title:
Intrinsic temperature-dependent evolutions in the electron-boson
  spectral density obtained from optical data

abstract:
  We investigate temperature smearing effects on the electron-boson spectral
density function ($I^2\chi(\omega)$) obtained from optical data using a maximum
entropy inversion method. We start with two simple model input
$I^2\chi(\omega)$, calculate the optical scattering rates at selected
temperatures using the model input spectral density functions and a generalized
Allen's formula, then extract back $I^2\chi(\omega)$ at each temperature from
the calculated optical scattering rate using the maximum entropy method (MEM)
which has been used for analysis of optical data of high-temperature
superconductors including cuprates, and finally compare the resulting
$I^2\chi(\omega)$ with the input ones. From this approach we find that the
inversion process can recover the input $I^2\chi(\omega)$ almost perfectly when
the quality of fits is good enough and also temperature smearing (or thermal
broadening) effects appear in the $I^2\chi(\omega)$ when the quality of fits is
not good enough. We found that the coupling constant and the logarithmically
averaged frequency are robust to the temperature smearing effects and/or the
quality of fits. We use these robust properties of the two quantities as
criterions to check whether experimental data have intrinsic
temperature-dependent evolutions or not. We carefully apply the MEM to two
material systems (one optimally doped and the other underdoped cuprates) and
conclude that the $I^2\chi(\omega)$ extracted from the optical data contain
intrinsic temperature-dependent evolutions.


title:
Comment about the use of Monte-Carlo methodology for the representation
  of atomic electronic densities

abstract:
  Representations of atomic orbitals based on Monte-Carlo (MC) approaches are
not always correct when using various sets of orthogonal coordinates other than
Cartesian coordinates. The analysis proposed here gives elements for a proper
use of MC methodology. It can be very useful for students and for teachers.


title: Cosmological Attractors and Asymptotic Freedom of the Inflaton Field

abstract:
  We show that the inflaton coupling to all other fields is exponentially
suppressed during inflation in the cosmological $\alpha$-attractor models. In
the context of supergravity, this feature is a consequence of the underlying
hyperbolic geometry of the moduli space which has a flat direction
corresponding to the inflaton field. A combination of these factors protects
the asymptotic flatness of the inflaton potential.


title: A congruence involving the quotients of Euler and its applications (III)

abstract:
  In this paper, we will present several new congruences involving binomial
coefficients under integer moduli, which are the continuation of the previous
two work by Cai \textit{et al.} (2002, 2007).


title: Throughput-Optimal Multi-hop Broadcast Algorithms

abstract:
  In this paper we design throughput-optimal dynamic broad- cast algorithms for
multi-hop networks with arbitrary topolo- gies. Most of the previous broadcast
algorithms route pack- ets along spanning trees, rooted at the source node. For
large dynamic networks, computing and maintaining a set of spanning trees is
not efficient, as the network-topology may change frequently. In this paper we
design a class of dynamic algorithms which makes packet-by-packet schedul- ing
and routing decisions and thus obviates the need for maintaining any global
topological structures, such as span- ning trees. Our algorithms may be
conveniently understood as a non-trivial generalization of the familiar
back-pressure algorithm which makes unicast packet routing and schedul- ing
decisions, based on queue-length information, without maintaining end-to-end
paths. However, in the broadcast problem, it is hard to define queuing
structures due to ab- sence of a work-conservation principle which results from
packet duplications. We design and prove the optimality of a virtual-queue
based algorithm, where a virtual-queue is de- fined for subsets of vertices. We
then propose a multi-class broadcast policy which combines the above scheduling
algo- rithm with a class-based in-order packet delivery constraint, resulting
in significant reduction in complexity. Finally, we evaluate performance of the
proposed algorithms via exten- sive numerical simulations.


title: Ordering-Free Inference from Locally Dependent Data

abstract:
  This paper focuses on a data-rich environment where the data set has a very
large cross-sectional dimension, is likely to exhibit local dependence, and yet
is hard to determine the dependence ordering. Such a situation arises, for
example, when the data set is collected from the Internet, through a method of
web crawling. This paper proposes an approach of randomized subsampling
inference, where one constructs a test statistic by aggregating many randomized
test statistics using random draws of subsamples, and uses for inference the
conditional distribution of the test statistic given data. This paper explores
two approaches of such inference: one based on an M-type statistic constructed
from randomized mean statistics and the other based on a U-type statistic
constructed from randomized U-statistics. This paper provides conditions for
local dependence, the number of the random draws, and the subsample size, under
which randomized subsampling inference is asymptotically valid. From the Monte
Carlo simulation studies, this paper finds that the randomized subsampling
inference based on the U-type statistics performs better than that based on the
M-type statistics.


title:
On local behavior of singular positive solutions to nonlocal elliptic
  equations

abstract:
  We study local behavior of positive solutions to the fractional Yamabe
equation with a singular set of fractional capacity zero.


title:
3D-R2N2: A Unified Approach for Single and Multi-view 3D Object
  Reconstruction

abstract:
  Inspired by the recent success of methods that employ shape priors to achieve
robust 3D reconstructions, we propose a novel recurrent neural network
architecture that we call the 3D Recurrent Reconstruction Neural Network
(3D-R2N2). The network learns a mapping from images of objects to their
underlying 3D shapes from a large collection of synthetic data. Our network
takes in one or more images of an object instance from arbitrary viewpoints and
outputs a reconstruction of the object in the form of a 3D occupancy grid.
Unlike most of the previous works, our network does not require any image
annotations or object class labels for training or testing. Our extensive
experimental analysis shows that our reconstruction framework i) outperforms
the state-of-the-art methods for single view reconstruction, and ii) enables
the 3D reconstruction of objects in situations when traditional SFM/SLAM
methods fail (because of lack of texture and/or wide baseline).


title:
Invariant imbedding theory of wave propagation in arbitrarily
  inhomogeneous stratified bi-isotropic media

abstract:
  Bi-isotropic media, which include isotropic chiral media and Tellegen media
as special cases, are the most general form of linear isotropic media where the
electric displacement and the magnetic induction are related to both the
electric field and the magnetic intensity. In inhomogeneous bi-isotropic media,
electromagnetic waves of two different polarizations are coupled to each other.
In this paper, we develop a generalized version of the invariant imbedding
method for the study of wave propagation in arbitrarily-inhomogeneous
stratified bi-isotropic media, which can be used to solve the coupled wave
propagation problem accurately and efficiently. We verify the validity and
usefulness of the method by applying it to several examples, including the wave
propagation in a uniform chiral slab, the surface wave excitation in a bilayer
system made of a layer of Tellegen medium and a metal layer, and the mode
conversion of transverse electromagnetic waves into longitudinal plasma
oscillations in inhomogeneous Tellegen media. In contrast to the case of
ordinary isotropic media, we find that the surface wave excitation and the mode
conversion occur for both s and p waves in bi-isotropic media.


title: Universal Gysin formulas for the universal Hall-Littlewood functions

abstract:
  It is known that the usual Schur $S$- and $P$-polynomials can be described
via the Gysin homomorphisms for flag bundles in the ordinary cohomology theory.
Recently, P. Pragacz generalized these Gysin formulas to the Hall-Littlewood
polynomials. In this paper, we introduce a {\it universal} analogue of the
Hall-Littlewood polynomials, which we call the {\it universal Hall-Littlewood
functions}, and give Gysin formulas for various flag bundles in the complex
cobordism theory. Furthermore, we give two kinds of the {\it universal}
analogue of the schur polynomials, and some Gysin formulas for these functions
are established.


title:
Ground-State Phase Diagram of the Bond-Alternating $S=2$ Quantum Spin
  Chain with the $XXZ$ and On-Site Anisotropies -- Symmetry Protected
  Topological Phase versus Trivial Phase

abstract:
  We investigate the ground-state phase diagram of the bond-alternating $S=2$
quantum spin chain with the $XXZ$ and on-site anisotropies. For the on-site
anisotropies, in addition to the popular $D_2 \sum_j (S_j^z)^2$ term, we
consider the $D_4 \sum_j (S_j^z)^4$ term. Mainly we use the exact
diagonalization and the level spectroscopy analysis. We show that the Haldane
state, large-$D$ state and the Dimer2 state belong to the same trivial phase,
by finding the existence of adiabatic paths directly connecting these states
without the quantum phase transition. Similarly, we show that the
intermediate-$D$ state and the Dimer1 state belong to the same symmetry
protected topological phase.


title: Warm-tachyon Gauss-Bonnet inflation in the light of Planck 2015 data

abstract:
  We study a warm-tachyon inflationary model non-minimally coupled to a
Gauss-Bonnet term. The general conditions required for reliability of the model
are obtained by considerations of a combined hierarchy of Hubble and
Gauss-Bonnet flow functions. The perturbed equations are comprehensively
derived in the longitudinal gauge in the presence of slow-roll and quasi-stable
conditions. General expressions for observable quantities of interest such as
the tensor-to-scalar ratio, scalar spectral index and its running are found in
the high dissipation regime. Finally, the model is solved using exponential and
inverse power-law potentials, which satisfy the properties of a tachyon
potential, with parameters of the model being constrained within the framework
of the Planck 2015 data. We show that the Gauss-Bonnet coupling constant
controls termination of inflation in such a way as to be in good agreement with
the Planck 2015 data.


title:
Explicit constructions of high-rate MDS array codes with optimal repair
  bandwidth

abstract:
  Maximum distance separable (MDS) codes are optimal error-correcting codes in
the sense that they provide the maximum failure-tolerance for a given number of
parity nodes. Suppose that an MDS code with $k$ information nodes and $r=n-k$
parity nodes is used to encode data in a distributed storage system. It is
known that if $h$ out of the $n$ nodes are inaccessible and $d$ surviving
(helper) nodes are used to recover the lost data, then we need to download at
least $h/(d+h-k)$ fraction of the data stored in each of the helper nodes
(Dimakis et. al., 2010 and Cadambe et al., 2013). If this lower bound is
achieved for the repair of any $h$ erased nodes from any $d$ helper nodes, we
say that the MDS code has the $(h,d)$-optimal repair property.
  We study high-rate MDS array codes with the optimal repair property. Explicit
constructions of such codes in the literature are only available for the cases
where there are at most 3 parity nodes, and these existing constructions can
only optimally repair a single node failure by accessing all the surviving
nodes.
  In this paper, given any $r$ and $n$, we present two explicit constructions
of MDS array codes with the $(h,d)$-optimal repair property for all $h\le r$
and $k\le d\le n-h$ simultaneously. Codes in the first family can be
constructed over any base field $F$ as long as $|F|\ge sn,$ where
$s=\text{lcm}(1,2,\dots,r).$ The encoding, decoding, repair of failed nodes,
and update procedures of these codes all have low complexity. Codes in the
second family have the optimal access property and can be constructed over any
base field $F$ as long as $|F|\ge n+1.$ Moreover, both code families have the
optimal error resilience capability when repairing failed nodes. We also
construct several other related families of MDS codes with the optimal repair
property.


title:
Forced field extrapolation of the magnetic structure of the Halpha
  fibrils in solar chromosphere

abstract:
  We present a careful assess of the forced field extrapolation using Solar
Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) magnetogram.
The convergence property is checked by several metrics. The extrapolated field
lines below 3600km appear to be aligned with most Halpha fibrils observed by
New Vacuum Solar Telescope (NVST). In the region where magnetic energy far
larger than potential energy, field lines computed by forced field
extrapolation still consistent with the patterns of Halpha fibrils while
non-linear force free field (NLFFF) results show large misalignment. The
horizontal average of lorentz force ratio shows the forced region where
force-free assumption is failed can reach the height of $1400-1800km$. The
non-force-free state of the chromosphere is also confirmed by recent radiation
magnetohydrodynamics (MHD) simulation.


title: A note on the affine-invariant plank problem

abstract:
  Suppose that $C$ is a bounded, convex subset of $\mathbb{R}^n$, and that
$P_1, \dots, P_k$ are planks which cover $C$ in respective directions $v_1,
\dots, v_k$ and with widths $w_1, \dots, w_k$. In 1951, Bang conjectured that
$$\sum_{i=1}^k \frac{w_i}{w_{v_i}(C)} \geq 1, $$ generalizing a previous
conjecture of Tarski. Here, $w_{v_i}(C)$ is the width of $C$ in the direction
$v_i$.
  In this note we give a short proof of this conjecture under the assumption
that, for every $m$ with $1 \leq m \leq k$, $ C \setminus \bigcup_{i = 1}^m P_i
$ is a convex set. In addition, we prove that if the projection of $C$ onto the
vector space spanned by the normal vectors of the planks has dimension $d$,
then $$ \sum_{i=1}^k \frac{w_i}{w_{v_i}(C)} \geq \frac{1}{d}. $$


title:
Stability of Analytic Neural Networks with Event-triggered Synaptic
  Feedbacks

abstract:
  In this paper, we investigate stability of a class of analytic neural
networks with the synaptic feedback via event-triggered rules. This model is
general and include Hopfield neural network as a special case. These
event-trigger rules can efficiently reduces loads of computation and
information transmission at synapses of the neurons. The synaptic feedback of
each neuron keeps a constant value based on the outputs of the other neurons at
its latest triggering time but changes at its next triggering time, which is
determined by certain criterion. It is proved that every trajectory of the
analytic neural network converges to certain equilibrium under this
event-triggered rule for all initial values except a set of zero measure. The
main technique of the proof is the Lojasiewicz inequality to prove the
finiteness of trajectory length. The realization of this event-triggered rule
is verified by the exclusion of Zeno behaviors. Numerical examples are provided
to illustrate the efficiency of the theoretical results.


title: Ground state properties of hard-core anyons in a harmonic potential

abstract:
  Using anyon-fermion mapping method, we investigate the ground state
properties of hard-core anyons confined in a one-dimensional harmonic trap. The
concise analytical formula of the reduced one-body density matrix are obtained.
Basing on the formula, we evaluated the momentum distribution, the natural
orbitals and their occupation distributions for different statistical
parameters. The occupation and occupation fraction of the lowest natural
orbital versus anyon number are also displayed. It is shown that the ground
state properties of anyons interplay between Bosons and Fermions continuously.
We can expect that the hard-core anyons of larger statistical parameter exhibit
the similar properties to the hard-core Bosons although anyon system satisfy
specific fractional statistics.


title:
Local pinning of networks of multi-agent systems with transmission and
  pinning delays

abstract:
  We study the stability of networks of multi-agent systems with local pinning
strategies and two types of time delays, namely the transmission delay in the
network and the pinning delay of the controllers. Sufficient conditions for
stability are derived under specific scenarios by computing or estimating the
dominant eigenvalue of the characteristic equation. In addition, controlling
the network by pinning a single node is studied. Moreover, perturbation methods
are employed to derive conditions in the limit of small and large pinning
strengths.Numerical algorithms are proposed to verify stability, and simulation
examples are presented to confirm the efficiency of analytic results.


title:
Connectivity of Wireless Sensor Networks Secured by Heterogeneous Key
  Predistribution Under an On/Off Channel Model

abstract:
  We investigate the connectivity of a wireless sensor network secured by the
heterogeneous key predistribution scheme under an independent on/off channel
model. The heterogeneous scheme induces an inhomogeneous random key graph,
denoted by $\mathbb{K}(n;\pmb{\mu},\pmb{K},P)$ and the on/off channel model
induces an Erd\H{o}s-R\'enyi graph, denoted by $\mathbb{H}(n,\alpha)$. Hence,
the overall random graph modeling the WSN is obtained by the intersection of
$\mathbb{K}(n;\pmb{\mu},\pmb{K},P)$ and $\mathbb{H}(n,\alpha)$. We present
conditions on how to scale the parameters of the intersecting graph with
respect to the network size $n$ such that the graph i) has no isolated nodes
and ii) is connected, both with high probability as the number of nodes gets
large. Our results are supported by a simulation study demonstrating that i)
despite their asymptotic nature, our results can in fact be useful in designing
finite-node wireless sensor networks so that they achieve secure connectivity
with high probability; and ii) despite the simplicity of the on/off
communication model, the probability of connectivity in the resulting wireless
sensor network approximates very well the case where the disk model is used.


title: Embedding Lexical Features via Low-Rank Tensors

abstract:
  Modern NLP models rely heavily on engineered features, which often combine
word and contextual information into complex lexical features. Such combination
results in large numbers of features, which can lead to over-fitting. We
present a new model that represents complex lexical features---comprised of
parts for words, contextual information and labels---in a tensor that captures
conjunction information among these parts. We apply low-rank tensor
approximations to the corresponding parameter tensors to reduce the parameter
space and improve prediction speed. Furthermore, we investigate two methods for
handling features that include $n$-grams of mixed lengths. Our model achieves
state-of-the-art results on tasks in relation extraction, PP-attachment, and
preposition disambiguation.


title:
Centralized and Decentralized Global Outer-synchronization of Asymmetric
  Recurrent Time-varying Neural Network by Data-sampling

abstract:
  In this paper, we discuss the outer-synchronization of the asymmetrically
connected recurrent time-varying neural networks. By both centralized and
decentralized discretization data sampling principles, we derive several
sufficient conditions based on diverse vector norms that guarantee that any two
trajectories from different initial values of the identical neural network
system converge together. The lower bounds of the common time intervals between
data samples in centralized and decentralized principles are proved to be
positive, which guarantees exclusion of Zeno behavior. A numerical example is
provided to illustrate the efficiency of the theoretical results.


title:
New Improved Massive Gravity and Three Dimensional Spacetimes of
  Constant Curvature and Constant Torsion

abstract:
  We derive the field equations for topologically massive gravity coupled with
the most general quadratic curvature terms using the language of exterior
differential forms and a first order constrained variational principle. We find
variational field equations both in the presence and absence of torsion. We
then show that spaces of constant negative curvature (i.e. the anti de-Sitter
space $AdS_3$) and constant torsion provide exact solutions.


title:
On the Strong Novikov Conjecture of Locally Compact Groups for Low
  Degree Cohomology Classes

abstract:
  The main result of this paper is non-vanishing of the image of the index map
from the $G$-equivariant $K$-homology of a proper $G$-compact $G$-manifold $X$
to the $K$-theory of the $C^{*}$-algebra of the group $G$. Under the assumption
that the Kronecker pairing of a $K$-homology class with a low-dimensional
cohomology class is non-zero, we prove that the image of this class under the
index map is non-zero. Neither discreteness of the locally compact group $G$
nor freeness of the action of $G$ on $X$ are required. The case of free actions
of discrete groups was considered earlier by B. Hanke and T. Schick.


title: Origin of Hawking Radiation: Firewall or Atmosphere?

abstract:
  The Unruh vacuum not admitting any outgoing flux at the horizon implies that
the origin of the outgoing Hawking radiation is the atmosphere of a
near-horizon quantum region without resort to the firewall; however, the
existence of the firewall of superplanckian excitations at the horizon can be
supported by the infinite Tolman temperature at the horizon. In an exactly
soluble model, we explicitly show that the firewall necessarily emerges out of
the Unruh vacuum so that the Tolman temperature in the Unruh vacuum is
divergent in essence due to the infinitely blueshifted negative ingoing flux
crossing the horizon rather than the outgoing flux. We also show that the
outgoing Hawking radiation in the Unruh vacuum indeed originates from the
atmosphere, not just at the horizon, which is of no relevance to the infinite
blueshift. Consequently, the firewall from the infinite Tolman temperature and
the Hawking radiation from the atmosphere turn out to be compatible, once we
waive the claim that the Hawking radiation in the Unruh vacuum originates from
the infinitely blueshifted outgoing excitations at the horizon.


title: Automatic Annotation of Structured Facts in Images

abstract:
  Motivated by the application of fact-level image understanding, we present an
automatic method for data collection of structured visual facts from images
with captions. Example structured facts include attributed objects (e.g.,
<flower, red>), actions (e.g., <baby, smile>), interactions (e.g., <man,
walking, dog>), and positional information (e.g., <vase, on, table>). The
collected annotations are in the form of fact-image pairs (e.g.,<man, walking,
dog> and an image region containing this fact). With a language approach, the
proposed method is able to collect hundreds of thousands of visual fact
annotations with accuracy of 83% according to human judgment. Our method
automatically collected more than 380,000 visual fact annotations and more than
110,000 unique visual facts from images with captions and localized them in
images in less than one day of processing time on standard CPU platforms.


title: Social contagions on weighted networks

abstract:
  We investigate critical behaviors of a social contagion model on weighted
networks. An edge-weight compartmental approach is applied to analyze the
weighted social contagion on strongly heterogenous networks with skewed degree
and weight distributions. We find that degree heterogeneity can not only alter
the nature of contagion transition from discontinuous to continuous but also
can enhance or hamper the size of adoption, depending on the unit transmission
probability. We also show that, the heterogeneity of weight distribution always
hinder social contagions, and does not alter the transition type.


title: Random-walk baryogenesis via primordial black holes

abstract:
  Gravitation violates baryon number $B$: A star has a huge amount of it, while
a black hole forming from the star has none. Consider primordial black holes
before the hadronic annihiliation in the early universe, encountering and
absorbing baryons and antibaryons: Each such absorption changes $B$ of the
universe by one unit, up or down. But the absorption events are $uncorrelated$
$and$ $random$, hence they amount to a random walk in $B$-space, leading to the
expectation of a net $|B|$ at the end.
  While the scale of this effect is most uncertain, it must exist. We explore
some ramifications, including the change of net $|B|$ with expansion,
connection with universe topology, and possible observational signatures.


title:
Fluctuations of electrical conductivity: a new source for astrophysical
  magnetic fields

abstract:
  We consider the generation of magnetic field by the flow of a fluid for which
the electrical conductivity is nonuniform. A new amplification mechanism is
found which leads to dynamo action for flows much simpler than those considered
so far. In particular, the fluctuations of the electrical conductivity provide
a way to bypass anti-dynamo theorems. For astrophysical objects, we show
through three-dimensional global numerical simulations that the
temperature-driven fluctuations of the electrical conductivity can amplify an
otherwise decaying large scale equatorial dipolar field. This effect could play
a role for the generation of the unusually tilted magnetic field of the iced
giants Neptune and Uranus.


title: Overlay Text Extraction From TV News Broadcast

abstract:
  The text data present in overlaid bands convey brief descriptions of news
events in broadcast videos. The process of text extraction becomes challenging
as overlay text is presented in widely varying formats and often with animation
effects. We note that existing edge density based methods are well suited for
our application on account of their simplicity and speed of operation. However,
these methods are sensitive to thresholds and have high false positive rates.
In this paper, we present a contrast enhancement based preprocessing stage for
overlay text detection and a parameter free edge density based scheme for
efficient text band detection. The second contribution of this paper is a novel
approach for multiple text region tracking with a formal identification of all
possible detection failure cases. The tracking stage enables us to establish
the temporal presence of text bands and their linking over time. The third
contribution is the adoption of Tesseract OCR for the specific task of overlay
text recognition using web news articles. The proposed approach is tested and
found superior on news videos acquired from three Indian English television
news channels along with benchmark datasets.


title: Nanofaceting as a stamp for periodic graphene charge carrier modulations

abstract:
  The exceptional electronic properties of monoatomic thin graphene sheets
triggered numerous original transport concepts, pushing quantum physics into
the realm of device technology for electronics, optoelectronics and
thermoelectrics. At the conceptual pivot point is the particular twodimensional
massless Dirac fermion character of graphene charge carriers and its volitional
modification by intrinsic or extrinsic means. Here, interfaces between
different electronic and structural graphene modifications promise exciting
physics and functionality, in particular when fabricated with atomic precision.
In this study we show that quasiperiodic modulations of doping levels can be
imprinted down to the nanoscale in monolayer graphene sheets. Vicinal copper
surfaces allow to alternate graphene carrier densities by several 10^13
carriers per cm^2 along a specific copper high-symmetry direction. The process
is triggered by a self-assembled copper faceting process during
high-temperature graphene chemical vapor deposition, which defines interfaces
between different graphene doping levels at the atomic level.


title:
Contact statistics highlight distinct organizing principles of proteins
  and RNA

abstract:
  Although both RNA and proteins have densely packed native structures, chain
organizations of these two biopolymers are fundamentally different. Motivated
by the recent discoveries in chromatin folding that interphase chromosomes have
territorial organization with signatures pointing to metastability, we analyzed
the biomolecular structures deposited in the Protein Data Bank and found that
the intrachain contact probabilities, $P(s)$ as a function of the arc length
$s$, decay in power-law $\sim s^{-\gamma}$ over the intermediate range of $s$,
$10\lesssim s\lesssim 110$. We found that the contact probability scaling
exponent is $\gamma\approx 1.11$ for large RNA ($N>110$), $\gamma\approx 1.41$
for small sized RNA ($N<110$), and $\gamma\approx 1.65$ for proteins. Given
that Gaussian statistics is expected for a fully equilibrated chain in polymer
melts, the deviation of $\gamma$ value from $\gamma=1.5$ for the subchains of
large RNA in the native state suggests that the chain configuration of RNA is
not fully equilibrated. It is visually clear that folded structures of large
sized RNA ($N\gtrsim 110$) adopt crumpled structures, partitioned into modular
multi-domains assembled by proximal sequences along the chain, whereas the
polypeptide chain of folded proteins looks better mixed with the rest of the
structure. Our finding of $\gamma\approx 1$ for large RNA might be an
ineluctable consequence of the hierarchical ordering of the secondary to
tertiary elements in the folding process.


title: The Ptolemaean Inequality in the closure of complex hyperbolic plane

abstract:
  We prove Ptolemaean Inequality and Ptolemaeus' Theorem in the closure complex
hyperbolic plane endowed with the Cygan metric.


title: New Conformal Invariants in Absolute Parallelism Geometry

abstract:
  The aim of the present paper is to investigate conformal changes in absolute
parallelism geometry. We find out some new conformal invariants in terms of the
Weitzenb\"ock connection and the Levi-Civita connection of an absolute
parallelism space.


title:
Robust video object tracking via Bayesian model averaging based feature
  fusion

abstract:
  In this article, we are concerned with tracking an object of interest in
video stream. We propose an algorithm that is robust against occlusion, the
presence of confusing colors, abrupt changes in the object feature space and
changes in object size. We develop the algorithm within a Bayesian modeling
framework. The state space model is used for capturing the temporal correlation
in the sequence of frame images by modeling the underlying dynamics of the
tracking system. The Bayesian model averaging (BMA) strategy is proposed for
fusing multi-clue information in the observations. Any number of object
features are allowed to be involved in the proposed framework. Every feature
represents one source of information to be fused and is associated with an
observation model. The state inference is performed by employing the particle
filter methods. In comparison with related approaches, the BMA based tracker is
shown to have robustness, expressivity, and comprehensibility.


title:
Determination of surface and interface magnetic properties for the
  multiferroic heterostructure Co/BaTiO3 using SPLEED and ARPES

abstract:
  Co/BaTiO$_3$(001) is one of the most interesting multiferroic
heterostructures as it combines different ferroic phases, setting this way the
fundamentals for innovative technical applications. Various theoretical
approaches have been applied to investigate the electronic and magnetic
properties of Co/BaTiO$_3$(001). Here we determine the magnetic properties of 3
ML Co/BaTiO$_3$ by calculating spin-polarized electron diffraction as well as
angle-resolved photoemission spectra, with both methods being well established
as surface sensitive techniques. Furthermore, we discuss the impact of altering
the BaTiO$_3$ polarization on the spectra and ascribe the observed changes to
characteristic details of the electronic structure.


title: Thermoelectric generation based on spin Seebeck effects

abstract:
  The spin Seebeck effect (SSE) refers to the generation of a spin current as a
result of a temperature gradient in magnetic materials including insulators.
The SSE is applicable to thermoelectric generation because the thermally
generated spin current can be converted into a charge current via spin-orbit
interaction in conductive materials adjacent to the magnets. The
insulator-based SSE device exhibits unconventional characteristics potentially
useful for thermoelectric applications, such as simple structure, device-design
flexibility, and convenient scaling capability. In this article, we review
recent studies on the SSE from the viewpoint of thermoelectric applications.
Firstly, we introduce the thermoelectric generation process and measurement
configuration of the SSE, followed by showing fundamental characteristics of
the SSE device. Secondly, a theory of the thermoelectric conversion efficiency
of the SSE device is presented, which clarifies the difference between the SSE
and conventional thermoelectric effects and the efficiency limit of the SSE
device. Finally, we show preliminary demonstrations of the SSE in various
device structures for future thermoelectric applications and discuss prospects
of the SSE-based thermoelectric technologies.


title:
State Space Model based Trust Evaluation over Wireless Sensor Networks:
  An Iterative Particle Filter Approach

abstract:
  In this paper we propose a state space modeling approach for trust evaluation
in wireless sensor networks. In our state space trust model (SSTM), each sensor
node is associated with a trust metric, which measures to what extent the data
transmitted from this node would better be trusted by the server node. Given
the SSTM, we translate the trust evaluation problem to be a nonlinear state
filtering problem. To estimate the state based on the SSTM, a component-wise
iterative state inference procedure is proposed to work in tandem with the
particle filter, and thus the resulting algorithm is termed as iterative
particle filter (IPF). The computational complexity of the IPF algorithm is
theoretically linearly related with the dimension of the state. This property
is desirable especially for high dimensional trust evaluation and state
filtering problems. The performance of the proposed algorithm is evaluated by
both simulations and real data analysis.


title: Purification of a single photon nonlinearity

abstract:
  We show that the lifetime-reduced fidelity of a semiconductor quantum
dot-cavity single photon nonlinearity can be restored by polarization pre- and
postselection. This is realized with a polarization degenerate microcavity in
the weak coupling regime, where an output polarizer enables quantum
interference of the two orthogonally polarized transmission amplitudes. This
allows us to transform incident coherent light into a stream of strongly
correlated photons with a second-order correlation function of g2(0)~40, larger
than previous experimental results even in the strong-coupling regime. This
purification technique might also be useful to improve the fidelity of quantum
dot based logic gates.


title: Three-Term Relations for 3F2(1)

abstract:
  For the hypergeometric function of unit argument 3F2(1) we prove the
existence and uniqueness of three-term relations with arbitrary integer shifts.
We show that not only the original 3F2(1) function but also other five
functions related to it satisfy one and the same three-term relation. This fact
is referred to as simultaneousness. The uniqueness and simultaneousness provide
three-term relations with a group symmetry of order 72.


title: The higher sharp I: on $M_1^\#$

abstract:
  We establish the descriptive set theoretic representation of the mouse
$M_n^{\#}$, which is called $0^{(n+1)\#}$. This part deals with the case $n=1$.


title: On single-photon wave function

abstract:
  We present in this paper how the single-photon wave function for transversal
photons (with the direct sum of ordinary unitary representations of helicity 1
and -1 acting on it) is subsumed within the formalism of Gupta-Bleuler for the
quantized free electromagnetic field in the Krein space (i.e. in the ordinary
Hilbert space endowed with the Gupta-Bleuler operator $\eta$). Rigorous
Gupta-Bleuler quantization of the free electromagnetic field is based on a
generalization of ours (published formerly) of the Mackey theory of induced
representations which includes representations preserving the indefinite Krein
inner-product given by the Gupta-Bleuler operator and acting in the Krein
space. The free electromagnetic field is constructed by application of the
Segal's second quantization functor to the specific Krein-isometric
representation. A closed subspace $\mathcal{H}_{\textrm{tr}}$ of the
single-photon Krein space on which the indefinite Krein-inner-product is
strictly positive is constructed such that the Krein-isometric single-photon
representation generates modulo unphysical states precisely the action of a
representation which preserves the positive inner product on
$\mathcal{H}_{\textrm{tr}}$ induced by the Krein inner product, and is equal to
the direct sum of ordinary unitary representations of helicity 1 and -1
respectively. Two states of single photon Krein space are physically equivalent
whenever differ by a state of Krein norm zero and whose projection on
$\mathcal{H}_{\textrm{tr}}$, in the sense of the Krein-inner-product, vanishes.
In particulart it follows that the results of Bia{\l}ynicki-Birula on the
single-photon wave function may be reconciled with the micro-local perturbative
approach to QED initiated by St\"uckelberg and Bogoliubov.


title:
Polyyne Electronic and Vibrational Properties under Environmental
  Interactions

abstract:
  Recently, the novel system of linear carbon chains inside of double-walled
carbon nanotubes has extended the length of $sp^1$ hybridized carbon chains
from 44 to thousands of atoms [L. Shi et al., Nat. Mater. 15, 634 (2016)]. The
optoelectronic properties of these ultra-long chains are poorly described by
current theoretical models, which are based on short chain experimental data
and assume a constant environment. As such, a physical understanding of the
system in terms of charge transfer and van der Waals interactions is widely
missing. We provide a reference for the intrinsic Raman frequency of polyynes
in vacuo and explicitly describe the interactions between polyynes and carbon
nanotubes. We find that van der Waals interactions strongly shift the Raman
frequency, which has been neither expected nor addressed before. As a
consequence of charge transfer from the tube to the chain, the Raman response
of long chains is qualitatively different from the known phonon dispersion of
polymers close to the $\Gamma$-point. Based on these findings we show how to
correctly interpret the Raman data, considering the nanotube's properties. This
is essential for its use as an analytical tool to optimize the growth process
for future applications.


title: G-stable support $\tau$-tilting modules

abstract:
  Motivated by $\tau$-tilting theory developed by Adachi, Iyama and Reiten, for
a finite-dimensional algebra $\Lambda$ with action by a finite group $G$, we
introduce the notion of $G$-stable support $\tau$-tilting modules. Then we
establish bijections among $G$-stable support $\tau$-tilting modules over
$\Lambda$, $G$-stable two-term silting complexes in the homotopy category of
bounded complexes of finitely generated projective $\Lambda$-modules, and
$G$-stable functorially finite torsion classes in the category of finitely
generated left $\Lambda$-modules. In the case when $\Lambda$ is the
endomorphism of a $G$-stable cluster-tilting object $T$ over a Hom-finite
2-Calabi-Yau triangulated category $\mathcal{C}$ with a $G$-action, these are
also in bijection with $G$-stable cluster-tilting objects in $\mathcal{C}$.
Moreover, we investigate the relationship between stable support $\tau$-tilitng
modules over $\Lambda$ and the skew group algebra $\Lambda G$.


title:
Light Walls Around Sunspots Observed by the Interface Region Imaging
  Spectrograph

abstract:
  The Interface Region Imaging Spectrograph (IRIS) mission provides
high-resolution observations of the chromosphere and transition region. We try
to determine whether the light walls exist somewhere else in active regions
besides light bridges. Employing half-year high tempo-spatial data from the
IRIS, we find lots of light walls either around sunspots or above light
bridges. For the first time, we report one light wall near an umbral-penumbral
boundary and another along a neutral line between two small sunspots. These new
observations reveal that these light walls are multi-layer and multi-thermal
structures which occur along magnetic neutral lines in active regions.


title:
New extremal binary self-dual codes of lengths 64 and 66 from bicubic
  planar graphs

abstract:
  In this work, connected cubic planar bipartite graphs and related binary
self-dual codes are studied. Binary self-dual codes of length 16 are obtained
by face-vertex incidence matrices of these graphs. By considering their lifts
to the ring R_2 new extremal binary self-dual codes of lengths 64 are
constructed as Gray images. More precisely, we construct 15 new codes of length
64. Moreover, 10 new codes of length 66 were obtained by applying a building-up
construction to the binary codes. Codes with these weight enumerators are
constructed for the first time in the literature. The results are tabulated.


title: Quantifying lymphocyte receptor diversity

abstract:
  To recognize pathogens, B and T lymphocytes are endowed with a wide
repertoire of receptors generated stochastically by V(D)J recombination.
Measuring and estimating the diversity of these receptors is of great
importance for understanding adaptive immunity. In this chapter we review
recent modeling approaches for analyzing receptor diversity from
high-throughput sequencing data. We first clarify the various existing notions
of diversity, with its many competing mathematical indices, and the different
biological levels at which it can be evaluated. We then describe inference
methods for characterizing the statistical diversity of receptors at different
stages of their history: generation, selection and somatic evolution. We
discuss the intrinsic difficulty of estimating the diversity of receptors
realized in a given individual from incomplete samples. Finally, we emphasize
the limitations of diversity defined at the level of receptor sequences, and
advocate the more relevant notion of functional diversity relative to the set
of recognized antigens.


title:
The conformal supercurrents in diverse dimensions and conserved
  superconformal currents

abstract:
  Given a conserved and traceless energy-momentum tensor and a conformal
Killing vector, one obtains a conserved current. We generalise this
construction to superconformal theories in three, four, five and six dimensions
with various amounts of supersymmetry by working in the appropriate
superspaces.


title:
Occurrence of discontinuities in the performance of finite-time quantum
  Otto cycles

abstract:
  We study a quantum Otto cycle in which the strokes are performed in finite
time. The cycle involves energy measurements at the end of each stroke to allow
for the respective determination of work. We then optimize for the work and
efficiency of the cycle by varying the time spent in the different strokes and
find that the optimal value of the ratio of time spent on each stroke goes
through sudden changes as the parameters of this cycle vary continuously. The
position of these discontinuities depends on the optimized quantity under
consideration such as the net work output or the efficiency.


title:
Operational calculus for holonomic distributions in the framework of
  D-module theory

abstract:
  Let $f$ be a real polynomial of $x = (x_1,\dots,x_n)$ and $\varphi$ be a
locally integrable function of $x$ which satisfies a holonomic system of linear
differential equations. We study the distribution $f_+^\lambda\varphi$ with a
meromorphic parameter $\lambda$, especially its Laurent expansion and
integration, from an algorithmic viewpoint in the framework of $D$-module
theory.


title: Communities unfolding in multislice networks

abstract:
  Discovering communities in complex networks helps to understand the behaviour
of the network. Some works in this promising research area exist, but
communities uncovering in time-dependent and/or multiplex networks has not
deeply investigated yet. In this paper, we propose a communities detection
approach for multislice networks based on modularity optimization. We first
present a method to reduce the network size that still preserves modularity.
Then we introduce an algorithm that approximates modularity optimization (as
usually adopted) for multislice networks, thus finding communities. The network
size reduction allows us to maintain acceptable performances without affecting
the effectiveness of the proposed approach.


title: Impact of the valence band structure of Cu$_{2}$O on excitonic spectra

abstract:
  We present a method to calculate the exciton spectra of all direct
semiconductors with a complex valence band structure. The Schr\"odinger
equation is solved using a complete basis set with Coulomb Sturmian functions.
This method also allows for the computation of oscillator strengths. Here we
apply this method to investigate the impact of the valence band structure of
cuprous oxide $\left(\mathrm{Cu_{2}O}\right)$ on the yellow exciton spectrum.
Results differ from those in [Phys. Rev. Lett. 115, 027402 (2015)]; the
differences are discussed and explained. The difference between the second and
third Luttinger parameter can be determined by comparisons with experiments,
however, the evaluation of all three Luttinger parameters is not uniquely
possible. Our results are consistent with band structure calculations.
Considering also a finite momentum $\hbar K$ of the center of mass, we show
that the large $K$-dependent line splitting observed for the $1S$ exciton state
[Phys. Rev. Lett. 91, 107401 (2003)] is not related to an exchange interaction
but rather to the complex valence band structure of $\mathrm{Cu_{2}O}$.


title: Steganography -- A Game of Hide and Seek in Information Communication

abstract:
  With the growth of communication over computer networks, how to maintain the
confidentiality and security of transmitted information have become some of the
important issues. In order to transfer data securely to the destination without
unwanted disclosure or damage, nature inspired hide and seek tricks such as,
cryptography and Steganography are heavily in use. Just like the Chameleon and
many other bio-species those change their body color and hide themselves in the
background in order to protect them from external attacks, Cryptography and
Steganography are techniques those are used to encrypt and hide the secret data
inside other media to ensure data security. This paper discusses the concept of
a simple spatial domain LSB Steganography that encrypts the secrets using
Fibonacci- Lucas transformation, before hiding, for better security.


title:
A Fully Convolutional Neural Network for Cardiac Segmentation in
  Short-Axis MRI

abstract:
  Automated cardiac segmentation from magnetic resonance imaging datasets is an
essential step in the timely diagnosis and management of cardiac pathologies.
We propose to tackle the problem of automated left and right ventricle
segmentation through the application of a deep fully convolutional neural
network architecture. Our model is efficiently trained end-to-end in a single
learning stage from whole-image inputs and ground truths to make inference at
every pixel. To our knowledge, this is the first application of a fully
convolutional neural network architecture for pixel-wise labeling in cardiac
magnetic resonance imaging. Numerical experiments demonstrate that our model is
robust to outperform previous fully automated methods across multiple
evaluation measures on a range of cardiac datasets. Moreover, our model is fast
and can leverage commodity compute resources such as the graphics processing
unit to enable state-of-the-art cardiac segmentation at massive scales. The
models and code are available at
https://github.com/vuptran/cardiac-segmentation


title: Vacuum polarization in asymptotically Lifshitz black holes

abstract:
  There has been considerable interest in applying the gauge/gravity duality to
condensed matter theories with particular attention being devoted to gravity
duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In
this context, black hole solutions with Lifshitz asymptotics have also been
constructed aiming at incorporating finite temperature effects. The goal here
is to look at quantum polarization effects in these spacetimes, and to this
aim, we develop a way to compute the coincidence limit of the Green's function
for massive, non-minimally coupled scalar fields, adapting to the present
situation the analysis developed for the case of asymptotically anti de Sitter
black holes. The basics are similar to previous calculations, however in the
Lifshitz case one needs to extend previous results to include a more general
form for the metric and dependence on the dynamical exponent. All formulae are
shown to reduce to the AdS case studied before once the value of the dynamical
exponent is set to unity and the metric functions are accordingly chosen. The
analytical results we present are general and can be applied to a variety of
cases, in fact, to all spherically symmetric Lifshitz black hole solutions. We
also implement the numerical analysis choosing some known Lifshitz black hole
solutions as illustration.


title: Manifestation of nonlocal electron-electron interaction in graphene

abstract:
  Graphene is an ideal platform to study many-body effects due to its
semimetallic character and the possibility to dope it over a wide range. Here
we study the width of graphene's occupied $\pi$-band as a function of doping
using angle-resolved photoemission. Upon increasing electron doping, we observe
the expected shift of the band to higher binding energies. However, this shift
is not rigid and the bottom of the band moves less than the Dirac point. We
show that the observed shift cannot be accounted for by band structure
calculations in the local density approximation but that non-local exchange
interactions must be taken into account.


title:
THz-Raman Identification of labile products in the system
  "phenol-semiquinone-quinone"

abstract:
  The paper presents the results of SERS studies of the dynamic behavior of
"phenol-semiquinone-quinone" system. This system is a key part of
chemiluminescent sensors for reactive oxygen species. The dynamics of the
system seems to be very important in the processes that determine the secondary
metabolism at the cellular level in molecular biology. THz Raman spectra were
recorded for the labile products formed in the processes initiated by proton
transfer. A mechanism of the proton-transfer-initiated reaction is proposed.


title: A Get-Together for Deaf and Dumb Robots in Three dimensional Space

abstract:
  This paper proposes a strategy for a group of deaf and dumb robots, carrying
clocks from different countries, to meet at a geographical location which is
not fixed in advanced. The robots act independently. They can observe others,
compute some locations and walk towards those locations. They can only get a
snapshot of the locations of other robots but can not detect whether they are
static or in motion. The robots are forgetful; once they have completed their
motion they forget their previous locations and observations. Again they decide
new destinations to move to. Eventually all the robots compute the same
destination and meet there. There exists no global positioning system. As they
stand, they agree on up and down directions. However, as they do not have any
compass, the other directions are not agreed upon. They also do not agree on
the clockwise direction. For determining a strategy, we imagine the robots to
be points on a three dimensional plane where all the robots are mutually
visible to each other always. The strategy we propose has to be obeyed by all
the robots independently with respect to their own clock and compass. Initially
the robots start from distinct locations. Some dead robots may be present in
the system or some may die any time before or after the get together. However,
the live robots are not aware of the presence of these dead robots.


title:
From Monge to Higgs: a survey of distance computations in noncommutative
  geometry

abstract:
  This is a review of explicit computations of Connes distance in
noncommutative geometry, covering finite dimensional spectral triples,
almost-commutative geometries, and spectral triples on the algebra of compact
operators. Several applications to physics are covered, like the metric
interpretation of the Higgs field, and the comparison of Connes distance with
the minimal length that emerges in various models of quantum spacetime. Links
with other areas of mathematics are studied, in particular the horizontal
distance in sub-Riemannian geometry. The interpretation of Connes distance as a
noncommutative version of the Monge-Kantorovich metric in optimal transport is
also discussed.

categories: math-ph gr-qc hep-th math.DG math.MP math.QA


title:
Elzar: Triple Modular Redundancy using Intel Advanced Vector Extensions
  (technical report)

abstract:
  Instruction-Level Redundancy (ILR) is a well-known approach to tolerate
transient CPU faults. It replicates instructions in a program and inserts
periodic checks to detect and correct CPU faults using majority voting, which
essentially requires three copies of each instruction and leads to high
performance overheads. As SIMD technology can operate simultaneously on several
copies of the data, it appears to be a good candidate for decreasing these
overheads. To verify this hypothesis, we propose Elzar, a compiler framework
that transforms unmodified multithreaded applications to support triple modular
redundancy using Intel AVX extensions for vectorization. Our experience with
several benchmark suites and real-world case-studies yields mixed results:
while SIMD may be beneficial for some workloads, e.g., CPU-intensive ones with
many floating-point operations, it exhibits higher overhead than ILR in many
applications we tested. We study the sources of overheads and discuss possible
improvements to Intel AVX that would lead to better performance.


title: Quantum steering: a review with focus on semidefinite programming

abstract:
  Quantum steering refers to the non-classical correlations that can be
observed between the outcomes of measurements applied on half of an entangled
state and the resulting post-measured states that are left with the other
party. From an operational point of view, a steering test can be seen as an
entanglement test where one of the parties performs uncharacterised
measurements. Thus, quantum steering is a form of quantum inseparability that
lies in between the well-known notions of Bell nonlocality and entanglement.
Moreover, quantum steering is also related to several asymmetric quantum
information protocols where some of the parties are considered untrusted.
Because of these facts, quantum steering has received a lot of attention both
theoretically and experimentally. The main goal of this review is to give an
overview of how to characterise quantum steering through semidefinite
programming. This characterisation provides efficient numerical methods to
address a number of problems, including steering detection, quantification, and
applications. We also give a brief overview of some important results that are
not directly related to semidefinite programming. Finally, we make available a
collection of semidefinite programming codes that can be used to study the
topics discussed in this article


title: Online Updating of Word Representations for Part-of-Speech Tagging

abstract:
  We propose online unsupervised domain adaptation (DA), which is performed
incrementally as data comes in and is applicable when batch DA is not possible.
In a part-of-speech (POS) tagging evaluation, we find that online unsupervised
DA performs as well as batch DA.


title: Discriminative Phrase Embedding for Paraphrase Identification

abstract:
  This work, concerning paraphrase identification task, on one hand contributes
to expanding deep learning embeddings to include continuous and discontinuous
linguistic phrases. On the other hand, it comes up with a new scheme TF-KLD-KNN
to learn the discriminative weights of words and phrases specific to paraphrase
task, so that a weighted sum of embeddings can represent sentences more
effectively. Based on these two innovations we get competitive state-of-the-art
performance on paraphrase identification.


title:
The critical energy of the Ising double chain -- the explanation for
  melting

abstract:
  The Ising double chain has been overlooked for more than 80 years, since one
was mostly interested in phase transitions. We consider two types of
degeneracy, spin occupation degeneracy and "bond" occupation degeneracy. We
show that bond occupation on "open nets" is of particular importance for the
understanding of melting. The number of open nets on a double chain is
determined analytically. If only one bond site of a net is occupied, this
already produces a definite number of bonds on sites, bonds that do not belong
to the net. All nets on a given chain of length $n$ then yield a total number
$i^{(n)}_{\rm tot}$ of bonds, allowing to calculate a characteristic energy
$u^{(n)}_{ch}$, an approximation of the critical energy $u_c$ of the infinite
double chain. We finally present an explanation for the critical energy $u^{\rm
KG}_c$ of the kagom\'e lattice in terms of the critical energies $u^{\rm TR}_c$
and $u^{\rm HC}_c$ of the triangular and honeycomb lattices.


title: On nonlinear superposition of shock waves for the KdV-Burgers equation

abstract:
  Superposition of explicit (analytic) monotone non-increasing shock waves for
the KdV-Burgers equation is studied, modelled numerically and graphically
presented. Initial profile chosen as a sum of two such shock waves gradually
transforms into a single shock wave of a somewhat complex yet predictable
structure. This transformation is demonstrated in detail.


title:
Stochastic Galerkin Framework with Locally Reduced Bases for Nonlinear
  Two-Phase Transport in Heterogeneous Formations

abstract:
  The generalized polynomial chaos method is applied to the Buckley-Leverett
equation. We consider a spatially homogeneous domain modeled as a random field.
The problem is projected onto stochastic basis functions which yields an
extended system of partial differential equations. Analysis and numerical
methods leading to reduced computational cost are presented for the extended
system of equations.
  The accurate representation of the evolution of a discontinuous stochastic
solution over time requires a large number of stochastic basis functions.
Adaptivity of the stochastic basis to reduce computational cost is challenging
in the stochastic Galerkin setting since the change of basis affects the system
matrix itself. To achieve adaptivity without adding overhead by rewriting the
entire system of equations for every grid cell, we devise a basis reduction
method that distinguishes between locally significant and insignificant modes
without changing the actual system matrices.
  Results are presented for problems in one and two spatial dimensions, with
varying number of stochastic dimensions. We show how to obtain stochastic
velocity fields from realistic permeability fields and demonstrate the
performance of the stochastic Galerkin method with local basis reduction. The
system of conservation laws is discretized with a finite volume method and we
demonstrate numerical convergence to the reference solution obtained through
Monte Carlo sampling.


title: Mathematical Modeling of Extinction of Inhomogeneous Populations

abstract:
  Mathematical models of population extinction have a variety of applications
in such areas as ecology, paleontology and conservation biology. Here we
propose and investigate two types of sub-exponential models of population
extinction.The results of performed analysis show that the principle of minimum
of information loss is the underlying law for the evolution of a broad class of
models of population extinction. Finally, we propose a possible application of
this modeling framework to mechanisms underlying time perception.


title: Using the knowledge of penumbra with a trick simulation

abstract:
  The study is about a basic shadow experiment, which was enriched with a
simulation to understand the reasoning of participants when we use a trick. Two
light sources create an umbra and penumbra behind the objects. With this
experiment, we asked what would happen when the penumbras interact. Most of the
participants predicted the correct solution, that there should be an umbra.
Some of the participants choose wrong alternative, and explained in terms of
the structure of penumbra.


title:
Adler function and Bjorken polarized sum rule: Perturbation expansions
  in powers of $SU(N_c)$ conformal anomaly and studies of the conformal
  symmetry limit

abstract:
  We consider a new form of analytical perturbation theory expansion in the
massless $SU(N_c)$ theory, for the non-singlet part of the
$e^+e^-$-annihilation to hadrons Adler function $D^{ns}$ and of the Bjorken sum
rule of the polarized lepton-hadron deep-inelastic scattering $C_{ns}^{Bjp}$,
and demonstrate its validity at the $O(\alpha_s^4)$-level at least. It is a
two-fold series in terms of powers of the conformal anomaly and of $SU(N_c)$
coupling $\alpha_s$. Explicit expressions are obtained for the
$\{\beta\}$-expanded perturbation coefficients at $O(\alpha_s^4)$ level in
$\bar{\rm MS}$ scheme, for both considered physical quqantities. Comparisons of
the terms in the $\{\beta\}$-expanded coefficients are made with the
corresponding terms obtained by using extra gluino degrees of freedom, or
skeleton-motivated expansion, or $R_{\delta}$-scheme motivated expansion in the
Principle of Maximal Conformality. Relations between terms of the
$\{\beta\}$-expansion for the $D^{ns}$- and $C_{ns}^{Bjp}$-functions, which
follow from the conformal symmetry limit and its violation, are presnted. The
relevance to the possible new analysis of the experimental data for the Adler
function and Bjorken sum rule is discussed.


title:
A Theoretical Prediction on the Intrinsic Half-Metallicity in the
  Surface-Oxygen-Passivated Cr2N MXene

abstract:
  Two-dimensional Cr2N MXene as well as the surface-passivated Cr2NF2,
Cr2N(OH)2 and Cr2NO2 are investigated by using density functional theory. The
Cr2N is an anti-ferromagnetic metal. The F atom or OH group-passivation does
not change the anti-ferromagnetic characteristics. However, Cr2NO2 has a
ferromagnetic ground state, which is a half-metal. The half-metallicity of
Cr2NO2 is still robust when bias is applied to the nanometer sized device. The
half-metallicity is intrinsic and does not require atomically clean surfaces.
Therefore the stable surface-oxygen-passivated MXene is a good candidate for
spintronics.


title:
Superhalogens as Building Blocks of Complex Hydrides for Hydrogen
  Storage

abstract:
  Superhalogens are species whose electron affinity (EA) or vertical detachment
energy (VDE) exceed to those of halogen. These species typically consist of a
central electropositive atom with electronegative ligands. The EA or VDE of
species can be further increased by using superhalogen as ligands, which are
termed as hyperhalogen. Having established BH4- as a superhalogen, we have
studied BH4-x(BH4)x- (x = 1 to 4) hyperhalogen anions and their Li-complexes,
LiBH4-x(BH4)x using density functional theory. The VDE of these anions is
larger than that of BH4-, which increases with the increase in the number of
peripheral BH4 moieties (x). The hydrogen storage capacity of LiBH4-x(BH4)x
complexes is higher but binding energy is smaller than that of LiBH4, a typical
complex hydride. The linear correlation between dehydrogenation energy of
LiBH4-x(BH4)x complexes and VDE of BH4-x(BH4)x- anions is established. These
complexes are found to be thermodynamically stable against dissociation into
LiBH4 and borane. This study not only demonstrates the role of superhalogen in
designing new materials for hydrogen storage, but also motivates
experimentalists to synthesize LiBH4-x(BH4)x (x = 1 to 4) complexes.


title: Birationally rigid complete intersections of codimension two

abstract:
  We prove that in the parameter space of $M$-dimensional Fano complete
intersections of index one and codimension two the locus of varieties that are
not birationally superrigid has codimension at least $\frac12 (M-9)(M-10)-1$.


title: Towards an accurate solution of wireless network design problems

abstract:
  The optimal design of wireless networks has been widely studied in the
literature and many optimization models have been proposed over the years.
However, most models directly include the signal-to-interference ratios
representing service coverage conditions. This leads to mixed-integer linear
programs with constraint matrices containing tiny coefficients that vary widely
in their order of magnitude. These formulations are known to be challenging
even for state-of-the-art solvers: the standard numerical precision supported
by these solvers is usually not sufficient to reliably guarantee feasible
solutions. Service coverage errors are thus commonly present. Though these
numerical issues are known and become evident even for small-sized instances,
just a very limited number of papers has tried to tackle them, by mainly
investigating alternative non-compact formulations in which the sources of
numerical instabilities are eliminated. In this work, we explore a new approach
by investigating how recent advances in exact solution algorithms for linear
and mixed-integer programs over the rational numbers can be applied to analyze
and tackle the numerical difficulties arising in wireless network design
models.


title:
Every meromorphic function is the Gauss map of a conformal minimal
  surface

abstract:
  Let $M$ be an open Riemann surface. We prove that every meromorphic function
on $M$ is the complex Gauss map of a conformal minimal immersion
$M\to\mathbb{R}^3$ which may furthermore be chosen as the real part of a
holomorphic null curve $M\to\mathbb{C}^3$. Analogous results are proved for
conformal minimal immersions $M\to\mathbb{R}^n$ for any $n>3$. We also show
that every conformal minimal immersion $M\to\mathbb{R}^n$ is isotopic through
conformal minimal immersions $M\to\mathbb{R}^n$ to a flat one, and we identify
the path connected components of the space of all conformal minimal immersions
$M\to\mathbb{R}^n$ for any $n\ge 3$.


title: On the Dual of the Coulter-Matthews Bent Functions

abstract:
  For any bent function, it is very interesting to determine its dual function
because the dual function is also bent in certain cases. For $k$ odd and
$\gcd(n, k)=1$, it is known that the Coulter-Matthews bent function
$f(x)=Tr(ax^{\frac{3^k+1}{2}})$ is weakly regular bent over $\mathbb{F}_{3^n}$,
where $a\in\mathbb{F}_{3^n}^{*}$, and
$Tr(\cdot):\mathbb{F}_{3^n}\rightarrow\mathbb{F}_3$ is the trace function. In
this paper, we investigate the dual function of $f(x)$, and dig out an
universal formula. In particular, for two cases, we determine the formula
explicitly: for the case of $n=3t+1$ and $k=2t+1$ with $t\geq 2$, the dual
function is given by
$$Tr\left(-\frac{x^{3^{2t+1}+3^{t+1}+2}}{a^{3^{2t+1}+3^{t+1}+1}}-\frac{x^{3^{2t}+1}}{a^{-3^{2t}+3^{t}+1}}+\frac{x^{2}}{a^{-3^{2t+1}+3^{t+1}+1}}\right);$$
and for the case of $n=3t+2$ and $k=2t+1$ with $t\geq 2$, the dual function is
given by
$$Tr\left(-\frac{x^{3^{2t+2}+1}}{a^{3^{2t+2}-3^{t+1}+3}}-\frac{x^{2\cdot3^{2t+1}+3^{t+1}+1}}{a^{3^{2t+2}+3^{t+1}+1}}+\frac{x^2}{a^{-3^{2t+2}+3^{t+1}+3}}\right).$$
As a byproduct, we find two new classes of ternary bent functions with only
three terms. Moreover, we also prove that in certain cases $f(x)$ is regular
bent.


title: Extension Groups for DG Modules

abstract:
  Let $M$ and $N$ be differential graded (DG) modules over a positively graded
commutative DG algebra $A$. We show that the Ext-groups
$\operatorname{Ext}^i_A(M,N)$ defined in terms of semi-projective resolutions
are not in general isomorphic to the Yoneda Ext-groups
$\operatorname{YExt}^i_A(M,N)$ given in terms of equivalence classes of
extensions. On the other hand, we show that these groups are isomorphic when
the first DG module is semi-projective.


title:
On the distribution of positive and negative values of Hardy's
  $Z$-function

abstract:
  We investigate the distribution of positive and negative values of Hardy's
function $$ Z(t) := \zeta(1/2+it){\chi(1/2+it)}^{-1/2}, \quad \zeta(s) =
\chi(s)\zeta(1-s). $$ In particular we prove that $$ \mu\bigl(I_{+}(T,T)\bigr)
\;\gg T\; \qquad \hbox{and}\qquad \mu\bigl(I_{-}(T, T)\bigr) \; \gg \; T, $$
where $\mu(\cdot)$ denotes the Lebesgue measure and \begin{align*}
  { I}_+(T,H) &\;=\; \bigl\{T< t\le T+H\,:\, Z(t)>0\bigr\},
  { I}_-(T,H) &\;=\; \bigl\{T< t\le T+H\,:\, Z(t)<0\bigr\}. \end{align*}


title: The Secular and Rotational Brightness Variations of Neptune

abstract:
  Neptune has brightened by more than 10% during the past several decades. We
report on the analysis of published Johnson-Cousins B and V magnitudes dating
back to 1954 along with new U, B, V, R, Rc, I and Ic photometry that we
recorded during the past 24 years. Characteristic magnitudes, colors and
albedos in all seven band-passes are derived from the ensemble of data.
Additionally, 25 spectra spanning 26 hours of observation on 5 nights are
analyzed. The spectrophotometry demonstrates that planetary flux and albedo is
inversely related to the equivalent widths of methane bands. We attribute the
changes in band strength, flux and albedo to the high altitude clouds which
rotate across the planet's visible disk. Bright clouds increase albedo and flux
while reducing methane absorption. Synthetic V magnitudes derived from the
spectroscopy also agree closely with the photometric quantities, which
cross-validates the two techniques. The spectroscopic and photometric results
are discussed within the framework of the secular brightness variations of
Neptune.


title: A Note on the Tattoo Index of Graphs

abstract:
  Consider a network $D$ of pipes which have to be cleaned using some cleaning
agents, called brushes, assigned to some vertices. The tattooing of a simple
connected directed graph $D$ is a particular type of the cleaning in which an
arc are coloured by the colour of the colour-brush transiting it and the tattoo
number of $D$ is a corresponding derivative of brush numbers in it. In this
paper, we introduce a new concept, called the tattoo index of a given graph
$G$, which is an efficiency index related to the tattooing sequence and we
establish some introductory results on this parameter.


title:
A natural approach to the asymptotic mean value property for the
  $p$-Laplacian

abstract:
  Let $1\le p\le\infty$. We show that a function $u\in C(\mathbb R^N)$ is a
viscosity solution to the normalized $p$-Laplace equation $\Delta_p^n u(x)=0$
if and only if the asymptotic formula $$ u(x)=\mu_p(\ve,u)(x)+o(\ve^2) $$ holds
as $\ve\to 0$ in the viscosity sense. Here, $\mu_p(\ve,u)(x)$ is the $p$-mean
value of $u$ on $B_\ve(x)$ characterized as a unique minimizer of $$
\inf_{\la\in\RR}\nr u-\la\nr_{L^p(B_\ve(x))}. $$ This kind of asymptotic mean
value property (AMVP) extends to the case $p=1$ previous (AMVP)'s obtained when
$\mu_p(\ve,u)(x)$ is replaced by other kinds of mean values. The natural
definition of $\mu_p(\ve,u)(x)$ makes sure that this is a monotonic and
continuous (in the appropriate topology) functional of $u$. These two
properties help to establish a fairly general proof of (AMVP), that can also be
extended to the (normalized) parabolic $p$-Laplace equation.


title: Hidden symmetries of the Higgs oscillator and the conformal algebra

abstract:
  We give a solution to the long-standing problem of constructing the
generators of hidden symmetries of the quantum Higgs oscillator, a particle on
a d-sphere moving in a central potential varying as the inverse cosine-squared
of the polar angle. This superintegrable system is known to possess a rich
algebraic structure, including a hidden SU(d) symmetry that can be deduced from
classical conserved quantities and degeneracies of the quantum spectrum. The
quantum generators of this SU(d) have not been constructed thus far, except at
d=2, and naive quantization of classical conserved quantities leads to deformed
Lie algebras with quadratic terms in the commutation relations. The nonlocal
generators we obtain here satisfy the standard su(d) Lie algebra, and their
construction relies on a recently discovered realization of the conformal
algebra, which contains a complete set of raising and lowering operators for
the Higgs oscillator. This operator structure has emerged from a relation
between the Higgs oscillator Schroedinger equation and the Klein-Gordon
equation in Anti-de Sitter spacetime. From such a point-of-view, the
construction of the hidden symmetry generators reduces to manipulations within
the abstract conformal algebra so(d,2).


title: Influence of Joule heating on current-induced domain wall depinning

abstract:
  The domain wall depinning from a notch in a Permalloy nanostrip on top of a
${\rm SiO_2/Si}$ substrate is studied theoretically under application of static
magnetic fields and the injection of short current pulses. The influence of
Joule heating on current-induced domain wall depinning is explored
self-consistently by coupling the magnetization dynamics in the ferromagnetic
strip to the heat transport throughout the system. Our results indicate that
Joule heating plays a remarkable role in these processes, resulting in a
reduction in the critical depinning field and/or in a temporary destruction of
the ferromagnetic order for typically injected current pulses. In agreement
with experimental observations, similar pinning-depinning phase diagrams can be
deduced for both current polarities when the Joule heating is taken into
account. These observations, which are incompatible with the sole contribution
of spin transfer torques, provide a deeper understanding of the physics
underlying these processes and establish the real scope of the spin transfer
torque. They are also relevant for technological applications based on
current-induced domain-wall motion along soft strips.


title:
A Hot and Massive Accretion Disk around the High-Mass Protostar IRAS
  20126+4104

abstract:
  We present new spectral line observations of the CH3CN molecule in the
accretion disk around the massive protostar IRAS 20126+4104 with the
Submillimeter Array that for the first time measure the disk density,
temperature, and rotational velocity with sufficient resolution (0.37",
equivalent to ~600 AU) to assess the gravitational stability of the disk
through the Toomre-Q parameter. Our observations resolve the central 2000 AU
region that shows steeper velocity gradients with increasing upper state
energy, indicating an increase in the rotational velocity of the hotter gas
nearer the star. Such spin-up motions are characteristics of an accretion flow
in a rotationally supported disk. We compare the observed data with synthetic
image cubes produced by three-dimensional radiative transfer models describing
a thin flared disk in Keplerian motion enveloped within the centrifugal radius
of an angular-momentum-conserving accretion flow. Given a luminosity of
1.3x10^4 Lsun, the optimized model gives a disk mass of 1.5 Msun and a radius
of 858 AU rotating about a 12.0 Msun protostar with a disk mass accretion rate
of 3.9x10^{-5} Msun/yr. Our study finds that, in contrast to some theoretical
expectations, the disk is hot and stable to fragmentation with Q > 2.8 at all
radii which permits a smooth accretion flow. These results put forward the
first constraints on gravitational instabilities in massive protostellar disks,
which are closely connected to the formation of companion stars and planetary
systems by fragmentation.


title: Colocalising subcategories of modules over finite group schemes

abstract:
  The Hom closed colocalising subcategories of the stable module category of a
finite group scheme are classified. This complements the classification of the
tensor closed localising subcategories in our previous work. Both
classifications involve pi-points in the sense of Friedlander and Pevtsova. We
identify for each pi-point an endofinite module which both generates the
corresponding minimal localising subcategory and cogenerates the corresponding
minimal colocalising subcategory.


title:
On regularity of primal and dual dynamic value functions related to
  investment problem

abstract:
  We study regularity properties of the dynamic value functions of primal and
dual problems of optimal investing for utility functions defined on the whole
real line. Relations between decomposition terms of value processes of primal
and dual problems and between optimal solutions of basic and conditional
utility maximization problems are established. These properties are used to
show that the value function satisfies a corresponding backward stochastic
partial differential equation.
  In the case of complete markets we give conditions on the utility function
when this equation admits a solution.


title: The Asynchronous PALM Algorithm for Nonsmooth Nonconvex Problems

abstract:
  We introduce the Asynchronous PALM algorithm, a new extension of the Proximal
Alternating Linearized Minimization (PALM) algorithm for solving nonsmooth,
nonconvex optimization problems. Like the PALM algorithm, each step of the
Asynchronous PALM algorithm updates a single block of coordinates; but unlike
the PALM algorithm, the Asynchronous PALM algorithm eliminates the need for
sequential updates that occur one after the other. Instead, our new algorithm
allows each of the coordinate blocks to be updated asynchronously and in any
order, which means that any number of computing cores can compute updates in
parallel without synchronizing their computations. In practice, this
asynchronization strategy often leads to speedups that increase linearly with
the number of computing cores.
  We introduce two variants of the Asynchronous PALM algorithm, one stochastic
and one deterministic. In the stochastic \textit{and} deterministic cases, we
show that cluster points of the algorithm are stationary points. In the
deterministic case, we show that the algorithm converges globally whenever the
Kurdyka-{\L}ojasiewicz property holds for a function closely related to the
objective function, and we derive its convergence rate in a common special
case. Finally, we provide a concrete case in which our assumptions hold.


title: A Decomposition Approach to Solve The Quay Crane Scheduling Problem

abstract:
  In this work we propose a decomposition approach to solve the quay crane
scheduling problem. This is an important maritime transportation problem faced
in container terminals where quay cranes are used to handle cargo. The
objective is to determine a sequence of loading and unloading operations for
each crane in order to minimize the completion time. We solve a mixed integer
programming formulation for the quay crane scheduling problem, decomposing it
into a vehicle routing problem and a corresponding scheduling problem. The
routing sub-problem is solved by minimizing the longest crane completion time
without taking crane interference into account. This solution provides a lower
bound for the makespan of the whole problem and is sent to the scheduling
sub-problem, where a completion time for each task and the makespan are
determined. This scheme resembles Benders' decomposition and, in particular,
the scheme underlying combinatorial Benders' cuts. We evaluate the proposed
approach by solving instances from the literature and comparing the results
with other available methods.


title: Holonomy groups of $G_2^*$-manifolds

abstract:
  We classify the holonomy algebras of manifolds admitting an indecomposable
torsion free $G_2^*$-structure, i.e. for which the holonomy representation does
not leave invariant any proper non-degenerate subspace. We realize some of
these Lie algebras as holonomy algebras of left-invariant metrics on Lie
groups.


title: Spontaneous fission of superheavy nucleus $^{286}$Fl

abstract:
  The decimal logarithm of spontaneous fission half-life of the superheavy
nucleus $^{286}$Fl experimentally determined is $\log_{10} T_f^{exp} (s) =
-0.632$. We present a method to calculate the half-life based on the cranking
inertia and the deformation energy, functions of two independent surface
coordinates, using the best asymmetric two center shell model. In the first
stage we study the statics. At a given mass asymmetry up to about $\eta=0.5$
the potential barrier has a two hump shape, but for larger $\eta$ it has only
one hump. The touching point deformation energy versus mass asymmetry shows the
three minima, produced by shell effects, corresponding to three decay modes:
spontaneous fission, cluster decay and $\alpha$~decay. The least action
trajectory is determined in the plane $(R,\eta)$ where $R$ is the separation
distance of the fission fragments and $\eta$ is the mass asymmetry. We may find
a sequence of several trajectories one of which gives the least action. The
parametrization with two deformation coordinates $(R,\eta)$ and the radius of
the light fragment, $R_2$, exponentially decreasing with $R$ is compared with
the simpler one, in which $R_2$~=constant. The latter is closer to the reality
and reminds us about the alpha or cluster preformation at the nuclear surface.


title:
An introduction to the study of critical points of solutions of elliptic
  and parabolic equations

abstract:
  We give a survey at an introductory level of old and recent results in the
study of critical points of solutions of elliptic and parabolic partial
differential equations. To keep the presentation simple, we mainly consider
four exemplary boundary value problems: the Dirichlet problem for the Laplace's
equation; the torsional creep problem; the case of Dirichlet eigenfunctions for
the Laplace's equation; the initial-boundary value problem for the heat
equation. We shall mostly address three issues: the estimation of the local
size of the critical set; the dependence of the number of critical points on
the boundary values and the geometry of the domain; the location of critical
points in the domain.


title: Modelling of anisotropic compact stars of emebedding class one

abstract:
  In the present article, we have constructed static anisotropic compact star
models of Einstein field equations for the spherical symmetric metric of
embedding class one. By assuming the particular form of metric function $\nu$,
We have solved the Einstein field equations for anisotropic matter
distribution. The anisotropic models are representing the realistic compact
objects such as SAX J 1808.4-3658 (SS1), Her X - 1, Vela X-12, PSR J1614-2230
and Cen X - 3. We have reported our results in details for compact star Her X-1
on the ground of physical properties such as pressure, density, velocity of
sound, energy conditions, TOV equation and red-shift etc. Along with these, we
have also discussed about stability of the compact star models. Finally we made
the comparison between our anisotropic stars with the realistic objects on the
key aspects as central density, central pressure, compactness and surface
red-shift.


title: Practical Quantum Metrology in Noisy Environments

abstract:
  The problem of estimating an unknown phase $ \varphi $ using two-level probes
in the presence of unital phase-covariant noise and using finite resources is
investigated. We introduce a simple model in which the phase-imprinting
operation on the probes is realized by a unitary transformation with a randomly
sampled generator. We determine the optimal phase sensitivity in a sequential
estimation protocol, and derive a general (tight-fitting) lower bound. The
sensitivity grows quadratically with the number of applications $ N $ of the
phase-imprinting operation, then attains a maximum at some $ N_\text{opt} $,
and eventually decays to zero. We provide an estimate of $ N_\text{opt} $ in
terms of accessible geometric properties of the noise and illustrate its
usefulness as a guideline for optimizing the estimation protocol. The use of
passive ancillas and of entangled probes in parallel to improve the phase
sensitivity is also considered. We find that multi-probe entanglement may offer
no practical advantage over single-probe coherence if the interrogation at the
output is restricted to measuring local observables.


title: Voronoi Region-Based Adaptive Unsupervised Color Image Segmentation

abstract:
  Color image segmentation is a crucial step in many computer vision and
pattern recognition applications. This article introduces an adaptive and
unsupervised clustering approach based on Voronoi regions, which can be applied
to solve the color image segmentation problem. The proposed method performs
region splitting and merging within Voronoi regions of the Dirichlet
Tessellated image (also called a Voronoi diagram) , which improves the
efficiency and the accuracy of the number of clusters and cluster centroids
estimation process. Furthermore, the proposed method uses cluster centroid
proximity to merge proximal clusters in order to find the final number of
clusters and cluster centroids. In contrast to the existing adaptive
unsupervised cluster-based image segmentation algorithms, the proposed method
uses K-means clustering algorithm in place of the Fuzzy C-means algorithm to
find the final segmented image. The proposed method was evaluated on three
different unsupervised image segmentation evaluation benchmarks and its results
were compared with two other adaptive unsupervised cluster-based image
segmentation algorithms. The experimental results reported in this article
confirm that the proposed method outperforms the existing algorithms in terms
of the quality of image segmentation results. Also, the proposed method results
in the lowest average execution time per image compared to the existing methods
reported in this article.


title:
A Green's function approach to the Casimir effect on topological
  insulators with planar symmetry

abstract:
  We investigate the Casimir stress on a topological insulator (TI) between two
metallic plates. The TI is assumed to be joined to one of the plates and its
surface in front of the other is covered by a thin magnetic layer, which turns
the TI into a full insulator. We also analyze the limit where one of the plates
is sent to infinity yielding the Casimir stress between a conducting plate and
a TI. To this end we employ a local approach in terms of the stress-energy
tensor of the system, its vacuum expectation value being subsequently evaluated
in terms of the appropriate Green's function. Finally, the construction of the
renormalised vacuum stress-energy tensor in the region between the plates
yields the Casimir stress. Numerical results are also presented.


title:
3D Global Coronal Density Structure and Associated Magnetic Field near
  Solar Maximum

abstract:
  Measurement of the coronal magnetic field is a crucial ingredient in
understanding the nature of solar coronal dynamic phenomena at all scales. We
employ STEREO/COR1 data obtained near maximum of solar activity in December
2012 (Carrington rotation, CR 2131) to retrieve and analyze the
three-dimensional (3D) coronal electron density in the range of heights from
$1.5$ to $4\ \mathrm{R}_\odot$ using a tomography method and qualitatively
deduce structures of the coronal magnetic field. The 3D electron density
analysis is complemented by the 3D STEREO/EUVI emissivity in 195 \AA \ band
obtained by tomography for the same CR period. We find that the magnetic field
configuration during CR 2131 has a tendency to become radially open at
heliocentric distances below $\sim 2.5 \ \mathrm{R}_\odot$. We compared the
reconstructed 3D coronal structures over the CR near the solar maximum to the
one at deep solar minimum. Results of our 3D density reconstruction will help
to constrain solar coronal field models and test the accuracy of the magnetic
field approximations for coronal modeling.


title: Improving SAT Solvers via Blocked Clause Decomposition

abstract:
  The decision variable selection policy used by the most competitive CDCL
(Conflict-Driven Clause Learning) SAT solvers is either VSIDS (Variable State
Independent Decaying Sum) or its variants such as exponential version EVSIDS.
The common characteristic of VSIDS and its variants is to make use of
statistical information in the solving process, but ignore structure
information of the problem. For this reason, this paper modifies the decision
variable selection policy, and presents a SAT solving technique based on BCD
(Blocked Clause Decomposition). Its basic idea is that a part of decision
variables are selected by VSIDS heuristic, while another part of decision
variables are selected by blocked sets that are obtained by BCD. Compared with
the existing BCD-based technique, our technique is simple, and need not to
reencode CNF formulas. SAT solvers for certified UNSAT track can apply also our
BCD-based technique. Our experiments on application benchmarks demonstrate that
the new variables selection policy based on BCD can increase the performance of
SAT solvers such as abcdSAT. The solver with BCD solved an instance from the
SAT Race 2015 that was not solved by any solver so far. This shows that in some
cases, the heuristic based on structure information is more efficient than that
based on statistical information.


title:
Reliability of the optimized perturbation theory in the 0-dimensional
  $O(N)$ scalar field model

abstract:
  We address the reliability of the Optimized Perturbation Theory (OPT) in the
context of the 0-dimensional $O(N)$ scalar field model. The effective
potential, the self-energy and the 1PI four-point Green's function for the
model are computed using different optimization schemes and the results
contrasted to the exact results for the model. Our results are also compared to
those obtained with the $1/N$-expansion and with those from ordinary
perturbation theory. The OPT results are shown to be stable even at large
couplings and to have better convergence properties than the ones produced in
the $1/N$-expansion. It is also shown that the principle of minimal sensitive
optimization procedure used in conjunction with the OPT method tends to always
produce better results, in particular when applied directly to the self-energy.


title: Diffusive heat blanketing envelopes of neutron stars

abstract:
  We construct new models of outer heat blanketing envelopes of neutron stars
composed of binary ion mixtures (H - He, He - C, C - Fe) in and out of
diffusive equilibrium. To this aim, we generalize our previous work on
diffusion of ions in isothermal gaseous or Coulomb liquid plasmas to handle
non-isothermal systems. We calculate the relations between the effective
surface temperature Ts and the temperature Tb at the bottom of heat blanketing
envelopes (at a density rhob= 1e8 -- 1e10 g/cc) for diffusively equilibrated
and non-equilibrated distributions of ion species at different masses DeltaM of
lighter ions in the envelope. Our principal result is that the Ts - Tb
relations are fairly insensitive to detailed distribution of ion fractions over
the envelope (diffusively equilibrated or not) and depend almost solely on
DeltaM. The obtained relations are approximated by analytic expressions which
are convenient for modeling the evolution of neutron stars.


title: Non-asymptotic results for Cornish--Fisher expansions

abstract:
  We get the computable error bounds for generalized Cornish-Fisher expansions
for quantiles of statistics provided that the computable error bounds for
Edgeworth-Chebyshev type expansions for distributions of these statistics are
known. The results are illustrated by examples.


title:
Nonparametric Conditional Density Estimation in a High-Dimensional
  Regression Setting

abstract:
  In some applications (e.g., in cosmology and economics), the regression
E[Z|x] is not adequate to represent the association between a predictor x and a
response Z because of multi-modality and asymmetry of f(z|x); using the full
density instead of a single-point estimate can then lead to less bias in
subsequent analysis. As of now, there are no effective ways of estimating
f(z|x) when x represents high-dimensional, complex data. In this paper, we
propose a new nonparametric estimator of f(z|x) that adapts to sparse
(low-dimensional) structure in x. By directly expanding f(z|x) in the
eigenfunctions of a kernel-based operator, we avoid tensor products in high
dimensions as well as ratios of estimated densities. Our basis functions are
orthogonal with respect to the underlying data distribution, allowing fast
implementation and tuning of parameters. We derive rates of convergence and
show that the method adapts to the intrinsic dimension of the data. We also
demonstrate the effectiveness of the series method on images, spectra, and an
application to photometric redshift estimation of galaxies.


title: What gravity waves are telling about quantum spacetime

abstract:
  We discuss various modified dispersion relations motivated by quantum gravity
which might affect the propagation of the recently observed gravitational-wave
signal of the event GW150914. We find that the bounds set by the data on the
characteristic quantum-gravity mass scale $M$ are too weak to constrain these
scenarios and, in general, much weaker than the expected $M> 10^4\,\text{eV}$
for a correction to the dispersion relation linear in $1/M$. We illustrate this
issue by giving lower bounds on $M$, plus an upper bound coming from
constraints on the size of a quantum ergosphere. We also show that a
phenomenological dispersion relation $\omega^2 = k^2(1+\alpha k^n/M^n)$ is
compatible with observations and, at the same time, has a phenomenologically
viable mass $M>10\,\text{TeV}$ only in the quite restrictive range $0<n<0.68$.
Remarkably, this is the domain of multiscale spacetimes but not of known
quantum-gravity models.


title:
Compact stable surfaces with constant mean curvature in Killing
  submersions

abstract:
  A Killing submersion is a Riemannian submersion from a 3-manifold to a
surface, both connected and orientable, whose fibres are the integral curves of
a Killing vector field, not necessarily unitary. The first part of this paper
deals with the classification of all Killing submersions in terms of two
geometric functions, namely the bundle curvature and the length of the Killing
vector field, which can be prescribed arbitrarily. In a second part, we show
that if the base is compact and the submersion admits a global section, then it
also admits a global minimal section. These turn out to be the only global
sections with constant mean curvature, which solves the Bernstein problem in
Killing submersions over compact base surfaces, as well as the Plateau problem
with empty boundary. Finally, we prove that any compact orientable stable
surface with constant mean curvature immersed in the total space of a Killing
submersion must be either an entire minimal section or everywhere tangent to
the Killing direction.


title:
Decomposing Linearly Constrained Nonconvex Problems by a Proximal Primal
  Dual Approach: Algorithms, Convergence, and Applications

abstract:
  In this paper, we propose a new decomposition approach named the proximal
primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained
optimization problems. The proposed approach is primal-dual based, where the
primal step minimizes certain approximation of the augmented Lagrangian of the
problem, and the dual step performs an approximate dual ascent. The
approximation used in the primal step is able to decompose the variable blocks,
making it possible to obtain simple subproblems by leveraging the problem
structures. Theoretically, we show that whenever the penalty parameter in the
augmented Lagrangian is larger than a given threshold, the Prox-PDA converges
to the set of stationary solutions, globally and in a sublinear manner (i.e.,
certain measure of stationarity decreases in the rate of $\mathcal{O}(1/r)$,
where $r$ is the iteration counter). Interestingly, when applying a variant of
the Prox-PDA to the problem of distributed nonconvex optimization (over a
connected undirected graph), the resulting algorithm coincides with the popular
EXTRA algorithm [Shi et al 2014], which is only known to work in convex cases.
Our analysis implies that EXTRA and its variants converge globally sublinearly
to stationary solutions of certain nonconvex distributed optimization problem.
There are many possible extensions of the Prox-PDA, and we present one
particular extension to certain nonconvex distributed matrix factorization
problem.