title:
Principled Random Finite Set Approximations of Labeled Multi-Object
  Densities

abstract:
  As a fundamental piece of multi-object Bayesian inference, multi-object
density has the ability to describe the uncertainty of the number and values of
objects, as well as the statistical correlation between objects, thus perfectly
matches the behavior of multi-object system. However, it also makes the set
integral suffer from the curse of dimensionality and the inherently
combinatorial nature of the problem. In this paper, we study the approximations
for the universal labeled multi-object (LMO) density and derive several
principled approximations including labeled multi-Bernoulli, labeled Poisson
and labeled independent identically clustering process based approximations.
Also, a detailed analysis on the characteristics (e.g., approximation error and
computational complexity) of the proposed approximations is provided. Then some
practical suggestions are made for the applications of these approximations
based on the preceding analysis and discussion. Finally, an numerical example
is given to support our study.


title:
Nonlinear generalized sections and vector bundle homomorphisms in
  Colombeau spaces of generalized functions

abstract:
  We define and characterize spaces of manifold-valued generalized functions
and generalized vector bundle homomorphisms in the setting of the full
diffeomorphism-invariant vector-valued Colombeau algebra. Furthermore, we
establish point value characterizations for these spaces.


title:
Versatile electric fields for the manipulation of ultracold NaK
  molecules

abstract:
  In this paper, we present an electrode geometry for the manipulation of
ultracold rovibrational ground state NaK molecules. The electrode system allows
to induce a dipole moment in trapped diatomic NaK molecules with a magnitude up
to $68 \%$ of their internal dipole moment along any direction in a given
two-dimensional plane. The strength, the sign and the direction of the induced
dipole moment is therefore fully tunable. Furthermore, the possibility to
create strong electric field gradients provides the opportunity to address
molecules in single layers of an optical lattice. The maximal relative
variation of the electric field over the trapping volume is below $10^{-6}$. At
the desired electric field value of 10 kV/cm this corresponds to a deviation of
0.01 V/cm. The electrode structure is made of transparent indium tin oxide and
combines large optical access for sophisticated optical dipole traps and
optical lattice configurations with the possibility to create versatile
electric field configurations.


title: Controllable circular Airy beams via dynamic linear potential

abstract:
  We investigate controllable spatial modulation of circular autofocusing Airy
beams, under action of different dynamic linear potentials, both theoretically
and numerically. We introduce a novel treatment method in which the circular
Airy beam is represented as a superposition of narrow azimuthally-modulated
one-dimensional Airy beams that can be analytically treated. The dynamic linear
potentials are appropriately designed, so that the autofocusing effect can
either be weakened or even eliminated when the linear potential exerts a
"pulling" effect on the beam, or if the linear potential exerts a "pushing"
effect, the autofocusing effect can be greatly strengthened. Numerical
simulations agree with the theoretical results very well.


title:
Ab initio Studies on Electronic and Magnetic Properties of X$_{2}$PtGa
  (X = Cr, Mn, Fe, Co) Heusler Alloys

abstract:
  Using first-principles calculations based on density functional theory, we
probe the electronic and magnetic properties of X$_{2}$PtGa (X being Cr, Mn,
Fe, Co) Heusler alloys. Our calculations predict that all these systems possess
inverse Heusler alloy structure in their respective ground states. Application
of tetragonal distortion leads to lowering of energy with respect to the cubic
phase for all the materials. The equilibrium volumes of both the phases are
nearly the same. These results of our calculations indicate that all these
materials are prone to undergo martensite transition, as has been recently
shown theoretically for Mn$_{2}$PtGa in the literature. Ground state with a
tetragonal symmetry of these materials is supported by the observation of soft
tetragonal shear constants in their cubic phase. By comparing the energies of
various types of magnetic configurations of these alloys we predict that
Cr$_{2}$PtGa and Mn$_{2}$PtGa possess ferrimagnetic configuration whereas
Fe$_{2}$PtGa and Co$_{2}$PtGa possess ferromagneic configuration in their
respective ground states.


title: Solovay functions and their applications in algorithmic randomness

abstract:
  Classical versions of Kolmogorov complexity are incomputable. Nevertheless,
in 1975 Solovay showed that there are computable functions $f > K+O(1)$ such
that for infinitely many strings $\sigma$, $f(\sigma)=K(\sigma)+O(1)$, where
$K$ denotes prefix-free Kolmogorov complexity (while $C$ denotes plain
Kolmogorov complexity). Such an $f$ is now called a Solovay function. We prove
that many classical results about $K$ can be obtained by replacing $K$ by a
Solovay function. For example, the three following properties of a function $g$
all hold for the function $K$.
  (i) The sum of the terms $\sum_n 2^{-g(n)}$ is a Martin-L\"of random real.
  (ii) A sequence A is Martin-L\"of random if and only if $C(A \upharpoonright
n) > n -g(n)-O(1)$.
  (iii) A sequence A is K-trivial if and only if $K(A \upharpoonright n) < g(n)
+ O(1)$.
  We show that when fixing any of these three properties, then among all
computable functions exactly the Solovay functions possess this property.
Furthermore, this characterization extends accordingly to the larger class of
right-c.e. functions.


title: Vapour-liquid phase diagram for an ionic fluid in a random porous medium

abstract:
  We study the vapour-liquid phase behaviour of an ionic fluid confined in a
random porous matrix formed by uncharged hard sphere particles. The ionic fluid
is modelled as an equimolar binary mixture of oppositely charged equisized hard
spheres, the so-called restricted primitive model (RPM). Considering the
matrix-fluid system as a partly-quenched model, we develop a theoretical
approach which combines the method of collective variables with the extension
of the scaled-particle theory (SPT) for a hard-sphere fluid confined in a
disordered hard-sphere matrix. The approach allows us to formulate the
perturbation theory using the SPT for the description of the thermodynamics of
the reference system. The phase diagrams of the RPM in matrices of different
porosities and for different size ratios of matrix and fluid particles are
calculated in the random-phase approximation and also when the effects of
higher-order correlations between ions are taken into account. Both
approximations correctly reproduce the basic effects of porous media on the
vapour-liquid phase diagram, i.e., with a decrease of porosity the critical
point shifts toward lower fluid densities and lower temperatures and the
coexistence region is getting narrower. For the fixed matrix porosity, both the
critical temperature and the critical density increase with an increase of size
of matrix particles and tend to the critical values of the bulk RPM.


title: Chandra ACIS Survey of X-ray Point Sources: The Source Catalog

abstract:
  The $Chandra$ archival data is a valuable resource for various studies on
different topics of X-ray astronomy. In this paper, we utilize this wealth and
present a uniformly processed data set, which can be used to address a wide
range of scientific questions. The data analysis procedures are applied to
10,029 ACIS observations, which produces 363,530 source detections, belonging
to 217,828 distinct X-ray sources. This number is twice the size of the
$Chandra$ Source Catalog (Version 1.1). The catalogs in this paper provide
abundant estimates of the detected X-ray source properties, including source
positions, counts, colors, fluxes, luminosities, variability statistics, etc.
Cross-correlation of these objects with galaxies shows 17,828 sources are
located within the $D_{25}$ isophotes of 1110 galaxies, and 7504 sources are
located between the $D_{25}$ and 2$D_{25}$ isophotes of 910 galaxies.
Contamination analysis with the log$N$--log$S$ relation indicates that 51.3\%
of objects within 2$D_{25}$ isophotes are truly relevant to galaxies, and the
"net" source fraction increases to 58.9\%, 67.3\%, and 69.1\% for sources with
luminosities above $10^{37}$, $10^{38}$, and $10^{39}$ erg s$^{-1}$. Among the
possible scientific uses of this catalog, we discuss the possibility to study
intra-observation variability, inter-observation variability, and supersoft
sources.


title: Timing calibration and spectral cleaning of LOFAR time series data

abstract:
  We describe a method for spectral cleaning and timing calibration of short
voltage time series data from individual radio interferometer receivers. It
makes use of the phase differences in Fast Fourier Transform (FFT) spectra
across antenna pairs. For strong, localized terrestrial sources these are
stable over time, while being approximately uniform-random for a sum over many
sources or for noise. Using only milliseconds-long datasets, the method finds
the strongest interfering transmitters, a first-order solution for relative
timing calibrations, and faulty data channels. No knowledge of gain response or
quiescent noise levels of the receivers is required. With relatively small data
volumes, this approach is suitable for use in an online system monitoring setup
for interferometric arrays.
  We have applied the method to our cosmic-ray data collection, a collection of
measurements of short pulses from extensive air showers, recorded by the LOFAR
radio telescope. Per air shower, we have collected 2 ms of raw time series data
for each receiver. The spectral cleaning has a calculated optimal sensitivity
corresponding to a power signal-to-noise ratio of 0.08 (or -11 dB) in a
spectral window of 25 kHz, for 2 ms of data in 48 antennas. This is well
sufficient for our application. Timing calibration across individual antenna
pairs has been performed at 0.4 ns precision; for calibration of signal clocks
across stations of 48 antennas the precision is 0.1 ns. Monitoring differences
in timing calibration per antenna pair over the course of the period 2011 to
2015 shows a precision of 0.08 ns, which is useful for monitoring and
correcting drifts in signal path synchronizations.
  A cross-check method for timing calibration is presented, using a pulse
transmitter carried by a drone flying over the array. Timing precision is
similar, 0.3 ns.


title:
Multi-Sensor Control for Multi-Target Tracking Using Cauchy-Schwarz
  Divergence

abstract:
  The paper addresses the problem of multi-sensor control for multi-target
tracking via labelled random finite sets (RFS) in the sensor network systems.
Based on an information theoretic divergence measure, namely Cauchy-Schwarz
(CS) divergence which admits a closed form solution for GLMB densities, we
propose two novel multi-sensor control approaches in the framework of
generalized Covariance Intersection (GCI). The first joint decision making
(JDM) method is optimal and can achieve overall good performance, while the
second independent decision making (IDM) method is suboptimal as a fast
realization with smaller amount of computations. Simulation in challenging
situation is presented to verify the effectiveness of the two proposed
approaches.


title:
Strength and Stability Analysis of a Single Walled Black Phosphorus Tube
  under Axial Compression

abstract:
  Few-layered black phosphorus materials recently attract much attention due to
its special electronic properties. As a Consequence, the nano-tube from a
single-layer black phosphorus has been theoretically built. The corresponding
electronic properties of such black phosphorus nano-tube were also evaluated
numerically.


title: A generalized GPU-based connected component labeling algorithm

abstract:
  We propose a generalized GPU-based connected component labeling (CCL)
algorithm that can be applied to both various lattices and to non-lattice
environments in a uniform fashion. We extend our recent GPU-based CCL algorithm
without the use of conventional iteration to the generalized method. As an
application of this algorithm, we deal with the bond percolation problem. We
investigate bond percolation on the honeycomb and triangle lattices to confirm
the correctness of this algorithm. Moreover, we deal with bond percolation on
the Bethe lattice as a substitute for a network structure, and demonstrate the
performance of this algorithm on those lattices.


title:
Fast, Exact and Multi-Scale Inference for Semantic Image Segmentation
  with Deep Gaussian CRFs

abstract:
  In this work we propose a structured prediction technique that combines the
virtues of Gaussian Conditional Random Fields (G-CRF) with Deep Learning: (a)
our structured prediction task has a unique global optimum that is obtained
exactly from the solution of a linear system (b) the gradients of our model
parameters are analytically computed using closed form expressions, in contrast
to the memory-demanding contemporary deep structured prediction approaches that
rely on back-propagation-through-time, (c) our pairwise terms do not have to be
simple hand-crafted expressions, as in the line of works building on the
DenseCRF, but can rather be `discovered' from data through deep architectures,
and (d) out system can trained in an end-to-end manner. Building on standard
tools from numerical analysis we develop very efficient algorithms for
inference and learning, as well as a customized technique adapted to the
semantic segmentation task. This efficiency allows us to explore more
sophisticated architectures for structured prediction in deep learning: we
introduce multi-resolution architectures to couple information across scales in
a joint optimization framework, yielding systematic improvements. We
demonstrate the utility of our approach on the challenging VOC PASCAL 2012
image segmentation benchmark, showing substantial improvements over strong
baselines. We make all of our code and experiments available at
{https://github.com/siddharthachandra/gcrf}


title:
Potholes Ahead: Impact of Transient Link Blockage on Beam Steering in
  Practical mm-Wave Systems

abstract:
  The practical realization of beam steering mechanisms in millimeter wave
communications has a large impact on performance. The key challenge is to find
a pragmatic trade-off between throughput performance and the overhead of
periodic beam sweeping required to improve link quality in case of transient
link blockage. This is particularly critical in commercial off-the-shelf
devices, which require simple yet efficient solutions. First, we analyze the
operation of such a commercial device to understand the impact of link blockage
in practice. To this end, we measure TCP throughput for different traffic loads
while blocking the link at regular intervals. Second, we derive a Markov model
based on our practical insights to compute throughput for the case of transient
blockage. We use this model to evaluate the trade-off between throughput and
periodic beam sweeping. Finally, we validate our results using throughput
traces collected using the aforementioned commercial device. Both our model and
our practical measurements show that transient blockage causes significant
signal fluctuation due to suboptimal beam realignment. In particular,
fluctuations increase with traffic load, limiting the achievable throughput. We
show that choosing lower traffic loads allows us to reduce fluctuations by 41%
while achieving the same net throughput than with higher traffic loads.


title: Lyapunov spectrum of Markov and Euclid trees

abstract:
  We study the Lyapunov exponents $\Lambda(x)$ for Markov dynamics as a
function of path determined by $x\in \mathbb RP^1$ on a binary planar tree,
describing the Markov triples and their "tropical" version - Euclid triples. We
show that the corresponding Lyapunov spectrum is $[0, \ln \varphi]$, where
$\varphi$ is the golden ratio, and prove that on the Markov-Hurwitz set
$\mathbb{X}$ of the most irrational numbers the corresponding function
$\Lambda_\mathbb{X}$ is monotonically increasing and in the Farey
parametrization is convex.


title:
On the second fundamental theorem of invariant theory for the
  orthosymplectic supergroup

abstract:
  The first fundamental theorem of invariant theory for the orthosymplectic
supergroup ${\rm OSp}(V)$ (where $V$ has superdimension $(m|2n)$) in the
endomorphism algebra setting states that there is a surjective algebra
homomorphism $F_r^r: B_r(m-2n)\rightarrow {\rm{End}}_{{\rm OSp}(V)}(V^{\otimes
r})$ from the Brauer algebra of degree $r$ to the endomorphism algebra of
$V^{\otimes r}$ over ${\rm OSp}(V)$. The second fundamental theorem in this
setting seeks to describe ${\rm Ker} F_r^r$ as a $2$-sided ideal of
$B_r(m-2n)$. We show that ${\rm Ker} F_r^r\neq 0$ if and only if $r\geq
r_c:=(m+1)(n+1)$, and present a basis and a dimension formulae for ${\rm Ker}
F_r^r$. As a 2-sided ideal, ${\rm Ker} F_r^r$ for any $r\ge r_c$ is generated
by ${\rm Ker} F_{r_c}^{r_c}$, for which a set of generators is explicitly
constructed in terms of Brauer diagrams. As applications of these results, we
obtain the necessary and sufficient conditions for the endomorphism algebra
$\rm{End}_{{\mathfrak {osp}}(V)}(V^{\otimes r})$ over the orthosymplectic Lie
superalgebra ${\mathfrak {osp}}(V)$ to be isomorphic to $B_r(m-2n)$, and give
new proofs for the main theorems in recent papers of G. Lehrer and R. Zhang on
the second fundamental theorem of invariant theory for the orthogonal and
symplectic groups.


title: Generalizing random real forcing for inaccessible cardinals

abstract:
  The two parallel concepts of "small" sets of the real line are meagre sets
and null sets. Those are equivalent to Cohen forcing and Random real forcing
for aleph_0^aleph_0; in spite of this similarity, the Cohen forcing and Random
Real Forcing have very different shapes. One of these differences is in the
fact that the Cohen forcing has an easy natural generalization for lambda 2
while lambda greater than aleph 0, corresponding to an extension for the meagre
sets, while the Random real forcing didn't seem to have a natural
generalization, as Lebesgue measure doesn't have a generalization for space 2
lambda while lambda greater than aleph 0. In work [1], Shelah found a forcing
resembling the properties of Random Real Forcing for 2 lambda while lambda is a
weakly compact cardinal. Here we describe, with additional assumptions, such a
forcing for 2 lambda while lambda is an Inaccessible Cardinal; this forcing is
less than lambda-complete and satisfies the lambda^+-c.c hence preserves
cardinals and cofinalities, however unlike Cohen forcing, does not add an
undominated real.


title:
Involving high school students in computational physics university
  research: Theory calculations of toluene adsorbed on graphene

abstract:
  To increase public awareness of theoretical materials physics, a small group
of high school students is invited to participate actively in a current
research projects at Chalmers University of Technology. The Chalmers research
group explores methods for filtrating hazardous and otherwise unwanted
molecules from drinking water, for example by adsorption in active carbon
filters. In this project, the students use graphene as an idealized model for
active carbon, and estimate the energy of adsorption of the methylbenzene
toluene on graphene with the help of the atomic-scale calculational method
density functional theory. In this process the students develop an insight into
applied quantum physics, a topic usually not taught at this educational level,
and gain some experience with a couple of state-of-the-art calculational tools
in materials research.


title:
A GMRT Study of Seyfert Galaxies NGC4235 & NGC4594: Evidence of Episodic
  Activity ?

abstract:
  Low frequency observations at 325 and 610 MHz have been carried out for two
"radio-loud" Seyfert galaxies, NGC4235 and NGC4594 (Sombrero galaxy), using the
Giant Meterwave Radio Telescope (GMRT). The 610 MHz total intensity and 325-610
MHz spectral index images of NGC4235 tentatively suggest the presence of a
"relic" radio lobe, most likely from a previous episode of AGN activity. This
makes NGC4235 only the second known Seyfert galaxy after Mrk6 to show
signatures of episodic activity. Spitzer and Herschel infrared spectral energy
distribution (SED) modelling using the clumpyDREAM code predicts star formation
rates (SFR) that are an order of magnitude lower than those required to power
the radio lobes in these Seyferts (~0.13-0.23 M_sun/yr compared to the required
SFR of ~2.0-2.7 M_sun/yr in NGC4594 and NGC4235, respectively). This finding
along with the detection of parsec and sub-kpc radio jets in both Seyfert
galaxies, that are roughly along the same position angles as the radio lobes,
strongly support the suggestion that Seyfert lobes are AGN-powered. SED
modelling supports the "true" type 2 classification of NGC4594: this galaxy
lacks significant dust obscuration as well as a prominent broad-line region.
Between the two Seyfert galaxies, there is an inverse relation between their
radio-loudness and Eddington ratio and a direct relation between their
Eddington-scaled jet power and bolometric power.


title: Thermal activation in permanent magnets

abstract:
  The coercive field of permanent magnets decays with temperature. At non-zero
temperature the system can overcome a finite energy barrier through thermal
fluctuations. Using finite element micromagnetic simulations, we quantify this
effect, which reduces coercivity in addition to the decrease of the coercive
field associated with the temperature dependence of the anisotropy field, and
validate the method through comparison with existing experimental data.


title:
Estimation of quadrature errors in layer potential evaluation using
  quadrature by expansion

abstract:
  In boundary integral methods it is often necessary to evaluate layer
potentials on or close to the boundary, where the underlying integral is
difficult to evaluate numerically. Quadrature by expansion (QBX) is a new
method for dealing with such integrals, and it is based on forming a local
expansion of the layer potential close to the boundary. In doing so, one
introduces a new quadrature error due to nearly singular integration in the
evaluation of expansion coefficients. Using a method based on contour
integration and calculus of residues, the quadrature error of nearly singular
integrals can be accurately estimated. This makes it possible to derive
accurate estimates for the quadrature errors related to QBX, when applied to
layer potentials in two and three dimensions. As examples we derive estimates
for the Laplace and Helmholtz single layer potentials. These results can be
used for parameter selection in practical applications.


title: Sparse Activity and Sparse Connectivity in Supervised Learning

abstract:
  Sparseness is a useful regularizer for learning in a wide range of
applications, in particular in neural networks. This paper proposes a model
targeted at classification tasks, where sparse activity and sparse connectivity
are used to enhance classification capabilities. The tool for achieving this is
a sparseness-enforcing projection operator which finds the closest vector with
a pre-defined sparseness for any given vector. In the theoretical part of this
paper, a comprehensive theory for such a projection is developed. In
conclusion, it is shown that the projection is differentiable almost everywhere
and can thus be implemented as a smooth neuronal transfer function. The entire
model can hence be tuned end-to-end using gradient-based methods. Experiments
on the MNIST database of handwritten digits show that classification
performance can be boosted by sparse activity or sparse connectivity. With a
combination of both, performance can be significantly better compared to
classical non-sparse approaches.


title: Exact statistics of record increments of random walks and L\'evy flights

abstract:
  We study the statistics of increments in record values in a time series
$\{x_0=0,x_1, x_2, \ldots, x_n\}$ generated by the positions of a random walk
(discrete time, continuous space) of duration $n$ steps. For arbitrary jump
length distribution, including L\'evy flights, we show that the distribution of
the record increment becomes stationary, i.e., independent of $n$ for large
$n$, and compute it explicitly for a wide class of jump distributions. In
addition, we compute exactly the probability $Q(n)$ that the record increments
decrease monotonically up to step $n$. Remarkably, $Q(n)$ is universal (i..e.,
independent of the jump distribution) for each $n$, decaying as $Q(n) \sim
{\cal A}/\sqrt{n}$ for large $n$, with a universal amplitude ${\cal A} =
e/\sqrt{\pi} = 1.53362\ldots$.

categories: cond-mat.stat-mech cond-mat.dis-nn math.PR physics.data-an


title:
Permutation-symmetric three-body O(6) hyperspherical harmonics in three
  spatial dimensions

abstract:
  We have constructed the three-body permutation symmetric O(6) hyperspherical
harmonics which can be used to solve the non-relativistic three-body Schr{\"
o}dinger equation in three spatial dimensions. We label the states with
eigenvalues of the $U(1) \otimes SO(3)_{rot} \subset U(3) \subset O(6)$ chain
of algebras and we present the corresponding $K \leq 4$ harmonics. Concrete
transformation properties of the harmonics are discussed in some detail.


title:
The Signed Positive Semidefinite Matrix Completion Problem for Odd-$K_4$
  Minor Free Signed Graphs

abstract:
  We give a signed generalization of Laurent's theorem that characterizes
feasible positive semidefinite matrix completion problems in terms of metric
polytopes. Based on this result, we give a characterization of the maximum rank
completions of the signed positive semidefinite matrix completion problem for
odd-$K_4$ minor free signed graphs. The analysis can also be used to bound the
minimum rank over the completions and to characterize uniquely solvable
completion problems for odd-$K_4$ minor free signed graphs. As a corollary we
derive a characterization of the universal rigidity of odd-$K_4$ minor free
spherical tensegrities, and also a characterization of signed graphs whose
signed Colin de Verdi\`ere parameter $\nu$ is bounded by two, recently shown by
Arav et al.


title:
Proceedings of the 13th International Workshop on Formal Engineering
  Approaches to Software Components and Architectures

abstract:
  The aim of the FESCA workshop is to bring together junior researchers from
formal methods, software engineering, and industry interested in the
development and application of formal modelling approaches as well as
associated analysis and reasoning techniques with practical benefits for
software engineering.
  In recent years, the growing importance of functional correctness and the
increased relevance of system quality properties (e.g. performance,
reliability, security) have stimulated the emergence of analytical and
modelling techniques for the design and development of software systems. With
the increasing complexity and utilization of today's software systems, FESCA
aims at addressing two research questions: (1) what role is played by the
software design phase in the systematic addressing of the analytical and
modelling challenges, and (2) how can formal and semi-formal techniques be
effectively applied to make the issues easier to address automatically, with
lower human intervention. We encourage submissions on (semi-)formal techniques
and their application that aid analysis, design and implementation of software
applications, especially those employed in interconnected, communicating
devices, devices interacting with the physical world, and cyber-physical
systems.


title:
The statistical uncertainties on X-ray flux and spectral parameters from
  Chandra ACIS-I observations of faint sources: Application to the Cygnus OB2
  Association

abstract:
  We investigate the uncertainties of fitted X-ray model parameters and fluxes
for relatively faint Chandra ACIS-I source spectra. Monte-Carlo (MC)
simulations are employed to construct a large set of 150,000 fake X-ray spectra
in the low photon count statistics regime (from 20 to 350 net counts) using the
XSPEC spectral model fitting package. The simulations employed both absorbed
thermal (APEC) and non-thermal (power-law) models, in concert with the Chandra
ACIS-I instrument response and interstellar absorption. Simulated X-ray spectra
were fit assuming a wide set of different input parameters and C-statistic
minimization criteria to avoid numerical artifacts in the accepted solutions.
Results provide an error estimate for each parameter (absorption, NH, plasma
temperature, kT, or power-law slope, Gamma, and flux, and for different
background contamination levels. The distributions of these errors are studied
as a function of the 1 sigma quantiles and we show how these correlate with
different model parameters, net counts in the spectra and relative background
level. Maps of uncertainty in terms of the 1 sigma quantiles for parameters and
flux are computed as a function of spectrum net counts. We find very good
agreement between our estimated X-ray spectral parameter and flux uncertainties
and those recovered from spectral fitting for a subset of the X-ray sources
detected in the Chandra Cygnus OB2 Legacy Survey diagnosed to be Association
members and that have between 20 and 350 net counts. Our method can provide
uncertainties for spectral parameters whenever formal X-ray spectral fits
cannot be well-constrained, or are unavailable, and predictions useful for
computing Chandra ACIS-I exposure times for observation planning.


title:
No full exceptional collections on non-split Brauer--Severi varieties of
  dimension $\leq 3$

abstract:
  In an earlier paper we showed that non-split Brauer--Severi curves do not
admit full strong exceptional collections. In the present note we extend this
observation and prove that there cannot exist full exceptional collections on
non-split Brauer--Severi varieties of dimension $\leq 3$.


title:
Ultrafast response of plasma-like reflectivity edge in (TMTTF)2AsF6
  driven by 7-fs, 1.5-cycle strong-light field

abstract:
  The strong light-field effect of (TMTTF)2AsF6 was investigated utilizing
1.5-cycle, 7-fs infrared pulses. The ultarfast (20 fs) and large (40%) response
of the plasma-like reflectivity edge (0.7 eV) was analyzed by the changes in
omega_p=sqrt(ne2/(epsilon_0*epsilon(infty)*m)} (n: number of charges in the 1/4
filled-band, m: mass of charge, epsilon(infty): dielectric constants for
high-frequency and vacuum, e: elementary charge). The 3% reduction in omega_p
is attributed to the 6% increase in m. Furthermore, 20 fs oscillation of
omega_p in the time domain indicates that the plasma-like edge is affected by
the charge gap (0.2 eV) nature. Theoretical calculations suggest that the
Coulomb repulsion plays an important role in the increase in m.


title: Single-ion quantum Otto engine with always-on bath interaction

abstract:
  We demonstrate how a quantum Otto engine (QOE) can be implemented using a
single ion and an always-on thermal environment. The internal degree of freedom
of the ion is chosen as the working fluid, while the motional degree of freedom
can be used as the cold bath. We show, that by adiabatically changing the local
magnetic field, the work efficiency can be asymptotically made unity. We
propose a projective measurement of the internal state of the ion that mimics
the release of heat into the cold bath during the engine cycle. In our
proposal, the coupling to the hot and the cold baths need not be switched off
and on in an alternative fashion during the engine cycle, unlike other existing
proposals of QOE. This renders the proposal experimentally feasible using the
available tapped-ion engineering technology.


title:
Quantum critical point of Dirac fermion mass generation without
  spontaneous symmetry breaking

abstract:
  We study a lattice model of interacting Dirac fermions in $(2+1)$ dimension
space-time with an SU(4) symmetry. While increasing interaction strength, this
model undergoes a {\it continuous} quantum phase transition from the weakly
interacting Dirac semimetal to a fully gapped and nondegenerate phase without
condensing any Dirac fermion bilinear mass operator. This unusual mechanism for
mass generation is consistent with recent studies of interacting topological
insulators/superconductors, and also consistent with recent progresses in
lattice QCD community.


title: Multiphase ISM in low luminosity radio galaxies: A case study of NGC 708

abstract:
  We present a multi-wavelength study of a nearby radio loud elliptical galaxy
NGC708, selected from the Bologna B2 sample of radio galaxies. We obtained
optical broad band and narrow images from IGO 2m telescope (Pune, India). We
supplement the multi-wavelength coverage of the observation by using X-ray data
from Chandra, infrared data from 2MASS, Spitzer and WISE and optical image from
DSS and HST. In order to investigate properties of interstellar medium, we have
generated unsharp-masked, color, residual, quotient, dust extinction, H_alph
emission maps. From the derived maps it is evident that cool gas, dust, warm
ionized H_alpha and hot X-ray gas are spatially associated with each other. We
investigate the inner and outer photometric and kinematic properties of the
galaxy using surface brightness profiles. From X-ray 2d beta model, unsharp
masking, surface brightness profiles techniques, it is evident that pair of
X-ray cavities are present in this system and which are ~5.6 Kpc away from the
central X-ray source.


title:
On the correspondence between Koopman mode decomposition, resolvent mode
  decomposition, and invariant solutions of the Navier-Stokes equations

abstract:
  The relationship between Koopman mode decomposition, resolvent mode
decomposition and exact invariant solutions of the Navier-Stokes equations is
clarified. The correspondence rests upon the invariance of the system operators
under symmetry operations such as spatial translation. The usual interpretation
of the Koopman operator is generalised to permit combinations of such
operations, in addition to translation in time. This invariance is related to
the spectrum of a spatio-temporal Koopman operator, which has a travelling wave
interpretation. The relationship leads to a generalisation of dynamic mode
decomposition, in which symmetry operations are applied to restrict the dynamic
modes to span a subspace subject to those symmetries. The resolvent is
interpreted as the mapping between the Koopman modes of the Reynolds stress
divergence and the velocity field. It is shown that the singular vectors of the
resolvent (the resolvent modes) are the optimal basis in which to express the
velocity field Koopman modes where the latter are not a priori known.


title: Probabilistic Programming for Malware Analysis

abstract:
  Constructing lineages of malware is an important cyber-defense task.
Performing this task is difficult, however, due to the amount of malware data
and obfuscation techniques by the authors. In this work, we formulate the
lineage task as a probabilistic model, and use a novel probabilistic
programming solution to jointly infer the lineage and creation times of
families of malware.


title:
Self-Propelled Pedestrian Dynamics Model: Application to Passenger
  Movement and Infection Propagation in Airplanes

abstract:
  Reducing the number of contacts between passengers on an airplane can
potentially curb the spread of infectious diseases. In this paper, a social
force based pedestrian movement model is formulated and applied to evaluate the
movement and contacts among passengers during boarding and deplaning of an
airplane. Within the social force modeling framework, we introduce location
dependence on the self-propelling momentum of pedestrian particles. The model
parameters are varied over a large design space and the results are compared
with experimental observations to validate the model. This model is then used
to assess the different approaches to minimize passenger contacts during
boarding and deplaning of airplanes. We find that smaller aircrafts are
effective in reducing the contacts between passengers. Column wise deplaning
and random boarding are found to be two strategies that reduced the number of
contacts during passenger movement, and can potentially lower the likelihood of
infection spread.


title:
Spin dynamics of hopping electrons in quantum wires: algebraic decay and
  noise

abstract:
  We study theoretically spin decoherence and intrinsic spin noise in
semiconductor quantum wires caused by an interplay of electron hopping between
the localized states and the hyperfine interaction of electron and nuclear
spins. At a sufficiently low density of localization sites the hopping rates
have an exponentially broad distribution. It allows the description of the spin
dynamics in terms of closely-situated "pairs" of sites and single "reaching"
states, from which the series of hops result in the electron localized inside a
"pair". The developed analytical model and numerical simulations demonstrate
disorder-dependent algebraic tails in the spin decay and power-law
singularity-like features in the low-frequency part of the spin noise spectrum.


title:
Boundaries, Mirror Symmetry, and Symplectic Duality in 3d
  $\mathcal{N}=4$ Gauge Theory

abstract:
  We introduce several families of $\mathcal{N}=(2,2)$ UV boundary conditions
in 3d $\mathcal N=4$ gauge theories and study their IR images in sigma-models
to the Higgs and Coulomb branches. In the presence of Omega deformations, a UV
boundary condition defines a pair of modules for quantized algebras of chiral
Higgs- and Coulomb-branch operators, respectively, whose structure we derive.
In the case of abelian theories, we use the formalism of hyperplane
arrangements to make our constructions very explicit, and construct a half-BPS
interface that implements the action of 3d mirror symmetry on gauge theories
and boundary conditions. Finally, by studying two-dimensional compactifications
of 3d $\mathcal{N}=4$ gauge theories and their boundary conditions, we propose
a physical origin for symplectic duality - an equivalence of categories of
modules associated to families of Higgs and Coulomb branches that has recently
appeared in the mathematics literature, and generalizes classic results on
Koszul duality in geometric representation theory. We make several predictions
about the structure of symplectic duality, and identify Koszul duality as a
special case of wall crossing.


title: Modelling income, wealth, and expenditure data by use of Econophysics

abstract:
  In the present paper, we identify several distributions from Physics and
study their applicability to phenomena such as distribution of income, wealth,
and expenditure. Firstly, we apply logistic distribution to these data and we
find that it fits very well the annual data for the entire income interval
including for upper income segment of population. Secondly, we apply
Fermi-Dirac distribution to these data. We seek to explain possible
correlations and analogies between economic systems and statistical
thermodynamics systems. We try to explain their behavior and properties when we
correlate physical variables with macroeconomic aggregates and indicators. Then
we draw some analogies between parameters of the Fermi-Dirac distribution and
macroeconomic variables. Thirdly, as complex systems are modeled using
polynomial distributions, we apply polynomials to the annual sets of data and
we find that it fits very well also the entire income interval. Fourthly, we
develop a new methodology to approach dynamically the income, wealth, and
expenditure distribution similarly with dynamical complex systems. This
methodology was applied to different time intervals consisting of consecutive
years up to 35 years. Finally, we develop a mathematical model based on a
Hamiltonian that maximizes utility function applied to Ramsey model using
Fermi-Dirac and polynomial utility functions. We find some theoretical
connections with time preference theory. We apply these distributions to a
large pool of data from countries with different levels of development, using
different methods for calculation of income, wealth, and expenditure.


title: Twenty Years of Precise Radial Velocities at Keck and Lick Observatories

abstract:
  The precise radial velocity survey at Keck Observatory began over 20 years
ago. Its survey of thousands of stars now has the time baseline to be sensitive
to planets with decade-long orbits, including Jupiter analogs. I present
several newly-finished orbital solutions for long-period giant planets.
Although hot Jupiters are generally "lonely" (i.e. they are not part of
multiplanet systems), those that are not appear to often have giant companions
at 5 AU or beyond. I present two of the highest period- ratios among planets in
a two-planet system, and some of the longest orbital periods ever measured for
exoplanets. In many cases, combining Keck radial velocities from those from
other long-term surveys at Lick Observatory, McDonald Observatory, HARPS, and,
of course, OHP spectrographs, produces superior orbital fits, constraining both
period and eccentricity better than could be possible with any single set
alone. Stellar magnetic activity cycles can masquerade as long-period planets.
In most cases this effect is very small, but a loud minority of stars,
including, apparently, HD 154345, show very strong RV-activity correlations.


title: Coeval intermediate-mass star formation in N4W

abstract:
  Protostars are mostly found in star-forming regions, where the natal
molecular gas still remains. In about 5' west of the molecular bubble N4, N4W
is identified as a star-forming clump hosting three Class II (IRS\,1\,--\,3),
and one Class I (IRS\,4) young stellar objects (YSOs), as well as a
submillimeter source SMM1. The near-IR polarization imaging data of N4W reveal
two infrared reflection nebulae close to each other, which are in favor of the
outflows of IRS\,1 and IRS\,2. The bipolar mid-IR emission centered on IRS\,4
and the arc-like molecular gas shell are lying on the same axis, indicating a
bipolar molecular outflow from IRS\,4. There are two dust temperature
distributions in N4W. The warmer one is widely distributed and has a
temperature $T_\mathrm{d}\gtrsim28\,\mathrm{K}$, with the colder one from the
embedded compact submillimeter source SMM1. N4W's mass is estimated to be
$\sim2.5\times10^3\,M_\odot$, and the mass of SMM1 is
$\sim5.5\times10^2\,M_\odot$ at $T_\mathrm{d}=15\,\mathrm{K}$, calculated from
the CO\,$1-0$ emission and $870\,\mu$m dust continuum emission, respectively.
Based on the estimates of bolometric luminosity of IRS\,1\,--\,4, these four
sources are intermediate-mass YSOs at least. SMM1 is gravitationally bound, and
is capable of forming intermediate-mass stars or even possibly massive stars.
The co-existence of the IR bright YSOs and the submillimeter source represents
potential sequential star formation processes separated by $\sim0.5$\,Myr in
N4W. This small age spread implies that the intermediate-mass star formation
processes happening in N4W are almost coeval.


title:
Higher order methylation features for clustering and prediction in
  epigenomic studies

abstract:
  Motivation: DNA methylation is an intensely studied epigenetic mark, yet its
functional role is incompletely understood. Attempts to quantitatively
associate average DNA methylation to gene expression yield poor correlations
outside of the well-understood methylation-switch at CpG islands.
  Results: Here we use probabilistic machine learning to extract higher order
features associated with the methylation profile across a defined region. These
features quantitate precisely notions of shape of a methylation profile,
capturing spatial correlations in DNA methylation across genomic regions. Using
these higher order features across promoter-proximal regions, we are able to
construct a powerful machine learning predictor of gene expression,
significantly improving upon the predictive power of average DNA methylation
levels. Furthermore, we can use higher order features to cluster
promoter-proximal regions, showing that five major patterns of methylation
occur at promoters across different cell lines, and we provide evidence that
methylation beyond CpG islands may be related to regulation of gene expression.
Our results support previous reports of a functional role of spatial
correlations in methylation patterns, and provide a mean to quantitate such
features for downstream analyses.
  Availability: https://github.com/andreaskapou/BPRMeth


title:
Post-processing procedure for industrial quantum key distribution
  systems

abstract:
  We present algorithmic solutions aimed on post-processing for industrial
quantum key distribution systems with hardware sifting. The main steps of the
procedure are error correction, parameter estimation, and privacy
amplification. Authentication of a classical public communication channel is
also considered.


title:
Improved Likelihood Estimation for the Generalized Extreme Value and the
  Inverse Gaussian Lifetime Distributions

abstract:
  In presence of nuisance parameters, profile likelihood inference is often
unreliable and biased, particularly in small sample scenario. Over past decades
several adjustments have been proposed to modify profile likelihood function in
literature including a modified profile likelihood estimation technique
introduced in Barndorff--Nielsen. In this study, adjustment of profile
likelihood function of parameter of interest in presence of nuisance parameter
is investigated. We particularly focuss to extend the Barndorff--Nielsen's
technique on Inverse Gaussian distribution for estimating its dispersion
parameter and on generalized extreme value (GEV) distribution for estimating
its shape parameter. The accelerated failure time models are used for lifetimes
having GEV distribution and the Inverse Gaussian distribution is used for
lifetime distribution. Monte-Carlo simulation studies are conducted to
demonstrate the performances of both approaches. Simulation results suggest the
superiority of the modified profile likelihood estimates over the profile
likelihood estimates for the parameters of interest. Particularly, it is found
that the modifications can improve the overall performance of the estimators
through reducing their biases and standard errors.


title: The Umwelt of an Embodied Agent -- A Measure-Theoretic Definition

abstract:
  We consider a general model of the sensorimotor loop of an agent interacting
with the world. This formalises Uexk\"ull's notion of a \emph{function-circle}.
Here, we assume a particular causal structure, mechanistically described in
terms of Markov kernels. In this generality, we define two $\sigma$-algebras of
events in the world that describe two respective perspectives: (1) the
perspective of an external observer, (2) the intrinsic perspective of the
agent. Not all aspects of the world, seen from the external perspective, are
accessible to the agent. This is expressed by the fact that the second
$\sigma$-algebra is a subalgebra of the first one. We propose the smaller one
as formalisation of Uexk\"ull's \emph{Umwelt} concept. We show that, under
continuity and compactness assumptions, the global dynamics of the world can be
simplified without changing the internal process. This simplification can serve
as a minimal world model that the system must have in order to be consistent
with the internal process.


title:
A Generic Inverted Index Framework for Similarity Search on the GPU -
  Technical Report

abstract:
  We propose a novel generic inverted index framework on the GPU (called
GENIE), aiming to reduce the programming complexity of the GPU for parallel
similarity search of different data types. Not every data type and similarity
measure are supported by GENIE, but many popular ones are. We present the
system design of GENIE, and demonstrate similarity search with GENIE on several
data types along with a theoretical analysis of search results. A new concept
of locality sensitive hashing (LSH) named $\tau$-ANN search, and a novel data
structure c-PQ on the GPU are also proposed for achieving this purpose.
Extensive experiments on different real-life datasets demonstrate the
efficiency and effectiveness of our framework. The implemented system has been
released as open source.


title: Adiabatic limits of co-associative Kovalev-Lefschetz fibrations

abstract:
  We study co-associative fibrations of G_{2}-manifolds. We propose that the
adiabatic limit of this structure should be given locally by a maximal
submanifold in a space of indefinite signature and set up global versions of
the constructions.


title:
The Electron Temperature and Anisotropy in the Solar Wind. I. Comparison
  of the Core and Halo Populations

abstract:
  Estimating the temperature of the solar wind particles and their anisotropies
is particularly important for understanding the origin of these deviations from
thermal equilibrium as well as their effects. In the absence of energetic
events the velocity distribution of electrons reveal a dual structure with a
thermal (Maxwellian) core and a suprathermal (Kappa) halo. This paper presents
a detailed observational analysis of these two components, providing
estimations of their temperatures and temperature anisotropies and decoding any
potential interdependence that their properties may indicate. The data set used
in this study includes more than 120$\,$000 the events detected by three
missions in the ecliptic within an extended range of heliocentric distances
from 0.3 to over 4~AU. The anti-correlation found for the core and halo
temperatures is consistent with the radial evolution of the Kappa model,
clarifying an apparent contradiction in previous observational analysis and
providing valuable clues about the temperature of the Kappa-distributed
populations. However, these two components manifest a clear tendency to deviate
from isotropy in the same direction, that seems to confirm the existence of
mechanisms with similar effects on both components, e.g., the solar wind
expansion, or the particle heating by the fluctuations. On the other hand, the
existence of plasma states with anti-correlated anisotropies of the core and
halo populations suggests a dynamic interplay of these components, mediated,
most probably, by the anisotropy-driven instabilities.


title: $k$-shot Broadcasting in Ad Hoc Radio Networks

abstract:
  We study distributed broadcasting protocols with few transmissions (`shots')
in radio networks where the topology is unknown. In particular, we examine the
case in which a bound $k$ is given and a node may transmit at most $k$ times
during the broadcasting protocol. Initially, we focus on oblivious algorithms
for $k$-shot broadcasting, that is, algorithms where each node decides whether
to transmit or not with no consideration of the transmission history. Our main
contributions are (a) a lower bound of $\Omega(n^2/k)$ on the broadcasting time
of any oblivious $k$-shot broadcasting algorithm and (b) an oblivious
broadcasting protocol that achieves a matching upper bound, namely $O(n^2/k)$,
for every $k \le \sqrt{n}$ and an upper bound of $O(n^{3/2})$ for every $k >
\sqrt{n}$. We also study the general case of adaptive broadcasting protocols
where nodes decide whether to transmit based on all the available information,
namely the transmission history known by each. We prove a lower bound of
$\Omega\left(n^{\frac{1+k}{k}}\right)$ on the broadcasting time of any protocol
by introducing the \emph{transmission tree} construction which generalizes
previous approaches.


title: Possible identification of massive and evolved galaxies At z > 5

abstract:
  We report on the identification of the old stellar population galaxy
candidates at z > 5. We developed a new infrared color selection scheme to
isolate galaxies with the strong Balmer breaks at z > 5, and applied it to the
ultra-deep and wide infrared survey data from the Spitzer Extended Deep Survey
(SEDS) and the UKIRT Infrared Deep Sky Survey. The eight objects satisfying K -
[3.6] > 1.3 and K - [3.6] > 2.4 ([3.6] - [4.5]) + 0.6 are selected in the 0.34
deg^2 SEDS Ultra Deep Survey field. Rich multi-wavelength imaging data from
optical to far-infrared are also used to reject blending sources and strong
nebular line emitters, and we finally obtained the three most likely evolved
galaxies at z > 5. Their stacked spectral energy distribution is fitted well
with the old stellar population template with M_{*} = (7.5+-1.5) x 10^{10}
Msun, star formation rate = 0.9 +- 0.2 Msun yr^{-1}, dust A_V < 1, and age =
0.7+-0.4 Gyr at z = 5.7+-0.6, where the dusty star-forming galaxies at z ~ 2.8
are disfavored because of the faintness in the 24um. The stellar mass density
of these evolved galaxy candidates, (6+-4) x 10^4 Msun Mpc^{-3}, is much lower
than that of star-forming galaxies, but the non-zero fraction suggests that
initial star-formation and quenching have been completed by z ~ 6.


title: Linear degenerations of flag varieties

abstract:
  Linear degenerate flag varieties are degenerations of flag varieties as
quiver Grassmannians. For type A flag varieties, we obtain characterizations of
flatness, irreducibility and normality of these degenerations via rank tuples.
Some of them are shown to be isomorphic to Schubert varieties and can be
realized as highest weight orbits of partially degenerate Lie algebras,
generalizing the corresponding results on degenerate flag varieties. To study
normality, cell decompositions of quiver Grassmannians are constructed in a
wider context of equioriented quivers of type A.


title: Inclusive electron scattering within the SuSAv2-MEC approach

abstract:
  We present our recent progress on the relativistic modeling of
electron-nucleus reactions and compare our predictions with inclusive $^{12}$C
($e,e'$) experimental data in a wide kinematical region. The model, originally
based on the superscaling phenomenon shown by electron-nucleus scattering data,
has recently been improved through the inclusion of Relativistic Mean Field
theory effects that take into account the enhancement of the transverse scaling
function compared with its longitudinal counterpart. We also discuss the impact
of meson-exchange currents (MEC) through the analysis of two-particle two-hole
longitudinal and transverse contributions to electromagnetic response functions
evaluated within the framework of the relativistic Fermi gas. The formalism is
also extended to include the complete inelastic spectrum -- resonant,
non-resonant and deep inelastic scattering (DIS). The results show quite good
agreement with data over the whole range of energy transfer, including the dip
region between the quasielastic peak and the $\Delta$ resonance.


title: Estimating the number of tissue resident macrophages

abstract:
  I provide a simple estimation for the number of macrophages in a tissue,
arising from the hypothesis that they should keep infections below a certain
threshold, above which neutrophils are recruited from blood circulation. The
estimation reads Nm=a Ncel^{\alpha}/Nmax, where a is a numerical coefficient,
the exponent {\alpha} is near 2/3, and Nmax is the maximal number of pathogens
a macrophage may engulf in the time interval, tr, between pathogen
replications.


title: On the stabilisers of locally 2-transitive graphs

abstract:
  For a connected locally $(G,s$)-arc-transitive graph $\Gamma$ with
$s\geqslant 2$ and an edge ${v,w}$, determining the amalgam $(G_v,G_w,G_{vw})$
is a fundamental problem in the area of symmetrical graph theory, but it is
very difficult. In this paper, we give a classification of $(G_v,G_w,G_{vw})$
in the case where the vertex stabilisers $G_v$ and $G_w$ are faithful on their
neighbourhoods, which shows that except for the case $G_v\cong G_w$, there are
exactly 16 such triples.


title: Moduli mediation without moduli-induced gravitino problem

abstract:
  We study the moduli-induced gravitino problem within the framework of the
phenomenologically attractive mirage mediations. The huge amount of gravitino
generated by the moduli decay can be successfully diluted by introducing an
extra light modulus field which does not induce the supersymmetry breaking.
Since the lifetime of extra modulus field becomes longer than usually
considered modulus field, our proposed mechanism is applied to both the low-
and high-scale supersymmetry breaking scenarios. We also point out that such an
extra modulus field appears in the flux compactification of type II string
theory.


title:
A classification of tetravalent edge-transitive metacirculants of odd
  order

abstract:
  In this paper a classification of tetravalent edge-transitive metacirculants
is given. It is shown that a tetravalent edge-transitive metacirculant $\Gamma$
is a normal graph except for four known graphs. If further, $\Gamma$ is a
Cayley graph of a non-abelian metacyclic group, then $\Gamma$ is
half-transitive.


title:
Lock-in range of PLL-based circuits with proportionally-integrating
  filter and sinusoidal phase detector characteristic

abstract:
  In the present work PLL-based circuits with sinusoidal phase detector
characteristic and active proportionally-integrating (PI) filter are
considered. The notion of lock-in range -- an important characteristic of
PLL-based circuits, which corresponds to the synchronization without cycle
slipping, is studied. For the lock-in range a rigorous mathematical definition
is discussed. Numerical and analytical estimates for the lock-in range are
obtained.


title: Approximation orders of real numbers by $\beta$-expansions

abstract:
  We prove that almost all real numbers (with respect to Lebesgue measure) are
approximated by the convergents of their $\beta$-expansions with the
exponential order $\beta^{-n}$. Moreover, the Hausdorff dimensions of sets of
the real numbers which are approximated by all other orders, are determined.
These results are also applied to investigate the orbits of real numbers under
$\beta$-transformation, the shrinking target type problem, the Diophantine
approximation and the run-length function of $\beta$-expansions.


title:
Unconventional Magnetism and Band Gap Formation in LiFePO4: Consequence
  of Polyanion Induced Non-planarity

abstract:
  Oxygen plays a critical role in strongly correlated transition metal oxides
as crystal field effect is one of the key factors that determine the degree of
localization of the valence d/f states. Based on the localization, a set of
conventional mechanisms such as Mott-Hubbard, Charge-transfer and Slater were
formulated to explain the antiferromagnetic and insulating (AFI) phenomena in
many of these correlated systems. From the case study on LiFePO4, through
density-functional calculations, we demonstrate that none of these mechanisms
are strictly applicable to explain the AFI behavior when the transition metal
oxides have polyanions such as (PO4)3-. The symmetry-lowering of the
metal-oxygen complex, to stabilize the polyanion, creates an asymmetric crystal
field for d/f states. In LiFePO4 this field creates completely non-degenerate
Fe-d states which, with negligible p-d and d-d covalent interactions, become
atomically localized to ensure a gap at the Fermi level. Due to large exchange
splitting, high spin state is favored and an antiferromagnetic configuration is
stabilized. For the prototype LiFePO4, independent electron approximation is
good enough to obtain the AFI ground state. Inclusion of additional correlation
measures like Hubbard U simply amplifies the gap and therefore LiFePO4 can be
preferably called as weakly coupled Mott insulator.


title: Ring Theoretic Properties of Partial Crossed products and related themes

abstract:
  In this paper we work with unital twisted partial actions. We investigate
ring theoretic properties of partial crossed products as artinianity,
noetherianity, perfect property, semilocalproperty, semiprimary property and we
also study the Krull dimension. Moreover, we consider triangular matrix
representation of partial skew group rings, weak and global dimensions of
partial crossed products Also we study when the partial crossed products are
Frobenius and symmetric algebras.


title: Conformal Invariance and the Metrication of the Fundamental Forces

abstract:
  We revisit Weyl's metrication (geometrization) of electromagnetism. We show
that by making Weyl's proposed geometric connection be pure imaginary, not only
are we able to metricate electromagnetism, an underlying local conformal
invariance makes the geometry be strictly Riemannian and prevents observational
gravity from being complex. Via torsion we achieve an analogous metrication for
axial-vector fields. We generalize our procedure to Yang-Mills theories, and
achieve a metrication of all the fundamental forces. Only in the gravity sector
does our approach differ from the standard picture of fundamental forces, with
our approach requiring that standard Einstein gravity be replaced by conformal
gravity. We show that quantum conformal gravity is a consistent and unitary
quantum gravitational theory, one that, unlike string theory, only requires
four spacetime dimensions.


title: The Gravitational Constant as a quantum mechanical expression

abstract:
  A quantitatively verifiable expression for the Gravitational Constant is
derived in terms of quantum mechanical quantities. This derivation appears to
be possible by selecting a suitable physical process in which the
transformation of the equation of motion into a quantum mechanical wave
equation can be obtained by Einstein's geodesic approach. The selected process
is the pi-meson, modeled as the one-body equivalent of a two-body quantum
mechanical oscillator in which the vibrating mass is modeled as the result of
the two energy fluxes from the quark and the antiquark. The quantum mechanical
formula for the Gravitational Constant appears to show a quantitatively
verifiable relationship with the Higgs boson as conceived in the Standard
Model.


title: Faddeev-Jackiw Quantization of Non-Autonomous Singular Systems

abstract:
  We extend the quantization \`a la Faddeev-Jackiw for non-autonomous singular
systems. This leads to a generalization of the Schr\"odinger equation for those
systems. The method is exemplified by the quantization of the damped harmonic
oscillator and the relativistic particle in an external electromagnetic field.


title:
Reissner-Nordstr\"{o}m black holes statistical ensembles and first order
  thermodynamic phase transition

abstract:
  We apply Debbasch proposal to obtain mean metric of coarse graining
(statistical ensemble) of quantum perturbed Reissner-Nordst\"{o}m black hole
$(RNBH).$ Then we seek its thermodynamic phase transition behavior. Our
calculations predict first order phase transition which it can take Bose
Einstein's condensation behavior.


title: Sphericons and D-forms: a crocheted connection

abstract:
  Sphericons and D-forms are 3D objects created and described by artists, which
have separately received attention in the mathematical literature in the last
15 or so years. The attempt to classify a seamed, crocheted form geometrically
led to the observation, which appears not to have been previously made
explicit, that these objects are related. General results concerning
$(N,k)$-icons and seam-, D- and pita-forms are given. Instructions to crochet
D-forms are given in the Appendix.


title:
A look at perpetuities via asymptotically homogeneous in space Markov
  chains

abstract:
  It is shown how a natural representation of perpetuities as asymptotically
homogeneous in space Markov chains allows to prove various asymptotic tail
results for stable perpetuities and limit theorems for unstable ones. Some of
these results are new while others essentially improve moment conditions known
in the literature. Both subexponential and Cram\'er's cases are considered.


title:
A mathematical form of force-free magnetosphere equation around Kerr
  black holes and its application to Meissner effect

abstract:
  Based on the Lagrangian of the steady axisymmetric force-free magnetosphere
(FFM) equation around Kerr black holes(KBHs), we find that the FFM equation can
be rewritten in a new form as $f_{,rr} / (1-\mu^{2}) + f_{,\mu\mu} / \Delta +
K(f(r,\mu),r,\mu) = 0$, where $\mu = -\cos\theta$. By coordinate
transformation, the form of the above equation can be given by $s_{,yy} +
s_{,zz} + D(s(y,z),y,z) = 0$. Based on the form, we prove finally that the
Meissner effect is not possessed by a KBH-FFM with the condition where
$d\omega/d A_{\phi} \leqslant 0$ and $H_{\phi}(dH_{\phi}/dA_{\phi}) \geqslant
0$, here $A_{\phi}$ is the $\phi$ component of the vector potential $\vec{A}$,
$\omega$ is the angular velocity of magnetic fields and ${H_{\phi}}$
corresponds to twice the poloidal electric current.


title: Perimeter as relaxed Minkowski content in metric measure spaces

abstract:
  In this note we prove that on general metric measure spaces the perimeter is
equal to the relaxation of the Minkowski content w.r.t.\ convergence in measure


title:
On the dimension of the algebra generated by two positive semi-commuting
  matrices

abstract:
  Gerstenhaber's theorem states that the dimension of the unital algebra
generated by two commuting $n\times n$ matrices is at most $n$. We study the
analog of this question for positive matrices with a positive commutator. We
show that the dimension of the unital algebra generated by the matrices is at
most $\frac{n(n+1)}{2}$ and that this bound can be attained. We also consider
the corresponding question if one of the matrices is a permutation or a
companion matrix or both of them are idempotents. In these cases, the upper
bound for the dimension can be reduced significantly. In particular, the unital
algebra generated by two semi-commuting positive idempotent matrices is at most
$9$-dimensional. This upper bound can be attained.


title: Strong $k$-commutativity preserving maps on 2$\times$2 matrices

abstract:
  Let ${\mathcal M}_2(\mathbb F)$ be the algebra of 2$\times$2 matrices over
the real or complex field $\mathbb F$. For a given positive integer $k\geq 1$,
the $k$-commutator of $A$ and $B$ is defined by $[A,B]_k=[[A,B]_{k-1},B]$ with
$[A,B]_0=A$ and $[A,B]_1=[A,B]=AB-BA$. The main result is shown that a map
$\Phi: {\mathcal M}_2(\mathbb F)\to {\mathcal M}_2(\mathbb F)$ with range
containing all rank one matrices satisfies that $[\Phi(A),\Phi(B)]_k = [A,B]_k
$ for all $A, B\in{\mathcal M}_2(\mathbb F)$ if and only if there exist a
functional $h :{\mathcal M}_2(\mathbb F) \rightarrow {\mathbb F}$ and a scalar
$\lambda \in{\mathbb F}$ with $\lambda^{k+1} = 1$ such that $\Phi(A) = \lambda
A + h(A)I$ for all $A \in{\mathcal M}_2(\mathbb F)$.


title:
On space-like generalized constant ratio hypersufaces in Minkowski
  spaces

abstract:
  A hypersurface in a Euclidean space $\mathbb{E}^{n+1}$ is said to be a
generalized constant ratio (GCR) hypersurface if the tangential part of its
position vector is one of its principle directions. In this work, we move the
study of generalized constant ratio hypersurfaces started in \cite%
{YuFu2014GCRS} into the Minkowski space. First, we get some geometrical
properties of non-degenerated GCR hypersurfaces in an arbitrary dimensional
Minkowski space. Then, we obtain complete classification of GCR surfaces in the
Minkowski 3-space. We also give some explicit examples.


title:
The Effect of Plasma Beta on High-n Ballooning Stability at Low Magnetic
  Shear

abstract:
  An explanation of the observed improvement in H-mode pedestal characteristics
with increasing core plasma pressure or poloidal beta, as observed in MAST and
JET, is sought in terms of the impact of the Shafranov shift, d', on ideal
ballooning MHD stability.


title:
From practical geometry to the laboratory method: the search for an
  alternative to Euclid in the history of teaching geometry

abstract:
  This paper wants to show how practical geometry, created to give a concrete
help to people involved in trade, in land-surveying and even in astronomy,
underwent a transformation that underlined its didactical value and turned it
first into a way of teaching via problem solving and then into an
experimental-intuitive teaching that could be an alternative to the
deductive-rational teaching of geometry. This evolution will be highlighted
using textbooks that proposed alternative presentations of geometry.


title: Classification of genus two knots which admit a (1,1) decomposition

abstract:
  We describe the genus two knots which admit a genus one, one bridge position.
These are divided into several families, one consists of vertical bandings of
two genus one $(1,1)$-knots, other consists of vertical bandings of two cross
cap number two 2-bridge knots, and the last one consists of genus two tunnel
number one satellite knots.


title:
Approximation properties of the Stancu type Dunkl generalization of the
  Kantorovich-Sz\'asz-Mirakjan-operators via q-calculus

abstract:
  In this paper we construct Stancu type q-Kantrovich-Sz\'asz-Mirakjan
operators generated by Dunkl generalization of the exponential function. We
obtain some approximation results using the Korovkin approximation theorem and
the weighted Korovkin-type theorem for these operators. We also study
convergence properties by using the modulus of continuity and the rate of
convergence of these operators for functions belonging to the Lipschitz class.
Furthermore, we obtain the rate of convergence in terms of the classical,
second order, and weighted modulus of continuity.


title: On a sum of positive rational numbers whose product is 1

abstract:
  In this note, we prove that for every two positive integers $m \geq n \geq
9$, there exist $n$ positive rational numbers whose product is 1 and sum is
$m$.


title: A straightforward solution to the Burnside Problem

abstract:
  We present a solution to the Burnside Problem for 2 generator groups of
prime-power exponent that does not rely on induced maps as in [2]. As before,
we construct a surjective map of a rank 2 free group to a solvable group G and
finish by showing that the Burnside group is an image of G. Theorem B in the
paper with H. A. Heilbronn and H. Y. Mochizuki [9] is indispensable in the
proof.


title:
A Gorenstein criterion for strongly $F$-regular and log terminal
  singularities

abstract:
  A conjecture of Hirose, Watanabe, and Yoshida offers a characterization of
when a standard graded strongly $F$-regular ring is Gorenstein, in terms of an
$F$-pure threshold. We prove this conjecture under the additional hypothesis
that the anti-canonical cover of the ring is Noetherian. Moreover, under this
hypothesis on the anti-canonical cover, we give a similar criterion for when a
normal $F$-pure (resp. log canonical) singularity is quasi-Gorenstein, in terms
of an $F$-pure (resp. log canonical) threshold.


title: Correlation bound for distant parts of factor of IID processes

abstract:
  We study factor of i.i.d. processes on the $d$-regular tree for $d \geq 3$.
We show that if such a process is restricted to two distant connected subgraphs
of the tree, then the two parts are basically uncorrelated. More precisely, any
functions of the two parts have correlation at most $k(d-1) / (\sqrt{d-1})^k$,
where $k$ denotes the distance of the subgraphs. This result can be considered
as a quantitative version of the fact that factor of i.i.d. processes have
trivial 1-ended tails.


title: Tropical refined curve counting via motivic integration

abstract:
  We propose a geometric interpretation of Block and G\"ottsche's refined
tropical curve counting invariants in terms of virtual
$\chi_{-y}$-specializations of motivic measures of semialgebraic sets in
relative Hilbert schemes. We prove that this interpretation is correct for
linear series of genus 1, and in arbitrary genus after specializing from
$\chi_{-y}$ to Euler characteristic.


title:
Towards the detecting of pseudo-Hermitian anomalies for negative square
  masses neutrinos in intensive magnetic fields

abstract:
  One of the primary goals of contemporary physics of neutrinos after discovery
of their masses become the investigation of their electromagnetic properties.
This is a necessary step for creation of new physics beyond the Standard Model
(SM), which no longer can claim the role theory explaining everything
phenomenon of the Universe. On this it should draw attention because SM remains
consistent local scheme for any value of the masses of particles $0\leq m
<\infty $. Now the masses of elementary particles can exceed even Planck's mass
$m_{Planck}\simeq 10^{19}GeV$, which is the largest scale mass in the Universe.
For solving this problem of studying of electromagnetic interactions of
neutrino we suggest use the methods of relativistic quantum theory with the
limiting mass $m\leq M$. The restriction of mass spectrum of fermions can be
obtained in the frame of non-Hermitian (pseudo-Hermitian) fermion systems
having the direct application to the neutrino physics. The systems of the
similar type include so-called parity-time-symmetric (${\cal PTS}$) - models,
which already are used in various fields of modern physics and, in particular
for experimental investigation of ${\cal PTS}$-optics. We also hope that
experimental problem neutrinos with the negative mass squared could be also
solved on the basis of ${\cal PTS}$-notions taking into account the
characteristics of neutrinos of new type ("exotic neutrino") emerging in the
theory with the Maximal Mass.


title: On the structure of graded Leibniz triple systems

abstract:
  We study the structure of a Leibniz triple system $\mathcal{E}$ graded by an
arbitrary abelian group $G$ which is considered of arbitrary dimension and over
an arbitrary base field $\mathbb{K}$. We show that $\mathcal{E}$ is of the form
$\mathcal{E}=U+\sum_{[j]\in \sum^{1}/\sim} I_{[j]}$ with $U$ a linear subspace
of the 1-homogeneous component $\mathcal{E}_{1}$ and any ideal $I_{[j]}$ of
$\mathcal{E}$, satisfying $\{I_{[j]},\mathcal{E},I_{[k]}\}
=\{I_{[j]},I_{[k]},\mathcal{E}\}=\{\mathcal{E},I_{[j]},I_{[k]}\}=0$ if $[j]\neq
[k]$, where the relation $\sim$ in $\sum^{1}=\{g \in G \setminus \{1\} :
L_{g}\neq 0\}$, defined by $g \sim h$ if and only if $g$ is connected to $h$.


title: Why Square Roots of Probabilities?

abstract:
  Square roots of probabilities appear in several contexts, which suggests that
they are somehow more fundamental than probabilities. Square roots of
probabilities appear in expressions of the Fisher-Rao Metric and the
Hellinger-Bhattacharyya distance. They also come into play in Quantum Mechanics
via the Born rule where probabilities are found by taking the squared modulus
of the quantum amplitude. Why should this be the case and why do these square
roots not arise in the various formulations of probability theory?
  In this short, inconclusive exploration, I consider quantifying a logical
statement with a vector defined by a set of components each quantifying one of
the atomic statements defining the hypothesis space. I show that conditional
probabilities (bi-valuations), such as $P(x|y)$, can be written as the dot
product of the two vectors quantifying the logical statements $x$ and $y$ each
normalized with respect to the vector quantifying the conditional $y$. The
components of the vectors are proportional to the square root of the
probability. As a result, this formulation is shown to be consistent with a
concept of orthogonality applied to the set of mutually exclusive atomic
statements such that the sum rule is represented as the sum of the squares of
the square roots of probability.


title: On the change of variables formula for multiple integrals

abstract:
  In this paper, we develop an elementary proof of the change of variables in
multiple integrals. Our proof is based on an induction argument. Assuming the
formula for (m-1)-integrals, we define the integral over hypersurface in Rm,
establish the divergent theorem and then use the divergent theorem to prove the
formula for m-integrals. In addition to its simplicity, an advantage of our
approach is that it yields the Brouwer Fixed Point Theorem as a corollary.


title: Wilson operator algebras and ground states for coupled BF theories

abstract:
  The multi-flavor $BF$ theories in (3+1) dimensions with cubic or quartic
coupling are the simplest topological quantum field theories that can describe
fractional braiding statistics between loop-like topological excitations
(three-loop or four-loop braiding statistics). In this paper, by canonically
quantizing these theories, we study the algebra of Wilson loop and Wilson
surface operators, and multiplets of ground states on three torus. In
particular, by quantizing these coupled $BF$ theories on the three-torus, we
explicitly calculate the $\mathcal{S}$- and $\mathcal{T}$-matrices, which
encode fractional braiding statistics and topological spin of loop-like
excitations, respectively. In the coupled $BF$ theories with cubic and quartic
coupling, the Hopf link and Borromean ring of loop excitations, together with
point-like excitations, form composite particles.


title:
A Note on the Computational Complexity of Unsmoothened Vertex Attack
  Tolerance

abstract:
  We have previously introduced vertex attack tolerance (VAT) and unsmoothened
VAT (UVAT), denoted respectively as $\tau(G) = \min_{S \subset V}
\frac{|S|}{|V-S-C_{max}(V-S)|+1}$ and $\hat{\tau}(G) = \min_{S \subset V}
\frac{|S|}{|V-S-C_{max}(V-S)|}$, where $C_{max}(V-S)$ is the largest connected
component in $V-S$, as appropriate mathematical measures of resilience in the
face of targeted node attacks for arbitrary degree networks. Here we prove the
hardness of approximating $\hat{\tau}$ under various plausible computational
complexity hypotheses.


title:
Cosmic shear measurement with maximum likelihood and maximum a
  posteriori inference

abstract:
  We investigate the problem of noise bias in maximum likelihood and maximum a
posteriori estimators for cosmic shear. We derive the leading and
next-to-leading order biases and compute them in the context of galaxy
ellipticity measurements, extending previous work on maximum likelihood
inference for weak lensing. We show that a large part of the bias on these
point estimators can be removed using information already contained in the
likelihood when a galaxy model is specified, without the need for external
calibration. We test these bias-corrected estimators on simulated galaxy images
similar to those expected from planned space-based weak lensing surveys, with
promising results. We find that the introduction of an intrinsic shape prior
can help with mitigation of noise bias, such that the maximum a posteriori
estimate can be made less biased than the maximum likelihood estimate.
Second-order terms offer a check on the convergence of the estimators, but are
largely sub-dominant. We show how biases propagate to shear estimates,
demonstrating in our simple setup that shear biases can be reduced by orders of
magnitude and potentially to within the requirements of planned space-based
surveys at mild signal-to-noise. We find that second-order terms can exhibit
significant cancellations at low signal-to-noise when Gaussian noise is
assumed, which has implications for inferring the performance of
shear-measurement algorithms from simplified simulations. We discuss the
viability of our point estimators as tools for lensing inference, arguing that
they allow for the robust measurement of ellipticity and shear.


title: Quantifying topological invariants of neuronal morphologies

abstract:
  Nervous systems are characterized by neurons displaying a diversity of
morphological shapes. Traditionally, different shapes have been qualitatively
described based on visual inspection and quantitatively described based on
morphometric parameters. Neither process provides a solid foundation for
categorizing the various morphologies, a problem that is important in many
fields. We propose a stable topological measure as a standardized descriptor
for any tree-like morphology, which encodes its skeletal branching anatomy.
More specifically it is a barcode of the branching tree as determined by a
spherical filtration centered at the root or neuronal soma. This Topological
Morphology Descriptor (TMD) allows for the discrimination of groups of random
and neuronal trees at linear computational cost.


title:
The graph structure of graph groups that are subgroups of Thompson's
  group $V$

abstract:
  We determine exactly which graph products, also known as Right Angled Artin
Groups, embed into Richard Thompson's group $V$. It was shown by Bleak and
Salazar-Diaz that $\mathbb{Z}^2 * \mathbb{Z}$ was an obstruction. We show that
this is the only obstruction. This is shown by proving a graph theory result
giving an alternate description of simple graphs without an appropriate induced
subgraph.


title: Exotic Physics

abstract:
  A selection of results for searches for exotic physics at the LHC are
presented. These include a search for massive resonances, dark matter with a
high energy jet in association with large missing transverse momentum,
long-lived neutral particles, and narrow dijet resonances. The results are
based on 20/fb of LHC proton-proton collisions at sqrt(s) = 8 TeV taken with
the CMS detector.


title:
Exact results for the temperature-field behavior of the thermodynamic
  Casimir force in a model of film system with a strong surface adsorption

abstract:
  When masless excitations are limited or modified by the presence of material
bodies one observes a force atcing between them generally called Casimir force.
Such excitations are present in any fluid system close to its true bulk
critical point. We derive exact analytical results for both the temperature and
external ordering field behavior of the thermodynamic Casimir force within the
mean-field Ginzburg-Landau Ising type model of a simple fluid or binary liquid
mixture. We investigate the case when under a film geometry the boundaries of
the system exhibit strong adsorption onto one of the phases (components) of the
system. We present analytical and numerical results for the (temperature-field)
surface of the force in both the critical region of the film close to its
finite-size or bulk critical points as well as in the capillary condensation
regime below the finite-size critical point.


title:
$\Upsilon(6S)$ and triangle singularity in $e^+e^- \to B_1(5721) \bar B
  \to Z_b(10610) \, \pi$

abstract:
  We discuss the possibility that production of final states with bottomonium
and light mesons at the peak $\Upsilon(6S)$ in the $e^+e^-$ annihilation at
approximately 11.00 GeV is in fact due to a triangular singularity at the
threshold of the heavy meson pair production $B_1(5721) \bar B + c.c.$ through
the process $e^+e^- \to B_1(5721) \bar B \to Z_b(10610) \, \pi$. The presence
of the hidden-bottom resonance $Z_b(10610)$ then explains the observed enhanced
production of the final channels with both ortho- and para- bottomonium states,
$\Upsilon(nS) \pi \pi$ and $h_b(kP) \pi \pi$. The discussed mechanism also
predicts a distinct pattern for production of hidden-bottom states at the
$\Upsilon(6S)$ energy that can be tested by experiment.


title: Resolving the rotation measure of the M87 jet on kilo-parsec scales

abstract:
  We investigate the distribution of Faraday rotation measure (RM) in the M87
jet at arc-second scales by using archival polarimetric VLA data at 8, 15, 22
and 43 GHz. We resolve the structure of the RM in several knots along the jet
for the first time. We derive the power spectrum in the arcsecond scale jet and
find indications that the RM cannot be associated with a turbulent magnetic
field with 3D Kolmogorov spectrum. Our analysis indicates that the RM probed on
jet scales has a significant contribution of a Faraday screen associated with
the vicinity of the jet, in contrast with that on kiloparsec scales, typically
assumed to be disconnected from the jet. Comparison with previous RM analyses
suggests that the magnetic fields giving rise to the RMs observed in jet scales
have different properties and are well less turbulent than these observed in
the lobes.


title: Several nonlocal sets of multipartite pure orthogonal product states

abstract:
  It is known that there exist sets of pure orthogonal product states which
cannot be perfectly distinguished by local operations and classical
communication (LOCC). Such sets are nonlocal sets which exhibit nonlocality
without entanglement. These nonlocal sets can be completable or uncompletable.
In this work both completable and uncompletable small nonlocal sets of
multipartite orthogonal product states are constructed. Apart from nonlocality,
these sets have other interesting properties. In particular, the completable
sets lead to the construction of a class of complete orthogonal product bases
with the property that if such a basis is given then no state can be eliminated
from that basis by performing orthogonality-preserving measurements. On the
other hand, an uncompletable set of the present kind contains several Shifts
unextendible product bases (UPBs) that belong to qubit subspaces. Identifying
these subspace UPBs, it is possible to obtain a class of high-dimensional
multipartite bound entangled states. Finally, it is shown that a two-qubit
maximally entangled Bell state shared between any two parties is sufficient as
a resource to distinguish the states of any completable set (of the above kind)
perfectly by LOCC. This constitutes an example where the amount of
entanglement, sufficient to accomplish the aforesaid task, depends neither on
the dimension of the individual subsystems nor on the number of parties.


title:
Semiclassical expansion of the ground state for a model of interacting
  spins in QED

abstract:
  In this article, we consider fixed spin 1/2 particles interacting through the
quantized electromagnetic field in a constant magnetic field. We give some
asymptotic expansions for the ground state and the ground state energy of the
Hamiltonian operator $H(h)$ describing this system. The first terms of these
expansions enable to recover elementary formulas for the energy and the
magnetic field of the spins when considered as magnets. A first order radiative
correction is computed for the energy.


title:
Holographic interpretation of 1-point toroidal block in the
  semiclassical limit

abstract:
  We propose the holographic interpretation of the 1-point conformal block on a
torus in the semiclassical regime. To this end we consider the linearized
version of the block and find its coefficients by means of the perturbation
procedure around natural seed configuration corresponding to the zero-point
block. From the AdS/CFT perspective the linearized block is given by the
geodesic length of the tadpole graph embedded into the thermal AdS plus the
holomorphic part of the thermal AdS action.


title:
Modelling the structure of molecular clouds: I. A multi-scale energy
  equipartition

abstract:
  We present a model for describing the general structure of molecular clouds
(MCs) at early evolutionary stages in terms of their mass-size relationship.
Sizes are defined through threshold levels at which equipartitions between
gravitational, turbulent and thermal energy $|W| \sim f(E_{\rm kin} + E_{\rm
th})$ take place, adopting interdependent scaling relations of velocity
dispersion and density and assuming a lognormal density distribution at each
scale. Variations of the equipartition coefficient $1\le f\le 4$ allow for
modelling of star-forming regions at scales within the size range of typical
MCs ($\gtrsim$4 pc). Best fits are obtained for regions with low or no star
formation (Pipe, Polaris) as well for such with star-forming activity but with
nearly lognormal distribution of column density (Rosette). An additional
numerical test of the model suggests its applicability to cloud evolutionary
times prior to the formation of first stars.


title: Finite Partially Exchangeable Laws are Signed Mixtures of Product Laws

abstract:
  Given a partition $\{I_1,\ldots,I_k\}$ of $\{1,\ldots,n\}$, let
$(X_1,\ldots,X_n)$ be random vector with each $X_i$ taking values in an
arbitrary measurable space $(S,\mathscr{S})$ such that their joint law is
invariant under finite permutations of the indexes within each class $I_j$.
Then, it is shown that this law has to be a signed mixture of independent laws
and identically distributed within each class $I_j$. The representation is
unique if and only if the set of these signed measures is weakly compact.
  We provide a necessary condition for the existence of a nonnegative directing
measure. This is related to the notions of infinite extendibility and
reinforcement. In the special case where $(X_1,\ldots,X_n)$ is an exchangeable
sequence of $\{0,1\}$-valued random variables, the directing measure can be
chosen nonnegative if and only if two effectively computable matrices are
positive semi-definite.


title:
A practical guide to density matrix embedding theory in quantum
  chemistry

abstract:
  Density matrix embedding theory (DMET) provides a theoretical framework to
treat finite fragments in the presence of a surrounding molecular or bulk
environment, even when there is significant correlation or entanglement between
the two. In this work, we give a practically oriented and explicit description
of the numerical and theoretical formulation of DMET. We also describe in
detail how to perform self-consistent DMET optimizations. We explore different
embedding strategies with and without a self-consistency condition in hydrogen
rings, beryllium rings, and a sample S$_{\text{N}}$2 reaction. The source code
for the calculations in this work can be obtained from
\url{https://github.com/sebwouters/qc-dmet}.


title: K\"ahler-Einstein metrics and algebraic structures on limit spaces

abstract:
  This is an expository article, closely following the author's lecture at the
2014 Journal Differential Geometry conference.


title:
A topological criterion for filtering information in complex brain
  networks

abstract:
  In many biological systems, the network of interactions between the elements
can only be inferred from experimental measurements. In neuroscience,
non-invasive imaging tools are extensively used to derive either structural or
functional brain networks in-vivo. As a result of the inference process, we
obtain a matrix of values corresponding to an unrealistic fully connected and
weighted network. To turn this into a useful sparse network, thresholding is
typically adopted to cancel a percentage of the weakest connections. The
structural properties of the resulting network depend on how much of the
inferred connectivity is eventually retained. However, how to fix this
threshold is still an open issue. We introduce a criterion, the efficiency cost
optimization (ECO), to select a threshold based on the optimization of the
trade-off between the efficiency of a network and its wiring cost. We prove
analytically and we confirm through numerical simulations that the connection
density maximizing this trade-off emphasizes the intrinsic properties of a
given network, while preserving its sparsity. Moreover, this density threshold
can be determined a-priori, since the number of connections to filter only
depends on the network size according to a power-law. We validate this result
on several brain networks, from micro- to macro-scales, obtained with different
imaging modalities. Finally, we test the potential of ECO in discriminating
brain states with respect to alternative filtering methods. ECO advances our
ability to analyze and compare biological networks, inferred from experimental
data, in a fast and principled way.


title: On Lie-isoclinic Leibniz algebras

abstract:
  In this paper we study the notion of isoclinism on Lie-central extensions of
Leibniz algebras, this yields to introduce the concept of Lie-isoclinic Leibniz
algebras. We provide several equivalent conditions under which Leibniz algebras
are Lie-isoclinic. We also define the concept of Schur Lie-multiplier and
analyze its connection with Lie-isoclinism.


title: Mutual Information in Rank-One Matrix Estimation

abstract:
  We consider the estimation of a n-dimensional vector x from the knowledge of
noisy and possibility non-linear element-wise measurements of xxT , a very
generic problem that contains, e.g. stochastic 2-block model, submatrix
localization or the spike perturbation of random matrices. We use an
interpolation method proposed by Guerra and later refined by Korada and Macris.
We prove that the Bethe mutual information (related to the Bethe free energy
and conjectured to be exact by Lesieur et al. on the basis of the non-rigorous
cavity method) always yields an upper bound to the exact mutual information. We
also provide a lower bound using a similar technique. For concreteness, we
illustrate our findings on the sparse PCA problem, and observe that (a) our
bounds match for a large region of parameters and (b) that it exists a phase
transition in a region where the spectum remains uninformative. While we
present only the case of rank-one symmetric matrix estimation, our proof
technique is readily extendable to low-rank symmetric matrix or low-rank
symmetric tensor estimation

categories: cs.IT cond-mat.dis-nn math.IT math.ST stat.TH


title: Quantum corrections to the Mukhanov-Sasaki equations

abstract:
  Recently, a lot of attention has been paid to the modifications of the power
spectrum of primordial fluctuations caused by quantum cosmology effects. The
origin of these modifications are corrections to the Mukhanov-Sasaki equations
that govern the propagation of the primeval cosmological perturbations. The
specific form of these corrections depends on a series of details of the
quantization approach and of the prescription followed to implement it.
Generally, nonetheless, the complexity of the theoretical quantum formulation
is simplified in practice appealing to a semiclassical or effective
approximation, in order to perform concrete numerical computations. In this
work, we introduce technical tools and design a procedure to deal with these
quantum corrections beyond the most direct approximations employed so far in
the literature. In particular, by introducing an interaction picture, we
extract the quantum dynamics of the homogeneous geometry in absence of scalar
field potential and inhomogeneities, dynamics that has been intensively studied
and that can be integrated. The rest of our analysis focuses on the interaction
evolution, putting forward methods to cope with it. The ultimate aim is to
develop treatments that increase our ability to discriminate between the
predictions of different quantization proposals for cosmological perturbations.


title:
Linear and non-linear thermodynamics of a kinetic heat engine with fast
  transformations

abstract:
  We investigate a kinetic heat engine model constituted by particles enclosed
in a box where one side acts as a thermostat and the opposite side is a piston
exerting a given pressure. Pressure and temperature are varied in a cyclical
protocol of period $\tau$ : their relative excursions, $\delta$ and $\epsilon$
respectively, constitute the thermodynamic forces dragging the system
out-of-equilibrium. The analysis of the entropy production of the system allows
to define the conjugated fluxes, which are proportional to the extracted work
and the consumed heat. In the limit of small $\delta$ and $\epsilon$ the fluxes
are linear in the forces through a $\tau$-dependent Onsager matrix whose
off-diagonal elements satisfy a reciprocal relation. The dynamics of the piston
can be approximated, through a coarse-graining procedure, by a Klein-Kramers
equation which - in the linear regime - yields analytic expressions for the
Onsager coefficients and the entropy production. A study of the efficiency at
maximum power shows that the Curzon-Ahlborn formula is always an upper limit
which is approached at increasing values of the thermodynamic forces, i.e.
outside of the linear regime. In all our analysis the adiabatic limit $\tau \to
\infty$ and the the small force limit $\delta,\epsilon \to 0$ are not directly
related.


title: Computational Topology: Isotopic Convergence to a Stick Knot

abstract:
  Computational topology is a vibrant contemporary subfield and this article
integrates knot theory and mathematical visualization. Previous work on
computer graphics developed a sequence of smooth knots that were shown to
converge point wise to a piecewise linear (PL) approximant. This is extended to
isotopic convergence, with that discovery aided by computational experiments.
Sufficient conditions to attain isotopic equivalence can be determined a
priori. These sufficient conditions need not be tight bounds, providing
opportunities for further optimizations. The results presented will facilitate
further computational experiments on the theory of PL knots (also known as
stick knots), where this theory is less mature than for smooth knots.


title:
Heralded single-photon source utilizing highly nondegenerate, spectrally
  factorable spontaneous parametric downconversion

abstract:
  We report on the generation of an indistinguishable heralded single-photon
state, using highly nondegenerate spontaneous parametric downconversion (SPDC).
Spectrally factorable photon pairs can be generated by incorporating a
broadband pump pulse and a group-velocity matching (GVM) condition in a
periodically-poled potassium titanyl phosphate (PPKTP) crystal. The heralding
photon is in the near IR, close to the peak detection efficiency of
off-the-shelf Si single-photon detectors; meanwhile, the heralded photon is in
the telecom L-band where fiber losses are at a minimum. We observe spectral
factorability of the SPDC source and consequently high purity (90%) of the
produced heralded single photons by several different techniques. Because this
source can also realize a high heralding efficiency (> 90%), it would be
suitable for time-multiplexing techniques, enabling a pseudo-deterministic
single-photon source, a critical resource for optical quantum information and
communication technology.