title:
Flexible and scalable particle-in-cell methods for massively parallel
  computations

abstract:
  Particle-in-cell methods couple mesh-based methods for the solution of
continuum mechanics problems, with the ability to advect and evolve particles.
They have a long history and many applications in scientific computing.
However, they have most often only been implemented for either sequential
codes, or parallel codes with static meshes that are statically partitioned. In
contrast, many mesh-based codes today use adaptively changing, dynamically
partitioned meshes, and can scale to thousands or tens of thousands of
processors. Consequently, there is a need to revisit the data structures and
algorithms necessary to use particle methods with modern, mesh-based methods.
Here we review commonly encountered requirements of particle-in-cell methods,
and describe efficient ways to implement them in the context of large-scale
parallel finite-element codes that use dynamically changing meshes. We also
provide practical experience for how to address bottlenecks that impede the
efficient implementation of these algorithms and demonstrate with numerical
tests both that our algorithms can be implemented with optimal complexity and
that they are suitable for very large-scale, practical applications. We provide
a reference implementation in ASPECT, an open source code for geodynamic
mantle-convection simulations built on the deal.II library.


title: The Lackadaisical Quantum Walker is NOT Lazy at all

abstract:
  In this paper, we study the properties of lackadaisical quantum walks on a
line. This model is first proposed in~\cite{wong2015grover} as a quantum
analogue of lazy random walks where each vertex is attached $\tau$ self-loops.
We derive an analytic expression for the localization probability of the walker
at the origin after infinite steps, and obtain the peak velocities of the
walker. We also calculate rigorously the wave function of the walker starting
from the origin and obtain a long time approximation for the entire probability
density function. As an application of the density function, we prove that
lackadaisical quantum walks spread ballistically for arbitrary $\tau$, and give
an analytic solution for the variance of the walker's probability distribution.


title: Rangzen: Anonymously Getting the Word Out in a Blackout

abstract:
  In recent years governments have shown themselves willing to impose blackouts
to shut off key communication infrastructure during times of civil strife, and
to surveil citizen communications whenever possible. However, it is exactly
during such strife that citizens need reliable and anonymous communications the
most. In this paper, we present Rangzen, a system for anonymous broadcast
messaging during network blackouts. Rangzen is distinctive in both aim and
design. Our aim is to provide an anonymous, one-to-many messaging layer that
requires only users' smartphones and can withstand network-level attacks. Our
design is a delay-tolerant mesh network which deprioritizes adversarial
messages by means of a social graph while preserving user anonymity. We built a
complete implementation that runs on Android smartphones, present benchmarks of
its performance and battery usage, and present simulation results suggesting
Rangzen's efficacy at scale.


title:
On Jacobian group and complexity of the generalized Petersen graph
  GP(n,k) through Chebyshev polynomials

abstract:
  In the present paper we find a simple algorithm for counting Jacobian group
of the generalized Petersen graph GP(n,k). Also, we obtain a closed formula for
the number of spanning trees of this graph in terms of Chebyshev polynomials.


title:
A probabilistic graphical model approach in 30 m land cover mapping with
  multiple data sources

abstract:
  There is a trend to acquire high accuracy land-cover maps using multi-source
classification methods, most of which are based on data fusion, especially
pixel- or feature-level fusions. A probabilistic graphical model (PGM) approach
is proposed in this research for 30 m resolution land-cover mapping with
multi-temporal Landsat and MODerate Resolution Imaging Spectroradiometer
(MODIS) data. Independent classifiers were applied to two single-date Landsat 8
scenes and the MODIS time-series data, respectively, for probability
estimation. A PGM was created for each pixel in Landsat 8 data. Conditional
probability distributions were computed based on data quality and reliability
by using information selectively. Using the administrative territory of Beijing
City (Area-1) and a coastal region of Shandong province, China (Area-2) as
study areas, multiple land-cover maps were generated for comparison.
Quantitative results show the effectiveness of the proposed method. Overall
accuracies promoted from 74.0% (maps acquired from single-temporal Landsat
images) to 81.8% (output of the PGM) for Area-1. Improvements can also be seen
when using MODIS data and only a single-temporal Landsat image as input
(overall accuracy: 78.4% versus 74.0% for Area-1, and 86.8% versus 83.0% for
Area-2). Information from MODIS data did not help much when the PGM was applied
to cloud free regions of. One of the advantages of the proposed method is that
it can be applied where multi-temporal data cannot be simply stacked as a
multi-layered image.


title: Beta-plane turbulence above monoscale topography

abstract:
  Using a one-layer QG model, we study the effect of random monoscale
topography on forced beta-plane turbulence. The forcing is a uniform steady
wind stress that produces both a uniform large-scale zonal flow $U(t)$ and
smaller-scale macroturbulence (both standing and transient eddies). The flow
$U(t)$ is retarded by Ekman drag and by the domain-averaged topographic form
stress produced by the eddies. The topographic form stress typically balances
most of the applied wind stress, while the Ekman drag provides all of the
energy dissipation required to balance the wind work. A collection of
statistically equilibrated solutions delineates the main flow regimes and the
dependence of the time-mean $U$ on the problem parameters and the statistical
properties of the topography.
  If $\beta$ is smaller than the topographic PV gradient then the flow consists
of stagnant pools attached to pockets of closed geostrophic contours. The
stagnant dead zones are bordered by jets and the flow through the domain is
concentrated into a narrow channel of open geostrophic contours.
  If $\beta$ is comparable to, or larger than, the topographic PV gradient then
all geostrophic contours are open and the flow is uniformly distributed
throughout the domain. In this case there is an "eddy saturation" regime in
which $U$ is insensitive to changes in the wind stress. We show that eddy
saturation requires strong transient eddies that act as PV diffusion. This PV
diffusion does not alter the energy of the standing eddies, but it does
increase the topographic form stress by enhancing the correlation between
topographic slope and the standing-eddy pressure field. Last, using bounds
based on the energy and enstrophy we show that as the wind stress increases the
flow transitions from a regime in which form stress balances the wind stress to
a regime in which the form stress is very small and large transport ensues.


title: Sample complexity of the distinct elements problem

abstract:
  We consider the distinct elements problem, where the goal is to estimate the
number of distinct colors in an urn containing $ k $ balls based on $n$ samples
drawn with replacements. Based on discrete polynomial approximation and
interpolation, we propose an estimator with additive error guarantee that
achieves the optimal sample complexity within $O(\log\log k)$ factors, and in
fact within constant factors for most cases. The estimator can be computed in
$O(n)$ time for an accurate estimation. The result also applies to sampling
without replacement provided the sample size is a vanishing fraction of the urn
size.
  One of the key auxiliary results is a sharp bound on the minimum singular
values of a real rectangular Vandermonde matrix, which might be of independent
interest.


title:
Revisiting Jackson-Hunt calculations: Unified theoretical analysis for
  generic multi-phase growth in a multi-component system

abstract:
  A straight-forward extension of the Jackson-Hunt theory for directionally
solidifying multi-phase growth where the number of components exceeds the
number of solid phases becomes difficult on account of the absence of the
required number of equations to determine the boundary layer compositions ahead
of the interface. In this paper, we therefore revisit the Jackson-Hunt(JH) type
calculations for any given situation of multi-phase growth in a multi-component
system and self-consistently derive the variations of the compositions of the
solid phases as well as their volume fractions, which grow such that the
composite solid-liquid interface is isothermal. This allows us to unify the
(JH) calculation schemes for both in-variant as well as multi-variant eutectic
reactions. The derived analytical expressions are then utilized to study the
effect of dissimilar solute diffusivities and interfacial energies on the
undercoolings and the solidified fractions. We also perform phase field
simulations to confirm our theoretical predictions and find a good agreement
between our analytical calculations and model predictions for model symmetric
alloys as well as for a particular Ni-Al-Zr alloy.


title: A chain transitive accessible partially hyperbolic diffeomorphism

abstract:
  In this paper, we construct a partially hyperbolic skew-product
diffeomorphism $f$ on $\mathbb{T}^3$, such that $f$ is accessible and chain
transitive, but not transitive.


title: Collider signals of $W'$ and $Z'$ bosons in the gauge-Higgs unification

abstract:
  In the $SO(5)\times U(1)$ gauge-Higgs unification (GHU), Kaluza-Klein (KK)
excited states of charged and neutral vector bosons, $W^{(1)}$, $W_R^{(1)}$,
$Z^{(1)}$, $\gamma^{(1)}$ and $Z_R^{(1)}$, can be observed as $W'$ and $Z'$
signals in collider experiments. In this paper we evaluate the decay rates of
the $W'$ and $Z'$, and $s$-channel cross sections mediated by $W'$ and $Z'$
bosons with final states involving the standard model (SM) fermion pair ($\ell
\nu$, $\ell\bar{\ell}$, $q\bar{q}'$), $WH$, $ZH$, $WW$ and $WZ$. $W'$ and $Z'$
resonances appear around 6.0 TeV (8.5 TeV) for $\theta_H=0.115$ (0.0737) where
$\theta_H$ is the Aharonov-Bohm phase in the fifth dimension in GHU. For decay
rates we find $\Gamma(W'\to WH) \simeq \Gamma(W'\to WZ)$ ($W'=W^{(1)}$,
$W_R^{(1)}$), $\Gamma(W^{(1)}\to WH,WZ) \sim\Gamma(W_R^{(1)}\to WH,WZ)$,
$\Gamma(Z^{(1)}\to ZH) \simeq\sum_{Z'=Z^{(1)},\gamma^{(1)}}\Gamma(Z'\to WW)$,
and $\Gamma(Z_R^{(1)}\to ZH) \simeq \Gamma(Z_R^{(1)}\to WW)$. $W'$ and $Z'$
signals of GHU can be best found at the LHC experiment in the processes $pp\to
W' (Z')+X$ followed by $W'\to t\bar{b}$, $WH$, and $Z'\to e^+ e^-$,
$\mu^+\mu^-, ZH$. For the lighter $Z'$ ($\theta_H = 0.115$) case, with
forthcoming 30 fb$^{-1}$ data of the 13 TeV LHC experiment we expect about ten
$\mu^+\mu^-$ events for the invariant mass range 3 to 7 TeV, though the number
of the events becomes much smaller when $\theta_H=0.0737$. In the process with
$WZ$ in the final state, it is confirmed that the unitarity is preserved,
provided that all KK excited intermediate states are taken into account.
Deviation of the $WWZ$ coupling from the SM is very tiny. Exotic partners
$t_T^{(1)}$ and $b_Y^{(1)}$ of the top and bottom quarks with electric charge
$+5/3$ and $-4/3$ have mass $M_{t_T^{(1)},b_Y^{(1)}}\simeq 4-5$ TeV, becoming
the lightest non-SM particles in GHU which can be singly produced in collider
experiments.


title:
Thermodynamics of a time dependent and dissipative oval billiard: a heat
  transfer and billiard approach

abstract:
  We study some statistical properties for the behavior of the average squared
velocity -- hence the temperature -- for an ensemble of classical particles
moving in a billiard whose boundary is time dependent. We assume the collisions
of the particles with the boundary of the billiard are inelastic leading the
average squared velocity to reach a steady state dynamics for large enough
time. The description of the stationary state is made by using two different
approaches: (i) heat transfer motivated by the Fourier law and, (ii) billiard
dynamics using either numerical simulations and theoretical description.


title: Curvature Induced Topological Defects of $p$-wave Superfluid on a Sphere

abstract:
  We study the ground state of spinless fermions living on a sphere across
$p$-wave Feschbach resonances. By construsting a microscopic model of fermions
on a general curved surface, we show that the Guassian curvature induces an
emergent magnetic field coupled to the $p\pm ip$ order parameters. In the case
of a sphere, the magnetic field corresponds to a Dirac monopole field, which
causes topological defects in the superfluid ground state. Using the BCS mean
field theory, we calculate its many-body ground state self consistently and
give the phase diagram. The ground state may exhibit two types of topological
defects, two voritces on the south and north pole or a domain wall which
separates $p_\theta+ ip_\phi$ and $p_\theta-ip_\phi$ superfluids.


title: Detecting planet pairs in mean motion resonances via astrometry method

abstract:
  GAIA leads us to step into a new era with a high astrometry precision of 10
uas. Under such a precision, astrometry will play important roles in detecting
and characterizing exoplanets. Specially, we can identify planet pairs in mean
motion resonances(MMRs) via astrometry, which constrains the formation and
evolution of planetary systems. In accordance with observations, we consider
two Jupiters or two super-Earths systems in 1:2, 2:3 and 3:4 MMRs. Our
simulations show the false alarm probabilities(FAPs) of a third planet are
extremely small while the real two planets can be good fitted with
signal-to-noise ratio(SNR)> 3. The probability of reconstructing a resonant
system is related with the eccentricities and resonance intensity. Generally,
when SNR >= 10, if eccentricities of both planets are larger than 0.01 and the
resonance is quite strong, the probabilities to reconstruct the planet pair in
MMRs >= 80%. Jupiter pairs in MMRs are reconstructed more easily than
super-Earth pairs with similar SNR when we consider the dynamical stability.
FAPs are also calculated when we detect planet pairs in or near MMRs. FAPs for
1:2 MMR are largest, i.e., FAPs > 15% when SNR <= 10. Extrapolating from the
Kepler planet pairs near MMRs and assuming SNR to be 3, we will discover and
reconstruct a few tens of Jupiter pairs and hundreds of super-Earth pairs in
2:3 and 1:2 MMRs within 30 pc. We also compare the differences between even and
uneven data cadence and find that planets are better measured with more uniform
phase coverage.


title: A Novel Motion Detection Method Resistant to Severe Illumination Changes

abstract:
  Recently, there has been a considerable attention given to the motion
detection problem due to the explosive growth of its applications in video
analysis and surveillance systems. While the previous approaches can produce
good results, an accurate detection of motion remains a challenging task due to
the difficulties raised by illumination variations, occlusion, camouflage,
burst physical motion, dynamic texture, and environmental changes such as those
on climate changes, sunlight changes during a day, etc. In this paper, we
propose a novel per-pixel motion descriptor for both motion detection and
dynamic texture segmentation which outperforms the current methods in the
literature particularly in severe scenarios. The proposed descriptor is based
on two complementary three-dimensional-discrete wavelet transform (3D-DWT) and
three-dimensional wavelet leader. In this approach, a feature vector is
extracted for each pixel by applying a novel three dimensional wavelet-based
motion descriptor. Then, the extracted features are clustered by a clustering
method such as well-known k-means algorithm or Gaussian Mixture Model (GMM).
The experimental results demonstrate the effectiveness of our proposed method
compared to the other motion detection approaches from the literature. The
application of the proposed method and additional experimental results for the
different datasets are available at
(http://dspl.ce.sharif.edu/motiondetector.html).


title: A survey of configurations

abstract:
  To any finite ordered subset and any finite partition of a group a set of
tuples of positive integers, named as configurations, is associated that
describes the group's behavior. The present paper provides an exposition of
this notion and related topics, including amenability, paradoxical
decomposition and the group theoretical properties.


title:
Locations of Roberge-Weiss transition endpoints in lattice QCD with
  $N_f=2$ improved KS quarks

abstract:
  Result on the locations of the tricritical points of $N_f=2$ lattice QCD with
imaginary chemical potential is presented. Simulations are carried out with
Symanzik improved gauge action and Asqtad fermion action. With imaginary
chemical potential $i\mu_I=i\pi T$, previous studies show that the
Roberge-Weiss (RW) transition endpoints are triple points at both large and
small quark masses, and second order transition points at intermediate quark
masses. The triple and second order endpoints are separated by two tricritical
ones. Our simulations are carried out at 7 values of quark mass $am$ ranging
from 0.024 to 0.070 on lattice volume $12^3\times 4, 16^3\times 4,\,
20^3\times4$. The susceptibility and Binder cumulant of the imaginary part of
Polyakov loop are employed to determine the nature of RW transition endpoints.
The simulations suggest that the two tricritical points are within the range
$0.024-0.026$ and $0.040-0.050$, respectively.


title:
Spatial Charge Inhomogeneity and Defect States in Topological Dirac
  Semimetal Thin Films

abstract:
  The close approach of the Fermi energy EF of a Dirac semimetal to the Dirac
point ED uncovers new physics such as velocity renormalization,1,2,3 and the
Dirac plasma 4,5 at |EF -ED| < kBT, where kBT is the thermal energy. In
graphene, substrate disorder drives fluctuations in EF. Three-dimensional
topological Dirac semimetals (TDS)6,7 obviate the substrate, and should show
reduced EF fluctuations due to better metallic screening and higher dielectric
constants. Here we map the potential fluctuations in TDS Na3Bi using a scanning
tunneling microscope. The rms potential fluctuations are significantly smaller
than room temperature ({\Delta}EF,rms = 4-6 meV = 40-70 K) and comparable to
the highest quality graphene on h-BN;8 far smaller than graphene on SiO2,9,10
or the Dirac surface state of a topological insulator.11 Surface Na vacancies
produce a novel resonance close to the Dirac point with surprisingly large
spatial extent and provides a unique way to tune the surface density of states
in a TDS thin-film material.


title:
Superconvergence analysis of DG-FEM based on the polynomial preserving
  recovery for Helmholtz equation with high wave number

abstract:
  We study superconvergence property of the linear discontinuous Galerkin
finite element method with the polynomial preserving recovery (PPR) and
Richardson extrapolation for the two dimensional Helmholtz equation. The error
estimate with explicit dependence on the wave number $k$, the penalty parameter
$\mu$ and the mesh condition parameter $\alpha$ is derived. First, we prove
that under the assumption $k(kh)^2\leq C_0$ ($h$ is the mesh size) and certain
mesh condition, the estimate between the finite element solution and the linear
interpolation of the exact solution is superconvergent under the
$\norme{\cdot}$-seminorm. Second, we prove a superconvergence result for the
recovered gradient by PPR. Furthermore, we estimate the error between the
finite element gradient and recovered gradient, which motivate us to define the
a posteriori error estimator. Finally, Some numerical examples are provided to
confirm the theoretical results of superconvergence analysis. All theoretical
findings are verified by numerical tests.


title:
Metallicities in long GRB host galaxies at z$<$0.5 calculated by the
  detailed modelling of optical and infrared line ratios

abstract:
  We revisited the line spectra emitted from long GRB (LGRB) host galaxies at
z<0.5 in order to calculate by the detailed modelling of the line ratios the
physical conditions and relative abundances in LGRB hosts in this redshift
range. We have found lower metallicities than in LGRB hosts at higher z. New
results about metallicities and physical conditions in the different regions
throughout the LGRB 980425 host at z=0.0085 are presented. In particular, we
have found that the effective starburst temperature in the supernova (SN)
region is the highest throughout the host galaxy. The low ionization parameter
reveals that the radiation source is far or somehow prevented from reaching the
emitting gas in the SN region. The models constrained by a few oxygen, nitrogen
and sulphur line ratios to Hb in LGRB 980425 host satisfactorily reproduce the
HeII/Hb and [ArIII]/Hb line ratios. The modelling of the observed
[SIV]10.51\mu/[SIII]18.71\mum and [NeIII]10.6\mum/[NeII]12.81\mum line ratios
from LGRB 031203 host galaxy at z=0.105 shows that the mid-IR lines are emitted
from geometrically thin shock dominated filaments which are not reached by the
photoionizing flux, while the optical lines are emitted from the radiation
dominated outflowing clouds.


title: Surface magnetism of cool stars

abstract:
  Magnetic fields are essential ingredients of many physical processes in the
interiors and envelopes of cool stars. Yet their direct detection and
characterisation is notoriously difficult, requiring high-quality observations
and advanced analysis techniques. Significant progress has been recently
achieved by several types of direct magnetic field studies on the surfaces of
cool active stars. In particular, complementary techniques of the field
topology mapping with polarisation data and total magnetic flux measurements
from intensity spectra have been systematically applied to different classes of
active stars leading to interesting and occasionally controversial results. In
this paper we summarise the current status of direct magnetic field studies of
cool stars, and investigations of surface inhomogeneities caused by the field,
based on the material presented at the Cool Stars 19 splinter session.


title: Central limit theorems for supercritical superprocesses with immigration

abstract:
  In this paper, we establish a central limit theorem for a large class of
general supercritical superprocesses with immigration with spatially dependent
branching mechanisms satisfying a second moment condition. This central limit
theorem extends and generalizes the results obtained by Ren, Song and
Zhang[2015]. We first give law of large numbers for supercritical
superprocesses with immigration since there is few convergence result on
immigration superprocesses, then based on these results, we establish the
central limit theorem.


title: On groups of H\"older diffeomorphisms and their regularity

abstract:
  We study the set $\mathcal D^{n,\beta}(\mathbb R^d)$ of orientation
preserving diffeomorphisms of $\mathbb R^d$ which differ from the identity by a
H\"older $C^{n,\beta}_0$-mapping, where $n \in \mathbb N_{\ge 1}$ and $\beta
\in (0,1]$. We show that $\mathcal D^{n,\beta}(\mathbb R^d)$ forms a group, but
left translations in $\mathcal D^{n,\beta}(\mathbb R^d)$ are in general
discontinuous. The groups $\mathcal D^{n,\beta-}(\mathbb R^d) :=
\bigcap_{\alpha < \beta} \mathcal D^{n,\alpha}(\mathbb R^d)$ (with its natural
Fr\'echet topology) and $\mathcal D^{n,\beta+}(\mathbb R^d) := \bigcup_{\alpha
> \beta} \mathcal D^{n,\alpha}(\mathbb R^d)$ (with its natural inductive
locally convex topology) however are $C^{0,\omega}$ Lie groups for any slowly
vanishing modulus of continuity $\omega$. In particular, $\mathcal
D^{n,\beta-}(\mathbb R^d)$ is a topological group and a so-called half-Lie
group (with smooth right translations). We prove that the H\"older spaces
$C^{n,\beta}_0$ are ODE closed, in the sense that pointwise time-dependent
$C^{n,\beta}_0$-vector fields $u$ have unique flows $\Phi$ in $\mathcal
D^{n,\beta}(\mathbb R^d)$. This includes, in particular, all Bochner integrable
functions $u \in L^1([0,1],C^{n,\beta}_0(\mathbb R^d,\mathbb R^d))$. For the
latter and $n\ge 2$, we show that the flow map $L^1([0,1],C^{n,\beta}_0(\mathbb
R^d,\mathbb R^d)) \to C([0,1],\mathcal D^{n,\alpha}(\mathbb R^d))$, $u \mapsto
\Phi$, is continuous (even $C^{0,\beta-\alpha}$), for every $\alpha < \beta$.
As an application we prove that the corresponding Trouv\'e group $\mathcal
G_{n,\beta}(\mathbb R^d)$ from image analysis coincides with the connected
component of the identity of $\mathcal D^{n,\beta}(\mathbb R^d)$.


title: Massive Neutral Gas Outflow in Reddened Quasar SDSS J072910.34+333634.3

abstract:
  SDSS J072910.34+333634.3 is a reddened quasar at z=0.96. The archivel
Keck/ESI spectrum and our new P200/TripleSpec spectrum reveal an absorption
line system in He I*, Ca II H\&K and Na ID. The absorption line system has a
width of $\sim$600 km/s and a blueshift velocity of $\sim$800 km/s relative to
the core of narrow emission lines, indicating an outflow. Using the Ca II
doublet, we determined that the outflowing gas covers $\sim$70\% of the
continuum. On the other hand, the HST/ACS image which taken in rest-frame 4130
\AA\ show that the fraction of the quasar emission in ESI aperture was $<$40\%.
We thus conclude that the absorbing gas covers a significant fraction of
extended starlight emission, and the best-estimated fraction of $\sim$50\%
yields a lower limit of the crosssectional area of the outflowing gas to be
$>$8 kpc$^2$. The strong Na\&Ca absorption suggests that the absorbing gas is
thick and mostly neutral, which is also supported by dust extinction
$A_V\sim3$. Using the best-estimated hydrogen column density
$N_H\sim3\times10^{22}$ cm$^{-2}$, the total mass of the outflowing gas is
$>3\times10^9 M_\odot$. The outflow is likely to be driven by AGN because of
the $\sim$800 km/s blueshift velocity, suggesting SDSS J072910.34+333634.3 is
undergoing one of the most violent AGN feedback we have seen. In the future,
one can find more such massive neutral gas outflows in other reddened quasars
using similar method, and this can shed new light on the study of AGN feedback.


title:
Analog curved spacetimes in the reversed dissipation regime of cavity
  optomechanics

abstract:
  In this paper, we theoretically propose an optomechanical scheme to explore
the possibility of simulating the propagation of the collective excitations of
the photon fluid in a curved spacetime. For this purpose, we introduce two
theoretical models for two-dimensional photon gas in a planar optomechanical
microcavity and a two-dimensional array of coupled optomechanical systems. In
the reversed dissipation regime (RDR) of cavity optomechanics where the
mechanical oscillator reaches equilibrium with its thermal reservoir much
faster than the cavity modes, the mechanical degrees of freedom can
adiabatically be eliminated. The adiabatic elimination of the mechanical mode
provides an effective nonlinear Kerr-type photon-photon interaction. Using the
nonlinear Schr\"{o}dinger equation (NLSE), we show that the phase fluctuations
in the two-dimensional photon fluid obey the Klein-Gordon equation for a
massless scalar field propagating in a curved spacetime. The results reveal
that the photon fluid as well as the corresponding metric can be controlled by
manipulating the system parameters.


title:
Exact recovery low-rank matrix via transformed affine matrix rank
  minimization

abstract:
  The goal of affine matrix rank minimization problem is to reconstruct a
low-rank or approximately low-rank matrix under linear constraints. In general,
this problem is combinatorial and NP-hard. In this paper, a nonconvex fraction
function is studied to approximate the rank of a matrix and translate this
NP-hard problem into a transformed affine matrix rank minimization problem. The
equivalence between these two problems is established, and we proved that the
uniqueness of the global minimizer of transformed affine matrix rank
minimization problem also solves affine matrix rank minimization problem if
some conditions are satisfied. Moreover, we also proved that the optimal
solution to the transformed affine matrix rank minimization problem can be
approximately obtained by solving its regularization problem for some proper
smaller $\lambda>0$. Lastly, the DC algorithm is utilized to solve the
regularization transformed affine matrix rank minimization problem and the
numerical experiments on image inpainting problems show that our method
performs effectively in recovering low-rank images compared with some
state-of-art algorithms.


title:
Quantum field theory and classical optics: determining the fine
  structure constant

abstract:
  The properties of the vacuum are described by quantum physics including the
response to external fields such as electromagnetic radiation. Of the two
parameters that govern the details of the electromagnetic field dynamics in
vacuum, one is fixed by the requirement of Lorentz invariance $c=
1/\sqrt{\varepsilon_{0} \mu_{0}}$. The other one, $Z_{0}=
\sqrt{\mu_{0}/\varepsilon_{0}} = 1/(c\varepsilon_{0})$ and its relation to the
quantum vacuum, is discussed in this contribution. Deriving $\varepsilon_{0}$
from the properties of the quantum vacuum implies the derivation of the fine
structure constant.


title: Magnetic-proximity-induced magnetoresistance on topological insulators

abstract:
  We theoretically study the magnetoresistance (MR) of two-dimensional massless
Dirac electrons as found on the surface of three-dimensional topological
insulators (3D TIs) that is capped by a ferromagnetic insulator (FI). We
calculate charge and spin transport by Kubo and Boltzmann theories, taking into
account the ladder-vertex correction and the in-scattering due to normal and
magnetic disorder. The induced exchange splitting is found to generate an
electric conductivity that depends on the magnetization orientation, but its
form is very different from both the anisotropic and spin Hall MR. The in-plane
MR vanishes identically for non-magnetic disorder, while out-of-plane
magnetizations cause a large MR ratio. On the other hand, we do find an
in-plane MR and planar Hall effect in the presence of magnetic disorder aligned
with the FI magnetization. Our results may help understand recent transport
measurements on TI|FI systems.


title: Point-contact function of the electron-phonon interaction in zirconium

abstract:
  Experimental study of the electron-phonon interaction (EPI) spectra of
zirconium was carried out using Yanson's point-contact (PC) spectroscopy. The
EPI spectral function and constant were determined. Both homocontacts ($Zr-Zr$)
and heterocontacts ($Zr-Cu$, $Zr-Ag$, and $Zr-Au$) were studied. No
contribution by copper, silver or gold to the heterocontact spectra was
detected. The positions of five phonon features of the EPI function were
observed at energies 5-6, 9-11, 13-15, 18-20, and 27-29 $meV$. The observed
diversity of the PC spectra was attributed to the anisotropy of $Zr$.
pacs{71.38.-k, 73.40.Jn, 74.25.Kc, 74.45.+c}


title: Axis systems of link projections

abstract:
  An axis of a link projection is a closed curve which lies symmetrically on
each region of the link projection. In this paper we define axis systems of
link projections and characterize axis systems of the standard projections of
twist knots.


title: Temperature dependence of the plastic scintillator detector for DAMPE

abstract:
  The Plastic Scintillator Detector (PSD) is one of the main sub-detectors in
the DArk Matter Particle Explorer (DAMPE) project. It will be operated over a
large temperature range from -$10$ to $30^{\circ}$C, so the temperature effect
of the whole detection system should be studied in detail. The temperature
dependence of the PSD system is mainly contributed by the three parts: the
plastic scintillator bar, the photomultiplier tube (PMT), and the Front End
Electronics (FEE). These three parts have been studied in detail and the
contribution of each part has been obtained and discussed. The temperature
coefficient of the PMT is $-0.320(\pm0.033)\%/^{\circ}$C, and the coefficient
of the plastic scintillator bar is $-0.036(\pm0.038)\%/^{\circ}$C. This result
means that after subtracting the FEE pedestal, the variation of the signal
amplitude of the PMT-scintillator system due to temperature mainly comes from
the PMT, and the plastic scintillator bar is not sensitive to temperature over
the operating range. Since the temperature effect cannot be ignored, the
temperature dependence of the whole PSD has been also studied and a correction
has been made to minimize this effect. The correction result shows that the
effect of temperature on the signal amplitude of the PSD system can be
suppressed.


title:
A parallel interaction potential approach coupled with the immersed
  boundary method for fully resolved simulations of deformable interfaces and
  membranes

abstract:
  In this paper we show and discuss the use of a versatile interaction
potential approach coupled with an immersed boundary method to simulate a
variety of flows involving deformable bodies. In particular, we focus on two
kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii)
flow in the left ventricle of the heart with either a mechanical or a natural
valve. Both examples have in common the two-way interaction of the flow with a
deformable interface or a membrane. The interaction potential approach (de
Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura,
Computational Biomechanics, 2016) with minor modifications can be used to
capture the deformation dynamics in both classes of problems. We show that the
approach can be used to replicate the deformation dynamics of liquid-liquid
interfaces through the use of ad-hoc elastic constants. The results from our
simulations agree very well with previous studies on the deformation of drops
in standard flow configurations such as deforming drop in a shear flow or a
cross flow. We show that the same potential approach can also be used to study
the flow in the left ventricle of the heart. The flow imposed into the
ventricle interacts dynamically with the mitral valve (mechanical or natural)
and the ventricle which are simulated using the same model. Results from these
simulations are compared with ad- hoc in-house experimental measurements.
Finally, a parallelisation scheme is presented, as parallelisation is
unavoidable when studying large scale problems involving several thousands of
simultaneously deforming bodies on hundreds of distributed memory computing
processors.


title: Towards a theoretical description of dense QCD

abstract:
  The properties of matter at finite baryon densities play an important role
for the astrophysics of compact stars as well as for heavy ion collisions or
the description of nuclear matter. Because of the sign problem of the quark
determinant, lattice QCD cannot be simulated by standard Monte Carlo at finite
baryon densities. I review alternative attempts to treat dense QCD with an
effective lattice theory derived by analytic strong coupling and hopping
expansions, which close to the continuum is valid for heavy quarks only, but
shows all qualitative features of nuclear physics emerging from QCD. In
particular, the nuclear liquid gas transition and an equation of state for
baryons can be calculated directly from QCD. A second effective theory based on
strong coupling methods permits studies of the phase diagram in the chiral
limit on coarse lattices.


title:
An Improved Diffuse Foreground Subtraction by ILC method: CMB Map and
  Angular Power Spectrum using Planck and WMAP Observations

abstract:
  We report an improved technique for diffuse foreground minimization from
Cosmic Microwave Background (CMB) maps using a new multi-phase iterative
internal-linear-combination (ILC) approach in harmonic space. The new procedure
consists of two phases. In phase 1, a diffuse foreground cleaned map is
obtained by performing a usual ILC operation in the harmonic space in a single
iteration over the desired portion of the sky. In phase 2, we obtain the final
foreground cleaned map using an iterative ILC approach also in the harmonic
space, however, now, during each iteration of foreground minimization, some of
the regions of the sky that are not being cleaned in the current iteration, are
replaced by the corresponding cleaned portions of the phase 1 cleaned map. The
new ILC method nullifies a foreground leakage signal that is otherwise
inevitably present in the old and usual harmonic space iterative ILC method.
The new method is flexible to handle input frequency maps, irrespective of
whether or not they initially have the same instrumental and pixel resolution,
by bringing them to a common and maximum possible beam and pixel resolution at
the beginning of the analysis. This dramatically reduces data redundancy and
hence memory usage and computational cost. During the ILC weight calculation it
avoids any need to deconvolve partial sky spherical harmonic coefficients by
the beam and pixel window functions, which in strict mathematical sense, is not
well-defined for azimuthally symmetric window functions. Using WMAP 9-year and
Planck-2015 published frequency maps we obtain a pair of foreground cleaned CMB
maps and CMB angular power spectrum. Our power spectrum match well with
Planck-2015 results, with some difference. Finally, we show that the weights
for ILC foreground minimization have an intrinsic characteristic that it tends
to produce a statistically isotropic CMB map as well.


title: Improved Quick Hypervolume Algorithm

abstract:
  In this paper, we present a significant improvement of Quick Hypervolume
algorithm, one of the state-of-the-art algorithms for calculating exact
hypervolume of the space dominated by a set of d-dimensional points. This value
is often used as a quality indicator in multiobjective evolutionary algorithms
and other multiobjective metaheuristics and the efficiency of calculating this
indicator is of crucial importance especially in the case of large sets or many
dimensional objective spaces. We use a similar divide and conquer scheme as in
the original Quick Hypervolume algorithm, but in our algorithm we split the
problem into smaller sub-problems in a different way. Through both theoretical
analysis and computational study we show that our approach improves
computational complexity of the algorithm and practical running times.


title:
Mechanisms of stochastic onset and termination of atrial fibrillation
  episodes: Insights using a cellular automaton model

abstract:
  Mathematical models of cardiac electrical excitation are increasingly
complex, with multiscale models seeking to represent and bridge physiological
behaviours across temporal and spatial scales. The increasing complexity of
these models makes it computationally expensive to both evaluate long term (>60
seconds) behaviour and determine sensitivity of model outputs to inputs. This
is particularly relevant in models of atrial fibrillation (AF), where
individual episodes last from seconds to days, and inter-episode waiting times
can be minutes to months. Potential mechanisms of transition between sinus
rhythm and AF have been identified but are not well understood, and it is
difficult to simulate AF for long periods of time using state-of-the-art
models. In this study, we implemented a Moe-type cellular automaton on a novel,
topologically correct surface geometry of the left atrium. We used the model to
simulate stochastic initiation and spontaneous termination of AF, arising from
bursts of spontaneous activation near pulmonary veins. The simplified
representation of atrial electrical activity reduced computational cost, and so
permitted us to investigate AF mechanisms in a probabilistic setting. We
computed large numbers (~10^5) of sample paths of the model, to infer
stochastic initiation and termination rates of AF episodes using different
model parameters. By generating statistical distributions of model outputs, we
demonstrated how to propagate uncertainties of inputs within our microscopic
level model up to a macroscopic level. Lastly, we investigated spontaneous
termination in the model and found a complex dependence on its past AF
trajectory, the mechanism of which merits future investigation.


title: Selective solute adsorption and partitioning around single PNIPAM chains

abstract:
  Thermoresponsive polymer architectures have become integral building blocks
of 'smart' functional materials in modern applications. For a large range of
developments, e.g., for drug delivery or nanocatalytic carrier systems, the
selective adsorption and partitioning of molecules (ligands or reactants)
inside the polymeric matrix are key processes that have to be controlled and
tuned for the desired material function. In order to gain insights into the
nanoscale structure and binding details in such systems, we here employ
molecular dynamics simulations of the popular poly(N-isopropylacrylamide)
(PNIPAM) polymer in explicit water in the presence of various representative
solute types with focus on aromatic model reactants. We model a PNIPAM polymer
chain and explore the influence of its elongation, stereochemistry, and
temperature on the solute binding affinities. While we find that the excess
adsorption generally raises with the size of the solute, the temperature-
dependent affinity to the chains is highly solute specific and has a
considerable dependence on the polymer elongation (i.e., polymer swelling
state). We elucidate the molecular mechanisms of the selective binding in
detail and eventually present how the results can be extrapolated to
macroscopic partitioning of the solutes in swollen polymer architectures, such
as hydrogels.


title:
Maximal Entanglement and Teleportation using an Arthurs-Kelly type
  Interaction for Qubits

abstract:
  We study entanglement generation between a system qubit and three apparatus
qubits using an exactly solvable Arthurs-Kelly type model. We demonstrate the
possibility of generating an EPR-like maximally entangled system-apparatus
state, in which the second qubit of the usual EPR state is replaced by a three
qubit state. We design a very simple protocol to transfer the unknown state of
the system onto one of the apparatus qubits which can then be sent elsewhere
via a quantum channel. This protocol can be seen as an alternative
teleportation scheme.


title:
Interacting Holographic Dark Energy model in Brans-Dicke cosmology and
  coincidence problem

abstract:
  We study the dynamics of interacting holographic dark energy model in
Brans-Dicke cosmology for the future event horizon and the Hubble horizon
cut-offs. We determine the system of first-order differential equations for the
future event horizon and Hubble horizon cut-offs, and obtain the corresponding
fixed points, attractors, repellers and saddle points. Finally, we investigate
the cosmic coincidence problem in this model for the future event horizon and
Hubble horizon cut-offs and find that for both cut-offs and for a variety of
Brans-Dicke parameters the coincidence problem is almost resolved.


title:
Regression-based variance reduction approach for strong approximation
  schemes

abstract:
  In this paper we present a novel approach towards variance reduction for
discretised diffusion processes. The proposed approach involves specially
constructed control variates and allows for a significant reduction in the
variance for the terminal functionals. In this way the complexity order of the
standard Monte Carlo algorithm ($\varepsilon^{-3}$) can be reduced down to
$\varepsilon^{-2}\sqrt{\left|\log(\varepsilon)\right|}$ in case of the Euler
scheme with $\varepsilon$ being the precision to be achieved. These theoretical
results are illustrated by several numerical examples.


title: Cohen-Macaulay properties under the amalgamated construction

abstract:
  Let $A$ and $B$ be commutative rings with unity, $f:A\to B$ a ring
homomorphism and $J$ an ideal of $B$. Then the subring
$A\bowtie^fJ:=\{(a,f(a)+j)|a\in A$ and $j\in J\}$ of $A\times B$ is called the
amalgamation of $A$ with $B$ along $J$ with respect to $f$. In this paper, we
study the property of Cohen-Macaulay in the sense of ideals which was
introduced by Asgharzadeh and Tousi, a general notion of the usual
Cohen-Macaulay property (in the Noetherian case), on the ring $A\bowtie^fJ$.
Among other things, we obtain a generalization of the well-known result that
when the Nagata's idealization is Cohen-Macaulay.


title: A New Spectral Method for Latent Variable Models

abstract:
  This paper presents an algorithm for the unsupervised learning of latent
variable models from unlabeled sets of data. We base our technique on spectral
decomposition, providing a technique that proves to be robust both in theory
and in practice. We also describe how to use this algorithm to learn the
parameters of two well known text mining models: single topic model and Latent
Dirichlet Allocation, providing in both cases an efficient technique to
retrieve the parameters to feed the algorithm. We compare the results of our
algorithm with those of existing algorithms on synthetic data, and we provide
examples of applications to real world text corpora for both single topic model
and LDA, obtaining meaningful results.


title: An abstract approach to Glivenko's theorem

abstract:
  The aim of this work is to provide a special kind of conservative translation
between abstract logics, namely an \textit{abstract Glivenko's theorem}.
Firstly we define institutions on the categories of logic, algebraizable
logics, and Lindenbaum algebraizable logic. In the sequel, we introduce the
notion os Glivenko's context relating two algebraizable logics (respectively,
Lindenbaum algebraizable logics) and we prove that for each Glivenko's context
can be associated an institutions morphism between the corresponding logical
institutions. As a consequence of the existence of such institutions morphisms,
we have established abstract versions of Glivenko's theorem between those
algebraizable logics (Lindenbaum algebraizable logics), generalizing the
results presented in \cite{To}. In particular, considering the institutions of
classical logic and of intuitionistic logic, we build a Glivenko's context and
thus an abstract Glivenko's theorem that is exactly the traditional Glivenko's
theorem. Finally we present a category of algebraizable logic with Glivenko's
context as morphisms. We can interpret the results of this work as an evidence
of the (virtually unexplored) relevance of institution theory in the study of
propositional logic.


title: Distribution of Points on Abelian Covers Over Finite Fields

abstract:
  We determine in this paper the distribution of the number of points on the
covers of $\mathbb{P}^1(\mathbb{F}_q)$ such that $K(C)$ is a Galois extension
and $\mbox{Gal}(K(C)/K)$ is abelian when $q$ is fixed and the genus, $g$, tends
to infinity. This generalizes the work of Kurlberg and Rudnick and Bucur,
David, Feigon and Lalin who considered different families of curves over
$\mathbb{F}_q$. In all cases, the distribution is given by a sum of $q+1$
random variables.


title: Non-Redundant Spectral Dimensionality Reduction

abstract:
  Spectral dimensionality reduction algorithms are widely used in numerous
domains, including for recognition, segmentation, tracking and visualization.
However, despite their popularity, these algorithms suffer from a major
limitation known as the "repeated Eigen-directions" phenomenon. That is, many
of the embedding coordinates they produce typically capture the same direction
along the data manifold. This leads to redundant and inefficient
representations that do not reveal the true intrinsic dimensionality of the
data. In this paper, we propose a general method for avoiding redundancy in
spectral algorithms. Our approach relies on replacing the orthogonality
constraints underlying those methods by unpredictability constraints.
Specifically, we require that each embedding coordinate be unpredictable (in
the statistical sense) from all previous ones. We prove that these constraints
necessarily prevent redundancy, and provide a simple technique to incorporate
them into existing methods. As we illustrate on challenging high-dimensional
scenarios, our approach produces significantly more informative and compact
representations, which improve visualization and classification tasks.


title:
Efficient Methods and Parallel Execution for Algorithm Sensitivity
  Analysis with Parameter Tuning on Microscopy Imaging Datasets

abstract:
  Background: We describe an informatics framework for researchers and clinical
investigators to efficiently perform parameter sensitivity analysis and
auto-tuning for algorithms that segment and classify image features in a large
dataset of high-resolution images. The computational cost of the sensitivity
analysis process can be very high, because the process requires processing the
input dataset several times to systematically evaluate how output varies when
input parameters are varied. Thus, high performance computing techniques are
required to quickly execute the sensitivity analysis process.
  Results: We carried out an empirical evaluation of the proposed method on
high performance computing clusters with multi-core CPUs and co-processors
(GPUs and Intel Xeon Phis). Our results show that (1) the framework achieves
excellent scalability and efficiency on a high performance computing cluster --
execution efficiency remained above 85% in all experiments; (2) the parameter
auto-tuning methods are able to converge by visiting only a small fraction
(0.0009%) of the search space with limited impact to the algorithm output
(0.56% on average).
  Conclusions: The sensitivity analysis framework provides a range of
strategies for the efficient exploration of the parameter space, as well as
multiple indexes to evaluate the effect of parameter modification to outputs or
even correlation between parameters. Our work demonstrates the feasibility of
performing sensitivity analyses, parameter studies, and auto-tuning with large
datasets with the use of high-performance systems and techniques. The proposed
technologies will enable the quantification of error estimations and output
variations in these pipelines, which may be used in application specific ways
to assess uncertainty of conclusions extracted from data generated by these
image analysis pipelines.


title:
Composite fermions in graphene fractional quantum Hall state at half
  filling: evidence for Dirac composite fermions

abstract:
  Composite fermions in fractional quantum Hall (FQH) systems are believed to
form a Fermi sea of weakly interacting particles at half filling $\nu=1/2$.
Recently, it was proposed (D. T. Son, Phys. Rev. X 5, 031027 (2015)) that these
composite fermions are Dirac particles. In our work, we demonstrate
experimentally that composite fermions found in monolayer graphene are Dirac
particles at half filling. Our experiments have addressed FQH states in
high-mobility, suspended graphene Corbino disks in the vicinity of $\nu=1/2$.
We find strong temperature dependence of conductivity $\sigma$ away from half
filling, which is consistent with the expected electron-electron interaction
induced gaps in the FQH state. At half filling, however, the temperature
dependence of conductivity $\sigma(T)$ becomes quite weak as expected for a
Fermi sea of composite fermions and we find only logarithmic dependence of
$\sigma$ on $T$. The sign of this quantum correction coincides with weak
antilocalization of composite fermions, which reveals the relativistic Dirac
nature of composite fermions in graphene.


title:
Superconductivity in Se-doped new materials EuSr2Bi2S4F4 and
  Eu2SrBi2S4F4

abstract:
  From our powder x ray diffraction pattern, electrical transport and magnetic
studies we report the effect of isovalent Se substitution at S sites in the
newly discovered systems EuSr2Bi2S4F4 and Eu2SrBi2S4F4. We have synthesized two
new variants of 3244 type superconductor with Eu replaced by Sr which is
reported elsewhere [Z. Haque et. al.]. We observe superconductivity at Tc 2.9 K
(resistivity) and 2.3 K (susceptibility) in EuSr2Bi2S4-xSexF4 series for x = 2.
In the other series Eu2SrBi2S4-xSexF4, two materials (x= 1.5; Tc = 2.6 K and x
= 2; Tc = 2.75 K) exhibit superconductivity.


title: An uniform General Neron Desingularization in dimension one

abstract:
  We give an uniform General Neron Desingularization for one dimensional local
rings with respect to morphisms which coincide modulo a high power of the
maximal ideal. The result has interesting applications in the case of
Cohen-Macaulay rings.


title: Symmetry breaking in light-front $\phi^4$ theory

abstract:
  We consider the symmetric and broken phases of light-front $\phi^4$ theory in
two dimensions. In both cases the mass of the lowest state is computed and its
dependence on the coupling used to infer critical coupling values. The
structure of the eigenstate is examined to determine whether it shows the signs
of critical behavior, specifically whether the one-body sector becomes
improbable relative to the higher Fock sectors. In attempts to establish this
behavior, we consider both sector-independent and sector-dependent constituent
masses.


title:
Total pion-proton cross-section from the new LHCf data on leading
  neutrons spectra

abstract:
  In the light of the latest data by LHCf collaboration of the LHC on leading
neutrons spectra it is possible to obtain total pion-proton cross-sections in
the TeV energy region. In this work the exact extraction procedure is shown.
Final numbers for the pion-proton cross-section are collected at several
different values of the colliding energy and compared with some popular
theoretical predictions. Errors of results are estimated.


title: Light-front versus equal-time quantization in $\phi^4$ theory

abstract:
  There is a discrepancy between light-front and equal-time values for the
critical coupling of two-dimensional $\phi^4$ theory. A proposed resolution is
to take into account the difference between mass renormalizations in the two
quantizations. This distinction was first discussed by M. Burkardt. It prevents
direct comparison of bare parameters; however, a method proposed here allows
calculation of the difference and thereby resolves the discrepancy. We also
consider the consequences of allowing a sector-dependent constituent mass.


title: Automorphisms of the little disks operad with torsion coefficients

abstract:
  We compute the automorphisms of the Bousfield-Kan completion at a prime p of
the little two-disks operads and show that they are given by the pro-p
Grothendieck-Teichm\"uller group. We also show that the
Grothendieck-Teichm\"uller group acts faithfully on the p-complete stable
little disks operad.


title:
Single crystal growth and physical property characterizations of mixed
  valent compound YbFe$_2$Al$_{10}$

abstract:
  We report single crystal growth and physical properties characterization of
YbFe$_2$Al$_{10}$ compounds. The measurements of resistivity, magnetic
susceptibility, and specific heat show different behaviors from previous
studies on polycrystal samples. A mixed valent characteristic with moderate
mass enhancement is indicated. In particular, the optical spectroscopy
measurement reveals formation of multiple hybridization energy gaps which
become progressively pronounced at low temperature. The multiple hybridization
energy gaps are likely caused by the hybridizations between the flat band from
Yb 4$f$ electrons and different bands of conduction electrons.


title: Nanoscale Phase Separation in Ferroelectric Materials

abstract:
  Many materials exhibit nanoscale phase separation, when inside the host
thermodynamic phase there arise nanosize embryos of another thermodynamic
phase. A prominent example of this phenomenon is provided by ferroelectric
materials. The theoretical description of such phase heterogeneous materials is
quite challenging, since they are essentially nonuniform, the nonuniformity is
random, and often they are quasiequilibrium, but not absolutely equilibrium. An
approach is suggested for the theoretical description of phase separated
ferroelectrics, consisting of a ferroelectric matrix with nanoscale
paraelectric inclusions. The properties of the heterophase ferroelectrics are
studied.


title: Ignorance is a bliss: mathematical structure of many-box models

abstract:
  We show that the propositional system of a many-box model is always a
set-representable effect algebra. In particular cases of 2-box and 1-box models
it is an orthomodular poset and an orthomodular lattice respectively. We
discuss the relation of the obtained results with the so-called Local
Orthogonality principle. We argue that non-classical properties of box models
are the result of a dual enrichment of the set of states caused by the
impoverishment of the set of propositions. On the other hand, quantum
mechanical models always have more propositions as well as more states than the
classical ones. Consequently, we show that the box models cannot be considered
as generalizations of quantum mechanical models and seeking for additional
principles that could allow to "recover quantum correlations" in box models is,
at least from the fundamental point of view, pointless.


title: Special matchings in Coxeter groups

abstract:
  Special matchings are purely combinatorial objects associated with a
partially ordered set, which have applications in Coxeter group theory. We
provide an explicit characterization and a complete classification of all
special matchings of any lower Bruhat interval. The results hold in any
arbitrary Coxeter group and have also applications in the study of the
corresponding parabolic Kazhdan--Lusztig polynomials.


title:
Auxiliary-Field Monte Carlo for lattice bosons: tackling strong
  interactions and frustration

abstract:
  We introduce a new numerical technique -- bosonic auxiliary-field Monte Carlo
(bAFMC) -- which allows to calculate the thermal properties of large
lattice-boson systems within a systematically improvable semiclassical
approach, and which is virtually applicable to any bosonic model. Our method
amounts to a decomposition of the lattice into clusters, and to an Ansatz for
the density matrix of the system in the form of a cluster-separable state --
with non-entangled, yet classically correlated clusters. This approximation
eliminates any sign problem, and can be systematically improved upon by using
clusters of growing size. Extrapolation in the cluster size allows to reproduce
numerically exact results for the superfluid transition of hardcore bosons on
the square lattice, and to provide a solid quantitative prediction for the
superfluid and chiral transition of hardcore bosons on the frustrated
triangular lattice.


title:
Reduced description method in the kinetic theory of Brownian motion with
  active fluctuations

abstract:
  We develop a microscopic approach to the kinetic theory of many-particle
systems with dissipative and potential interactions in presence of active
fluctuations. The approach is based on a generalization of
Bogolyubov--Peletminsky reduced description method applied to the systems of
many active particles. It is shown that the microscopic approach developed
allows to construct the kinetic theory of two- and three-dimensional systems of
active particles in presence of non-linear friction (dissipative interaction)
and an external random field with active fluctuations. The kinetic equations
for these systems in case of a weak interaction between the particles (both
potential and dissipative) and low-intensity active fluctuations are obtained.
We demonstrate particular cases in which the derived kinetic equations have
solutions that match the results known in the literature. It is shown that the
display of the head-tail asymmetry and self-propelling even in the case of a
linear friction, is one of the consequences of the local nature of the active
fluctuations.


title: Monogamy inequality for entanglement and local contextuality

abstract:
  We derive a monogamy inequality for entanglement and local contextuality, for
any finite bipartite system. It essentially results from the relations between
the purity of a local state and the entanglement of the global state, and
between the purity of a state and its ability to violate a given
noncontextuality inequality. We build an explicit entanglement monotone that
satisfies the found monogamy inequality. An important consequence of this
inequality, is that there are global states too entangled to violate the local
noncontextuality inequality.


title: Riccati-regularized Precision Matrices for Neuroimaging

abstract:
  The introduction of graph theory in neuroimaging has pro- vided invaluable
tools for the study of brain connectivity. These methods require the definition
of a graph, which is typically derived by estimating the effective connectivity
between brain regions through the optimization of an ill-posed inverse problem.
Considerable efforts have been devoted to the development of methods extracting
sparse connectivity graphs. The present paper aims at highlighting the benefits
of an alternative ap- proach. We investigate low-rank L2 regularized matrices
recently intro- duced under the denomination of Riccati regularized precision
matrices. We demonstrate their benefits for the analysis of cortical thickness
map and for the extraction of functional biomarkers from resting state fMRI
scans. In addition, we explain how speed and result quality can be further
improved with random projections. The promising results obtained using the
Human Connectome Project dataset as well as the numerous possi- ble extensions
and applications suggest that Riccati precision matrices might usefully
complement current sparse approaches.


title:
Large stable oscillations due to Hopf bifurcations in amplitude dynamics
  of colliding soliton sequences

abstract:
  We demonstrate that the amplitudes of optical solitons in nonlinear
multisequence optical waveguide coupler systems with weak linear and cubic
gain-loss exhibit large stable oscillations along ultra-long distances. The
large stable oscillations are caused by supercritical Hopf bifurcations of the
equilibrium states of the Lotka-Volterra (LV) models for dynamics of soliton
amplitudes. The predictions of the LV models are confirmed by numerical
simulations with the coupled cubic nonlinear Schr\"odinger (NLS) propagation
models with $2 \le N \le 4$ pulse sequences. Thus, we provide the first
demonstration of intermediate nonlinear amplitude dynamics in multisequence
soliton systems, described by the cubic NLS equation. Our findings are also an
important step towards realization of spatio-temporal chaos with multiple
periodic sequences of colliding NLS solitons.


abstract:
  This paper is an introduction to the eleven works of the special issue on
Quantum and Classical Frontiers of Noise. The weather, and its butterfly
effect, is the typical example that explain why many natural phenomena are, in
fact, not predictable with certainty. Noise in classical or quantum phenomena,
understood as the difference between the empirical output of an experiment and
its statistical prediction, is a measure of such uncertainty. One of the great
contributions of noise appeared in 1905 when Einstein showed how the noisy
(Brownian) motion of a dust particle seen in a microscope provided
uncontroversial evidences on the existence of the (unseen) atoms. The aim of
this special issue is to provoke discussions on how noise can help us to better
understand (the reality behind) classical and quantum theories, and the
frontier between them.


title: Singular integrals and a problem on mixing flows

abstract:
  We prove a result related to Bressan's mixing problem. We establish an
inequality for the change of Bianchini semi-norms of characteristic functions
under the flow generated by a divergence free time dependent vector field. The
approach leads to a bilinear singular integral operator for which we prove
bounds on Hardy spaces. We include additional observations about the approach
and a discrete toy version of Bressan's problem.


title:
Detection of the liquid-liquid transition in the deeply cooled water
  confined in MCM-41 with elastic neutron scattering technique

abstract:
  In this paper we present a review on our recent experimental investigations
into the phase behavior of the deeply cooled water confined in a nanoporous
silica material, MCM-41, with elastic neutron scattering technique. Under such
strong confinement, the homogeneous nucleation process of water is avoided,
which allows the confined water to keep its liquid state at temperatures and
pressures that are inaccessible to the bulk water. By measuring the average
density of the confined heavy water, we observe a likely first-order
low-density liquid (LDL) to high-density liquid (HDL) transition in the deeply
cooled region of the confined heavy water. The phase separation starts from
1.12 +- 0.17 kbar and 215 +- 1K and extends to higher pressures and lower
temperatures in the phase diagram. This starting point could be the
liquid-liquid critical point of the confined water. The locus of the Widom line
is also estimated. The observation of the liquid-liquid transition in the
confined water has potential to explain the mysterious behaviors of water at
low temperatures. In addition, it may also have impacts on other disciplines,
because the confined water system represents many biological and geological
systems in which water resides in nanoscopic pores or in the vicinity of
hydrophilic or hydrophobic surfaces.


title: A Model of Multi-Agent Consensus for Vague and Uncertain Beliefs

abstract:
  Consensus formation is investigated for multi-agent systems in which agents'
beliefs are both vague and uncertain. Vagueness is represented by a third truth
state meaning \emph{borderline}. This is combined with a probabilistic model of
uncertainty. A belief combination operator is then proposed which exploits
borderline truth values to enable agents with conflicting beliefs to reach a
compromise. A number of simulation experiments are carried out in which agents
apply this operator in pairwise interactions, under the bounded confidence
restriction that the two agents' beliefs must be sufficiently consistent with
each other before agreement can be reached. As well as studying the consensus
operator in isolation we also investigate scenarios in which agents are
influenced either directly or indirectly by the state of the world. For the
former we conduct simulations which combine consensus formation with belief
updating based on evidence. For the latter we investigate the effect of
assuming that the closer an agent's beliefs are to the truth the more visible
they are in the consensus building process. In all cases applying the consensus
operators results in the population converging to a single shared belief which
is both crisp and certain. Furthermore, simulations which combine consensus
formation with evidential updating converge faster to a shared opinion which is
closer to the actual state of the world than those in which beliefs are only
changed as a result of directly receiving new evidence. Finally, if agent
interactions are guided by belief quality measured as similarity to the true
state of the world, then applying the consensus operator alone results in the
population converging to a high quality shared belief.


title:
Counting the number of excited states in organic semiconductor systems
  using topology

abstract:
  Exciton Scattering (ES) theory attributes excited electronic states to
standing waves in quasi-one-dimensional molecular materials by assuming a
quasi-particle picture of optical excitations. The quasi-particle properties at
branching centers are described by the corresponding scattering matrices. Here
we identify the topological invariant of scattering center, referred to as its
winding number, and apply topological intersection theory to count the number
of quantum states in a quasi-one-dimensional system.


title: Depth with respect to a family of convex sets

abstract:
  We propose a notion of depth with respect to a finite family $\mathcal{F}$ of
convex sets in $\mathbb{R}^d$ which we call $\text{dep}_\mathcal{F}$. We begin
showing that $\text{dep}_\mathcal{F}$ satisfies some expected properties for a
measure of depth and that this definition is closely related to the notion of
depth proposed by J. Tukey. We show that some properties of Tukey depth extend
to $\text{dep}_\mathcal{F}$ and we point out some key differences.
  We then focus on the following centerpoint-type question: what is the best
depth $\alpha_{d,k}$ that we can guarantee under the hypothesis that the family
$\mathcal{F}$ is $k$-intersecting? We show a key connection between this
problem and a purely combinatorial problem on hitting sets. The relationship is
useful in both directions. On the one hand, for values of $k$ close to $d$ the
combinatorial interpretation gives a good bound for $k$. On the other hand, for
low values of $k$ we can use the classic Rado's centerpoint theorem to get
combinatorial results of independent interest. For intermediate values of $k$
we present a probabilistic framework to improve the bounds and illustrate its
use in the case $k\approx d/2$. These results can be though of as an
interpolation between Helly's theorem and Rado's centerpoint theorem.
  As an application of these results we find a Helly-type theorem for
fractional hyperplane transversals. We also give an alternative and simpler
proof for a transversal result of A. Holmsen.


title:
Electronic origin of spin-phonon coupling effect in transition-metal
  perovskites

abstract:
  By applying Wannier-based extended Kugel-Khomskii model, we carry out
first-principles calculations and electronic structure analysis to understand
the spin-phonon coupling effect in transition-metal perovskites. We demonstrate
the successful application of our approach to SrMnO$_3$ and BiFeO$_3$. We show
that both the electron orbitals under crystal field splitting and the
electronic configuration should be taken into account in order to understand
the large variances of spin-phonon coupling effects among various phonon modes
as well as in different materials.


title:
The Effect of Strange Quark on the Chiral Symmetry Breaking in Magnetic
  Background in the framework of logarithmic quark-sigma model

abstract:
  The chiral symmetry breaking in the presence of an external magnetic field is
studied in the framework of logarithmic quark-sigma model with three flavors
(u,d,s). The effective logarithmic mesonic potential is extended to strange
quark and is numerically solved in the mean-field approximation. The present
results show that the chiral symmetry breaking is sensitive for the strange
quark flavour in the presence an external magnetic field. In addition, the
effect of the free parameters is studied. A comparison with original sigma
model is discussed.


title:
Heavy-Light Exotics from QCD Laplace Sum Rules at N2LO in the chiral
  limit

abstract:
  These talks review and summarize our results in [1,2] on $XYZ$-like spectra
obtained from QCD Laplace Sum Rules in the chiral limit at next-to-next-leading
order (N2LO) of perturbation theory (PT) and including leading order (LO)
contributions of dimensions $d\leq 6-8$ non-perturbative condensates. We
conclude that the observed $XZ$ states are good candidates for $1^{+}$ and
$0^+$ molecules or / and four-quark states while the predictions for $1^-$ and
$0^-$ states are about 1.5 GeV above the $Y_{c,b}$ experimental candidates and
hadronic thresholds. We (numerically) find that these exotic molecules couple
weakly to the corresponding interpolating currents than ordinary $D,B$
heavy-light mesons while we observe that these couplings decrease faster
[$1/m_b^{3/2}$ (resp. $1/m_b$) for the $1^+,0^+$ (resp. $1^-,0^-)$ states] than
$1/m_b^{1/2}$. Our results do not also confirm the existence of the $X(5568)$
state in agreement with LHCb findings.


title: An electron of helium atom under a high-intensity laser field

abstract:
  We scrutinize the behavior of eigenvalues of an electron of Helium atom as it
interacts with electric field directed along $z$-axis and exposed to linearly
polarized intense laser field radiation. In order to achieve this, we freeze
one electron of the helium atom at its ionic ground state and the motion of the
second electron in the ion core is treated via a more general case of screened
Coulomb potential model. Using the Kramers-Henneberger (KH) unitary
transformation, which is semiclassical counterpart of the Block-Nordsieck
transformation in the quantized field formalism, the squared vector potential
that appears in the equation of motion is eliminated and the resultant equation
is expressed in KH frame. Within this frame, the resulting potential and the
corresponding wave function have been expanded in Fourier series and using
Ehlotzkys approximation, we obtain a laser-dressed potential to simulate
intense laser field. By fitting the more general case of screened Coulomb
potential model into the laser-dressed potential, and then expanding it in
Taylor series up to $\mathcal{O}(r^4,\alpha_0^9)$, we obtain the solution
(eigenvalues and wave function) of an electron of Helium atom under the
influence of external electric field and high-intensity laser field, within the
framework of perturbation theory formalism. We found that the variation in
frequency of laser radiation has no effect on the eigenvalues of an electron of
helium for a particular electric field intensity directed along $z$-axis. Also,
for a very strong external electric field and an infinitesimal screening
parameter, the system is strongly bound. This work has potential application in
the areas of atomic and molecular processes in external fields including
interactions with strong fields and short pulses.


title:
A Note on the Radiative and Collisional Branching Ratios in Polarized
  Radiation Transport with Coherent Scattering

abstract:
  We discuss the implementation of physically meaningful branching ratios
between the CRD and PRD contributions to the emissivity of a polarized
multi-term atom in the presence of both inelastic and elastic collisions. Our
derivation is based on a recent theoretical formulation of partially coherent
scattering, and it relies on a heuristic diagrammatic analysis of the various
radiative and collisional processes to determine the proper form of the
branching ratios. The expression we obtain for the emissivity is
$\varepsilon=\left[\varepsilon^{\tiny (1)}-\varepsilon^{\tiny (2)}_{\rm f.s.}
\right]+\varepsilon^{\tiny (2)}$, where $\varepsilon^{\tiny (1)}$ and
$\varepsilon^{\tiny (2)}$ are the emissivity terms for the redistributed and
partially coherent radiation, respectively, and where "f.s." implies that the
corresponding term must be evaluated assuming a flat-spectrum average of the
incident radiation.


title: Lock-Free Optimization for Non-Convex Problems

abstract:
  Stochastic gradient descent~(SGD) and its variants have attracted much
attention in machine learning due to their efficiency and effectiveness for
optimization. To handle large-scale problems, researchers have recently
proposed several lock-free strategy based parallel SGD~(LF-PSGD) methods for
multi-core systems. However, existing works have only proved the convergence of
these LF-PSGD methods for convex problems. To the best of our knowledge, no
work has proved the convergence of the LF-PSGD methods for non-convex problems.
In this paper, we provide the theoretical proof about the convergence of two
representative LF-PSGD methods, Hogwild! and AsySVRG, for non-convex problems.
Empirical results also show that both Hogwild! and AsySVRG are convergent on
non-convex problems, which successfully verifies our theoretical results.


title: Bistability induced by two cross-correlated Gaussian white noises

abstract:
  A prototype model of a stochastic one-variable system with a linear restoring
force driven by two cross-correlated multiplicative and additive Gaussian white
noises was considered earlier [S. I. Denisov et al., Phys. Rev. E 68, 046132
(2003)]. The multiplicative factor was assumed to be quadratic in the vicinity
of a stable equilibrium point. It was determined that a negative
cross-correlation can induce nonequilibrium transitions. In this paper, we
investigate this model in more detail and calculate explicit expressions of the
stationary probability density. We construct a phase diagram and show that both
additive and multiplicative noises can also generate bimodal probability
distributions of the state variable in the presence of anti-correlation. We
find the order parameter and determine that the additive noise has a
disordering effect and the multiplicative noise has an ordering effect. We
explain the mechanism of this bistability and specify its key ingredients.


title: The endpoint distribution of directed polymers

abstract:
  Probabilistic models of directed polymers in random environment have received
considerable attention in recent years. Much of this attention has focused on
integrable models. In this paper, we introduce some new computational tools
that do not require integrability. We begin by defining a new kind of abstract
limit object, called "partitioned subprobability measure", to describe the
limits of endpoint distributions of directed polymers. Inspired by a recent
work of Mukherjee and Varadhan on large deviations of the occupation measure of
Brownian motion, we define a suitable topology on the space of partitioned
subprobability measures and prove that this topology is compact. Then using a
variant of the cavity method from the theory of spin glasses, we show that any
limit law of a sequence of endpoint distributions must satisfy a fixed point
equation on this abstract space, and that the limiting free energy of the model
can be expressed as the solution of a variational problem over the set of fixed
points. As a first application of the theory, we prove that in an environment
with finite exponential moment, the endpoint distribution is asymptotically
purely atomic if and only if the system is in the low temperature phase. The
analogous result for a heavy-tailed environment was proved by Vargas in 2007.
As a second application, we prove a subsequential version of the longstanding
conjecture that in the low temperature phase, the endpoint distribution is
asymptotically localized in a region of stochastically bounded diameter. All
our results hold in arbitrary dimensions, and make no use of integrability.


title: Quantum bifurcation diagrams

abstract:
  Asymptotic state of an open quantum system can undergo qualitative changes
upon small variation of system parameters. We demonstrate it that such 'quantum
bifurcations' can be appropriately defined and made visible as changes in the
structure of the asymptotic density matrix. By using an $N$-boson open quantum
dimer, we present quantum diagrams for the pitchfork and saddle-node
bifurcations in the stationary case and visualize a period-doubling transition
to chaos for the periodically modulated dimer. In the latter case, we also
identify a specific bifurcation of purely quantum nature.


title:
Fractional Differential Equations with Periodic Boundary Conditions of
  Constant Ratio

abstract:
  This article is concerned with the existence and uniqueness of solutions to
some fractional order boundary value problems. Our results are based on some
fixed point theorems. For the applicability of our results, we provide an
example.


title: Q-tensor model for electrokinetics in nematic liquid crystals

abstract:
  We use a variational principle to derive a mathematical model for a nematic
electrolyte in which the liquid crystalline component is described in terms of
a second-rank order tensor. The model extends the previously developed
director-based theory and accounts for presence of disclinations and possible
biaxiality. We verify the model by considering a simple but illustrative
example of liquid crystal-enabled electro-osmotic flow (LCEO) around a
stationary dielectric spherical particle placed at the center of a large
cylindrical container filled with a nematic electrolyte. Assuming homeotropic
anchoring of the nematic on the surface of the particle and uniform
distribution of the director on the surface of the container, we consider two
configurations with a disclination equatorial ring and with a hyperbolic
hedgehog, respectively. The computed electro-osmotic flows show a strong
dependence on the director configurations and on the anisotropies of dielectric
permittivity and electric conductivity of the nematic characteristic of liquid
crystal-enabled electrokinetics. Further, the simulations demonstrate space
charge separation around the dielectric sphere, even in the case of isotropic
permittivity and conductivity. This is in agreement with the induced-charge
electro-osmotic effect described for isotropic electrolytes surrounding
dielectric spheres.


title:
The Spinon Fermi Surface U(1) Spin Liquid in a Spin-Orbit-Coupled
  Triangular Lattice Mott Insulator YbMgGaO4

abstract:
  Motivated by the recent progress on the spin-orbit-coupled triangular lattice
spin liquid candidate YbMgGaO4, we carry out a systematic projective symmetry
group analysis and mean-field study of candidate U(1) spin liquid ground
states. Due to the spin-orbital entanglement of the Yb moments, the space group
symmetry operation transforms both the position and the orientation of the
local moments, and hence brings different features for the projective
realization of the lattice symmetries from the cases with spin-only moments.
Among the eight U(1) spin liquids that we find with the fermionic parton
construction, only one spin liquid state, that was proposed and analyzed in Yao
Shen, et al, Nature 540, 559-562 (2016) and labeled as U1A00 in the present
work, stands out and gives a large spinon Fermi surface and provides a
consistent explanation for the spectroscopic results in YbMgGaO4. Further
connection of this spinon Fermi surface U(1) spin liquid with YbMgGaO4 and the
future directions are discussed. Finally, our results may apply to other
spin-orbit-coupled triangular lattice spin liquid candidates, and more broadly,
our general approach can be well extended to spin-orbit-coupled spin liquid
candidate materials.


title: CSMA-based Packet Broadcast in Radio Channels with Hidden Stations

abstract:
  Carrier Sense Multiple Access (CSMA) MAC protocols are known to suffer from
the hidden station (HS) problem. The complete mathematical analysis of CSMA
networks with HSs is still an open problem, even for broadcast communication
with a simple linear network topology. In this paper we address this challenge
by introducing a MAC layer modeling methodology based on time- and space-domain
Markov processes. Using this methodology we derive the closed-form solution for
the steady-state performance in infinite one-dimensional (1-D) CSMA networks
with HSs. The analytical results are validated by simulation and establish
that: 1) under the assumption of fixed frame duration, if the conditional
channel access probability at each station exceeds a certain threshold, the
CSMA system enters the status of "synchronized transmissions", where a large
number of adjacent stations transmit in overlap and interfere each other
resulting in null system goodput. 2) The maximum system goodput of CSMA
broadcast communication increases with increased station density but becomes
increasingly sensitive to the conditional channel access probability. In [25]
we validate the analytical results gained in this paper by simulation of a
multi-lane highway scenario, and provide quantitative guidance for congestion
control algorithms in vehicular networks.


title:
IEEE 802.11p-based Packet Broadcast in Radio Channels with Hidden
  Stations and Congestion Control

abstract:
  The Decentralized Congestion Control (DCC) algorithms specified in ETSI ITS
standards [1] address the IEEE 802.11p MAC and provide reliability of periodic
broadcast messages at high density of vehicles. However, the deterministic
relation between controllable parameters, e.g. transmit power, frame duration,
frame transmit rate and channel clear assessment threshold, and the effects of
DCC algorithms, e.g. channel busy duration, frame interference-free reception
probability and frame channel access delay, is still unknown since a correct
mathematical analysis of the hidden station problem in CSMA networks is
lacking. In this work, the hidden station problem in a linear IEEE 802.11p
broadcast network is analyzed based on analytical results developed in [18]
employing a modified MAC protocol model based on [3]. Simulation results
validate the new analytical model for linear IEEE 802.11p networks w.r.t
reliability and latency performances of Cooperative Awareness Message
broadcast. Evidence is given that the model not only is valid for single-lane
highways but also provides good approximate results for multi-lane highway
scenarios. Our MAC layer analytical model of IEEE 802.11p broadcast reveals the
quantitative relation between DCC parameters and congestion control effects in
closed-form solution for linear vehicular networks.


title: Noisy subspace clustering via matching pursuits

abstract:
  Sparsity-based subspace clustering algorithms have attracted significant
attention thanks to their excellent performance in practical applications. A
prominent example is the sparse subspace clustering (SSC) algorithm by
Elhamifar and Vidal, which performs spectral clustering based on an adjacency
matrix obtained by sparsely representing each data point in terms of all the
other data points via the Lasso. When the number of data points is large or the
dimension of the ambient space is high, the computational complexity of SSC
quickly becomes prohibitive. Dyer et al. observed that SSC-OMP obtained by
replacing the Lasso by the greedy orthogonal matching pursuit (OMP) algorithm
results in significantly lower computational complexity, while often yielding
comparable performance. The central goal of this paper is an analytical
performance characterization of SSC-OMP for noisy data. Moreover, we introduce
and analyze the SSC-MP algorithm, which employs matching pursuit (MP) in lieu
of OMP. Both SSC-OMP and SSC-MP are proven to succeed even when the subspaces
intersect and when the data points are contaminated by severe noise. The
clustering conditions we obtain for SSC-OMP and SSC-MP are similar to those for
SSC and for the thresholding-based subspace clustering (TSC) algorithm due to
Heckel and B\"olcskei. Analytical results in combination with numerical results
indicate that both SSC-OMP and SSC-MP with a data-dependent stopping criterion
automatically detect the dimensions of the subspaces underlying the data.
Moreover, experiments on synthetic and on real data show that SSC-MP compares
very favorably to SSC, SSC-OMP, TSC, and the nearest subspace neighbor
algorithm, both in terms of clustering performance and running time. In
addition, we find that, in contrast to SSC-OMP, the performance of SSC-MP is
very robust with respect to the choice of parameters in the stopping criteria.


title:
Identification and Model Testing in Linear Structural Equation Models
  using Auxiliary Variables

abstract:
  We developed a novel approach to identification and model testing in linear
structural equation models (SEMs) based on auxiliary variables (AVs), which
generalizes a widely-used family of methods known as instrumental variables.
The identification problem is concerned with the conditions under which causal
parameters can be uniquely estimated from an observational, non-causal
covariance matrix. In this paper, we provide an algorithm for the
identification of causal parameters in linear structural models that subsumes
previous state-of-the-art methods. In other words, our algorithm identifies
strictly more coefficients and models than methods previously known in the
literature. Our algorithm builds on a graph-theoretic characterization of
conditional independence relations between auxiliary and model variables, which
is developed in this paper. Further, we leverage this new characterization for
allowing identification when limited experimental data or new substantive
knowledge about the domain is available. Lastly, we develop a new procedure for
model testing using AVs.


title:
Energy Allocation Policy for Cellular Networks Powered by Renewable
  Energy

abstract:
  The explosive wireless data service requirement accompanied with carbon
dioxide emission and consumption of traditional energy has put pressure on both
industry and academia. Wireless networks powered with the uneven and
intermittent generated renewable energy have been widely researched and lead to
a new research paradigm called green communication. In this paper, we
comprehensively consider the total generated renewable energy, QoS requirement
and channel quality, then propose a utility based renewable energy allocation
policy. The utility here means the satisfaction degree of users with a certain
amount allocated renewable energy. The energy allocation problem is formulated
as a constraint optimization problem and a heuristic algorithm with low
complexity is derived to solve the raised problem. Numerical results show that
the renewable energy allocation policy is applicable for any situation. When
the renewable energy is very scarce, only users with good channel quality can
achieve allocated energy.


title:
Fiber bunching and cohomology for Banach cocycles over hyperbolic
  systems

abstract:
  We consider Holder continuous cocycles over hyperbolic dynamical systems with
values in the group of invertible bounded linear operators on a Banach space.
We show that two fiber bunched cocycles are Holder continuously cohomologous if
and only if they have Holder conjugate periodic data. The fiber bunching
condition means that non-conformality of the cocycle is dominated by the
expansion and contraction in the base system. We show that this condition can
be established based on the periodic data of a cocycle. We also establish
Holder continuity of a measurable conjugacy between a fiber bunched cocycle and
one with values in a set which is compact in strong operator topology.


title:
Normal forms on contracting foliations: smoothness and homogeneous
  structure

abstract:
  In this paper we consider a diffeomorphism $f$ of a compact manifold $M$
which contracts an invariant foliation $W$ with smooth leaves. If the
differential of $f$ on $TW$ has narrow band spectrum, there exist coordinates
$H _x:W_x\to T_xW$ in which $f|_W$ has polynomial form. We present a modified
approach that allows us to construct maps $H_x$ that depend smoothly on $x$
along the leaves of $W$. Moreover, we show that on each leaf they give a
coherent atlas with transition maps in a finite dimensional Lie group. Our
results apply, in particular, to $C^1$-small perturbations of algebraic
systems.


title: Vector Gaussian Rate-Distortion with Variable Side Information

abstract:
  We consider rate-distortion with two decoders, each with distinct side
information. This problem is well understood when the side information at the
decoders satisfies a certain degradedness condition. We consider cases in which
this degradedness condition is violated but the source and the side information
consist of jointly Gaussian vectors. We provide a hierarchy of four lower
bounds on the optimal rate. These bounds are then used to determine the optimal
rate for several classes of instances.


title: Baby-Step Giant-Step Algorithms for the Symmetric Group

abstract:
  We study discrete logarithms in the setting of group actions. Suppose that
$G$ is a group that acts on a set $S$. When $r,s \in S$, a solution $g \in G$
to $r^g = s$ can be thought of as a kind of logarithm. In this paper, we study
the case where $G = S_n$, and develop analogs to the Shanks baby-step /
giant-step procedure for ordinary discrete logarithms. Specifically, we compute
two sets $A, B \subseteq S_n$ such that every permutation of $S_n$ can be
written as a product $ab$ of elements $a \in A$ and $b \in B$. Our
deterministic procedure is optimal up to constant factors, in the sense that
$A$ and $B$ can be computed in optimal asymptotic complexity, and $|A|$ and
$|B|$ are a small constant from $\sqrt{n!}$ in size. We also analyze randomized
"collision" algorithms for the same problem.


title: Consus: Taming the Paxi

abstract:
  Consus is a strictly serializable geo-replicated transactional key-value
store. The key contribution of Consus is a new commit protocol that reduces the
cost of executing a transaction to three wide area message delays in the common
case. Augmenting the commit protocol are multiple Paxos implementations
optimized for different purposes. Together the different implementations and
optimizations comprise a cohesive system that provides low latency, high
availability, and strong guarantees. This paper describes the techniques
implemented in the open source release of Consus, and lays the groundwork for
evaluating Consus once the system implementation is sufficiently robust for a
thorough evaluation.


title: A-Discriminants for Complex Exponents, and Counting Real Isotopy Types

abstract:
  We extend the definition of $\mathcal{A}$-discriminant varieties, and
Kapranov's parametrization of $\mathcal{A}$-discriminant varieties, to complex
exponents. As an application, we study the special case where $\mathcal{A}$ is
a fixed real $n\times (n+3)$ matrix whose columns form the spectrum of an
$n$-variate exponential sum $g$ with fixed sign vector for its coefficients: We
prove that the number of possible isotopy types for the real zero set of $g$ is
$O(n^2)$. The best previous upper bound was $2^{O(n^4)}$. Along the way, we
also show that the singular loci of our generalized $\mathcal{A}$-discriminants
are images of low-degree algebraic sets under certain analytic maps.


title: LP Bounds for Rate-Distortion with Variable Side Information

abstract:
  We consider a rate-distortion problem with side information at multiple
decoders. Several upper and lower bounds have been proposed for this general
problem or special cases of it. We provide an upper bound for general instances
of this problem, which takes the form of a linear program, by utilizing random
binning and simultaneous decoding techniques and compare it with the existing
bounds. We also provide a lower bound for the general problem, which was
inspired by a linear-programming lower bound for index coding, and show that it
subsumes most of the lower bounds in literature. Using these upper and lower
bounds, we explicitly characterize the rate-distortion function of a problem
that can be seen as a Gaussian analogue of the "odd-cycle" index coding
problem.


title: Spectral Triples for nonarchimedean local fields

abstract:
  Using associated trees, we construct a spectral triple for the C$^*$-algebra
of continuous functions on the ring of integers $R$ of a nonarchimedean local
field $F$ of characteristic zero, and investigate its properties. Remarkably,
the spectrum of the spectral triple operator is closely related to the roots of
a $q$-hypergeometric function. We also study a non compact version of this
construction for the C$^*$-algebra of continuous functions on $F$, vanishing at
infinity.


title: Low-complexity Pruned 8-point DCT Approximations for Image Encoding

abstract:
  Two multiplierless pruned 8-point discrete cosine transform (DCT)
approximation are presented. Both transforms present lower arithmetic
complexity than state-of-the-art methods. The performance of such new methods
was assessed in the image compression context. A JPEG-like simulation was
performed, demonstrating the adequateness and competitiveness of the introduced
methods. Digital VLSI implementation in CMOS technology was also considered.
Both presented methods were realized in Berkeley Emulation Engine (BEE3).


title:
Phase diagram for the trapped p-wave fermionic superfluid with
  population imbalance

abstract:
  We consider the problem of spin-triplet p-wave superfluid pairing with total
spin projection $m_s=0$ in atomic Fermi gas across the Feshbach resonance. We
allow for imbalanced populations and take into account the effects due to
presence of a parabolic trapping potential. Within the mean-field approximation
for the one- and two-channel pairing models we show that depending on the
distance from the center of a trap at least two superfluid states will have the
lowest energy. Superfluid shells which emerge in a trap may have two out of
three angular components of the p-wave superfluid order parameter equal to
zero.


title: Phase Structure of XX0 Spin Chain and Nonintersecting Brownian Motion

abstract:
  We study finite size and temperature XX0 Heisenberg spin chain in weak and
strong coupling regimes. By using an elegant connection of the model to
integrable combinatorics and probability, we explore and interpret a possible
phase structure of the model in asymptotic limit: the limit of large inverse
temperature and size. First, partition function and free energy of the model
are derived by using techniques and results from random matrix models and
nonintersecting Brownian motion. We show that, in the asymptotic limit,
partition function of the model, written in terms of matrix integral, is
governed by the Tracy-Widom distribution. Second, the exact analytic results
for the free energy, which is obtained by the asymptotic analysis of the
Tracy-Widom distribution, indicate a completely new and sophisticated phase
structure of the model. This phase structure consists of second- and
third-order phase transitions. Finally, to shed light on our new results, we
provide a possible interpretation of the phase structure in terms of dynamical
behavior of magnons in the spin chain. We demonstrate distinct features of the
phases with schematic spin configurations which have definite features in each
region of the phase diagram.

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