title: The Equatorial Ekman Layer

abstract:
  The steady incompressible viscous flow in the wide gap between spheres
rotating about a common axis at slightly different rates (small Ekman number E)
has a long and celebrated history. The problem is relevant to the dynamics of
geophysical and planetary core flows, for which, in the case of electrically
conducting fluids, the possible operation of a dynamo is of considerable
interest. A comprehensive asymptotic study, in the limit E<<1, was undertaken
by Stewartson (J. Fluid Mech. 1966, vol. 26, pp. 131-144). The mainstream flow,
exterior to the E^{1/2} Ekman layers on the inner/outer boundaries and the
shear layer on the inner sphere tangent cylinder C, is geostrophic. Stewartson
identified a complicated nested layer structure on C, which comprises
relatively thick quasi-geostrophic E^{2/7} (inside C) and E^{1/4} (outside C)
layers. They embed a thinner E^{1/3} ageostrophic shear layer (on C), which
merges with the inner sphere Ekman layer to form the E^{2/5} Equatorial Ekman
layer of axial length E^{1/5}. Under appropriate scaling, this $E^{2/5}$--layer
problem may be formulated, correct to leading order, independent of E.
Accordingly, the Ekman boundary layer and ageostrophic shear layer become
features of the far-field (as identified by the large value of the scaled axial
co-ordinate z) solution. We present a numerical solution, which uses a
non-local integral boundary condition at finite $z$ to account for the
far-field behaviour. Adopting z^{-1} as a small parameter we extend
Stewartson's similarity solution for the ageostrophic shear layer to higher
orders. This far-field solution agrees well with that obtained from our
numerical model.


title: Approximation hardness of Shortest Common Superstring variants

abstract:
  The shortest common superstring (SCS) problem has been studied at great
length because of its connections to the de novo assembly problem in
computational genomics. The base problem is APX-complete, but several
generalizations of the problem have also been studied. In particular, previous
results include that SCS with Negative strings (SCSN) is in Log-APX (though
there is no known hardness result) and SCS with Wildcards (SCSW) is
Poly-APX-hard. Here, we prove two new hardness results: (1) SCSN is
Log-APX-hard (and therefore Log-APX-complete) by a reduction from Minimum Set
Cover and (2) SCS with Negative strings and Wildcards (SCSNW) is NPOPB-hard by
a reduction from Minimum Ones 3SAT.


title:
Multiphase Allen-Cahn and Cahn-Hilliard Models and Their Discretizations
  with the Effect of Pairwise Surface Tensions

abstract:
  In this paper, the mathematical properties and numerical discretizations of
multiphase models that simulate the phase separation of an $N$-component
mixture are studied. For the general choice of phase variables, the unisolvent
property of the coefficient matrix involved in the $N$-phase models based on
the pairwise surface tensions is established. Moreover, the symmetric
positive-definite property of the coefficient matrix on an $(N-1)$-dimensional
hyperplane --- which is of fundamental importance to the well-posedness of the
models --- can be proved equivalent to some physical condition for pairwise
surface tensions. The $N$-phase Allen-Cahn and $N$-phase Cahn-Hilliard
equations can then be derived from the free-energy functional. A natural
property is that the resulting dynamics of concentrations are independent of
phase variables chosen. Finite element discretizations for $N$-phase models can
be obtained as a natural extension of the existing discretizations for the
two-phase model. The discrete energy law of the numerical schemes can be proved
and numerically observed under some restrictions pertaining to time step size.
Numerical experiments including the spinodal decomposition and the evolution of
triple junctions are described in order to investigate the effect of pairwise
surface tensions.


title: Presentations and representations of surface singular braid monoids

abstract:
  The surface singular braid monoid corresponds to marked graph diagrams of
knotted surfaces in braid form. In a quest to resolve linearity problem for
this monoid, we will show that if it is defined on at least two or at least
three strands, then its two or respectively three dimensional representations
are not faithful. We will also derive new presentations for the surface
singular braid monoid, one with reduced the number of defining relations, and
the other with reduced the number of its singular generators. We include
surface singular braid formulations of all knotted surfaces in Yoshikawa's
table.


title: Scattering of Waves by Impurities in Precompressed Granular Chains

abstract:
  We study scattering of waves by impurities in strongly precompressed granular
chains. We explore the linear scattering of plane waves and identify a
closed-form expression for the reflection and transmission coefficients for the
scattering of the waves from both a single impurity and a double impurity. For
single-impurity chains, we show that, within the transmission band of the host
granular chain, high-frequency waves are strongly attenuated (such that the
transmission coefficient vanishes as the wavenumber $k\rightarrow \pm\pi$),
whereas low-frequency waves are well-transmitted through the impurity. For
double-impurity chains, we identify a resonance --- enabling full transmission
at a particular frequency --- in a manner that is analogous to the
Ramsauer--Townsend (RT) resonance from quantum physics. We also demonstrate
that one can tune the frequency of the RT resonance to any value in the pass
band of the host chain. We corroborate our theoretical predictions both
numerically and experimentally, and we directly observe complete transmission
for frequencies close to the RT resonance frequency. Finally, we show how this
RT resonance can lead to the existence of reflectionless modes even in granular
chains (including disordered ones) with multiple double impurities.


title:
A Tutorial: Adaptive Runge-Kutta Integration for Stiff Systems :
  Comparing the Nos\'e and Nos\'e-Hoover Oscillator Dynamics

abstract:
  "Stiff" differential equations are commonplace in engineering and dynamical
systems. To solve them we need flexible integrators that can deal with
rapidly-changing righthand sides. This tutorial describes the application of
"adaptive" [ variable timestep ] integrators to "stiff" mechanical problems
encountered in modern applications of Gibbs' 1902 statistical mechanics. Linear
harmonic oscillators subject to nonlinear thermal constraints can exhibit
either stiff or smooth dynamics. Two closely-related examples, Nos\'e's 1984
dynamics and Nos\'e-Hoover 1985 dynamics, are both based on Hamiltonian
mechanics, as was ultimately clarified by Dettmann and Morriss in 1996. Both
these dynamics are consistent with Gibbs' canonical ensemble. Nos\'e's dynamics
is "stiff" and can present severe numerical difficulties. Nos\'e-Hoover
dynamics, though it follows exactly the same trajectory, is "smooth" and
relatively trouble-free. Our tutorial emphasises the power of adaptive
integrators to resolve stiff problems like the Nos\'e oscillator. The solutions
obtained illustrate the power of computer graphics to enrich numerical
solutions. Adaptive integration with computer graphics are basic to an
understanding of dynamical systems and statistical mechanics. These tools lead
naturally into the visualization of intricate fractal structures formed by
chaos as well as elaborate knots tied by regular nonchaotic dynamics. This work
was invited by the American Journal of Physics.

categories: cond-mat.stat-mech nlin.CD physics.class-ph physics.comp-ph


title: Dijkstra Graphs

abstract:
  We revisit a concept that has been central in some early stages of computer
science, that of structured programming: a set of rules that an algorithm must
follow in order to acquire a structure that is desirable in many aspects. While
much has been written about structured programming, an important issue has been
left unanswered: given an arbitrary, compiled program, describe an algorithm to
decide whether or not it is structured, that is, whether it conforms to the
stated principles of structured programming. We refer to the classical concept
of structured programming, as described by Dijkstra. By employing a graph model
and graph-theoretic techniques, we formulate an efficient algorithm for
answering this question. To do so, we first introduce the class of graphs which
correspond to structured programs, which we call Dijkstra Graphs. Our problem
then becomes the recognition of such graphs, for which we present a greedy
$O(n)$-time algorithm. Furthermore, we describe an isomorphism algorithm for
Dijkstra graphs, whose complexity is also linear in the number of vertices of
the graph. Both the recognition and isomorphism algorithms have potential
important applications, such as in code similarity analysis.


title: Testing for parameter change in general integer-valued time series

abstract:
  We consider the structural change in a class of discrete valued time series
that the conditional distribution follows a one-parameter exponential family.
We propose a change-point test based on the maximum likelihood estimator of the
parameter of the model. Under the null hypothesis (of no change), the test
statistics converges to a well known distribution, allowing for the calculation
of the critical values of the test. The test statistic diverges to infinity
under the alternative, that is, the test asymptotically has power one. Some
simulation results and real data applications are reported to show the
applicability of the test procedure.


title:
Shuffle and Fa\`a di Bruno Hopf Algebras in the Center Problem for
  Ordinary Differential Equations

abstract:
  In this paper we describe the Hopf algebra approach to the center problem for
the differential equation $\frac{dv}{dx}=\sum_{i=1}^{\infty}a_{i}(x)v^{i+1}$,
$x\in [0,T]$, and study some combinatorial properties of the first return map
of this equation. The paper summarizes and extends previously developed
approaches to the center problem due to Devlin and the author.


title: Quantum Arthur-Merlin with single-qubit measurements

abstract:
  We show that the class QAM does not change even if the verifier's ability is
restricted to only single-qubit measurements. To show the result, we use the
idea of the measurement-based quantum computing: the verifier, who can do only
single-qubit measurements, can test the graph state sent from the prover and
use it for his measurement-based quantum computing. We also introduce a new
QMA-complete problem related to the stabilizer test.


title:
QuotationFinder - Searching for Quotations and Allusions in Greek and
  Latin Texts and Establishing the Degree to Which a Quotation or Allusion
  Matches Its Source

abstract:
  The software programs generally used with the TLG (Thesaurus Linguae Graecae)
and the CLCLT (CETEDOC Library of Christian Latin Texts) CD-ROMs are not well
suited for finding quotations and allusions. QuotationFinder uses more
sophisticated criteria as it ranks search results based on how closely they
match the source text, listing search results with literal quotations first and
loose verbal parallels last.


title:
Interference Avoidance Algorithm (IAA) for Multi-hop Wireless Body Area
  Network Communication

abstract:
  In this paper, we propose a distributed multi-hop interference avoidance
algorithm, namely, IAA to avoid co-channel interference inside a wireless body
area network (WBAN). Our proposal adopts carrier sense multiple access with
collision avoidance (CSMA/CA) between sources and relays and a flexible time
division multiple access (FTDMA) between relays and coordinator. The proposed
scheme enables low interfering nodes to transmit their messages using base
channel. Depending on suitable situations, high interfering nodes double their
contention windows (CW) and probably use switched orthogonal channel.
Simulation results show that proposed scheme has far better minimum SINR (12dB
improvement) and longer energy lifetime than other schemes (power control and
opportunistic relaying). Additionally, we validate our proposal in a
theoretical analysis and also propose a probabilistic approach to prove the
outage probability can be effectively reduced to the minimal.


title: Differential equations for Changhee polynomials and their applications

abstract:
  Recently, the non-linear Changhee differential equations were introduced in
[5] and these differential equations turned out to be very useful for studying
special polynomials and mathematical physics. Some interesting identities and
properties of Changhee polynomials can also be derived from umbral calculus
(see [7]). In this paper, we consider differential equations arising from
Changhee polynomials and derive some new and explicit formulae and identities
from our differential equations.


title:
Mathematical design of a novel gesture-based instruction/input device
  using wave detection

abstract:
  In this paper, we present a conceptual design of a novel gesture-based
instruction/input device using wave detection. The device recogonizes/detects
gestures from a person and based on which to give the specific orders/inputs to
the computing machine that is connected to it. The gestures are modelled as the
shapes of some impenetrable or penetrable scatterers from a certain admissible
class, called a dictionary. The device generates time-harmonic point signals
for the gesture recognition/detection. It then collects the scattered wave in a
relatively small backscattering aperture on a bounded surface containing the
point sources. The recognition algorithm consists of two steps and requires
only two incident waves of different wavenumbers. The approximate location of
the scatterer is first determined by using the measured data at a small
wavenumber and the shape of the scatterer is then identified using the computed
location of the scatterer and the measured data at a regular wavenumber. We
provide the mathematical principle with rigorous justifications underlying the
design. Numerical experiments show that the proposed device works effectively
and efficiently in some practical scenarios.


title: First law of black hole mechanics in variable background fields

abstract:
  It is well known that in general theories of gravity with the diffeomorphism
symmetry, the black hole entropy is a Noether charge. But what will happen if
the symmetry is explicitly broken? By investigating the covariant first law of
black hole mechanics with background fields, we show that the Noether entropy
is still applicable due to the local nature of the black hole entropy.
Moreover, motivated by the proposal that the cosmological constant behaves as a
thermodynamic variable, we allow the non-dynamical background fields to be
varied. To illustrate this general formalism, we study a generic static black
brane in the massive gravity. Using the first law and the scaling argument, we
obtain two Smarr formulas. We show that both of them can be retrieved without
relying on the first law, hence providing a self-consistent check of the
theory.


title:
REEL-BF Design: Achieving the SDP Bound for Downlink Beamforming with
  Arbitrary Shaping Constraints

abstract:
  This paper considers the beamforming design for a multiuser multiple-input
single-output (MISO) downlink with an arbitrary number of (context-specific)
shaping constraints. In this setup, the state-of-the-art beamforming schemes
cannot attain the well-known performance bound promised by the semidefinite
program (SDP) relaxation technique. To close the gap, we propose a
redundant-signal embedded linear beamforming (REEL-BF) scheme, where each user
is assigned with one information beamformer and several shaping beamformers. It
is shown that the proposed REEL-BF scheme can perform general rank-$K$
beamforming for user symbols in a low-complexity and structured manner. In
addition, sufficient conditions are derived to guarantee that the REEL-BF
scheme always achieves the SDP bound for linear beamforming schemes. Based on
such conditions, an efficient algorithm is then developed to obtain the optimal
REEL-BF solution in polynomial time. Numerical results demonstrate that the
proposed scheme enjoys substantial performance gains over the existing
alternatives.


title:
A High Order Multi-Dimensional Characteristic Tracing Strategy for the
  Vlasov-Poisson System

abstract:
  In this paper, we consider a finite difference grid-based semi-Lagrangian
approach in solving the Vlasov-Poisson (VP) system. Many of existing methods
are based on dimensional splitting, which decouples the problem into solving
linear advection problems, see {\em Cheng and Knorr, Journal of Computational
Physics, 22(1976)}. However, such splitting is subject to the splitting error.
If we consider multi-dimensional problems without splitting, difficulty arises
in tracing characteristics with high order accuracy. Specifically, the
evolution of characteristics is subject to the electric field which is
determined globally from the distribution of particle densities via the
Poisson's equation. In this paper, we propose a novel strategy of tracing
characteristics high order in time via a two-stage multi-derivative
prediction-correction approach and by using moment equations of the VP system.
With the foot of characteristics being accurately located, we proposed to use
weighted essentially non-oscillatory (WENO) interpolation to recover function
values between grid points, therefore to update solutions at the next time
level. The proposed algorithm does not have time step restriction as Eulerian
approach and enjoys high order spatial and temporal accuracy. However, such
finite difference algorithm does not enjoy mass conservation; we discuss one
possible way of resolving such issue and its potential challenge in numerical
stability. The performance of the proposed schemes are numerically demonstrated
via classical test problems such as Landau damping and two stream
instabilities.


title:
On the Exit Time and Stochastic Homogenization of Isotropic Diffusions
  in Large Domains

abstract:
  Stochastic homogenization is achieved for a class of elliptic and parabolic
equations describing the lifetime, in large domains, of stationary diffusion
processes in random environment which are small, statistically isotropic
perturbations of Brownian motion in dimension at least three. Furthermore, the
homogenization is shown to occur with an algebraic rate. Such processes were
first considered in the continuous setting by Sznitman and Zeitouni [21], upon
whose results the present work relies strongly, and more recently their
smoothed exit distributions from large domains were shown to converge to those
of a Brownian motion by the author [10]. This work shares in philosophy with
[10], but requires substantially new methods in order to control the
expectation of exit times which are generically unbounded in the microscopic
scale due to the emergence of a singular drift in the asymptotic limit.


title:
Strain-induced enhancement of thermoelectric performance in a ZrS2
  monolayer

abstract:
  The increase of a thermoelectric material's figure of merit (ZT value) is
limited by the interplay of the transport coefficients. Here we report the
greatly enhanced thermoelectric performance of a ZrS2 monolayer by the biaxial
tensile strain, due to the simultaneous increase of the Seebeck coefficient and
decrease of the thermal conductivity. Based on the first-principles
calculations combined with the Boltzmann transport theory, we predict the band
gap of the ZrS2 monolayer can be effectively engineered by the strain and the
Seebeck coefficient is significantly increased. The thermal conductivity is
reduced by the applied tensile strain due to the phonon softening. At the
strain of 6%, the maximal ZT value of 2.4 is obtained for the p-type doped ZrS2
monolayer at 300 K, which is 4.3 times larger than that of the unstrained
system.


title: Epistemic Impact on Group Problem Solving for Different Science Majors

abstract:
  Implementation of cognitive apprenticeship in an introductory physics lab
group problem solving exercise may be mitigated by epistemic views toward
physics of non-physics science majors. Quantitative pre-post data of the Force
Concept Inventory (FCI) and Colorado Learning Attitudes About Science Survey
(CLASS) of 39 students of a first-semester algebra-based introductory physics
course, while describing typical results for a traditional-format course
overall (g = +0.14), suggest differences in epistemic views between health
science majors and life science majors which may correlate with differences in
pre-post conceptual understanding. Audiovisual data of student lab groups
working on a context-rich problem and students' written reflections described
each group's typical dynamics and invoked epistemic games. We examined the
effects of framework-based orientation (favored by biology majors) and
performance-based orientation (favored by computer science, chemistry, and
health science majors) on pre-post attitude survey performance. We also
investigated possible correlations of these orientations with individual
quantitative survey results, and with qualitative audiovisual data of lab
groups' choice of epistemic games.


title: Proof of some properties of transfer using noncommutative determinants

abstract:
  A transfer is a group homomorphism from a finite group to an abelian quotient
group of a subgroup of the group. In this paper, we explain some of the
properties of transfers by using noncommutative determinants. These properties
enable us to understand transfers more naturally.


title: Speex: A Free Codec For Free Speech

abstract:
  The Speex project has been started in 2002 to address the need for a free,
open-source speech codec. Speex is based on the Code Excited Linear Prediction
(CELP) algorithm and, unlike the previously existing Vorbis codec, is optimised
for transmitting speech for low latency communication over an unreliable packet
network. This paper presents an overview of Speex, the technology involved in
it and how it can be used in applications. The most recent developments in
Speex, such as the fixed-point port, acoustic echo cancellation and noise
suppression are also addressed.


title: Interval k-Graphs and Orders

abstract:
  An interval $k$-graph is the intersection graph of a family $\mathcal{I}$ of
intervals of the real line partitioned into at most $k$ classes with vertices
adjacent if and only if their corresponding intervals intersect and belong to
different classes. In this paper we discuss the interval $k$-graphs that are
the incomparability graphs of orders; i.e., cocomparability interval $k$-graphs
or interval $k$-orders. Interval $2$-orders have been characterized in many
ways, but we show that analogous characterizations do not carry over to
interval $k$-orders, for $k > 2$. We describe the structure of interval
$k$-orders, for any $k$, characterize the interval $3$-orders (cocomparability
interval $3$-graphs) via one forbidden suborder (subgraph), and state a
conjecture for interval $k$-orders (any $k$) that would characterize them via
two forbidden suborders.


title:
Effects of Galactic Disc Inclination and Resolution on Observed GMC
  Properties and Larson's Scaling Relations

abstract:
  With ALMA making it possible to resolve giant molecular clouds (GMCs) in
other galaxies, it is becoming necessary to quantify the observational bias on
measured GMC properties. Using a hydrodynamical simulation of a barred spiral
galaxy, we compared the physical properties of GMCs formed in
position-position-position space (PPP) to the observational
position-position-velocity space (PPV). We assessed the effect of disc
inclination: face-on (PPV_face) and edge-on (PPV_edge), and resolution: 1.5 pc
versus 24 pc, on GMC properties and the further implications of using Larson's
scaling relations for mass-radius and velocity dispersion-radius. The
low-resolution PPV data are generated by simulating ALMA Cycle 3 observations
using the CASA package. Results show that the median properties do not differ
strongly between PPP and PPV_face under both resolutions, but PPV_edge clouds
deviate from these two. The differences become magnified when switching to the
lower, but more realistic resolution. The discrepancy can lead to opposite
results for the virial parameter's measure of gravitational binding, and
therefore the dynamical state of the clouds. The power-law indices for the two
Larson's scaling relations decrease going from PPP, PPV_face to PPV_edge and
decrease from high to low resolutions. We conclude that the relations are not
entirely driven by the underlying physical origin and therefore have to be used
with caution when considering the environmental dependence, dynamical state,
and the extragalactic CO-to-H2 conversion factor of GMCs.


title: Lie Access Neural Turing Machine

abstract:
  Following the recent trend in explicit neural memory structures, we present a
new design of an external memory, wherein memories are stored in an Euclidean
key space $\mathbb R^n$. An LSTM controller performs read and write via
specialized read and write heads. It can move a head by either providing a new
address in the key space (aka random access) or moving from its previous
position via a Lie group action (aka Lie access). In this way, the "L" and "R"
instructions of a traditional Turing Machine are generalized to arbitrary
elements of a fixed Lie group action. For this reason, we name this new model
the Lie Access Neural Turing Machine, or LANTM.
  We tested two different configurations of LANTM against an LSTM baseline in
several basic experiments. We found the right configuration of LANTM to
outperform the baseline in all of our experiments. In particular, we trained
LANTM on addition of $k$-digit numbers for $2 \le k \le 16$, but it was able to
generalize almost perfectly to $17 \le k \le 32$, all with the number of
parameters 2 orders of magnitude below the LSTM baseline.


title:
Spectral theory for nonlocal dispersal operators with time periodic
  indefinite weight functions and applications

abstract:
  In this paper, we study the spectral theory for nonlocal dispersal operators
with time periodic indefinite weight functions subject to Dirichlet type,
Neumann type and spatial periodic type boundary conditions.
  We first obtain necessary and sufficient conditions for the existence of a
unique positive principal spectrum point for such operators. We then
investigate upper bounds of principal spectrum points and sufficient conditions
for the principal spectrum points to be principal eigenvalues. Finally we
discuss the applications to nonlinear mathematical models from biology.


title: Eigenvalue bounds for matrix polynomials in generalized bases

abstract:
  We derive inclusion regions for the eigenvalues of matrix polynomials
expressed in a general polynomial basis, which can lead to significantly better
results than traditional bounds. We present several applications to engineering
problems.


title: Stellar mass functions of galaxies, disks and spheroids at z~0.1

abstract:
  We present the stellar mass functions (SMF) and mass densities of galaxies,
and their spheroid and disk components in the local (z~0.1) universe over the
range 8.9 <= log(M/M_solar) <= 12 from spheroid+disk decompositions and
corresponding stellar masses of a sample of over 600,000 galaxies in the
SDSS-DR7 spectroscopic sample. The galaxy SMF is well represented by a single
Schechter function (M* = 11.116+/-0.011, alpha = -1.145+/-0.008), though with a
hint of a steeper faint end slope. The corresponding stellar mass densities are
(2.670+/-0.110), (1.687+/-0.063) and (0.910+/-0.029)x10^8 M_solar Mpc^-3 for
galaxies, spheroids and disks respectively. We identify a crossover stellar
mass of log(M/M_solar) = 10.3+/-0.030 at which the spheroid and disk SMFs are
equal. Relative contributions of four distinct spheroid/disk dominated
sub-populations to the overall galaxy SMF are also presented. The mean
disk-to-spheroid stellar mass ratio shows a five fold disk dominance at the low
mass end, decreasing monotonically with a corresponding increase in the
spheroidal fraction till the two are equal at a galaxy stellar mass,
log(M/M_solar)=10.479+/-0.013, the dominance of spheroids then grows with
increasing stellar mass. The relative numbers of composite disk and spheroid
dominated galaxies show peaks in their distributions, perhaps indicative of a
preferred galaxy mass. Our characterization of the low redshift galaxy
population provides stringent constraints for numerical simulations to
reproduce.


title: Quantified Self Meets Social Media: Sharing of Weight Updates on Twitter

abstract:
  An increasing number of people use wearables and other smart devices to
quantify various health conditions, ranging from sleep patterns, to body
weight, to heart rates. Of these Quantified Selfs many choose to openly share
their data via online social networks such as Twitter and Facebook. In this
study, we use data for users who have chosen to connect their smart scales to
Twitter, providing both a reliable time series of their body weight, as well as
insights into their social surroundings and general online behavior.
Concretely, we look at which social media features are predictive of physical
status, such as body weight at the individual level, and activity patterns at
the population level. We show that it is possible to predict an individual's
weight using their online social behaviors, such as their self-description and
tweets. Weekly and monthly patterns of quantified-self behaviors are also
discovered. These findings could contribute to building models to monitor
public health and to have more customized personal training interventions.
  While there are many studies using either quantified self or social media
data in isolation, this is one of the few that combines the two data sources
and, to the best of our knowledge, the only one that uses public data.


title:
Rich gauge structures from an unitary approach of some massless gauge
  fields of spins one and two

abstract:
  Considering a bosonic ($1$-)form-valued $k$-form with a second-order
Lagrangian dynamics [depending on two arbitrary real constants] we firstly
perform the Dirac analysis. The procedure implies a partition of cardinally
seven for the plane of the real parameters that label the starting Lagrangian.
In each of the seven partition's components one determines the number and the
nature of independent degrees of freedom and also a generating set of gauge
transformations. Secondly, with the help of some auxiliary gauge/matter tensor
gauge fields, in each of the seven situations, we construct the first-order
Lagrangian density corresponding to the second-order one.


title:
The mechanism and process of spontaneous boron doping in graphene in the
  theoretical perspective

abstract:
  A theoretical model is presented to reveal the mechanism of B doping into
graphene in the microwave plasma experiment choosing trimethylboron as the
doping source (ACS NANO 6 (2012) 1970). The results show that the reason for B
doping comes from the combinational interaction of B and other groups (C, H,
CH, CH2 or CH3) decomposing from trimethylboron and the doping undergoes two
crucial steps. The minimal energy path for the first step are determined. The
obtained energy barrier of considered cases fall into the range of 0.02-0.43
eV, supporting the fact that the substituting B for C can easily realized even
at room temperature. As the second step, after removing irrelevant groups in
vertical direction through H saturation, the perfect B doping is realized at
last. This work successfully explain the above experimental phenomenon and
propose a novel and feasible method aiming at B doping of graphene.


title:
Robust hyperparameter estimation protects against hypervariable genes
  and improves power to detect differential expression

abstract:
  One of the most common analysis tasks in genomic research is to identify
genes that are differentially expressed (DE) between experimental conditions.
Empirical Bayes (EB) statistical tests using moderated genewise variances have
been very effective for this purpose, especially when the number of biological
replicate samples is small. The EB procedures can however be heavily influenced
by a small number of genes with very large or very small variances. This
article improves the differential expression tests by robustifying the
hyperparameter estimation procedure. The robust procedure has the effect of
decreasing the informativeness of the prior distribution for outlier genes
while increasing its informativeness for other genes. This effect has the
double benefit of reducing the chance that hypervariable genes will be
spuriously identified as DE while increasing statistical power for the main
body of genes. The robust EB algorithm is fast and numerically stable. The
procedure allows exact small-sample null distributions for the test statistics
and reduces exactly to the original EB procedure when no outlier genes are
present. Simulations show that the robustified tests have similar performance
to the original tests in the absence of outlier genes but have greater power
and robustness when outliers are present. The article includes case studies for
which the robust method correctly identifies and downweights genes associated
with hidden covariates and detects more genes likely to be scientifically
relevant to the experimental conditions. The new procedure is implemented in
the limma software package freely available from the Bioconductor repository.


title: Kerr black holes as accelerators of spinning test particles

abstract:
  It has been shown that ultraenergetic collisions can occur near the horizon
of an extremal Kerr black hole. Previous studies mainly focused on geodesic
motions of particles. In this paper, we consider spinning test particles whose
orbits are non-geodesic. By employing the Mathisson-Papapetrou-Dixon equation,
we find the critical angular momentum satisfies $J=2E$ for extremal Kerr black
holes. Although the conserved angular momentum $J$ and energy $E$ have been
redefined in the presence of spin, the critical condition remains the same
form. If a particle with this angular momentum collides with another particle
arbitrarily close to the horizon of the black hole, the center-of-mass energy
can be arbitrarily high. We also prove that arbitrarily high energies cannot be
obtained for spinning particles near the horizons of non-extremal Kerr black
holes.


title: Measuring and Predicting Tag Importance for Image Retrieval

abstract:
  Textual data such as tags, sentence descriptions are combined with visual
cues to reduce the semantic gap for image retrieval applications in today's
Multimodal Image Retrieval (MIR) systems. However, all tags are treated as
equally important in these systems, which may result in misalignment between
visual and textual modalities during MIR training. This will further lead to
degenerated retrieval performance at query time. To address this issue, we
investigate the problem of tag importance prediction, where the goal is to
automatically predict the tag importance and use it in image retrieval. To
achieve this, we first propose a method to measure the relative importance of
object and scene tags from image sentence descriptions. Using this as the
ground truth, we present a tag importance prediction model to jointly exploit
visual, semantic and context cues. The Structural Support Vector Machine (SSVM)
formulation is adopted to ensure efficient training of the prediction model.
Then, the Canonical Correlation Analysis (CCA) is employed to learn the
relation between the image visual feature and tag importance to obtain robust
retrieval performance. Experimental results on three real-world datasets show a
significant performance improvement of the proposed MIR with Tag Importance
Prediction (MIR/TIP) system over other MIR systems.


title: Critical exponents and the pseudo-$\epsilon$ expansion

abstract:
  We present the pseudo-$\epsilon$ expansions ($\tau$-series) for the critical
exponents of a $\lambda\phi^4$ three-dimensional $O(n)$-symmetric model
obtained on the basis of six-loop renormalization-group expansions. Concrete
numerical results are presented for physically interesting cases $n = 1$, $n =
2$, $n = 3$ and $n = 0$, as well as for $4 \le n \le 32$ in order to clarify
the general properties of the obtained series. The pseudo-$\epsilon$-expansions
for the exponents $\gamma$ and $\alpha$ have small and rapidly decreasing
coefficients. So, even the direct summation of the $\tau$-series leads to fair
estimates for critical exponents, while addressing Pade approximants enables
one to get high-precision numerical results. In contrast, the coefficients of
the pseudo-$\epsilon$ expansion of the scaling correction exponent $\omega$ do
not exhibit any tendency to decrease at physical values of $n$. But the
corresponding series are sign-alternating, and to obtain reliable numerical
estimates, it also suffices to use simple Pad\'e approximants in this case. The
pseudo-$\epsilon$ expansion technique can therefore be regarded as a specific
resummation method converting divergent renormalization-group series into
expansions that are computationally convenient.


title:
The controllable super-high energetic electrons by external magnetic
  fields at relativistic laser-solid interactions in the presence of large
  scale pre-plasmas

abstract:
  The two stage electron acceleration model [arXiv: 1512.02411 and arXiv:
1512.07546] is extended to the study of laser magnetized-plasmas interactions
at relativistic intensities and in the presence of large-scale preformed
plasmas. It is shown that the cut-off electron kinetic energy is controllable
by the external magnetic field strength and directions. Further studies
indicate that for a right-hand circularly polarized laser (RH-CP) of intensity
$10^{20}\ \text{W}/\text{cm}^2$ and pre-plasma scale length $10\ \mu\text{m}$,
the cut-off electron kinetic energy can be as high as $500\ \text{MeV}$, when a
homogeneous external magnetic field of exceeding $10000\ \text{T}$ (or
$B=\omega_{c}/\omega_0>1$) is loaded along the laser propagation direction,
which is a significant increase compared with that $120\ \text{MeV}$ without
external magnetic field. A laser front sharpening mechanism is identified at
relativistic laser magnetized-plasmas interactions with
$B=\omega_{c}/\omega_0>1$, which is responsible for these super-high energetic
electrons.


title:
Some results on a conjecture of Voisin for surfaces of geometric genus
  one

abstract:
  Inspired by the Bloch-Beilinson conjectures, Voisin has formulated a
conjecture concerning the behaviour of 0-cycles on self-products of varieties
of geometric genus one. This note presents some new examples of surfaces for
which Voisin's conjecture is verified.


title: Combinatorial properties of poly-Bernoulli relatives

abstract:
  In this note we augment the poly-Bernoulli family with two new combinatorial
objects. We derive formulas for the relatives of the poly-Bernoulli numbers
using the appropriate variations of combinatorial interpretations. Our goal is
to show connections between the different areas where poly-Bernoulli numbers
and their relatives appear and give examples how the combinatorial methods can
be used for deriving formulas between integer arrays.


title:
High spatial frequency periodic structures induced on ferric ion-doped
  Polyvinyl Pyrrolidone film by femtosecond laser pulses

abstract:
  Utilizing continues-wave or pulsed laser to induce nano-structures on various
material surfaces is one significant method in nano-fabrication technology. In
this report, we investigate the formation of high spatial frequency periodic
structures on Polyvinyl Pyrrolidone (PVP) film by a linearly polarized
femtosecond laser. Ferric (Fe) ions are introduced into the film to improve the
photosensitivity. Regular nano-gratings with spatial periods at the range of
60-100nm, which are about one tenth of the irradiating wavelength, can be
induced. The period direction of the nano-gratings is perpendicular to the
polarization of the femtosecond laser. By tuning the laser energy and scanning
speed, we find that the nano-gratings can be formed in a wide range of
experimental parameters. As high laser energy can excite not only metals, but
also semiconductors and polymers, we believe the formation of the nano-gratings
is due to the interaction between the incident femtosecond laser and surface
plasmons. The laser processable PVP-based materials and the induced
nano-gratings will have potential applications in biophotonics and
nanophotonics.


title: Free-fall Frame Black Hole in Gravity's Rainbow

abstract:
  Doubly special relativity (DSR) is an effective model for encoding quantum
gravity in flat spacetime. To incorporate DSR into general relativity, one
could use "Gravity's rainbow", where the spacetime background felt by a test
particle would depend on its energy. In this scenario, one could rewrite the
rainbow metric $g_{\mu\nu}\left( E\right) $ in terms of some orthonormal frame
fields and use the modified equivalence principle to determine the energy
dependence of $g_{\mu\nu}\left( E\right) $. Obviously, the form of
$g_{\mu\nu}\left( E\right) $ depends on the choice of the orthonormal frame.
For a static black hole, there are two natural orthonormal frames, the static
one hovering above it and freely falling one along geodesics. The cases with
the static orthonormal frame have been extensively studied by many authors. The
aim of this paper is to investigate properties of rainbow black holes in the
scenario with the free-fall orthonormal frame. We first derive the metric of
rainbow black holes and their Hawking temperatures in this free-fall scenario.
Then, the thermodynamics of a rainbow Schwarzschild black hole is studied.
Finally, we use the brick wall model to compute the thermal entropy of a
massless scalar field near the horizon of a Schwarzschild rainbow black hole in
this free-fall scenario.


title:
Multiwinner Analogues of Plurality Rule: Axiomatic and Algorithmic
  Perspectives

abstract:
  We characterize the class of committee scoring rules that satisfy the
fixed-majority criterion. In some sense, the committee scoring rules in this
class are multiwinner analogues of the single-winner Plurality rule, which is
uniquely characterized as the only single-winner scoring rule that satisfies
the simple majority criterion. We define top-$k$-counting committee scoring
rules and show that the fixed majority consistent rules are a subclass of the
top-$k$-counting rules. We give necessary and sufficient conditions for a
top-$k$-counting rule to satisfy the fixed-majority criterion. We find that,
for most of the rules in our new class, the complexity of winner determination
is high (that is, the problem of computing the winners is NP-hard), but we also
show examples of rules with polynomial-time winner determination procedures.
For some of the computationally hard rules, we provide either exact FPT
algorithms or approximate polynomial-time algorithms.


title: New volume and inverse volume operators for loop quantum gravity

abstract:
  A new alternative volume operator is constructed for loop quantum gravity by
using the so-called cotriad operators as building blocks. It is shown that the
new volume operator shares the same qualitative properties with the standard
volume operator. Moreover, a new alternative inverse volume operator is also
constructed in the light of the construction of the alternative volume
operator, which is possessed of the same qualitative properties as those of the
alternative volume operator. The new inverse volume operator can be employed to
construct the Hamiltonian operator of matter fields, which may lead to an
anomaly-free on-shell quantum constraint algebra without any special
restriction on the regularization procedure for gravity coupled to matter
fields.


title: Temperature jump in second Stokes' problem by nonlinear analysis

abstract:
  The second Stokes problem about behavior of the viscous fluid (matter)
filling half-space is considered. A flat surface limiting half-space makes
harmonious oscillations in the eigen plane. The equations of mechanics of the
continuous environment are used. It is shown, that in considered process there
is the temperature difference between temperature of a surface and temperature
environments far from a surface. Usually similar difference is called as
temperature jump. The method of small parameter is applied. Temperature jump in
the second approach is found out.


title: Neutrino oscillations in the presence of super-light sterile neutrinos

abstract:
  In this paper, we study the effect of conversion of super-light sterile
neutrino (SLSN) to electron neutrino in matter like that of the Earth. In the
Sun the resonance conversion between SLSN and electron neutrino via the neutral
current is suppressed due to the smallness of neutron number. On the other
hand, neutron number density can play an important role in the Earth, making
the scenario of SLSN quite interesting. The effect of CP-violating phases on
active-SLSN oscillations is also discussed. Reactor neutrino experiments with
medium or short baseline may probe the scenario of SLSN.


title: Landau-Zener Bloch oscillations with perturbed flat bands

abstract:
  Sinusoidal Bloch oscillations appear in band structures exposed to external
fields. Landau-Zener (LZ) tunneling between different bands is usually a
counteracting effect limiting Bloch oscillations. Here we consider a flat band
network with two dispersive and one flat bands, e.g. for ultracold atoms and
optical waveguide networks. Using external synthetic gauge and gravitational
fields we obtain a perturbed yet gapless band structure with almost flat parts.
The resulting Bloch oscillations consist of two parts - a fast scan through the
nonflat part of the dispersion structure, and an almost complete halt for
substantial time when the atomic wave packet is trapped in the original flat
band part of the unperturbed spectrum, made possible due to LZ tunneling.


title:
Effective field theory and the scattering process for magnons in the
  ferromagnet, antiferromagnet, and ferrimagnet

abstract:
  We discuss that a low-energy effective Lagrangian relying on SO(3)
$\rightarrow$ SO(2) is applicable for a ferrimagnet as well as a ferromagnet
and an antiferromagnet. The analysis of the particle states shows that there
exist not only massless modes with the dispersion relations $\omega \propto
|\bm{k}|,\, |\bm{k}|^2$, i.e., the so-called type-I and type-II Nambu-Goldstone
modes, respectively, but also gapped modes with $\omega \propto
m^2+|\bm{k}|^2$. We clarify how the coefficients of the terms with one time
derivative and those with two time derivatives in the effective Lagrangian
determine the order parameters specifying whether the system is in a
ferromagnetic, antiferromagnetic or ferrimagnetic state; we stress that the
gapped mode related to the spontaneous symmetry breaking appears only in the
ferrimagnetic system and not in the ferromagnetic and antiferromagnetic
systems. We also establish the power counting scheme and calculate the
scattering amplitudes and thereby the scattering lengths between the two
Nambu-Goldstone bosons. We show that the scattering length of the gapped mode
is finite and proportional to the gap. This characteristic property of the
gapped NG mode can be used to discriminate it from gapped excitations which
originate in other mechanisms. Finally, we study the effects of the explicit
symmetry breaking that are given by an external magnetic field and a single-ion
anisotropy, and show that the external magnetic fields do not have any effects
on the scattering amplitudes in all the spin systems as was known for the
ferromagnet system. In contrast, the anisotropy does affect the scattering
amplitudes, the phase shift, and the scattering length except for spin 1/2
systems. This result supports the possibility of the Efimov effect in spin
systems discussed in previous studies.

categories: cond-mat.str-el cond-mat.other hep-ph nucl-th


title: Peculiar Stationary EUV Wave Fronts in the eruption on 2011 May 11

abstract:
  We present and interpret the observations of extreme ultraviolet (EUV) waves
associated with a filament eruption on 2011 May 11.The filament eruption also
produces a small B-class two ribbon flare and a coronal mass ejection (CME).
The event is observed by the Solar Dynamic Observatory (SDO) with high
spatio-temporal resolution data recorded by Atmospheric Imaging Assembly (AIA).
As the filament erupts, we observe two types of EUV waves (slow and fast)
propagating outwards. The faster EUV wave has a propagation velocity of ~ 500
km/s and the slower EUV wave has an initial velocity of ~ 120 km/s. We report
for the first time that not only the slower EUV wave stops at a magnetic
separatrix to form bright stationary fronts, but also the faster EUV wave
transits a magnetic separatrix, leaving another stationary EUV front behind.


title:
Fourier-Mukai transform on Weierstrass cubics and commuting differential
  operators

abstract:
  In this article, we describe the spectral sheaves of algebras of commuting
differential operators of genus one and rank two with singular spectral curve,
solving a problem posed by Previato and Wilson. We also classify all
indecomposable semi-stable sheaves of slope one and ranks two or three on a
cuspidal Weierstrass cubic.


title: Density-based crystal plasticity : from the discrete to the continuum

abstract:
  Because of the enormous range of time and space scales involved in
dislocation dynamics, plastic modeling at macroscale requires a continuous
formulation. In this paper, we present a rigorous formulation of the transition
between the discrete, where plastic flow is resolved at the scale of individual
dislocations, and the continuum, where dislocations are represented by
densities. First, we focus on the underlying coarse-graining procedure and show
that the emerging correlation-induced stresses are scale-dependent. Each of
these stresses can be expanded into the sum of two components. The first one
depends on the local values of the dislocation densities and always opposes the
sum of the applied stress and long-range mean field stress generated by the
geometrically necessary dislocation (GND) density; this stress acts as a
friction stress. The second component depends on the local gradients of the
dislocation densities and is inherently associated to a translation of the
elastic domain; therefore, it acts as a back-stress. We also show that these
friction and back- stresses contain symmetry-breaking components that make the
local stress experienced by dislocations to depend on the sign of their Burgers
vector.


title: Modelling of lung cancer survival data for critical illness insurances

abstract:
  We derive a general multiple state model for critical illness insurances. In
contrast to the classical model, we take into account that the probability of
death for a dread disease sufferer may depend on the duration of the disease,
and the payment of benefits associated with a severe disease depends not only
on the diagnosis but also on the disease stage. We apply the introduced model
to the analysis of a critical illness insurance against the risk of lung
cancer. Based on the real data for the Lower Silesian Voivodship in Poland, we
estimate the transition matrix, related to the discrete-time Markov model. The
obtained probabilistic structure of the model can be directly used to cost not
only critical illness insurances and life insurances with accelerated death
benefits option, but also to viatical settlement contracts.


title: Black Holes and Abelian Symmetry Breaking

abstract:
  Black hole configurations offer insights on the non-linear aspects of
gravitational theories, and can suggest testable predictions for modifications
of General Relativity. In this work, we examine exact black hole configurations
in vector-tensor theories, originally proposed to explain dark energy by
breaking the Abelian symmetry with a non-minimal coupling of the vector to
gravity. We are able to evade the no-go theorems by Bekenstein on the existence
of regular black holes in vector-tensor theories with Proca mass terms, and
exhibit regular black hole solutions with a profile for the longitudinal vector
polarization, characterised by an additional charge. We analytically find the
most general static, spherically symmetric black hole solutions with and
without a cosmological constant, and study in some detail their features, such
as how the geometry depends on the vector charges. We also include angular
momentum, and find solutions describing slowly-rotating black holes. Finally,
we extend some of these solutions to higher dimensions.


title: Equal Sums of Like Powers with Minimum Number of Terms

abstract:
  This paper is concerned with the diophantine system, $\sum_{i=1}^{s_1}
x_i^r=\sum_{i=1}^{s_2} y_i^r,\, r=1,\,2,\,\ldots,\,k, $ where $s_1$ and $s_2$
are integers such that the total number of terms on both sides, that is,
$s_1+s_2,$ is as small as possible. We define $\beta(k)$ to be the minimum
value of $s_1+s_2$ for which there exists a nontrivial solution of this
diophantine system. We find nontrivial integer solutions of this diophantine
system when $k < 6$, and thereby show that $\beta(2) =4,\;\, \beta(3) = 6,\;\,
7 \leq \beta(4) \leq 8$ and $8 \leq \beta(5) \leq 10$.


title:
Measurement of the front-end dead-time of the LHCb muon detector and
  evaluation of its contribution to the muon detection inefficiency

abstract:
  A method is described which allows to deduce the dead-time of the front-end
electronics of the LHCb muon detector from a series of measurements performed
at different luminosities at a bunch-crossing rate of 20 MHz. The measured
values of the dead-time range from 70 ns to 100 ns. These results allow to
estimate the performance of the muon detector at the future bunch-crossing rate
of 40 MHz and at higher luminosity.


title:
Demographic stochasticity and resource autocorrelation control
  biological invasions in heterogeneous landscapes

abstract:
  Classical models of biological invasions assess species spread in homogeneous
landscapes by assuming constant growth rates and random local movement.
Mounting evidence suggests, however, that demographic stochasticity,
environmental heterogeneity and non-random movement of individuals affect
considerably the spread dynamics. Here, we show that the dynamics of biological
invasions are controlled by the spatial heterogeneity of the resource
distribution. We show theoretically that increasing the landscape resource
autocorrelation length causes a reduction in the average speed of species
spread. Demographic stochasticity plays a key role in the slowdown, which is
streghtened when individuals can actively move towards resources. The reduction
in the front propagation speed is verified in laboratory microcosm experiments
with the flagellated protist Euglena gracilis by comparing spread in habitats
characterized by different resource heterogeneity. Our theoretical and
experimental findings highlight the need to account for the intrinsic
stochasticity of population dynamics to describe spread in spatially extended
landscapes, which are inevitably characterized by heterogeneous spatial
distributions of resources controlling vital rates. Our work identifies the
resource autocorrelation length as a key modulator and a simple measure of
landscape susceptibility to biological invasions, with implications for
predicting the characters of biological invasions within naturally
heterogeneous environmental corridors.


title: Existence and regularity for a class of rate-independent systems

abstract:
  Despite the many applications of rate-independent systems, their regularity
theory is still largely unexplored. Usually, only weak solution with
potentially very low regularity are considered, which requires non-smooth
techniques. In this work, however, we directly prove the existence of
H\"older-regular strong solutions for a class of rate-independent systems. We
also establish further assertions about higher regularity of our solutions. The
proof proceeds via a time-discrete Rothe approximation, careful elliptic
regularity estimates in the discrete situation and evolutionary techniques.


title: Stochastic Thermodynamics of a Particle in a Box

abstract:
  The piston system (particles in a box) is the simplest and paradigmatic model
in traditional thermodynamics. However, the recently established framework of
stochastic thermodynamics (ST) fails to apply to this model system due to the
embedded singularity in the potential. In this Letter we study the stochastic
thermodynamics of a particle in a box by adopting a novel coordinate
transformation technique. Through comparing with the exact solution of a
breathing harmonic oscillator, we obtain analytical results of work
distribution for an arbitrary protocol in the linear response regime, and
verify various predictions of the Fluctuation-Dissipation Relation. When
applying to the Brownian Szilard's engine model, we obtain the optimal protocol
$\lambda_t = \lambda_0 2^{t/\tau}$ for a given sufficiently long total time
$\tau$. Our study not only establishes a paradigm for studying ST of a particle
in a box, but also bridges the long-standing gap in the development of ST.


title:
On the redshift of the very high energy {\gamma}-ray BL Lac object S2
  0109+22

abstract:
  The determination of the redshift of extragalactic gamma ray sources is of
fundamental importance for the interpretation of their emission models and
extragalactic population studies, AGN classification schemes, and to study the
interaction with the extragalactic background light. Here we focus on the BL
Lac S2 0109+22, recently detected at very high energies. We obtained a high
signal-to-noise optical spectrum at Gran Telescopio Canarias for the source
over the spectral range 4000-10000 Angstrom, to search for spectral features of
the host galaxy and/or of the nuclear source and it was compared with previous
observations in order to confirm and/or dispute its redshift determination. We
find the S2 0109+22 optical spectrum is well represented by a power law
continuum without any absorption or emission feature of Equivalent Width >0.1
Angstrom. Based on the new optical spectrum we are able to set a redshift lower
limit z>0.35, assuming the source is hosted by a massive elliptical galaxy
typical for this class of sources. The redshift z=0.265 proposed in the
literature for this object is most probably referred to a r=18.3 galaxy at 15"
from S2 0109. This galaxy could belong to a group of faint galaxies located at
z~0.26.


title: Chemical abundance analysis of 19 barium stars

abstract:
  We aim at deriving accurate atmospheric parameters and chemical abundances of
19 barium (Ba) stars, including both strong and mild Ba stars, based on the
high signal-to-noise ratio and high resolution Echelle spectra obtained from
the 2.16 m telescope at Xinglong station of National Astronomical
Observatories, Chinese Academy of Sciences. The chemical abundances of the
sample stars were obtained from an LTE, plane-parallel and line-blanketed
atmospheric model by inputting the atmospheric parameters (effective
temperatures, surface gravities, metallicity and microturbulent velocity) and
equivalent widths of stellar absorption lines. These samples of Ba stars are
giants indicated by atmospheric parameters, metallicities and kinematic
analysis about UVW velocity. Chemical abundances of 17 elements were obtained
for these Ba stars. Their light elements (O, Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr,
Mn and Ni) are similar to the solar abundances. Our samples of Ba stars show
obvious overabundances of neutron-capture (n-capture) process elements relative
to the Sun. Their median abundances of [Ba/Fe], [La/Fe] and [Eu/Fe] are 0.54,
0.65 and 0.40, respectively. The YI and ZrI abundances are lower than Ba, La
and Eu, but higher than the light elements for the strong Ba stars and similar
to the iron-peak elements for the mild stars. There exists a positive
correlation between Ba intensity and [Ba/Fe]. For the n-capture elements (Y,
Zr, Ba, La), there is an anti-correlation between their [X/Fe] and [Fe/H]. We
identify nine of our sample stars as strong Ba stars with [Ba/Fe]>0.6 where
seven of them have Ba intensity Ba=2-5, one has Ba=1.5 and another one has
Ba=1.0. The remaining ten stars are classified as mild Ba stars with
0.17<[Ba/Fe]<0.54.


title: Leading log expansion of combinatorial Dyson Schwinger equations

abstract:
  We study combinatorial Dyson Schwinger equations, expressed in the Hopf
algebra of words with a quasi shuffle product. We map them into an algebra of
polynomials in one indeterminate L and show that the leading log expansion one
obtains with such a mapping are simple power law like expression


title:
Systematic Assessment of the Static Stress-Triggering Hypothesis using
  Inter-earthquake Time Statistics

abstract:
  A likely source of earthquake clustering is static stress transfer between
individual events. Previous attempts to quantify the role of static stress for
earthquake triggering generally considered only the stress changes caused by
large events, and often discarded data uncertainties. We conducted a robust
two-fold empirical test of the static stress change hypothesis by accounting
for all events of magnitude M>=2.5 and their location and focal mechanism
uncertainties provided by catalogs for Southern California between 1981 and
2010, first after resolving the focal plane ambiguity and second after randomly
choosing one of the two nodal planes. For both cases, we find compelling
evidence supporting the static triggering with stronger evidence after
resolving the focal plane ambiguity above significantly small (about 10 Pa) but
consistently observed stress thresholds. The evidence for the static triggering
hypothesis is robust with respect to the choice of the friction coefficient,
Skempton's coefficient and magnitude threshold. Weak correlations between the
Coulomb Index (fraction of earthquakes that received positive Coulomb stress
change) and the coefficient of friction indicate that the role of normal stress
in triggering is rather limited. Last but not the least, we determined that the
characteristic time for the loss of the stress change memory of a single event
is nearly independent of the amplitude of the Coulomb stress change and varies
between ~95 and ~180 days implying that forecasts based on static stress
changes will have poor predictive skills beyond times that are larger than a
few hundred days on average.


title:
Higgs Branching Ratios in Constrained Minimal and Next-to-Minimal
  Supersymmetry Scenarios Surveyed

abstract:
  In the CMSSM the heaviest scalar and pseudo-scalar Higgs bosons decay largely
into b-quarks and tau-leptons because of the large $\tan\beta$ values favored
by the relic density. In the NMSSM the number of possible decay modes is much
richer. In addition to the CMSSM-like scenarios, the decay of the heavy Higgs
bosons is preferentially into top quark pairs (if kinematically allowed),
lighter Higgs bosons or neutralinos, leading to invisible decays. We provide a
scan over the NMSSM parameter space to project the 6D parameter space of the
Higgs sector on the 3D space of the Higgs masses to determine the range of
branching ratios as function of the Higgs boson mass for all Higgs bosons.
Specific LHC benchmark points are proposed, which represent the salient NMSSM
features.


title:
Problems for the WELS classification of planetary nebulae central stars:
  Self-consistent nebular modelling of four candidates

abstract:
  We present integral field unit (IFU) spectroscopy and self-consistent
photoionisation modelling for a sample of four southern Galactic planetary
nebulae (PNe) with supposed weak emission-line (WEL) central stars. The Wide
Field Spectrograph (WiFeS) on the ANU 2.3 m telescope has been used to provide
IFU spectroscopy for NGC 3211, NGC 5979, My 60, and M 4-2 covering the spectral
range of 3400-7000{\AA}. All objects are high excitation non-Type I PNe, with
strong He II emission, strong [Ne V] emission, and weak low-excitation lines.
They all appear to be predominantly optically-thin nebulae excited by central
stars with $T_{\rm eff} > 10^5$K. Three PNe of the sample have central stars
which have been previously classified as weak emission-line stars (WELS), and
the fourth also shows the characteristic recombination lines of a WELS.
However, the spatially-resolved spectroscopy shows that rather than arising in
the central star, the C IV and N III recombination line emission is distributed
in the nebula, and in some cases concentrated in discrete nebular knots. This
may suggest that the WELS classification is spurious, and that, rather, these
lines arise from (possibly chemically enriched) pockets of nebular gas. Indeed,
from careful background subtraction we were able to identify three of the
sample as being hydrogen rich O(H)-Type. We have constructed fully
self-consistent photoionization models for each object. This allows us to
independently determine the chemical abundances in the nebulae, to provide new
model-dependent distance estimates, and to place the central stars on the H-R
diagram. All four PNe have similar initial mass ($1.5 < M/M_{\odot} <2.0$) and
are at a similar evolutionary stage.


title:
Spin Precession of Slow Neutrons in Einstein-Cartan Gravity with
  Torsion, Chameleon and Magnetic Field

abstract:
  We analyse a spin precession of slow neutrons in the Einstein-Cartan gravity
with torsion, chameleon and magnetic field. For the derivation of the
Heisenberg equation of motion of the neutron spin we use the effective
low-energy potential, derived by Ivanov and Wellenzohn (Phys. Rev. D92, 125004
(2015)) for slow neutrons, coupled to gravitational, chameleon and torsion
fields to order 1/m, where m is the neutron mass. In addition to this
low-energy interactions we switch on the interaction of slow neutrons with a
magnetic field. We show that to linear order approximation with respect to
gravitational, chameleon and torsion fields the Dirac Hamilton operator for
fermions (neutrons), moving in spacetimes created by rotating coordinate
systems, contains the anti-Hermitian operators of torsion-fermion (neutron)
interactions, caused by torsion scalar and tensor degrees of freedom. Such
anti-Hermitian operators violate CP and T invariance. One may assume that in
the rotating Universe and galaxies the obtained anti-Hermitian torsion-fermion
interactions might be an origin of i) violation of CP and T invariance in the
Universe and ii) of baryon asymmetry.


title:
Dynamic Channel Access Scheme for Interference Mitigation in
  Relay-assisted Intra-WBANs

abstract:
  This work addresses problems related to interference mitigation in a single
wireless body area network (WBAN). In this paper, We propose a distributed
\textit{C}ombined carrier sense multiple access with collision avoidance
(CSMA/CA) with \textit{F}lexible time division multiple access (\textit{T}DMA)
scheme for \textit{I}nterference \textit{M}itigation in relay-assisted
intra-WBAN, namely, CFTIM. In CFTIM scheme, non interfering sources
(transmitters) use CSMA/CA to communicate with relays. Whilst, high interfering
sources and best relays use flexible TDMA to communicate with coordinator (C)
through using stable channels. Simulation results of the proposed scheme are
compared to other schemes and consequently CFTIM scheme outperforms in all
cases. These results prove that the proposed scheme mitigates interference,
extends WBAN energy lifetime and improves the throughput. To further reduce the
interference level, we analytically show that the outage probability can be
effectively reduced to the minimal.


title:
Analysis of the $X(5568)$ as scalar tetraquark state in the
  diquark-antidiquark model with QCD sum rules

abstract:
  In this article, we take the $X(5568)$ as the diquark-antidiquark type
tetraquark state with the spin-parity $J^P=0^+$, construct the
scalar-diquark-scalar-antidiquark type current, carry out the operator product
expansion up to the vacuum condensates of dimension-10, and study the mass and
pole residue in details with the QCD sum rules. We obtain the value
$M_X=\left(5.57\pm0.12 \right) \,\rm{GeV}$, which is consistent with the
experimental data. The present prediction favors assigning the $X(5568)$ to be
the scalar tetraquark state.


title: On the entropy numbers of the mixed smoothness function classes

abstract:
  Behavior of the entropy numbers of classes of multivariate functions with
mixed smoothness is studied here. This problem has a long history and some
fundamental problems in the area are still open. The main goal of this paper is
to develop a new method of proving the upper bounds for the entropy numbers.
This method is based on recent developments of nonlinear approximation, in
particular, on greedy approximation. This method consists of the following two
steps strategy. At the first step we obtain bounds of the best m-term
approximations with respect to a dictionary. At the second step we use general
inequalities relating the entropy numbers to the best m-term approximations.
For the lower bounds we use the volume estimates method, which is a well known
powerful method for proving the lower bounds for the entropy numbers. It was
used in a number of previous papers.


title:
An Algorithm for Solving Linear Nonhomogeneous Quaternion-valued
  Differential Equations

abstract:
  In this paper we presents an algorithm for finding a solution of the linear
nonhomogeneous quaternionic-valued differential equations. Moveover, several
examples shows the feasibility of our algorithm.


title:
Lossy Compression for Compute-and-Forward in Limited Backhaul Uplink
  Multicell Processing

abstract:
  We study the transmission over a cloud radio access network in which multiple
base stations (BS) are connected to a central processor (CP) via
finite-capacity backhaul links. We propose two lattice-based coding schemes. In
the first scheme, the base stations decode linear combinations of the
transmitted messages, in the spirit of compute-and-forward (CoF), but differs
from it essentially in that the decoded equations are remapped to linear
combinations of the channel input symbols, sent compressed in a lossy manner to
the central processor, and are not required to be linearly independent. Also,
by opposition to the standard CoF, an appropriate multi-user decoder is
utilized to recover the sent messages. The second coding scheme generalizes the
first one by also allowing, at each relay node, a joint compression of the
decoded equation and the received signal. Both schemes apply in general, but
are more suited for situations in which there are more users than base
stations. We show that both schemes can outperform standard CoF and successive
Wyner-Ziv schemes in certain regimes, and illustrate the gains through some
numerical examples.


title: Identification of Parallel Passages Across a Large Hebrew/Aramaic Corpus

abstract:
  We propose a method for efficiently finding all parallel passages in a large
corpus, even if the passages are not quite identical due to rephrasing and
orthographic variation. The key ideas are the representation of each word in
the corpus by its two most infrequent letters, finding matched pairs of strings
of four or five words that differ by at most one word and then identifying
clusters of such matched pairs. Using this method, over 4600 parallel pairs of
passages were identified in the Babylonian Talmud, a Hebrew-Aramaic corpus of
over 1.8 million words, in just over 30 seconds. Empirical comparisons on
sample data indicate that the coverage obtained by our method is essentially
the same as that obtained using slow exhaustive methods.


title: The Erd\H{o}s-Hajnal hypergraph Ramsey problem

abstract:
  Given integers $2\le t \le k+1 \le n$, let $g_k(t,n)$ be the minimum $N$ such
that every red/blue coloring of the $k$-subsets of $\{1, \ldots, N\}$ yields
either a $(k+1)$-set containing $t$ red $k$-subsets, or an $n$-set with all of
its $k$-subsets blue. Erd\H{o}s and Hajnal proved in 1972 that for fixed $2\le
t \le k$, there are positive constants $c_1$ and $c_2$ such that $$ 2^{c_1 n} <
g_k(t, n) < twr_{t-1} (n^{c_2}),$$ where $twr_{t-1}$ is a tower of 2's of
height $t-2$. They conjectured that the tower growth rate in the upper bound is
correct. Despite decades of work on closely related and special cases of this
problem by many researchers, there have been no improvements of the lower bound
for $2<t<k$. Here we settle the Erd\H{o}s-Hajnal conjecture in almost all cases
in a strong form, by determining the correct tower growth rate, and in half of
the cases we also determine the correct power of $n$ within the tower.
Specifically, we prove that if $2<t<k-1$ and $k - t$ is even, then $$g_k(t, n)
= twr_{t-1} (n^{k-t+1 + o(1)}).$$ Similar results are proved for $k - t$ odd.


title: Perverse Results on Milnor Fibers inside Parameterized Hypersurfaces

abstract:
  We discuss some results on parameterized hypersurfaces which follow quickly
from results in the category of perverse sheaves


title:
Phase transition via entanglement entropy in $AdS_3/CFT_2$
  superconductors

abstract:
  The purpose of this report is to provide a framework for defining phase
transition processes in two dimensional holographic superconductors, and to
illustrate how they are useful to be described by holographic entanglement
entropy. We study holographic entanglement entropy in a two dimensional fully
backrected model for holographic superconductors. We prove that phase
transition could be observe using a discontinuty in the first order of entropy.


title: Walrasian Pricing in Multi-unit Auctions

abstract:
  Multi-unit auctions are a paradigmatic model, where a seller brings multiple
units of a good, while several buyers bring monetary endowments. It is well
known that Walrasian equilibria do not always exist in this model, however
compelling relaxations such as (Walrasian) envy-free pricing do. In this paper
we design an optimal envy-free mechanism for multi-unit auctions with budgets.
When the market is even mildly competitive, the approximation ratios of this
mechanism are small constants for both the revenue and welfare objectives, and
in fact for welfare the approximation converges to 1 as the market becomes
fully competitive. We also give an impossibility theorem, showing that
truthfulness requires discarding resources and, in particular, is incompatible
with (Pareto) efficiency.


title:
Entanglement Entropy for time dependent two dimensional holographic
  superconductor

abstract:
  We studied entanglement entropy for a time dependent two dimensional
holographic superconductor. We showed that the conserved charge of the system
plays the role of the critical parameter to have condensation.


title: Flexible Caching in Trie Joins

abstract:
  Traditional algorithms for multiway join computation are based on rewriting
the order of joins and combining results of intermediate subqueries. Recently,
several approaches have been proposed for algorithms that are "worst-case
optimal" wherein all relations are scanned simultaneously. An example is
Veldhuizen's Leapfrog Trie Join (LFTJ). An important advantage of LFTJ is its
small memory footprint, due to the fact that intermediate results are full
tuples that can be dumped immediately. However, since the algorithm does not
store intermediate results, recurring joins must be reconstructed from the
source relations, resulting in excessive memory traffic. In this paper, we
address this problem by incorporating caches into LFTJ. We do so by adopting
recent developments on join optimization, tying variable ordering to tree
decomposition. While the traditional usage of tree decomposition computes the
result for each bag in advance, our proposed approach incorporates caching
directly into LFTJ and can dynamically adjust the size of the cache.
Consequently, our solution balances memory usage and repeated computation, as
confirmed by our experiments over SNAP datasets.


title: Theory of high-energy messengers

abstract:
  Knowledge of the distant high-energy universe comes from photons, ultra-high
energy cosmic rays (UHECRs), high-energy neutrinos, and gravitational waves.
The theory of high-energy messengers reviewed here focuses on the extragalactic
background light at all wavelengths, cosmic rays and magnetic fields in
intergalactic space, and neutrinos of extragalactic origin. Comparisons are
drawn between the intensities of photons and UHECRs in intergalactic space, and
the high-energy neutrinos recently detected with IceCube at about the
Waxman-Bahcall flux. Source candidates for UHECRs and high-energy neutrinos are
reviewed, focusing on star-forming and radio-loud active galaxies. HAWC and
Advanced LIGO are just underway, with much anticipation.


title: Free subgroup numbers modulo prime powers: the non-periodic case

abstract:
  In [J. Algebra 452 (2016), 372-389], we characterise when the sequence of
free subgroup numbers of a finitely generated virtually free group $\Gamma$ is
ultimately periodic modulo a given prime power. Here, we show that, in the
remaining cases, in which the sequence of free subgroup numbers is not
ultimately periodic modulo a given prime power, the number of free subgroups of
index~$\lambda$ in $\Gamma$ is - essentially - congruent to a binomial
coefficient times a rational function in $\lambda$ modulo a power of a prime
that divides a certain invariant of the group $\Gamma$, respectively to a
binomial sum involving such numbers. These results, apart from their intrinsic
interest, in particular allow for a much more efficient computation of
congruences for free subgroup numbers in these cases compared to the direct
recursive computation of these numbers implied by the generating function
results in [J. London Math. Soc. (2) 44 (1991), 75-94].


title:
The kinetic theory to problem of attenuation transversal sound waves in
  metal

abstract:
  Earlier electron influence on sound absorption in metal on basis of the
assumption of deformation of Fermi-surfaces under the influence of a sound wave
was considered. In the present work other approach to this problem will be
considered. Our approach based on the account of dynamic (kinetic) interaction
of electronic gas with lattice fluctuations. The analysis of influence of
electric field on process of attenuation of sound fluctuations is carried out.
It is shown that in the long-wave limit this influence is essential.


title:
Einstein-Podolsky-Rosen steering in non-Hermitian, nonlinear soliton
  surface plasmons

abstract:
  We investigate the dynamics of Einstein-Podolsky-Rosen steering in a
soliplasmonic system where the asymmetrical coupling between linear solitons
and nonlinear plasmons is controlled by the weak soliton amplitude. We employ
non-Hermitian quantum dynamics to evaluate quantum steering witnesses for
different coupling strengths. Quantum steering is examined for an initially
Fock state and we briefly discuss Einstein-Podolsky-Rosen entanglement for
initially coherent states. We numerically investigate the adjustability of the
witnessing periods of quantum steering via tunable coupling strength of
soliton-plasmon interaction and discuss the possibility of the nonlinear
soliplasmonic systems as a robust platform for implementing one-sided quantum
key distributions.


title: Parton distribution functions from Lattice QCD

abstract:
  We present recent results on the first moments of parton distributions using
gauge configurations generated with two degenerate flavors of light twisted
mass quarks with pion mass fixed approximately to its physical value. We also
present a first study of the vector parton distribution function using a
twisted mass ensemble at pion mass of 373 MeV.


title:
PetIGA-MF: a multi-field high-performance toolbox for
  structure-preserving B-splines spaces

abstract:
  We describe the development of a high-performance solution framework for
isogeometric discrete differential forms based on B-splines: PetIGA-MF. Built
on top of PetIGA, PetIGA-MF is a general multi-field discretization tool. To
test the capabilities of our implementation, we solve different viscous flow
problems such as Darcy, Stokes, Brinkman, and Navier-Stokes equations. Several
convergence benchmarks based on manufactured solutions are presented assuring
optimal convergence rates of the approximations, showing the accuracy and
robustness of our solver.


title: Cache Size Allocation in Backhaul Limited Wireless Networks

abstract:
  Caching popular content at base stations is a powerful supplement to existing
limited backhaul links for accommodating the exponentially increasing mobile
data traffic. Given the limited cache budget, we investigate the cache size
allocation problem in cellular networks to maximize the user success
probability (USP), taking wireless channel statistics, backhaul capacities and
file popularity distributions into consideration. The USP is defined as the
probability that one user can successfully download its requested file either
from the local cache or via the backhaul link. We first consider a single-cell
scenario and derive a closed-form expression for the USP, which helps reveal
the impacts of various parameters, such as the file popularity distribution.
More specifically, for a highly concentrated file popularity distribution, the
required cache size is independent of the total number of files, while for a
less concentrated file popularity distribution, the required cache size is in
linear relation to the total number of files. Furthermore, we study the
multi-cell scenario, and provide a bisection search algorithm to find the
optimal cache size allocation. The optimal cache size allocation is verified by
simulations, and it is shown to play a more significant role when the file
popularity distribution is less concentrated.


title:
Asymmetric Forward-Backward-Adjoint Splitting for Solving Monotone
  Inclusions Involving Three Operators

abstract:
  In this work we propose a new splitting technique, namely Asymmetric
Forward-Backward-Adjoint splitting, for solving monotone inclusions involving
three terms, a maximally monotone, a cocoercive and a bounded linear operator.
Classical operator splitting methods, like Douglas-Rachford and
Forward-Backward splitting are special cases of our new algorithm. Asymmetric
Forward-Backward-Adjoint splitting unifies, extends and sheds light on the
connections between many seemingly unrelated primal-dual algorithms for solving
structured convex optimization problems proposed in recent years. More
importantly, it greatly extends the scope and applicability of splitting
techniques to a wider variety of problems. One important special case leads to
a Douglas-Rachford type scheme that includes a third cocoercive operator.


title: Improved bounds and algorithms for graph cuts and network reliability

abstract:
  Karger (SIAM Journal on Computing, 1999) developed the first fully-polynomial
approximation scheme to estimate the probability that a graph $G$ becomes
disconnected, given that its edges are removed independently with probability
$p$. This algorithm runs in $n^{5+o(1)} \epsilon^{-3}$ time to obtain an
estimate within relative error $\epsilon$.
  We improve this run-time through algorithmic and graph-theoretic advances.
First, there is a certain key sub-problem encountered by Karger, for which a
generic estimation procedure is employed, we show that this has a special
structure for which a much more efficient algorithm can be used. Second, we
show better bounds on the number of edge cuts which are likely to fail. Here,
Karger's analysis uses a variety of bounds for various graph parameters, we
show that these bounds cannot be simultaneously tight. We describe a new graph
parameter, which simultaneously influences all the bounds used by Karger, and
obtain much tighter estimates of the cut structure of $G$. These techniques
allow us to improve the runtime to $n^{3+o(1)} \epsilon^{-2}$, our results also
rigorously prove certain experimental observations of Karger & Tai (Proc.
ACM-SIAM Symposium on Discrete Algorithms, 1997). Our rigorous proofs are
motivated by certain non-rigorous differential-equation approximations which,
however, provably track the worst-case trajectories of the relevant parameters.
  A key driver of Karger's approach (and other cut-related results) is a bound
on the number of small cuts: we improve these estimates when the min-cut size
is "small" and odd, augmenting, in part, a result of Bixby (Bulletin of the
AMS, 1974).


title: Yetter-Drinfeld modules for weak Hom-Hopf algebras

abstract:
  The aim of this paper is to define and study Yetter-Drinfeld modules over
weak Hom-Hopf algebras. We show that the category ${}_H{\cal WYD}^H$ of
Yetter-Drinfeld modules with bijective structure maps over weak Hom-Hopf
algebras is a rigid category and a braided monoidal category, and obtain a new
solution of quantum Hom-Yang-Baxter equation. It turns out that, If $H$ is
quasitriangular (respectively, coquasitriangular)weak Hom-Hopf algebras, the
category of modules (respectively, comodules) with bijective structure maps
over $H$ is a braided monoidal subcategory of the category ${}_H{\cal WYD}^H$
of Yetter-Drinfeld modules over weak Hom-Hopf algebras.


title:
Hylomorphic solitons for the Benjamin-Ono and the fractional KdV
  equations

abstract:
  This paper concerns with the existence of solitons, namely stable solitary
waves, for the Benjamin-Ono and the fractional KdV equations.


title: Warped anti-de Sitter in 3d (2,0) Supergravity

abstract:
  We comment on the ubiquity of the so-called warped anti-de Sitter spacetimes
in three-dimensional (2,0) supergravity theory. By using isometry-invariant
tensors and simple counting, we prove their existence for arbitrary $(2,0)$
supergravity models suitably defined close to a minimal model. We also analyze
their offshell supersymmetry and the supersymmetry of two geometric orbifolds.


title:
A Structured Variational Auto-encoder for Learning Deep Hierarchies of
  Sparse Features

abstract:
  In this note we present a generative model of natural images consisting of a
deep hierarchy of layers of latent random variables, each of which follows a
new type of distribution that we call rectified Gaussian. These rectified
Gaussian units allow spike-and-slab type sparsity, while retaining the
differentiability necessary for efficient stochastic gradient variational
inference. To learn the parameters of the new model, we approximate the
posterior of the latent variables with a variational auto-encoder. Rather than
making the usual mean-field assumption however, the encoder parameterizes a new
type of structured variational approximation that retains the prior
dependencies of the generative model. Using this structured posterior
approximation, we are able to perform joint training of deep models with many
layers of latent random variables, without having to resort to stacking or
other layerwise training procedures.


title:
Heuristics for the Variable Sized Bin Packing Problem Using a Hybrid
  P-System and CUDA Architecture

abstract:
  The Variable Sized Bin Packing Problem has a wide range of application areas
including packing, scheduling, and manufacturing. Given a list of items and
variable sized bin types, the objective is to minimize the total size of the
used bins. This problem is known to be NP-hard. In this article, we present two
new heuristics for solving the problem using a new variation of P systems with
active membranes, which we call a hybrid P system, implemented in CUDA. Our
hybrid P-system model allows using the polarity and labels of membranes to
represent object properties which results in reducing the complexity of
implementing the P-system. We examine the performance of the two heuristics,
and compare the results with those of other known algorithms. The numerical
results show that good solutions for large instances (10000 items) of this
problem could be obtained in a very short time (seconds) using our CUDA
simulator.


title:
Uniqueness of the extremal graph in the problem of maximizing the number
  of independent sets in regular graphs

abstract:
  The main purpose of this paper is to prove the uniqueness of a graph
attaining the maximum of the number of independent sets over all $k$-regular
graphs on $n$ vertices for $2k|n$.


title:
Characteristic polynomials for 1D random band matrices from the
  localization side

abstract:
  We study the special case of $n\times n$ 1D Gaussian Hermitian random band
matrices, when the covariance of the elements is determined by
$J=(-W^2\triangle+1)^{-1}$. Assuming that the band width $W\ll \sqrt{n}$, we
prove that the limit of the normalized second mixed moment of characteristic
polynomials (as $W, n\to \infty$) is equal to one, and so it does not coincides
with those for GUE. This complements the previous result of T. Shcherbina and
proves the expected crossover for 1D Hermitian random band matrices at $W\sim
\sqrt{n}$ on the level of characteristic polynomials.


title:
On the cylindrically symmetric wormholes WhCR^e: The motion of test
  particles

abstract:
  In this article we partially implement the program outlined in the previous
paper of the authors [A. V. Aminova and P. I. Chumarov, Phys. Rev. D 88, 044005
(2013)]. The program owes its origins to the following comment in paper [M.
Cveti\v{c} and D. Youm, Nucl. Phys. B, 438, 182 (1995), Addendum-ibid. 449,146
(1995)], where a class of static spherically symmetric solutions in
$(4+n)$-dimensional Kaluza--Klein theory was studied: "...We suspect that the
same thing [as for spherical symmetry] will happen for axially symmetric
stationary configurations, but it remains to be proven". We study the radial
and non-radial motion of test particles in the cylindrically symmetric
wormholes found in the authors'paper of type $\rm WhCR^e$ in 6-dimensional
reduced Kaluza--Klein theory with Abelian gauge field and two dilaton fields,
with particular attention to the extent to which the wormhole is traversable.
In the case of non-radial motion along a hypersurface z=const we show that, as
in the Kerr and Schwarzschild geometries, we should distinguish between orbits
with impact parameters greater resp. less than a certain critical value $D_c$,
which corresponds to the unstable circular orbit of radius $u_c$ $(r_c)$. For
$D^2>D_c^2$ there are two kinds of orbits: orbits of the first kind arrive from
infinity and have pericenter distances greater than $u_c$, whereas orbits of
the second kind have apocenter distances less than $u_c$ and terminate at the
singularity at $u=-\infty$ $(r=0)$. For $D=D_c$ orbits of the first and second
kinds merge and both orbits spiral an infinite number of times toward the
unstable circular orbit $u=u_c$. For $D^2<D_c^2$ we have only orbits of one
kind: starting at infinity, they cross the wormhole throat and terminate at the
singularity.


title: Homotopy composition of cospans

abstract:
  It is well known that the category of finite sets and cospans, composed by
pushout, contains the universal {\em special} commutative Frobenius algebra. In
this note we observe that the same construction yields also general commutative
Frobenius algebras, if just the pushouts are changed to homotopy pushouts.


title: Uniform symplicity of groups with proximal action

abstract:
  We prove that groups acting boundedly and order-primitively on linear orders
or acting extremly proximality on a Cantor set (the class including various
Higman-Thomson groups and Neretin groups of almost automorphisms of regular
trees, also called groups of spheromorphisms) are uniformly simple. Explicit
bounds are provided.


title:
Gibberish Semantics: How Good is Russian Twitter in Word Semantic
  Similarity Task?

abstract:
  The most studied and most successful language models were developed and
evaluated mainly for English and other close European languages, such as
French, German, etc. It is important to study applicability of these models to
other languages. The use of vector space models for Russian was recently
studied for multiple corpora, such as Wikipedia, RuWac, lib.ru. These models
were evaluated against word semantic similarity task. For our knowledge Twitter
was not considered as a corpus for this task, with this work we fill the gap.
Results for vectors trained on Twitter corpus are comparable in accuracy with
other single-corpus trained models, although the best performance is currently
achieved by combination of multiple corpora.


title:
Optimizing the Learning Order of Chinese Characters Using a Novel
  Topological Sort Algorithm

abstract:
  We present a novel algorithm for optimizing the order in which Chinese
characters are learned, one that incorporates the benefits of learning them in
order of usage frequency and in order of their hierarchal structural
relationships. We show that our work outperforms previously published orders
and algorithms. Our algorithm is applicable to any scheduling task where nodes
have intrinsic differences in importance and must be visited in topological
order.


title: Chekanov-type theorem for spherized cotangent bundles

abstract:
  We prove a Chekanov-type theorem for the spherization of the cotangent bundle
$ST^*B$ of a closed manifold $B$. It claims that for Legendrian submanifolds in
$ST^*B$ the property "to be given by a generating family quadratic at infinity"
persists under Legendrian isotopies.


title:
Positive-homogeneous operators, heat kernel estimates and the
  Legendre-Fenchel transform

abstract:
  We consider a class of homogeneous partial differential operators on a
finite-dimensional vector space and study their associated heat kernels. The
heat kernels for this general class of operators are seen to arise naturally as
the limiting objects of the convolution powers of complex-valued functions on
the square lattice in the way that the classical heat kernel arises in the
(local) central limit theorem. These so-called positive-homogeneous operators
generalize the class of semi-elliptic operators in the sense that the
definition is coordinate-free. More generally, we introduce a class of
variable-coefficient operators, each of which is uniformly comparable to a
positive-homogeneous operator, and we study the corresponding Cauchy problem
for the heat equation. Under the assumption that such an operator has
H\"{o}lder continuous coefficients, we construct a fundamental solution to its
heat equation by the method of E. E. Levi, adapted to parabolic systems by A.
Friedman and S. D. Eidelman. Though our results in this direction are implied
by the long-known results of S. D. Eidelman for $2\vec{b}$-parabolic systems,
our focus is to highlight the role played by the Legendre-Fenchel transform in
heat kernel estimates. Specifically, we show that the fundamental solution
satisfies an off-diagonal estimate, i.e., a heat kernel estimate, written in
terms of the Legendre-Fenchel transform of the operator's principal symbol--an
estimate which is seen to be sharp in many cases.


title: Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics

abstract:
  We study the variation of a smooth volume form along extremals of a
variational problem with nonholonomic constraints and an action-like
Lagrangian. We introduce a new invariant describing the interaction of the
volume with the dynamics and we study its basic properties. We then show how
this invariant, together with curvature-like invariants of the dynamics, appear
in the expansion of the volume at regular points of the exponential map. This
generalizes the well-known expansion of the Riemannian volume in terms of Ricci
curvature to a wide class of geometric structures, including all sub-Riemannian
manifolds.


title: On Short-Range Enhancement of Van-der-Waals Forces

abstract:
  We show that for nanoparticles with giant polarizability $\alpha$ (a
prominent example being the recently studied Na$_{14}$F$_{13}$ molecular
clusters) van der Waals forces are significantly enhanced at interparticle
distances shorter than $R_0=(\alpha/2\pi\epsilon_0)^{1/3}$. For an adequate
description of this phenomenon, nonlinear effects must be taken into account.
We show that, contrary to some theoretical claims, an accurate treatment of
nonlinearity does not lead to any repulsive forces.


title:
Reciprocal and unidirectional scattering of parity-time symmetric
  structures

abstract:
  Parity-time (PT) symmetry is of great interest. The reciprocal and
unidirectional features are intriguing besides the PT symmetry phase
transition. Recently, the reciprocal transmission, unidirectional
reflectionless and invisibility are intensively studied. Here, we show the
reciprocal reflection/transmission in PT -symmetric system is closely related
to the type of PT symmetry, that is, the axial (reflection) PT symmetry leads
to reciprocal reflection (transmission). The results are further elucidated by
studying the scattering of rhombic ring form coupled resonators with enclosed
synthetic magnetic flux. The nonreciprocal phase shift induced by the magnetic
flux and gain/loss break the parity (P) and time-reversal (T) symmetry but keep
the parity-time (PT) symmetry. The reciprocal reflection (transmission) and
unidirectional transmission (reflection) are found in the axial (reflection)
PT-symmetric ring center. The explorations of symmetry and asymmetry from PT
symmetry may shed light on novel one-way optical devices and application of PT
metamaterials.


title: Quasiadiabatic modes from viscous inhomogeneities

abstract:
  The viscous inhomogeneities of a relativistic plasma determine a further
class of entropic modes whose amplitude must be sufficiently small since
curvature perturbations are observed to be predominantly adiabatic and Gaussian
over large scales. When the viscous coefficients only depend on the energy
density of the fluid the corresponding curvature fluctuations are shown to be
almost adiabatic. After addressing the problem in a gauge-invariant
perturbative expansion, the same analysis is repeated at a non-perturbative
level by investigating the nonlinear curvature inhomogeneities induced by the
spatial variation of the viscous coefficients. It is demonstrated that the
quasiadiabatic modes are suppressed in comparison with a bona fide adiabatic
solution. Because of its anomalously large tensor to scalar ratio the
quasiadiabatic mode cannot be a substitute for the conventional adiabatic
paradigm so that, ultimately, the present findings seems to exclude the
possibility of a successful accelerated dynamics solely based on relativistic
viscous fluids. If the dominant adiabatic mode is not affected by the viscosity
of the background a sufficiently small fraction of entropic fluctuations of
viscous origin cannot be a priori ruled out.