title: The calibration of the vector polarimeter POLIS

abstract:
  In this diploma thesis, the calibration of the vector polarimeter POLIS will
be described. The instrument is built by the Kiepenheuer-Institut fuer
Sonnenphysik (Freiburg/Germany) in cooperation with the High Altitude
Observatory (Boulder/USA) and will be operated at the German Vacuum Tower
Telescope in Tenerife. The instrument yields simultaneously the polarization
state of light in two spectral ranges at 396 nm and 630 nm. The measurement is
performed with a rotating retarder, which modulates the incident polarization.
The modulation is transformed into a varying intensity through polarizing
beamsplitters. The demodulation uses a weighted integration scheme to obtain
the full Stokes vector of the radiation. The calibration of the polarimeter is
performed through the evaluation of a calibration data set produced with a
calibration unit consisting of a linear polarizer and a retarder. The
instrumental calibration and the polarimetric model of the telescope are
described in detail.
  This document is an unaltered version of my diploma thesis from 2002. Parts
of it have been re-used in later publications, but in a very compressed way
removing a lot of details. Its currrent intended use would be as introductory
literature to polarimetry and its application in solar physics for students. I
have used it a few times already for exactly this purpose.


title: MadDM v.1.0: Computation of Dark Matter Relic Abundance Using MadGraph5

abstract:
  We present MadDM v.1.0, a numerical tool to compute dark matter relic
abundance in a generic model. The code is based on the existing MadGraph 5
architecture and as such is easily integrable into any MadGraph collider study.
A simple Python interface offers a level of user-friendliness characteristic of
MadGraph 5 without sacrificing functionality. MadDM is able to calculate the
dark matter relic abundance in models which include a multi-component dark
sector, resonance annihilation channels and co-annihilations. We validate the
code in a wide range of dark matter models by comparing the relic density
results from MadDM to the existing tools and literature.


title: PSR J1723-2837: An Eclipsing Binary Radio Millisecond Pulsar

abstract:
  We present a study of PSR J1723-2837, an eclipsing, 1.86 ms millisecond
binary radio pulsar discovered in the Parkes Multibeam survey. Radio timing
indicates that the pulsar has a circular orbit with a 15 hr orbital period, a
low-mass companion, and a measurable orbital period derivative. The eclipse
fraction of ~15% during the pulsar's orbit is twice the Roche lobe size
inferred for the companion. The timing behavior is significantly affected by
unmodeled systematics of astrophysical origin, and higher-order orbital period
derivatives are needed in the timing solution to account for these variations.
We have identified the pulsar's (non-degenerate) companion using archival
ultraviolet, optical, and infrared survey data and new optical photometry.
Doppler shifts from optical spectroscopy confirm the star's association with
the pulsar and indicate a pulsar-to-companion mass ratio of 3.3 +/- 0.5,
corresponding to a companion mass range of 0.4 to 0.7 Msun and an orbital
inclination angle range of between 30 and 41 degrees, assuming a pulsar mass
range of 1.4-2.0 Msun. Spectroscopy indicates a spectral type of G for the
companion and an inferred Roche-lobe-filling distance that is consistent with
the distance estimated from radio dispersion. The features of PSR J1723-2837
indicate that it is likely a "redback" system. Unlike the five other Galactic
redbacks discovered to date, PSR J1723-2837 has not been detected as a
gamma-ray source with Fermi. This may be due to an intrinsic spin-down
luminosity that is much smaller than the measured value if the unmeasured
contribution from proper motion is large.


title:
Discrete localized modes supported by an inhomogeneous defocusing
  nonlinearity

abstract:
  We report that infinite and semi-infinite lattices with spatially
inhomogeneous self-defocusing (SDF)\ onsite nonlinearity, whose strength
increases rapidly enough toward the lattice periphery, support stable
unstaggered (UnST) discrete bright solitons, which do not exist in lattices
with the spatially uniform SDF nonlinearity. The UnST solitons coexist with
stable staggered (ST) localized modes, which are always possible under the
defocusing onsite nonlinearity. The results are obtained in a numerical form,
and also by means of variational approximation (VA). In the semi-infinite
(truncated) system, some solutions for the UnST surface solitons are produced
in an exact form. On the contrary to surface discrete solitons in uniform
truncated lattices, the threshold value of the norm vanishes for the UnST
solitons in the present system. Stability regions for the novel UnST solitons
are identified. The same results imply the existence of ST discrete solitons in
lattices with the spatially growing self-focusing nonlinearity, where such
solitons cannot exist either if the nonlinearity is homogeneous. In addition, a
lattice with the uniform onsite SDF nonlinearity and exponentially decaying
inter-site coupling is introduced and briefly considered too. Via a similar
mechanism, it may also support UnST discrete solitons, under the action of the
SDF nonlinearity. The results may be realized in arrayed optical waveguides and
collisionally inhomogeneous Bose-Einstein condensates trapped in deep optical
lattices. A generalization for a two-dimensional system is briefly considered
too.


title:
Prediction of Debye-Scherrer diffraction patterns in arbitrarily
  strained samples

abstract:
  The prediction of Debye-Scherrer diffraction patterns from strained samples
is typically conducted in the small strain limit. Although valid for small
deviations from the hydrostat (such as the conditions of finite strength
typically observed in diamond anvil cells) this assertion is likely to fail for
the large strain anisotropies (often of order 10% in normal strain) such as
those found in uniaixally loaded dynamic compression experiments. In this paper
we derive a general form for the (\theta_B, \phi) dependence of the diffraction
for an arbitrarily deformed sample in arbitrary geometry. We show that this
formula is consistent with ray traced diffraction for highly strained
computationally generated polycrystals, and that the formula shows deviations
from the small strain solutions previously reported.


title:
In-situ measurement of vacuum window birefringence by atomic
  spectroscopy

abstract:
  We present an in-situ method to measure the birefringence of a single vacuum
window by means of microwave spectroscopy on an ensemble of cold atoms.
Stress-induced birefringence can cause an ellipticity in the polarization of an
initially linearly-polarized laser beam. The amount of ellipticity can be
reconstructed by measuring the differential vector light shift of an atomic
hyperfine transition. Measuring the ellipticity as a function of the linear
polarization angle allows us to infer the amount of birefringence $\Delta n$ at
the level of $10^{-8}$ and identify the orientation of the optical axes. The
key benefit of this method is the ability to separately characterize each
vacuum window, allowing the birefringence to be precisely compensated in
existing vacuum apparatuses.


title:
Gluon spectral functions and transport coefficients in Yang--Mills
  theory

abstract:
  We compute non-perturbative gluon spectral functions at finite temperature in
quenched QCD with the maximum entropy method. We also provide a closed loop
equation for the spectral function of the energy-momentum tensor in terms of
the gluon spectral function. This setup is then used for computing the shear
viscosity over entropy ratio $\eta/s$ in a temperature range from about $0.4\,
T_c$ to $4.5\, T_c$. The ratio $\eta /s$ has a minimum at about $1.25\, T_c$
with the value of about 0.115. We also discuss extensions of the present
results to QCD.


title: A note on the scale evolution of tri-gluon correlations

abstract:
  We reexamine the scale dependence of the gluonic pole tri-gluon correlations
relevant for the transverse single spin asymmetries. Our results differ from
those of all previous similar calculations. The corresponding asymptotic
behavior of tri-gluon correlations at small x is also briefly discussed.


title: Vacuum Compatibility of 3D-Printed Materials

abstract:
  The fabrication fidelity and vacuum properties are tested for currently
available 3D-printed materials including polyamide, glass, acrylic, and
sterling silver. The silver was the only material found to be suitable to
ultrahigh vacuum environments due to outgassing and sublimation observed in
other materials.


title:
Existence and non-existence of area-minimizing hypersurfaces in
  manifolds of non-negative Ricci curvature

abstract:
  We study minimal hypersurfaces in manifolds of non-negative Ricci curvature,
Euclidean volume growth and quadratic curvature decay at infinity. By
comparison with capped spherical cones, we identify a precise borderline for
the Ricci curvature decay. Above this value, no complete area-minimizing
hypersurfaces exist. Below this value, in contrast, we construct examples.


title: Entanglement and Thermal Entropy of Gauge Fields

abstract:
  We consider the universal logarithmic divergent term in the entanglement
entropy of gauge fields in the Minkowski vacuum with an entangling sphere.
Employing the mapping in arXiv:1102.0440, we analyze the corresponding thermal
entropy on open Einstein universe and on the static patch of de Sitter. Using
the heat kernel of the vector Laplacian we resolve a discrepancy between the
free field calculation and the expected Euler conformal anomaly. The resolution
suggests a modification of the well known formulas for the vacuum expectation
value of the spin-1 energy-momentum tensor on conformally flat space-times.


title:
A proposal for a Chinese keyboard for cellphones, smartphones, ipads and
  tablets

abstract:
  In this paper, we investigate the possibility to use two tilings of the
hyperbolic plane as basic frame for devising a way to input texts in Chinese
characters into messages of cellphones, smartphones, ipads and tablets.


title:
Mesoscale phenomena in solutions of 3-methylpyridine, heavy water, and
  an antagonistic salt

abstract:
  We have investigated controversial issues regarding the mesoscale behavior of
3-methylpyridine (3MP), heavy water, and sodium tetraphenylborate (NaBPh4)
solutions by combining results obtained from dynamic light scattering (DLS) and
small-angle neutron scattering (SANS). We have addressed three questions: (i)
what is the origin of the mesoscale inhomogeneities (order of 100 nm in size)
manifested by the "slow mode" in DLS? (ii) Is the periodic structure observed
from SANS an inherent property of this system? (iii) What is the universality
class of critical behavior in this system? Our results confirm that the "slow
mode" observed from DLS experiments corresponds to long-lived, highly stable
mesoscale droplets (order of 100 nm in size), which occur only when the solute
(3MP) is contaminated by hydrophobic impurities. SANS data confirm the presence
of a periodic structure with a periodicity of about 10 nm. This periodic
structure cannot be eliminated by nanopore filtration and thus is indeed an
inherent solution property. The critical behavior of this system, in the range
of concentration and temperatures investigated by DLS experiments, indicates
that the criticality belongs to the universality class of the 3-dimensional
Ising model.


title:
The asymptotic strong Feller property does not imply the e-property for
  Markov-Feller semigroups

abstract:
  T. Szarek [Stud. Math. 189 (2008), {\S} 4] have discussed the relationship
between two important notions concerning Markov semigroups: the asymptotic
strong Feller property and the e-property, asserting that the former property
implies the latter one. In this very short note we rectify this issue
exhibiting a simple example of a Markov-Feller semigroup enjoying the
asymptotic strong Feller property, for which the e-property is not satisfied.
(See also the comment on a connection between the asymptotic strong Feller
property and the e-property by T. Szarek, D. Worm [ETDS 32 (2012), {\S} 1]).
Additionally we give a very simple example - in comparing with the one given by
T. Szarek [Stud. Math. 189 (2008), {\S} 4] - showing that also the converse
implication does not hold.


title:
Viscoelastic Tidal Dissipation in Giant Planets and Formation of Hot
  Jupiters Through High-Eccentricity Migration

abstract:
  We study the possibility of tidal dissipation in the solid cores of giant
planets and its implication for the formation of hot Jupiters through
high-eccentricity migration. We present a general framework by which the tidal
evolution of planetary systems can be computed for any form of tidal
dissipation, characterized by the imaginary part of the complex tidal Love
number, ${\rm Im}[{\tilde k}_2(\omega)]$, as a function of the forcing
frequency $\omega$. Using the simplest viscoelastic dissipation model (the
Maxwell model) for the rocky core and including the effect of a nondissipative
fluid envelope, we show that with reasonable (but uncertain) physical
parameters for the core (size, viscosity and shear modulus), tidal dissipation
in the core can accommodate the tidal-Q constraint of the Solar system gas
giants and at the same time allows exoplanetary hot Jupiters to form via tidal
circularization in the high-e migration scenario. By contrast, the often-used
weak friction theory of equilibrium tide would lead to a discrepancy between
the Solar system constraint and the amount of dissipation necessary for high-e
migration. We also show that tidal heating in the rocky core can lead to modest
radius inflation of the planets, particularly when the planets are in the
high-eccentricity phase ($e\sim 0.6$) during their high-e migration. Finally,
as an interesting by-product of our study, we note that for a generic tidal
response function ${\rm Im}[{\tilde k}_2(\omega)]$, it is possible that spin
equilibrium (zero torque) can be achieved for multiple spin frequencies (at a
given $e$), and the actual pseudo-synchronized spin rate depends on the
evolutionary history of the system.


title:
Optimal interdependence between networks for the evolution of
  cooperation

abstract:
  Recent research has identified interactions between networks as crucial for
the outcome of evolutionary games taking place on them. While the consensus is
that interdependence does promote cooperation by means of organizational
complexity and enhanced reciprocity that is out of reach on isolated networks,
we here address the question just how much interdependence there should be.
Intuitively, one might assume the more the better. However, we show that in
fact only an intermediate density of sufficiently strong interactions between
networks warrants an optimal resolution of social dilemmas. This is due to an
intricate interplay between the heterogeneity that causes an asymmetric
strategy flow because of the additional links between the networks, and the
independent formation of cooperative patterns on each individual network.
Presented results are robust to variations of the strategy updating rule, the
topology of interdependent networks, and the governing social dilemma, thus
suggesting a high degree of universality.

categories: physics.soc-ph cond-mat.stat-mech cs.SI q-bio.PE


title: Universal Resistivity from Holographic Massive Gravity

abstract:
  Massive gravity provides a holographic model for theories exhibiting momentum
dissipation. We provide an analytic expression for the DC conductivity. The
result is universal, depending only on properties of the infra-red horizon, and
holds at finite temperature and charge density. In addition, we provide a
derivation of black hole thermodynamics in holographic massive gravity and show
that the resulting physics is sensible.


title: MY Serpentis: a high-mass triple system in the Ser OB2 association

abstract:
  We present spectroscopic observations of the massive multiple system
HD\,167971, located in the open cluster NGC\,6604. The brighter component of
the triple system is the overcontact eclipsing binary MY\,Ser with an orbital
period of 3.32\,days. The radial velocities and the previously published UBV
data obtained by \citet{may10} and the UBVRI light curves by \citet{dav88} are
analysed for the physical properties of the components. We determine the
following absolute parameters: for the primary star M$_p$=32.23$\pm$0.54
M$_{\odot}$, R$_p$=14.23$\pm$0.75 R$_{\odot}$; and for the secondary star
M$_s$=30.59$\pm$0.53 M$_{\odot}$, R$_s$=13.89$\pm$0.75 R$_{\odot}$.
Photoelectric times of minimum light are analyzed under the consideration of
the light-time orbit. The center-of-mass of the eclipsing binary is orbiting
around the common center-of-gravity of the triple system with a period of
21.2$\pm$0.7\,yr and with a projected semi-major axis of 5.5$\pm$0.7\,AU. The
mass function for the third star was calculated as 0.370$\pm$0.036 M$_{\odot}$.
The light contributions of the third star to the triple system in the UBV
pass-bands were derived and the intrinsic magnitudes and colors were calculated
individually for the three stars. The components of the eclipsing pair were
classified as O7.5 {\sc iii} and O9.5 {\sc iii}. The intrinsic color indices
for the third star yield a spectral type of (O9.5-B0) {\sc iii-i}. {\bf This
classification leads to constrain the inclination of the third-body orbit,
which should be about 30$^{o}$, and therefore its mass should be about 29
M$_{\odot}$. MY\,Ser is one of the rare massive O-type triple system at a
distance of 1.65$\pm$0.13\,kpc, the same as for the NGC\,6604 embedded in the
Ser\,OB2 association.}


title: The tensor hierarchy simplified

abstract:
  A compact formulation of the field-strengths, Bianchi identities and gauge
transformations for tensor hierarchies in gauged maximal supergravity theories
is given. A key role in the construction is played by the recently-introduced
tensor hierarchy algebra.


title: Fermions with Lorentz-violating operators of arbitrary dimension

abstract:
  The theoretical description of fermions in the presence of Lorentz and CPT
violation is developed. We classify all Lorentz- and CPT-violating and
invariant terms in the quadratic Lagrange density for a Dirac fermion,
including operators of arbitrary mass dimension. The exact dispersion relation
is obtained in closed and compact form, and projection operators for the
spinors are derived. The Pauli hamiltonians for particles and antiparticles are
extracted, and observable combinations of operators are identified. We
characterize and enumerate the coefficients for Lorentz violation for any
operator mass dimension via a decomposition using spin-weighted spherical
harmonics. The restriction of the general theory to various special cases is
presented, including isotropic models, the nonrelativistic and
ultrarelativistic limits, and the minimal Standard-Model Extension. Expressions
are derived in several limits for the fermion dispersion relation, the
associated fermion group velocity, and the fermion spin-precession frequency.
We connect the analysis to some other formalisms and use the results to extract
constraints from astrophysical observations on isotropic ultrarelativistic
spherical coefficients for Lorentz violation.


title: Simulations of disk galaxies with cosmic ray driven galactic winds

abstract:
  We present results from high-resolution hydrodynamic simulations of isolated
SMC- and Milky Way-sized galaxies that include a model for feedback from
galactic cosmic rays (CRs). We find that CRs are naturally able to drive winds
with mass loading factors of up to ~10 in dwarf systems. The scaling of the
mass loading factor with circular velocity between the two simulated systems is
consistent with \propto v_c^{1-2} required to reproduce the faint end of the
galaxy luminosity function. In addition, simulations with CR feedback reproduce
both the normalization and the slope of the observed trend of wind velocity
with galaxy circular velocity. We find that winds in simulations with CR
feedback exhibit qualitatively different properties compared to SN driven
winds, where most of the acceleration happens violently in situ near star
forming sites. In contrast, the CR-driven winds are accelerated gently by the
large-scale pressure gradient established by CRs diffusing from the
star-forming galaxy disk out into the halo. The CR-driven winds also exhibit
much cooler temperatures and, in the SMC-sized system, warm (T~10^4 K) gas
dominates the outflow. The prevalence of warm gas in such outflows may provide
a clue as to the origin of ubiquitous warm gas in the gaseous halos of galaxies
detected via absorption lines in quasar spectra.


title:
Driven dipole oscillations and the lowest energy excitations of strongly
  interacting lattice bosons in a harmonic trap

abstract:
  We show that the analysis of the time evolution of the occupation of site and
momentum modes of harmonically trapped lattice hard-core bosons, under driven
dipole oscillations, allows one to determine the energy of the lowest
one-particle excitations of the system in equilibrium. The analytic solution of
a single particle in the absence of a lattice is used to identify which
function of those time-dependent observables is best fit for the analysis, as
well as to relate the dynamic response of the system to its single-particle
spectrum. In the presence of the lattice and of multiple particles, a much
richer and informative dynamical response is observed under the drive.


title:
Evolution of quantum field, particle content and classicality in the
  three stage universe

abstract:
  We study the evolution of a quantum scalar field in a toy universe which has
three stages of evolution, viz., (i) an early (inflationary) de Sitter phase
(ii) radiation dominated phase and (iii) late-time (cosmological constant
dominated) de Sitter phase. Using Schr\"odinger picture, the scalar field
equations are solved separately for the three stages and matched at the
transition points. The boundary conditions are chosen so that field modes in
the early de Sitter evolves from Bunch-Davies vacuum state. We determine the
(time-dependent) particle content of this quantum state for the entire
evolution of the universe and describe the various features both numerically
and analytically. We also describe the quantum to classical transition in terms
of a {\it classicality parameter} which tracks the particle creation and its
effect on phase space correlation of the quantum field.


title:
Rubidium abundances in the globular clusters NGC 6752, NGC 1904 and NGC
  104 (47 Tuc)

abstract:
  Large star-to-star variations of the abundances of proton-capture elements,
such as Na and O, in globular clusters (GCs) are interpreted as the effect of
internal pollution resulting from the presence of multiple stellar populations.
To better constrain this scenario we investigate the abundance distribution of
the heavy element rubidium (Rb) in NGC 6752, NGC 1904, and NGC 104 (47 Tuc).
Combining the results from our sample with those in the literature, we found
that Rb exhibits no star-to-star variations, regardless the cluster
metallicity, with the possible intriguing, though very uncertain, exception of
the metal-rich bulge cluster NGC 6388. If no star-to-star variations will be
confirmed for all GCs, it implies that the stellar source of the proton-capture
element variations must not have produced significant amounts of Rb. This
element is observed to be enhanced at extremely high levels in
intermediate-mass AGB (IM-AGB) stars in the Magellanic Clouds (i.e., at a
metallicity similar to 47 Tuc and NGC 6388). This may present a challenge to
this popular candidate polluter, unless the mass range of the observed IM-AGB
stars does not participate in the formation of the second-generation stars in
GCs. A number of possible solutions are available to resolve this conundrum,
also given that the Magellanic Clouds observations are very uncertain and may
need to be revised. The fast rotating massive stars scenario would not face
this potential problem as the slow mechanical winds of these stars during their
main-sequence phase do not carry any Rb enhancements; however, these candidates
face even bigger issues such as the production of Li and the close
over-imposition with core-collapse supernova timescales. Observations of Sr,
Rb, and Zr in metal-rich clusters such as NGC 6388 and NGC 6441 are sorely
needed to clarify the situation.


title:
Traverse the landscape of the mind by walking: an exploration of a new
  brainstorming practice

abstract:
  Group brainstorming is a well-known idea generation technique, which plays a
key role in software development processes. Despite this, the relevant
literature has had little to offer in advancing our understanding of the
effectiveness of group brainstorming sessions. In this paper we present a
research-in-progress on brainstorming while walking, which is a practice built
upon the relationship between thinking and walking. The objective is to better
understand how to conduct group brainstorming effectively. We compared two
brainstorming sessions, one performed during a mountain walk, the other
traditionally in a room. Three preliminary findings are obtained: walking can
lead to an effective idea generation session; brainstorming while walking can
encourage team members to participate in and contribute to the session in an
equal manner; and it can help a team to maintain sustainable mental energy. Our
study opens up an avenue for future exploration of effective group
brainstorming practices.


title:
Bounds on Dark Matter Properties from Radio Observations of Ursa Major
  II using the Green Bank Telescope

abstract:
  Radio observations of the Ursa Major II dwarf spheroidal galaxy obtained
using the Green Bank Telescope are used to place bounds on WIMP dark matter
properties. Dark matter annihilation releases energy in the form of charged
particles which emit synchrotron radiation in the magnetic field of the dwarf
galaxy. We compute the expected synchrotron radiation intensity from WIMP
annihilation to various primary channels. The predicted synchrotron radiation
is sensitive to the distribution of dark matter in the halo, the diffusion
coefficient D_0, the magnetic field strength B, the particle mass m_\chi, the
annihilation rate <\sigma v>, and the annihilation channel. Limits on <\sigma
v>, m_\chi, B, and D_0 are obtained for the e^+ e^-, \mu^+ \mu^-, \tau^+
\tau^-, and b \bar b channels. Constraints on these parameters are sensitive to
uncertainties in the measurement of the dark matter density profile. For the
best fit halo parameters derived from stellar kinematics, we exclude 10 GeV
WIMPs annihilating directly to e^+ e^- at the thermal rate <\sigma v> = 2.18 x
10^{-26} cm^3/s at the 2\sigma level, for B > 0.6 microGauss (1.6 microGauss)
and D_0 = 0.1 (1.0) x the Milky Way diffusion value.


title: Solving 2D QCD with an adjoint fermion analytically

abstract:
  We present an analytic approach to solving 1+1 dimensional QCD with an
adjoint Majorana fermion. In the UV this theory is described by a trivial CFT
containing free fermions. The quasi-primary operators of this CFT lead to a
discrete basis of states which is useful for diagonalizing the Hamiltonian of
the full strongly interacting theory. Working at large-$N$, we find that the
decoupling of high scaling-dimension quasi-primary operators from the
low-energy spectrum occurs exponentially fast in their scaling-dimension. This
suggests a scheme, whereby, truncating the basis to operators of dimension
below $\Delta_{max}$, one can calculate the low-energy spectrum, parametrically
to an accuracy of $e^{-\Delta_{max}}$ (although the precise accuracy depends on
the state). Choosing $\Delta_{max} =9.5$ we find very good agreement with the
known spectrum obtained earlier by numerical DLCQ methods. Specifically, below
the first three-particle threshold, we are able to identify all six
single-particle bound-states, as well as several two-particle thresholds.


title: Vortex states in mesoscopic three-band superconductors

abstract:
  Using multi-component Ginzburg-Landau simulations, we show a plethora of
vortex states possible in mesoscopic three-band superconductors. We find that
mesoscopic confinement stabilizes chiral states, with non-trivial phase
differences between the band-condensates, as the ground state of the system. As
a consequence, we report the broken-symmetry vortex states, the chiral states
where vortex cores in different band condensates do not coincide (split-core
vortices), as well as fractional vortex states with broken time-reversal
symmetry.


title:
The Third Gravitational Lensing Accuracy Testing (GREAT3) Challenge
  Handbook

abstract:
  The GRavitational lEnsing Accuracy Testing 3 (GREAT3) challenge is the third
in a series of image analysis challenges, with a goal of testing and
facilitating the development of methods for analyzing astronomical images that
will be used to measure weak gravitational lensing. This measurement requires
extremely precise estimation of very small galaxy shape distortions, in the
presence of far larger intrinsic galaxy shapes and distortions due to the
blurring kernel caused by the atmosphere, telescope optics, and instrumental
effects. The GREAT3 challenge is posed to the astronomy, machine learning, and
statistics communities, and includes tests of three specific effects that are
of immediate relevance to upcoming weak lensing surveys, two of which have
never been tested in a community challenge before. These effects include
realistically complex galaxy models based on high-resolution imaging from
space; spatially varying, physically-motivated blurring kernel; and combination
of multiple different exposures. To facilitate entry by people new to the
field, and for use as a diagnostic tool, the simulation software for the
challenge is publicly available, though the exact parameters used for the
challenge are blinded. Sample scripts to analyze the challenge data using
existing methods will also be provided. See http://great3challenge.info and
http://great3.projects.phys.ucl.ac.uk/leaderboard/ for more information.


title: The effect of points fattening in dimension three

abstract:
  There has been increased recent interest in understanding the relationship
between the symbolic powers of an ideal and the geometric properties of the
corresponding variety. While a number of results are available for the
two-dimensional case, the higher-dimensional case is largely unexplored. In the
present paper we study a natural conjecture arising from a result by Bocci and
Chiantini. As a first step towards understanding the higher-dimensional
picture, we show that this conjecture is true in dimension three. Also, we
provide examples showing that the hypotheses of the conjecture may not be
weakened.


title: Quantum criticality of the imperfect Bose gas in d dimensions

abstract:
  We study the low-temperature limit of the d-dimensional imperfect Bose gas.
Relying on an exact analysis of the microscopic model, we establish the
existence of a second-order quantum phase transition to a phase involving the
Bose-Einstein condensate. The transition is triggered by varying the chemical
potential and persists at non-zero temperatures T for d>2. We extract the exact
phase diagram and identify the scaling regimes in the vicinity of the quantum
critical point focusing on the behavior of the correlation length \xi. The
length \xi develops an essential singularity exclusively for d=2. We follow the
evolution of the phase diagram varying d. For d>2 our results agree with
renormalization-group based analysis of the effective bosonic order-parameter
models with the dynamical exponent z=2.


title: Bell's Experiment in Quantum Mechanics and Classical Physics

abstract:
  Both the quantum mechanical and classical Bells experiment are within the
focus of this paper. The fact that one measures different probabilities in both
experiments is traced back to the superposition of two orthogonal but
nonentangled substates in the quantum mechanical case. This superposition
results in an interference term that can be splitted into two additional states
representing a sink and a source of probabilities in the classical event space
related to Bells experiment. As a consequence, a statistical operator can be
related to the quantum mechanical Bells experiment that contains already
negative quasi probabilities, as usually known from quantum optics in
conjunction with the Glauber-Sudarshan equation. It is proven that the
existence of such negative quasi probabilities are neither a sufficient nor a
necessary condition for entanglement. The equivalence of using an interaction
picture in a fixed basis or of employing a change of basis to describe Bells
experiment is demonstrated afterwards. The discussion at the end of this paper
regarding the application of the complementarity principle to the quantum
mechanical Bells experiment is supported by very recent double slit experiments
performed with polarization entangled photons.


title: Molecular Detectability in Exoplanetary Emission Spectra

abstract:
  Of the many recently discovered worlds orbiting distant stars, very little is
yet known of their chemical composition. With the arrival of new transit
spectroscopy and direct imaging facilities, the question of molecular
detectability as a function of signal-to-noise (SNR), spectral resolving power
and type of planets has become critical. In this paper, we study the
detectability of key molecules in the atmospheres of a range of planet types,
and report on the minimum detectable abundances at fixed spectral resolving
power and SNR. The planet types considered - hot Jupiters, hot super-Earths,
warm Neptunes, temperate Jupiters and temperate super-Earths - cover most of
the exoplanets characterisable today or in the near future. We focus on key
atmospheric molecules, such as CH4, CO, CO2, NH3, H2O, C2H2, C2H6, HCN, H2S and
PH3. We use two methods to assess the detectability of these molecules: a
simple measurement of the deviation of the signal from the continuum, and an
estimate of the level of confidence of a detection through the use of the
likelihood ratio test over the whole spectrum (from 1 to 16$\mu m$). We find
that for most planetary cases, SNR=5 at resolution R=300 ($\lambda < 5\mu m$)
and R=30 ($\lambda > 5\mu m$) is enough to detect the very strongest spectral
features for the most abundant molecules, whereas an SNR comprised between 10
and 20 can reveal most molecules with abundances 10^-6 or lower, often at
multiple wavelengths. We test the robustness of our results by exploring
sensitivity to parameters such as vertical thermal profile, mean molecular
weight of the atmosphere and relative water abundances. We find that our main
conclusions remain valid except for the most extreme cases. Our analysis shows
that the detectability of key molecules in the atmospheres of a variety of
exoplanet cases is within realistic reach, even with low SNR and spectral
resolving power.


title: A variable absorption feature in the X-ray spectrum of a magnetar

abstract:
  Soft gamma-ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are slowly
rotating, isolated neutron stars that sporadically undergo episodes of
long-term flux enhancement (outbursts) generally accompanied by the emission of
short bursts of hard X-rays. This behaviour can be understood in the magnetar
model, according to which these sources are mainly powered by their own
magnetic energy. This is supported by the fact that the magnetic fields
inferred from several observed properties of AXPs and SGRs are greater than -
or at the high end of the range of - those of radio pulsars. In the peculiar
case of SGR 0418+5729, a weak dipole magnetic moment is derived from its timing
parameters, whereas a strong field has been proposed to reside in the stellar
interior and in multipole components on the surface. Here we show that the
X-ray spectrum of SGR 0418+5729 has an absorption line, the properties of which
depend strongly on the star's rotational phase. This line is interpreted as a
proton cyclotron feature and its energy implies a magnetic field ranging from
2E14 gauss to more than 1E15 gauss.


title:
Breaking the Obscuring Screen: A Resolved Molecular Outflow in a Buried
  QSO

abstract:
  We present Keck laser guide star adaptive optics observations of the nearby
buried QSO F08572+3915:NW. We use near-infrared integral field data taken with
OSIRIS to reveal a compact disk and molecular outflow using Pa-alpha and H_2
rotational-vibrational transitions at a spatial resolution of 100 pc. The
outflow emerges perpendicular to the disk into a bicone of one-sided opening
angle 100 degrees up to distances of 400 pc from the nucleus. The integrated
outflow velocities, which reach at least -1300 km/s, correspond exactly to
those observed in (unresolved) OH absorption, but are smaller (larger) than
those observed on larger scales in the ionized (neutral atomic) outflow. These
data represent a factor of >10 improvement in the spatial resolution of
molecular outflows from mergers/QSOs, and plausibly represent the early stages
of the excavation of the dust screen from a buried QSO.


title:
THELI -- Convenient reduction of any optical, near- and mid-infrared
  imaging data

abstract:
  The last 15 years have seen a surge of new multi-chip optical and near-IR
imagers. While some of them are accompanied by specific reduction pipelines,
user-friendly and generic reduction tools are uncommon. In this paper I
introduce THELI, an easy-to-use graphical interface driving an end-to-end
pipeline for the reduction of any optical, near-IR and mid-IR imaging data. The
advantages of THELI when compared to other approaches are highlighted.
Combining a multitude of processing algorithms and third party software, THELI
provides researchers with a single, homogeneous tool. A short learning curve
ensures quick success for new and more experienced observers alike. All tasks
are largely automated, while at the same time a high level of flexibility and
alternative reduction schemes ensure that widely different scientific
requirements can be met. Over 90 optical and infrared instruments at
observatories world-wide are pre-configured, while more can be added by the
user. The online Appendices contain three walk-through examples using public
data (optical, near-IR and mid-IR). Additional extensive online documentation
is available for training and troubleshooting.


title: Symmetries and hidden symmetries for fields outside black holes

abstract:
  This note surveys how energy generation and strengthening has been used to
prove Morawetz estimates for various field equations in Minkowski space, the
exterior of the Schwarzschild spacetime, and the exterior of the Kerr
spacetime. It briefly outlines an approach to proving a decay estimate for the
Maxwell equation outside a Kerr black hole.


title: Non-commutative Hilbert modular symbols

abstract:
  The main goal of this paper is to construct non-commutative Hilbert modular
symbols. However, we also construct commutative Hilbert modular symbols. Both
the commutative and the non-commutative Hilbert modular symbols are
generalizations of Manin's classical and non-commutative modular symbols. We
prove that many cases of (non-)commutative Hilbert modular symbols are periods
in the sense on Kontsevich-Zagier. Hecke operators act naturally on them.
  Manin defines the non-commutative modilar symbol in terms of iterated path
integrals. In order to define non-commutative Hilbert modular symbols, we use a
generalization of iterated path integrals to higher dimensions, which we call
iterated integrals on membranes. Manin examines similarities between
non-commutative modular symbol and multiple zeta values both in terms of
infinite series and in terms of iterated path integrals. Here we examine
similarities in the formulas for non-commutative Hilbert modular symbol and
multiple Dedekind zeta values, recently defined by the author, both in terms of
infinite series and in terms of iterated integrals on membranes.


title: A dynamical Shafarevich theorem for twists of rational morphisms

abstract:
  Let $K$ denote a number field and a finite set $S$ of places of $K$ and
$\phi:\PP^n\rightarrow\PP^n$ be rational morphism defined over $K$. The main
result of this paper proves that there are only finitely many twists of $\phi$
defined over $K$ which have good reduction at all places outside $S$. This
answers a question of Silverman in the affirmative.


title:
Spectrum of the open QCD flux tube in d=2+1 and its effective string
  description

abstract:
  Simulations in lattice gauge theory suggest that the formation of a flux tube
between quark and antiquark leads to quark confinement. It is conjectured that
the infrared behaviour of the flux tube is governed by an effective string
theory and simulations show good agreement between lattice data and its
predictions. To next-to leading order ($R^{-3}$) in the inverse $q\bar{q}$
separation $R$ the effective string theory is equivalent to Nambu-Goto string
theory. For the open flux tube in three dimensions corrections appear at order
$R^{-4}$. We compare these predictions to high-accuracy measurements of the
groundstate energy of the flux tube in 3d SU(2) and SU(3) gauge theory and
extract the coefficient of the leading order boundary term in the effective
action.


title:
Matrix Completion in Colocated MIMO Radar: Recoverability, Bounds &
  Theoretical Guarantees

abstract:
  It was recently shown that low rank matrix completion theory can be employed
for designing new sampling schemes in the context of MIMO radars, which can
lead to the reduction of the high volume of data typically required for
accurate target detection and estimation. Employing random samplers at each
reception antenna, a partially observed version of the received data matrix is
formulated at the fusion center, which, under certain conditions, can be
recovered using convex optimization. This paper presents the theoretical
analysis regarding the performance of matrix completion in colocated MIMO radar
systems, exploiting the particular structure of the data matrix. Both Uniform
Linear Arrays (ULAs) and arbitrary 2-dimensional arrays are considered for
transmission and reception. Especially for the ULA case, under some mild
assumptions on the directions of arrival of the targets, it is explicitly shown
that the coherence of the data matrix is both asymptotically and approximately
optimal with respect to the number of antennas of the arrays involved and
further, the data matrix is recoverable using a subset of its entries with
minimal cardinality. Sufficient conditions guaranteeing low matrix coherence
and consequently satisfactory matrix completion performance are also presented,
including the arbitrary 2-dimensional array case.


title: Localizing algebras and invariant subspaces

abstract:
  It is shown that the algebra \(L^\infty(\mu)\) of all bounded measurable
functions with respect to a finite measure \(\mu\) is localizing on the Hilbert
space \(L^2(\mu)\) if and only if the measure \(\mu\) has an atom. Next, it is
shown that the algebra \(H^\infty({\mathbb D})\) of all bounded analytic
multipliers on the unit disc fails to be localizing, both on the Bergman space
\(A^2({\mathbb D})\) and on the Hardy space \(H^2({\mathbb D}).\) Then, several
conditions are provided for the algebra generated by a diagonal operator on a
Hilbert space to be localizing. Finally, a theorem is provided about the
existence of hyperinvariant subspaces for operators with a localizing subspace
of extended eigenoperators. This theorem extends and unifies some previously
known results of Scott Brown and Kim, Moore and Pearcy, and Lomonosov, Radjavi
and Troitsky.


title:
On the Impossibility of Dimension Reduction for Doubling Subsets of
  $\ell_p$, $p>2$

abstract:
  A major open problem in the field of metric embedding is the existence of
dimension reduction for $n$-point subsets of Euclidean space, such that both
distortion and dimension depend only on the {\em doubling constant} of the
pointset, and not on its cardinality. In this paper, we negate this possibility
for $\ell_p$ spaces with $p>2$. In particular, we introduce an $n$-point subset
of $\ell_p$ with doubling constant O(1), and demonstrate that any embedding of
the set into $\ell_p^d$ with distortion $D$ must have
$D\ge\Omega\left(\left(\frac{c\log
n}{d}\right)^{\frac{1}{2}-\frac{1}{p}}\right)$.


title: Energy and Asymptotics of Ricci-Flat 4-Manifolds with a Killing Field

abstract:
  Given a complete, Ricci-flat 4-manifold with a Killing field, we give an
estimate on the manifold's energy in terms of a certain asymptotic quantity of
the Killing field. If the Killing field has no zeros and satisfies a certain
asymptotic condition, the manifold is flat.


title: The two definitions of the index difference

abstract:
  Given two metrics of positive scalar curvature metrics on a closed spin
manifold, there is a secondary index invariant in real $K$-theory. There exist
two definitions of this invariant, one of homotopical flavour, the other one
defined by a index problem of Atiyah-Patodi-Singer type. We give a complete and
detailed proof of the folklore result that both constructions yield the same
answer. Moreover, we generalize this to the case of two families of positive
scalar curvature metrics, parametrized by a compact space. In essence, we prove
a generalization of the classical "spectral-flow-index theorem" to the case of
families of real operators.


title:
Incorporating Text Analysis into Evolution of Social Groups in
  Blogosphere

abstract:
  Data reflecting social and business relations has often form of network of
connections between entities (called social network). In such network important
and influential users can be identified as well as groups of strongly connected
users. Finding such groups and observing their evolution becomes an
increasingly important research problem. One of the significant problems is to
develop method incorporating not only information about connections between
entities but also information obtained from text written by the users. Method
presented in this paper combine social network analysis and text mining in
order to understand groups evolution.


title: Smoothing and Decomposition for Analysis Sparse Recovery

abstract:
  We consider algorithms and recovery guarantees for the analysis sparse model
in which the signal is sparse with respect to a highly coherent frame. We
consider the use of a monotone version of the fast iterative shrinkage-
thresholding algorithm (MFISTA) to solve the analysis sparse recovery problem.
Since the proximal operator in MFISTA does not have a closed-form solution for
the analysis model, it cannot be applied directly. Instead, we examine two
alternatives based on smoothing and decomposition transformations that relax
the original sparse recovery problem, and then implement MFISTA on the relaxed
formulation. We refer to these two methods as smoothing-based and
decomposition-based MFISTA. We analyze the convergence of both algorithms, and
establish that smoothing- based MFISTA converges more rapidly when applied to
general nonsmooth optimization problems. We then derive a performance bound on
the reconstruction error using these techniques. The bound proves that our
methods can recover a signal sparse in a redundant tight frame when the
measurement matrix satisfies a properly adapted restricted isometry property.
Numerical examples demonstrate the performance of our methods and show that
smoothing-based MFISTA converges faster than the decomposition-based
alternative in real applications, such as MRI image reconstruction.


title:
Information processing and the second law of thermodynamics: an
  inclusive, Hamiltonian approach

abstract:
  We obtain generalizations of the Kelvin-Planck, Clausius, and Carnot
statements of the second law of thermodynamics, for situations involving
information processing. To this end, we consider an information reservoir
(representing, e.g. a memory device) alongside the heat and work reservoirs
that appear in traditional thermodynamic analyses. We derive our results within
an inclusive framework in which all participating elements -- the system or
device of interest, together with the heat, work and information reservoirs --
are modeled explicitly by a time-independent, classical Hamiltonian. We place
particular emphasis on the limits and assumptions under which cyclic motion of
the device of interest emerges from its interactions with work, heat, and
information reservoirs.


title: On manifolds with multiple lens space filings

abstract:
  An irreducible 3--manifold with torus boundary either is a Seifert fibered
space or admits at most three lens space fillings according to the Cyclic
Surgery Theorem. We examine the sharpness of this theorem by classifying the
non-hyperbolic manifolds with more than one lens space filling, classifying the
hyperbolic manifolds obtained by filling of the Minimally Twisted 5 Chain
complement that have three lens space fillings, showing that the doubly
primitive knots in $S^3$ and $S^1 \times S^2$ have no unexpected extra lens
space surgery, and showing that the Figure Eight Knot Sister Manifold is the
only non-Seifert fibered manifold with a properly embedded essential
once-punctured torus and three lens space fillings.


title: TMD Evolution: Matching SIDIS to Drell-Yan and W/Z Boson Production

abstract:
  We examine the QCD evolution for the transverse momentum dependent
observables in hard processes of semi-inclusive hadron production in deep
inelastic scattering and Drell-Yan lepton pair production in $pp$ collisions,
including the spin-average cross sections and Sivers single transverse spin
asymmetries. We show that the evolution equations derived by a direct integral
of the Collins-Soper-Sterman evolution kernel from low to high Q can describe
well the transverse momentum distribution of the unpolarized cross sections in
the Q^2 range from 2 to 100 GeV^2. In addition, the matching is established
between our evolution and the Collins-Soper-Sterman resummation with
b*-prescription and Konychev-Nodalsky parameterization of the non-perturbative
form factors, which are formulated to describe the Drell-Yan lepton pair and
W/Z boson production in hadronic collisions. With these results, we present the
predictions for the Sivers single transverse spin asymmetries in Drell-Yan
lepton pair production and $W^\pm$ boson production in polarized pp and $\pi^-
p$ collisions for several proposed experiments. We emphasize that these
experiments will not only provide crucial test of the sign change of the Sivers
asymmetry, but also provide important opportunities to study the QCD evolution
effects.


title: Exploring semiconductor substrates for Silicene epitaxy

abstract:
  We have carried out first-principles based DFT calculation on electronic
properties of silicene monolayer on various (111) semi-conducting surfaces. We
find that the relative stability and other properties of the silicene overlayer
depends sensitively on whether the interacting top layer of the substrate is
metal or non-metal terminated. The nature of silicene-monolayer on the metal
termi- nated surface can be metallic or even magnetic, depending upon the
choice of the substrate. The silicene overlayer undergoes n-type doping on
metal terminated surface while it undergoes p-type doping on non metal
terminated surfaces of the semiconductor substrates.


title: Geometric quantum discord with Bures distance: the qubit case

abstract:
  The minimal Bures distance of a quantum state of a bipartite system AB to the
set of classical states for subsystem A defines a geometric measure of quantum
discord. When A is a qubit, we show that this geometric quantum discord is
given in terms of the eigenvalues of a (2 n_B) x (2 n_B) hermitian matrix, n_B
being the Hilbert space dimension of the other subsystem B. As a first
application, we calculate the geometric discord for the output state of the
DQC1 algorithm. We find that it takes its highest value when the unitary matrix
from which the algorithm computes the trace has its eigenvalues uniformly
distributed on the unit circle modulo a symmetry with respect to the origin. As
a second application, we derive an explicit formula for the geometric discord
of two-qubit states with maximally mixed marginals and compare it with other
measures of quantum correlations. We also determine the closest classical
states to such two-qubit states.


title: Searching for the M+T binary needle in the brown dwarf haystack

abstract:
  Multiplicity is a key statistic for understanding the formation of very low
mass (VLM) stars and brown dwarfs. Currently, the separation distribution of
VLM binaries remains poorly constrained at small separations (< 1 AU), leading
to uncertainty in the overall binary fraction. We approach this problem by
searching for spectral binaries whose identification is independent of
separation. The combined spectra of these systems exhibit traces of methane
imposed on an earlier-type spectra. When the primary of such a system is a
late-type M or early-type L dwarf, however, the relative faintness of the T
dwarf secondary (up to 5 magnitudes at K-band) renders these features extremely
subtle. We present a set of spectral indices newly designed to identify these
systems, and a spectral fitting method to confirm and characterize them. We
apply this method to a library of over 750 spectra from the SpeX Prism Spectral
Libraries. We present new spectral binary candidates, compare them to recent
discoveries, and describe ongoing followup to search for resolved companions
and/or radial velocity variability.


title: Interacting Ricci-like holographic dark energy

abstract:
  In a flat Friedmann-Lema\^itre-Robertson-Walker background, a scheme of dark
matter-dark energy interaction is studied considering a holographic Ricci-like
model for the dark energy. Without giving a priori some specific model for the
interaction function, we show that this function can experience a change of
sign during the cosmic evolution. The parameters involved in the holographic
model are adjusted with Supernova data and we obtained results compatible with
the observable universe.


title: Gravitational field of gyratons on various background spacetimes

abstract:
  In this work we have found and analyzed several gyraton solutions on various
non--trivial backgrounds in the large Kundt class of spacetimes. Namely, the
gyraton solutions on direct product spacetimes, gyraton solutions on Melvin
universe and its generalization which includes the cosmological constant. These
solutions are of algebraic type II. Also we have investigated type III
solutions within the Kundt class and we have found the gyratons on de Sitter
spacetime. We have generalized the gyraton solutions on direct product
spacetimes to higher dimensions. The chapters 4 and 5 are published for the
first time.


title: Quantum nonlocal correlations are not dominated

abstract:
  We show that no probability distribution of spin measurement outcomes on
pairs of spin 1/2 particles is unambiguously more nonlocal than the quantum
correlations. That is, any distribution that produces a CHSH violation larger
than the quantum violation for some axis choices also produces a smaller CHSH
violation for some other axis choices. In this sense, it is not possible for
nature to be strictly more nonlocal than quantum theory allows.


title: Sentiment in New York City: A High Resolution Spatial and Temporal View

abstract:
  Measuring public sentiment is a key task for researchers and policymakers
alike. The explosion of available social media data allows for a more
time-sensitive and geographically specific analysis than ever before. In this
paper we analyze data from the micro-blogging site Twitter and generate a
sentiment map of New York City. We develop a classifier specifically tuned for
140-character Twitter messages, or tweets, using key words, phrases and
emoticons to determine the mood of each tweet. This method, combined with
geotagging provided by users, enables us to gauge public sentiment on extremely
fine-grained spatial and temporal scales. We find that public mood is generally
highest in public parks and lowest at transportation hubs, and locate other
areas of strong sentiment such as cemeteries, medical centers, a jail, and a
sewage facility. Sentiment progressively improves with proximity to Times
Square. Periodic patterns of sentiment fluctuate on both a daily and a weekly
scale: more positive tweets are posted on weekends than on weekdays, with a
daily peak in sentiment around midnight and a nadir between 9:00 a.m. and noon.


title: The full Kostant-Toda hierarchy on the positive flag variety

abstract:
  We study some geometric and combinatorial aspects of the solution to the full
Kostant-Toda (f-KT) hierarchy, when the initial data is given by an arbitrary
point on the totally non-negative (tnn) flag variety of SL_n(R). The f-KT flows
on the tnn flag variety are complete, and their asymptotics are completely
determined by the cell decomposition of the tnn flag variety given by Rietsch.
We define the f-KT flow on the weight space via the moment map, and show that
the closure of each f-KT flow forms an interesting convex polytope generalizing
the permutohedron which we call a Bruhat interval polytope. We also prove
analogous results for the full symmetric Toda hierarchy, by mapping our f-KT
solutions to those of the full symmetric Toda hierarchy. In the Appendix we
show that Bruhat interval polytopes are generalized permutohedra, in the sense
of Postnikov, and that their edges correspond to cover relations in the Bruhat
order.

categories: math.RT math-ph math.AG math.CO math.MP nlin.SI


title:
Ultrafast Energy Transfer Between Molecular Assemblies and Surface
  Plasmons in the Strong Coupling Regime

abstract:
  The nonlinear optical dynamics of nano-materials comprised of plasmons
interacting with quantum emitters is investigated by a self-consistent model
based on the coupled Maxwell-Liouville-von Neumann equations. It is shown that
ultra-short resonant laser pulses significantly modify the optical properties
of such hybrid systems. It is further demonstrated that the energy transfer
between interacting molecules and plasmons occurs on a femtosecond time scale
and can be controlled with both material and laser parameters.


title:
Nonlocal Operators, Parabolic-type Equations, and Ultrametric Random
  Walks

abstract:
  In this article we introduce a new type of nonlocal operators and study the
Cauchy problem for certain parabolic-type pseudodifferential equations
naturally associated to these operators. Some of these equations are the p-adic
master equations of certain models of complex systems introduced by Avetisov et
al. The fundamental solutions of these parabolic-type equations are transition
functions of random walks on the n-dimensional vector space over the field of
p-adic numbers. We study some properties of these random walks, including the
first passage time.


title: Identifying AF-algebras that are graph C*-algebras

abstract:
  We consider the problem of identifying exactly which AF-algebras are
isomorphic to a graph C*-algebra. We prove that any separable, unital, Type I
C*-algebra with finitely many ideals is isomorphic to a graph C*-algebra. This
result allows us to prove that a unital AF-algebra is isomorphic to a graph
C*-algebra if and only if it is a Type I C*-algebra with finitely many ideals.
We also consider nonunital AF-algebras that have a largest ideal with the
property that the quotient by this ideal is the only unital quotient of the
AF-algebra. We show that such an AF-algebra is isomorphic to a graph C*-algebra
if and only if its unital quotient is Type I, which occurs if and only if its
unital quotient is isomorphic to M_k for some natural number k. All of these
results provide vast supporting evidence for the conjecture that an AF-algebra
is isomorphic to a graph C*-algebra if and only if each unital quotient of the
AF-algebra is Type I with finitely many ideals, and bear relevance for the
intrigiung question of finding K-theoretical criteria for when an extension of
two graph C*-algebras is again a graph C*-algebra.


title: The Simple Rules of Social Contagion

abstract:
  It is commonly believed that information spreads between individuals like a
pathogen, with each exposure by an informed friend potentially resulting in a
naive individual becoming infected. However, empirical studies of social media
suggest that individual response to repeated exposure to information is
significantly more complex than the prediction of the pathogen model. As a
proxy for intervention experiments, we compare user responses to multiple
exposures on two different social media sites, Twitter and Digg. We show that
the position of the exposing messages on the user-interface strongly affects
social contagion. Accounting for this visibility significantly simplifies the
dynamics of social contagion. The likelihood an individual will spread
information increases monotonically with exposure, while explicit feedback
about how many friends have previously spread it increases the likelihood of a
response. We apply our model to real-time forecasting of user behavior.


title: Optical and X-ray Studies of Ten X-ray Selected Cataclysmic Binaries

abstract:
  We report on ground-based optical observations of ten cataclysmic binaries
that were discovered through their X-ray emission. Time-resolved radial
velocity spectroscopy yields unambiguous orbital periods for eight objects and
ambiguous results for the remaining two. The orbital periods range from 87 min
to 9.38 hr. We also obtained time-series optical photometry for six targets,
four of which have coherent pulsations. These periods are 1218 s for 1RXS
J045707.4+452751, 628 s for AX J1740.2-2903, 477 s for AX J1853.3-0128, and 935
s for IGR J19267+1325. A total of seven of the sources have coherent
oscillations in X-rays or optical, indicating that they are intermediate polars
(DQ Herculis stars). Time-resolved spectroscopy of one object, Swift
J2218.4+1925, shows that it is an AM Herculis star, or polar, and IGR
J19552+0044 may also be in that class. For another object, Swift J0476.2-1611,
we find an orbital period of 9.384 hr and detect the spectrum of the secondary
star. The secondary's spectral contribution implies a distance of 900 (+190,
-150) pc, where the error bars are estimated using a Monte Carlo technique to
account for correlated uncertainties.


title: Discovery of a new TeV gamma-ray source: VER J0521+211

abstract:
  We report the detection of a new TeV gamma-ray source, VER J0521+211, based
on observations made with the VERITAS imaging atmospheric Cherenkov telescope
array. These observations were motivated by the discovery of a cluster of
>30GeV photons in the first year of Fermi-LAT observations. VER J0521+211 is
relatively bright at TeV energies, with a mean photon flux of 1.93 +/-
0.13_stat +/- 0.78_sys 10^-11 cm-2 s-1 above 0.2 TeV during the period of the
VERITAS observations. The source is strongly variable on a daily timescale
across all wavebands, from optical to TeV, with a peak flux corresponding to
~0.3 times the steady Crab Nebula flux at TeV energies. Follow-up observations
in the optical and X-ray bands classify the newly-discovered TeV source as a BL
Lac-type blazar with uncertain redshift, although recent measurements suggest
z=0.108. VER J0521+211 exhibits all the defining properties of blazars in
radio, optical, X-ray, and gamma-ray wavelengths.


title:
On some classes of discrete polynomials and ordinary difference
  equations

abstract:
  We introduce two classes of discrete polynomials and construct discrete
equations admitting a Lax representation in terms of these polynomials. Also we
give an approach which allows to construct lattice integrable hierarchies in
its explicit form and show some examples.


title: A Taylor series approach to pricing and implied vol for LSV models

abstract:
  Using classical Taylor series techniques, we develop a unified approach to
pricing and implied volatility for European-style options in a general
local-stochastic volatility setting. Our price approximations require only a
normal CDF and our implied volatility approximations are fully explicit (ie,
they require no special functions, no infinite series and no numerical
integration). As such, approximate prices can be computed as efficiently as
Black-Scholes prices, and approximate implied volatilities can be computed
nearly instantaneously.


title: Automorphisms of decompositions

abstract:
  Harding showed that the direct product decompositions of many different types
of structures, such as sets, groups, vector spaces, topological spaces, and
relational structures, naturally form orthomodular posets. When applied to the
direct product decompositions of a Hilbert space, this construction yields the
familiar orthomodular lattice of closed subspaces of the Hilbert space.
  In this note we consider orthomodular posets Fact X of decompositions of a
finite set X. We consider the structure of these orthomodular posets, such as
their size, shape, and connectedness, states, and begin a study of their
automorphism groups in the context of the natural map \Gamma from the group of
permutations of X to the automorphism group of Fact X.
  We show \Gamma is an embedding except when |X| is prime or 4, and completely
describe the situation when |X| has two or fewer prime factors, when |X|=8 and
when |X|=27. The bulk of our effort lies in a series of combinatorial arguments
to show \Gamma is an isomorphism when |X|=27. We conjecture that this is the
case whenever |X| has sufficiently many prime factors of sufficient size, and
hope that our arguments here might be adapted to the general case.


title:
Bohm Trajectories as Approximations to Properly Fluctuating Quantum
  Trajectories

abstract:
  We explain the approximate nature of particle trajectories in Bohm's quantum
mechanics. They are streamlines of a superfluid in Madelung's reformulation of
the Schr\"{o}dinger wave function, around which the proper particle
trajectories perform their quantum mechanical fluctuations to ensure
Heisenberg's uncertainty relation between position and momentum.


title: Tuning plasmonic cloaks with an external magnetic field

abstract:
  We propose a mechanism to actively tune the operation of plasmonic cloaks
with an external magnetic field by investigating electromagnetic scattering by
a dielectric cylinder coated with a magneto-optical shell. In the long
wavelength limit we show that the presence of an external magnetic field may
drastically reduce the scattering cross-section at all observation angles. We
demonstrate that the application of external magnetic fields can modify the
operation wavelength without the need of changing material and/or geometrical
parameters. We also show that applied magnetic fields can reversibly switch on
and off the cloak operation. These results, which could be achieved for
existing magneto-optical materials, are shown to be robust to material losses,
so that they may pave the way for developing actively tunable, versatile
plasmonic cloaks.


title:
Physical parameters and the projection factor of the classical Cepheid
  in the binary system OGLE-LMC-CEP-0227

abstract:
  A novel method of analysis of double-lined eclipsing binaries containing a
radially pulsating star is presented. The combined pulsating-eclipsing light
curve is built up from a purely eclipsing light curve grid created using an
existing modeling tool. For every pulsation phase the instantaneous radius and
surface brightness are taken into account, being calculated from the
disentangled radial velocity curve of the pulsating star and from its
out-of-eclipse pulsational light curve and the light ratio of the components,
respectively. The best model is found using the Markov Chain Monte Carlo
method.
  The method is applied to the eclipsing binary Cepheid OGLE-LMC-CEP-0227
(P_puls = 3.80 d, P_orb = 309 d). We analyze a set of new spectroscopic and
photometric observations for this binary, simultaneously fitting OGLE V-band,
I-band and Spitzer 3.6 {\mu}m photometry. We derive a set of fundamental
parameters of the system significantly improving the precision comparing to the
previous results obtained by our group. The Cepheid mass and radius are M_1 =
4.165 +/- 0.032 M_solar and R_1 = 34.92 +/- 0.34 R_solar, respectively.
  For the first time a direct, geometrical and distance-independent
determination of the Cepheid projection factor is presented. The value p = 1.21
+/- 0.03(stat.) +/- 0.04(syst.) is consistent with theoretical expectations for
a short period Cepheid and interferometric measurements for {\delta} Cep. We
also find a very high value of the optical limb darkening coefficients for the
Cepheid component, in strong disagreement with theoretical predictions for
static atmospheres at a given surface temperature and gravity.


title:
Electronic and magnetic properties of twisted graphene nanoribbon and
  M\"obius strips: first-principles calculations

abstract:
  The geometrical, electronic, and magnetic properties of twisted zigzag-edged
graphene nanoribbons (ZGNRs) and novel graphene M\"obius strips (GMS) are
systematically investigated using first-principles density functional
calculations. The structures of ZGNRs and GMS are optimized, and their
stabilities are examined. The molecular energy levels and the spin polarized
density of states are calculated. It is found that for twisted ZGNRs, the
atomic bonding energy decreases quadratically with the increase of the twisted
angle, and the HOMO-LUMO gap are varying in a sine-like behavior with the
twisted angle. The calculated spin densities reveal that the ZGNRs and GMS have
antiferromagnetic ground states, which persist during the twisting. The spin
flips on the zigzag edges of GMS are observed at some positions.


title: Development of A Modified Quasi-periodic Undulator for HLS

abstract:
  A modified quasi periodic undulator (QPU) is developed and to be installed at
Hefei Light Source (HLS).Magnet dimensions optimization is applied. High
harmonics contamination is eliminated from the fundamental emission effectively
according to the field tests. The depression ratio of 3rd harmonic is increased
by an order of magnitude than the current device with other harmonics well
reduced simultaneously. The significance of the modification measure is
verified practically. The design, measurement and commissioning of the device
is described.


title: Peristaltic Pumping near Post-CME Supra-Arcade Current Sheets

abstract:
  Measurements of temperature and density near supra-arcade current sheets
suggest that plasma on unreconnected field lines may experience some degree of
"pre-heating" and "pre-densification" prior to their reconnection. Models of
patchy reconnection allow for heating and acceleration of plasma along
reconnected field lines but do not offer a mechanism for transport of thermal
energy across field lines. Here we present a model in which a reconnected flux
tube retracts, deforming the surrounding layer of unreconnected field. The
deformation creates constrictions that act as peristaltic pumps, driving plasma
flow along affected field lines. Under certain circumstances these flows lead
to shocks that can extend far out into the unreconnected field, altering the
plasma properties in the affected region. These findings have direct
implications for observations in the solar corona, particularly in regard to
such phenomena as high temperatures near current sheets in eruptive solar
flares and wakes seen in the form of descending regions of density depletion or
supra-arcade downflows.


title:
Constraints on Common Envelope Magnetic Fields from Observations of Jets
  in Planetary Nebulae

abstract:
  The common envelope (CE) interaction describes the swallowing of a nearby
companion by a growing, evolving star. CEs that take place during the
asymptotic giant branch phase of the primary and may lead to the formation of a
planetary nebula (PN) with a post-CE close binary in the middle. We have used
published observations of masses and kinematics of jets in four post-CE PN to
infer physical characteristics of the CE interaction. In three of the four
systems studied, Abell 63, ETHOS 1 and the Necklace PN, the kinematics indicate
that the jets were launched a few thousand years before the CE and we favour a
scenario where this happened before Roche lobe overflow, although better models
of wind accretion and wind Roche lobe overflow are needed. The magnetic fields
inferred to launch pre-CE jets are of the order of a few Gauss. In the fourth
case, NGC 6778, the kinematics indicate that the jets were launched about 3000
years after the CE interaction. Magnetic fields of the order of a few hundreds
to a few thousands Gauss are inferred in this case, approximately in line with
predictions of post-CE magnetic fields. However, we remark that in the case of
this system, it is impossible to find a reasonable scenario for the formation
of the two jet pairs observed: the small orbital separation would preclude the
formation of even one accretion disk able to supply the necessary accretion
rate to cause the observed jets.


title: Tight frames, partial isometries, and signal reconstruction

abstract:
  This article gives a procedure to convert a frame which is not a tight frame
into a Parseval frame for the same space, with the requirement that each
element in the resulting Parseval frame can be explicitly written as a linear
combination of the elements in the original frame. Several examples are
considered, such as a Fourier frame on a spiral. The procedure can be applied
to the construction of Parseval frames for L^2(B(0,R)), the space of square
integrable functions whose domain is the ball of radius R. When a finite number
of measurements are used to reconstruct a signal in L^2(B(0,R)), error
estimates arising from such approximation are discussed.


title:
Computing Equilibria of Semi-algebraic Economies Using Triangular
  Decomposition and Real Solution Classification

abstract:
  In this paper, we are concerned with the problem of determining the existence
of multiple equilibria in economic models. We propose a general and complete
approach for identifying multiplicities of equilibria in semi-algebraic
economies, which may be expressed as semi-algebraic systems. The approach is
based on triangular decomposition and real solution classification, two
powerful tools of algebraic computation. Its effectiveness is illustrated by
two examples of application.


title: Ultrawide-band Unidirectional Surface Plasmon Polariton Launchers

abstract:
  Plasmonic devices and circuits, bridging the gap between integrated photonic
and microelectronic technology, are promising candidates to realize on-chip
ultrawide-band and ultrahigh-speed information processing. Unfortunately, the
wideband surface plasmon source, one of the most important core components of
integrated plasmonic circuits, is still unavailable up to now. This has
seriously restricted the practical applications of plasmonic circuits. Here, we
report an ultrawide-band unidirectional surface plasmon polariton launcher with
high launching efficiency ratio and large extinction ratio, realized by
combining plasmonic bandgap engineering and linear interference effect. This
device offers excellent performances over an ultrabroad wavelength range from
690 to 900 nm, together with a high average launching efficiency ratio of 1.25,
large average extinction ratio of 30 dB, and ultracompact lateral dimension of
less than 4 um. Compared with previous reports, the operating bandwidth is
enlarged 210 folds, while the largest launching efficiency ratio, largest
extinction ratio, and small feature size are maintained simultaneously. This
provides a strategy for constructing on-chip surface plasmon source, and also
paving the way for the study of integrated plasmonic circuits.


title:
Analysis of a proposal for a realistic loophole-free Bell test with
  atom-light entanglement

abstract:
  The violation of Bell inequalities where both detection and locality
loopholes are closed is crucial for device independent assessments of quantum
information. While of technological nature, the simultaneous closing of both
loopholes still remains a challenge. In Nat. Commun. 4:2104(2013), a realistic
setup to produce an atom-photon entangled state that could reach a loophole
free Bell inequality violation within current experimental technology was
proposed. Here we improve the analysis of this proposal by giving an analytical
treatment that shows that the state proposed in Nat. Commun. 4:2104(2013) could
in principle violate a Bell inequality for arbitrarily low photodetection
efficiency. Moreover, it is also able to violate a Bell inequality considering
only atomic and homodyne measurements eliminating the need to consider
inefficient photocounting measurements. In this case, the maximum
Clauser-Horne-Shimony-Holt (CHSH) inequality violation achievable is 2.29, and
the minimum transmission required for violation is about 68%. Finally, we show
that by postselecting on an atomic measurement, one can engineer superpositions
of coherent states for various coherent state amplitudes.


title: How Did Humans Become So Creative? A Computational Approach

abstract:
  This paper summarizes efforts to computationally model two transitions in the
evolution of human creativity: its origins about two million years ago, and the
'big bang' of creativity about 50,000 years ago. Using a computational model of
cultural evolution in which neural network based agents evolve ideas for
actions through invention and imitation, we tested the hypothesis that human
creativity began with onset of the capacity for recursive recall. We compared
runs in which agents were limited to single-step actions to runs in which they
used recursive recall to chain simple actions into complex ones. Chaining
resulted in higher diversity, open-ended novelty, no ceiling on the mean
fitness of actions, and greater ability to make use of learning. Using a
computational model of portrait painting, we tested the hypothesis that the
explosion of creativity in the Middle/Upper Paleolithic was due to onset of
con-textual focus: the capacity to shift between associative and analytic
thought. This resulted in faster convergence on portraits that resembled the
sitter, employed painterly techniques, and were rated as preferable. We
conclude that recursive recall and contextual focus provide a computationally
plausible explanation of how humans evolved the means to transform this planet.


title:
A hybrid evolutionary algorithm with importance sampling for
  multi-dimensional optimization

abstract:
  A hybrid evolutionary algorithm with importance sampling method is proposed
for multi-dimensional optimization problems in this paper. In order to make use
of the information provided in the search process, a set of visited solutions
is selected to give scores for intervals in each dimension, and they are
updated as algorithm proceeds. Those intervals with higher scores are regarded
as good intervals, which are used to estimate the joint distribution of optimal
solutions through an interaction between the pool of good genetics, which are
the individuals with smaller fitness values. And the sampling probabilities for
good genetics are determined through an interaction between those estimated
good intervals. It is a cross validation mechanism which determines the
sampling probabilities for good intervals and genetics, and the resulted
probabilities are used to design crossover, mutation and other stochastic
operators with importance sampling method. As the selection of genetics and
intervals is not directly dependent on the values of fitness, the resulted
offsprings may avoid the trap of local optima. And a purely random EA is also
combined into the proposed algorithm to maintain the diversity of population.
30 benchmark test functions are used to evaluate the performance of the
proposed algorithm, and it is found that the proposed hybrid algorithm is an
efficient algorithm for multi-dimensional optimization problems considered in
this paper.


title: The Evolution of Intelligence

abstract:
  How did the human species evolve the capacity not just to communicate complex
ideas to one another but to hold such conversations from across the globe,
using remote devices constructed from substances that do not exist in the
natural world, the raw materials for which may have been hauled up from the
bowels of the earth? How did we come to be so intelligent? Research at the
interface of psychology, biology, anthropology, archaeology, and cognitive
science is culminating in an increasingly sophisticated understanding of how
human intelligence evolved. Studies of the brains of living humans and great
apes and the intellectual abilities they support are enabling us to assess what
is unique about human intelligence and what we share with our primate
relatives. Examining the habitats and skeletons of our ancestors gives cues as
to environmental, social, and anatomical factors that both constrain and enable
the evolution of human intelligence. Relics of the past also have much to tell
us about the thoughts, beliefs, and abilities of the individuals who invented
and used them.


title:
Strong gravitational lensing in a black-hole spacetime dominated by dark
  energy

abstract:
  We study the influence of phantom fields on strong field gravitational
lensing. Supposing that the gravitational field of the supermassive central
object of the Galaxy is described by a phantom black hole metric, we estimate
the numerical values of the coefficients and observations and find that the
influence of the phantom fields is somewhat similar to that of the electric
charge in a Reissner-Norstr\"{o}m black hole, i.e., the deflect angle and
angular separation increase with the phantom constant $b$. However, other
observations are contrary to the Reissner-Norstr\"{o}m case and show the
effects of dark energy, such as (i) compressing the usual black hole and more
powerfully attracting photons, (ii) making the relativistic Einstein ring
larger than that of the usual black hole, and (iii) not weakening the usual
relative magnitudes, which will facilitate observations.


title: Likelihood Adaptively Modified Penalties

abstract:
  A new family of penalty functions, adaptive to likelihood, is introduced for
model selection in general regression models. It arises naturally through
assuming certain types of prior distribution on the regression parameters. To
study stability properties of the penalized maximum likelihood estimator, two
types of asymptotic stability are defined. Theoretical properties, including
the parameter estimation consistency, model selection consistency, and
asymptotic stability, are established under suitable regularity conditions. An
efficient coordinate-descent algorithm is proposed. Simulation results and real
data analysis show that the proposed method has competitive performance in
comparison with existing ones.


title:
Revenge of the 'Neurds': Characterizing Creative Thought in terms of the
  Structure and Dynamics of Memory

abstract:
  There is cognitive, neurological, and computational support for the
hypothesis that defocusing attention results in divergent or associative
thought, conducive to insight and finding unusual connections, while focusing
attention results in convergent or analytic thought, conducive to rule-based
operations. Creativity appears to involve both. It is widely believed that it
is possible to escape mental fixation by spontaneously and temporarily engaging
in a more associative mode of thought. The resulting insight (if found) may be
refined in a more analytic mode of thought. The questions addressed here are:
(1) how does the architecture of memory support these two modes of thought, and
(2) what is happening at the neural level when one shifts between them? Recent
advances in neuroscience shed light on this. Activated cell assemblies are
composed of multiple neural cliques, groups of neurons that respond
differentially to general or context-specific aspects of a situation. I refer
to neural cliques that would not be included in the assembly if one were in an
analytic mode, but would be if one were in an associative mode, as neurds. It
is posited that the shift to a more associative mode of thought is accomplished
by recruiting neurds that respond to abstract or atypical microfeatures of the
problem or task. Since memory is distributed and content-addressable, this
fosters the forging of associations to potentially relevant items previously
encoded in those neurons. Thus it is proposed that creative thought not by
searching a space of predefined alternatives and blindly tweaking those that
hold promise, but by evoking remotely associated items through the recruitment
of neurds in a distributed, content-addressable memory.


title:
Group-Sparse Signal Denoising: Non-Convex Regularization, Convex
  Optimization

abstract:
  Convex optimization with sparsity-promoting convex regularization is a
standard approach for estimating sparse signals in noise. In order to promote
sparsity more strongly than convex regularization, it is also standard practice
to employ non-convex optimization. In this paper, we take a third approach. We
utilize a non-convex regularization term chosen such that the total cost
function (consisting of data consistency and regularization terms) is convex.
Therefore, sparsity is more strongly promoted than in the standard convex
formulation, but without sacrificing the attractive aspects of convex
optimization (unique minimum, robust algorithms, etc.). We use this idea to
improve the recently developed 'overlapping group shrinkage' (OGS) algorithm
for the denoising of group-sparse signals. The algorithm is applied to the
problem of speech enhancement with favorable results in terms of both SNR and
perceptual quality.


title:
Theorems to demostrate the presence of antiferromagnetism in the
  periodic Anderson model

abstract:
  Anderson model is an important model in the theory of strongly correlated
electron system. In this study, we explore the ground state of this model and
the concept of electron correlation by bipartite lattice and prove rigorously
theorems leading to the presence of spin singlet in the model. By using the
results of Ueda et al (1992) and Tian (1994), we show theoretically that the
ground state of the symmetric periodic Anderson model has a short range order
antiferromagnetism.


title:
Impact of eddy currents on the dispersion relation of surface spin waves
  in thin conducting magnetic films

abstract:
  We propose a rigorous solution to a long-standing problem of the impact of
eddy currents on the dispersion relation of surface spin waves propagating in
thin conducting magnetic films. Our results confirm the prediction of the
Almeida-Mill's exchange-free theory that the inclusion of the eddy current
contribution results in a deviation of the dispersion curve for the fundamental
mode from the Damon-Eshbach law and a substantial linewidth broadening in a
large wave vector range. We show that the decrease in the spin wave frequency
is due to an increase in the in-plane component of the dynamic magnetic field
within the conducting film. The decrease in the frequency is accompanied by a
drastic change in the asymmetry of the modal profiles for the waves. This
effect is not observable in magneto-insulating films and therefore it is
unambiguously attributed to eddy currents that appear in conducting films only.
We also show that the wave vector range in which eddy currents affect the
dispersion curve is strongly correlated with the value of the film
conductivity. This result holds for conducting films with the thickness 10-100
nm, which are considered promising for future magnonic and spintronic
applications.


title: An analogue of the prime number theorem for finite fields

abstract: We prove an analogue of the prime number theorem for finite fields.


title:
An approximate solution to the decentralized two-controller
  infinite-horizon scalar LQG problem: Part II- slow dynamics

abstract:
  Continuing the first part of the paper, we consider scalar decentralized
average-cost infinite-horizon LQG problems with two controllers. This paper
focuses on the slow dynamics case when the eigenvalue of the system is small
and prove that the single-controller optimal strategies ---linear strategies---
are constant ratio optimal among all distributed control strategies.


title:
Broadband light coupling to dielectric slot waveguides with tapered
  plasmonic nanoantennas

abstract:
  We propose and theoretically verify an efficient mechanism of broadband
coupling between incident light and on-chip dielectric slot waveguide by
employing a tapered plasmonic nanoantenna. Nanoantenna receives free space
radiation and couples it to a dielectric slot waveguide with the efficiency of
up to 20% in a broad spectral range, having a small footprint as compared with
the currently used narrowband dielectric grating couplers. We argue that the
frequency selective properties of such nanoantennas also allow for using them
as ultrasmall on-chip multiplexer/demultiplexer devices.


title:
An approximate solution to the decentralized two-controller
  infinite-horizon scalar LQG problem: Part I- fast dynamics

abstract:
  We consider scalar decentralized average-cost infinite-horizon LQG problems
with two controllers, focusing on the fast dynamics case when the (scalar)
eigenvalue of the system is large. It is shown that the best linear
controllers' performance can be an arbitrary factor worse than the optimal
performance. We propose a set of finite-dimensional nonlinear controllers, and
prove that the proposed set contains an easy-to-find approximately optimal
solution that achieves within a constant ratio of the optimal quadratic cost.
The insight for nonlinear strategies comes from revealing the relationship
between information flow in control and wireless information flow. More
precisely, we discuss a close relationship between the high-SNR limit in
wireless communication and fast-dynamics case in decentralized control, and
justify how the proposed nonlinear control strategy can be understood as
exploiting the generalized degree-of-freedom gain in wireless communication
theory. For a rigorous justification of this argument, we develop new
mathematical tools and ideas. To reveal the relationship between
infinite-horizon problems and generalized MIMO Witsenhausen's counterexamples,
we introduce the idea of geometric slicing. To analyze the nonlinear strategy
performance, we introduce an approximate-comb-lattice model for the relevant
random variables.


title:
Network Coding meets Decentralized Control: Network Linearization and
  Capacity-Stabilizablilty Equivalence

abstract:
  We take a unified view of network coding and decentralized control. Precisely
speaking, we consider both as linear time-invariant systems by appropriately
restricting channels and coding schemes of network coding to be linear
time-invariant, and the plant and controllers of decentralized control to be
linear time-invariant as well. First, we apply linear system theory to network
coding. This gives a novel way of converting an arbitrary relay network to an
equivalent acyclic single-hop relay network, which we call Network
Linearization. Based on network linearization, we prove that the fundamental
design limit, mincut, is achievable by a linear time-invariant network-coding
scheme regardless of the network topology.
  Then, we use the network-coding to view decentralized linear systems. We
argue that linear time-invariant controllers in a decentralized linear system
"communicate" via linear network coding to stabilize the plant. To justify this
argument, we give an algorithm to "externalize" the implicit communication
between the controllers that we believe must be occurring to stabilize the
plant. Based on this, we show that the stabilizability condition for
decentralized linear systems comes from an underlying communication limit,
which can be described by the algebraic mincut-maxflow theorem. With this
re-interpretation in hand, we also consider stabilizability over LTI networks
to emphasize the connection with network coding. In particular, in broadcast
and unicast problems, unintended messages at the receivers will be modeled as
secrecy constraints.


title: The Fractal Dimension of SAT Formulas

abstract:
  Modern SAT solvers have experienced a remarkable progress on solving
industrial instances. Most of the techniques have been developed after an
intensive experimental testing process. Recently, there have been some attempts
to analyze the structure of these formulas in terms of complex networks, with
the long-term aim of explaining the success of these SAT solving techniques,
and possibly improving them.
  We study the fractal dimension of SAT formulas, and show that most industrial
families of formulas are self-similar, with a small fractal dimension. We also
show that this dimension is not affected by the addition of learnt clauses. We
explore how the dimension of a formula, together with other graph properties
can be used to characterize SAT instances. Finally, we give empirical evidence
that these graph properties can be used in state-of-the-art portfolios.


title:
Expectation value of the axial-vector current in the external
  electromagnetic field

abstract:
  We are calculated the expectation value of the axial-vector current induced
by the vacuum polarization effect of the Dirac field in constant external
electromagnetic field. In calculations we use Schwinger's proper time method.
The effective Lagrangian has very simple Lorenz invariant form. Along with the
anomaly term, it also contains two Lorenz invariant terms. The result is
compared with our previous calculation of the photon - Z boson mixing in the
magnetic field.


title: Probing quantum many-body dynamics in nuclear systems

abstract:
  Quantum many-body nuclear dynamics is treated at the mean-field level with
the time-dependent Hartree-Fock (TDHF) theory. Low-lying and high-lying nuclear
vibrations are studied using the linear response theory. The fusion mechanism
is also described for light and heavy systems. The latter exhibit fusion
hindrance due to quasi-fission. Typical characteristics of quasi-fission, such
as contact time and partial symmetrisation of the fragments mass in the exit
channel, are reproduced by TDHF calculations. The (multi-)nucleon transfer at
sub-barrier energies is also discussed.


title: Low-discrepancy point sets for non-uniform measures

abstract:
  In the present paper we prove several results concerning the existence of
low-discrepancy point sets with respect to an arbitrary non-uniform measure
$\mu$ on the $d$-dimensional unit cube. We improve a theorem of Beck, by
showing that for any $d \geq 1$, $N \geq 1,$ and any non-negative, normalized
Borel measure $\mu$ on $[0,1]^d$ there exists a point set $x_1, \dots, x_N \in
[0,1]^d$ whose star-discrepancy with respect to $\mu$ is of order $$ D_N^*(x_1,
\dots, x_N; \mu) \ll \frac{(\log N)^{(3d+1)/2}}{N}. $$ For the proof we use a
theorem of Banaszczyk concerning the balancing of vectors, which implies an
upper bound for the linear discrepancy of hypergraphs. Furthermore, the theory
of large deviation bounds for empirical processes indexed by sets is discussed,
and we prove a numerically explicit upper bound for the inverse of the
discrepancy for Vapnik--\v{C}ervonenkis classes. Finally, using a recent
version of the Koksma--Hlawka inequality due to Brandolini, Colzani, Gigante
and Travaglini, we show that our results imply the existence of cubature rules
yielding fast convergence rates for the numerical integration of functions
having discontinuities of a certain form.


title: Encoding certainty in bump attractors

abstract:
  Persistent activity in neuronal populations has been shown to represent the
spatial position of remembered stimuli. Networks that support bump attractors
are often used to model such persistent activity. Such models usually exhibit
translational symmetry. Thus activity bumps are neutrally stable, and
perturbations in position do not decay away. We extend previous work on bump
attractors by constructing model networks capable of encoding the certainty or
salience of a stimulus stored in memory. Such networks support bumps that are
not only neutrally stable to perturbations in position, but also perturbations
in amplitude. Possible bump solutions then lie on a two-dimensional attractor,
determined by a continuum of positions and amplitudes. Such an attractor
requires precisely balancing the strength of recurrent synaptic connections.
The amplitude of activity bumps represents certainty, and is determined by the
initial input to the system. Moreover, bumps with larger amplitudes are more
robust to noise, and over time provide a more faithful representation of the
stored stimulus. In networks with separate excitatory and inhibitory
populations, generating bumps with a continuum of possible amplitudes, requires
tuning the strength of inhibition to precisely cancel background excitation.


title:
Uncertainty and certainty relations for the Pauli observables in terms
  of the R\'{e}nyi entropies of order $\alpha\in(0;1]$

abstract:
  We obtain uncertainty and certainty relations of state-independent form for
the three Pauli observables with use of the R\'enyi entropies of order
$\alpha\in(0;1]$. It is shown that these entropic bounds are tight in the sense
that they are always reached with certain pure states. A new result is the
conditions for equality in R\'enyi-entropy uncertainty relations for the Pauli
observables. Upper entropic bounds in the pure-state case are also novel.
Combining the presented bounds leads to a band, in which the rescaled average
R\'enyi $\alpha$-entropy ranges for a pure measured state. A width of this band
is compared with the Tsallis formulation derived previously.