title: On the Witten asymptotic conjecture for Seifert manifolds

abstract:
  We give a new proof of Witten asymptotic conjecture for Seifert manifolds
with non vanishing Euler class and one exceptional fiber. Our method is based
on semiclassical analysis on a two dimensional phase space torus. We prove that
the Witten-Reshetikhin-Turaev invariant of a Seifert manifold is the scalar
product of two Lagrangian states, and we estimate this scalar product in the
large level limit. The leading order terms of the expansion are naturally given
in terms of character varieties, the Chern-Simons invariants and some
symplectic volumes. For the analytic part, we establish some singular
stationary phase lemma for discrete oscillatory sums.


title: Young tableaux and representations of Hecke algebras of type ADE

abstract:
  We introduce and study some affine Hecke algebras of type ADE, generalising
the affine Hecke algebras of GL. We construct irreducible calibrated
representations and describe the calibrated spectrum. This is done in terms of
new families of combinatorial objects equipped with actions of the
corresponding Weyl groups. These objects are built from and generalise the
usual standard Young tableaux, and are controlled by the considered affine
Hecke algebras. By restriction and limiting procedure, we obtain several
combinatorial models for representations of finite Hecke algebras and Weyl
groups of type ADE. Representations are constructed by explicit formulas, in a
seminormal form.


title: Thermalization and hydrodynamization in the color-flux-tube model

abstract:
  The study of transverse-momentum spectra of quarks and gluons produced by the
color electric flux tube decaying through the Schwinger tunneling mechanism is
reviewed. The hints for a fast hydrodynamization in the ultra-relativistic
heavy-ion collisions are found.


title: Sampling in unitary invariant subspaces associated to LCA groups

abstract:
  In this paper a sampling theory for unitary invariant subspaces associated to
locally compact abelian (LCA) groups is deduced. Working in the LCA group
context allows to obtain, in a unified way, sampling results valid for a wide
range of problems which are interesting in practice, avoiding also cumbersome
notation. Along with LCA groups theory, the involved mathematical technique is
that of frame theory which meets matrix analysis when appropriate dual frames
are computed.


title: Diversity of Low-Density Lattices

abstract:
  The non-ergodic fading channel is a useful model for various wireless
communication channels in both indoor and outdoor environments. Building on
Poltyrev's work on infinite lattice constellations for the Gaussian channel, we
derive a Poltyrev outage limit (POL) for lattices in presence of block fading.
We prove that the diversity order of this POL is equal to the number of degrees
of freedom in the channel. Further, we describe full-diversity constructions of
real lattices defined by their integer-check matrix, i.e., the inverse of their
generator matrix. In the first construction suited to maximum-likelihood
decoding, these lattices are defined by sparse (low-density) or non-sparse
integer-check matrices. Based on a special structure of the lattice binary
image, a second full-diversity lattice construction is described for sparse
integer-check matrices in the context of iterative probabilistic decoding. Full
diversity is theoretically proved in both cases. We also propose a method to
construct lattices for diversity order 4 suitable for iterative probabilistic
decoding. Computer simulation results for diversity order L = 2 and L = 4
confirm that the proposed low-density lattices attain the maximal diversity
order. The newly defined POL is used during this simulation to declare an
outage error without decoding, which drastically improves the decoding runtime.


title:
With Whom Do I Interact? Detecting Social Interactions in Egocentric
  Photo-streams

abstract:
  Given a user wearing a low frame rate wearable camera during a day, this work
aims to automatically detect the moments when the user gets engaged into a
social interaction solely by reviewing the automatically captured photos by the
worn camera. The proposed method, inspired by the sociological concept of
F-formation, exploits distance and orientation of the appearing individuals
-with respect to the user- in the scene from a bird-view perspective. As a
result, the interaction pattern over the sequence can be understood as a
two-dimensional time series that corresponds to the temporal evolution of the
distance and orientation features over time. A Long-Short Term Memory-based
Recurrent Neural Network is then trained to classify each time series.
Experimental evaluation over a dataset of 30.000 images has shown promising
results on the proposed method for social interaction detection in egocentric
photo-streams.


title: New low surface brightness dwarf galaxies in the Centaurus group

abstract:
  We conducted an extensive CCD search for faint, unresolved dwarf galaxies of
very low surface brightness in the whole Centaurus group region encompassing
the Cen A and M 83 subgroups lying at a distance of roughly 4 and 5 Mpc,
respectively. The aim is to significantly increase the sample of known
Centaurus group members down to a fainter level of completeness, serving as a
basis for future studies of the 3D structure of the group. Following our
previous survey of 60 square degrees covering the M 83 subgroup, we extended
and completed our survey of the Centaurus group region by imaging another 500
square degrees area in the g and r bands with the wide-field Dark Energy Survey
Camera at the 4m Blanco telescope at CTIO. The limiting central surface
brightness reached for suspected Centaurus members is $\mu_r \approx 29$ mag
arcsec$^{-2}$, corresponding to an absolute magnitude $M_r \approx -9.5$. The
images were enhanced using different filtering techniques. We found 41 new
dwarf galaxy candidates, which together with the previously discovered 16 dwarf
candidates in the M 83 subgroup amounts to almost a doubling of the number of
known galaxies in the Centaurus complex, if the candidates are confirmed. We
carried out surface photometry in g and r, and report the photometric
parameters derived therefrom, for all new candidates as well as previously
known members in the surveyed area. The photometric properties of the
candidates, when compared to those of LG dwarfs and previously known Centaurus
dwarfs, suggest membership in the Centaurus group. The sky distribution of the
new objects is generally following a common envelope around the Cen A and M 83
subgroups. How the new dwarfs are connected to the intriguing double-planar
feature recently reported by Tully et al. (2015) must await distance
information for the candidates.


title: Barzilai-Borwein Step Size for Stochastic Gradient Descent

abstract:
  One of the major issues in stochastic gradient descent (SGD) methods is how
to choose an appropriate step size while running the algorithm. Since the
traditional line search technique does not apply for stochastic optimization
algorithms, the common practice in SGD is either to use a diminishing step
size, or to tune a fixed step size by hand, which can be time consuming in
practice. In this paper, we propose to use the Barzilai-Borwein (BB) method to
automatically compute step sizes for SGD and its variant: stochastic variance
reduced gradient (SVRG) method, which leads to two algorithms: SGD-BB and
SVRG-BB. We prove that SVRG-BB converges linearly for strongly convex objective
functions. As a by-product, we prove the linear convergence result of SVRG with
Option I proposed in [10], whose convergence result is missing in the
literature. Numerical experiments on standard data sets show that the
performance of SGD-BB and SVRG-BB is comparable to and sometimes even better
than SGD and SVRG with best-tuned step sizes, and is superior to some advanced
SGD variants.


title: Extreme-Value Statistics of Fractional Brownian Motion Bridges

abstract:
  Fractional Brownian motion is a self-affine, non-Markovian and
translationally invariant generalization of Brownian motion, depending on the
Hurst exponent $H$. Here we investigate fractional Brownian motion where both
the starting and the end point are zero, commonly referred to as bridge
processes. Observables are the time $t_+$ the process is positive, the maximum
$m$ it achieves, and the time $t_{\rm max}$ when this maximum is taken. Using a
perturbative expansion around Brownian motion ($H=\frac12$), we give the
first-order result for the probability distribution of these three variables,
and the joint distribution of $m$ and $t_{\rm max}$. Our analytical results are
tested, and found in excellent agreement, with extensive numerical simulations,
both for $H>\frac12$ and $H<\frac12$. This precision is achieved by sampling
processes with a free endpoint, and then converting each realization to a
bridge process, in generalization to what is usually done for Brownian motion.


title: Fragmentation of magnetism in artificial kagome dipolar spin ice

abstract:
  Geometrical frustration in magnetic materials often gives rise to exotic,
low-temperature states of matter, like the ones observed in spin ices. Here we
report the imaging of the magnetic states of a thermally-active artificial
magnetic ice that reveal the fingerprints of a spin fragmentation process. This
fragmentation corresponds to a splitting of the magnetic degree of freedom into
two channels and is evidenced in both real and reciprocal space. Furthermore,
the internal organization of both channels is interpreted within the framework
of a hybrid spin-charge model that directly emerges from the parent spin model
of the kagome dipolar spin ice. Our experimental and theoretical results
provide insights into the physics of frustrated magnets and deepen our
understanding of emergent fields through the use of tailor-made magnetism.


title: Numerical schemes of the time tempered fractional Feynman-Kac equation

abstract:
  This paper focuses on providing the computation methods for the backward time
tempered fractional Feynman-Kac equation, being one of the models recently
proposed in [Wu, Deng, and Barkai, Phys. Rev. E, 84 (2016) 032151]. The
discretization for the tempered fractional substantial derivative is derived,
and the corresponding finite difference and finite element schemes are designed
with well established stability and convergence. The performed numerical
experiments show the effectiveness of the presented schemes.


title: Online Optimization Methods for the Quantification Problem

abstract:
  The estimation of class prevalence, i.e., the fraction of a population that
belongs to a certain class, is a very useful tool in data analytics and
learning, and finds applications in many domains such as sentiment analysis,
epidemiology, etc. For example, in sentiment analysis, the objective is often
not to estimate whether a specific text conveys a positive or a negative
sentiment, but rather estimate the overall distribution of positive and
negative sentiments during an event window. A popular way of performing the
above task, often dubbed quantification, is to use supervised learning to train
a prevalence estimator from labeled data.
  Contemporary literature cites several performance measures used to measure
the success of such prevalence estimators. In this paper we propose the first
online stochastic algorithms for directly optimizing these
quantification-specific performance measures. We also provide algorithms that
optimize hybrid performance measures that seek to balance quantification and
classification performance. Our algorithms present a significant advancement in
the theory of multivariate optimization and we show, by a rigorous theoretical
analysis, that they exhibit optimal convergence. We also report extensive
experiments on benchmark and real data sets which demonstrate that our methods
significantly outperform existing optimization techniques used for these
performance measures.


title: The Largest Respectful Function

abstract:
  Respectful functions were introduced by Sangiorgi as a compositional tool to
formulate short and clear bisimulation proofs. Usually, the larger the
respectful function, the easier the bisimulation proof. In particular the
largest respectful function, defined as the pointwise union of all respectful
functions, has been shown to be very useful. We here provide an explicit and
constructive characterization of it.


title: On uniqueness for a rough transport-diffusion equation

abstract:
  In this Note, we study a transport-diffusion equation with rough coefficients
and we prove that solutions are unique in a low-regularity class.


title:
Constraints on interacting dark energy models from Planck 2015 and
  redshift-space distortion data

abstract:
  We investigate phenomenological interactions between dark matter and dark
energy and constrain these models by employing the most recent cosmological
data including the cosmic microwave background radiation anisotropies from
Planck 2015, Type Ia supernovae, baryon acoustic oscillations, the Hubble
constant and redshift-space distortions. We find that the interaction in the
dark sector parameterized as an energy transfer from dark matter to dark energy
is strongly suppressed by the whole updated cosmological data. On the other
hand, an interaction between dark sectors with the energy flow from dark energy
to dark matter is proved in better agreement with the available cosmological
observations. This coupling between dark sectors is needed to alleviate the
coincidence problem.


title: Porosity governs normals stresses in polymer gels

abstract:
  When sheared, most elastic solids such as metals, rubbers and polymer
hydrogels dilate in the direction perpendicular to the shear plane. This
well-known behaviour known as the Poynting effect is characterized by a
positive normal stress. Surprisingly, biopolymer gels made of fibrous proteins
such as fibrin and collagen, as well as many biological tissues exhibit the
opposite effect, contracting under shear and displaying a negative normal
stress. Here we show that this anomalous behaviour originates from the open
network structure of biopolymer gels, which facilitates interstitial fluid flow
during shear. Using fibrin networks with a controllable pore size as a model
system, we show that the normal stress response to an applied shear is positive
at short times, but decreases to negative values with a characteristic time
scale set by pore size. Using a two-fluid model, we develop a quantitative
theory that unifies the opposite behaviours encountered in synthetic and
biopolymer gels. Synthetic polymer gels are impermeable to solvent flow and
thus effectively incompressible at typical experimental time scales, whereas
biopolymer gels are effectively compressible. Our findings suggest a new route
to tailor elastic instabilities such as the die-swell effect that often hamper
processing of polymer materials and furthermore show that poroelastic effects
play a much more important role in the mechanical properties of cells and
tissues than previously anticipated.


title:
Discrete-time analysis of traveling wave solutions and steady-state of
  PASEP with open boundaries

abstract:
  We consider the dynamics of a single shock in a partially asymmetric simple
exclusion process (PASEP) on a finite lattice with open boundaries in the
sublattice-parallel updating scheme. We then construct the steady state of the
system by considering a linear superposition of these shocks. It is shown that
this steady state can also be written in terms of a product of four non-
commuting matrices. One of the main results obtained here is that these
matrices have exactly the same generic structure as the matrices first
introduced in Jafarpour and Masharian (2009 Phys. Rev. E 79 051124) indicating
that the steady state of a one-dimensional driven-diffusive system can be
written as a linear superposition of product shock measures. It is now easy to
explain the two-dimensional matrix representation of the PASEP with parallel
dynamics introduced in Essler and Rittenberg (1996 J. Phys. A: Math. Gen. 29
3375) and Honecker and Peschel (1997 J. Stat. Phys. 88 319).


title: Electronic properties of germanene nanoribbons in external fields

abstract:
  Germanene nanoribbons, with buckled structures, exhibit unique electronic
properties. The complicated relations among the quantum confinement, the
spin-orbital coupling, the magnetic quantization, the electric-field dominated
quantum numbers, energy dispersions, energy gap, state degeneracy, and wave
functions. Such mechanisms can diversify spatial charge distributions and spin
configurations on distinct sublattices. There exist the spin-split quasi-Landau
levels and the valley-dependent asymmetric energy spectrum in a composite
electric and magnetic field, manly owing to the destruction of z=0 mirror
symmetry. The rich electronic structures are revealed in density of states as a
lot of special structures. The predicted results could be directly verified by
the scanning tunneling spectroscopy.


title: On the category of stratifolds

abstract:
  Stratifolds are considered from a categorical point of view. We show among
others that the category of stratifolds fully faithfully embeds into the
category of ${\mathbb R}$-algebras as does the category of smooth manifolds. We
prove that a variant of the Serre-Swan theorem holds for stratifolds. In
particular, the category of vector bundles over a stratifold is shown to be
equivalent to the category of vector bundles over an associated affine scheme
although the latter is in general larger than the stratifold itself.


title: Proof that Casimir force does not originate from vacuum energy

abstract:
  We present a simple general proof that Casimir force cannot originate from
the vacuum energy of electromagnetic (EM) field. The full QED Hamiltonian
consists of 3 terms: the pure electromagnetic term $H_{\rm em}$, the pure
matter term $H_{\rm matt}$ and the interaction term $H_{\rm int}$. The $H_{\rm
em}$-term commutes with all matter fields because it does not have any explicit
dependence on matter fields. As a consequence, $H_{\rm em}$ cannot generate any
forces on matter. Since it is precisely this term that generates the vacuum
energy of EM field, it follows that the vacuum energy does not generate the
forces. The misleading statements in the literature that vacuum energy
generates Casimir force can be boiled down to the fact that $H_{\rm em}$
attains an implicit dependence on matter fields by the use of the equations of
motion and the illegitimate treatment of the implicit dependence as if it was
explicit. The true origin of the Casimir force is van der Waals force generated
by $H_{\rm int}$.

categories: hep-th cond-mat.stat-mech gr-qc quant-ph


title:
Estimating the number of receiving nodes in 802.11 networks via machine
  learning techniques

abstract:
  Nowadays, most mobile devices are equipped with multiple wireless interfaces,
causing an emerging research interest in device to device (D2D) communication:
the idea behind the D2D paradigm is to exploit the proper interface to directly
communicate with another user, without traversing any network infrastructure. A
first issue related to this paradigm consists in the need for a coordinator,
called controller, able to decide when activating a D2D connection is
appropriate and eventually able to manage such connection. In this view, the
paradigm of Software Defined Networking (SDN), can be exploited both to handle
the data flows among the devices and to interact directly with every device.
  This work is focused on a scenario where a device is selected by the SDN
controller, in order to become the master node of a WiFi-Direct network. The
remaining nodes, called clients, can exchange data with other nodes through the
master. The objective is to infer, through different Machine Learning
approaches, the number of nodes actively involved in receiving data, exploiting
only the information available at the client side and without modifying any
standard communication protocol. The information about the number of client
nodes is crucial when, e.g., a user desires a precise prediction of the
transmission estimated time of arrival (ETA) while downloading a file.


title:
Near-infrared spatially resolved spectroscopy of (136108) Haumea's
  multiple system

abstract:
  The transneptunian region of the solar system is populated by a wide variety
of icy bodies showing great diversity. The dwarf planet (136108) Haumea is
among the largest TNOs and displays a highly elongated shape and hosts two
moons, covered with crystalline water ice like Hamuea. Haumea is also the
largest member of the sole TNO family known to date. A catastrophic collision
is likely responsible for its unique characteristics. We report here on the
analysis of a new set of observations of Haumea obtained with SINFONI at the
ESO VLT. Combined with previous data, and using light-curve measurements in the
optical and far infrared, we carry out a rotationally resolved spectroscopic
study of the surface of Haumea. We describe the physical characteristics of the
crystalline water ice present on the surface of Haumea for both regions, in and
out of the Dark Red Spot (DRS), and analyze the differences obtained for each
individual spectrum. The presence of crystalline water ice is confirmed over
more than half of the surface of Haumea. Our measurements of the average
spectral slope confirm the redder characteristic of the spot region. Detailed
analysis of the crystalline water-ice absorption bands do not show significant
differences between the DRS and the remaining part of the surface. We also
present the results of applying Hapke modeling to our data set. The best
spectral fit is obtained with a mixture of crystalline water ice (grain sizes
smaller than 60 micron) with a few percent of amorphous carbon. Improvements to
the fit are obtained by adding ~10% of amorphous water ice. Additionally, we
used the IFU-reconstructed images to measure the relative astrometric position
of the largest satellite Hi`iaka and determine its orbital elements. An orbital
solution was computed with our genetic-based algorithm GENOID and our results
are in full agreement with recent results.


title: Geometrie der Zahlen. Ein \"Uberblick

abstract:
  This article provides a historical overview of Geometry of Numbers.
  1. Figures, 2. The circuit problem and its relatives, 3. Minkowski lattice
point set, 4. The young Hermann Minkowski, 5. The geometry of numbers develops,
6. Minkowski geometry in the context of time, 7. Successive minima, 8.
Minkowski space-time, 9. Voronoi and Blichfeldt, 10. The schools in Manchester
and Vienna, 11. packing problems


title:
Characteristic classes of star products on Marsden-Weinstein reduced
  symplectic manifolds

abstract:
  In this note we consider a quantum reduction scheme in deformation
quantization on symplectic manifolds proposed by Bordemann, Herbig and Waldmann
based on BRST cohomology. We explicitly construct the induced map on
equivalence classes of star products which will turn out to be an analogue to
the Kirwan map but in the Cartan model of equivariant cohomology. As a
byproduct we shall see that every star product on a (suitable) reduced manifold
is equivalent to a reduced star product.


title: How to compute the barycenter of a weighted graph

abstract:
  Discrete structures like graphs make it possible to naturally and flexibly
model complex phenomena. Since graphs that represent various types of
information are increasingly available today, their analysis has become a
popular subject of research. The graphs studied in the field of data science at
this time generally have a large number of nodes that are not fairly weighted
and connected to each other, translating a structural specification of the
data. Yet, even an algorithm for locating the average position in graphs is
lacking although this knowledge would be of primary interest for statistical or
representation problems. In this work, we develop a stochastic algorithm for
finding the Frechet mean of weighted undirected metric graphs. This method
relies on a noisy simulated annealing algorithm dealt with using
homogenization. We then illustrate our algorithm with two examples (subgraphs
of a social network and of a collaboration and citation network).


title:
Switching of Charge-Current-Induced Spin Polarization in the Topological
  Insulator BiSbTeSe2

abstract:
  The charge-current-induced spin polarization is a key property of topological
insulators for their applications in spintronics. However, topological surface
states are expected to give rise to only one type of spin polarization for a
given current direction, which has been a limiting factor for spin
manipulations. Here we report that in devices based on the bulk-insulating
topological insulator BiSbTeSe2, an unexpected switching of spin polarization
was observed upon changing the chemical potential. The spin polarization
expected from the topological surface states was detected in a heavily
electron-doped device, whereas the opposite polarization was reproducibly
observed in devices with low carrier densities. We propose that the latter type
of spin polarization stems from topologically-trivial two-dimensional states
with a large Rashba spin splitting, which are caused by a strong band bending
at the surface of BiSbTeSe2 beneath the ferromagnetic electrode used as a spin
detector. This finding paves the way for realizing the "spin transistor"
operation in future topological spintronic devices.


title:
Slow growth of solutions of super-fast diffusion equations with
  unbounded initial data

abstract:
  We study positive solutions of the super-fast diffusion equation in the whole
space with initial data which are unbounded as $|x|\to\infty$. We find an
explicit dependence of the slow temporal growth rate of solutions on the
initial spatial growth rate. A new class of self-similar solutions plays a
significant role in our analysis.


title: Perception-aware Path Planning

abstract:
  In this paper, we give a double twist to the problem of planning under
uncertainty. State-of-the-art planners seek to minimize the localization
uncertainty by only considering the geometric structure of the scene. In this
paper, we argue that motion planning for vision-controlled robots should be
perception aware in that the robot should also favor texture-rich areas to
minimize the localization uncertainty during a goal-reaching task. Thus, we
describe how to optimally incorporate the photometric information (i.e.,
texture) of the scene, in addition to the the geometric one, to compute the
uncertainty of vision-based localization during path planning. To avoid the
caveats of feature-based localization systems (i.e., dependence on feature type
and user-defined thresholds), we use dense, direct methods. This allows us to
compute the localization uncertainty directly from the intensity values of
every pixel in the image. We also describe how to compute trajectories online,
considering also scenarios with no prior knowledge about the map. The proposed
framework is general and can easily be adapted to different robotic platforms
and scenarios. The effectiveness of our approach is demonstrated with extensive
experiments in both simulated and real-world environments using a
vision-controlled micro aerial vehicle.


title:
The role of ionic sizes in inducing the cubic to tetragonal distortion
  in AV$_{2}$O$_{4}$ and ACr$_{2}$O$_{4}$ (A=Zn, Mg and Cd) compounds

abstract:
  Cubic to tetragonal distortion in spinel compounds have been a contentious
issue for last two decades. Different groups have proposed different mechanisms
to understand such a distortion in these spinels, which are: (i) spin lattice
coupling mechanism known as the spin driven Jahn-Teller (JT) effect, (ii) the
strong relativistic spin-orbit coupling, a moderate JT distortion and weak V-V
interactions and (iii) the JT effect. Now, in order to know the possible cause
for such a distortion, we have avoided these complexities (various interactions
among spin, electronic, orbital and lattice degrees of freedom) by carrying out
spin unpolarized calculations. The calculated values of bulk moduli for
ZnV$_{2}$O$_{4}$ (ZnCr$_{2}$O$_{4}$), MgV$_{2}$O$_{4}$ (MgCr$_{2}$O$_{4}$) and
CdV$_{2}$O$_{4}$ (CdCr$_{2}$O$_{4}$) are found to be $\sim$289 ($\sim$254),
$\sim$244 ($\sim$243) and $\sim$230 ($\sim$233) GPa, respectively. For
vanadates and chromates, the order of calculated values of lattice parameter
$a$ are found to CdV$_{2}$O$_{4}$$>$MgV$_{2}$O$_{4}$$>$ZnV$_{2}$O$_{4}$ and
CdCr$_{2}$O$_{4}$$>$MgCr$_{2}$O$_{4}$$>$ZnCr$_{2}$O$_{4}$, respectively and are
consistent with the experimental results. The calculated values of cubic to
tetragonal distortion (c/a), with c/a$<$1 for ZnV$_{2}$O$_{4}$
(ZnCr$_{2}$O$_{4}$), MgV$_{2}$O$_{4}$ (MgCr$_{2}$O$_{4}$) and CdV$_{2}$O$_{4}$
(CdCr$_{2}$O$_{4}$) are $\sim$0.996 ($\sim$0.997), $\sim$0.995 ($\sim$0.994)
and $\sim$0.997 ($\sim$0.998), respectively. These values are in good agreement
with the experimental data for ZnV$_{2}$O$_{4}$, MgV$_{2}$O$_{4}$,
ZnCr$_{2}$O$_{4}$ and MgCr$_{2}$O$_{4}$ compounds. The present study clearly
shows the role of ionic sizes in inducing the cubic to tetragonal distortion in
these spinels. These mechanisms also appear to be responsible for deciding the
other physical properties of these compounds.


title:
Distributions of covariances as a window into the operational regime of
  neuronal networks

abstract:
  Massively parallel recordings of spiking activity in cortical networks show
that covariances vary widely across pairs of neurons. Their low average is well
understood, but an explanation for the wide distribution in relation to the
static (quenched) disorder of the connectivity in recurrent random networks was
so far elusive. We here derive a finite-size mean-field theory that reduces a
disordered to a highly symmetric network with fluctuating auxiliary fields. The
exposed analytical relation between the statistics of connections and the
statistics of pairwise covariances shows that both, average and dispersion of
the latter, diverge at a critical coupling. At this point, a network of
nonlinear units transits from regular to chaotic dynamics. Applying these
results to recordings from the mammalian brain suggests its operation close to
this edge of criticality.


title:
System-environment correlations for dephasing two-qubit states coupled
  to thermal baths

abstract:
  Based on the exact dynamics of a two-qubit system and environment, we
investigate system-environment (SE) quantum and classical correlations. The
coupling is chosen to represent a dephasing channel for one of the qubits and
the environment is a proper thermal bath. First we discuss the general issue of
dilation for qubit phase damping. Based on the usual thermal bath of harmonic
oscillators, we derive criteria of separability and entanglement between an
initial $X$ state and the environment. Applying these criteria to initial
Werner states, we find that entanglement between the system and environment is
built up in time for temperatures below a certain critical temperature
$T_{\mathrm{crit}}$. On the other hand, the total state remains separable
during those short times that are relevant for decoherence and loss of
entanglement in the two-qubit state. Close to $T_{\mathrm{crit}}$ the SE
correlations oscillate between separable and entangled. Even though these
oscillations are also observed in the entanglement between the two qubits, no
simple relation between the loss of entanglement in the two-qubit system and
the build-up of entanglement between the system and environment is found.


title:
Inferring the IGM thermal history during reionisation with the
  Lyman-$\alpha$ forest power spectrum at redshift $z \simeq 5$

abstract:
  We use cosmological hydrodynamical simulations to assess the feasibility of
constraining the thermal history of the intergalactic medium during
reionisation with the Ly$\alpha$ forest at $z\simeq5$. The integrated thermal
history has a measureable impact on the transmitted flux power spectrum that
can be isolated from Doppler broadening at this redshift. We parameterise this
using the cumulative energy per proton, $u_0$, deposited into a gas parcel at
the mean background density, a quantity that is tightly linked with the gas
density power spectrum in the simulations. We construct mock observations of
the line of sight Ly$\alpha$ forest power spectrum and use a Markov Chain Monte
Carlo approach to recover $u_{0}$ at redshifts $5 \leq z \leq 12$. A
statistical uncertainty of $\sim 20$ per cent is expected (at 68 per cent
confidence) at $z\simeq 5$ using high resolution spectra with a total redshift
path length of $\Delta z=4$ and a typical signal-to-noise ratio of $\rm S/N=15$
per pixel. Estimates for the expected systematic uncertainties are comparable,
such that existing data should enable a measurement of $u_0$ to within $\sim
30$ per cent. This translates to distinguishing between reionisation scenarios
with similar instantaneous temperatures at $z\simeq 5$, but with an energy
deposited per proton that differs by $2$-$3\, \rm eV$ over the redshift
interval $5\leq z \leq 12$. For an initial temperature of $T\sim 10^{4}\rm\,K$
following reionisation, this corresponds to the difference between early
($z_{\rm re}=12$) and late ($z_{\rm re}=7$) reionisation in our models.


title:
Rational B\'ezier Curves Approximated by Bernstein-Jacobi Hybrid
  Polynomial Curves

abstract:
  In this paper, we propose a linear method for $C^{(r,s)}$ approximation of
rational B\'{e}zier curve with arbitrary degree polynomial curve. Based on
weighted least-squares, the problem be converted to an approximation between
two polynomial curves. Then applying Bernstein-Jacobi hybrid polynomials, we
obtain the resulting curve. In order to reduce error, degree reduction method
for B\'{e}zier curve is used. A error bound between rational B\'{e}zier curve
and B\'{e}zier curve is presented. Finally, some examples and figures were
offered to demonstrate the efficiency, simplicity, and stability of our
methods.


title: Topological transition in coated wire medium

abstract:
  We develop a theory of nonlocal homogenization for metamaterial consisting of
parallel metallic wires with dielectric coating. It is demonstrated that
manipulation of dielectric contrast between wire dielectric shell and host
material results in switching of metamaterial dispersion regime from elliptic
to the hyperbolic one, i.e. the topological transition takes place. We confirm
our theoretical predictions by full-wave numerical simulations.


title:
Efficient dynamical correction of the transition state theory rate
  estimate for a flat energy barrier

abstract:
  The recrossing correction to the transition state theory estimate of a
thermal rate can be difficult to calculate when the energy barrier is flat.
This problem arises, for example, in polymer escape if the polymer is long
enough to stretch between the initial and final state energy wells while the
polymer beads undergo diffusive motion back and forth over the barrier. We
present an efficient method for evaluating the correction factor by
constructing a sequence of hyperplanes starting at the transition state and
calculating the probability that the system advances from one hyperplane to
another towards the product. This is analogous to what is done in forward flux
sampling except that there the hyperplane sequence starts at the initial state.
The method is applied to the escape of polymers with up to 64 beads from a
potential well. For high temperature, the results are compared with direct
Langevin dynamics simulations as well as forward flux sampling and excellent
agreement between the three rate estimates is found. The use of a sequence of
hyperplanes in the evaluation of the recrossing correction speeds up the
calculation by an order of magnitude as compared with the traditional approach.
As the temperature is lowered, the direct Langevin dynamics simulations as well
as the forward flux simulations become computationally too demanding, while the
harmonic transition state theory estimate corrected for recrossings can be
calculated without significant increase in the computational effort.


title: Reduced dynamical maps in the presence of initial correlations

abstract:
  We introduce a general framework for the construction of completely positive
dynamical evolutions in the presence of system-environment initial
correlations. The construction relies upon commutativity of the compatibility
domain obtained by considering the marginals with respect to the environmental
degrees of freedom of the considered class of correlated states. Our approach
allows to consider states whose discord is not necessarily zero and explicitly
show the non-uniqueness of the completely positive extensions of the obtained
dynamical map outside the compatibility domain. The relevance of such maps for
the treatment of open quantum system dynamics is discussed and connection to
previous literature is critically assessed.


title: Searching Lattice Data Structures of Varying Degrees of Sortedness

abstract:
  Lattice data structures are space efficient and cache-suitable data
structures. The basic searching, insertion, and deletion operations are of time
complexity $O(\sqrt{N})$. We give a jump searching algorithm of time complexity
$O(J(L)\log(N))$, where $J(L)$ is the jump factor of the lattice. $J(L)$
approaches $4$ when the degree of sortedness of the lattice approaches
$\sqrt{N}$. A sorting procedure of time complexity $O(\sqrt{N})$ that can be
used, during the system idle time, to increase the degree of sortedness of the
lattice is given.


title:
Scaling laws and flow structures of double diffusive convection in the
  finger regime

abstract:
  Direct numerical simulations are conducted for double diffusive convection
(DDC) bounded by two parallel plates, with fluid properties similar to the
values of seawater. The DDC flow is driven by an unstable salinity difference
and stabilized at the same time by a temperature difference. For these
conditions the flow can be in the finger regime. We develop scaling laws for
three key response parameters of the system: The non-dimensional salinity flux
$Nu_S$ mainly depends on the salinity Rayleigh number $Ra_S$, which measures
the strength of the salinity difference, and exhibits a very weak dependence on
the density ratio $\Lambda$, which is the ratio of the buoyancy forces induced
by two scalar differences. The non-dimensional flow velocity $Re$ and the
non-dimensional heat flux $Nu_T$ are dependent on both $Ra_S$ and $\Lambda$.
However, the rescaled Reynolds number $Re\Lambda^{\alpha^{\rm eff}_u}$ and the
rescaled convective heat flux $(Nu_T-1)\Lambda^{\alpha^{\rm eff}_T}$ depend
only on $Ra_S$. The two exponents are dependent on the fluid properties and are
determined from the numerical results. Moreover, the behaviors of $Nu_S$ and
$Re\Lambda^{\alpha^{\rm eff}_u}$ agree with the predictions of the
Grossmann-Lohse theory which was originally developed for the
Rayleigh-B\'{e}nard flow. The non-dimensional salt-finger width and the
thickness of the velocity boundary layers, after being rescaled by
$\Lambda^{\alpha^{\rm eff}_u/2}$, collapse and obey a similar power-law scaling
relation with $Ra_S$. When $Ra_S$ is large enough, salt fingers do not extend
from one plate to the other and horizontal zonal flows emerge in the bulk
region. We then show that the current scaling strategy can be successfully
applied to the experimental results of a heat-copper-ion system~(Hage and
Tilgner, Phys. Fluids, 22, 076603, 2010).


title:
Rieger-type periodicity during solar cycles 14-24: estimation of dynamo
  magnetic field strength in the solar interior

abstract:
  Solar activity undergoes a variation over time scales of several months known
as Rieger-type periodicity, which usually occurs near maxima of sunspot cycles.
An early analysis showed that the periodicity appears only in some cycles, and
is absent in other cycles. But the appearance/absence during different cycles
has not been explained. We performed a wavelet analysis of sunspot data from
the Greenwich Royal Observatory and the Royal Observatory of Belgium during
cycles 14-24. We found that the Rieger-type periods occur in all cycles, but
they are cycle-dependent: shorter periods occur during stronger cycles. Our
analysis revealed a periodicity of 185-195 days during the weak cycles 14-15
and 24, and a periodicity of 155-165 days during the stronger cycles 16-23. We
derived the dispersion relation of the spherical harmonics of the magnetic
Rossby waves in the presence of differential rotation and a toroidal magnetic
field in the dynamo layer near the base of the convection zone. This showed
that the harmonic of fast Rossby waves with m=1 and n=4, where m (n) indicate
the toroidal (poloidal) wavenumbers, respectively, perfectly fit with the
observed periodicity. The variation of the toroidal field strength from weaker
to stronger cycles may lead to the different periods found in those cycles,
which explains the observed enigmatic feature of the Rieger-type periodicity.
Finally, we used the observed periodicity to estimate the dynamo field strength
during cycles 14-24. Our estimations suggest a field strength of 40 kG for the
stronger cycles, and 20 kG for the weaker cycles.


title: Sasakian structures. A foliated approach

abstract:
  Recent renewed interest in Sasakian manifolds is due mainly to the fact that
they can provide examples of generalized Einstein manifolds, manifolds which
are of great interest in mathematical models of various aspects of physical
phenomena. Sasakian manifolds are odd dimensional counterparts of K\"ahlerian
manifolds to which they are closely related. The book of Ch. Boyer and K.
Galicki, Sasakian Geometry is both the best introduction to the subject and at
the same time it gathers state of the art information and results on these
manifolds. However, although the authors are well aware that a Sasakian
structure is a very special one-dimensional Riemannian foliation with
K\"ahlerian transverse structure, they use this fact only in a few very special
cases.
  The paper presents an approach to Sasakian manifolds on which the author gave
several lectures, most recently at the Workshop on almost hermitian and contact
geometry at the Banach Center in B\c{e}dlewo in October 2015 and at University
of the Basque Country in February 2016. The first lectures on the topic the
author gave at Universidad de Sevilla in October 1988 and then presented the
consequence for the geometry of Sasakian manifolds, in particular the
relationns between various curvatures and those of the transverse K\"ahler
manifold. The results were published in several sections of \cite{WO_S} as well
as in \cite{Wo_deb}. The most general theory of geometrical structures
"adapted" to a foliation was presented in \cite{WO_T}, see also \cite{WO_S}.
The paper concentrates on cohomological properties of Sasakian manifolds and of
transversely holomorphic and K\"ahlerian foliations. These properties permit to
formulate obstructions to the existence of Sasakian structures on compact
manifolds. The presented results are due to the author as well as his former
and present Ph.D. students.


title:
Nonlinear Ordinary Differential Equations: A discussion on Symmetries
  and Singularities

abstract:
  Two essential methods, the symmetry analysis and of the singularity analysis,
for the study of the integrability of nonlinear ordinary differential equations
are discussed. The main similarities and differences of these two different
methods are given.


title: The LOFAR search for radio pulsars and fast transients in M33, M81 & M82

abstract:
  The radio pulsar and rotating radio transient populations are only known in
and near the Milky Way. Investigating such populations in other galaxies
requires deep pulsar and transient searches. We performed 4-h radio
observations of nearby galaxies M33, M81 and M82 with LOFAR. Our main purpose
was to characterise the bright end of the pulsar population in other galaxies,
and compare it to that of the Milky Way. We searched for extragalactic radio
pulsars through a periodic-pulse search, and for sporadic fast radio transients
through a single-pulse search. We coherently combined at most 23 LOFAR Core
High-Band Antenna (HBA) stations and covered M33, M81, and M82 in their
entirety using multiple tied-array beams. No pulsating sources or single pulses
were found. We have, therefore established stricter limits on the extragalactic
pulsar flux density at lower frequencies than those obtained in previous
Arecibo, GBT, and WSRT searches. We conclude that in nearby galaxies M33, M81,
and M82 there are no pulsars shining toward Earth with pseudo luminosities
greater than a few times that of the brightest pulsars in our Milky Way.


title:
PeppyChains: Simplifying the assembly of 3D-printed generic protein
  models

abstract:
  Peppytides is a coarse-grained, accurate, physical model of the polypeptide
chain. I have shared instructions to make your own polypeptide chain and STL
files of Peppytides in MAKE magazine in Jan 2014 issue. However, Peppytides
involves a lot of steps and assembly of units. People were asking me, 'Is there
any easier way to make these models?'. I have been at several workshops,
hands-on sessions, talks and a science events with Peppytides. From the
feedback that I got everywhere, most of the makers, teachers and students want
something that is 3D-Print-&-Go, or at least easier to make, even at the cost
of some features.
  I have designed a new version of the model, named PeppyChains, in which the
backbone chain of the model can be 3d-printed as a single unit. PeppyChains
design eliminates the assembling of parts to form the backbone chain, but with
the cost of losing the ability to use bias-magnets to favor certain phi/psi
angles in the backbone. I have been demonstrating PeppyChains at various talks
and workshops along with Peppytides, and I have received requests for making
the STL file public. On popular demand, here I am sharing this STL and
providing the step-by-step instructions to make PeppyChains. Just add the
hydrogen-bond magnets, paint and color-code the atoms, and you are ready to go!
No drilling. No time consuming assembly.


title: Reply to "Comment on Testing Planck-Scale Gravity with Accelerators"

abstract:
  Results of a 2012 PRL Letter have recently been questioned by T. Kalaydzhyan
in arXiv:1604.04486. Here we confirm our original results and conclusions by
addressing all concerns raised in the Comment.


title:
Cosmological constraints on Lorentz Invariance violation in gravity and
  dark matter

abstract:
  This brief contribution is devoted to phenomenological consequences of
deviations from Lorentz invariance in gravity and dark matter. We will discuss
main effects on cosmological observables and current constraints derived from
astrophysical and cosmological data.


title: Design of a plasmonic near-field tip for super-resolution IR-imaging

abstract:
  The concepts of spoof surface plasmon polaritons and adiabatic field
compression are employed to design metallic near-field probes that allow
guiding and focusing of mid-infrared wavelength electromagnetic radiation and
provides subwavelength field confinements and a lateral optical resolution of
about 10 nm.


title: Enhancement of Tc by point-like disorder and anisotropic gap in FeSe

abstract:
  A highly anisotropic superconducting gap is found in single crystals of FeSe
by studying the London penetration depth, $\Delta \lambda$, measured down to 50
mK in samples before and after 2.5 MeV electron irradiation. The gap minimum
increases with introduced point - like disorder, indicating the absence of
symmetry - imposed nodes. Surprisingly, the superconducting transition
temperature, $T_c$, \textit{increases} by 0.4 K from $T_{c0} \approx$ 8.8 K
while the structural transition temperature, $T_s$, \textit{decreases} by 0.9 K
from $T_{s0} \approx$91.2 K after electron irradiation. We discuss several
explanations for the $T_c$ enhancement, and propose that local strengthening of
the pair interaction by irradiation-induced Frenkel defects most likely
explains the phenomenon.


title:
Defect engineering of the electronic transport through cuprous oxide
  interlayers

abstract:
  The electronic transport through Au-(Cu$_{2}$O)$_n$-Au junctions is
investigated using first-principles calculations and the nonequilibrium Green's
function method. The effect of varying the thickness (i.e., $n$) is studied as
well as that of point defects and anion substitution. For all Cu$_{2}$O
thicknesses the conductance is more enhanced by bulk-like (in contrast to
near-interface) defects, with the exception of O vacancies and Cl
substitutional defects. A similar transmission behavior results from Cu
deficiency and N substitution, as well as from Cl substitution and N
interstitials for thick Cu$_{2}$O junctions. In agreement with recent
experimental observations, it is found that N and Cl doping enhances the
conductance. A Frenkel defect, i.e., a superposition of an O interstitial and O
substitutional defect, leads to a remarkably high conductance. From the
analysis of the defect formation energies, Cu vacancies are found to be
particularly stable, in agreement with earlier experimental and theoretical
work.


title:
Predictions for the Majorana CP Violation Phases in the Neutrino Mixing
  Matrix and Neutrinoless Double Beta Decay

abstract:
  We obtain predictions for the Majorana phases $\alpha_{21}/2$ and
$\alpha_{31}/2$ of the $3\times 3$ unitary neutrino mixing matrix $U =
U_e^{\dagger} \, U_{\nu}$, $U_e$ and $U_{\nu}$ being the $3\times 3$ unitary
matrices resulting from the diagonalisation of the charged lepton and neutrino
Majorana mass matrices, respectively. We focus on forms of $U_e$ and $U_{\nu}$
permitting to express $\alpha_{21}/2$ and $\alpha_{31}/2$ in terms of the Dirac
phase $\delta$ and the three neutrino mixing angles of the standard
parametrisation of $U$, and the angles and the two Majorana-like phases
$\xi_{21}/2$ and $\xi_{31}/2$ present, in general, in $U_{\nu}$. The concrete
forms of $U_{\nu}$ considered are fixed by, or associated with, symmetries
(tri-bimaximal, bimaximal, etc.), so that the angles in $U_{\nu}$ are fixed.
For each of these forms and forms of $U_e$ that allow to reproduce the measured
values of the three neutrino mixing angles $\theta_{12}$, $\theta_{23}$ and
$\theta_{13}$, we derive predictions for phase differences $(\alpha_{21}/2 -
\xi_{21}/2)$, $(\alpha_{31}/2 - \xi_{31}/2)$, etc., which are completely
determined by the values of the mixing angles. We show that the requirement of
generalised CP invariance of the neutrino Majorana mass term implies $\xi_{21}
= 0$ or $\pi$ and $\xi_{31} = 0$ or $\pi$. For these values of $\xi_{21}$ and
$\xi_{31}$ and the best fit values of $\theta_{12}$, $\theta_{23}$ and
$\theta_{13}$, we present predictions for the effective Majorana mass in
neutrinoless double beta decay for both neutrino mass spectra with normal and
inverted ordering.


title: Finite Conformal Quantum Gravity and Nonsingular Spacetimes

abstract:
  We explicitly prove that a class of finite quantum gravitational theories (in
odd as well as in even dimension) is actually a range of anomaly-free
conformally invariant theories in the spontaneously broken phase of the
conformal Weyl symmetry. At classical level we show how the Weyl conformal
invariance is likely able to tame the spacetime singularities that plague not
only Einstein gravity, but also local and weakly non-local higher derivative
theories. This latter statement is rigorously proved by a singularity theorem
that applies to a large class of weakly non-local theories. Following the
seminal paper by Narlikar and Kembhavi, we provide an explicit construction of
singularity-free black hole exact solutions conformally equivalent to the
Schwarzschild metric. Furthermore, we show that the FRW cosmological solutions
and the Belinski, Khalatnikov, Lifshitz (BKL) spacetimes, which exactly solve
the classical equations of motion, are conformally equivalent to regular
spacetimes. Finally, we prove that the Oppenheimer-Volkov gravitational
collapse is a an exact (singularity-free) solution of the non-local conformally
invariant theory compatible with the bounce paradigm.

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


title:
Simultaneous Measurement of Complementary Observables with Compressive
  Sensing

abstract:
  The more information a measurement provides about a quantum system's position
statistics, the less information a subsequent measurement can provide about the
system's momentum statistics. This information trade-off is embodied in the
entropic formulation of the uncertainty principle. Traditionally, uncertainty
relations correspond to resolution limits; increasing a detector's position
sensitivity decreases its momentum sensitivity and vice-versa. However, this is
not required in general; for example, position information can instead be
extracted at the cost of noise in momentum. Using random, partial projections
in position followed by strong measurements in momentum, we efficiently
determine the transverse-position and transverse-momentum distributions of an
unknown optical field with a single set of measurements. The momentum
distribution is directly imaged, while the position distribution is recovered
using compressive sensing. At no point do we violate uncertainty relations;
rather, we economize the use of information we obtain.


title:
Truncatable bootstrap equations in algebraic form and critical surface
  exponents

abstract:
  We describe examples of drastic truncations of conformal bootstrap equations
encoding much more information than that obtained by a direct numerical
approach. A three-term truncation of the four point function of a free scalar
in any space dimensions provides algebraic identities among conformal block
derivatives which generate the exact spectrum of the infinitely many primary
operators contributing to it. In boundary conformal field theories, we point
out that the appearance of free parameters in the solutions of bootstrap
equations is not an artifact of truncations, rather it reflects a physical
property of permeable conformal interfaces which are described by the same
equations. Surface transitions correspond to isolated points in the parameter
space. We are able to locate them in the case of 3d Ising model, thanks to a
useful algebraic form of 3d boundary bootstrap equations. It turns out that the
low-lying spectra of the surface operators in the ordinary and the special
transitions of 3d Ising model form two different solutions of the same
polynomial equation. Their interplay yields an estimate of the surface
renormalization group exponent, $y_{h}=0.72558(18)$ for the ordinary
universality class and $y_{h}=1.646(2)$ for the special universality class,
which compare well with the most recent Monte Carlo calculations. Estimates of
other surface exponents as well as OPE coefficients are also obtained.


title:
Non Axisymmetric Relativistic Wind Accretion with Velocity Gradients
  onto a Rotating Black Hole

abstract:
  We model, for the first time, the Bondi-Hoyle accretion of a fluid with
velocity gradients onto a Kerr black hole, by numerically solving the fully
relativistic hydrodynamics equations. Specifically, we consider a supersonic
ideal gas, which has velocity gradients perpendicular to the relative motion.
We measure the mass and specific angular accretion rates to illustrate whether
the fluid presents unstable patterns or not. The initial parameters, we
consider in this work, are the velocity gradient $\epsilon_{v}$, the black hole
spin $a$, the asymptotic Mach number ${\cal M}_{\infty}$ and adiabatic index
$\Gamma$. We show that the flow accretion reaches a fairly stationary regime,
unlike in the Newtonian case, where significant fluctuations of the mass and
angular momentum accretion rates are found. On the other hand, we consider a
special case where both density and velocity gradients of the fluid are taken
into account. The spin of the black hole and the asymptotic Newtonian Mach
number, for this case, are $a=0.98$ and ${\cal M}_{\infty}=1$, respectively. A
kind of flip-flop behavior is found at the early times; nevertheless, the
system also reaches a steady state.


title:
Knowledge-Enabled Robotic Agents for Shelf Replenishment in Cluttered
  Retail Environments

abstract:
  Autonomous robots in unstructured and dynamically changing retail
environments have to master complex perception, knowledgeprocessing, and
manipulation tasks. To enable them to act competently, we propose a framework
based on three core components: (o) a knowledge-enabled perception system,
capable of combining diverse information sources to cope with occlusions and
stacked objects with a variety of textures and shapes, (o) knowledge processing
methods produce strategies for tidying up supermarket racks, and (o) the
necessary manipulation skills in confined spaces to arrange objects in
semi-accessible rack shelves. We demonstrate our framework in an simulated
environment as well as on a real shopping rack using a PR2 robot. Typical
supermarket products are detected and rearranged in the retail rack, tidying up
what was found to be misplaced items.


title: Nonlinear elliptic equations and systems with linear part at resonance

abstract:
  The famous result of Landesman and Lazer [10] dealt with resonance at a
simple eigenvalue. Soon after publication of [10], Williams [14] gave an
extension for repeated eigenvalues. The conditions in Williams [14] are rather
restrictive, and no examples were ever given. We show that seemingly different
classical result by Lazer and Leach [11], on forced harmonic oscillators at
resonance, provides an example for this theorem. The article by Williams [14]
also contained a shorter proof. We use a similar approach to study resonance
for $2 \times 2$ systems. We derive conditions for existence of solutions,
which turned out to depend on the spectral properties of the linear part.


title: Crystal Chemistry and Structural Design of Iron-Based Superconductors

abstract:
  The second class of high-temperature superconductors (HTSCs), iron-based
pnictides and chalcogenides, necessarily contain Fe$_2$$X_2$ ("$X$" refers to a
pnictogen or a chalcogen element) layers, just like the first class of HTSCs
which possess the essential CuO$_2$ sheets. So far, dozens of iron-based HTSCs,
classified into nine groups, have been discovered. In this article, the
crystal-chemistry aspects of the known iron-based superconductors are reviewed
and summarized by employing "hard and soft acids and bases (HSAB)" concept.
Based on these understandings, we propose an alternative route to exploring new
iron-based superconductors via rational structural design.


title: Semantometrics: Towards Fulltext-based Research Evaluation

abstract:
  Over the recent years, there has been a growing interest in developing new
research evaluation methods that could go beyond the traditional citation-based
metrics. This interest is motivated on one side by the wider availability or
even emergence of new information evidencing research performance, such as
article downloads, views and Twitter mentions, and on the other side by the
continued frustrations and problems surrounding the application of purely
citation-based metrics to evaluate research performance in practice.
Semantometrics are a new class of research evaluation metrics which build on
the premise that full-text is needed to assess the value of a publication. This
paper reports on the analysis carried out with the aim to investigate the
properties of the semantometric contribution measure, which uses semantic
similarity of publications to estimate research contribution, and provides a
comparative study of the contribution measure with traditional bibliometric
measures based on citation counting.


title:
Antenna-cavity hybrids: matching polar opposites for Purcell
  enhancements at any linewidth

abstract:
  Strong interaction between light and a single quantum emitter is essential to
a great number of applications, including single photon sources. Microcavities
and plasmonic antennas have been used frequently to enhance these interactions
through the Purcell effect. Both can provide large emission enhancements: the
cavity typically through long photon lifetimes (high $Q$), and the antenna
mostly through strong field enhancement (low mode volume $V$). In this work, we
demonstrate that a hybrid system, which combines a cavity and a dipolar
antenna, can achieve stronger emission enhancements than the cavity or antenna
alone. We show that such systems can be used as a versatile platform to tune
the bandwidth of enhancement to any desired value, while simultaneously
boosting emission enhancement. Our fully consistent analytical model allows to
identify the underlying mechanisms of boosted emission enhancement in hybrid
systems, which include radiation damping and constructive interference between
multiple-scattering paths. Additionally, we find excellent agreement between
strongly boosted enhancement spectra from our analytical model and from
finite-element simulations on a realistic cavity-antenna system. Finally, we
demonstrate that hybrid systems can simultaneously boost emission enhancement
and maintain a near-unity outcoupling efficiency into a single cavity decay
channel, such as a waveguide.


title: Nanostructure-induced distortion in single-emitter microscopy

abstract:
  Single-emitter microscopy has emerged as a promising method of imaging
nanostructures with nanoscale resolution. This technique uses the centroid
position of an emitters far-field radiation pattern to infer its position to a
precision that is far below the diffraction limit. However, nanostructures
composed of high-dielectric materials such as noble metals can distort the
far-field radiation pattern. Nanoparticles also exhibit a more complex range of
distortions, because in addition to introducing a high dielectric surface, they
also act as efficient scatterers. Thus, the distortion effects of nanoparticles
in single-emitter microscopy remains poorly understood. Here we demonstrate
that metallic nanoparticles can significantly distort the accuracy of
single-emitter imaging at distances exceeding 300 nm. We use a single quantum
dot to probe both the magnitude and the direction of the metallic
nanoparticle-induced imaging distortion and show that the diffraction spot of
the quantum dot can shift by more than 35 nm. The centroid position of the
emitter generally shifts away from the nanoparticle position, in contradiction
to the conventional wisdom that the nanoparticle is a scattering object that
will pull in the diffraction spot of the emitter towards its center. These
results suggest that dielectric distortion of the emission pattern dominates
over scattering. We also show that by monitoring the distortion of the quantum
dot diffraction spot we can obtain high-resolution spatial images of the
nanoparticle, providing a new method for performing highly precise,
sub-diffraction spatial imaging. These results provide a better understanding
of the complex near-field coupling between emitters and nanostructures, and
open up new opportunities to perform super-resolution microscopy with higher
accuracy.


title:
Energy Gap Evolution Across the Superconductivity Dome in Single
  Crystals of (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$

abstract:
  The mechanism of unconventional superconductivity in iron-based
superconductors (IBSs) is one of the most intriguing questions in current
materials research. Among non-oxide IBSs, (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ has
been intensively studied because of its high superconducting transition
temperature and fascinating evolution of the superconducting gap structure from
being fully isotropic at optimal doping (\(x\approx\)0.4) to becoming nodal at
$x > $0.8. Although this marked evolution was identified in several independent
experiments, there are no details of the gap evolution to date because of the
lack of high-quality single crystals covering the entire K-doping range of the
superconducting dome. We conducted a systematic study of the London penetration
depth, $\lambda (T)$, across the full phase diagram for different
concentrations of point-like defects introduced by 2.5 MeV electron
irradiation. Fitting the low-temperature variation with the power law, $\Delta
\lambda \sim T^{n}$, we find that the exponent $n$ is the highest and $T_c$
suppression rate with disorder is the smallest at optimal doping, and they
evolve with doping being away from optimal, which is consistent with increasing
gap anisotropy, including an abrupt change around $x\simeq 0.8$, indicating the
onset of nodal behavior. Our analysis using a self-consistent $t$-matrix
approach suggests the ubiquitous and robust nature of s$_{\pm}$ pairing in IBSs
and argues against a previously suggested transition to a $d-$wave state near
$x=1$ in this system.


title: Scalable Information Inequalities for Uncertainty Quantification

abstract:
  In this paper we demonstrate the only available scalable information bounds
for quantities of interest of high dimensional probabilistic models.
Scalability of inequalities allows us to (a) obtain uncertainty quantification
bounds for quantities of interest in the large degree of freedom limit and/or
at long time regimes; (b) assess the impact of large model perturbations as in
nonlinear response regimes in statistical mechanics; (c) address model-form
uncertainty, i.e. compare different extended models and corresponding
quantities of interest. We demonstrate some of these properties by deriving
robust uncertainty quantification bounds for phase diagrams in statistical
mechanics models.


title:
Pinning down neutrino oscillation parameters in the 2-3 sector with a
  mgnetised atmospheric neutrino detector: a new study

abstract:
  We determine the sensitivity to neutrino oscillation parameters from a study
of atmospheric neutrinos in a magnetised detector such as the ICAL at the
proposed India-based Neutrino Observatory. In such a detector that can {\em
separately} count $\nu_\mu$ and $\overline{\nu}_\mu$-induced events, the
relatively smaller (about 5\%) uncertainties on the neutrino--anti-neutrino
flux ratios translate to a constraint in the $\chi^2$ analysis that results in
a significant improvement in the precision with which neutrino oscillation
parameters such as $\sin^2\theta_{23}$ can be determined. Such an effect is
unique to all magnetisable detectors and constitutes a great advantage in
determining neutrino oscillation parameters using such detectors. Such a study
has been performed for the first time here. Along with an increase in the
kinematic range compared to earlier analyses, this results in sensitivities to
oscillation parameters in the 2--3 sector that are comparable to or better than
those from accelerator experiments where the fluxes are significantly higher.
For example, the $1\sigma$ precisions on $\sin^2\theta_{23}$ and
$|\Delta{m^2_{32(31)}}|$ achievable for 500 kTon yr exposure of ICAL are
$\sim9\%$ and $\sim2.5\%$ respectively for both normal and inverted
hierarchies. The mass hierarchy sensitivity achievable with this combination
when the true hierarchy is normal (inverted) for the same exposure is
$\Delta\chi^2\approx8.5$ ($\Delta\chi^2\approx9.5$).


title:
Finite Volume Method for the Relativistic Burgers Model on a
  (1+1)-Dimensional de Sitter Spacetime

abstract:
  Several generalizations of the relativistic models of Burgers equations have
recently been established and developed on different spacetime geometries. In
this work, we take into account the de Sitter spacetime geometry, introduce our
relativistic model by a technique based on the vanishing pressure Euler
equations of relativistic compressible fluids on a (1+1)-dimensional background
and construct a second order Godunov type finite volume scheme to examine
numerical experiments within an analysis of the cosmological constant.
Numerical results demonstrate the efficiency of the method for solutions
containing shock and rarefaction waves.


title: Investigating the origin of hot gas lines in Herbig Ae/Be Stars

abstract:
  We analyze high-resolution UV spectra of a small sample of Herbig Ae/Be stars
(HAEBES) in order to explore the origin of the $T\sim10^5$ K gas in these
stars. The C IV 1548,1550 \AA\ line luminosities are compared to
non--simultaneous accretion rate estimates for the objects showing C IV
emission. We show that the correlation between $L_{CIV}$ and $\dot{M}$
previously established for classical T Tauri stars (CTTSs) seems to extend into
the HAEBE mass regime, although the large spread in literature $\dot{M}$ and
$A_V$ values makes the actual relationship highly uncertain. With the exception
of DX Cha, we find no evidence for hot, optically thick winds in our HAEBE
sample. All other objects showing clear doublet emission in C IV can be well
described by a two component (i.e., a single component for each doublet member)
or four component (i.e., two components for each doublet member) Gaussian
emission line fit. The morphologies and peak-flux velocities of these lines
suggest they are formed in weak, optically thin stellar winds and not in an
accretion flow, as is the case for the hot lines observed in CTTSs. The lack of
strong outflow signatures and lack of evidence for line formation in accretion
flows is consistent with the conclusion presented in our recent optical and He
I 10830 \AA\ studies that the immediate circumstellar environments of HAEBES,
in general, are not scaled-up analogs of the immediate environments around
CTTSs. The conclusions presented here for hot gas lines around HAEBES should be
verified with a larger sample of objects.


title: Existence of quantum time crystals

abstract:
  The existence of quantum time crystals is investigated and shown to be
possible in pure phases defined by a state invariant under a group of space
translations, as displayed by explicit examples.


title:
Parameters of Innermost Stable Circular Orbits of Spinning Test
  Particles: Numerical and Analytical Calculations

abstract:
  The motion of classical spinning test particles in the equatorial plane of a
Kerr black hole is considered for the case where the particle spin is
perpendicular to the equatorial plane. We review some results of our recent
research of the innermost stable circular orbits (ISCO) [P.I. Jefremov, O.Yu.
Tsupko and G.S. Bisnovatyi-Kogan, Phys.Rev. D 91 124030 (2015)] and present
some new calculations. The ISCO radius, total angular momentum, energy, and
orbital angular frequency are considered. We calculate the ISCO parameters
numerically for different values of the Kerr parameter $a$ and investigate
their dependence on both black hole and test particle spins. Then we describe
in details how to calculate analytically small-spin corrections to the ISCO
parameters for an arbitrary values of $a$. The cases of Schwarzschild, slowly
rotating Kerr and extreme Kerr black hole are considered. The use of the
orbital angular momentum is discussed. We also consider the ISCO binding
energy. It is shown that the efficiency of accretion onto an extreme Kerr black
hole can be larger than the maximum known efficiency (42 %) if the test body
has a spin.


title:
Orbifolds, geometric structures and foliations. Applications to harmonic
  maps

abstract:
  In recent years a lot of attention has been paid to topological spaces which
are a bit more general than smooth manifolds - orbifolds. Orbifolds are
intuitively speaking manifolds with some singularities. The formal definition
is also modelled on that of manifolds, an orbifold is a topological space which
locally is homeomorphic to the orbit space of a finite group acting on $R^n$.
Orbifolds were defined by Satake, as V-manifolds, then studied by W. Thurston,
who introduced the term "orbifold". Due to their importance in physics, and in
particular in the string theory, orbifolds have been drawing more and more
attention. In this paper we propose to show that the classical theory of
geometrical structures, easily translates itself to the context of orbifolds
and is closely related to the theory of foliated geometrical structures, cf.
\cite{Wo0}. Finally, we propose a foliated approach to the study of harmonic
maps between Riemannian orbifolds based on our previous research into
transversely harmonic maps.


title:
Fluids with competing interactions: I. Decoding the structure factor to
  detect and characterize self-limited clustering

abstract:
  We use liquid state theory and computer simulations to gain insights into the
shape of the structure factor for fluids of particles interacting via a
combination of short-range attractions and long-range repulsions. Such systems
can reversibly morph between homogeneous phases and states comprising compact
self-limiting clusters. We first highlight trends with respect to the presence
and location of the intermediate-range order (IRO) pre-peak in the structure
factor, which is commonly associated with clustering, for wide ranges of the
tunable parameters that control interparticle interactions (e.g., Debye
screening length). Next, for approximately 100 different cluster phases at
various conditions (where aggregates range in size from six to sixty monomers),
we quantitatively relate the shape of the structure factor to physical
characteristics including intercluster distance and cluster size. We also test
two previously postulated criteria for identifying the emergence of clustered
phases that are based on IRO peak-height and -width, respectively. We find that
the criterion based on peak-width, which encodes the IRO thermal correlation
length, is more robust across a wide range of conditions and interaction
strengths but nonetheless approximate. Ultimately, we recommend a hybrid
heuristic drawing on both pre-peak height and width for positively identifying
the emergence of clustered states.


title: Robust On-line Matrix Completion on Graphs

abstract:
  We study online robust matrix completion on graphs. At each iteration a
vector with some entries missing is revealed and our goal is to reconstruct it
by identifying the underlying low-dimensional subspace from which the vectors
are drawn. We assume there is an underlying graph structure to the data, that
is, the components of each vector correspond to nodes of a certain (known)
graph, and their values are related accordingly. We give algorithms that
exploit the graph to reconstruct the incomplete data, even in the presence of
outlier noise. The theoretical properties of the algorithms are studied and
numerical experiments using both synthetic and real world datasets verify the
improved performance of the proposed technique compared to other state of the
art algorithms.


title:
On the semi-classical analysis of the groundstate energy of the
  Dirichlet Pauli operator

abstract:
  We discuss the results of a recent paper by Ekholm, Kova\v{r}\'ik and
Portmann in connection with a question of C. Guillarmou about the semiclassical
expansion of the lowest eigenvalue of the Pauli operator with Dirichlet
conditions. We exhibit connections with the properties of the torsion function
in mechanics, the exit time of a Brownian motion and the analysis of the low
eigenvalues of some Witten Laplacian.


title: Quantum-Proof Extractors: Optimal up to Constant Factors

abstract:
  We give the first construction of a family of quantum-proof extractors that
has optimal seed length dependence $O(\log(n/\varepsilon))$ on the input length
$n$ and error $\varepsilon$. Our extractors support any min-entropy
$k=\Omega(\log{n} + \log^{1+\alpha}(1/\varepsilon))$ and extract
$m=(1-\alpha)k$ bits that are $\varepsilon$-close to uniform, for any desired
constant $\alpha > 0$. Previous constructions had a quadratically worse seed
length or were restricted to very large input min-entropy or very few output
bits.
  Our result is based on a generic reduction showing that any strong classical
condenser is automatically quantum-proof, with comparable parameters. The
existence of such a reduction for extractors is a long-standing open question,
here we give an affirmative answer for condensers. Once this reduction is
established, to obtain our quantum-proof extractors one only needs to consider
high entropy sources. We construct quantum-proof extractors with the desired
parameters for such sources by extending a classical approach to extractor
construction, based on the use of block-sources and sampling, to the quantum
setting.
  Our extractors can be used to obtain improved protocols for
device-independent randomness expansion and for privacy amplification.


title: Testing the validity of the ray-tracing code GYOTO

abstract:
  In the next few years, the near-infrared interferometer GRAVITY will be able
to observe the Galactic center. Astrometric data will be obtained with an
anticipated accuracy of 10 $\mu$as. To analyze these future data, we have
developed a code called GYOTO to compute orbits and images. We want to assess
the validity and accuracy of GYOTO in a variety of contexts, in particular for
stellar astrometry in the Galactic center. Furthermore, we want to tackle and
complete a study made on the astrometric displacements that are due to lensing
effects of a star of the central parsec with GYOTO. We first validate GYOTO in
the weak-deflection limit (WDL) by studying primary caustics and primary
critical curves obtained for a Kerr black hole. We compare GYOTO results to
available analytical approximations and estimate GYOTO errors using an
intrinsic estimator. In the strong-deflection limit (SDL), we choose to compare
null geodesics computed by GYOTO and the ray-tracing code named Geokerr.
Finally, we use GYOTO to estimate the apparent displacements of a star for
different angles from Sagittarius A* (Sgr A*). We have demonstrated that GYOTO
is accurate to a very high level, orders of magnitude better than the GRAVITY
requirements. GYOTO is also valid in weak- and strong-deflection regimes and
for very long integrations. At the astrometric precision that GRAVITY is aiming
for, lensing effects must always be taken into account when fitting stellar
orbits in the central parsec of the Galaxy.


title:
On the construction of Tesla transformers. Period of oscillation and
  self-inductance of the coil. (Zur construction von Teslatransformatoren.
  Schwingungsdauer und Selbstinduction von Drahtspulen)

abstract:
  English Translation of Paul Drude's 1902 investigation into the factors
affecting the self-resonance of single-layer solenoid coils. The ratio of the
self-resonant half-wavelength to the conductor length is is found to be
principally dependent on the height-to diameter ratio of the coil and the
dielectric constants of any insulating materials involved in the construction.


title: Cosmological Constant in the Thermodynamic Models of Gravity

abstract:
  Within thermodynamic models of gravity, where the universe is considered as a
finite ensemble of quantum particles, cosmological constant in the Einstein's
equations appears as a constant of integration. Then it can be bounded using
Karolyhazy uncertainty relation applied for horizon distances, as the amount of
information in principle accessible to an external observer.


title:
Degree, mixing, and absolutely continuous spectrum of cocycles with
  values in compact Lie groups

abstract:
  We consider skew products $$T_\phi:X\times G\to X\times
G,~~(x,g)\mapsto(F_1(x),g\;\!\phi(x)),$$ where $X$ is a compact manifold with
probability measure, $G$ a compact Lie group with Lie algebra $\frak g$,
$F_1:X\to X$ the time-one map of a measure-preserving flow, and $\phi\in
C^1(X,G)$ a cocycle. Then, we define the degree of $\phi$ as a suitable
function $P_\phi M_\phi:X\to\frak g$, we show that it transforms in a natural
way under Lie group homomorphisms and under the relation of $C^1$-cohomology,
and we explain how it generalises previous definitions of degree of a cocycle.
For each finite-dimensional irreducible representation $\pi$ of $G$, and $\frak
g_\pi$ the Lie algebra of $\pi(G)$, we define in an analogous way the degree of
$\pi\circ\phi$ as a suitable function
$P_{\pi\circ\phi}M_{\pi\circ\phi}:X\to\frak g_\pi$. If $F_1$ is uniquely
ergodic and the functions $\pi\circ\phi$ diagonal, or if $T_\phi$ is uniquely
ergodic, then the degree of $\phi$ reduces to a constant in $\frak g$ given by
an integral over $X$. As a by-product, we obtain that there is no uniquely
ergodic skew product $T_\phi$ with nonzero degree if $G$ is a connected
semisimple compact Lie group.
  Next, we show that $T_\phi$ is mixing in the orthocomplement of the kernel of
$P_{\pi\circ\phi}M_{\pi\circ\phi}$, and under some additional assumptions we
show that $U_\phi$ has purely absolutely continuous spectrum in that
orthocomplement if $(iP_{\pi\circ\phi}M_{\pi\circ\phi})^2$ is strictly
positive. Summing up these results for each $\pi$, one obtains a global result
for the mixing and the absolutely continuous spectrum of $T_\phi$. As an
application, we present four explicit cases: when $G$ is a torus, $G=SU(2)$,
$G=SO(3,\mathbb R)$, and $G=U(2)$. In each case, the results we obtain are new,
or generalise previous results.
  Our proofs rely on new results on positive commutator methods for unitary
operators.


title:
Spiral spin-liquid and the emergence of a vortex-like state in
  MnSc$_2$S$_4$

abstract:
  Spirals and helices are common motifs of long-range order in magnetic solids,
and they may also be organized into more complex emergent structures such as
magnetic skyrmions and vortices. A new type of spiral state, the spiral
spin-liquid, in which spins fluctuate collectively as spirals, has recently
been predicted to exist. Here, using neutron scattering techniques, we
experimentally prove the existence of a spiral spin-liquid in MnSc$_2$S$_4$ by
directly observing the 'spiral surface' - a continuous surface of spiral
propagation vectors in reciprocal space. We elucidate the multi-step ordering
behavior of the spiral spin-liquid, and discover a vortex-like triple-q phase
on application of a magnetic field. Our results prove the effectiveness of the
$J_1$-$J_2$ Hamiltonian on the diamond lattice as a model for the spiral
spin-liquid state in MnSc$_2$S$_4$, and also demonstrate a new way to realize a
magnetic vortex lattice.


title:
The polynomiality of the Poisson center and semi-center of a Lie algebra
  and Dixmier's fourth problem

abstract:
  Let L be a finite dimensional Lie algebra over an algebraically closed field
k of characteristic zero. We provide necessary and also some sufficient
conditions in order for its Poisson center and semi-center to be polynomial
algebras over k. This occurs for instance if L is quadratic of index 2 with L
not equal to [L,L] and also if L is nilpotent of index at most 2. The converse
holds for filiform Lie algebras of type Ln, Qn, Rn and Wn. We also show how
Dixmier's fourth problem for an algebraic Lie algebra L can be reduced to that
of its canonical truncation. Moreover, Dixmier's statement holds for all Lie
algebras of dimension at most eight. The nonsolvable, indecomposable ones among
them possess a polynomial Poisson center and semi-center.


title:
Rate region boundary of the SISO Z-interference channel with improper
  signaling

abstract:
  This paper provides a complete characterization of the boundary of an
achievable rate region, called the Pareto boundary, of the single-antenna Z
interference channel (Z-IC), when interference is treated as noise and users
transmit complex Gaussian signals that are allowed to be improper. By
considering the augmented complex formulation, we derive a necessary and
sufficient condition for improper signaling to be optimal. This condition is
stated as a threshold on the interference channel coefficient, which is a
function of the interfered user rate and which allows insightful
interpretations into the behavior of the achievable rates in terms of the
circularity coefficient (i.e., degree of impropriety). Furthermore, the optimal
circularity coefficient is provided in closed form. The simplicity of the
obtained characterization permits interesting insights into when and how
improper signaling outperforms proper signaling in the single-antenna Z-IC. We
also provide an in-depth discussion on the optimal strategies and the
properties of the Pareto boundary.


title:
Embedded star clusters as sources of high-energy cosmic rays: Modelling
  and constraints

abstract:
  Massive stars are mainly found in stellar associations. These massive star
clusters occur in the heart of giant molecular clouds. The strong stellar wind
activity in these objects generates large bubbles and induces collective
effects that could accelerate particles up to high energy and produce gamma
rays. The best way to input an acceleration origin to the stellar wind
interaction in massive stellar cluster is to observe young massive star
clusters in which no supernova explosion has occurred yet.
  This work aims to constrain the part of stellar wind mechanical energy that
is converted into energetic particles using the sensitivity of the ongoing
Fermi/LAT instrument. This work further provides detailed predictions of
expected gamma-ray fluxes in the view of the on-set of the next generation of
imaging atmospheric Cherenkov telescopes.
  A one-zone model where energetic particles are accelerated by repeated
interactions with strong supersonic shocks occurring in massive star clusters
was developed. The particle escape from the star cluster and subsequent
interaction with the surrounding dense material and magnetic fields of the HII
region was computed. We applied this model to a selection of eight embedded
star clusters constricted by existing observations. We evaluated the gamma-ray
signal from each object, combining both leptonic and hadronic contributions. We
searched for these emissions in the Fermi/LAT observations in the energy range
from 3 to 300 GeV and compared them to the sensitivity of the Cherenkov
Telescope Array.
  No significant gamma-ray emission from these star clusters has been found.
Less than 10% of stellar wind luminosities are supplied to the relativistic
particles. Some clusters even show acceleration efficiency of less than 1%. The
CTA would be able to detect gamma-ray emission from several clusters in the
case of an acceleration efficiency of close to 1%.


title: Computing complex and real tropical curves using monodromy

abstract:
  Tropical varieties capture combinatorial information about how coordinates of
points in a classical variety approach zero or infinity. We present algorithms
for computing the rays of a complex and real tropical curve defined by
polynomials with constant coefficients. These algorithms rely on homotopy
continuation, monodromy loops, and Cauchy integrals. Several examples are
presented which are computed using an implementation that builds on the
numerical algebraic geometry software Bertini.


title: Analytical solutions in $R+qR^{n}$ cosmology from singularity analysis

abstract:
  The integrability of higher-order theories of gravity is of importance in the
determining the properties of these models and so their viability as models of
reality. An important tool in the establishment of integrability is the
singularity analysis. We apply this analysis to the case of fourth-order theory
of gravity $f(R) = R + qR^{n}$ to establish those values of the free parameters
$q$ and $n$ for which integrability in this sense exists. As a prelininary we
examine the well-known case of $n = 4/3$.


title: Defect zero characters predicted by local structure

abstract:
  Let $G$ be a finite group and let $p$ be a prime. Assume that there exists a
prime $q$ dividing $|G|$ which does not divide the order of any $p$-local
subgroup of $G$. If $G$ is $p$-solvable or $q$ divides $p-1$, then $G$ has a
$p$-block of defect zero. The case $q=2$ is a well-known result by Brauer and
Fowler.


title: Vertex Degrees in Planar Maps

abstract:
  We prove a general multi-dimensional central limit theorem for the expected
number of vertices of a given degree in the family of planar maps whose vertex
degrees are restricted to an arbitrary (finite or infinite) set of positive
integers D. Our results rely on a classical bijection with mobiles (objects
exhibiting a tree structure), combined with refined analytic tools to deal with
the systems of equations on infinite variables that arise. We also discuss some
possible extension to maps of higher genus.


title:
Functional lower bounds for arithmetic circuits and connections to
  boolean circuit complexity

abstract:
  We say that a circuit $C$ over a field $F$ functionally computes an
$n$-variate polynomial $P$ if for every $x \in \{0,1\}^n$ we have that $C(x) =
P(x)$. This is in contrast to syntactically computing $P$, when $C \equiv P$ as
formal polynomials. In this paper, we study the question of proving lower
bounds for homogeneous depth-$3$ and depth-$4$ arithmetic circuits for
functional computation. We prove the following results :
  1. Exponential lower bounds homogeneous depth-$3$ arithmetic circuits for a
polynomial in $VNP$.
  2. Exponential lower bounds for homogeneous depth-$4$ arithmetic circuits
with bounded individual degree for a polynomial in $VNP$.
  Our main motivation for this line of research comes from our observation that
strong enough functional lower bounds for even very special depth-$4$
arithmetic circuits for the Permanent imply a separation between ${\#}P$ and
$ACC$. Thus, improving the second result to get rid of the bounded individual
degree condition could lead to substantial progress in boolean circuit
complexity. Besides, it is known from a recent result of Kumar and Saptharishi
[KS15] that over constant sized finite fields, strong enough average case
functional lower bounds for homogeneous depth-$4$ circuits imply
superpolynomial lower bounds for homogeneous depth-$5$ circuits.
  Our proofs are based on a family of new complexity measures called shifted
evaluation dimension, and might be of independent interest.


title:
A Statistical Approach to Describe Highly Excited Heavy and Superheavy
  Nuclei

abstract:
  A statistical approach based on the Weisskopf evaporation theory has been
developed to describe the de-excitation process of highly excited heavy and
superheavy nuclei, in particular for the proton-rich nuclei. The excited
nucleus is cooled by evaporating $\gamma$-ray, light particles (neutrons,
protons, $\alpha$ etc) in competition with the binary fission, in which the
structure effects (shell correction, fission barrier, particle separation
energy) contribute to the processes. The formation of residual nuclei is
evaluated via sequential emission of possible particles above the separation
energies. The available data of fusion-evaporation excitation functions in the
$^{28}$Si+$^{198}$Pt reaction can be reproduced nicely well within the
approach.


title: Sobolev Algebra Counterexamples

abstract:
  In the Euclidean setting the Sobolev spaces $W^{\alpha,p}\cap L^\infty$ are
algebras for the pointwise product when $\alpha>0$ and $p\in(1,\infty)$. This
property has recently been extended to a variety of geometric settings. We
produce a class of fractal examples where it fails for a wide range of the
indices $\alpha,p$.


title:
Iterative Precision Measurement of Branching Ratios Applied to 5P states
  in 88Sr+

abstract:
  We report on a method for measuring the branching ratios of dipole
transitions of trapped atomic ions by performing nested sequences of population
inversions. This scheme is broadly applicable and does not use ultrafast pulsed
or narrow linewidth lasers. It is simple to perform and insensitive to
experimental variables such as laser and magnetic field noise as well as ion
heating. To demonstrate its effectiveness, we make the most accurate
measurements thus far of the branching ratios of both 5P1/2 and 5P3/2 states in
88Sr+ with sub-1% uncertainties. We measure 17.175(27) for the branching ratio
of 5P1/2-5S1/2, 15.845(71) for 5P3/2-5S1/2, and 0.05609(21) for 5P3/2-4D5/2,
ten- fold and thirty-fold improvements in precision for 5P1/2 and 5P3/2
branching ratios respectively over the best previous experimental values.


title:
On the mass of atoms in molecules: Beyond the Born-Oppenheimer
  approximation

abstract:
  Describing the dynamics of nuclei in molecules requires a potential energy
surface, which is traditionally provided by the Born-Oppenheimer or adiabatic
approximation. However, we also need to assign masses to the nuclei. There, the
Born-Oppenheimer picture does not account for the inertia of the electrons and
only bare nuclear masses are considered. Nowadays, experimental accuracy
challenges the theoretical predictions of rotational and vibrational spectra
and requires to include the participation of electrons in the internal motion
of the molecule. More than 80 years after the original work of Born and
Oppenheimer, this issue still is not solved in general. Here, we present a
theoretical and numerical framework to address this problem in a general and
rigorous way. Starting from the exact factorization of the electron-nuclear
wave function, we include electronic effects beyond the Born-Oppenheimer regime
in a perturbative way via position-dependent corrections to the bare nuclear
masses. This maintains an adiabatic-like point of view: the nuclear degrees of
freedom feel the presence of the electrons via a single potential energy
surface, whereas the inertia of electrons is accounted for and the total mass
of the system is recovered. This constitutes a general framework for describing
the mass acquired by slow degrees of freedom due to the inertia of light,
bounded particles. We illustrate it with a model of proton transfer, where the
light particle is the proton, and with corrections to the vibrational spectra
of molecules. Inclusion of the light particle inertia allows to gain orders of
magnitude in accuracy.


title: Multiple Correspondence Analysis & the Multilogit Bilinear Model

abstract:
  Multiple Correspondence Analysis (MCA) is a dimension reduction method which
plays a large role in the analysis of tables with categorical nominal variables
such as survey data. Though it is usually motivated and derived using geometric
considerations, in fact we prove that it amounts to a single proximal Newtown
step of a natural bilinear exponential family model for categorical data the
multinomial logit bilinear model. We compare and contrast the behavior of MCA
with that of the model on simulations and discuss new insights on the
properties of both exploratory multivariate methods and their cognate models.
One main conclusion is that we could recommend to approximate the multilogit
model parameters using MCA. Indeed, estimating the parameters of the model is
not a trivial task whereas MCA has the great advantage of being easily solved
by singular value decomposition and scalable to large data.


title:
Spin injection into multilayer graphene from highly spin-polarized
  Co2FeSi Heusler alloy

abstract:
  We demonstrate electrical spin injection into multilayer graphene (MLG) in a
lateral spin valve device from a highly spin-polarized Co2FeSi (CFS) Huesler
electrode. Exfoliated MLG was transferred onto pre-patterned epitaxial CFS
wires grown on an Si(111) substrate by a polymer-based transfer method. This
method enabled us to fabricate multiple single-crystal CFS electrodes in
contact with MLG. Electrical spin injection from CFS to MLG was detected
through non-local magnetoresistance (MR) measurement. A non-local spin signal
of 430 ohm was observed; this is the largest value among all reported non-local
MR values in graphene-based devices.


title: Possible Evolution of Supermassive Black Holes from FRI quasars

abstract:
  We explore the question of the rapid buildup of black hole mass in the early
universe employing a growing black hole mass-based determination of both jet
and disk powers predicted in recent theoretical work on black hole accretion
and jet formation. Despite simplified, even artificial assumptions about
accretion and mergers, we identify an interesting low probability channel for
the growth of one billion solar mass black holes within hundreds of millions of
years of the Big Bang without appealing to super Eddington accretion. This
result is made more compelling by the recognition of a connection between this
channel and an end product involving active galaxies with FRI radio morphology
but weaker jet powers in mildly sub-Eddington accretion regimes. While FRI
quasars have already been shown to occupy a small region of the available
parameter space for black hole feedback in the paradigm, we further suggest
that the observational dearth of FRI quasars is also related to their
connection to the most massive black hole growth due to both these FRIs high
redshifts and relative weakness. Our results also allow us to construct the AGN
luminosity function at high redshift, that agree with recent studies. In short,
we produce a connection between the unexplained paucity of a given family of
active galactic nuclei and the rapid growth of supermassive black holes, two
heretofore seemingly unrelated aspects of the physics of active galactic
nuclei.


title: Multipulse storage and manipulation via solitonic solutions

abstract:
  Solutions to the Maxwell-Bloch equations for a $\Lambda$ system are computed
using the single-soliton Darboux transformation and the nonlinear superposition
principle. These allow complete control of information deposited by a signal
pulse (with the help of an auxiliary control pulse) in the coherence of the
medium's ground states by injecting sub-sequential pulses. Additionally, we
study the encoding of two signal pulses and their manipulation by a control
pulse and show that multipulse storage and control are possible as long as the
imprints made by encoding the signal pulses are sufficiently separated.


title:
Fermi LAT Gamma-ray Detections of Classical Novae V1369 Centauri 2013
  and V5668 Sagittarii 2015

abstract:
  We report the Fermi Large Area Telescope (LAT) detections of high-energy
(>100 MeV) gamma-ray emission from two recent optically bright classical novae,
V1369 Centauri 2013 and V5668 Sagittarii 2015. At early times, Fermi
target-of-opportunity observations prompted by their optical discoveries
provided enhanced LAT exposure that enabled the detections of gamma-ray onsets
beginning ~2 days after their first optical peaks. Significant gamma-ray
emission was found extending to 39-55 days after their initial LAT detections,
with systematically fainter and longer duration emission compared to previous
gamma-ray detected classical novae. These novae were distinguished by multiple
bright optical peaks that encompassed the timespans of the observed gamma rays.
The gamma-ray light curves and spectra of the two novae are presented along
with representative hadronic and leptonic models, and comparisons to other
novae detected by the LAT are discussed.