title: Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays

abstract:
  Understanding the local behaviour of structured multi-dimensional data is a
fundamental problem in various areas of computer science. As the amount of data
is often huge, it is desirable to obtain sublinear time algorithms, and
specifically property testers, to understand local properties of the data.
  We focus on the natural local problem of testing pattern freeness: given a
large $d$-dimensional array $A$ and a fixed $d$-dimensional pattern $P$ over a
finite alphabet, we say that $A$ is $P$-free if it does not contain a copy of
the forbidden pattern $P$ as a consecutive subarray. The distance of $A$ to
$P$-freeness is the fraction of entries of $A$ that need to be modified to make
it $P$-free. For any $\epsilon \in [0,1]$ and any large enough pattern $P$ over
any alphabet, other than a very small set of exceptional patterns, we design a
tolerant tester that distinguishes between the case that the distance is at
least $\epsilon$ and the case that it is at most $a_d \epsilon$, with query
complexity and running time $c_d \epsilon^{-1}$, where $a_d < 1$ and $c_d$
depend only on $d$.
  To analyze the testers we establish several combinatorial results, including
the following $d$-dimensional modification lemma, which might be of independent
interest: for any large enough pattern $P$ over any alphabet (excluding a small
set of exceptional patterns for the binary case), and any array $A$ containing
a copy of $P$, one can delete this copy by modifying one of its locations
without creating new $P$-copies in $A$.
  Our results address an open question of Fischer and Newman, who asked whether
there exist efficient testers for properties related to tight substructures in
multi-dimensional structured data. They serve as a first step towards a general
understanding of local properties of multi-dimensional arrays, as any such
property can be characterized by a fixed family of forbidden patterns.


title:
Inductive intrinsic localized modes in a 1D nonlinear electric
  transmission line

abstract:
  The experimental properties of intrinsic localized modes (ILM) have long been
compared with theoretical dynamical lattice models that make use of nonlinear
onsite and/or nearest neighbor intersite potentials. Here it is shown for a 1-D
lumped electrical transmission line a nonlinear inductive component in an
otherwise linear parallel capacitor lattice makes possible a new kind of ILM
outside the plane wave spectrum. To simplify the analysis the nonlinear
inductive current equations are transformed to flux transmission line equations
with analogue onsite hard potential nonlinearities. Approximate analytic
results compare favorably with those obtained from a driven damped lattice
model and with eigenvalue simulations. For this mono-element lattice ILMs above
the top of the plane wave spectrum are the result. We find that the current ILM
is spatially compressed relative to the corresponding flux ILM. Finally this
study makes the connection between the dynamics of mass and force constant
defects in the harmonic lattice and ILMs in a strongly anharmonic lattice.


title: Solar Obliquity Induced by Planet Nine

abstract:
  The six-degree obliquity of the sun suggests that either an asymmetry was
present in the solar system's formation environment, or an external torque has
misaligned the angular momentum vectors of the sun and the planets. However,
the exact origin of this obliquity remains an open question. Batygin & Brown
(2016) have recently shown that the physical alignment of distant Kuiper Belt
orbits can be explained by a 5-20 Earth-mass planet on a distant, eccentric,
and inclined orbit, with an approximate perihelion distance of ~250 AU. Using
an analytic model for secular interactions between Planet Nine and the
remaining giant planets, here we show that a planet with similar parameters can
naturally generate the observed obliquity as well as the specific pole position
of the sun's spin axis, from a nearly aligned initial state. Thus, Planet Nine
offers a testable explanation for the otherwise mysterious spin-orbit
misalignment of the solar system.


title:
Thermo-optic and thermal expansion coefficients of RTP and KTP crystals
  over 300-350 K

abstract:
  We report new measurements of the thermal expansion and thermo-optic
coefficients of RbTiOPO$_4$ (RTP) and KTiOPO$_4$ (KTP) crystals over the
temperature range 300-350 K. For RTP/KTP our coefficients of linear thermal
expansion at 305 K are: $\alpha_x=9.44/7.88\times 10^{-6}$/K,
$\alpha_y=12.49/9.48\times 10^{-6}$/K, $\alpha_z=-4.16/0.02\times 10^{-6}$/K.
Our normalized thermo-optic coefficients $\beta=(1/n)dn/dT$ at 632.8 nm and 305
K are: $\beta_x=5.39/3.78\times 10^{-6}$/K, $\beta_y=7.11/5.24\times
10^{-6}$/K, $\beta_z=12.35/9.34\times 10^{-6}$/K.


title:
Distribution of Cold ($\lesssim 300$K) Atomic Gas in Galaxies: Results
  from the GBT HI Absorption Survey Probing the Inner Halos ($\rho<20$kpc) of
  Low-z Galaxies

abstract:
  We present the Green Bank Telescope absorption survey of cold atomic hydrogen
($\lesssim 300$K) in the inner halo of low-redshift galaxies. The survey aims
to characterize the cold gas distribution and to address where condensation -
the process where ionized gas accreted by galaxies condenses into cold gas
within the disks of galaxies - occurs. Our sample consists of 16 galaxy-quasar
pairs with impact parameters of $\le$ 20kpc. We detected an HI absorber
associated with J0958+3222 (NGC 3067) and HI emission from six galaxies. We
also found two \ion{Ca}{2} absorption system in the archival SDSS data
associated with galaxies J0958+3222 and J1228+3706, although the sample was not
selected based on the presence of metals in absorption. Our detection rate of
HI absorbers with optical depths of $\ge 0.06$ is $\sim$7\%. We also find that
cold HI phase ($\lesssim$300K) is 44($\pm$18)\% of the total atomic gas in the
sightline probing J0958+3222. We find no correlation between the peak optical
depth and impact parameter or stellar and HI radii normalized impact
parameters, $\rho/\rm R_{90}$ and $\rho/\rm R_{HI}$. We conclude that the
process of condensation of inflowing gas into cold ($\lesssim$ 300K) HI occurs
at the $\rho << 20$kpc. However, the warmer phase of neutral gas (T $\sim$
1000K) can exists out to much larger distances as seen in emission maps.
Therefore, the process of condensation of warm to cold HI is likely occurring
in stages from ionized to warm HI in the inner halo and then to cold HI very
close to the galaxy disk.


title: The effects of velocities and lensing on moments of the Hubble diagram

abstract:
  We consider the dispersion on the supernova distance-redshift relation due to
peculiar velocities and gravitational lensing, and the sensitivity of these
effects to the amplitude of the matter power spectrum. We use the MeMo lensing
likelihood developed by Quartin, Marra & Amendola (2014), which accounts for
the characteristic non-Gaussian distribution caused by lensing magnification
with measurements of the first four central moments of the distribution of
magnitudes. We build on the MeMo likelihood by including the effects of
peculiar velocities directly into the model for the moments. In order to
measure the moments from sparse numbers of supernovae, we take a new approach
using Kernel Density Estimation to estimate the underlying probability density
function of the magnitude residuals. We also describe a bootstrap re-sampling
approach to estimate the data covariance matrix. We then apply the method to
the Joint Light-curve Analysis (JLA) supernova catalogue. When we impose only
that the intrinsic dispersion in magnitudes is independent of redshift, we find
$\sigma_8=0.44^{+0.63}_{-0.44}$ at the one standard deviation level, although
we note that in tests on simulations, this model tends to overestimate the
magnitude of the intrinsic dispersion, and underestimate $\sigma_8$. We note
that the degeneracy between intrinsic dispersion and the effects of $\sigma_8$
is more pronounced when lensing and velocity effects are considered
simultaneously, due to a cancellation of redshift dependence when both effects
are included. Keeping the model of the intrinsic dispersion fixed as a Gaussian
distribution of width 0.14 mag, we find $\sigma_8 = 1.07^{+0.50}_{-0.76}$.


title: Concatenated image completion via tensor augmentation and completion

abstract:
  This paper proposes a novel framework called concatenated image completion
via tensor augmentation and completion (ICTAC), which recovers missing entries
of color images with high accuracy. Typical images are second- or third-order
tensors (2D/3D) depending if they are grayscale or color, hence tensor
completion algorithms are ideal for their recovery. The proposed framework
performs image completion by concatenating copies of a single image that has
missing entries into a third-order tensor, applying a dimensionality
augmentation technique to the tensor, utilizing a tensor completion algorithm
for recovering its missing entries, and finally extracting the recovered image
from the tensor. The solution relies on two key components that have been
recently proposed to take advantage of the tensor train (TT) rank: A tensor
augmentation tool called ket augmentation (KA) that represents a low-order
tensor by a higher-order tensor, and the algorithm tensor completion by
parallel matrix factorization via tensor train (TMac-TT), which has been
demonstrated to outperform state-of-the-art tensor completion algorithms.
Simulation results for color image recovery show the clear advantage of our
framework against current state-of-the-art tensor completion algorithms.


title: Magnetic field induced mixed-level Kondo effect in two-level systems

abstract:
  We consider a two-orbital impurity system with intra and inter-level Coulomb
repulsion that is coupled to a single conduction channel. This situation can
generically occur in multilevel quantum dots or in systems of coupled quantum
dots. For finite energy-spacing between spin-degenerate orbitals, an in-plane
magnetic field drives the system from a local singlet ground state to a
"mixed-level" Kondo regime, where the Zeeman-split levels are degenerate for
opposite spin states. We use the numerical renormalization group approach to
fully characterize this mixed level Kondo state and discuss its properties in
terms of the applied Zeeman field, temperature and system parameters. Under
suitable conditions, the total spectral function is shown to develop a Fermi
level resonance, so that the linear conductance of the system peaks at a finite
Zeeman field while it decreases as function of temperature. These features, as
well as the local moment and entropy contribution of the impurity system are
commensurate with Kondo physics, which can be studied in suitably tuned quantum
dot systems.


title: Minimal determinantal representations of bivariate polynomials

abstract:
  For a square-free bivariate polynomial $p$ of degree $n$ we introduce a
simple and fast numerical algorithm for the construction of $n\times n$
matrices $A$, $B$, and $C$ such that $\det(A+xB+yC)=p(x,y)$. This is the
minimal size needed to represent a bivariate polynomial of degree $n$. Combined
with a square-free factorization one can now compute $n \times n$ matrices for
any bivariate polynomial of degree $n$. The existence of such symmetric
matrices was established by Dixon in 1902, but, up to now, no simple numerical
construction has been found, even if the matrices can be nonsymmetric. Such
representations may be used to efficiently numerically solve a system of two
bivariate polynomials of small degree via the eigenvalues of a two-parameter
eigenvalue problem. The new representation speeds up the computation
considerably.


title: X(16.7) Production in Electron-Position Collision

abstract:
  The anomaly found in the excited $^8\text{Be}$ nuclear transition to its
ground state is attributed to a spin-1 gauge boson $X(16.7)$. To hunt for this
boson, we propose two traps: $e^+e^-\to X\gamma$ and $J/\psi\to X\gamma$, both
following with $X\to e^+e^-$ decay. We adopt the "vector minus axial-vector"
interaction hypothesis. Analysis on the $X(16.7)$ decay length, production
rates, differential distribution with respect to the $e^+e^-$ invariant-mass
spectrum, and the signal-to-noise ratios (SNR) after the smearing at BESIII
detector are discussed in detail. Given the coupling strength of $X$ to
vector/axial-vector currents $g_f^{v/a}\sim10^{-3}$ at BESIII: (1) there would
be about $6000$ $X$ measurable events per year in electron-positron collision,
yet with a large background after smearing, (2) while in $J/\psi$ decays, we
find that the axial-vector current may come into play, though merely 52 events
may appear, the SNR are inspiring even after smearing.


title: 8th European Conference on Python in Science (EuroSciPy 2015)

abstract:
  The 8th edition of the European Conference on Python in Science, EuroSciPy
was held for the second time in the beautiful city of Cambridge, UK from
August, 26th to 29th, 2014. More than 200 participants, both from academia and
industry, attended the conference.
  As usual, the conference kicked off with two days of tutorials, divided into
an introductory and an advanced track. The introductory track, presented by
Joris Vankerschaver, Valerio Maggio Joris Van den Bossche, Stijn Van Hoey and
Nicolas Rougier, gave a quick but thorough overview of the SciPy stack, while
the experience track focused on different advanced topics. This second track
began with an introduction to Bokeh, by Bryan Van den Ven, followed by an image
processing tutorial with scikit-image by Emmanuelle Gouillart and Juan
Nunez-Iglesias. The afternoon continued with two tutorials on data analysis:
the first, intitulated "How 'good' is your model, and how can you make it
better?" (by Chih-Chun Chen, Dimitry Foures, Elena Chatzimichali, Giuseppe
Vettigli) focused on the challenges face while attempting model selections, and
the first day concluded with a statistics in python tutorial by Gael Varoquaux.
During the second day, the attendees tackled an in depth 4 hour tutorial on
Cython, presented by Stefan Behnel, and a crash course on "Evidence-Based
Teaching: What We Know and How to Use It", by Greg Wilson.


title: $F$-singularities under generic linkage

abstract:
  Let $R=k[x_1,\dots,x_n]$ be a polynomial ring over a prefect field of
positive characteristic. Let $I$ be an unmixed ideal in $R$ and let $J$ be a
generic link of $I$ in $S=R[u_{ij}]_{c \times r}$. We describe the parameter
test submodule of $S/J$ in terms of the test ideal of the pair $(R, I)$ when a
reduction of $I$ is a complete intersection or almost complete intersection. As
an application, we deduce a criterion for when $S/J$ has $F$-rational
singularities in these cases. We also compare the $F$-pure threshold of $(R,
I)$ and $(S, J)$.


title: Observable cosmological vector mode in the dark ages

abstract:
  The second-order vector mode is inevitably induced from the coupling of
first-order scalar modes in cosmological perturbation theory and might hinder a
possible detection of primordial gravitational waves from inflation through
21cm lensing observations. Here, we investigate the weak lensing signal in 21cm
photons emitted by neutral hydrogen atoms in the dark ages induced by the
second-order vector mode by decomposing the deflection angle of the 21cm
lensing signal into the gradient and curl modes. The curl mode is a good tracer
of the cosmological vector and tensor modes since the scalar mode does not
induce the curl one. By comparing angular power spectra of the 21cm lensing
curl mode induced by the second-order vector mode and primordial gravitational
waves whose amplitude is parametrized by the tensor-to-scalar ratio $r$, we
find that the 21cm curl mode from the second-order vector mode dominates over
that from primordial gravitational waves on almost all scales if $r \lesssim
10^{-5}$. If we use the multipoles of the power spectrum up to $\ell_{\rm max}
= 10^{5}$ and $10^{6}$ in reconstructing the curl mode from 21cm temperature
maps, the signal-to-noise ratios of the 21cm curl mode from the second-order
vector mode achieve ${\rm S/N} \approx 0.46$ and $73$, respectively.
Observation of 21cm radiation is, in principle, a powerful tool to explore not
only the tensor mode but also the cosmological vector mode.


title:
Effect of Energy Band Gap in Graphene on Negative Refraction through the
  Veselago Lens and Electron Conductance

abstract:
  A remarkable property of intrinsic graphene is that upon doping, electrons
and holes travel through the monolayer thick material with constant velocity
which does not depend on energy up to about $0.3$ eV (Dirac fermions), as
though the electrons and holes are massless particles and antiparticles which
move at the Fermi velocity $v_F$. Consequently, there is Klein tunneling at a
$p-n$ junction, in which there is no backscattering at normal incidence of
massless Dirac fermions. However, this process yielding perfect transmission at
normal incidence is expected to be affected when the group velocity of the
charge carriers is energy dependent and there is non-zero effective mass for
the target particle. We investigate how away from normal incidence the combined
effect of incident electron energy $\epsilon$ and band gap parameter $\Delta$
can determine whether a $p-n$ junction would allow focusing of an electron beam
by behaving like a Veselago lens with negative refractive index. We demonstrate
that there is a specific region in $\epsilon-\Delta$ space where the index of
refraction is negative, i.e., where monolayer graphene behaves as a
metamaterial. Outside this region, the refractive index may be positive or
there may be no refraction at all. We compute the ballistic conductance across
a $p-n$ junction as a function of $\Delta$ and $\epsilon$ and compare our
results with those for a single electrostatic potential barrier and multiple
barriers.


title:
Estimating and Controlling the False Discovery Rate for the PC Algorithm
  Using Edge-Specific P-Values

abstract:
  The PC algorithm allows investigators to estimate a complete partially
directed acyclic graph (CPDAG) from a finite dataset, but few groups have
investigated strategies for estimating and controlling the false discovery rate
(FDR) of the edges in the CPDAG. In this paper, we introduce PC with p-values
(PC-p), a fast algorithm which robustly computes edge-specific p-values and
then estimates and controls the FDR across the edges. PC-p specifically uses
the p-values returned by many conditional independence tests to upper bound the
p-values of more complex edge-specific hypothesis tests. The algorithm then
estimates and controls the FDR using the bounded p-values and the
Benjamini-Yekutieli FDR procedure. Modifications to the original PC algorithm
also help PC-p accurately compute the upper bounds despite non-zero Type II
error rates. Experiments show that PC-p yields more accurate FDR estimation and
control across the edges in a variety of CPDAGs compared to alternative
methods.


title:
Structure of the Harmonic Oscillator in the space of $n$-particle
  Glauber correlators

abstract:
  We map the Hilbert space of the quantum Harmonic oscillator to the space of
Glauber's $n$th-order intensity correlators, in effect showing "the
correlations between the correlators" for a random sampling of the quantum
states. In particular, we show how the popular $g^{(2)}$ function is correlated
to the mean population and how a recurrent criterion to identify
single-particle states or emitters, namely $g^{(2)}<1/2$, is incorrect as
states exist that satisfy this condition with average population larger than
one. Our charting of the Hilbert space allows to capture its structure in a
simpler and physically more intuitive way that can be used to classify quantum
sources by surveying which territory they can access.


title: Reading and Writing Single-Atom Magnets

abstract:
  The highest-density magnetic storage media will code data in single-atom
bits. To date, the smallest individually addressable bistable magnetic bits on
surfaces consist of 5-12 atoms. Long magnetic relaxation times were
demonstrated in molecular magnets containing one lanthanide atom, and recently
in ensembles of single holmium (Ho) atoms supported on magnesium oxide (MgO).
Those experiments indicated the possibility for data storage at the fundamental
limit, but it remained unclear how to access the individual magnetic centers.
Here we demonstrate the reading and writing of individual Ho atoms on MgO, and
show that they independently retain their magnetic information over many hours.
We read the Ho states by tunnel magnetoresistance and write with current pulses
using a scanning tunneling microscope. The magnetic origin of the long-lived
states is confirmed by single-atom electron paramagnetic resonance (EPR) on a
nearby Fe sensor atom, which shows that Ho has a large out-of-plane moment of
$(10.1 \pm 0.1)$ $\mu_{\rm B}$ on this surface. In order to demonstrate
independent reading and writing, we built an atomic scale structure with two Ho
bits to which we write the four possible states and which we read out remotely
by EPR. The high magnetic stability combined with electrical reading and
writing shows that single-atom magnetic memory is possible.


title:
Uniqueness of a phaseless inverse scattering problem for the generalized
  3-D Helmholtz equation

abstract:
  An inverse scattering problems for the 3-D generalized Helmholtz equation is
considered. Only the modulus of the complex valued scattered wave field is
assumed to be measured and the phase is not measured. Uniqueness theorem is
proved.


title: Resource Planning For Rescue Operations

abstract:
  After an earthquake, disaster sites pose a multitude of health and safety
concerns. A rescue operation of people trapped in the ruins after an earthquake
disaster requires a series of intelligent behavior, including planning. For a
successful rescue operation, given a limited number of available actions and
regulations, the role of planning in rescue operations is crucial. Fortunately,
recent developments in automated planning by artificial intelligence community
can help different organization in this crucial task. Due to the number of
rules and regulations, we believe that a rule based system for planning can be
helpful for this specific planning problem. In this research work, we use logic
rules to represent rescue and related regular regulations, together with a
logic based planner to solve this complicated problem. Although this research
is still in the prototyping and modeling stage, it clearly shows that rule
based languages can be a good infrastructure for this computational task. The
results of this research can be used by different organizations, such as
Iranian Red Crescent Society and International Institute of Seismology and
Earthquake Engineering (IISEE).


title: HR 8799: The Benchmark Directly-Imaged Planetary System

abstract:
  HR 8799 harbors arguably the first and best-studied directly-imaged planets.
In this brief article, I describe how the HR 8799 planetary system is a
benchmark system for studying the atmospheres, orbital properties, dynamical
stability, and formation of young superjovian planets. Multi-wavelength
photometry and spectroscopy show that HR 8799 bcde appear to have thicker
clouds than do field brown dwarfs of similar effective temperatures and exhibit
evidence for non-equilibrium carbon chemistry, features that are likely
connected to the planets' low surface gravities. Over 17 years of astrometric
data constrain the planets' orbits to not be face on but possibly in multiple
orbital resonances. At orbital separations of 15--70 au and with masses of
$\approx$ 5--7 $M_{\rm J}$, HR 8799 bcde probe the extremes of jovian planet
formation by core accretion: medium-resolution spectroscopy may provide clues
about these planets' formation conditions. Data from the next generation of 30
m-class telescopes should better constrain the planets' orbits, chemistry,
gravity, and formation history.


title: Every finite group has a normal bi-Cayley graph

abstract:
  A graph $\G$ with a group $H$ of automorphisms acting semiregularly on the
vertices with two orbits is called a {\em bi-Cayley graph} over $H$. When $H$
is a normal subgroup of $\Aut(\G)$, we say that $\G$ is {\em normal} with
respect to $H$. In this paper, we show that every finite group has a connected
normal bi-Cayley graph. This improves Theorem~5 of [M. Arezoomand, B. Taeri,
Normality of 2-Cayley digraphs, Discrete Math. 338 (2015) 41--47], and provides
a positive answer to the Question of the above paper.


title: Galaxy groups in the 2MASS Redshift Survey

abstract:
  A galaxy group catalog is constructed from the 2MASS Redshift Survey (2MRS)
with the use of a halo-based group finder. The halo mass associated with a
group is estimated using a `GAP' method based on the luminosity of the central
galaxy and its gap with other member galaxies. Tests using mock samples shows
that this method is reliable, particularly for poor systems containing only a
few members. On average 80% of all the groups have completeness >0.8, and about
65% of the groups have zero contamination. Halo masses are estimated with a
typical uncertainty $\sim 0.35\,{\rm dex}$. The application of the group finder
to the 2MRS gives 29,904 groups from a total of 43,246 galaxies at $z \leq
0.08$, with 5,286 groups having two or more members. Some basic properties of
this group catalog is presented, and comparisons are made with other groups
catalogs in overlap regions. With a depth to $z\sim 0.08$ and uniformly
covering about 91% of the whole sky, this group catalog provides a useful data
base to study galaxies in the local cosmic web, and to reconstruct the mass
distribution in the local Universe.


title:
Dynamics of a coupled spin vortex pair in dipolar spinor Bose-Einstein
  condensates

abstract:
  The collisional and magnetic field quench dynamics of a coupled spin-vortex
pair in dipolar spinor Bose-Einstein condensates in a double well potential are
numerically investigated in the mean field theory. Upon a sudden release of the
potential barrier the two layers of condensates collide with each other in the
trap center with the chirality of the vortex pair exchanged after each
collision, showing the typical signature of in-phase collision for the parallel
spin vortex phase, and out-of-phase collision for the antiparallel phase. When
quenching the transverse magnetic field, the vortex center in the
single-layered condensate starts to make a helical motion with oval-shaped
trajectories and the displacement of the center position is found to exhibit a
damped simple harmonic oscillation with an intrinsic frequency and damping
rate. The oscillation mode of the spin vortex pair may be tuned by the initial
magnetic field and the height of the Gaussian barrier, e.g. the gyrotropic
motions for parallel spin vortex pair are out of sync with each other in the
two layers, while those for the antiparallel pair exhibit a
double-helix-structure with the vortex centers moving opposite to each other
with the same amplitude.


title: Radial stability of anisotropic strange quark stars

abstract:
  The influence of the anisotropy in the equilibrium and stability of strange
stars is investigated through the numerical solution of the hydrostatic
equilibrium equation and the radial oscillation equation, both modified from
their original version to include this effect. The strange matter inside the
quark stars is described by the MIT bag model equation of state. For the
anisotropy two different kinds of local anisotropic $\sigma=p_t-p_r$ are
considered, where $p_t$ and $p_r$ are respectively the tangential and the
radial pressure: one that is null at the star's surface defined by $p_r(R)=0$,
and one that is nonnull on at the surface, namely, $\sigma_s=0$ and
$\sigma_s\neq0$. In the case $\sigma_s=0$, the maximum mass value and the zero
frequency of oscillation are found at the same central energy density,
indicating that the maximum mass marks the onset of the instability. For the
case $\sigma_s\neq0$, we show that the maximum mass point and the zero
frequency of oscillation coincide in the same central energy density value only
in a sequence of equilibrium configurations with the same value of $\sigma_s$.
Thus, the stability star regions are determined always by the condition
$dM/d\rho_c>0$ only when the tangential pressure is maintained fixed at the
star surface's $p_t(R)$. These results are also quite important to analyze the
stability of other anisotropic compact objects such as neutron stars, boson
stars and gravastars.


title:
Heavy quark potential and jet quenching parameter in a D-instanton
  background

abstract:
  Using the AdS/CFT correspondence, we study the heavy quark potential and the
jet quenching parameter in the near horizon limit of D3-D(-1) background. The
results are compared with those of conformal cases. It is shown that the
presence of instantons tends to suppress the heavy quark potential and enhance
the jet quenching parameter.


title: Radiative proton capture cross sections in the mass range $40-55$

abstract:
  Proton capture cross sections in the energy range of astrophysical interest
for mass region 40-54 have been calculated in the Hauser-Feshbach formalism
with reaction code TALYS1.6. The density dependent M3Y effective
nucleon-nucleon interaction folded with target radial matter densities from
relativistic mean field approach is used to obtain the semi-microscopic optical
potential. A definite normalization of potential-well depths has been used over
the entire mass region. The $(p,\gamma)$ rates of some reactions, important in
the astrophysical scenario, are calculated using the potential in the relevant
mass region.


title:
Construction of a Model of Monopolium and its Search via Multi-Photon
  Channels at LHC

abstract:
  A model of monopolium is constructed based on an electromagnetic dual
formulation of Zwanziger and lattice gauge theory. To cope with the strong
coupling nature of the magnetic charge, for which the monopole is confined, $
U(1) $ lattice gauge theory is applied. The monopole is assumed to have a
finite-sized inner structure based on a 't Hooft-Polyakov like solution in
which the magnetic charge is uniformly distributed on the surface of a sphere.
The monopole and antimonopole potential becomes linear plus Coulomb outside the
sphere and is constant inside. Numerical estimation gives two kinds of
solutions: One which has a small binding energy, and hence the para-($ J=0 $)
and ortho-($ J=1 $) monopoliums have degenerate masses. For the parameter
choices considered, they both have $ \mathcal{O}(1-10) $ TeV masses and are
very short-lived. The other solution has a small monopole mass and large
binding energy, with an illustrative example of parameter choices giving a 750
GeV para-monopolium and 1.4 TeV ortho-monopolium. The production rate of the
former is one order of magnitude smaller than the announced enhancement, but
they may be the target of future LHC searches and the 100 TeV colliders.


title:
Local regularity of super-potentials and equidistribution of positive
  closed currents of $\mathbb{P}^k$

abstract:
  In this paper, we introduce notions about local regularity of the
super-potential and prove equidistribution of positive closed $(p, p)$-currents
of $\mathbb{P}^k$ whose super-potentials are bounded near an invariant analytic
subset, for holomorphic endomorphisms of $\mathbb{P}^k$ and for regular
polynomial automorphisms of $\mathbb{C}^k$.


title: Large-momentum distribution of a polarized Fermi gas and p-wave contacts

abstract:
  We present a derivation of the adiabatic energy relations as well as the
large momentum distribution of a polarized Fermi gas near p-wave Feshbach
resonances. The leading asymptotic behavior ($k^{-2}$) and subleading behavior
($k^{-4}$) of the large momentum distribution have recently been predicted by
Yu et al. [Phys. Rev. Lett. 115, 135304 (2015)] and by He et al. [Phys. Rev.
Lett. 116, 045301 (2016)] using two different approaches. Here, we show that
the subleading asymptotic behavior ($\sim k^{-4}$) can not fully be captured by
the contact defined from the adiabatic energy relation related to the p-wave
effective range, and there should be an extra term resulted from the
center-of-mass motion of the pairs. The omission of this extra term is perhaps
a reasonable approximation at zero temperature. However, it should be taken
into account at finite temperature and should be of significant importance to
understand the recently measured momentum distribution in a resonant p-wave
Fermi gas of ultracold $^{40}$K atoms [Luciuk et al., Nature Phys. 12, 599
(2016)].


title: Fast Algorithms for Segmented Regression

abstract:
  We study the fixed design segmented regression problem: Given noisy samples
from a piecewise linear function $f$, we want to recover $f$ up to a desired
accuracy in mean-squared error.
  Previous rigorous approaches for this problem rely on dynamic programming
(DP) and, while sample efficient, have running time quadratic in the sample
size. As our main contribution, we provide new sample near-linear time
algorithms for the problem that -- while not being minimax optimal -- achieve a
significantly better sample-time tradeoff on large datasets compared to the DP
approach. Our experimental evaluation shows that, compared with the DP
approach, our algorithms provide a convergence rate that is only off by a
factor of $2$ to $4$, while achieving speedups of three orders of magnitude.


title:
Vision-based Traffic Flow Prediction using Dynamic Texture Model and
  Gaussian Process

abstract:
  In this paper, we describe work in progress towards a real-time vision-based
traffic flow prediction (TFP) system. The proposed method consists of three
elemental operators, that are dynamic texture model based motion segmentation,
feature extraction and Gaussian process (GP) regression. The objective of
motion segmentation is to recognize the target regions covering the moving
vehicles in the sequence of visual processes. The feature extraction operator
aims to extract useful features from the target regions. The extracted features
are then mapped to the number of vehicles through the operator of GP
regression. A training stage using historical visual data is required for
determining the parameter values of the GP. Using a low-resolution visual data
set, we performed preliminary evaluations on the performance of the proposed
method. The results show that our method beats a benchmark solution based on
Gaussian mixture model, and has the potential to be developed into qualified
and practical solutions to real-time TFP.


title:
Reduced-Shifted Conjugate-Gradient Method for a Green's Function:
  Efficient Numerical Approach in a Nano-structured Superconductor

abstract:
  We propose the reduced-shifted Conjugate-Gradient (RSCG) method, which is
numerically efficient to calculate a matrix element of a Green's function
defined as a resolvent of a Hamiltonian operator, by solving linear equations
with a desired accuracy. This method does not calculate solution vectors of
linear equations but does directly calculate a matrix element of the resolvent.
The matrix elements with different frequencies are simultaneously obtained.
Thus, it is easy to calculate the exception value expressed as a Matsubara
summation of these elements. To illustrate a power of our method, we choose a
nano-structured superconducting system with a mean-field Bogoliubov-de Gennes
(BdG) approach. This method allows us to treat with the system with the
fabrication potential, where one can not effectively use the
kernel-polynomial-based method. We consider the d-wave nano-island
superconductor by simultaneously solving the linear equations with a large
number (~ 50000) of Matsubara frequencies.


title:
Quantum many-body theory for electron spin decoherence in nanoscale
  nuclear spin baths

abstract:
  Decoherence of electron spins in nanoscale systems is important to quantum
technologies such as quantum information processing and magnetometry. It is
also an ideal model problem for studying the crossover between quantum and
classical phenomena. At low temperatures or in light-element materials where
the spin-orbit coupling is weak, the phonon scattering in nanostructures is
less important and the fluctuations of nuclear spins become the dominant
decoherence mechanism for electron spins. Since 1950s, semiclassical noise
theories have been developed for understanding electron spin decoherence. In
spin-based solid-state quantum technologies, the relevant systems are in the
nanometer scale and the nuclear spin baths are quantum objects which require a
quantum description. Recently, quantum pictures have been established to
understand the decoherence and quantum many-body theories have been developed
to quantitatively describe this phenomenon. Anomalous quantum effects have been
predicted and some have been experimentally confirmed. A systematically
truncated cluster correlation expansion theory has been developed to account
for the many-body correlations in nanoscale nuclear spin baths that are built
up during the electron spin decoherence. The theory has successfully predicted
and explained a number of experimental results in a wide range of physical
systems. In this review, we will cover these recent progresses. The limitations
of the present quantum many-body theories and possible directions for future
development will also be discussed.


title:
Different Electronic Charges in Two-Component Superconductor by Coherent
  State

abstract:
  Recently, the different electronic charges, which are related to the
different coupling constants with magnetic field, in the two-component
superconductor have been studied in frame of Ginzburg-Landau theory. In order
to study the electronic charges in detail we suggest the wave function in the
two-component superconductor to be coherent state. We find the different
electronic charges exist not only in the coherent state but the incoherent
state. But the ratio of the different charges in the coherent state is
different from ratio in the incoherence. The expressions of the coupling
constants are given directly based on the coherence effects. We also discuss
the winding number in such system.


title:
On the extrema of a nonconvex functional with double-well potential in
  higher dimensions

abstract:
  This paper mainly addresses the extrema of a nonconvex functional with
double-well potential in higher dimensions through the approach of nonlinear
partial differential equations. Based on the canonical duality method, the
corresponding Euler--Lagrange equation with Neumann boundary condition can be
converted into a cubic dual algebraic equation, which will help find the local
extrema for the primal problem. In comparison with the 1D case discussed by D.
Gao and R. Ogden, there exists huge difference in higher dimensions, which will
be explained in the theorem.


title:
Flux-limited solutions and state constraints for quasi-convex
  Hamilton-Jacobi equations

abstract:
  Imbert and Monneau proved that Soner's formulation of state constraint
problems on a bounded interval is equivalent to the so-called flux-limited
formulation they introduced recently. In the multidimensional setting, we show
this result for a general $\mathcal{C}^{1}$ bounded open set of
$\mathbb{R}^{d}$ and obtain the result in the stationary and the evolution type
cases.


title: Theta Products and Eta Quotients of Level $24$ and Weight $2$

abstract:
  We find bases for the spaces
$M_2\Big(\Gamma_0(24),\Big(\frac{d}{\cdot}\Big)\Big)$ ($d=1,8,12, 24$) of
modular forms. We determine the Fourier coefficients of all $35$ theta products
$\varphi[a_1,a_2,a_3,a_4](z)$ in these spaces. We then deduce formulas for the
number of representations of a positive integer $n$ by diagonal quaternary
quadratic forms with coefficients $1$, $2$, $3$ or $6$ in a uniform manner, of
which $14$ are Ramanujan's universal quaternary quadratic forms. We also find
all the eta quotients in the Eisenstein spaces
$E_2\Big(\Gamma_0(24),\Big(\frac{d}{\cdot}\Big)\Big)$ ($d=1,8,12,24$) and give
their Fourier coefficients.


title: Comparison principle for stochastic heat equation on $\mathbb{R}^d$

abstract:
  We establish the strong comparison principle and strict positivity of
solutions to the following nonlinear stochastic heat equation on $\mathbb{R}^d$
\[ \left(\frac{\partial }{\partial t} -\frac{1}{2}\Delta \right) u(t,x) =
\rho(u(t,x)) \:\dot{M}(t,x), \] for measure-valued initial data, where
$\dot{M}$ is a spatially homogeneous Gaussian noise that is white in time and
$\rho$ is Lipschitz continuous. These results are obtained under the condition
that $\int_{\mathbb{R}^d}(1+|\xi|^2)^{\alpha-1}\hat{f}(\text{d} \xi)<\infty$
for some $\alpha\in(0,1]$, where $\hat{f}$ is the spectral measure of the
noise. {The weak comparison principle and nonnegativity of solutions to the
same equation are obtained under Dalang's condition, i.e., $\alpha=0$.} As some
intermediate results, we obtain handy upper bounds for $L^p(\Omega)$-moments of
$u(t,x)$ for all $p\ge 2$, and also prove that $u$ is a.s. H\"older continuous
with order $\alpha-\epsilon$ in space and $\alpha/2-\epsilon$ in time for any
small $\epsilon>0$.


title: Spin-orbit Misalignment as a Driver of the Kepler Dichotomy

abstract:
  During its 5 year mission, the Kepler spacecraft has uncovered a diverse
population of planetary systems with orbital configurations ranging from
single-transiting planets to systems of multiple planets co-transiting the
parent star. By comparing the relative occurrences of multiple to
single-transiting systems, recent analyses have revealed a significant
over-abundance of singles. Dubbed the "Kepler Dichotomy," this feature has been
interpreted as evidence for two separate populations of planetary systems: one
where all orbits are confined to a single plane, and a second where the
constituent planetary orbits possess significant mutual inclinations, allowing
only a single member to be observed in transit at a given epoch. In this work,
we demonstrate that stellar obliquity, excited within the disk-hosting stage,
can explain this dichotomy. Young stars rotate rapidly, generating a
significant quadrupole moment which torques the planetary orbits, with inner
planets influenced more strongly. Given nominal parameters, this torque is
sufficiently strong to excite significant mutual inclinations between planets,
enhancing the number of single-transiting planets, sometimes through a
dynamical instability. Furthermore, as hot stars appear to possess
systematically higher obliquities, we predict that single-transiting systems
should be relatively more prevalent around more massive stars. We analyze the
Kepler data and confirm this signal to be present.


title: Strange Nonchaotic Self-Oscillator

abstract:
  An example of strange nonchaotic attractor (SNA) is discussed in a
dissipative system of mechanical nature driven by constant torque applied to
one of the elements of the construction. So the external force is not
oscillatory, and the system is autonomous. Components of the motion with
incommensurable frequencies emerge due to the irrational ratio of sizes of the
involved rotating elements. We regard the phenomenon as strange nonchaotic
self-oscillations, and its existence sheds new light on the question of
feasibility of SNA in autonomous systems.


title: Hamiltonian paths in m x n projective checkerboards

abstract:
  For any two squares A and B of an m x n checkerboard, we determine whether it
is possible to move a checker through a route that starts at A, ends at B, and
visits each square of the board exactly once. Each step of the route moves to
an adjacent square, either to the east or to the north, and may step off the
edge of the board in a manner corresponding to the usual construction of a
projective plane by applying a twist when gluing opposite sides of a rectangle.
This generalizes work of M.H.Forbush et al. for the special case where m = n.


title: Directed Hamiltonicity and Out-Branchings via Generalized Laplacians

abstract:
  We are motivated by a tantalizing open question in exact algorithms: can we
detect whether an $n$-vertex directed graph $G$ has a Hamiltonian cycle in time
significantly less than $2^n$? We present new randomized algorithms that
improve upon several previous works:
  1. We show that for any constant $0<\lambda<1$ and prime $p$ we can count the
Hamiltonian cycles modulo $p^{\lfloor (1-\lambda)\frac{n}{3p}\rfloor}$ in
expected time less than $c^n$ for a constant $c<2$ that depends only on $p$ and
$\lambda$. Such an algorithm was previously known only for the case of counting
modulo two [Bj\"orklund and Husfeldt, FOCS 2013].
  2. We show that we can detect a Hamiltonian cycle in $O^*(3^{n-\alpha(G)})$
time and polynomial space, where $\alpha(G)$ is the size of the maximum
independent set in $G$. In particular, this yields an $O^*(3^{n/2})$ time
algorithm for bipartite directed graphs, which is faster than the
exponential-space algorithm in [Cygan et al., STOC 2013].
  Our algorithms are based on the algebraic combinatorics of "incidence
assignments" that we can capture through evaluation of determinants of
Laplacian-like matrices, inspired by the Matrix--Tree Theorem for directed
graphs. In addition to the novel algorithms for directed Hamiltonicity, we use
the Matrix--Tree Theorem to derive simple algebraic algorithms for detecting
out-branchings. Specifically, we give an $O^*(2^k)$-time randomized algorithm
for detecting out-branchings with at least $k$ internal vertices, improving
upon the algorithms of [Zehavi, ESA 2015] and [Bj\"orklund et al., ICALP 2015].
We also present an algebraic algorithm for the directed $k$-Leaf problem, based
on a non-standard monomial detection problem.


title:
Spectra and elliptic flow of (multi-)strange hadrons at RHIC and LHC
  within viscous hydrodynamics+hadron cascade hybrid model

abstract:
  Using the (2+1)-dimensional ultrarelativistic viscous hydrodynamics+hadron
cascade, VISHNU, hybrid model, we study the $p_{\rm T}$-spectra and elliptic
flow of $\Lambda$, $\Xi$, and $\Omega$ in Au+Au collisions at
$\sqrt{s_{NN}}$=200 GeV and in Pb+Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV.
Comparing our model results with the data measurements, we find that the VISHNU
model gives general descriptions of the measurements of these strange and
multi-strange hadrons at several centrality classes at RHIC and LHC. Mass
ordering of elliptic flow $v_{2}$ among $\pi$, $K$, $p$, $\Lambda$, $\Xi$, and
$\Omega$ are further investigated and discussed at the two collision systems.
We find, at both RHIC and LHC, the $v_{2}$ mass ordering among $\pi$, $K$, $p$,
and $\Omega$ are fairly reproduced within the VISHNU hybrid model, and more
improvements are needed to implement for well describing the $v_{2}$ mass
ordering among $p$, $\Lambda$, and $\Xi$.


title: Filter Design for Generalized Frequency-Division Multiplexing

abstract:
  In this paper, optimal filter design for generalized frequency-division
multiplexing (GFDM) is considered under two design criteria: rate maximization
and out-of-band (OOB) emission minimization. First, the problem of GFDM filter
optimization for rate maximization is formulated by expressing the transmission
rate of GFDM as a function of GFDM filter coefficients. It is shown that
Dirichlet filters are rate-optimal in additive white Gaussian noise (AWGN)
channels with no carrier frequency offset (CFO) under linear zero-forcing (ZF)
or minimum mean-square error (MMSE) receivers, but in general channels
perturbed by CFO a properly designed nontrivial GFDM filter can yield better
performance than Dirichlet filters by adjusting the subcarrier waveform to cope
with the channel-induced CFO. Next, the problem of GFDM filter design for OOB
emission minimization is formulated by expressing the power spectral density
(PSD) of the GFDM transmit signal as a function of GFDM filter coefficients,
and it is shown that the OOB emission can be reduced significantly by designing
the GFDM filter properly. Finally, joint design of GFDM filter and window for
the two design criteria is considered.


title: Characterizing minimum-length coordinated motions for two discs

abstract:
  We study the problem of determining optimal coordinated motions for two disc
robots in an otherwise obstacle-free plane. Using the total path length traced
by the two disc centres as a measure of distance, we give an exact
characterization of a shortest collision-avoiding motion for all initial and
final configurations of the robots. The individual paths are composed of at
most six (straight or circular-arc) segments, and their total length can be
expressed as a simple integral with a closed form solution depending only on
the initial and final configuration of the robots. Furthermore, the paths can
be parametrized in such a way that (i) only one robot is moving at any given
time (decoupled motion), or (ii) the angle between the two robots' centres
changes monotonically.


title:
Spin dynamics of diamond nitrogen-vacancy centres at the ground state
  level anti-crossing and all-optical low frequency magnetic field sensing

abstract:
  We investigate the photo-induced spin dynamics of single nitrogen-vacancy
(NV) centres in diamond near the electronic ground state level anti-crossing
(GSLAC), which occurs at an axial magnetic field around 1024 G. Using optically
detected magnetic resonance spectroscopy, we first find that the electron spin
transition frequency can be tuned down to 100 kHz for the \NV{14} centre, while
for the \NV{15} centre the transition strength vanishes for frequencies below
about 2 MHz owing to the GSLAC level structure. Using optical pulses to prepare
and readout the spin state, we observe coherent spin oscillations at 1024 G for
the \NV{14}, which originate from spin mixing induced by residual transverse
magnetic fields. This effect is responsible for limiting the smallest
observable transition frequency, which can span two orders of magnitude from
100 kHz to tens of MHz depending on the local magnetic noise. A similar feature
is observed for the \NV{15} centre at 1024 G. As an application of these
findings, we demonstrate all-optical detection and spectroscopy of
externally-generated fluctuating magnetic fields at frequencies from 8 MHz down
to 500 kHz, using a \NV{14} centre. Since the Larmor frequency of most nuclear
spin species lies within this frequency range near the GSLAC, these results
pave the way towards all-optical, nanoscale nuclear magnetic resonance
spectroscopy, using longitudinal spin cross-relaxation.


title:
$\Delta$ (1232) effects in density-dependent relativistic Hartree-Fock
  theory and neutron stars

abstract:
  The density-dependent relativistic Hartree-Fock (DDRHF) theory is extended to
include $\Delta$-isobars for the study of dense nuclear matter and neutron
stars. To this end, we solve the Rarita-Schwinger equation for spin-3/2
particle. Both the direct and exchange terms of the $\Delta$-isobars'
self-energies are evaluated in details. In comparison with the relativistic
mean field theory (Hartree approximation), a weaker parameter dependence is
found for DDRHF. An early appearance of $\Delta$-isobars is recognized at
$\rho_B\sim0.27$fm$^{-3}$, comparable with that of hyperons. Also, we find that
the $\Delta$-isobars' softening of the equation of state is found to be mainly
due to the reduced Fock contributions from the coupling of the isoscalar
mesons, while the pion contributions are found negligibly small. We finally
conclude that with typical parameter sets, neutron stars with $\Delta$-isobars
in their interiors could be as heavy as the two massive pulsars whose masses
are precisely measured, with slightly smaller radii than normal neutron stars.


title:
Multiple Staggered Mesh Ewald: Boosting the Accuracy of the Smooth
  Particle Mesh Ewald Method

abstract:
  The smooth particle mesh Ewald (SPME) method is the standard method for
computing the electrostatic interactions in the molecular simulations. In this
work, the multiple staggered mesh Ewald (MSME) method is proposed to boost the
accuracy of the SPME method. Unlike the SPME that achieves higher accuracy by
refining the mesh, the MSME improves the accuracy by averaging the standard
SPME forces computed on, e.g. $M$, staggered meshes. We prove, from theoretical
perspective, that the MSME is as accurate as the SPME, but uses $M^2$ times
less mesh points in a certain parameter range. In the complementary parameter
range, the MSME is as accurate as the SPME with twice of the interpolation
order. The theoretical conclusions are numerically validated both by a uniform
and uncorrelated charge system, and by a three-point-charge water system that
is widely used as solvent for the bio-macromolecules.


title:
Incompressible immiscible multiphase flows in porous media: a
  variational approach

abstract:
  We describe the competitive motion of (N + 1) incompressible immiscible
phases within a porous medium as the gradient flow of a singular energy in the
space of non-negative measures with prescribed mass endowed with some tensorial
Wasserstein distance. We show the convergence of the approximation obtained by
a minimization schem\`e a la [R. Jordan, D. Kinder-lehrer \& F. Otto, SIAM J.
Math. Anal, 29(1):1--17, 1998]. This allow to obtain a new existence result for
a physically well-established system of PDEs consisting in the Darcy-Muskat law
for each phase, N capillary pressure relations, and a constraint on the volume
occupied by the fluid. Our study does not require the introduction of any
global or complementary pressure.


title: Acyclicity and reduction

abstract:
  The literature provides dichotomies involving homomorphisms (like the G 0
dichotomy) or reductions (like the characterization of sets potentially in a
Wadge class of Borel sets, which holds on a subset of a product). However, part
of the motivation behind the latter result was to get reductions on the whole
product, like in the classical notion of Borel reducibility considered in the
study of analytic equivalence relations. This is not possible in general. We
show that, under some acyclicity (and also topological) assumptions, this is
widely possible. In particular, we prove that, for any non-self dual Borel
class {\Gamma}, there is a concrete finite =< c-antichain basis for the class
of Borel relations, whose closure has acyclic symmetrization, and which are not
potentially in {\Gamma}. Along similar lines, we provide a sufficient condition
for =< c-reducing G 0. We also prove a similar result giving a minimum set
instead of an antichain if we allow rectangular reductions.


title:
Acoustically mediated long-range interaction among multiple spherical
  particles exposed to a plane standing wave

abstract:
  In this work, we study the acoustically mediated interaction forces among
multiple well-separated spherical particles trapped in the same node or
antinode plane of a standing wave. An analytical expression of the acoustic
interaction force is derived, which is accurate even for the particles beyond
the Rayleigh limit. Interestingly, the multi-particle system can be decomposed
into a series of independent two-particle systems described by pairwise
interactions. Each pairwise interaction is a long-range interaction, as
characterized by a soft oscillatory attenuation (at the power exponent of n=-1
or -2). The vector additivity of the acoustic interaction force, which is not
well expected considering the nonlinear nature of the acoustic radiation force,
is greatly useful for exploring a system consisting of a large number of
particles. The capability of self-organizing a big particle cluster can be
anticipated through such acoustically controllable long-range interaction.


title: Computing the Action of Trigonometric and Hyperbolic Matrix Functions

abstract:
  We derive a new algorithm for computing the action $f(A)V$ of the cosine,
sine, hyperbolic cosine, and hyperbolic sine of a matrix $A$ on a matrix $V$,
without first computing $f(A)$. The algorithm can compute $\cos(A)V$ and
$\sin(A)V$ simultaneously, and likewise for $\cosh(A)V$ and $\sinh(A)V$, and it
uses only real arithmetic when $A$ is real. The algorithm exploits an existing
algorithm \texttt{expmv} of Al-Mohy and Higham for $\mathrm{e}^AV$ and its
underlying backward error analysis. Our experiments show that the new algorithm
performs in a forward stable manner and is generally significantly faster than
alternatives based on multiple invocations of \texttt{expmv} through formulas
such as $\cos(A)V = (\mathrm{e}^{\mathrm{i}A}V +
\mathrm{e}^{\mathrm{-i}A}V)/2$.


title:
Topological insulators from the perspective of non-commutative geometry
  and index theory

abstract:
  Topological insulators are solid state systems of independent electrons for
which the Fermi level lies in a mobility gap, but the Fermi projection is
nevertheless topologically non-trivial, namely it cannot be deformed into that
of a normal insulator. This non-trivial topology is encoded in adequately
defined invariants and implies the existence of surface states that are not
susceptible to Anderson localization. This non-technical review reports on
recent progress in the understanding of the underlying mathematical structures,
with a particular focus on index theory.


title: Existence of multiple solutions for a quasilinear elliptic problem

abstract:
  In this paper we prove the existence of multiple solutions for a quasilinear
elliptic boundary value problem, when the p-derivative at zero and the
p-derivative at infinity of the nonlinearity are greater than the first
eigenvalue of the p-Laplace operator. Our proof uses bifurcation from infinity
and bifurcation from zero to prove the existence of unbounded branches of
positive solutions (resp. of negative solutions). We show the existence of
multiple solutions and we provide qualitative properties of these solutions.


title:
The influence of near-wall density and viscosity gradients on turbulence
  in channel flows

abstract:
  The influence of near-wall density and viscosity gradients on near-wall
turbulence in a channel are studied by means of Direct Numerical Simulation
(DNS) of the low-Mach number approximation of the Navier--Stokes equations.
Different constitutive relations for density and viscosity as a function of
temperature are used in order to mimic a wide range of fluid behaviours and to
develop a generalised framework for studying turbulence modulations in variable
property flows. Instead of scaling the velocity solely based on local density,
as done for the van Driest transformation, we derive an extension of the
scaling that is based on gradients of the semi-local Reynolds number
$Re_\tau^*$. This extension of the van Driest transformation is able to
collapse velocity profiles for flows with near-wall property gradients as a
function of the semi-local wall coordinate. However, flow quantities like
mixing length, turbulence anisotropy and turbulent vorticity fluctuations do
not show a universal scaling very close to the wall. This is attributed to
turbulence modulations, which play a crucial role on the evolution of turbulent
structures and turbulence energy transfer. We therefore investigate the
characteristics of streamwise velocity streaks and quasi-streamwise vortices
and found that, similar to turbulent statistics, the turbulent structures are
also strongly governed by $Re_\tau^*$ profiles and that their dependence on
individual density and viscosity profiles is minor. Flows with near-wall
gradients in $Re_\tau^*$ ($d {Re_\tau^*}/dy \neq 0$) showed significant changes
in the inclination and tilting angles of quasi-streamwise vortices. These
structural changes are responsible for the observed modulation of the Reynolds
stress generation mechanism and the inter-component energy transfer in flows
with strong near-wall $Re_\tau^*$ gradients.


title:
Variational tensor network renormalization in imaginary time: benchmark
  results in the Hubbard model at finite temperature

abstract:
  A Gibbs operator $e^{-\beta H}$ for a 2D lattice system with a Hamiltonian
$H$ can be represented by a 3D tensor network, the third dimension being the
imaginary time (inverse temperature) $\beta$. Coarse-graining the network along
$\beta$ results in an accurate 2D projected entangled-pair operator (PEPO) with
a finite bond dimension. The coarse-graining is performed by a tree tensor
network of isometries that are optimized variationally to maximize the accuracy
of the PEPO. The algorithm is applied to the two-dimensional Hubbard model on
an infinite square lattice. Benchmark results are obtained that are consistent
with the best cluster dynamical mean-field theory and power series expansion in
the regime of parameters where they yield mutually consistent results.


title:
A multifrequency MUSIC algorithm for locating small inhomogeneities in
  inverse scattering

abstract:
  We consider an inverse scattering problem for time-harmonic acoustic or
electromagnetic waves. The goal is to localize several small penetrable objects
embedded inside an otherwise homogeneous background medium from observations of
far field patterns of scattered fields corresponding to plane wave incident
fields with one fixed incident direction but several different frequencies.
Taking advantage of the smallness of the scatterers with respect to wave length
we utilize an asymptotic representation formula for the far field pattern to
design and analyze a MUSIC-type reconstruction method for this setup. We
establish lower bounds on the number of frequencies and receiver directions
required to recover the number and the positions of the scatterers for a given
configuration by the reconstruction algorithm. Furthermore we apply the method
to the practically interesting case of multifrequency backscattering data.
Numerical examples are presented to document the potentials and limitations of
this approach.


title:
Unravelling the physical meaning of the Jaffe-Manohar decomposition of
  the nucleon spin

abstract:
  A general consensus now is that there are two physically inequivalent
complete decompositions of the nucleon spin, i.e. the decomposition of the
canonical type and that of mechanical type. The well-known Jaffe-Manohar
decomposition is of the former type. Unfortunately, there is a wide-spread
misbelief that this decomposition matches the partonic picture, which states
that motion of quarks in the nucleon is approximately free. In the present
monograph, we reveal that this understanding is not necessarily correct and
that the Jaffe-Manohar decomposition is not such a decomposition, which
natively reflects the intrinsic (or static) orbital angular momentum structure
of the nucleon.


title:
Strong coupling between two spin ensembles via a large Josephson
  junction

abstract:
  We propose a method to achieve strong coupling between a spin ensemble and a
large Josephson junctions (LJJ). Then, the strong coupling between two spin
ensembles can be induced by a LJJ. A non-adiabatic holonomic single-qubit
quantum gates is realized. Moreover, with the dispersive interaction between
the spin ensembles and the LJJ, the high-fidelity two-qubit phase gate can be
implemented with two spin ensembles within an operation time 0.41 ns and $\pi$
phase-swap gate can be realized within an operation time 103.11 ns with a high
fidelity greater than 99%.


title:
On the constituent counting rules for hard exclusive processes involving
  multiquark states

abstract:
  At high energies, the cross section of a hard exclusive process at finite
scattering angle falls off as a negative power of the center-of-mass energy
$\sqrt{s}$. If all involved quark-gluon compositions undergo hard momentum
transfers, the scaling of the fall-off is determined by the underlying valence
structures of the initial and final states, known as the constituent counting
rules. It was argued in the literature that the counting rules are a powerful
tool to determine the valence degrees of freedom inside multiquark states when
applied to exclusive production processes. However, we demonstrate that for
hadrons with hidden flavors the naive application of the constituent counting
rules is problematic, since it is not mandatory for all components to
participate the hard scattering at the scale $\sqrt{s}$. The correct scaling
rules can be obtained easily by using effective field theory. A few examples
involving the $Z_c(3900)^\pm$ and $X(3872)$ are discussed.


title: Steady states of elastically-coupled extensible double-beam systems

abstract:
  Given $\beta\in\mathbb{R}$ and $\varrho,k>0$, we analyze an abstract version
of the nonlinear stationary model in dimensionless form $$\begin{cases} u"" -
\Big(\beta+ \varrho\int_0^1 |u'(s)|^2\,{\rm d} s\Big)u" +k(u-v) = 0 v"" -
\Big(\beta+ \varrho\int_0^1 |v'(s)|^2\,{\rm d} s\Big)v" -k(u-v) = 0 \end{cases}
$$ describing the equilibria of an elastically-coupled extensible double-beam
system subject to evenly compressive axial loads. Necessary and sufficient
conditions in order to have nontrivial solutions are established, and their
explicit closed-form expressions are found. In particular, the solutions are
shown to exhibit at most three nonvanishing Fourier modes. In spite of the
symmetry of the system, nonsymmetric solutions appear, as well as solutions for
which the elastic energy fails to be evenly distributed. Such a feature turns
out to be of some relevance in the analysis of the longterm dynamics, for it
may lead up to nonsymmetric energy exchanges between the two beams, mimicking
the transition from vertical to torsional oscillations.


title: General relativistic effects in quantum interference of "clocks"

abstract:
  Quantum mechanics and general relativity have been each successfully tested
in numerous experiments. However, the regime where both theories are jointly
required to explain physical phenomena remains untested by laboratory
experiments, and is also not fully understood by theory. This contribution
reviews recent ideas for a new type of experiments: quantum interference of
"clocks", which aim to test novel quantum effects that arise from time
dilation. "Clock" interference experiments could be realised with atoms or
photons in near future laboratory experiments.


title:
Heavy quark production in $pA$ collisions: the double parton scattering
  contribution

abstract:
  In this paper we estimate the double parton scattering (DPS) contribution for
the heavy quark production in $pA$ collisions at the LHC. The cross sections
for the charm and bottom production are estimated using the dipole approach and
taking into account the saturation effects, which are important for high
energies and for the scattering with a large nucleus. We compare the DPS
contribution with the single parton scattering one and demonstrate that in the
case of charm production both are similar in the kinematical range probed by
the LHC. Predictions for the rapidity range analysed by the LHCb Collaboration
are also presented. Our results indicate that the study of the DPS contribution
for the heavy quark production in $pPb$ collisions at the LHC is feasible and
can be useful to probe the main assumptions of the approach.


title: Testing the two planes of satellites in the Centaurus Group

abstract:
  The existence of satellite galaxy planes poses a major challenge for the
standard picture of structure formation with non-baryonic dark matter. Recently
Tully et al. (2015) reported the discovery of two almost parallel planes in the
nearby Cen A group using mostly high-mass galaxies (M$_B$ $<$ -10 mag) in their
analysis. Our team detected a large number of new group member candidates in
the Cen A group (M\"uller et al. 2016). This dwarf galaxy sample combined with
other recent results from the literature enables us to test the galaxy
distribution in the direction of the Cen A group and to determine the
statistical significance of the geometric alignment. Taking advantage of the
fact that the two galaxy planes lie almost edge-on along the line of sight, the
newly found 13 group members by Crnojevic et al. (2014, 2016) and our 16 new
Cen A group candidates (M\"uller et al. 2016) can be assigned relative to the
two planes. We use various statistical methods to test whether the distribution
of galaxies follows a single normal distribution or shows evidence of
bimodality as it has been reported earlier. We confirm that the data used for
the Tully et al. (2015) study support the picture of a bimodal structure.
However, when the new galaxy samples are included, the gap between the two
galaxy planes is closing and the significance level of the bimodality is
reduced. Instead, the plane that contains Cen A becomes more prominent. We
found evidence that the galaxy system around Cen A is made up of only one plane
of satellites. This plane is almost orthogonal to the dust plane of Cen A.
Accurate distances to the new dwarf galaxies will be required to measure the
precise 3D distribution of the galaxies around Cen A.


title: Experiments with Synchronizing Automata

abstract:
  We have improved an algorithm generating synchronizing automata with a large
length of the shortest reset words. This has been done by refining some known
results concerning bounds on the reset length. Our improvements make possible
to consider a number of conjectures and open questions concerning synchronizing
automata, checking them for automata with a small number of states and
discussing the results. In particular, we have verified the \v{C}ern\'y
conjecture for all binary automata with at most 12 states, and all ternary
automata with at most 8 states.


title: A new characterization of convexity with respect to Chebyshev systems

abstract:
  The notion of $n$th order convexity in the sense of Hopf and Popoviciu is
defined via the nonnegativity of the $(n+1)$st order divided differences of a
given real-valued function. In view of the well-known recursive formula for
divided differences, the nonnegativity of $(n+1)$st order divided differences
is equivalent to the $(n-k-1)$st order convexity of the $k$th order divided
differences which provides a characterization of $n$th order convexity.
  The aim of this paper is to apply the notion of higher-order divided
differences in the context of convexity with respect to Chebyshev systems
introduced by Karlin in 1968. Using a determinant identity of Sylvester, we
then establish a formula for the generalized divided differences which enables
us to obtain a new characterization of convexity with respect to Chebyshev
systems. Our result generalizes that of W\k{a}sowicz which was obtained in
2006. As an application, we derive a necessary condition for functions which
can be written as the difference of two functions convex with respect to a
given Chebyshev system.


title: Remarks on factoriality and $q$-deformations

abstract:
  We prove that the mixed $q$-Gaussian algebra $\Gamma_{Q}(H_{\mathbb{R}})$
associated to a real Hilbert space $H_{\mathbb{R}}$ and a real symmetric matrix
$Q=(q_{ij})$ with $\sup|q_{ij}|<1$, is a factor as soon as $\dim
H_{\mathbb{R}}\geq2$. We also discuss the factoriality of $q$-deformed
Araki-Woods algebras, in particular showing that the $q$-deformed Araki-Woods
algebra $\Gamma_{q}(H_{\mathbb{R}},U_{t})$ given by a real Hilbert space
$H_{\mathbb{R}}$ and a strongly continuous group $U_{t}$ is a factor when $\dim
H_{\mathbb{R}}\geq2$ and $U_{t}$ admits an invariant eigenvector.


title: Fractional Diffusion Limits of Non-Classical Transport Equations

abstract:
  We establish asymptotic diffusion limits of the non-classical transport
equation derived in [E. W. Larsen, A generalized Boltzmann equation for
non-classical particle transport, Joint international topical meeting on
mathematics & computation and supercomputing in nuclear applications, 2007]. By
introducing appropriate scaling parameters, the limits will be either regular
or fractional diffusion equations depending on the tail behaviour of the
path-length distribution. Our analysis uses the Fourier transform combined with
a moment method. We conclude with remarks on the diffusion limit of the
periodic Lorentz gas equation.


title: A new B-L model without right-handed neutrinos

abstract:
  We propose and study a novel extension of the Standard Model based on the B-L
gauge symmetry that can account for dark matter and neutrino masses. In this
model, right-handed neutrinos are absent and the gauge anomalies are canceled
instead by four chiral fermions with fractional B-L charges. After the breaking
of $U(1)_{B-L}$, these fermions arrange themselves into two Dirac particles,
the lightest of which is automatically stable and plays the role of the dark
matter. We determine the regions of the parameter space consistent with the
observed dark matter density and show that they can be partially probed via
direct and indirect dark matter detection or collider searches at the LHC.
Neutrino masses, on the other hand, can be explained by a variant of the
type-II seesaw mechanism involving one of the two scalar fields responsible for
the dark matter mass.


title: The Extended Mapping Class Group Can Be Generated by Two Torsions

abstract:
  Let $S_g$ be the closed oriented surface of genus g and let
$\text{Mod}^{\pm}(S_g)$ be the extended mapping class group of $S_g$. When the
genus is at least 5, we prove that $\text{Mod}^{\pm}(S_g)$ can be generated by
two torsion elements. One of these generators is an order 2 element, and the
other one is an order 4g+2 element.


title: State complexity of multiple catenation

abstract:
  We improve some results relative to the state complexity of the multiple
catenation described by Gao and Yu. In particular we nearly divide by 2 the
size of the alphabet needed for witnesses. We also give some refinements to the
algebraic expression of the state complexity, which is especially complex with
this operation. We obtain these results by using peculiar DFAs defined by
Brzozowski.


title: Adaptive Gray World-Based Color Normalization of Thin Blood Film Images

abstract:
  This paper presents an effective color normalization method for thin blood
film images of peripheral blood specimens. Thin blood film images can easily be
separated to foreground (cell) and background (plasma) parts. The color of the
plasma region is used to estimate and reduce the differences arising from
different illumination conditions. A second stage normalization based on the
database-gray world algorithm transforms the color of the foreground objects to
match a reference color character. The quantitative experiments demonstrate the
effectiveness of the method and its advantages against two other general
purpose color correction methods: simple gray world and Retinex.


title: Proceedings 3rd Workshop on Horn Clauses for Verification and Synthesis

abstract:
  This volume contains the proceedings of HCVS 2016, the Third Workshop on Horn
Clauses for Verification and Synthesis which was held on April 3, 2016 in
Eindhoven, The Netherlands as a satellite event of the European Joint
Conferences on Theory and Practice of Software (ETAPS 2016). Many program
verification and synthesis problems of interest can be modeled directly using
Horn clauses and many recent advances in the CLP and CAV communities have
centered around efficiently solving problems presented as Horn clauses. The
Third Workshop on Horn Clauses for Verification and Synthesis was organised
with the aim to bring together researchers working in the two communities of
Constraint/Logic Programming and Program Verification on the topic of Horn
clause based analysis, verification and synthesis. Horn clauses for
verification and synthesis have been advocated by these two communities in
different times and from different perspectives, and this workshop is organized
to stimulate interaction and a fruitful exchange and integration of
experiences.


title:
On the category of finite-dimensional representations of $\OSPrn$: Part
  I

abstract:
  We study the combinatorics of the category F of finite-dimensional modules
for the orthosymplectic Lie supergroup OSP(r|2n). In particular we present a
positive counting formula for the dimension of the space of homomorphism
between two projective modules. This refines earlier results of Gruson and
Serganova. Moreover, for each block B of F we construct an algebra A(B) whose
module category shares the combinatorics with B. It arises as a subquotient of
a suitable limit of type D Khovanov algebras. It will turn out that A(B) is
isomorphic to the endomorphism algebra of a minimal projective generator of B.
This provides a direct link from F to parabolic categories O of type B or D,
with maximal parabolic of type A, to the geometry of isotropic Grassmannians of
types B/D and to Springer fibres of types C/D. We also indicate why F is not
highest weight in general.


title:
Simulation of diffusive particle propagation and related TeV gamma-ray
  emission at the Galactic Center

abstract:
  Observations of the Galactic Center (GC) region in very-high-energy (VHE,
>100 GeV) gamma rays, conducted with the High Energy Stereoscopic System
(H.E.S.S.), led to the detection of an extended region of diffuse gamma-ray
emission in 2006. To date, the exact origin of this emission has remained
unclear, although a tight spatial correlation between the density distribution
of the molecular material of the Central Molecular Zone (CMZ) and the
morphology of the observed gamma-ray excess points towards a hadronic
production scenario. In this proceeding, we present a numerical study of the
propagation of high-energy cosmic rays (CRs) through a turbulent environment
such as the GC region. In our analysis, we derive an energy-dependent
parametrization for the diffusion coefficient which we use for our simulation
of the diffuse gamma-ray emission at the GC. Assuming that hadronic CRs have
been released by a single impulsive event at the center of our Galaxy, we probe
the question whether or not the interaction processes of the diffusing hadrons
with ambient matter can explain the observed diffuse gamma-ray excess. Our
results disfavor this scenario, as our analysis indicates that the diffusion
process is, on timescales compared to the typical proton lifetime at the GC
region, too slow to explain the extension of the observed emission.


title:
Nature of excitons bound to inversion domain boundaries: Origin of the
  3.45-eV luminescence lines in spontaneously formed GaN nanowires on Si(111)

abstract:
  We investigate the 3.45-eV luminescence band of spontaneously formed GaN
nanowires on Si(111) by photoluminescence and cathodoluminescence spectroscopy.
This band is found to be particularly prominent for samples synthesized at
comparatively low temperatures. At the same time, these samples exhibit a
peculiar morphology, namely, isolated long nanowires are interspersed within a
dense matrix of short ones. Cathodoluminescence intensity maps reveal the
3.45-eV band to originate primarily from the long nanowires. Transmission
electron microscopy shows that these long nanowires are either Ga polar and are
joined by an inversion domain boundary with their short N-polar neighbors, or
exhibit a Ga-polar core surrounded by a N-polar shell with a tubular inversion
domain boundary at the core/shell interface. For samples grown at high
temperatures, which exhibit a uniform nanowire morphology, the 3.45-eV band is
also found to originate from particular nanowires in the ensemble and thus
presumably from inversion domain boundaries stemming from the coexistence of N-
and Ga-polar nanowires. For several of the investigated samples, the 3.45-eV
band splits into a doublet. We demonstrate that the higher-energy component of
this doublet arises from the recombination of two-dimensional excitons free to
move in the plane of the inversion domain boundary. In contrast, the
lower-energy component of the doublet originates from excitons localized in the
plane of the inversion domain boundary. We propose that this in-plane
localization is due to shallow donors in the vicinity of the inversion domain
boundaries.


title:
Production of $\Lambda\Lambda$ and $\bar{\Lambda \text{n}}$ in central
  Pb+Pb collisions at $\sqrt{s_{NN}}$=2.76 TeV within a covariant coalescence
  model

abstract:
  We study the production of $\Lambda\Lambda$ and $\overline{\Lambda \text{n}}$
exotic states in central Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV at LHC
via both hadron and quark coalescence within a covariant coalescence model with
a blast-wave-like parametrization for the phase-space configurations of
constituent particles at freezeout. In the hadron coalescence, the two states
are considered as molecular states while they are considered as six-quark
states in the quark coalescence.For $\overline{\Lambda \text{n}}$, we find that
the yields of both molecular and six-quark states are much larger than the
experimental upper-limits. For $\Lambda\Lambda$, while the molecule-state yield
is much larger than the experimental upper-limits, the six-quark-state yield
could be lower than the upper-limits. The higher molecule-state yields are
mainly due to the large contribution of short-lived strong resonance decays
into (anti-)nucleons and (anti-)$\Lambda$ which can significantly enhance the
molecule-state yields of $\Lambda\Lambda$ and $\overline{\Lambda \text{n}}$ via
hadron coalescence. Our results suggest that the current experimental
measurement at LHC cannot exclude the existence of the $\Lambda\Lambda$ as an
exotic six-quark state, and if $\Lambda\Lambda$ is a six-quark state, it is
then on the brink of being discovered.


title: Magnetic moment evolution and spin freezing in doped BaFe$_{2}$As$_{2}$

abstract:
  Fe-K$_{\beta}$ X-ray emission spectroscopy measurements reveal an asymmetric
doping dependence of the magnetic moments $\mu_\text{bare}$ in electron- and
hole-doped BaFe$_{2}$As$_{2}$. At low temperature, $\mu_\text{bare}$ is nearly
constant in hole-doped samples, whereas it decreases upon electron doping.
Increasing temperature substantially enhances $\mu_\text{bare}$ in the
hole-doped region, which is naturally explained by the theoretically predicted
crossover into a spin-frozen state. Our measurements demonstrate the importance
of Hund's coupling and electronic correlations, especially for hole-doped
BaFe$_{2}$As$_{2}$, and the inadequacy of a fully localized or fully itinerant
description of the 122 family of Fe pnictides.


title:
Comparing cluster-level dynamic treatment regimens using sequential,
  multiple assignment, randomized trials: Regression estimation and sample size
  considerations

abstract:
  Cluster-level dynamic treatment regimens can be used to guide sequential,
intervention or treatment decision-making at the cluster level in order to
improve outcomes at the individual or patient-level. In a cluster-level DTR,
the intervention or treatment is potentially adapted and re-adapted over time
based on changes in the cluster that could be impacted by prior intervention,
including based on aggregate measures of the individuals or patients that
comprise it. Cluster-randomized sequential multiple assignment randomized
trials (SMARTs) can be used to answer multiple open questions preventing
scientists from developing high-quality cluster-level DTRs. In a
cluster-randomized SMART, sequential randomizations occur at the cluster level
and outcomes are at the individual level. This manuscript makes two
contributions to the design and analysis of cluster-randomized SMARTs: First, a
weighted least squares regression approach is proposed for comparing the mean
of a patient-level outcome between the cluster-level DTRs embedded in a SMART.
The regression approach facilitates the use of baseline covariates which is
often critical in the analysis of cluster-level trials. Second, sample size
calculators are derived for two common cluster-randomized SMART designs for use
when the primary aim is a between-DTR comparison of the mean of a continuous
patient-level outcome. The methods are motivated by the Adaptive Implementation
of Effective Programs Trial, which is, to our knowledge, the first-ever
cluster-randomized SMART in psychiatry.


title:
Enhanced Star Formation of Less Massive Galaxies in a Proto-Cluster at
  z=2.5

abstract:
  We investigate a correlation between star-formation rate (SFR) and stellar
mass for Halpha emission line galaxies (HAEs) in one of the richest
proto-clusters ever known at z~2.5, USS 1558-003 proto-cluster. This study is
based on a 9.7-hour narrow-band imaging data with MOIRCS on the Subaru
telescope. We are able to construct a sample, in combination with additional
H-band data taken with WFC3 on Hubble Space Telescope (HST), of 100 HAEs
reaching the dust-corrected SFRs down to 3 Msun/yr and the stellar masses down
to $10^{8.0}$ Msun. We find that while the star-forming galaxies with
>$10^{9.3}$ Msun are located on the universal SFR-mass main sequence
irrespective of the environment, less massive star-forming galaxies with
<$10^{9.3}$ Msun show a significant upward scatter from the main sequence in
this proto-cluster. This suggests that some less massive galaxies are in a
starburst phase, although we do not know yet if this is due to environmental
effects.


title:
A flat spectrum candidate for a track-type high energy neutrino emission
  event, the case of blazar PKS 0723-008

abstract:
  By cross-correlating both the Parkes Catalogue and the Second Planck
Catalogue of Compact Sources with the arrival direction of the track-type
neutrinos detected by the IceCube Neutrino Observatory, we find the
flat-spectrum blazar PKS 0723-008 as a good candidate for the high-energy
neutrino event 5 (ID5). Apart from its coordinates matching those of ID5, PKS
0723-008 exhibits further interesting radio properties. Its spectrum is flat up
to high Planck frequencies, and it produced a fivefold-increased radio flux
density through the last decade. Based upon these radio properties we propose a
scenario of binary black hole evolution leading to the observed high-energy
neutrino emission. The main contributing events are the spin-flip of the
dominant black hole, the formation of a new jet with significant particle
acceleration and interaction with the surrounding material, with the
corresponding increased radio flux. Doppler boosting from the underlying jet
pointing to the Earth makes it possible to identify the origin of the
neutrinos, so the merger itself is the form of an extended flat-spectrum radio
emission, a key selection criterion to find traces of this complex process.


title:
Local Petrovskii lacunas at parabolic singular points of wavefronts of
  strictly hyperbolic PDE's

abstract:
  We enumerate the local Petrovskii lacunas (that is, the domains of local
regularity of the principal fundamental solutions) of strictly hyperbolic PDE's
with constant coefficients in $R^N$ at the parabolic singular points of their
wavefronts. These points form the next difficult family of classes of the
natural classification of singular points after the so-called simple
singularities, studied previously.
  Also we promote a computer program counting for topologically different
morsifications of critical points of smooth functions, and hence also for local
components of the complement of a generic wavefront at its singular points.


title:
Lie groupoids and algebroids applied to the study of uniformity and
  homogeneity of material bodies

abstract:
  A Lie groupoid, called \textit{material Lie groupoid}, is associated in a
natural way to any elastic material. The corresponding Lie algebroid, called
\textit{material algebroid}, is used to characterize the uniformity and the
homogeneity properties of the material. The relation to previous results in
terms of $G-$structures is discussed in detail. An illustrative example is
presented as an application of the theory.


title: On arithmetic lattices in the plane

abstract:
  We investigate similarity classes of arithmetic lattices in the plane. We
introduce a natural height function on the set of such similarity classes, and
give asymptotic estimates on the number of all arithmetic similarity classes,
semi-stable arithmetic similarity classes, and well-rounded arithmetic
similarity classes of bounded height as the bound tends to infinity. We also
briefly discuss some properties of the $j$-invariant corresponding to
similarity classes of planar lattices.


title:
Persistence probabilities and a decorrelation inequality for the
  Rosenblatt process and Hermite processes

abstract:
  We study persistence probabilities of Hermite processes. As a tool, we derive
a general decorrelation inequality for the Rosenblatt process, which is
reminiscent of Slepian's lemma for Gaussian processes or the FKG inequality and
which may be of independent interest. This allows to compute the persistence
exponent for the Rosenblatt process. For general Hermite processes, we derive
upper and lower bounds for the persistence probabilites with the conjectured
persistence exponent, but with non-matching boundaries.

categories: math.PR cond-mat.stat-mech math-ph math.MP


title:
Gauged $U(1)_{L_\mu - L_\tau}$ model in light of muon $g-2$ anomaly,
  neutrino mass and dark matter phenomenology

abstract:
  Gauged $U(1)_{L_\mu - L_\tau}$ model has been advocated for a long time in
light of muon $g-2$ anomaly, which is a more than $3\sigma$ discrepancy between
the experimental measurement and the standard model prediction. We augment this
model with three right-handed neutrinos $(N_e, N_\mu, N_\tau)$ and a
vector-like singlet fermion $(\chi)$ to explain simultaneously the non-zero
neutrino mass and dark matter content of the Universe, while satisfying
anomalous muon $g-2$ constraints. It is shown that in a large parameter space
of this model we can explain positron excess, observed at PAMELA, Fermi-LAT and
AMS-02, through dark matter annihilation, while satisfying the relic density
and direct detection constraints.


title:
A Principal-Agent Model of Trading Under Market Impact -Crossing
  networks interacting with dealer markets-

abstract:
  We use a principal-agent model to analyze the structure of a book-driven
dealer market when the dealer faces competition from a crossing network or dark
pool. The agents are privately informed about their types (e.g. their
portfolios), which is something that the dealer must take into account when
engaging his counterparties. Instead of trading with the dealer, the agents may
chose to trade in a crossing network. We show that the presence of such a
network results in more types being serviced by the dealer and that, under
certain conditions and due to reduced adverse selection effects, the book's
spread shrinks. We allow for the pricing on the dealer market to determine the
structure of the crossing network and show that the same conditions that lead
to a reduction of the spread imply the existence of an equilibrium
book/crossing network pair.


title: Shapes of unit lattices and escape of mass

abstract:
  We study the collection of points on the modular surface obtained from the
logarithm embeddings of the groups of units in totally real cubic number
fields. We conjecture that this set is dense and show that its closure contains
countably many explicit curves and give a strategy to show that it has
non-empty interior. The results are obtained by constructing explicit families
of orders (generalizing the so called simplest cubic fields) and calculating
their groups of units. We also address the question of escape of mass for the
compact orbits of the diagonal group associated to these orders.


title:
Complex heavy-quark potential and Debye mass in a gluonic medium from
  lattice QCD

abstract:
  We improve and extend our study of the complex in-medium heavy quark
potential and its Debye mass $m_D$ in a gluonic medium with a finer scan around
the deconfinement transition and newly generated ensembles closer to the
thermodynamic limit. On the lattices with larger physical volume, Re[V] shows
signs of screening, i.e. a finite $m_D$, only in the deconfined phase,
reminiscent of a genuine phase transition. Consistently Im[V] exhibits nonzero
values also only above $T_C$. We compare the behavior of Re[V] with the color
singlet free-energies that have been used historically to extract the Debye
mass. An effective coupling constant is computed to assess the residual
influence of the confining part of the potential at $T>0$. Our previous finding
of a gradual screening of Re[V] around $T_C$ on finer lattices is critically
reassessed and interpreted to originate from finite volume artifacts that
affect the deployed $\beta=7$, $\xi_b=3.5$ parameter set at $N_s=32$.


title: Topological pumping of photons in nonlinear resonator arrays

abstract:
  We show how to implement topological or Thouless pumping of interacting
photons in one dimensional nonlinear resonator arrays, by simply modulating the
frequency of the resonators periodically in space and time. The interplay
between interactions and the adiabatic modulations enables robust transport of
Fock states with few photons per site. We analyze the transport mechanism via
an effective analytic model and study its topological properties and its
protection to noise. We conclude by a detailed study of an implementation with
existing circuit QED architectures.


title: Two-instanton approximation to the Coulomb blockade problem

abstract:
  We develop the two-instanton approximation to the current-voltage
characteristic of a single electron transistor within the
Ambegaokar-Eckern-Sch\"on model. We determine the temperature and gate voltage
dependence of the Coulomb blockade oscillations of the conductance and the
effective charge. We find that a small (in comparison with the charging energy)
bias voltage leads to significant suppression of the Coulomb blockade
oscillations and to appearance of the bias-dependent phase shift.


title: Functional Cliques in Developmentally Correlated Neural Networks

abstract:
  We consider a sparse random network of excitatory leaky integrate-and-fire
neurons with short-term synaptic depression. Furthermore to mimic the dynamics
of a brain circuit in its first stages of development we introduce for each
neuron correlations among in-degree and out-degree as well as among
excitability and the corresponding total degree, We analyze the influence of
single neuron stimulation and deletion on the collective dynamics of the
network. We show the existence of a small group of neurons capable of
controlling and even silencing the bursting activity of the network. These
neurons form a functional clique since only their activation in a precise order
and within specific time windows is capable to ignite population bursts.


title: Quark mass dependence of H-dibaryon in $\Lambda\Lambda$ scattering

abstract:
  We study the quark mass dependence of the H-dibaryon in the strangeness
$S=-2$ baryon-baryon scattering. A low-energy effective field theory is used to
describe the coupled-channel scattering, in which the quark mass dependence is
incorporated so as to reproduce the lattice QCD data by the HAL QCD
collaboration in the SU(3) limit. We point out the existence of the
Castillejo-Dalitz-Dyson (CDD) pole in the $\Lambda\Lambda$ scattering amplitude
below the threshold in the SU(3) limit, which may cause the Ramsauer-Townsend
effect near the $N\Xi$ threshold at the physical point. The H-dibaryon is
unbound at the physical point, and a resonance appears just below the $N\Xi$
threshold. As a consequence of the coupled-channel dynamics, the pole
associated with the resonance is not continuously connected to the bound state
in the SU(3) limit. Through the extrapolation in quark masses, we show that the
unitary limit of the $\Lambda\Lambda$ scattering is achieved between the
physical point and the SU(3) limit. We discuss the possible realization of the
"H-matter" in the unphysical quark mass region.


title: Pulse Width Modulation for Simulating Time-Dependent Quantum Systems

abstract:
  This paper proposes a numerical method for solving time-dependent Schrodinger
equations with finite spectral bandwidth, which applies to both periodic and
non-periodic cases. We introduce the concept of Pulse Width Modulation (PWM),
which is broadly used in classical control engineering, to simulate
time-dependent quantum dynamics by switching between a finite number of
constant Hamiltonians. The switching timings can be programmed to improve the
precision and save computational resources. The effectiveness of the PWM method
is demonstrated by numerical simulations, which shows that it is faster and
more robust than the standard piecewise constant control systems. Moreover, we
also propose the realization of PWM method for potential implementation in
experimental systems.


title: On Arithmetical Truth of the Self-Referential Sentences

abstract:
  We take an argument of G\"odel's from his ground-breaking 1931 paper,
generalize it, and examine its validity. The argument in question is this: the
sentence $G$ says about itself that it is not provable, and $G$ is indeed not
provable; therefore, $G$ is true.


title:
Deep observations of the Super-CLASS super-cluster at 325 MHz with the
  GMRT: the low-frequency source catalogue

abstract:
  We present the results of 325 MHz GMRT observations of a super-cluster field,
known to contain five Abell clusters at redshift $z \sim 0.2$. We achieve a
nominal sensitivity of $34\,\mu$Jy beam$^{-1}$ toward the phase centre. We
compile a catalogue of 3257 sources with flux densities in the range
$183\,\mu\rm{Jy}\,-\,1.5\,\rm{Jy}$ within the entire $\sim 6.5$ square degree
field of view. Subsequently, we use available survey data at other frequencies
to derive the spectral index distribution for a sub-sample of these sources,
recovering two distinct populations -- a dominant population which exhibit
spectral index trends typical of steep-spectrum synchrotron emission, and a
smaller population of sources with typically flat or rising spectra. We
identify a number of sources with ultra-steep spectra or rising spectra for
further analysis, finding two candidate high-redshift radio galaxies and three
gigahertz-peaked-spectrum radio sources. Finally, we derive the
Euclidean-normalised differential source counts using the catalogue compiled in
this work, for sources with flux densities in excess of $223 \, \mu$Jy. Our
differential source counts are consistent with both previous observations at
this frequency and models of the low-frequency source population. These
represent the deepest source counts yet derived at 325 MHz. Our source counts
exhibit the well-known flattening at mJy flux densities, consistent with an
emerging population of star-forming galaxies; we also find marginal evidence of
a downturn at flux densities below $308 \, \mu$Jy, a feature so far only seen
at 1.4 GHz.