title:
Parametric representation of univalent functions with boundary regular
  fixed points

abstract:
  Given a set $\mathfrak S$ of conformal maps of the unit disk $\mathbb D$ into
itself that is closed under composition, we address the question whether
$\mathfrak S$ can be represented as the reachable set of a Loewner - Kufarev -
type ODE $\mathrm{d}w_t/\mathrm{d}t=G_t\circ w_t$, $w_0=\mathsf{id}_{\mathbb
D}$, where the control functions $t\mapsto G_t$ form a convex cone $\mathcal
M_{\mathfrak S}$. For the set of all conformal $\varphi:\mathbb D\to\mathbb D$
with $\varphi(0)=0$, $\varphi'(0)>0$, an affirmative answer to this question is
the essence of Loewner's well-known Parametric Representation of univalent
functions [Math. Ann. 89 (1923), 103-121]. In this paper, we study classes of
conformal self-maps defined by their boundary regular fixed points and, in part
of the cases, establish their Loewner-type representability.


title:
On MAXCUT in strictly supercritical random graphs, and coloring of
  random graphs and random tournaments

abstract:
  We use a theorem by Ding, Lubetzky and Peres describing the structure of the
giant component of random graphs in the strictly supercritical regime, in order
to determine the typical size of MAXCUT of $G\sim G\left(n,\frac
{1+\varepsilon}n\right)$ in terms of $\varepsilon$. We then apply this result
to prove the following conjecture by Frieze and Pegden. For every
$\varepsilon>0$ there exists $\ell_\varepsilon$ such that \whp $G\sim G(n,\frac
{1+\varepsilon}n)$ is not homomorphic to the cycle on $2\ell_\varepsilon+1$
vertices. We also consider the coloring properties of biased random
tournaments. A $p$-random tournament on $n$ vertices is obtained from the
transitive tournament by reversing each edge independently with probability
$p$. We show that for $p=\Theta(\frac 1n)$ the chromatic number of a $p$-random
tournament behaves similarly to that of a random graph with the same edge
probability. To treat the case $p=\frac {1+\varepsilon}n$ we use the
aforementioned result on MAXCUT.


title:
A case of multivariate Birkhoff interpolation using high order
  derivatives

abstract:
  We consider a specific scheme of multivariate Birkhoff polynomial
interpolation. Our samples are derivatives of various orders $k_j$ at fixed
points $v_j$ along fixed straight lines through $v_j$ in directions $u_j$,
under the following assumption: the total number of sampled derivatives of
order $k, \ k=0,1,\ldots$ is equal to the dimension of the space homogeneous
polynomials of degree $k$. We show that this scheme is regular for general
directions. Specifically this scheme is regular independent of the position of
the interpolation nodes. In the planar case, we show that this scheme is
regular for distinct directions.
  Next we prove a "Birkhoff-Remez" inequality for our sampling scheme extended
to larger sampling sets. It bounds the norm of the interpolation polynomial
through the norm of the samples, in terms of the geometry of the sampling set.


title:
Image and Depth from a Single Defocused Image Using Coded Aperture
  Photography

abstract:
  Depth from defocus and defocus deblurring from a single image are two
challenging problems that are derived from the finite depth of field in
conventional cameras. Coded aperture imaging is one of the techniques that is
used for improving the results of these two problems. Up to now, different
methods have been proposed for improving the results of either defocus
deblurring or depth estimation. In this paper, a multi-objective function is
proposed for evaluating and designing aperture patterns with the aim of
improving the results of both depth from defocus and defocus deblurring.
Pattern evaluation is performed by considering the scene illumination condition
and camera system specification. Based on the proposed criteria, a single
asymmetric pattern is designed that is used for restoring a sharp image and a
depth map from a single input. Since the designed pattern is asymmetric,
defocus objects on the two sides of the focal plane can be distinguished. Depth
estimation is performed by using a new algorithm, which is based on image
quality assessment criteria and can distinguish between blurred objects lying
in front or behind the focal plane. Extensive simulations as well as
experiments on a variety of real scenes are conducted to compare our aperture
with previously proposed ones.


title: Sobolev homeomorphisms with gradients of low rank via laminates

abstract:
  Let $\Omega\subset \mathbb{R}^{n}$ be a bounded open set. Given $2\leq m\leq
n$, we construct a convex function $\phi :\Omega\to \mathbb{R}$ whose gradient
$f= \nabla \phi$ is a H\"older continuous homeomorphism, $f$ is the identity on
$\partial \Omega$, the derivative $D f$ has rank $m-1$ a.e.\ in $\Omega$ and $D
f$ is in the weak $L^{m}$ space $L^{m,w}$. The proof is based on convex
integration and staircase laminates.


title:
The conditions for the preservation of duality symmetry in a linear
  medium

abstract:
  Electric magnetic duality symmetry is well understood in vacuum. For light
propagating through a medium this symmetry is typically broken. We investigate
under what conditions duality transformation is preserved in a linear medium
and employ these conditions to generalise the definition of optical helicity to
a general linear medium. We will discuss some unique properties duality
symmetric media possess, provided they exist and reformulate Maxwell's equation
in such a way that they explicitly show the decoupling of opposite helicities.
The feasibility of constructing a duality symmetric medium is discussed.


title: On the k-metric Dimension of Metric Spaces

abstract:
  The metric dimension of a general metric space was defined in 1953, applied
to the set of vertices of a graph metric in 1975, and developed further for
metric spaces in 2013. It was then generalised in 2015 to the k-metric
dimension of a graph for each positive integer k, where k=1 corresponds to the
original definition. Here, we discuss the k-metric dimension of general metric
spaces.


title: Focal Radius, Rigidity, and Lower Curvature Bounds

abstract:
  We show that the focal radius of any submanifold $N$ of positive dimension in
a manifold $M$ with sectional curvature greater than or equal to $1$ does not
exceed $\frac{\pi }{2}.$ In the case of equality, we show that $N$ is totally
geodesic in $M$ and the universal cover of $M$ is isometric to a sphere or a
projective space with their standard metrics, provided $N$ is closed.
  Our results also hold for $k^{th}$--intermediate Ricci curvature, provided
the submanifold has dimension $\geq k.$ Thus in a manifold with Ricci curvature
$\geq n-1,$ all hypersurfaces have focal radius $\leq \frac{\pi }{2},$ and
space forms are the only such manifolds where equality can occur, if the
submanifold is closed.
  To prove these results, we develop a new comparison lemma for Jacobi fields
that exploits Wilking's transverse Jacobi equation.


title: Non-vanishing elements in finite groups

abstract:
  Many results have been established about determining whether or not an
element evaluates to zero on an irreducible character of a group. In this note
it is shown that if a group $G$ has a normal nilpotent subgroup $N$, and $P$ is
a Sylow $p$-subgroup of $G$, then no irreducible character of $G$ vanishes on
$N\cap Z(P)$.


title: Tail diameter upper bounds for polytopes and polyhedra

abstract:
  In 1992, Kalai and Kleitman proved a quasipolynomial upper bound on the
diameters of convex polyhedra. Todd and Sukegawa-Kitahara proved
tail-quasipolynomial bounds on the diameters of polyhedra. These tail bounds
apply when the number of facets is greater than a certain function of the
dimension. We prove tail-quasipolynomial bounds on the diameters of polytopes
and normal simplicial complexes. We also prove tail-polynomial upper bounds on
the diameters of polyhedra.


title:
Search for new physics with the MT2 variable in all-jets final states
  produced in pp collisions at sqrt(s) = 13 TeV

abstract:
  A search for new physics is performed using events that contain one or more
jets, no isolated leptons, and a large transverse momentum imbalance, as
measured through the MT2 variable, which is an extension of the transverse mass
in events with two invisible particles. The results are based on a sample of
proton-proton collisions collected at a center-of-mass energy of 13 TeV with
the CMS detector at the LHC, and that corresponds to an integrated luminosity
of 2.3 inverse femtobarns. The observed event yields in the data are consistent
with predictions for the standard model backgrounds. The results are
interpreted using simplified models of supersymmetry and are expressed in terms
of limits on the masses of potential new colored particles. Assuming that the
lightest neutralino is stable and has a mass less than about 500 GeV, gluino
masses up to 1550-1750 GeV are excluded at 95% confidence level, depending on
the gluino decay mechanism. For the scenario of direct production of
squark-antisquark pairs, top squarks with masses up to 800 GeV are excluded,
assuming a 100% branching fraction for the decay to a top quark and neutralino.
Similarly, bottom squark masses are excluded up to 880 GeV, and masses of
light-flavor squarks are excluded up to 600-1260 GeV, depending on the degree
of degeneracy of the squark masses.


title:
Accurate, robust and reliable calculations of Poisson-Boltzmann binding
  energies

abstract:
  Poisson-Boltzmann (PB) model is one of the most popular implicit solvent
models in biophysical modeling and computation. The ability of providing
accurate and reliable PB estimation of electrostatic solvation free energy,
$\Delta G_{\text{el}}$, and binding free energy, $\Delta\Delta G_{\text{el}}$,
is of tremendous significance to computational biophysics and biochemistry.
Recently, it has been warned in the literature (Journal of Chemical Theory and
Computation 2013, 9, 3677-3685) that the widely used grid spacing of $0.5$ \AA
$ $ produces unacceptable errors in $\Delta\Delta G_{\text{el}}$ estimation
with the solvent exclude surface (SES). In this work, we investigate the grid
dependence of our PB solver (MIBPB) with SESs for estimating both electrostatic
solvation free energies and electrostatic binding free energies. It is found
that the relative absolute error of $\Delta G_{\text{el}}$ obtained at the grid
spacing of $1.0$ \AA $ $ compared to $\Delta G_{\text{el}}$ at $0.2$ \AA $ $
averaged over 153 molecules is less than 0.2\%. Our results indicate that the
use of grid spacing $0.6$ \AA $ $ ensures accuracy and reliability in
$\Delta\Delta G_{\text{el}}$ calculation. In fact, the grid spacing of $1.1$
\AA $ $ appears to deliver adequate accuracy for high throughput screening.


title:
Construction of cyclic DNA codes over the Ring $\Z_4[u]/\langle u^2-1
  \rangle $ Based on the deletion distance

abstract:
  In this paper, we develop the theory for constructing DNA cyclic codes of odd
length over $R=\Z_4[u]/\langle u^2-1 \rangle$ based on the deletion distance.
Firstly, we relate DNA pairs with a special 16 elements of ring $R$. Cyclic
codes of odd length over $R$ satisfy the reverse constraint and the
reverse-complement constraint are discussed in this paper. We also study the
$GC$-content of these codes and their deletion distance. The paper concludes
with some examples of cyclic DNA codes with $GC$-content and their respective
deletion distance.


title:
Negative Magnetoresistance in Topological Semimetals of Transition-Metal
  Dipnictides with Nontrivial Z2 Indices

abstract:
  Negative magnetoresistance (NMR) induced by the Adler-Bell-Jackiw anomaly is
regarded as the most prominent quantum signature of Weyl semimetals when
electrical field $E$ is collinear with the external magnetic field $B$. In this
article, we report universal NMR in nonmagnetic, centrosymmetric transition
metal dipnictides MPn$_{2}$ (M=Nb and Ta; Pn=As and Sb), in which the existence
of Weyl fermions can be explicitly excluded. Using temperature-dependent
magnetoresistance, Hall and thermoelectric coefficients of Nernst and Seebeck
effects, we determine that the emergence of the NMR phenomena in MPn$_{2}$ is
coincident with a Lifshitz transition, corresponding to the formation of unique
electron-hole-electron ($e$-$h$-$e$) pockets along the $I-L-I'$ direction.
First-principles calculations reveal that, along the $I-L-I'$ line, the
$d_{xy}$ and $d_{x^{2}-y^{2}}$ orbitals of the transition metal form tilted
nodal rings of band crossing well below the Fermi level. Strong spin-orbital
coupling gaps all the crossing points and creates the characteristic
$e$-$h$-$e$ structure, making MPn$_{2}$ a topological semimetal with
$\mathbb{Z}_2$ indices of [0;(111)]. By excluding the weak localization
contribution of the bulk states, we conclude that the universal NMR in
MPn$_{2}$ may have an exotic origin in topological surface states, which
appears in pairs with opposite spin-momentum locking on nontrivial surfaces.


title:
Characterization of subhalo structural properties and implications for
  dark matter annihilation signals

abstract:
  A prediction of the standard LCDM cosmology is that dark matter (DM) halos
are teeming with numerous self-bound substructure, or subhalos. The precise
properties of these subhalos represent important probes of the underlying
cosmological model. We use data from Via Lactea II and ELVIS N-body simulations
to learn about the structure of subhalos with masses 1e6 - 1e11 Msun/h. Thanks
to a superb subhalo statistics, we study subhalo properties as a function of
distance to host halo center and subhalo mass, and provide a set of fits that
accurately describe the subhalo structure. We also investigate the role of
subhalos on the search for DM annihilation. Previous work has shown that
subhalos are expected to boost the DM signal of their host halos significantly.
Yet, these works traditionally assumed that subhalos exhibit similar structural
properties than those of field halos, while it is known that subhalos are more
concentrated. Building upon our N-body data analysis, we refine the
substructure boost model of Sanchez-Conde & Prada (2014), and find boosts that
are a factor 2-3 higher. We further refine the model to include unavoidable
tidal stripping effects on the subhalo population. For field halos, this
introduces a moderate 20-30% suppression. Yet, for subhalos like those hosting
dwarf galaxy satellites, tidal stripping plays a critical role, the boost being
at the level of a few tens of percent at most. We provide a parametrization of
the boost for field halos that can be safely applied over a wide halo mass
range.


title: Phloem loading through plasmodesmata: a biophysical analysis

abstract:
  In many species, sucrose en route out of the leaf migrates from
photosynthetically active mesophyll cells into the phloem down its
concentration gradient via plasmodesmata, i.e., symplastically. In some of
these plants the process is entirely passive, but in others phloem sucrose is
actively converted into larger sugars, raffinose and stachyose, and segregated
(trapped), thus raising total phloem sugar concentration to a level higher than
in the mesophyll. Questions remain regarding the mechanisms and selective
advantages conferred by both of these symplastic loading processes. Here we
present an integrated model - including local and global transport and the
kinetics of oligomerization - for passive and active symplastic loading. We
also propose a physical model of transport through the plasmodesmata. With
these models, we predict that: 1) relative to passive loading, oligomerization
of sucrose in the phloem, even in the absence of segregation, lowers the sugar
content in the leaf required to achieve a given export rate and accelerates
export for a given concentration of sucrose in the mesophyll; and 2)
segregation of oligomers and the inverted gradient of total sugar content can
be achieved for physiologically reasonable parameter values, but even higher
export rates can be accessed in scenarios in which polymers are allowed to
diffuse back into the mesophyll. We discuss these predictions in relation to
further studies aimed at the clarification of loading mechanisms, fitness of
active and passive symplastic loading, and potential targets for engineering
improved rates of export.


title:
Algorithmic aspects of branched coverings II/V. Sphere bisets and their
  decompositions

abstract:
  We consider "Thurston maps": branched self-coverings of the sphere with
ultimately periodic critical points, and prove that the Thurston equivalence
problem between them (continuous deformation of maps along with their critical
orbits) is decidable.
  More precisely, we consider the action of mapping class groups, by pre- and
post-composition, on branched coverings, and encode them algebraically as
"mapping class bisets". We show how the mapping class biset of maps preserving
a multicurve decomposes into mapping class bisets of smaller complexity, called
"small mapping class bisets".
  We phrase the decision problem of Thurston equivalence between branched
self-coverings of the sphere in terms of the conjugacy and centralizer problems
in a mapping class biset. Our decomposition results on mapping class bisets
reduce these decision problems to small mapping class bisets; they correspond
to rational maps, homeomorphisms and maps double covered by a torus
endomorphism, and their conjugacy and centralizer problems are solvable
respectively in terms of complex analysis, group theory and linear algebra.
  Branched coverings themselves are also encoded into bisets, with actions of
the fundamental groups. We characterize those bisets that arise from branched
coverings between topological spheres, and extend this correspondence to maps
between spheres with multicurves, whose algebraic counterparts are "sphere
trees of bisets".
  To illustrate the difference between Thurston maps and homeomorphisms, we
produce a Thurston map with infinitely generated centralizer --- while
centralizers of homeomorphisms are always finitely generated.


title: Modelling Developable Ribbons Using Ruling Bending Coordinates

abstract:
  This paper presents a new method for modelling the dynamic behaviour of
developable ribbons, two dimensional strips with much smaller width than
length. Instead of approximating such surface with a general triangle mesh, we
characterize it by a set of creases and bending angles across them. This
representation allows the developability to be satisfied everywhere while still
leaves enough degree of freedom to represent salient global deformation. We
show how the potential and kinetic energies can be properly discretized in this
configuration space and time integrated in a fully implicit manner. The result
is a dynamic simulator with several desirable features: We can model
non-trivial deformation using much fewer elements than conventional FEM method.
It is stable under extreme deformation, external force or large timestep size.
And we can readily handle various user constraints in Euclidean space.


title: Fractional Galilean Symmetries

abstract:
  We generalize the differential representation of the operators of the
Galilean algebras to include fractional derivatives. As a result a whole new
class of scale invariant Galilean algebras are obtained. The first member of
this class has dynamical index $z=2$ similar to the Schr\"odinger algebra. The
second member of the class has dynamical index $z=3/2$, which happens to be the
dynamical index Kardar-Parisi-Zhang equation.


title:
Near-locality of exchange and correlation density functionals for 1- and
  2-electron systems

abstract:
  The uniform electron gas and the hydrogen atom play fundamental roles in
condensed matter physics and quantum chemistry. The former has an infinite
number of electrons uniformly distributed over the neutralizing
positively-charged background, and the latter only one electron bound to the
proton. The uniform electron gas was used to derive the local spin density
approximation (LSDA) to the exchange-correlation functional that undergirds the
development of the Kohn-Sham density functional theory. We show here that the
ground-state exchange-correlation energies of the hydrogen atom and many other
1- and 2-electron systems are modeled surprisingly well by a different local
spin density approximation (LSDA0). Our LSDA0 is constructed to satisfy exact
constraints, but agrees surprisingly well with the exact results for a uniform
two-electron density in a finite, curved three-dimensional space. We also apply
LSDA0 to excited or noded 1-electron densities. Furthermore, we show that the
locality of an orbital can be measured by the ratio between the exact exchange
energy and its optimal lower bound.


title:
Effects of dark energy and flat rotation curve on the gravitational time
  delay of particle with non-zero mass

abstract:
  The effects of several dark energy models on gravitational time delay of
particles with non-zero mass are investigated and analytical expressions for
the same are obtained at the first order accuracy. Also the expression for
gravitational time delay under the influence of conformal gravity potential
that well describes the flat rotation curve of spiral galaxies is derived. The
findings suggest that i) the conformal gravity description of dark matter
reduces the net time delay in contrast to the effect of normal dark matter and
therefore in principle the models can be discriminated using gravitational time
delay observations and ii)the effect of dark energy/flat rotation curve may be
revealed from high precision measurements of gravitational time delay of
particles involving megaparsec and beyond distance-scale.


title: A Grothendieck-type inequality for local maxima

abstract:
  A large number of problems in optimization, machine learning, signal
processing can be effectively addressed by suitable semidefinite programming
(SDP) relaxations. Unfortunately, generic SDP solvers hardly scale beyond
instances with a few hundreds variables (in the underlying combinatorial
problem). On the other hand, it has been observed empirically that an effective
strategy amounts to introducing a (non-convex) rank constraint, and solving the
resulting smooth optimization problem by ascent methods. This non-convex
problem has --generically-- a large number of local maxima, and the reason for
this success is therefore unclear.
  This paper provides rigorous support for this approach. For the problem of
maximizing a linear functional over the elliptope, we prove that all local
maxima are within a small gap from the SDP optimum. In several problems of
interest, arbitrarily small relative error can be achieved by taking the rank
constraint $k$ to be of order one, independently of the problem size.


title:
ExoMol molecular line lists - XIV: The rotation-vibration spectrum of
  hot SO$_2$

abstract:
  Sulphur dioxide is well-known in the atmospheres of planets and satellites,
where its presence is often associated with volcanism, and in circumstellar
envelopes of young and evolved stars as well as the interstellar medium. This
work presents a line list of 1.3 billion $^{32}$S$^{16}$O$_2$
vibration-rotation transitions computed using an empirically-adjusted potential
energy surface and an ab initio dipole moment surface. The list gives complete
coverage up to 8000 cm$^{-1}$ (wavelengths longer than 1.25 $\mu$m) for
temperatures below 2000 K. Infrared absorption cross sections are recorded at
300 and 500 C are used to validated the resulting ExoAmes line list. The line
list is made available in electronic form as supplementary data to this article
and at www.exomol.com.


title:
Local circular law for the product of a deterministic matrix with a
  random matrix

abstract:
  It is well known that the spectral measure of eigenvalues of a rescaled
square non-Hermitian random matrix with independent entries satisfies the
circular law. We consider the product $TX$, where $T$ is a deterministic
$N\times M$ matrix and $X$ is a random $M\times N$ matrix with independent
entries having zero mean and variance $(N\wedge M)^{-1}$. We prove a general
local circular law for the empirical spectral distribution (ESD) of $TX$ at any
point $z$ away from the unit circle under the assumptions that $N\sim M$, and
the matrix entries $X_{ij}$ have sufficiently high moments. More precisely, if
$z$ satisfies $||z|-1|\ge \tau$ for arbitrarily small $\tau>0$, the ESD of $TX$
converges to $\tilde \chi_{\mathbb D}(z) dA(z)$, where $\tilde \chi_{\mathbb
D}$ is a rotation-invariant function determined by the singular values of $T$
and $dA$ denotes the Lebesgue measure on $\mathbb C$. The local circular law is
valid around $z$ up to scale $(N\wedge M)^{-1/4+\epsilon}$ for any
$\epsilon>0$. Moreover, if $|z|>1$ or the matrix entries of $X$ have vanishing
third moments, the local circular law is valid around $z$ up to scale $(N\wedge
M)^{-1/2+\epsilon}$ for any $\epsilon>0$.


title: Space Bounds for Adaptive Renaming

abstract:
  We study the space complexity of implementing long-lived and one-shot
adaptive renaming from multi-reader multi-writer registers, in an asynchronous
distributed system with $n$ processes. As a result of an $f$-adaptive renaming
algorithm each participating process gets a distinct name in the range
$\{1,\dots,f(k)\}$ provided $k$ processes participate.
  Let $f: \{1,\dots,n\} \rightarrow \mathbb{N}$ be a non-decreasing function
satisfying $f(1) \leq n-1$ and let $d = \max\{x ~|~ f(x) \leq n-1\}$. We show
that any non-deterministic solo-terminating long-lived $f$-adaptive renaming
object requires $d + 1$ registers. This implies a lower bound of $n-c$
registers for long-lived $(k+c)$-adaptive renaming, which we observe is tight.
  We also prove a lower bound of $\lfloor \frac{2(n - c)}{c+2} \rfloor$
registers for implementing any non-deterministic solo-terminating one-shot
$(k+c)$-adaptive renaming. We provide two one-shot renaming algorithms: a
wait-free algorithm and an obstruction-free algorithm. Each algorithm employs a
parameter to depict the tradeoff between space and adaptivity. When these
parameters are chosen appropriately, this results in a wait-free one-shot
$(\frac{3k^2}{2})$-adaptive renaming algorithm from $\lceil \sqrt{n} \rceil +
1$ registers, and an obstruction-free one-shot $f$-adaptive renaming algorithm
from only $\min\{n, x ~|~ f(x) \geq 2n\} + 1$ registers.


title: A Signaling Game Approach to Databases Querying and Interaction

abstract:
  As most users do not precisely know the structure and/or the content of
databases, their queries do not exactly reflect their information needs. The
database management systems (DBMS) may interact with users and use their
feedback on the returned results to learn the information needs behind their
queries. Current query interfaces assume that users do not learn and modify the
way way they express their information needs in form of queries during their
interaction with the DBMS. Using a real-world interaction workload, we show
that users learn and modify how to express their information needs during their
interactions with the DBMS and their learning is accurately modeled by a
well-known reinforcement learning mechanism. As current data interaction
systems assume that users do not modify their strategies, they cannot discover
the information needs behind users' queries effectively. We model the
interaction between users and DBMS as a game with identical interest between
two rational agents whose goal is to establish a common language for
representing information needs in form of queries. We propose a reinforcement
learning method that learns and answers the information needs behind queries
and adapts to the changes in users' strategies and prove that it improves the
effectiveness of answering queries stochastically speaking. We propose two
efficient implementation of this method over large relational databases. Our
extensive empirical studies over real-world query workloads indicate that our
algorithms are efficient and effective.


title: Ballistic Majorana nanowire devices

abstract:
  Majorana modes are zero-energy excitations of a topological superconductor
that exhibit non-Abelian statistics. Following proposals for their detection in
a semiconductor nanowire coupled to an s-wave superconductor, several tunneling
experiments reported characteristic Majorana signatures. Reducing disorder has
been a prime challenge for these experiments because disorder can mimic the
zero-energy signatures of Majoranas, and renders the topological properties
inaccessible. Here, we show characteristic Majorana signatures in InSb nanowire
devices exhibiting clear ballistic transport properties. Application of a
magnetic field and spatial control of carrier density using local gates
generates a zero bias peak that is rigid over a large region in the parameter
space of chemical potential, Zeeman energy, and tunnel barrier potential. The
reduction of disorder allows us to resolve separate regions in the parameter
space with and without a zero bias peak, indicating topologically distinct
phases. These observations are consistent with the Majorana theory in a
ballistic system, and exclude for the first time the known alternative
explanations that invoke disorder or a nonuniform chemical potential.


title: A Super-Eddington Compton-Thick Wind in GRO J1655-40?

abstract:
  During its 2005 outburst, GRO J1655-40 was observed at high spectral
resolution with the Chandra HETGS, revealing a spectrum rich with blueshifted
absorption lines indicative of an accretion disk wind -- apparently too hot,
too dense, and too close to the black hole to be driven by radiation pressure
or thermal pressure (Miller et al.). But this exotic wind represents just one
piece of the puzzle in this outburst, as its presence coincides with an
extremely soft and curved X-ray continuum spectrum, remarkable X-ray
variability (Uttley & Klein-Wolt), and a bright, unexpected optical/infrared
blackbody component that varies on the orbital period. Focusing on the X-ray
continuum and the optical/infrared/UV spectral energy distribution, we argue
that the unusual features of this "hypersoft state" are natural consequences of
a super-Eddington Compton-thick wind from the disk: the optical/infrared
blackbody represents the cool photosphere of a dense, extended outflow, while
the X-ray emission is explained as Compton scattering by the relatively cool,
optically thick wind. This wind obscures the intrinsic luminosity of the inner
disk, which we suggest may have been at or above the Eddington limit.


title:
Search for the Giant Pulses Search for the Giant Pulses - an extreme
  phenomenon in radio pulsar emission

abstract:
  Here we present results of our search for Giant Pulses(GPs) from pulsars of
Northern Hemisphere. Our survey was carried out at a frequency of 111 MHz using
the Large Phased Array (LPA) radio telescope. Up to now we have detected
regular generation of strong pulses satisfying the criteria of GPs from 2
pulsars: B1133+16, B1237+25.


title: Perpendicular magnetic anisotropy in Co$_2$Fe$_{0.4}$Mn$_{0.6}$Si

abstract:
  We report perpendicular magnetic anisotropy (PMA) in the half-metallic
ferromagnetic Heusler alloy Co$_2$Fe$_{0.4}$Mn$_{0.6}$Si (CFMS) in a
MgO/CFMS/Pd trilayer stack. PMA is found for CFMS thicknesses between 1 and 2
nm, with a magnetic anisotropy energy density of $K_U = 1.5\times 10^6$
erg/cm$^3$ for t$_{\tiny \textrm{CFMS}} = 1.5$ nm. Both the MgO and Pd layer
are necessary to induce the PMA. We measure a tunable anomalous Hall effect,
where its sign and magnitude vary with both the CFMS and Pd thickness.


title:
Analysis of Schwarz methods for a hybridizable discontinuous Galerkin
  discretization: the many subdomain case

abstract:
  Schwarz methods are attractive parallel solution techniques for solving
large-scale linear systems obtained from discretizations of partial
differential equations (PDEs). Due to the iterative nature of Schwarz methods,
convergence rates are an important criterion to quantify their performance.
Optimized Schwarz methods (OSM) form a class of Schwarz methods that are
designed to achieve faster convergence rates by employing optimized
transmission conditions between subdomains. It has been shown recently that for
a two-subdomain case, OSM is a natural solver for hybridizable discontinuous
Galerkin (HDG) discretizations of elliptic PDEs. In this paper, we generalize
the preceding result to the many-subdomain case and obtain sharp convergence
rates with respect to the mesh size and polynomial degree, the subdomain
diameter, and the zeroth-order term of the underlying PDE, which allows us for
the first time to give precise convergence estimates for OSM used to solve
parabolic problems by implicit time stepping. We illustrate our theoretical
results with numerical experiments.


title: On ultra high energy cosmic rays and their resultant gamma rays

abstract:
  The Fermi Large Area Telescope (Fermi LAT) collaboration has recently
reported on 50 months of measurements of the isotropic Extragalactic Gamma Ray
Background (EGRB) spectrum between $100\mbox{MeV}$ and $820\mbox{GeV}$.
Ultrahigh Energy Cosmic Ray (UHECR) protons interact with the Cosmic Microwave
Background (CMB) photons and produce cascade photons of energies
$10\mbox{MeV}\mbox{-}1\mbox{TeV}$ that contribute to the EGRB flux. We examine
seven possible evolution models for UHECRs and find that UHECR sources that
evolve as the Star Formation Rate (SFR), medium low luminosity active galactic
nuclei type-1 ($L = 10^{43.5}\mbox{erg sec}^{-1}$ in the
$[0.5\mbox{-}2]\mbox{KeV}$ band), and BL Lacertae objects (BL Lacs) are the
most acceptable given the constraints imposed by the observed EGRB. Other
possibilities produce too much secondary $\gamma$-radiation. In all cases, the
decaying dark matter contribution improves the fit at high energy, but the
contribution of still unresolved blazars, which would leave the smallest role
for decaying dark matter, may yet provide an alternative improvement.
  The possibility that the entire EGRB can be fitted with resolvable but
not-yet-resolved blazars, as recently claimed by Ajello et al. (2015), would
leave little room in the EGRB to accommodate $\gamma$-rays from extragalactic
UHECR production, even for many source evolution rates that would otherwise be
acceptable. We find that, under the assumption of UHECRs being mostly protons,
there is not enough room for producing extragalactic UHECRs with AGN, GRB, or
even SFR source evolution. Sources that evolve as BL Lacs on the other hand,
would produce much less secondary $\gamma$-radiation and would remain a viable
source of UHECRs, provided that they dominate.


title:
Theory-Agnostic Constraints on Black-Hole Dipole Radiation with
  Multi-Band Gravitational-Wave Astrophysics

abstract:
  The aLIGO detection of the black-hole binary GW150914 opened a new era for
probing extreme gravity. Many gravity theories predict the emission of dipole
gravitational radiation by binaries. This is excluded to high accuracy in
binary pulsars, but entire classes of theories predict this effect
predominantly (or only) in binaries involving black holes. Joint observations
of GW150914-like systems by aLIGO and eLISA will improve bounds on dipole
emission from black-hole binaries by six orders of magnitude relative to
current constraints, provided that eLISA is not dramatically descoped.


title: Twisted characteristic $p$ zeta functions

abstract:
  We propose a "twisted" variation of zeta functions introduced by David Goss
in 1979.


title: Speed and structure of turbulent fronts in pipe flow

abstract:
  Using extensive direct numerical simulations, the dynamics of
laminar-turbulent fronts in pipe flow is investigated for Reynolds numbers
between $Re=2000$ and $5500$. We here investigate the physical distinction
between the fronts of weak and strong slugs both by analysing the turbulent
kinetic energy budget and by comparing the downstream front motion to the
advection speed of bulk turbulent structures. Our study shows that weak
downstream fronts travel slower than turbulent structures in the bulk and
correspond to decaying turbulence at the front. At $Re\simeq 2900$ the
downstream front speed becomes faster than the advection speed, marking the
onset of strong fronts. In contrast to weak fronts, turbulent eddies are
generated at strong fronts by feeding on the downstream laminar flow. Our study
also suggests that temporal fluctuations of production and dissipation at the
downstream laminar-turbulent front drive the dynamical switches between the two
types of front observed up to $Re\simeq 3200$.


title: Charge quantization from a number operator

abstract:
  We explain how an unexpected algebraic structure, the division algebras, can
be seen to underlie a generation of quarks and leptons. From this new vantage
point, electrons and quarks are simply excitations from the neutrino, which
formally plays the role of a vacuum state. Using the ladder operators which
exist within the system, we build a number operator in the usual way. It turns
out that this number operator, divided by 3, mirrors the behaviour of electric
charge. As a result, we see that electric charge is quantized because number
operators can only take on integer values.
  Finally, we show that a simple hermitian form, built from these ladder
operators, results uniquely in the nine generators of $SU(3)_c$ and
$U(1)_{em}$. This gives a direct route to the two unbroken gauge symmetries of
the standard model.


title:
Indoor 5G 3GPP-like Channel Models for Office and Shopping Mall
  Environments

abstract:
  Future mobile communications systems are likely to be very different to those
of today with new service innovations driven by increasing data traffic demand,
increasing processing power of smart devices and new innovative applications.
To meet these service demands the telecommunications industry is converging on
a common set of 5G requirements which includes network speeds as high as 10
Gbps, cell edge rate greater than 100 Mbps, and latency of less than 1 msec. To
reach these 5G requirements the industry is looking at new spectrum bands in
the range up to 100 GHz where there is spectrum availability for wide bandwidth
channels. For the development of new 5G systems to operate in bands up to 100
GHz there is a need for accurate radio propagation models which are not
addressed by existing channel models developed for bands below 6 GHz. This
paper presents a preliminary overview of the 5G channel models for bands up to
100 GHz in indoor offices and shopping malls, derived from extensive
measurements across a multitude of bands. These studies have found some
extensibility of the existing 3GPP models to the higher frequency bands up to
100 GHz. The measurements indicate that the smaller wavelengths introduce an
increased sensitivity of the propagation models to the scale of the environment
and show some frequency dependence of the path loss as well as increased
occurrence of blockage. Further, the penetration loss is highly dependent on
the material and tends to increase with frequency. The small-scale
characteristics of the channel such as delay spread and angular spread and the
multipath richness is somewhat similar over the frequency range, which is
encouraging for extending the existing 3GPP models to the wider frequency
range. Further work will be carried out to complete these models, but this
paper presents the first steps for an initial basis for the model development.


title: A Stochastic Approach to STDP

abstract:
  We present a digital implementation of the Spike Timing Dependent Plasticity
(STDP) learning rule. The proposed digital implementation consists of an
exponential decay generator array and a STDP adaptor array. On the arrival of a
pre- and post-synaptic spike, the STDP adaptor will send a digital spike to the
decay generator. The decay generator will then generate an exponential decay,
which will be used by the STDP adaptor to perform the weight adaption. The
exponential decay, which is computational expensive, is efficiently implemented
by using a novel stochastic approach, which we analyse and characterise here.
We use a time multiplexing approach to achieve 8192 (8k) virtual STDP adaptors
and decay generators with only one physical implementation of each. We have
validated our stochastic STDP approach with measurement results of a balanced
excitation/inhibition experiment. Our stochastic approach is ideal for
implementing the STDP learning rule in large-scale spiking neural networks
running in real time.


title: Amperean Pairing at the Surface of Topological Insulators

abstract:
  The surface of a 3D topological insulator is described by a helical electron
state with the electron's spin and momentum locked together. We show that in
the presence of ferromagnetic fluctuations the surface of a topological
insulator is unstable towards a superconducting state with unusual pairing,
dubbed Amperean pairing. The key idea is that the dynamical fluctuations of a
ferromagnetic layer deposited on the surface of a topological insulator couple
to the electrons as gauge fields. The transverse components of the magnetic
gauge fields are unscreened and can mediate an effective interaction between
electrons. There is an attractive interaction between electrons with momenta in
the same direction which makes the pairing to be of Amperean type. We show that
this attractive interaction leads to a $p$-wave pairing instability of the
Fermi surface in the Cooper channel.


title:
Three-dimensional, global, radiative GRMHD simulations of a thermally
  unstable disc

abstract:
  We present results of a set of three-dimensional, general relativistic
radiation magnetohydrodynamics simulations of thin accretion discs around a
non-rotating black hole to test their thermal stability. We consider two cases,
one that is initially radiation pressure dominated and expected to be thermally
unstable and another that is initially gas-pressure dominated and expected to
remain stable. Indeed, we find that cooling dominates over heating in the
radiation pressure dominated model, causing the disc to collapse vertically on
roughly the local cooling timescale. We also find that heating and cooling
within the disc have a different dependence on the mid-plane pressure, a
prerequisite of thermal instability. Comparison of our data with the relevant
thin-disc thermal equilibrium curve suggests that our disc may be headed for
the thermally stable, gas-pressure-dominated branch. However, because the disc
collapses to the point that we are no longer able to resolve it, we had to
terminate the simulation. On the other hand, the gas pressure dominated model,
which was run for twice as long as the radiation pressure dominated one,
remains stable, with heating and cooling roughly in balance. Finally, the
radiation pressure dominated simulation shows some evidence of viscous
instability. The strongest evidence is in plots of surface density, which show
the disc breaking up into rings.


title: On the simultaneous Approximation of coefficients of schlicht functions

abstract:
  A modified Version of the Hardy-Littlewood tauberian Theorem is used to prove
under which conditions the moduli of the coefficients |a(n)/n| of schlicht
functions tend uniformly to their Hayman Indexes as n tends to infinity.


title: Optimization of a relativistic quantum mechanical engine

abstract:
  We present an optimal analysis for a quantum mechanical engine working
between two energy baths within the framework of relativistic quantum
mechanics, adopting a first-order correction. This quantum mechanical engine,
with the direct energy leakage between the energy baths, consists of two
adiabatic and two isoenergetic processes and uses a three-level system of two
non-interacting fermions as its working substance. Assuming that the potential
wall moves at a finite speed, we derive the expression of power output and, in
particular, reproduce the expression for the efficiency at maximum power.


title: Server-side verification of client behavior in cryptographic protocols

abstract:
  Numerous exploits of client-server protocols and applications involve
modifying clients to behave in ways that untampered clients would not, such as
crafting malicious packets. In this paper, we demonstrate practical
verification of a cryptographic protocol client's messaging behavior as being
consistent with the client program it is believed to be running. Moreover, we
accomplish this without modifying the client in any way, and without knowing
all of the client-side inputs driving its behavior. Our toolchain for verifying
a client's messages explores multiple candidate execution paths in the client
concurrently, an innovation that we show is both specifically useful for
cryptographic protocol clients and more generally useful for client
applications of other types, as well. In addition, our toolchain includes a
novel approach to symbolically executing the client software in multiple passes
that defers expensive functions until their inputs can be inferred and
concretized. We demonstrate client verification on OpenSSL to show that, e.g.,
Heartbleed exploits can be detected without Heartbleed-specific filtering and
within seconds of the first malicious packet, and that verification of
legitimate clients can keep pace with, e.g., Gmail workloads.


title: On distinct residues of factorials

abstract:
  We investigate the existence of primes $p > 5$ for which the residues of
$2!$, $3!$, \dots, $(p-1)!$ modulo $p$ are all distinct. We describe the
connection between this problem and Kurepa's left factorial function, and
report that there are no such primes less than $10^{11}$.


title: Automorphisms of singular three-dimensional cubic hypersurfaces

abstract:
  In this paper we classify three-dimensional singular cubic hypersurfaces with
an action of a finite group $G$, which are not $G$-rational, are not
$G$-birationally isomorphic to a quadric and have no birational structure of
$G$-Mori fiber space with the base of positive dimension. Also we prove the
$A_{5}$ -birational superrigidity of the Segre cubic.


title:
Product generalized local Morrey spaces and commutators of
  multi-sublinear operators generated by multilinear Calder\'on-Zygmund
  operators and local Campanato functions

abstract:
  The aim of this paper is to get the boundedness of the commutators of
multi-sublinear operators generated by local campanato functions and
multilinear Calder\'on-Zygmund operators on the product generalized local
Morrey spaces.


title: Radiation Pressure Force from Optical Cycling on a Polyatomic Molecule

abstract:
  We demonstrate multiple photon cycling and radiative force deflection on the
triatomic free radical strontium monohydroxide (SrOH). Optical cycling is
achieved on SrOH in a cryogenic buffer-gas beam by employing the rotationally
closed $P\left(N''=1\right)$ branch of the vibronic transition
$\tilde{X}^{2}\Sigma^{+}\left(000\right)\leftrightarrow\tilde{A}^{2}\Pi_{1/2}\left(000\right)$.
A single repumping laser excites the Sr-O stretching vibrational mode, and
photon cycling of the molecule deflects the SrOH beam by an angle of
$0.2^{\circ}$ via scattering of $\sim100$ photons per molecule. This approach
can be used for direct laser cooling of SrOH and more complex, isoelectronic
species.


title:
Magnetic ordering in the ultra-pure site-diluted spin chain materials
  SrCu$_{1-x}$Ni$_x$O$_2$

abstract:
  Muon spin rotation technique is used to study magnetic ordering in ultra-pure
samples of SrCu$_{1-x}$Ni$_x$O$_2$, an archetypical $S=1/2$ antiferromagnetic
Heisenberg chain system with a small amount of $S=1$ defects. The ordered state
in the parent compound is shown to be highly homogeneous, contrary to previous
report [M. Matsuda et al., Phys. Rev. B \textbf{55}, R11953 (1997)]. Even
minute amount of Ni impurities result in inhomogeneous order and a decrease of
the transition temperature. At as little as $0.5$~\% Ni concentration, magnetic
ordering is entirely suppressed. The results are compared to previous
theoretical studies of weakly coupled spin chains with site-defects.


title: Generic Points for Dynamical Systems with Average Shadowing

abstract:
  It is proved that to every invariant measure of a compact dynamical system
one can associate a certain asymptotic pseudo orbit such that any point
asymptotically tracing in average that pseudo orbit is generic for the measure.
It follows that the asymptotic average shadowing property implies that every
invariant measure has a generic point. The proof is based on the properties of
the Besicovitch pseudometric DB which are of independent interest. It is proved
among the other things that the set of generic points of ergodic measures is a
closed set with respect to DB. It is also showed that the weak specification
property implies the average asymptotic shadowing property thus the theory
presented generalizes most known results on the existence of generic points for
arbitrary invariant measures.


title:
Plasmons in tunnel-coupled graphene layers: backward waves with quantum
  cascade gain

abstract:
  Plasmons in van der Waals heterostructures comprised of graphene and related
layered materials demonstrate deep subwavelength confinement and large
propagation length. In this letter, we show that graphene-insulator-graphene
tunnel structures can serve as plasmonic gain media. The gain stems from the
stimulated electron tunneling accompanied by the emission of coherent plasmons
under interlayer population inversion. The probability of tunneling with
plasmon emission appears to be resonantly large at certain values of frequency
and interlayer voltage corresponding to the transitions between electron states
with collinear momenta - a feature unique to the linear band structure of
graphene. The dispersion of plasmons undergoes a considerable transformation
due to the tunneling as well, demonstrating negative group velocity in several
frequency ranges.


title: Adjusted Jackknife Empirical Likelihood

abstract:
  Jackknife empirical likelihood (JEL) is an effective modified version of
empirical likelihood method (EL). Through the construction of the jackknife
pseudo-values, JEL overcomes the computational difficulty of EL method when its
constraints are nonlinear while maintaining the same asymptotic results for one
sample and two-sample U statistics. In this paper, we propose an adjusted
version of JEL to guarantee that the adjusted jackknife empirical likelihood
(AJEL) statistic is well-defined for all the values of the parameter, instead
of restricting on the convex hull of the estimation equation. The properties of
JEL have been preserved for AJEL.


title: Design and Implementation of an Improved Carry Increment Adder

abstract:
  A complex digital circuit comprises of adder as a basic unit. The performance
of the circuit depends on the design of this basic adder unit. The speed of
operation of a circuit is one of the important performance criteria of many
digital circuits which ultimately depends on the delay of the basic adder unit.
Many research works have been devoted in improving the delay of the adder
circuit. In this paper we have proposed an improved carry increment adder (CIA)
that improves the delay performance of the circuit. The improvement is achieved
by incorporating carry look adder (CLA) in the design of CIA contrary to the
previous design of CIA that employs ripple carry adder (RCA). A simulation
study is carried out for comparative analysis. The coding is done in Verilog
hardware description language (HDL) and the simulation is carried out in Xilinx
ISE 13.1 environment.


title:
The Rudin-Shapiro polynomials and The Fekete polynomials are not
  $L^\alpha$-flat

abstract:
  We establish that the Rudin-Shapiro polynomials are not $L^\alpha$-flat, for
any $\alpha \geq 0$. We further prove that the "truncated" Rudin-Shapiro
sequence cannot generate a sequence of $L^\alpha$-flat polynomials, for any
$\alpha \geq 0$. In the appendix, we present a simple proof of the fact that
the Fekete polynomials and the modified or shifted Fekete polynomials are not
$L^\alpha$-flat, for any $\alpha \geq 0$.


title: Multi-Target Tracking Using A Randomized Hypothesis Generation Technique

abstract:
  In this paper, we present a randomized version of the finite set statistics
(FISST) Bayesian recursions for multi-object tracking problems. We propose a
hypothesis level derivation of the FISST equations that shows that the
multi-object tracking problem may be considered as a finite state space
Bayesian filtering problem, albeit with a growing state space. We further show
that the FISST and Multi-Hypothesis Tracking (MHT) methods for multi-target
tracking are essentially the same. We propose a randomized scheme, termed
randomized FISST (R-FISST), where we sample the highly likely hypotheses using
Markov Chain Monte Carlo (MCMC) methods which allows us to keep the problem
computationally tractable. We apply the R-FISST technique to a fifty-object
birth and death Space Situational Awareness (SSA) tracking and detection
problem. We also compare the R-FISST technique to the Hypothesis Oriented
Multiple Hypothesis Tracking (HOMHT) method using an SSA example.


title: Multidimensional solitons: Well-established results and novel findings

abstract:
  A brief review is given of some well-known and some very recent results
obtained in studies of two- and three-dimensional (2D and 3D) solitons. Both
zero-vorticity (fundamental) solitons and ones carrying vorticity S = 1 are
considered. Physical realizations of multidimensional solitons in atomic
Bose-Einstein condensates (BECs) and nonlinear optics are briefly discussed
too. Unlike 1D solitons, which are typically stable, 2D and 3D ones are
vulnerable to instabilities induced by the occurrence of the critical and
supercritical collapse, respectively, in the same 2D and 3D models that give
rise to the solitons. Vortex solitons are subject to a still stronger splitting
instability. For this reason, a central problem is search for physical settings
in which 2D and 3D solitons may be stabilized. The brief review addresses one
well-established topic, viz., the stabilization of the 3D and 2D states, with S
= 0 and 1, trapped in harmonic-oscillator (HO) potentials, and another topic
which was developed very recently: the stabilization of 2D and 3D free-space
solitons, which juxtapose components with S = 0 and (+/-)1 (semi-vortices and
mixed modes), in a binary system with the spin-orbit coupling (SOC) between its
components. The former model is based on the single cubic nonlinear
Schroedinger/Gross-Pitaevskii equation (NLSE/GPE), while the latter one is
represented by a system of two coupled GPEs. In both cases, generic situations
are drastically different in the 2D and 3D geometries. In the 2D settings, the
stabilization mechanism creates a stable ground state (GS, which was absent
without the stabilization), whose norm falls below the threshold value at which
the critical collapse sets in. In the 3D geometry, the supercritical collapse
does not allow to create a GS, but metastable solitons can be constructed.


title: On the Analysis of a Continuous-Time Bi-Virus Model

abstract:
  Motivated by the spread of opinions on different social networks, we study a
distributed continuous-time bi-virus model for a system of groups of
individuals. An in-depth stability analysis is performed for more general
models than have been previously considered, for the healthy and epidemic
states. In addition, we investigate sensitivity properties of some nontrivial
equilibria and obtain an impossibility result for distributed feedback control.


title: Contagion and Stability in Financial Networks

abstract:
  This paper investigates two mechanisms of financial contagion that are,
firstly, the correlated exposure of banks to the same source of risk, and
secondly the direct exposure of banks in the interbank market. It will consider
a random network of banks which are connected through the inter-bank market and
will discuss the desirable level of banks exposure to the same sources of risk,
that is investment in similar portfolios, for different levels of network
connectivity when peering through the lens of the systemic cost incurred to the
economy from the banks simultaneous failure. It demonstrates that for all
levels of network connectivity, certain levels of diversifying individual banks
diversifications are not optimum under any condition. So, given an acceptable
level of systemic cost, the regulator could let banks decrease their capital
buffers by moving away from the non-optimum area.


title:
Modified Virtual Grid Difference for Discretizing the Laplace-Beltrami
  Operator on Point Clouds

abstract:
  We propose a new and simple discretization, named the Modified Virtual Grid
Difference (MVGD), for numerical approximation of the Laplace-Beltrami (LB)
operator on manifolds sampled by point clouds. The key observation is that both
the manifold and a function defined on it can both be parametrized in a local
Cartesian coordinate system and approximated using least squares. Based on the
above observation, we first introduce a local virtual grid with a scale adapted
to the sampling density centered at each point. Then we propose a modified
finite difference scheme on the virtual grid to discretize the LB operator.
Instead of using the local least squares values on all virtual grid points like
the typical finite difference method, we use the function value explicitly at
the grid located at the center (coincided with the data point). The new
discretization provides more diagonal dominance to the resulting linear system
and improves its conditioning. We show that the linear system can be robustly,
efficiently and accurately solved by existing fast solver such as the Algebraic
Multigrid (AMG) method. We will present numerical tests and comparison with
other exiting methods to demonstrate the effectiveness and the performance of
the proposed approach.


title: Meson's Correlation Functions in a Nuclear Medium

abstract:
  We investigate meson's spectrum, decay constant and form factor in a nuclear
medium through holographic two- and three-point correlation functions. To
describe a nuclear medium composed of protons and neutrons, we consider a hard
wall model on the thermal charged AdS geometry and show that due to the isospin
interaction with a nuclear medium, there exist splittings of the meson's
spectrum, decay constant and form factor relying on the isospin charge. In
addition, we show that the $\rho$-meson's form factor describing an interaction
with pseudoscalar fluctuation decreases when the nuclear density increases,
while the interaction with a longitudinal part of an axial vector meson
increases.


title:
Physical Properties of Galactic Planck Cold Cores revealed by the Hi-GAL
  survey

abstract:
  Previous studies of the initial conditions of massive star formation have
mainly targeted Infrared-Dark Clouds (IRDCs) toward the inner Galaxy. This is
due to the fact that IRDCs were first detected in absorption against the bright
mid-IR background, requiring a favourable location to be observed. By
selection, IRDCs represent only a fraction of the Galactic clouds capable of
forming massive stars and star clusters. Due to their low dust temperatures,
IRDCs are bright in the far-IR and millimeter and thus, observations at these
wavelengths have the potential to provide a complete sample of star-forming
massive clouds across the Galaxy. Our aim is to identify the clouds at the
initial conditions of massive star formation across the Galaxy and compare
their physical properties as a function of their Galactic location. We have
examined the physical properties of a homogeneous galactic cold core sample
obtained with the Planck satellite across the Galactic Plane. With the use of
Herschel Hi-GAL observations, we have characterized the internal structure of
them. By using background-subtracted Herschel images, we have derived the H2
column density and dust temperature maps for 48 Planck clumps. Their basic
physical parameters have been calculated and analyzed as a function of location
within the Galaxy. These properties have also been compared with the empirical
relation for massive star formation derived by Kauffmann & Pillai (2010). Most
of the Planck clumps contain signs of star formation. About 25% of them are
massive enough to form high mass stars. Planck clumps toward the Galactic
center region show higher peak column densities and higher average dust
temperatures than those of the clumps in the outer Galaxy. Although we only
have seven clumps without associated YSOs, the Hi-GAL data show no apparent
differences in the properties of Planck cold clumps with and without star
formation.


title:
Probing Out-of-Plane Charge Transport in Black Phosphorus with
  Graphene-Contacted Vertical Field-Effect Transistors

abstract:
  Black phosphorus (BP) has recently emerged as a promising narrow band gap
layered semiconductor with optoelectronic properties that bridge the gap
between semi-metallic graphene and wide band gap transition metal
dichalcogenides such as MoS2. To date, BP field-effect transistors have
utilized a lateral geometry with in-plane transport dominating device
characteristics. In contrast, we present here a vertical field-effect
transistor geometry based on a graphene/BP van der Waals heterostructure. The
resulting device characteristics include high on-state current densities (>
1600 A/cm2) and current on/off ratios exceeding 800 at low temperature. Two
distinct charge transport mechanisms are identified, which are dominant for
different regimes of temperature and gate voltage. In particular, the Schottky
barrier between graphene and BP determines charge transport at high
temperatures and positive gate voltages, whereas tunneling dominates at low
temperatures and negative gate voltages. These results elucidate out-of-plane
electronic transport in BP, and thus have implications for the design and
operation of BP-based van der Waals heterostructures.


title: On zeros of analytic functions satisfying non-radial growth conditions

abstract:
  Extending the results of Borichev--Golinskii--Kupin [2009], we obtain refined
Blaschke-type necessary conditions on the zero distribution of analytic
functions on the unit disk and on the complex plane with a cut along the
positive semi-axis satisfying some non-radial growth restrictions.


title:
Equilibrium properties of the mixed state in superconducting niobium in
  a transverse magnetic field: Experiment and theoretical model

abstract:
  Equilibrium magnetic properties of the mixed state in type-II superconductors
were measured with high purity bulk and film niobium samples in parallel and
perpendicular magnetic fields using dc magnetometry and scanning Hall-probe
microscopy. Equilibrium magnetization data for the perpendicular geometry were
obtained for the first time. It was found that none of the existing theories is
consistent with these new data. To address this problem, a theoretical model is
developed and experimentally validated. The new model describes the mixed state
in an averaged limit, i.e. %without detailing the samples' magnetic structure
and therefore ignoring interactions between vortices. It is quantitatively
consistent with the data obtained in a perpendicular field and provides new
insights on properties of vortices. % and the entire mixed state. At low values
of the Ginzburg-Landau parameter, the model converts to that of Peierls and
London for the intermediate state in type-I superconductors. It is shown that
description of the vortex matter in superconductors in terms of a 2D gas is
more appropriate than the frequently used crystal- and glass-like scenarios.


title: On the Hodge theory of stratified spaces

abstract:
  This article is a survey of recent work of the author, together with Markus
Banagl, Eric Leichtnam, Rafe Mazzeo, and Paolo Piazza, on the Hodge theory of
stratified spaces. We discuss how to resolve a Thom-Mather stratified space to
a manifold with corners with an iterated fibration structure and the
generalization of a perversity in the sense of Goresky-MacPherson to a
mezzoperversity. We define Cheeger spaces and their signatures and describe how
to carry out the analytic proof of the Novikov conjecture on these spaces.
Finally we review the reductive Borel-Serre compactification of a locally
symmetric space to a stratified space and describe its resolution to a manifold
with corners.


title: Interpolating between random walk and rotor walk

abstract:
  We introduce a family of stochastic processes on the integers, depending on a
parameter $p \in [0,1]$ and interpolating between the deterministic rotor walk
(p=0) and the simple random walk (p=1/2). This p-rotor walk is not a Markov
chain but it has a local Markov property: for each $x \in \mathbb{Z}$ the
sequence of successive exits from $x$ is a Markov chain. The main result of
this paper identifies the scaling limit of the p-rotor walk with two-sided
i.i.d. initial rotors. The limiting process takes the form
$\sqrt{\frac{1-p}{p}} X(t)$, where $X$ is a doubly perturbed Brownian motion,
that is, it satisfies the implicit equation \begin{equation} X(t) =
\mathcal{B}(t) + a \sup_{s\leq t} X(s) + b \inf_{s\leq t} X(s) \end{equation}
for all $t \in [0,\infty)$. Here $\mathcal{B}(t)$ is a standard Brownian motion
and $a,b<1$ are constants depending on the marginals of the initial rotors on
$\mathbb{N}$ and $-\mathbb{N}$ respectively. Chaumont and Doney [CD99] have
shown that the above equation has a pathwise unique solution $X(t)$, and that
the solution is almost surely continuous and adapted to the natural filtration
of the Brownian motion. Moreover, $\limsup X(t) = +\infty$ and $\liminf X(t) =
-\infty$ [CDH00]. This last result, together with the main result of this
paper, implies that the p-rotor walk is recurrent for any two-sided i.i.d.
initial rotors and any $0<p<1$.


title:
Fundamental limits to collective concentration sensing in cell
  populations

abstract:
  The precision of concentration sensing is improved when cells communicate.
Here we derive the physical limits to concentration sensing for cells that
communicate over short distances by directly exchanging small molecules
(juxtacrine signaling), or over longer distances by secreting and sensing a
diffusive messenger molecule (autocrine signaling). In the latter case, we find
that the optimal cell spacing can be large, due to a tradeoff between
maintaining communication strength and reducing signal cross-correlations. This
leads to the surprising result that autocrine signaling allows more precise
sensing than juxtacrine signaling for sufficiently large populations. We
compare our results to data from a wide variety of communicating cell types.


title:
Combinatorial rigidity of Incidence systems and Application to
  Dictionary learning

abstract:
  Given a hypergraph $H$ with $m$ hyperedges and a set $Q$ of $m$ \emph{pinning
subspaces}, i.e.\ globally fixed subspaces in Euclidean space $\mathbb{R}^d$, a
\emph{pinned subspace-incidence system} is the pair $(H, Q)$, with the
constraint that each pinning subspace in $Q$ is contained in the subspace
spanned by the point realizations in $\mathbb{R}^d$ of vertices of the
corresponding hyperedge of $H$. This paper provides a combinatorial
characterization of pinned subspace-incidence systems that are \emph{minimally
rigid}, i.e.\ those systems that are guaranteed to generically yield a locally
unique realization.
  Pinned subspace-incidence systems have applications in the \emph{Dictionary
Learning (aka sparse coding)} problem, i.e.\ the problem of obtaining a sparse
representation of a given set of data vectors by learning \emph{dictionary
vectors} upon which the data vectors can be written as sparse linear
combinations. Viewing the dictionary vectors from a geometry perspective as the
spanning set of a subspace arrangement, the result gives a tight bound on the
number of dictionary vectors for sufficiently randomly chosen data vectors, and
gives a way of constructing a dictionary that meets the bound. For less
stringent restrictions on data, but a natural modification of the dictionary
learning problem, a further dictionary learning algorithm is provided. Although
there are recent rigidity based approaches for low rank matrix completion, we
are unaware of prior application of combinatorial rigidity techniques in the
setting of Dictionary Learning. We also provide a systematic classification of
problems related to dictionary learning together with various algorithms, their
assumptions and performance.


title:
Geometry of Interest (GOI): Spatio-Temporal Destination Extraction and
  Partitioning in GPS Trajectory Data

abstract:
  Nowadays large amounts of GPS trajectory data is being continuously collected
by GPS-enabled devices such as vehicles navigation systems and mobile phones.
GPS trajectory data is useful for applications such as traffic management,
location forecasting, and itinerary planning. Such applications often need to
extract the time-stamped Sequence of Visited Locations (SVLs) of the mobile
objects. The nearest neighbor query (NNQ) is the most applied method for
labeling the visited locations based on the IDs of the POIs in the process of
SVL generation. NNQ in some scenarios is not accurate enough. To improve the
quality of the extracted SVLs, instead of using NNQ, we label the visited
locations as the IDs of the POIs which geometrically intersect with the GPS
observations. Intersection operator requires the accurate geometry of the
points of interest which we refer to them as the Geometries of Interest (GOIs).
In some application domains (e.g. movement trajectories of animals), adequate
information about the POIs and their GOIs may not be available a priori, or
they may not be publicly accessible and, therefore, they need to be derived
from GPS trajectory data. In this paper we propose a novel method for
estimating the POIs and their GOIs, which consists of three phases: (i)
extracting the geometries of the stay regions; (ii) constructing the geometry
of destination regions based on the extracted stay regions; and (iii)
constructing the GOIs based on the geometries of the destination regions. Using
the geometric similarity to known GOIs as the major evaluation criterion, the
experiments we performed using long-term GPS trajectory data show that our
method outperforms the existing approaches.


title: On a question proposed by K. Mahler concerning Liouville numbers

abstract:
  In 1906, Maillet proved that given a non-constant rational function $f$, with
rational coefficients, if $\xi$ is a Liouville number, then so is $f(\xi)$.
Motivated by this fact, in 1984, Mahler raised the question about the existence
of transcendental entire functions with this property. In this work, we provide
an uncountable subset of Liouville numbers for which there exists a
transcendental entire function taking this set into the set of the Liouville
numbers.


title:
Iterative Methods for Efficient Sampling-Based Optimal Motion Planning
  of Nonlinear Systems

abstract:
  This paper extends the RRT* algorithm, a recently developed but widely-used
sampling-based optimal motion planner, in order to effectively handle nonlinear
kinodynamic constraints. Nonlinearity in kinodynamic differential constraints
often leads to difficulties in choosing appropriate distance metric and in
computing optimized trajectory segments in tree construction. To tackle these
two difficulties, this work adopts the affine quadratic regulator-based pseudo
metric as the distance measure and utilizes iterative two-point boundary value
problem solvers for computing the optimized segments. The proposed extension
then preserves the inherent asymptotic optimality of the RRT* framework, while
efficiently handling a variety of kinodynamic constraints. Three numerical case
studies validate the applicability of the proposed method.


title:
Iterative diagonalization of the non-Hermitian transcorrelated
  Hamiltonian using a plane-wave basis set: Application to $sp$-electron
  systems with deep core states

abstract:
  We develop an iterative diagonalization scheme in solving a one-body
self-consistent-field equation in the transcorrelated (TC) method using a
plane-wave basis set. Non-Hermiticity in the TC method is well handled with a
block-Davidson algorithm. We verify the required computational cost is
efficiently reduced by our algorithm. In addition, we apply our
plane-wave-basis TC calculation to some simple $sp$-electron systems with deep
core states to elucidate an impact of the pseudopotential approximation to the
calculated band structures. We find a position of the deep valence bands is
improved by an explicit inclusion of core states, but an overall band structure
is consistent with a regular setup that includes core states into the
pseudopotentials. This study offers an important understanding for the future
application of the TC method to strongly correlated solids.


title: A Characterization of the Critical Catenoid

abstract:
  We show that an embedded minimal annulus $\Sigma^2 \subset B^3$ which
intersects $\partial B^3$ orthogonally and is invariant under reflection
through the coordinate planes is the critical catenoid. The proof uses nodal
domain arguments and a characterization, due to Fraser and Schoen, of the
critical catenoid as the unique free boundary minimal annulus in $B^n$ with
lowest Steklov eigenvalue equal to 1. We also give more general criteria which
imply that a free boundary minimal surface in $B^3$ invariant under a group of
reflections has lowest Steklov eigenvalue 1.


title: A study for testing the Kerr metric with AGN iron line eclipses

abstract:
  Recently, two of us have studied iron line reverberation mapping to test
black hole candidates, showing that the time information in reverberation
mapping can better constrain the Kerr metric than the time-integrated approach.
Motivated by this finding, here we explore the constraining power of another
time-dependent measurement: an AGN iron line eclipse. An obscuring cloud passes
between the AGN and the distant observer, covering different parts of the
accretion disk at different times. Similar to the reverberation measurement, an
eclipse might help to better identify the relativistic effects affecting the
X-ray photons. However, this is not what we find. In our study, we employ the
Johannsen-Psaltis parametrisation, but we argue that our conclusions hold in a
large class of non-Kerr metrics. We explain our results pointing out an
important difference between reverberation and eclipse measurements.


title: Learning Binary Codes and Binary Weights for Efficient Classification

abstract:
  This paper proposes a generic formulation that significantly expedites the
training and deployment of image classification models, particularly under the
scenarios of many image categories and high feature dimensions. As a defining
property, our method represents both the images and learned classifiers using
binary hash codes, which are simultaneously learned from the training data.
Classifying an image thereby reduces to computing the Hamming distance between
the binary codes of the image and classifiers and selecting the class with
minimal Hamming distance. Conventionally, compact hash codes are primarily used
for accelerating image search. Our work is first of its kind to represent
classifiers using binary codes. Specifically, we formulate multi-class image
classification as an optimization problem over binary variables. The
optimization alternatively proceeds over the binary classifiers and image hash
codes. Profiting from the special property of binary codes, we show that the
sub-problems can be efficiently solved through either a binary quadratic
program (BQP) or linear program. In particular, for attacking the BQP problem,
we propose a novel bit-flipping procedure which enjoys high efficacy and local
optimality guarantee. Our formulation supports a large family of empirical loss
functions and is here instantiated by exponential / hinge losses. Comprehensive
evaluations are conducted on several representative image benchmarks. The
experiments consistently observe reduced complexities of model training and
deployment, without sacrifice of accuracies.


title: Multi-modal Tracking for Object based SLAM

abstract:
  We present an on-line 3D visual object tracking framework for monocular
cameras by incorporating spatial knowledge and uncertainty from semantic
mapping along with high frequency measurements from visual odometry. Using a
combination of vision and odometry that are tightly integrated we can increase
the overall performance of object based tracking for semantic mapping. We
present a framework for integration of the two data-sources into a coherent
framework through information based fusion/arbitration. We demonstrate the
framework in the context of OmniMapper[1] and present results on 6 challenging
sequences over multiple objects compared to data obtained from a motion capture
systems. We are able to achieve a mean error of 0.23m for per frame tracking
showing 9% relative error less than state of the art tracker.


title:
Active Algorithms For Preference Learning Problems with Multiple
  Populations

abstract:
  In this paper we model the problem of learning preferences of a population as
an active learning problem. We propose an algorithm can adaptively choose pairs
of items to show to users coming from a heterogeneous population, and use the
obtained reward to decide which pair of items to show next. We provide
computationally efficient algorithms with provable sample complexity guarantees
for this problem in both the noiseless and noisy cases. In the process of
establishing sample complexity guarantees for our algorithms, we establish new
results using a Nystr{\"o}m-like method which can be of independent interest.
We supplement our theoretical results with experimental comparisons.


title:
Exploratory Gradient Boosting for Reinforcement Learning in Complex
  Domains

abstract:
  High-dimensional observations and complex real-world dynamics present major
challenges in reinforcement learning for both function approximation and
exploration. We address both of these challenges with two complementary
techniques: First, we develop a gradient-boosting style, non-parametric
function approximator for learning on $Q$-function residuals. And second, we
propose an exploration strategy inspired by the principles of state abstraction
and information acquisition under uncertainty. We demonstrate the empirical
effectiveness of these techniques, first, as a preliminary check, on two
standard tasks (Blackjack and $n$-Chain), and then on two much larger and more
realistic tasks with high-dimensional observation spaces. Specifically, we
introduce two benchmarks built within the game Minecraft where the observations
are pixel arrays of the agent's visual field. A combination of our two
algorithmic techniques performs competitively on the standard
reinforcement-learning tasks while consistently and substantially outperforming
baselines on the two tasks with high-dimensional observation spaces. The new
function approximator, exploration strategy, and evaluation benchmarks are each
of independent interest in the pursuit of reinforcement-learning methods that
scale to real-world domains.


title: Fast response electromagnetic follow-ups from low latency GW triggers

abstract:
  We investigate joint low-latency gravitational wave (GW) detection and prompt
electromagnetic (EM) follow-up observations of coalescing binary neutron stars
(BNSs). Assuming that BNS mergers are associated with short duration gamma ray
bursts (SGRBs), we evaluate if rapid EM follow-ups can capture the prompt
emission, early engine activity or reveal any potential by-products such as
magnetars or fast radio bursts. To examine the expected performance of extreme
low-latency search pipelines, we simulate a population of coalescing BNSs and
use these to estimate the detectability and localisation efficiency at
different times before merger. Using observational SGRB flux data corrected to
the range of the advanced GW interferometric detectors, we determine what EM
observations could be achieved from low-frequency radio up to high energy
$\gamma$-ray. We show that while challenging, breakthrough multi-messenger
science is possible through low latency pipelines.


title: Line k-Arboricity in Product Networks

abstract:
  A \emph{linear $k$-forest} is a forest whose components are paths of length
at most $k$. The \emph{linear $k$-arboricity} of a graph $G$, denoted by ${\rm
la}_k(G)$, is the least number of linear $k$-forests needed to decompose $G$.
Recently, Zuo, He and Xue studied the exact values of the linear
$(n-1)$-arboricity of Cartesian products of various combinations of complete
graphs, cycles, complete multipartite graphs. In this paper, for general $k$ we
show that $\max\{{\rm la}_{k}(G),{\rm la}_{\ell}(H)\}\leq {\rm
la}_{\max\{k,\ell\}}(G\Box H)\leq {\rm la}_{k}(G)+{\rm la}_{\ell}(H)$ for any
two graphs $G$ and $H$. Denote by $G\circ H$, $G\times H$ and $G\boxtimes H$
the lexicographic product, direct product and strong product of two graphs $G$
and $H$, respectively. We also derive upper and lower bounds of ${\rm
la}_{k}(G\circ H)$, ${\rm la}_{k}(G\times H)$ and ${\rm la}_{k}(G\boxtimes H)$
in this paper. The linear $k$-arboricity of a $2$-dimensional grid graph, a
$r$-dimensional mesh, a $r$-dimensional torus, a $r$-dimensional generalized
hypercube and a $2$-dimensional hyper Petersen network are also studied.


title: Graphical Log-linear Models: Fundamental Concepts and Applications

abstract:
  We present a comprehensive study of graphical log-linear models for
contingency tables. High dimensional contingency tables arise in many areas
such as computational biology, collection of survey and census data and others.
Analysis of contingency tables involving several factors or categorical
variables is very hard. To determine interactions among various factors,
graphical and decomposable log-linear models are preferred. First, we explore
connections between the conditional independence in probability and graphs;
thereafter we provide a few illustrations to describe how graphical log-linear
model are useful to interpret the conditional independences between factors. We
also discuss the problem of estimation and model selection in decomposable
models.


title: On a Critical Case of Rallis Inner Product Formula

abstract:
  Let $\pi$ be a genuine cuspidal representation of the metaplectic group of
rank $n$. We consider the theta lifts to the orthogonal group associated to a
quadratic space of dimension $2n+1$. We show a case of regularised Rallis inner
product formula that relates the pairing of theta lifts to the central value of
the Langlands $L$-function of $\pi$ twisted by a character. The bulk of this
article focuses on proving a case of regularised Siegel-Weil formula, on which
the Rallis inner product formula is based and whose proof is missing in the
literature.


title: Giambelli Identity in Super Chern-Simons Matrix Model

abstract:
  A classical identity due to Giambelli in representation theory states that
the character in any representation is expressed as a determinant whose
components are characters in the hook representation constructed from all the
combinations of the arm and leg lengths of the original representation.
Previously it was shown that the identity persists in taking, for each
character, the matrix integration in the super Chern-Simons matrix model in the
grand canonical ensemble. We prove here that this Giambelli compatibility still
holds in the deformation of the fractional-brane background.


title:
Event-triggered leader-following tracking control for multivariable
  multi-agent systems

abstract:
  The paper considers event-triggered leader-follower tracking control for
multi-agent systems with general linear dynamics. For both undirected and
directed follower graphs, we propose event triggering rules which guarantee
bounded tracking errors. With these rules, we also prove that the systems do
not exhibit Zeno behavior, and the bounds on the tracking errors can be tuned
to a desired small value. We also show that the combinational state required
for the proposed event triggering conditions can be continuously generated from
discrete communications between the neighboring agents occurring at event
times. The efficacy of the proposed methods is discussed using a simulation
example.


title: Parameter Limits for Neutrino Oscillation with Decoherence in KamLAND

abstract:
  In the framework of quantum open systems we analyze data from KamLAND by
using a model that considers neutrino oscillation in a three-family
approximation with the inclusion of the decoherence effect. Using a $\chi^2$
test we find new limits for the decoherence parameter which we call $\gamma$,
considering the most recent data by KamLAND. Assuming an energy dependence of
the type $ \gamma = \gamma_0 \left( E/E_0 \right) ^n$, in 95 \% C.L. the limits
found are $3.7 \times 10^{-24} GeV$ for $ n=-1$, $6.8 \times 10^{-22} GeV$ for
$ n=0$, and $1.5 \times 10^{-19} GeV$ for $ n=1 $ on the energy dependence.


title: Scalable boson sampling with a single-photon device

abstract:
  Boson sampling is a problem intractable for classical computers, but can be
naturally solved on a specialized photonic quantum simulator which requires
less resources than building a universal quantum computer. The biggest
challenge to implement boson sampling with a large number of photons has been
the lack of reliable single-photon sources. Here we demonstrate a scalable
architecture of boson sampling using a solid-state single-photon source with
simultaneously high efficiency, purity, and indistinguishability. The single
photons are time-bin encoded and interfered in an electrically programmable
loop-based network. We implement and validate boson sampling with input three
and four single photons, and track the dynamical multi-photon evolution inside
the circuit. With further refinement of the system efficiency, our approach may
be feasible to be scaled up to >20-boson sampling to outperform classical
computers, and thus provide experimental evidence against the Extended
Church-Turing Thesis.


title:
Optimal Event-Driven Multi-Agent Persistent Monitoring of a Finite Set
  of Targets

abstract:
  We consider the problem of controlling the movement of multiple cooperating
agents so as to minimize an uncertainty metric associated with a finite number
of targets. In a one-dimensional mission space, we adopt an optimal control
framework and show that the solution is reduced to a simpler parametric
optimization problem: determining a sequence of locations where each agent may
dwell for a finite amount of time and then switch direction. This amounts to a
hybrid system which we analyze using Infinitesimal Perturbation Analysis (IPA)
to obtain a complete on-line solution through an event-driven gradient-based
algorithm which is also robust with respect to the uncertainty model used. The
resulting controller depends on observing the events required to excite the
gradient-based algorithm, which cannot be guaranteed. We solve this problem by
proposing a new metric for the objective function which creates a potential
field guaranteeing that gradient values are non-zero. This approach is compared
to an alternative graph-based task scheduling algorithm for determining an
optimal sequence of target visits. Simulation examples are included to
demonstrate the proposed methods.


title: Elliptic Quantum Groups U_{q,p}(gl_N) and E_{q,p}(gl_N)

abstract:
  We reformurate a central extension of Felder's elliptic quantum group in the
FRST formulation as a topological algebra E_{q,p}(gl_N) over the ring of formal
power series in p. We then discuss the isomorphism between E_{q,p}(gl_N) and
the elliptic algebra U_{q,p}(gl_N) of the Drinfeld realization. An evaluation
H-algebra homomorphism from U_{q,p}(gl_N) to a dynamical extension of the
quantum affine algebra U_q(gl_N) resolves the problem into the one discussed by
Ding and Frenkel in the trigonometric case. We also provide some useful
formulas for the elliptic quantum determinants.

categories: math.QA hep-th math-ph math.AG math.MP math.RT


title:
A lower bound for $p_c$ in range-$R$ bond percolation in two and three
  dimensions

abstract:
  We use the connection between bond percolation and SIR epidemics to establish
lower bounds for the critical percolation probability in $2$ and $3$ dimensions
as the range becomes large. The bound agrees with the conjectured asymptotics
for the long range critical probability, refines results of M. Penrose, and
complements results of van der Hofstad and Sakai in dimensions greater than
$6$.


title:
Model of the Songbird Nucleus HVC as a Network of Central Pattern
  Generators

abstract:
  We propose a functional architecture of the adult songbird nucleus HVC in
which the core element is a "functional syllable unit" (FSU). In this model,
HVC is organized into FSUs, each of which provides the basis for the production
of one syllable in vocalization. Within each FSU, the inhibitory neuron
population takes one of two operational states: (A) simultaneous firing wherein
all inhibitory neurons fire simultaneously, and (B) competitive firing of the
inhibitory neurons. Switching between these basic modes of activity is
accomplished via changes in the synaptic strengths among the inhibitory
neurons. The inhibitory neurons connect to excitatory projection neurons such
that during state (A) the activity of projection neurons is suppressed, while
during state (B) patterns of sequential firing of projection neurons can occur.
The latter state is stabilized by feedback from the projection to the
inhibitory neurons. Song composition for specific species is distinguished by
the manner in which different FSUs are functionally connected to each other.
  Ours is a computational model built with biophysically based neurons. We
illustrate that many observations of HVC activity are explained by the dynamics
of the proposed population of FSUs, and we identify aspects of the model that
are currently testable experimentally. In addition, and standing apart from the
core features of an FSU, we propose that the transition between modes may be
governed by the biophysical mechanism of neuromodulation.


title:
A Novel Method for the Extrinsic Calibration of a 2D Laser Rangefinder
  and a Camera

abstract:
  We present a novel method for extrinsically calibrating a camera and a 2D
Laser Rangefinder (LRF) whose beams are invisible from the camera image. We
show that point-to-plane constraints from a single observation of a V-shaped
calibration pattern composed of two non-coplanar triangles suffice to uniquely
constrain the relative pose between two sensors. Next, we present an approach
to obtain analytical solutions using point-to-plane constraints from single or
multiple observations. Along the way, we also show that previous solutions, in
contrast to our method, have inherent ambiguities and therefore must rely on a
good initial estimate. Real and synthetic experiments validate our method and
show that it achieves better accuracy than previous methods.


title: Merging droplets in double nano-contact spin torque oscillators

abstract:
  We demonstrate how magnetic droplet soliton pairs, nucleated by two separated
nano-contact (NC) spin torque oscillators, can merge into a single droplet
soliton. A detailed description of the magnetization dynamics of this merger
process is obtained by micromagnetic simulations: A droplet pair with a
steady-state in-phase spin precession is generated through the spin-transfer
torque effect underneath two separate NCs, followed by a gradual expansion of
the droplets volume and the out phase of magnetization on the inner side of the
two droplets, resulting in the droplets merging into a larger droplet. This
merger occurs only when the NC separation is smaller than a critical value. A
transient breathing mode is observed before the merged droplet stabilizes into
a steady precession state. The precession frequency of the merged droplet is
lower than that of the droplet pair, consistent with its larger size. Merged
droplets can again break up into droplet pairs at high enough magnetic field
with a strong hysteretic response.


title:
RISAS: A Novel Rotation, Illumination, Scale Invariant Appearance and
  Shape Feature

abstract:
  This paper presents a novel appearance and shape feature, RISAS, which is
robust to viewpoint, illumination, scale and rotation variations. RISAS
consists of a keypoint detector and a feature descriptor both of which utilise
texture and geometric information present in the appearance and shape channels.
A novel response function based on the surface normals is used in combination
with the Harris corner detector for selecting keypoints in the scene. A
strategy that uses the depth information for scale estimation and background
elimination is proposed to select the neighbourhood around the keypoints in
order to build precise invariant descriptors. Proposed descriptor relies on the
ordering of both grayscale intensity and shape information in the
neighbourhood. Comprehensive experiments which confirm the effectiveness of the
proposed RGB-D feature when compared with CSHOT and LOIND are presented.
Furthermore, we highlight the utility of incorporating texture and shape
information in the design of both the detector and the descriptor by
demonstrating the enhanced performance of CSHOT and LOIND when combined with
RISAS detector.


title:
Strong cooperative coupling of pressure-induced magnetic order and
  nematicity in FeSe

abstract:
  A hallmark of the iron-based superconductors is the strong coupling between
magnetic, structural and electronic degrees of freedom. However, a universal
picture of the normal state properties of these compounds has been confounded
by recent investigations of FeSe where the nematic (structural) and magnetic
transitions appear to be decoupled. Here, using synchrotron-based high-energy
x-ray diffraction and time-domain Moessbauer spectroscopy, we show that
nematicity and magnetism in FeSe under applied pressure are indeed strongly
coupled. Distinct structural and magnetic transitions are observed for
pressures, 1.0 GPa <= p <= 1.7 GPa, which merge into a single first-order phase
line for p >= 1.7 GPa, reminiscent of what has been observed, both
experimentally and theoretically, for the evolution of these transitions in the
prototypical doped system, Ba(Fe[1-x]Co[x])2As2. Our results support a
spin-driven mechanism for nematic order in FeSe and provide an important step
towards a universal description of the normal state properties of the
iron-based superconductors.


title: On the Influence of Momentum Acceleration on Online Learning

abstract:
  The article examines in some detail the convergence rate and
mean-square-error performance of momentum stochastic gradient methods in the
constant step-size and slow adaptation regime. The results establish that
momentum methods are equivalent to the standard stochastic gradient method with
a re-scaled (larger) step-size value. The size of the re-scaling is determined
by the value of the momentum parameter. The equivalence result is established
for all time instants and not only in steady-state. The analysis is carried out
for general strongly convex and smooth risk functions, and is not limited to
quadratic risks. One notable conclusion is that the well-known bene ts of
momentum constructions for deterministic optimization problems do not
necessarily carry over to the adaptive online setting when small constant
step-sizes are used to enable continuous adaptation and learn- ing in the
presence of persistent gradient noise. From simulations, the equivalence
between momentum and standard stochastic gradient methods is also observed for
non-differentiable and non-convex problems.


title: Flat-Space Holography and Stress Tensor of Kerr Black Hole

abstract:
  We propose a stress tensor for the Kerr black hole written in the
Boyer-Lindquist coordinate. To achieve this, we use the dictionary of the
Flat/CCFT correspondence and take the flat-space limit from the quasi-local
stress tensor of the four-dimensional Kerr-AdS black hole. The proposed stress
tensor yields the correct values for the mass and angular momentum of the Kerr
black hole at spatial infinity. We also calculate some components of the energy
momentum tensor of the three dimensional CCFT and show that they are consistent
with the holographic calculation of the Kerr black hole. The calculation we
present in this paper is another confirmation for the Flat/CCFT proposal.


title:
Crystalline spin-orbit interaction and the Zeeman splitting in
  Pb$_{1-x}$Sn$_x$Te

abstract:
  The ratio of the Zeeman splitting to the cyclotron energy ($M=\Delta E_Z /
\hbar \omega_c$), which characterizes the relative strength of the spin-orbit
interaction in crystals, is examined for the narrow gap IV-VI semiconductors
PbTe, SnTe, and their alloy Pb$_{1-x}$Sn$_x$Te on the basis of the multiband
$k\cdot p$ theory. The inverse mass $\alpha$, the g-factor $g$, and $M$ are
calculated numerically by employing the relativistic empirical tight-binding
band calculation. On the other hand, a simple but exact formula of $M$ is
obtained for the six-band model based on the group theoretical analysis. It is
shown that $M<1$ for PbTe and $M>1$ for SnTe, which are interpreted in terms of
the relevance of the interband couplings due to the crystalline spin-orbit
interaction. It is clarified both analytically and numerically that $M=1$ just
at the band inversion point, where the transition from trivial to nontrivial
topological crystalline insulator occurs. By using this property, one can
detect the transition point only with the bulk measurements. It is also
proposed that $M$ is useful to evaluate quantitatively a degree of the Dirac
electrons in solids.