compatible if they could represent the assignments of observers with
differing information about the system. A criterion for compatibility was
proposed in [Phys. Rev. A 65, 032315 (2002)]; however, this leaves unanswered
the question of whether there are degrees of compatibility which could be
represented by some quantitative measure, and whether there is a
straightforward procedure whereby the observers can pool their information to
arrive at a unique joint state assignment. We argue that such measures are only
sensible given some assumption about what kind of information was used in
making the state assignments in the first place, and that in general state
assignments do not represent all of the information possessed by the observers.
However, we examine one particular measure, and show that it has a
straightforward interpretation, assuming that the information was acquired from
a particular type of measurement, and that in this case there is a natural rule
for pooling information. We extend this measure to compatibility of states for
k observers, and show that the value is the solution to a semidefinite program.
Similar compatibility measures can be defined for alternative notions of state
compatibility, including Post-Peierls (PP) and Equal Support (ES)
compatibility.


title: Teichm\"{u}ller parameters for multiple BTZ black hole spacetime

abstract:
  We investigate the Teichm\"{u}ller parameters for a Euclidean multiple BTZ
black hole spacetime. To induce a complex structure in the asymptotic boundary
of such a spacetime, we consider the limit in which two black holes are at a
large distance from each other. In this limit, we can approximately determine
the period matrix (i.e., the Teichm\"{u}ller parameters) for the spacetime
boundary by using a pinching parameter. The Teichm\"{u}ller parameters are
essential in describing the partition function for the boundary conformal field
theory (CFT). We provide an interpretation of the partition function for the
genus two extremal boundary CFT proposed by Gaiotto and Yin that it is relevant
to double BTZ black hole spacetime.


title: Exclusive processes in pp collisions in CMS

abstract:
  We report the results on the searches of exclusive production of low- and
high-mass pairs with the Compact Muon Solenoid (CMS) detector in proton-proton
collisions at $\sqrt{s}$ = 7 TeV. The analyses comprise the central exclusive
$\gamma\gamma$ production, the exclusive two-photon production of dileptons,
$e^{+}e^{-}$ and $\mu^{+}\mu^{-}$, and the exclusive two-photon production of
$W$ pairs in the asymmetric $e^{\pm}\mu^{\mp}$ decay channel. No diphotons
candidates are observed in data and an upper limit on the cross section is set
to 1.18 pb with 95% confidence level for $E_{T}(\gamma)>$ 5.5 GeV and
$|\eta(\gamma)|<$ 2.5. In the measurement of exclusive dilepton production,
seventeen $e^{+}e^{-}$ candidates are observed in data with $E_{T}(e)>$ 5.5 GeV
and $|\eta(e)|<$ 2.5, and the cross section for the exclusive dimuon production
is set to $\sigma(pp\to p\,\mu^{+}\mu^{-}\,p)=3.38^{+0.58}_{-0.55}$ (stat.)
$\pm$ 0.16 (syst.) $\pm$ 0.14 (lumi.) pb for $m(\mu^{+}\mu^{-})>$ 11.5 GeV,
$p_{\textrm{T}}(\mu)>$ 4 GeV and $|\eta(\mu)|<$ 2.1, both in agreement with the
theoretical predictions. For high-mass systems, two events are observed in data
for the exclusive two-photon production of $W$ pairs for $p_{\textrm{T}}(\mu)>$
4 GeV, $|\eta(\mu)|<$ 2.4 and $m(e^{\pm}\mu^{\mp})>$ 20 GeV. Moreover, the
study of the tail of the dilepton transverse momentum distribution resulted in
model-independent upper limits for the anomalous quartic gauge couplings, which
are of the order of 10$^{-4}$.


title: Conservative and PT-symmetric compactons in waveguide networks

abstract:
  Stable discrete compactons in arrays of inter-connected three-line waveguide
arrays are found in linear and nonlinear limits in conservative and in
parity-time PT symmetric models. The compactons result from the interference of
the fields in the two lines of waveguides ensuring that the third (middle) line
caries no energy. PT-symmetric compactons require not only the presence of gain
and losses in the two lines of the waveguides but also complex coupling, i.e.
gain and losses in the coupling between the lines carrying the energy and the
third line with zero field. The obtained compactons can be stable and their
branches can cross the branches of the dissipative solitons. Unusual
bifurcations of branches of solitons from linear compactons are described.


title: Nonequilibrium dynamical mean-field theory and its applications

abstract:
  The study of nonequilibrium phenomena in correlated lattice systems has
developed into an active and exciting branch of condensed matter physics. This
research field provides rich new insights that could not be obtained from the
study of equilibrium situations, and the theoretical understanding of the
physics often requires the development of new concepts and methods. On the
experimental side, ultra-fast pump-probe spectroscopies enable studies of
excitation and relaxation phenomena in correlated electron systems, while
ultra-cold atoms in optical lattices provide a new way to control and measure
the time-evolution of interacting lattice systems with a vastly different
characteristic timescale compared to electron systems. A theoretical
description of these phenomena is challenging because, firstly, we have to
compute the quantum-mechanical time-evolution of many-body systems out of
equilibrium, and secondly, deal with strong-correlation effects which can be of
nonperturbative nature. In this review, we discuss the nonequilibrium extension
of the dynamical mean field theory (DMFT), which treats quantum fluctuations in
the time domain and works directly in the thermodynamic limit. The method
reduces the complexity of the calculation via a mapping to a self-consistent
impurity problem. Particular emphasis is placed on a detailed derivation of the
formalism, and on a discussion of numerical techniques, which enable solutions
of the effective nonequilibrium DMFT impurity problem. We summarize the
insights gained into the properties of the infinite-dimensional Hubbard model
under strong non-equilibrium conditions. These examples illustrate the current
ability of the theoretical framework to reproduce and understand fundamental
nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators,
photo-doping, and collapse-and-revival oscillations in quenched systems.


title: Tronqu\'ee solutions of the Painlev\'e equation \P1

abstract:
  We analyze the one parameter family of tronqu\'ee solutions of the Painlev\'e
equation \P1 in the pole-free sectors together with the region of the first
array of poles. We find a convergent expansion for these solutions, containing
one free parameter multiplying exponentially small corrections to the Borel
summed power series. We link the position of the poles in the first array to
the free parameter, and find the asymptotic expansion of the pole positions in
this first array (in inverse powers of the independent variable). We show that
the tritronqu\'ees are given by the condition that the parameter be zero. We
show how this analysis in conjunction with the asymptotic study of the pole
sector of the tritronqu\'ee in \cite{inprep} leads to a closed form expression
for the Stokes multiplier directly from the Painlev\'e property, not relying on
isomonodromic or related type of results.


title:
Magnetic orders of LaTiO$_3$ under epitaxial strain: a first-principles
  study

abstract:
  Perovskite LaTiO$_3$ bulk is a typical Mott-insulator with G-type
antiferromagnetic order. In this work, the biaxial strain effects on the ground
magnetic order of LaTiO$_3$ films grown on various substrates have been
studied. For the compressive strain, LaTiO$_3$ films grown on LaAlO$_3$,
LaGaO$_3$, and SrTiO$_3$ substrates undergo a phase transition from the
original G-type antiferromagnet to A-type antiferromagnet. The underlying
physical mechanisms are the lattice distortions tunned by strain. While for the
tensile strain, the BaTiO$_3$ and LaScO$_3$ substrates have been tested, which
show a tendency to transit the LaTiO$_3$ to the C-type antiferromagnet.
Furthermore, our calculations find that the magnetic transitions under
epitaxial strain do not change the insulating fact of LaTiO$_3$.


title:
Particle physics @ $\sqrt{s_{pp}}$ > 50 TeV with the Pierre Auger
  Observatory

abstract:
  The Pierre Auger Observatory in Argentina provides the largest data sample of
the cosmic ray events with energy above 10$^{18}$ eV. These high energy events
can be used to test our understanding of the hadronic interactions at energies
beyond the reach of colliders and to probe the basic properties of these
interactions such as the inelastic cross-section of proton-air collisions. The
combination of an array of surface detectors and the fluorescence telescopes of
the Pierre Auger Observatory reduces significantly the dependency of the shower
energy estimation on MC simulations. Despite that, the interpretation of mass
sensitive quantities such as the shower maximum in terms of chemical
composition of cosmic rays still depends on the hadronic interaction models.
This contribution describes the main results of the observatory concerning the
chemical composition of the cosmic rays and focuses on the problem of muon
deficit in hadronic interaction models and on the estimation of proton-air
cross-section from air-shower data.


title:
Electromagnetic waves in an axion-active relativistic plasma
  non-minimally coupled to gravity

abstract:
  We consider cosmological applications of a new self-consistent system of
equations, accounting for a nonminimal coupling of the gravitational,
electromagnetic and pseudoscalar (axion) fields in a relativistic plasma. We
focus on dispersion relations for electromagnetic perturbations in an initially
isotropic ultrarelativistic plasma coupled to the gravitational and axion
fields in the framework of isotropic homogeneous cosmological model of the de
Sitter type. We classify the longitudinal and transversal electromagnetic modes
in an axionically active plasma and distinguish between waves (damping,
instable or running), and nonharmonic perturbations (damping or instable). We
show that for the special choice of the guiding model parameters the
transversal electromagnetic waves in the axionically active plasma,
nonminimally coupled to gravity, can propagate with the phase velocity less
than speed of light in vacuum, thus displaying a possibility for a new type of
resonant particle-wave interactions.

categories: gr-qc astro-ph.CO hep-th physics.plasm-ph


title: Lightlike Membranes in Black Hole and Wormhole Physics, and Cosmology

abstract:
  We shortly outline the principal results concerning the
reparametrization-invariant world-volume Lagrangian formulation of lightlike
brane dynamics and its impact as a source for gravity and (nonlinear)
electromagnetism in black hole and wormhole physics.


title: Interacting dark sector with variable vacuum energy

abstract:
  We examine a cosmological scenario where dark matter is coupled to a variable
vacuum energy while baryons and photons are two decoupled components for a
spatially flat Friedmann-Robertson-Walker spacetime. We apply the $\chi^{2}$
method to the updated observational Hubble data for constraining the
cosmological parameters and analyze the amount of dark energy in the radiation
era. We show that our model fulfills the severe bound of $\Omega_{x}(z\simeq
1100)<0.009$ at the $2\sigma$ level, so it is consistent with the recent
analysis that includes cosmic microwave background anisotropy measurements from
the Planck survey, the Atacama Cosmology Telescope, and the South Pole
Telescope along with the future constraints achievable by the Euclid and CMBPol
experiments, and fulfills the stringent bound $\Omega_{x}(z\simeq
10^{10})<0.04$ at the $2\sigma$ level in the big-bang nucleosynthesis epoch.


title: The skew-t factor analysis model

abstract:
  Factor analysis is a classical data reduction technique that seeks a
potentially lower number of unobserved variables that can account for the
correlations among the observed variables. This paper presents an extension of
the factor analysis model by assuming jointly a restricted version of
multivariate skew t distribution for the latent factors and unobservable
errors, called the skew-t factor analysis model. The proposed model shows
robustness to violations of normality assumptions of the underlying latent
factors and provides flexibility in capturing extra skewness as well as heavier
tails of the observed data. A computationally feasible ECM algorithm is
developed for computing maximum likelihood estimates of the parameters. The
usefulness of the proposed methodology is illustrated by a real-life example
and results also demonstrates its better performance over various existing
methods.


title:
Dynamical Couplings and Charge Confinement/Deconfinement from Gravity
  Coupled to Nonlinear Gauge Fields

abstract:
  We briefly outline several main results concerning various new physically
relevant features found in gravity -- both ordinary Einstein or $f(R)=R+R^2$
gravity in the first-order formalism, coupled to a special kind of nonlinear
electrodynamics containing a square-root of the standard Maxwell Lagrangian and
known to produce charge confinement in flat spacetime.


title:
Cosmological Evolution of Einstein-Aether Models with Power-law-like
  Potential

abstract:
  The so-called Einstein-Aether theory is General Relativity coupled (at second
derivative order) to a dynamical unit time-like vector field (the aether). It
is a Lorentz-violating theory, and gained much attention in the recent years.
In the present work, we study the cosmological evolution of Einstein-Aether
models with power-law-like potential, by using the method of dynamical system.
In the case without matter, there are two attractors which correspond to an
inflationary universe in the early epoch, or a de Sitter universe in the late
time. In the case with matter but there is no interaction between dark energy
and matter, there are only two de Sitter attractors, and no scaling attractor
exists. So, it is difficult to alleviate the cosmological coincidence problem.
Therefore, we then allow the interaction between dark energy and matter. In
this case, several scaling attractors can exist under some complicated
conditions, and hence the cosmological coincidence problem could be alleviated.


title: Quadrupolar gravitational fields described by the $q-$metric

abstract:
  We investigate the Zipoy-Voorhees metric ($q-$metric) as the simplest static,
axially symmetric solution of Einstein's vacuum field equations that possesses
as independent parameters the mass and the quadrupole moment. In accordance
with the black holes uniqueness theorems, the presence of the quadrupole
completely changes the geometric properties of the corresponding spacetime that
turns out to contain naked singularities for all possible values of the
quadrupole parameter. The naked singularities, however, can be covered by
interior solutions that correspond to perfect fluid sources with no specific
equations of state. We conclude that the $q-$metric can be used to describe the
entire spacetime generated by static deformed compact objects.


title:
Integrable Scalar Cosmologies II. Can they fit into Gauged Extended
  Supergavity or be encoded in N=1 superpotentials?

abstract:
  The question whether the integrable one-field cosmologies classified in a
previous paper by Fre, Sagnotti and Sorin can be embedded as consistent
one-field truncations into Extended Gauged Supergravity or in N=1 supergravity
gauged by a superpotential without the use of D-terms is addressed in this
paper. The answer is that such an embedding is very difficult and rare but not
impossible. Indeed we were able to find two examples of integrable models
embedded in Supergravity in this way. Both examples are fitted into N=1
Supergravity by means of a very specific and interesting choice of the
superpotential W(z). The question whether there are examples of such an
embedding in extended Gauged Supergravity remains open. In the present paper,
relying on the embedding tensor formalism we classified all gaugings of the N=2
STU model, confirming, in the absence on hypermultiplets, the uniqueness of the
stable de Sitter vacuum found several years ago by Fre, Trigiante and Van
Proeyen and excluding the embedding of any integrable cosmological model. A
detailed analysis of the space of exact solutions of the first Supergravity
embedded integrable cosmological model revealed several new features worth an
in depth consideration. When the scalar potential has an extremum at a negative
value, the universe necessarily collapses into a Big Crunch notwithstanding its
spatial flatness. The causal structure of these universes is quite different
from that of the closed, positive curved, universe: indeed in this case the
particle and event horizons do not coincide and develop complicated patterns.
The cosmological consequences of this unexpected mechanism deserve careful
consideration.


title: Impurity effects in Cu$_2$O

abstract:
  The doping of wide gap semiconductors is an interesting problem both from the
scientific and technological point of view. A well known example of this
problem is the doping of Cu$_2$O. The only element which has produced an order
of magnitude increase in the conductivity of Cu$_2$O bulk samples is chlorine,
as previously reported by us and others. However the solar cells produced with
this material do not show any improvement in performances because of the
reduction in the minority carrier diffusion length. In this paper we
investigate the effect of other impurities in order to check their possible use
as dopants and to assess their effects on the minority carrier diffusion
length. Seven impurities have been introduced by evaporation on the starting
copper sheet before the oxidation used to produce Cu$_2$O: chromium (Cr), iron
(Fe), silver (Ag), silicon (Si), sodium (Na), sulfur (S) and phosphorus (P).
The experiments show that a 20 ppm of concentration of these dopants does not
give any relevant effect neither on the resistivity, nor on the mobility. The
effect on minority carrier diffusion length is also negligible except for
sodium which produces a slight degradation of the samples.


title:
Conventional BCS, Unconventional BCS, and Non-BCS Hidden Dineutron
  Phases in Neutron Matter

abstract:
  The nature of pairing correlations in neutron matter is re-examined. Working
within the conventional approximation in which the $nn$ pairing interaction is
provided by a realistic bare $nn$ potential fitted to scattering data, it is
demonstrated that the standard BCS theory fails in regions of neutron number
density where the pairing constant $\lambda$, depending crucially on density,
has a non-BCS negative sign. We are led to propose a non-BCS scenario for
pairing phenomena in neutron matter that involves the formation of a hidden
dineutron state. In low-density neutron matter where the pairing constant has
the standard BCS sign, two phases organized by pairing correlations are
possible and compete energetically: a conventional BCS phase and a dineutron
phase. In dense neutron matter, where $\lambda$ changes sign, only the
dineutron phase survives and exists until the critical density for termination
of pairing correlations is reached at approximately twice the neutron density
in heavy atomic nuclei.


title: Abelian Groups With Isomorphic Intersection Graphs

abstract:
  Let G be a group. The intersection graph G(G) of G is an undirected graph
without loops and multiple edges defined as follows: the vertex set is the set
of all proper nontrivial subgroups of G; and there is an edge between two
distinct vertices X and Y if and only if X \ Y 6= 1 where 1 denotes the trivial
subgroup of G: It was conjectured in [2] that two (non cyclic) finite abelian
groups with isomorphic intersection graphs are isomorphic. In this paper we
study this conjecture and show that it is almost true. For any inite abelian
group D let Dnc be the product of all noncyclic Sylow subgroups of D: Our main
result is that: given any two (nontrivial) inite abelian groups A and B; their
intersection graphs G(A) and G(B) are isomorphic if and only if the groups Anc
and Bnc are isomorphic, and there is a bijection between the sets of
(nontrivial) cyclic Sylow subgroups of A and B satisfying a certain condition.
So, in particular, two finite abelian groups with isomorphic intersection
graphs will be isomorphic provided that one of the groups has no (nontrivial)
cyclic Sylow subgroup. Our methods are elementary.


title: On the syzygies and Hodge theory of nodal hypersurfaces

abstract:
  We give sharp lower bounds for the degree of the syzygies involving the
partial derivatives of a homogeneous polynomial defining an even dimensional
nodal hypersurface. This implies the validity of formulas due to M. Saito, L.
Wotzlaw and the author for the graded pieces with respect to the Hodge
filtration of the top cohomology of the hypersurface complement in many new
cases. A classical result by Severi on the position of the singularities of a
nodal surface in $\mathbb{P}^3$ is improved and applications to deformation
theory of nodal surfaces are given.


title:
On Gevrey orders of power expansions of solutions to the third and fifth
  Painlev\'{e} equations

abstract:
  The question under consideration is Gevrey summability of power expansions of
solutions to the third and fifth Painlev\'{e} equations near infinity. Methods
of French and Japaneese schools are used to analyse these properties of formal
power-series solutions. The results obtained are compared with the ones
obtained by means of Power Geometry.


title: Some observations concerning reducibility of quadrinomials

abstract:
  In a recent paper \cite{Jan}, Jankauskas proved some interesting results
concerning the reducibility of quadrinomials of the form $f(4,x)$, where
$f(a,x)=x^{n}+x^{m}+x^{k}+a$. He also obtained some examples of reducible
quadrinomials $f(a,x)$ with $a\in\Z$, such that all the irreducible factors of
$f(a,x)$ are of degree $\geq 3$.
  In this paper we perform a more systematic approach to the problem and ask
about reducibility of $f(a,x)$ with $a\in\Q$. In particular by computing the
set of rational points on some genus two curves we characterize in several
cases all quadrinomials $f(a,x)$ with degree $\leq 6$ and divisible by a
quadratic polynomial. We also give further examples of reducible $f(a,x)$,
$a\in\Q$, such that all irreducible factors are of degree $\geq 3$.


title: Bayesian Extensions of Kernel Least Mean Squares

abstract:
  The kernel least mean squares (KLMS) algorithm is a computationally efficient
nonlinear adaptive filtering method that "kernelizes" the celebrated (linear)
least mean squares algorithm. We demonstrate that the least mean squares
algorithm is closely related to the Kalman filtering, and thus, the KLMS can be
interpreted as an approximate Bayesian filtering method. This allows us to
systematically develop extensions of the KLMS by modifying the underlying
state-space and observation models. The resulting extensions introduce many
desirable properties such as "forgetting", and the ability to learn from
discrete data, while retaining the computational simplicity and time complexity
of the original algorithm.


title: A symmetrical theory of nonrelativistic quantum mechanics

abstract:
  This paper presents a new Symmetrical Theory (ST) of nonrelativistic quantum
mechanics which postulates: quantum mechanics is a theory about complete
experiments, not particles; a complete experiment is maximally described by a
complex transition amplitude density; and this transition amplitude density
never collapses. This new ST is compared to the Conventional Theory (CT) of
nonrelativistic quantum mechanics for the analysis of a beam-splitter
experiment. The ST makes several experimentally testable predictions that
differ from the CT, which can be checked using existing technology. The ST also
solves one part of the CT measurement problem, and resolves some of the
paradoxes of the CT. This nonrelativistic ST is the low energy limit of a
relativistic ST presented in an earlier paper \cite{Heaney1}.


title:
First results with the boloSource() algorithm: Photometry of faint
  standard stars observed by Herschel/PACS

abstract:
  The boloSource() algorithm is a tool to separate the signal of compact
sources from that of the diffuse background in the timeline of far-infrared
measurements performed by the PACS camera of the Herschel Space Observatory. An
important characteristic and quality indicator of this method is that how well
it can reproduce the flux of faint standard stars which have reliable flux
estimates. For this propose we selected a few calibrator targets and
constructed light curves by extracting point source flux for each repetition of
the measurements independently using standard aperture photometry methods.
These were compared with the light curves obtained using the boloSource()
method on the same dataset. The results indicate that boloSource() provides a
similar level of photometric accuracy and reproducibility as the usual flux
extraction and photometry methods. This new technique will be developed further
and also tested against other methods in more complex fields with the goal to
make it usable for large-scale studies in the future.


title: Time Delay between Relativistic Images as a probe of Cosmic Censorship

abstract:
  We study the time delay between successive relativistic images in
gravitational lensing as a possible discriminator between various collapse end
states and hence as a probe of cosmic censorship. Specifically we consider both
black hole and naked singularity spacetimes admitting photon spheres where an
infinite number of relativistic Einstein Rings can be formed at almost the same
radius and naked singularity spacetimes without a photon sphere where multiple
relativistic Einstein Rings can form almost up to the center of the lens. The
metrics we have considered to sample these scenarios are the Schwarzschild
black hole, Janis-Newman-Winicour (naked singularity with photon sphere),
Joshi-Malafarina-Narayan, and Tolman-VI (naked singularities without photon
sphere) which are a fair sample of the theoretical possibilities. We show that
the differential time delay between the relativistic images for naked
singularities without a photon sphere progressively decreases for the models we
study as opposed to that for black holes and naked singularities with a photon
sphere, where it is known to be roughly constant. This characteristic
difference in the time delay between successive images for these two cases can
be potentially exploited for a source with known intrinsic variability to
discriminate between these scenarios even when the images are not spatially
resolved.


title: A brief remark on the topological entropy for linear switched systems

abstract:
  In this brief note, we investigate the topological entropy for linear
switched systems. Specifically, we use the Levi-Malcev decomposition of
Lie-algebra to establish a connection between the basic properties of the
topological entropy and the stability of switched linear systems. For such
systems, we show that the topological entropy for the evolution operator
corresponding to a semi-simple subalgebra is always bounded from above by the
negative of the largest real part of the eigenvalue that corresponds to the
evolution operator of a maximal solvable ideal part.


title:
Evaluation of layer potentials close to the boundary for Laplace and
  Helmholtz problems on analytic planar domains

abstract:
  Boundary integral equations are an efficient and accurate tool for the
numerical solution of elliptic boundary value problems. The solution is
expressed as a layer potential; however, the error in its evaluation grows
large near the boundary if a fixed quadrature rule is used. Firstly, we analyze
this error for Laplace's equation with analytic density and the global periodic
trapezoid rule, and find an intimate connection to the complexification of the
boundary parametrization. Our main result is then a simple and efficient scheme
for accurate evaluation up to the boundary for single- and double-layer
potentials for the Laplace and Helmholtz equations, using surrogate local
expansions about centers placed near the boundary. The scheme---which also
underlies the recent QBX Nystr\"om quadrature---is asymptotically exponentially
convergent (we prove this in the analytic Laplace case), requires no
adaptivity, generalizes simply to three dimensions, and has O(N) complexity
when executed via a locally-corrected fast multipole sum. We give an example of
high-frequency scattering from an obstacle with perimeter 700 wavelengths long,
evaluating the solution at $2\times 10^5$ points near the boundary with
11-digit accuracy in 30 seconds in MATLAB on a single CPU core.


title: A brief introduction to modern amplitude methods

abstract:
  I provide a basic introduction to modern helicity amplitude methods,
including color organization, the spinor helicity formalism, and factorization
properties. I also describe the BCFW (on-shell) recursion relation at tree
level, and explain how similar ideas - unitarity and on-shell methods - work at
the loop level. These notes are based on lectures delivered at the 2012 CERN
Summer School and at TASI 2013.


title: The overlap in glassy systems

abstract:
  In this paper I will consider many of the various definitions of the overlap
and of its probability distribution that have been introduced in the literature
starting from the original papers of Edwards and Anderson; I will present also
some of the most recent results on the probability distribution of the local
overlap in spin glasses. These quantities are related to the fluctuation
dissipation relations both in their local and in their global versions.


title: Size Effect on Order-Disorder Transition Kinetics of FePt Nanoparticles

abstract:
  The kinetics of order-disorder transition of FePt nanoparticles during high
temperature annealing is theoretically investigated. A model is developed to
address the influence of large surface to volume ratio of nanoparticles on both
the thermodynamic and kinetic aspect of the ordering process; specifically, the
nucleation and growth of L10 ordered domain within disordered nanoparticles.
The size- and shape-dependence of transition kinetics are quantitatively
addressed by a revised Johnson-Mehl-Avrami equation that included corrections
for deviations caused by the domination of surface nucleation in nanoscale
systems and the non-negligible size of the ordered nuclei. Calculation results
based on the model suggested that smaller nanoparticles are kinetically more
active but thermodynamically less transformable. The major obstacle in
obtaining completely ordered nanoparticles is the elimination of antiphase
boundaries. The results also quantitatively confirmed the existence of a
size-limit in ordering, beyond which, inducing order-disorder transitions
through annealing is impossible. A good agreement is observed between theory,
experiment and computer simulation results.


title: Rewiring the network. What helps an innovation to diffuse?

abstract:
  A fundamental question related to innovation diffusion is how the social
network structure influences the process. Empirical evidence regarding
real-world influence networks is very limited. On the other hand, agent-based
modeling literature reports different and at times seemingly contradictory
results. In this paper we study innovation diffusion processes for a range of
Watts-Strogatz networks in an attempt to shed more light on this problem. Using
the so-called Sznajd model as the backbone of opinion dynamics, we find that
the published results are in fact consistent and allow to predict the role of
network topology in various situations. In particular, the diffusion of
innovation is easier on more regular graphs, i.e. with a higher clustering
coefficient. Moreover, in the case of uncertainty - which is particularly high
for innovations connected to public health programs or ecological campaigns - a
more clustered network will help the diffusion. On the other hand, when social
influence is less important (i.e. in the case of perfect information), a
shorter path will help the innovation to spread in the society and - as a
result - the diffusion will be easiest on a random graph.


title: Projective lines as groupoids with projection structure

abstract:
  The coordinate projective line over a field is seen as a groupoid with a
further `projection' structure. We investigate conversely to what extent such
an, abstractly given, groupoid may be coordinatized by a suitable field
constructed out of the geometry.


title:
The motion of a single heavy sphere in ambient fluid: a benchmark for
  interface-resolved particulate flow simulations with significant relative
  velocities

abstract:
  Detailed data describing the motion of a rigid sphere settling in unperturbed
fluid is generated by means of highly-accurate spectral/spectral-element
simulations with the purpose of serving as a future benchmark case. A single
solid-to-fluid density ratio of 1.5 is chosen, while the value of the Galileo
number is varied from 144 to 250 such as to cover the four basic regimes of
particle motion (steady vertical, steady oblique, oscillating oblique,
chaotic). This corresponds to a range of the particle Reynolds number from 185
to 365. In addition to the particle velocity data, extracts of the fluid
velocity field are provided, as well as the pressure distribution on the
sphere's surface. Furthermore, the same solid-fluid system is simulated with a
particular non-boundary-conforming approach, i.e. the immersed boundary method
proposed by Uhlmann (JCP 2005), using various spatial resolutions. It is shown
that the current benchmark case allows to adjust the resolution requirements
for a given error tolerance in each flow regime.


title:
Association schemes on general measure spaces and zero-dimensional
  Abelian groups

abstract:
  Association schemes form one of the main objects of algebraic combinatorics,
classically defined on finite sets. In this paper we define association schemes
on arbitrary, possibly uncountable sets with a measure. We study operator
realizations of the adjacency algebras of schemes and derive simple properties
of these algebras. To develop a theory of general association schemes, we focus
on schemes on topological Abelian groups where we can employ duality theory and
the machinery of harmonic analysis. We construct translation association
schemes on such groups using the language of spectrally dual partitions. Such
partitions are shown to arise naturally on topological zero-dimensional Abelian
groups, for instance, Cantor-type groups or the groups of p-adic numbers. This
enables us to construct large classes of dual pairs of association schemes on
zero-dimensional groups with respect to their Haar measure, and to compute
their eigenvalues and intersection numbers. We also derive properties of
infinite metric schemes, connecting them with the properties of the
non-Archimedean metric on the group.
  Pursuing the connection between schemes on zero-dimensional groups and
harmonic analysis, we show that the eigenvalues have a natural interpretation
in terms of Littlewood-Paley wavelet bases, and in the (equivalent) language of
martingale theory. For a class of nonmetric schemes constructed in the paper,
the eigenvalues coincide with values of orthogonal functions on
zero-dimensional groups. We observe that these functions, which we call
Haar-like bases, have the properties of wavelets on the group, including in
some special cases the self-similarity property. This establishes a seemingly
new link between algebraic combinatorics and harmonic analysis.
  We conclude the paper by studying some analogs of problems of classical
coding theory related to the theory of association schemes.


title: A Bottom-Up Model of Self-Organized Criticality on Networks

abstract:
  The Bak-Tang-Wiesenfeld (BTW) sandpile process is an archetypal, stylized
model of complex systems with a critical point as an attractor of their
dynamics. This phenomenon, called self-organized criticality (SOC), appears to
occur ubiquitously in both nature and technology. Initially introduced on the
2D lattice, the BTW process has been studied on network structures with great
analytical successes in the estimation of macroscopic quantities, such as the
exponents of asymptotically power-law distributions. In this article, we take a
microscopic perspective and study the inner workings of the process through
both numerical and rigorous analysis. Our simulations reveal fundamental flaws
in the assumptions of past phenomenological models, the same models that
allowed accurate macroscopic predictions; we mathematically justify why
universality may explain these past successes. Next, starting from scratch, we
obtain microscopic understanding that enables mechanistic models; such models
can, for example, distinguish a cascade's area from its size. In the special
case of a 3-regular network, we use self-consistency arguments to obtain a
zero-parameters, mechanistic (bottom-up) approximation that reproduces
nontrivial correlations observed in simulations and that allows the study of
the BTW process on networks in regimes otherwise prohibitively costly to
investigate. We then generalize some of these results to configuration model
networks and explain how one could continue the generalization. The numerous
tools and methods presented herein are known to enable studying the effects of
controlling the BTW process and other self-organizing systems. More broadly,
our use of multitype branching processes to capture information bouncing
back-and-forth in a network could inspire analogous models of systems in which
consequences spread in a bidirectional fashion.


title: Metastability of the False Vacuum in a Higgs-Seesaw Model of Dark Energy

abstract:
  In a recently proposed Higgs-Seesaw model the observed scale of dark energy
results from a metastable false vacuum energy associated with mixing of the
standard model Higgs particle and a scalar associated with new physics at the
GUT or Planck scale. Here we address the issue of how to ensure metastability
of this state over cosmological time. We consider new tree-level operators, the
presence of a thermal bath of hidden sector particles, and quantum corrections
to the effective potential. We find that in the thermal scenario many
additional light degrees of freedom are typically required unless coupling
constants are somewhat fine-tuned. However quantum corrections arising from as
few as one additional light scalar field can provide the requisite support. We
also briefly consider implications of late-time vacuum decay for the perdurance
of observed structures in the universe in this model.


title: New Approach to Duality-Invariant Nonlinear Electrodynamics

abstract:
  We survey a new approach to the duality-invariant systems of nonlinear
electrodynamics, based on introducing auxiliary bi-spinor fields. In this
approach, the entire information about the given self-dual system is encoded in
the U(1) invariant interaction of the auxiliary fields, while the standard
self-dual Lagrangians appear on shell as a result of eliminating auxiliary
fields by their equations of motion. Starting from the simplest U(1) duality,
we show how this approach can be generalized to the U(N) duality (with N
independent Maxwell field strengths), as well as to self-dual systems of {\cal
N}=1 supersymmetric electrodynamics. Also, it works perfectly for self-dual
systems with higher derivatives in the action.


title:
MuPAD codes which implement limit-computable functions that cannot be
  bounded by any computable function

abstract:
  For a positive integer n, let f(n) denote the smallest non-negative integer b
such that for each system S \subseteq {x_k=1,x_i+x_j=x_k,x_i*x_j=x_k: i,j,k \in
{1,...,n}} with a solution in non-negative integers x_1,...,x_n, there exists a
solution of S in {0,...,b}^n. We prove that the function f is strictly
increasing and dominates all computable functions. We present an infinite loop
in MuPAD which takes as input a positive integer n and returns a non-negative
integer on each iteration. Let g(n,m) denote the number returned on the m-th
iteration, if n is taken as input. Then, g(n,m) \leq m-1, 0=g(n,1)<1=g(n,2)
\leq g(n,3) \leq g(n,4) \leq ... and
g(n,f(n))<f(n)=g(n,f(n)+1)=g(n,f(n)+2)=g(n,f(n)+3)=....
  A MuPAD code constructed on another principle contains a repeat-until loop
and implements a limit-computable function \xi: N-->N that cannot be bounded by
any computable function. This code takes as input a non-negative integer n,
immediately returns 0, and computes a system S of polynomial equations. If the
loop terminates for S, then the next instruction is executed and returns
\xi(n).


title: Stable Type of the Mapping Class Group

abstract:
  We use dynamics of the Teichm$\ddot{\mathrm{u}}$ller geodesic flow to show
that the action of the mapping class group on the space of projective measured
foliations has stable type $III_{\lambda}$ for some $\lambda>0$. We do this by
generalizing a criterion due to Bowen for a number to be in the stable ratio
set, and proving some Patterson-Sullivan type results for the Thurston measure
on $PMF$.


title: Minimal faithful modules over Artinian rings

abstract:
  Let R be a left Artinian ring, and M a faithful left R-module which is
minimal, in the sense that no proper submodule or proper homomorphic image of M
is faithful.
  If R is local, and socle(R) is central in R, we show that
length(M/J(R)M)+length(socle(M))$\leq$ length(socle(R))+1, strengthening a
result of T. Gulliksen.
  Most of the rest of the paper is devoted to the situation where the Artinian
ring R is not necessarily local, and does not necessarily have central socle.
In the case where R is a finite-dimensional algebra over an algebraically
closed field, we get an inequality similar to the above, with the length of
socle(R) interpreted as its length as a bimodule, and with the final summand +1
replaced by the Euler characteristic of a bipartite graph determined by the
structure of socle(R). More generally, that inequality holds if, rather than
assuming k algebraically closed, we assume that R/J(R) is a direct product of
full matrix algebras over k, and exclude the case where k has small finite
cardinality. Examples show that the restriction on the cardinality of k is
needed; we do not know whether versions of our result hold with other
hypotheses significantly weakened.
  The situation for faithful modules with only one minimality property, i.e.,
having no faithful proper submodules or having no faithful proper homomorphic
images, is more straightforward: The length of M/J(R)M in the former case, and
of socle(M) in the latter, is $\leq$ length(socle(R)) (again meaning length as
a bimodule). The final section, essentially independent of the rest of the
note, obtains these bounds, and shows that every faithful module over a left
Artinian ring has a faithful submodule with the former minimality condition and
a faithful factor module with the latter. The proofs involve some nice general
results on decompositions of modules.


title:
A guided stochastic energy-domain formulation of the second order
  M{\o}ller-Plesset perturbation theory

abstract:
  We develop an alternative formulation in the energy-domain to calculate the
second order M{\o}ller-Plesset (MP2) perturbation energies. The approach is
based on repeatedly choosing four random energies using a non-separable guiding
function, filtering four random orbitals at these energies, and averaging the
resulting Coulomb matrix elements to obtain a statistical estimate of the MP2
correlation energy. In contrast to our time-domain formulation, the present
approach is useful for both quantum chemistry and real-space/plane wave basis
sets. The scaling of the MP2 calculation is roughly linear with system size,
providing a useful tool to study dispersion energies in large systems. This is
demonstrated on a structure of 64 fullerenes within the SZ basis as well as on
silicon nanocrystals using real-space grids.


title: Balanced Allocations: A Simple Proof for the Heavily Loaded Case

abstract:
  We provide a relatively simple proof that the expected gap between the
maximum load and the average load in the two choice process is bounded by
$(1+o(1))\log \log n$, irrespective of the number of balls thrown. The theorem
was first proven by Berenbrink et al. Their proof uses heavy machinery from
Markov-Chain theory and some of the calculations are done using computers. In
this manuscript we provide a significantly simpler proof that is not aided by
computers and is self contained. The simplification comes at a cost of weaker
bounds on the low order terms and a weaker tail bound for the probability of
deviating from the expectation.


title: CMS Results on Hard Diffraction

abstract:
  In these proceedings we present CMS results on hard diffraction. Diffractive
dijet production in pp collisions at $\sqrt{s}$=7 TeV is discussed. The cross
section for dijet production is presented as a function of $\tilde{\xi}$,
representing the fractional momentum loss of the scattered proton in
single-diffractive events. The observation of W and Z boson production in
events with a large pseudo-rapidity gap is also presented.


title:
The unusual photometric behavior of the new FUor star V2493 Cyg (HBC
  722)

abstract:
  The recent results from photometric study of the new FUor star found in the
field of NGC 7000/IC 5070 are presented in the paper. The outburst of V2493 Cyg
in the summer of 2010 generated considerable interest among the astronomical
community. V2493 Cyg is the first FUor object, whose outburst was observed from
its very beginning in all spectral ranges. After reaching the firs maximum in
September/October 2010, the brightness of V2493 Cyg declined slowly, having
weakened by 1.45 mag. (V) by the spring/early summer of 2011. Since the autumn
of 2011, another light increase occurred and the star became brighter by 1.8
mag. (V) until April 2013. The recent photometric data show that the star keeps
its maximum brightness during the period April - August 2013 and the recorded
amplitude of the outburst reaches Delta V=5.1 mag. Consequently, the outburst
of V2493 Cyg lasts for more than three years. We expect that the interest in
this object will increase in the coming years and the results will help to
explore the nature of young stars.


title: Topological Order and Reflection Positivity

abstract:
  The interplay between the two fundamental concepts of topological order and
reflection positivity allows one to characterize the ground states of certain
many-body Hamiltonians. We define topological order in an appropriate fashion
and show that certain operators have positive expectation value in all ground
states. We apply our method to vortex loops in a model relevant to topological
quantum memories.

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


title: Intrinsic scaling properties for nonlocal operators

abstract:
  We study growth lemmas and questions of regularity for generators of Markov
processes. The generators are allowed to have an arbitrary order of
differentiability less than 2. In general, this order is represented by a
function and not by a number. The approach enables a careful study of
regularity issues up to the phase boundary between integro-differential
(positive order of differentiability) and integral operators (nonnegative order
of differentiability). The proof is based on intrinsic scaling properties of
the underlying operators and stochastic processes.


title: An Almost Sudden Jump in Quantum Complexity

abstract:
  The Quantum Satisfiability problem (QSAT) is the generalization of the
canonical NP-complete problem - Boolean Satisfiability. (k,s)-QSAT is the
following variant of the problem: given a set of projectors of rank 1, acting
non-trivially on k qubits out of n qubits, such that each qubit appears in at
most s projectors, decide whether there exists a quantum state in the null
space of all the projectors. Let f*(k) be the maximal integer s such that every
(k,s)-QSAT instance is satisfiable. Deciding (k,f*(k))-QSAT is computationally
easy: by definition the answer is "satisfiable". But, by relaxing the
conditions slightly, we show that (k,f*(k)+2)-QSAT is QMA_1-hard, for k >=15.
This is a quantum analogue of a classical result by Kratochv\'il et al.
[KST93]. We use the term "an almost sudden jump" to stress that the complexity
of (k,f*(k)+1)-QSAT is open, where the jump in the classical complexity is
known to be sudden.
  We present an implication of this finding to the quantum PCP conjecture,
arguably one of the most important open problems in the field of Hamiltonian
complexity. Our implications impose constraints on one possible way to refute
the quantum PCP.


title: Geometric presentations of Lie groups and their Dehn functions

abstract:
  We study the Dehn function of connected Lie groups. We show that this
function is always exponential or polynomially bounded, according to the
geometry of weights and of the 2-cohomology of their Lie algebras. Our work,
which also addresses algebraic groups over local fields, uses and extends
Abels' theory of multiamalgams of graded Lie algebras, in order to provide
workable presentations of these groups.


title: k-fold Sidon sets

abstract:
  Let $k \geq 1$ be an integer. A set $A \subset \mathbb{Z}$ is a $k$-fold
Sidon set if $A$ has only trivial solutions to each equation of the form $c_1
x_1 + c_2 x_2 + c_3 x_3 + c_4 x_4 = 0$ where $0 \leq |c_i | \leq k$, and $c_1 +
c_2 + c_3 + c_4 = 0$. We prove that for any integer $k \geq 1$, a $k$-fold
Sidon set $A \subset [N]$ has at most $(N/k)^{1/2} + O((Nk)^{1/4})$ elements.
Indeed we prove that given any $k$ positive integers $c_1<\cdots <c_k$, any set
$A\subset [N]$ that contains only trivial solutions to
$c_i(x_1-x_2)=c_j(x_3-x_4)$ for each $1 \le i \le j \le k$, has at most
$(N/k)^{1/2}+O((c_k^2N/k)^{1/4})$ elements. On the other hand, for any $k \geq
2$ we can exhibit $k$ positive integers $c_1,\dots, c_k$ and a set $A\subset
[N]$ with $|A|\ge (\frac 1k+o(1))N^{1/2}$, such that $A$ has only trivial
solutions to $c_i(x_1 - x_2) = c_j (x_3 - x_4)$ for each $1 \le i \le j\le k$.


title:
Seeking for ultrashort "non-bonded" hydrogen-hydrogen contacts in some
  rigid hydrocarbons and their chlorinated derivatives

abstract:
  In this communication a systematic computational survey on some rigid
hydrocarbon skeletons, e.g. half-cage pentacyclododecanes and
tetracyclododecanes, and their chlorinated derivatives in order to seek for the
so-called ultrashort "non-bonded" hydrogen-hydrogen contacts is done. It is
demonstrated that upon a proper choice and modifications of the main
hydrocarbon backbones, and addition of some chlorine atoms instead of the
original hydrogen atoms in parts of the employed hydrocarbons, the resulting
strain triggers structural changes yielding ultrashort hydrogen-hydrogen
contacts with inter-nuclear distances as small as 1.38 Angstrom. Such
ultrashort contacts are clearly less than the world record of an ultrashort
non-bonded hydrogen-hydrogen contact, 1.56 Angstrom, very recently realized
experimentally by Pascal and coworkers in in,in-bis(hydrosilane) [J. Am. Chem.
Soc. 135, 13235 (2013)]. The resulting computed structures as well as the
developed methodology for structure design open the door for constructing a
proper set of molecules for future studies on the nature of the so-called
non-bonded hydrogen-hydrogen interactions that is now an active and
controversial area of research.


title: Hypermap-Homology Quantum Codes (Ph.D. thesis)

abstract:
  We introduce a new type of sparse CSS quantum error correcting code based on
the homology of hypermaps. Sparse quantum error correcting codes are of
interest in the building of quantum computers due to their ease of
implementation and the possibility of developing fast decoders for them. Codes
based on the homology of embeddings of graphs, such as Kitaev's toric code,
have been discussed widely in the literature and our class of codes generalize
these. We use embedded hypergraphs, which are a generalization of graphs that
can have edges connected to more than two vertices. We develop theorems and
examples of our hypermap-homology codes, especially in the case that we choose
a special type of basis in our homology chain complex. In particular the most
straightforward generalization of the $m \times m$ toric code to
hypermap-homology codes gives us a $[(3/2)m^2,2,m]$ code as compared to the
toric code which is a $[2m^2,2,m]$ code. Thus we can protect the same amount of
quantum information, with the same error-correcting capability, using less
physical qubits.


title:
Numerical Approximations to Fractional Problems of the Calculus of
  Variations and Optimal Control

abstract:
  This chapter presents some numerical methods to solve problems in the
fractional calculus of variations and fractional optimal control. Although
there are plenty of methods available in the literature, we concentrate mainly
on approximating the fractional problem either by discretizing the fractional
term or expanding the fractional derivatives as a series involving integer
order derivatives. The former method, as a subclass of direct methods in the
theory of calculus of variations, uses finite differences, Grunwald-Letnikov
definition in this case, to discretize the fractional term. Any quadrature rule
for integration, regarding the desired accuracy, is then used to discretize the
whole problem including constraints. The final task in this method is to solve
a static optimization problem to reach approximated values of the unknown
functions on some mesh points.
  The latter method, however, approximates fractional problems by classical
ones in which only derivatives of integer order are present. Precisely, two
continuous approximations for fractional derivatives by series involving
ordinary derivatives are introduced. Local upper bounds for truncation errors
are provided and, through some test functions, the accuracy of the
approximations are justified. Then we substitute the fractional term in the
original problem with these series and transform the fractional problem to an
ordinary one. Hereafter, we use indirect methods of classical theory, e.g.
Euler-Lagrange equations, to solve the approximated problem. The methods are
mainly developed through some concrete examples which either have obvious
solutions or the solution is computed using the fractional Euler-Lagrange
equation.


title:
Complexifying Lie group actions on homogeneous manifolds of non-compact
  dimension two

abstract:
  If $X$ is a connected complex manifold with $d_X = 2$ that admits the
holomorphic and transitive action of a (connected) Lie group $G$, then the
action extends to an action of the complexification $\hat{G}$ of $G$ on $X$
except when either the unit disk or else a strictly pseudoconcave homogeneous
complex manifold is involved as base or fiber in some homogeneous fibration of
$X$.


title: Nonequilibrium stationary state for a damped rotator

abstract:
  Perturbative construction of the nonequilibrium steady state of a rotator
under a stochastic forcing while subject to torque and friction