title: The IBM Quantum Computer and the IBM Quantum Experience

abstract:
  The announcement of a quantum computer that can be accessed remotely by
anyone from its laptop is a big event for the quantum computation scientist. In
this work we present the International Business Machines (IBM) quantum computer
and its platform IBM Quantum Experience (IBM-QE) as a didactic proposal in
quantum computation and information. In addition we also consider this paper as
scientific divulgation of the IMB advertisement. In this paper we show the main
tool (quantum gates) present in the IBM-QE and, through a simple strategy, we
discuss about a possible decoherence source in the IBM 5 q-bit chips. As an
example of application of our study, we show how to implement the quantum
teleportation using the IBM-QE.


title: Troubles with the radiation reaction in electrodynamics

abstract:
  The dynamics of a radiating charge is one of the oldest unsettled problems in
classical physics. The standard Lorentz-Abraham-Dirac (LAD) equation of motion
is known to suffer from several pathologies and ambiguities. This paper briefly
reviews these issues, and reports on a new model that fixes these difficulties
in a natural way. This model is based on a hypothesis that there is an
infinitesimal time delay between action and reaction. This can be related to
Feynman's regularization scheme, leading to a quasi-local QED with a natural UV
cutoff, hence without the need for renormalization as the divergences are
absent. Besides leading to a pathology-free equation of motion, the new model
predicts a modification of the Larmor formula that is testable with current and
near future ultra-intense lasers.


title:
Polarization Squeezing in Degenerate Parametric Amplification of
  Coherent Light

abstract:
  We study polarization squeezing of a light beam initially in the coherent
state using the nonlinear interaction hamiltonian $ H=k\big(\hat
a_{x}^{\dagger2}+{\hat a_{x}}^2\big)$. For the degree of polarization
squeezing, we use a definition written in the final form by the authors and
also used in earlier papers. We find that the polarization squeezing can be
very high and the degree of polarization squeezing can be less than unity by a
very small amount. We achieve the polarization squeezing even for very low beam
intensity under some conditions involving phase angles in the polarization
modes.


title:
A proof of the butterfly theorem using the scale factor between the two
  wings

abstract:
  We give a new proof of the butterfly theorem, based on the use of several
expressions involving the scale factor between the two wings.


title: Efficient Certified Resolution Proof Checking

abstract:
  We present a novel propositional proof tracing format that eliminates complex
processing, thus enabling efficient (formal) proof checking. The benefits of
this format are demonstrated by implementing a proof checker in C, which
outperforms a state-of-the-art checker by two orders of magnitude. We then
formalize the theory underlying propositional proof checking in Coq, and
extract a correct-by-construction proof checker for our format from the
formalization. An empirical evaluation using 280 unsatisfiable instances from
the 2015 and 2016 SAT competitions shows that this certified checker usually
performs comparably to a state-of-the-art non-certified proof checker. Using
this format, we formally verify the recent 200 TB proof of the Boolean
Pythagorean Triples conjecture.


title:
Spectral Angle Based Unary Energy Functions for Spatial-Spectral
  Hyperspectral Classification using Markov Random Fields

abstract:
  In this paper, we propose and compare two spectral angle based approaches for
spatial-spectral classification. Our methods use the spectral angle to generate
unary energies in a grid-structured Markov random field defined over the pixel
labels of a hyperspectral image. The first approach is to use the exponential
spectral angle mapper (ESAM) kernel/covariance function, a spectral angle based
function, with the support vector machine and the Gaussian process classifier.
The second approach is to directly use the minimum spectral angle between the
test pixel and the training pixels as the unary energy. We compare the proposed
methods with the state-of-the-art Markov random field methods that use support
vector machines and Gaussian processes with squared exponential
kernel/covariance function. In our experiments with two datasets, it is seen
that using minimum spectral angle as unary energy produces better or comparable
results to the existing methods at a smaller running time.


title:
${\Upsilon}(1S)$ ${\to}$ $B_{c}{\pi}$, $B_{c}K$ decays with perturbative
  QCD approach

abstract:
  With the potential prospects of the ${\Upsilon}(1S)$ at high-luminosity
dedicated heavy-flavor factories, the bottom-changing ${\Upsilon}(1S)$ ${\to}$
$B_{c}{\pi}$, $B_{c}K$ weak decays are studied with the pQCD approach. It is
found that branching ratio for the color-favored and CKM-favored
${\Upsilon}(1S)$ ${\to}$ $B_{c}{\pi}$ decay can reach up to ${\cal
O}(10^{-11})$. So the ${\Upsilon}(1S)$ ${\to}$ $B_{c}{\pi}$ decay might be
measured promisingly by the future experiments.


title: Multitask Learning of Vegetation Biochemistry from Hyperspectral Data

abstract:
  Statistical models have been successful in accurately estimating the
biochemical contents of vegetation from the reflectance spectra. However, their
performance deteriorates when there is a scarcity of sizable amount of ground
truth data for modeling the complex non-linear relationship occurring between
the spectrum and the biochemical quantity. We propose a novel Gaussian process
based multitask learning method for improving the prediction of a biochemical
through the transfer of knowledge from the learned models for predicting
related biochemicals. This method is most advantageous when there are few
ground truth data for the biochemical of interest, but plenty of ground truth
data for related biochemicals. The proposed multitask Gaussian process
hypothesizes that the inter-relationship between the biochemical quantities is
better modeled by using a combination of two or more covariance functions and
inter-task correlation matrices. In the experiments, our method outperformed
the current methods on two real-world datasets.


title: Mathematical Theory for Quantum Phase Transitions

abstract:
  Quantum Phase Transition (QPT) is a phase transition between different
quantum states by adjusting some control parameters. Based on the Principle of
Hamilton Dynamics (PHD) and the Principle of Lagrangian Dynamics (PLD), a
general QPT model is established. Also, a definition of QPT is given. The
important point is that the QPT model is applied to Bose-Einstein Condensate
(BEC) and the corresponding bifurcation solutions (i.e., the quantum states)
are obtained by using steady state bifurcation theory.


title: Enhanced spin-orbit torque via modulation of spin current absorption

abstract:
  The magnitude of spin-orbit torque (SOT), exerted to a ferromagnet (FM) from
an adjacent heavy metal (HM), strongly depends on the amount of spin currents
absorbed in the FM. We exploit the large spin absorption at the Ru interface to
manipulate the SOTs in HM/FM/Ru multilayers. While the FM thickness is smaller
than its spin dephasing length of 1.2 nm, the top Ru layer largely boosts the
absorption of spin currents into the FM layer and substantially enhances the
strength of SOT acting on the FM. Spin-pumping experiments induced by
ferromagnetic resonance support our conclusions that the observed increase in
the SOT efficiency can be attributed to an enhancement of the spin-current
absorption. A theoretical model that considers both reflected and transmitted
mixing conductances at the two interfaces of FM is developed to explain the
results.


title:
Finite Basis for Radical Well-Mixed Difference Ideals Generated by
  Binomials

abstract:
  In this paper, we prove a finite basis theorem for radical well-mixed
difference ideals generated by binomials. As a consequence, every strictly
ascending chain of radical well-mixed difference ideals generated by binomials
in a difference polynomial ring is finite, which answers a question raised by
E. Hrushovski in the binomial case.


title:
Relating Microstructure and Particle-level Stress in Colloidal Crystals
  Under Increased Confinement

abstract:
  The mechanical properties of crystalline materials can be substantially
modified under confinement. Such modified macroscopic properties are usually
governed by the altered microstructures and internal stress fields. Here, we
use a parallel plate geometry to apply a quasi-static squeeze flow crushing a
colloidal polycrystal while simultaneously imaging it with confocal microscopy.
The confocal images are used to quantify the local structure order and, in
conjunction with Stress Assessment from Local Structural Anisotropy (SALSA),
determine the stress at the single-particle scale. We find that during
compression, the crystalline regions break into small domains with different
geometric packing. These domains are characterized by a pressure and deviatoric
stress that are highly localized with correlation lengths that are half those
found in bulk. Furthermore, the mean deviatoric stress almost doubles,
suggesting a higher brittleness in the highly-confined samples.


title:
Sensitivity of stellar electron-capture rates to parent neutron number:
  A case study on a continuous chain of twenty Vanadium isotopes

abstract:
  Gamow-Teller (GT) strength distributions (B(GT)) in electron-capture (EC)
daughters stemming from the parent ground state are computed with the
shell-model in the full pf-shell space, with quasi-particle random-phase
approximation (QRPA) in the formalism of Krumlinde and M\"oller and with an
Approximate Method (AM) for assigning an effective B(GT). These are compared to
data available from decay and charge-exchange (CE) experiments across titanium
isotopes in the pf-shell from A=43 to A=62, the largest set available for any
chain of isotopes in the pf-shell. The present study is the first to examine
B(GT) and the associated EC rates across a particular chain of isotopes with
the purpose of examining rate sensitivities as neutron number increases. EC
rates are also computed for a wide variety of stellar electron densities and
temperatures providing concise estimates of the relative size of rate
sensitivities for particular astrophysical scenarios. This work underscores the
astrophysical motivation for CE experiments in inverse kinematics for nuclei
away from stability at the luminosities of future Radioactive Ion Beam
Facilities.


title:
A Finite-Element Coarse-Grid Projection Method: A Dual Acceleration/Mesh
  Refinement Tool for Incompressible Flows

abstract:
  Coarse grid projection (CGP) methodology is a novel multigrid method for
systems involving decoupled nonlinear evolution equations and linear elliptic
Poisson equations. The nonlinear equations are solved on a fine grid and the
linear equations are solved on a corresponding coarsened grid. Mapping
operators execute data transfer between the grids. The CGP framework is
constructed upon spatial and temporal discretization schemes. This framework
has been established for finite volume/difference discretizations as well as
explicit time integration methods. In this article we present for the first
time a version of CGP for finite element discretizations, which uses a
semi-implicit time integration scheme. The mapping functions correspond to the
finite-element shape functions. With the novel data structure introduced, the
mapping computational cost becomes insignificant. We apply CGP to
pressure-correction schemes used for the incompressible Navier-Stokes flow
computations. This version is validated on standard test cases with realistic
boundary conditions using unstructured triangular meshes. We also pioneer
investigations of the effects of CGP on the accuracy of the pressure field. It
is found that although CGP reduces the pressure field accuracy, it preserves
the accuracy of the pressure gradient and thus the velocity field, while
achieving speedup factors ranging from approximately 2 to 30. Exploring the
influence of boundary conditions on CGP, the minimum speedup occurs for
velocity Dirichlet boundary conditions, while the maximum speedup occurs for
open boundary conditions. We discuss the CGP method as a guide for partial mesh
refinement of incompressible flow computations and show its application for
simulations of flow over a backward-facing step and flow past a cylinder.


title:
Production of charmed baryon $\Lambda_c(2940)$ by kaon-induced reaction
  on a proton target

abstract:
  We investigate the possibility to study the charmed baryon $\Lambda_c(2940)$
by kaon-induced reaction on a proton target. By assuming the $\Lambda_c(2940)$
as a $pD^{*0}$ molecular state with spin-parity $J^{p}=1/2^{\pm}$, an effective
Lagrangian approach was adopted to calculate the cross section, the $D^0p$
invariant mass spectrum and Dalitz plot of the $\Lambda(2940)$ production. The
total cross section of the $K^{-}p\to\Lambda_c(2940)D_s^{-}$ reaction is found
at an order of magnitude about 10 $\mu$b. By considering the sub sequential
decay $\Lambda_c(2940)\to{}D^0p$ with contributions from the $\Lambda_c(2286)$
and the $\Sigma_c(2455)$ as background, the $K^{-}p\to{}D_{s}^{-}D^{0}p$
reaction are studied. It is found that the $\Lambda_c(2940)$ is produced mainly
at forward angles. The $\Lambda_c(2940)$ signal is predicted to be significant
in the $D^0p$ invariant mass spectrum and the Dalitz plot of the
$K^{-}p\to{}D_{s}^{-}D^{0}p$ reaction. The results suggest that it is promising
to study the $\Lambda_c(2940)$ with high-energy kaon beam on a proton target in
experiment.


title:
Modeling and Analysis of Uplink Non-Orthogonal Multiple Access (NOMA) in
  Large-Scale Cellular Networks Using Poisson Cluster Processes

abstract:
  Non-orthogonal multiple access (NOMA) serves multiple users by superposing
their distinct message signals. The desired message signal is decoded at the
receiver by applying successive interference cancellation (SIC). Using the
theory of Poisson cluster process (PCP), we provide a framework to analyze
multi-cell uplink NOMA systems. Specifically, we characterize the rate coverage
probability of a NOMA user who is at rank $m$ (in terms of the distance from
its serving BS) among all users in a cell and the mean rate coverage
probability of all users in a cell. Since the signal-to-interference-plus-noise
ratio (SINR) of $m$-th user relies on efficient SIC, we consider three
scenarios, i.e., perfect SIC (in which the signals of $m-1$ interferers who are
stronger than $m$-th user are decoded successfully), imperfect SIC (in which
the signals of of $m-1$ interferers who are stronger than $m$-th user may or
may not be decoded successfully), and imperfect worst case SIC (in which the
decoding of the signal of $m$-th user is always unsuccessful whenever the
decoding of its relative $m-1$ stronger users is unsuccessful). The derived
expressions are customized to capture the performance of a user at rank $m$ in
an equivalent orthogonal multiple access (OMA) system. Finally, numerical
results are presented to validate the derived expressions.


title: Efficient verification of imperative programs using auto2

abstract:
  Auto2 is a recently introduced prover for the proof assistant Isabelle. It is
designed to be both highly customizable from within Isabelle, and also have a
powerful proof search mechanism. In this paper, we apply auto2 to the
verification of imperative programs. We describe the setup of auto2 for both
stages of the proof process: verification of a functional version of the
program, and refining to the imperative version using separation logic. As
examples, we verify several data structures, including red-black trees,
interval trees, priority queues, and union-find. We also verify several
algorithms making use of these data structures. These examples show that our
framework is able to verify complex algorithms efficiently and in a modular
manner.


title:
The Area Term of the Entanglement Entropy of a Supersymmetric $O(N)$
  Vector Model in Three Dimensions

abstract:
  We studied the leading area term of the entanglement entropy of
$\mathcal{N}=1$ supersymmetric $O(N)$ vector model in $2+1$ dimensions close to
the line of second order phase transition in the large $N$ limit. We found that
the area term is independent of the varying interaction coupling along the
critical line, unlike what is expected in a perturbative theory. Along the way,
we studied non-commuting limits $n-1\to 0$ verses UV cutoff $r\to 0$ when
evaluating the gap equation and found a match only when appropriate counter
term is introduced and whose coupling is chosen to take its fixed point value.
As a bonus, we also studied Fermionic Green's functions in the conical
background. We made the observation of a map between the problem and the
relativistic hydrogen atom.


title:
Ranking of classification algorithms in terms of mean-standard deviation
  using A-TOPSIS

abstract:
  In classification problems when multiples algorithms are applied to different
benchmarks a difficult issue arises, i.e., how can we rank the algorithms? In
machine learning it is common run the algorithms several times and then a
statistic is calculated in terms of means and standard deviations. In order to
compare the performance of the algorithms, it is very common to employ
statistical tests. However, these tests may also present limitations, since
they consider only the means and not the standard deviations of the obtained
results. In this paper, we present the so called A-TOPSIS, based on TOPSIS
(Technique for Order Preference by Similarity to Ideal Solution), to solve the
problem of ranking and comparing classification algorithms in terms of means
and standard deviations. We use two case studies to illustrate the A-TOPSIS for
ranking classification algorithms and the results show the suitability of
A-TOPSIS to rank the algorithms. The presented approach is general and can be
applied to compare the performance of stochastic algorithms in machine
learning. Finally, to encourage researchers to use the A-TOPSIS for ranking
algorithms we also presented in this work an easy-to-use A-TOPSIS web
framework.


title:
Global Stabilisation of Underactuated Mechanical Systems via PID
  Passivity-Based Control

abstract:
  In this note we identify a class of underactuated mechanical systems whose
desired constant equilibrium position can be globally stabilised with the
ubiquitous PID controller. The class is characterised via some easily
verifiable conditions on the systems inertia matrix and potential energy
function, which are satisfied by many benchmark examples. The design proceeds
in two main steps, first, the definition of two new passive outputs whose
weighted sum defines the signal around which the PID is added. Second, the
observation that it is possible to construct a Lyapunov function for the
desired equilibrium via a suitable choice of the aforementioned weights and the
PID gains and initial conditions. The results reported here follow the same
research line as [7] and [20]---bridging the gap between the Hamiltonian and
the Lagrangian formulations used, correspondingly, in these papers. Two
additional improvements to our previous works are the removal of a non-robust
cancellation of a potential energy term and the establishment of equilibrium
attractivity under weaker assumptions.


title: A novel nuclear dependence of nucleon-nucleon short-range correlations

abstract:
  A linear correlation is found between the magnitude of nucleon-nucleon
short-range correlations and the nuclear binding energy per nucleon with
pairing energy removed. By using this relation, the strengths of
nucleon-nucleon short-range correlations of some unmeasured nuclei are
predicted. Discussions on nucleon-nucleon pairing energy and nucleon-nucleon
short-range correlations are made. The found nuclear dependence of
nucleon-nucleon short-range correlations may shed some lights on the
short-range structure of nucleus.


title:
Anomalous Hall effects beyond Berry magnetic fields in a Weyl metal
  phase

abstract:
  Applying time-varying magnetic fields to Weyl metals, a pair of Weyl points
become oscillating. This oscillating monopole and anti-monopole pair gives rise
to AC Berry magnetic fields, responsible for the emergence of Berry electric
fields, which have not been discussed before at least in the context of Weyl
metals. Introducing this novel information into Boltzmann transport theory, we
find anomalous Hall effects beyond Berry magnetic fields as a fingerprint of
Berry electric fields.


title:
Lick Indices and Spectral Energy Distribution Analysis based on an M31
  Star Cluster Sample: Comparisons of Methods and Models

abstract:
  Application of fitting techniques to obtain physical parameters---such as
ages, metallicities, and $\alpha$-element to iron ratios---of stellar
populations is an important approach to understand the nature of both galaxies
and globular clusters (GCs). In fact, fitting methods based on different
underlying models may yield different results, and with varying precision. In
this paper, we have selected 22 confirmed M31 GCs for which we do not have
access to previously known spectroscopic metallicities. Most are located at
approximately one degree (in projection) from the galactic center. We performed
spectroscopic observations with the 6.5 m MMT telescope, equipped with its Red
Channel Spectrograph. Lick/IDS absorption-line indices, radial velocities,
ages, and metallicities were derived based on the $\rm EZ\_Ages$ stellar
population parameter calculator. We also applied full spectral fitting with the
ULySS code to constrain the parameters of our sample star clusters. In
addition, we performed $\chi^2_{\rm min}$ fitting of the clusters' Lick/IDS
indices with different models, including the Bruzual & Charlot models (adopting
Chabrier or Salpeter stellar initial mass functions and 1994 or 2000 Padova
stellar evolutionary tracks), the GALEV, and the Thomas et al. models. For
comparison, we collected their $UVBRIJK$ photometry from the Revised Bologna
Catalogue (v.5) to obtain and fit the GCs' spectral energy distributions
(SEDs). Finally, we performed fits using a combination of Lick/IDS indices and
SEDs. The latter results are more reliable and the associated error bars become
significantly smaller than those resulting from either our Lick/IDS
indices-only or our SED-only fits.


title:
Delay Spectrum with Phase-Tracking Arrays: Extracting the HI power
  spectrum from the Epoch of Reionization

abstract:
  The Detection of redshifted 21 cm emission from the epoch of reionization
(EoR) is a challenging task owing to strong foregrounds that dominate the
signal. In this paper, we propose a general method, based on the delay spectrum
approach, to extract HI power spectra that is applicable to tracking
observations using an imaging radio interferometer (Delay Spectrum with Imaging
Arrays (DSIA)). Our method is based on modelling the HI signal taking into
account the impact of wide field effects such as the $w$-term which are then
used as appropriate weights in cross-correlating the measured visibilities. Our
method is applicable to any radio interferometer that tracks a phase center and
could be utilized for arrays such as MWA, LOFAR, GMRT, PAPER and HERA. In the
literature the delay spectrum approach has been implemented for near-redundant
baselines using drift scan observations. In this paper we explore the scheme
for non-redundant tracking arrays, and this is the first application of delay
spectrum methodology to such data to extract the HI signal. We analyze 3 hours
of MWA tracking data on the EoR1 field. We present both 2-dimensional
($k_\parallel,k_\perp$) and 1-dimensional (k) power spectra from the analysis.
Our results are in agreement with the findings of other pipelines developed to
analyse the MWA EoR data.


title: Inferring Population Preferences via Mixtures of Spatial Voting Models

abstract:
  Understanding political phenomena requires measuring the political
preferences of society. We introduce a model based on mixtures of spatial
voting models that infers the underlying distribution of political preferences
of voters with only voting records of the population and political positions of
candidates in an election. Beyond offering a cost-effective alternative to
surveys, this method projects the political preferences of voters and
candidates into a shared latent preference space. This projection allows us to
directly compare the preferences of the two groups, which is desirable for
political science but difficult with traditional survey methods. After
validating the aggregated-level inferences of this model against results of
related work and on simple prediction tasks, we apply the model to better
understand the phenomenon of political polarization in the Texas, New York, and
Ohio electorates. Taken at face value, inferences drawn from our model indicate
that the electorates in these states may be less bimodal than the distribution
of candidates, but that the electorates are comparatively more extreme in their
variance. We conclude with a discussion of limitations of our method and
potential future directions for research.


title:
Tables of prehomogeneous modules and \'etale modules of reductive
  algebraic groups

abstract:
  This document contains tables with the classification of prehomogeneous
modules for reductive algebraic groups with up to two simple factors due to
Sato, Kimura and many others, as well as corresponding tables of the \'etale
modules appearing in this list, determined by the author. It is intended as a
convenient reference for examples of \'etale module for reductive algebraic
group.


title:
Large negative transconductance in multilayer graphene: The role of
  intersubband scattering

abstract:
  We calculate the transport properties of multilayer graphene, considering the
effect of multisubband scattering in a high density regime, where higher
subbands are occupied by charge carriers. To calculate the conductivity of
multilayer graphene, we use the coupled multiband Boltzmann transport theory
while fully incorporating the multiband scattering effects. We show that the
allowed scattering channels, screening effects, chiral nature of the electronic
structure, and type of impurity scatterings determine the transport behavior of
multilayer graphene. We find that the conductivity of multilayer graphene shows
a sudden change when the carriers begin to occupy the higher subbands, and
therefore a large negative transconductance (NTC) appears as the carrier
density varies. These phenomena arise mostly from the intersubband scattering
and the change in the density of states at the band touching density. Based on
our results, it is possible to build novel devices utilizing the large NTC in
multilayer graphene.


title:
On weak Fano manifolds with small contractions obtained by blow-ups of a
  product of projective spaces

abstract:
  We consider weak Fano manifolds with small contractions obtained by blowing
up successively curves and subvarieties of codimension 2 in products of
projective spaces. We give a classification result for a special case. In the
process of proof, we describe explicitly the structure of nef cones and compute
the self intersection numbers of anti-canonical divisors for such weak Fano
manifolds.


title: Optimization on Submanifolds of Convolution Kernels in CNNs

abstract:
  Kernel normalization methods have been employed to improve robustness of
optimization methods to reparametrization of convolution kernels, covariate
shift, and to accelerate training of Convolutional Neural Networks (CNNs).
However, our understanding of theoretical properties of these methods has
lagged behind their success in applications. We develop a geometric framework
to elucidate underlying mechanisms of a diverse range of kernel normalization
methods. Our framework enables us to expound and identify geometry of space of
normalized kernels. We analyze and delineate how state-of-the-art kernel
normalization methods affect the geometry of search spaces of the stochastic
gradient descent (SGD) algorithms in CNNs. Following our theoretical results,
we propose a SGD algorithm with assurance of almost sure convergence of the
methods to a solution at single minimum of classification loss of CNNs.
Experimental results show that the proposed method achieves state-of-the-art
performance for major image classification benchmarks with CNNs.


title:
DeepSpace: An Online Deep Learning Framework for Mobile Big Data to
  Understand Human Mobility Patterns

abstract:
  In the recent years, the rapid spread of mobile device has create the vast
amount of mobile data. However, some shallow-structure models such as support
vector machine (SVM) have difficulty dealing with high dimensional data with
the development of mobile network. In this paper, we analyze mobile data to
predict human trajectories in order to understand human mobility pattern via a
deep-structure model called "DeepSpace". To the best of out knowledge, it is
the first time that the deep learning approach is applied to predicting human
trajectories. Furthermore, we develop the vanilla convolutional neural network
(CNN) to be an online learning system, which can deal with the continuous
mobile data stream. In general, "DeepSpace" consists of two different
prediction models corresponding to different scales in space (the coarse
prediction model and fine prediction models). This two models constitute a
hierarchical structure, which enable the whole architecture to be run in
parallel. Finally, we test our model based on the data usage detail records
(UDRs) from the mobile cellular network in a city of southeastern China,
instead of the call detail records (CDRs) which are widely used by others as
usual. The experiment results show that "DeepSpace" is promising in human
trajectories prediction.


title: On time-reversal anomaly of 2+1d topological phases

abstract:
  We describe a method to find the anomaly of the time-reversal symmetry of
2+1d topological quantum field theories, by computing the fractional anomalous
momentum on the cross-cap background. This allows us, for example, to identify
the parameter $\nu$ mod 16 of the bulk 3+1d topological superconductor with
$\mathsf{T}^2=(-1)^F$ on whose boundary a given 2+1d time-reversal-invariant
topological phase can appear.


title:
Light flavor-singlet scalars and walking signals in $N_f=8$ QCD on the
  lattice

abstract:
  Based on the highly improved staggered quark action, we perform lattice
simulations of $N_f=8$ QCD and confirm our previous observation of a
flavor-singlet scalar meson (denoted as $\sigma$) as light as the pion and
various "walking signals" through low-lying spectra, with higher statistics,
smaller fermion masses $m_f$, and larger volumes. We measure $M_\pi$, $F_\pi$,
$M_\rho$, $M_{a_0}$, $M_{a_1}$, $M_{b_1}$, $M_N$, $M_\sigma$, $F_\sigma$,
$\langle \bar{\psi} \psi\rangle$ (both directly and through the GMOR relation),
and the string tension. The data are consistent with the spontaneously broken
phase of the chiral symmetry, in agreement with the previous results: ratios of
the quantities to $M_\pi$ monotonically increase in the smaller $m_f$ region
towards the chiral limit similarly to $N_f=4$ QCD, in sharp contrast to
$N_f=12$ QCD where the ratios become flattened. The hyperscaling relation holds
with roughly a universal value of the anomalous dimension, $\gamma_m \simeq 1$,
with a notable exception of $M_\pi$ with $\gamma_m \simeq 0.6$ as in the
previous results. This is a salient feature ("walking signal") of $N_f=8$,
unlike either $N_f=4$ which has no hyperscaling relation at all, or $N_f=12$
QCD which exhibits universal hyperscaling. We further confirm the previous
observation of the light $\sigma$ with mass comparable to the pion in the
studied $m_f$ region. In a chiral limit extrapolation of the $\sigma$ mass
using the dilaton chiral perturbation theory and also using the simple linear
fit, we find the value consistent with the 125 GeV Higgs boson within errors.
Our results suggest that the theory could be a good candidate for walking
technicolor model, having anomalous dimension $\gamma_m \simeq 1$ and a light
flavor-singlet scalar meson as a technidilaton, which can be identified with
the 125 GeV composite Higgs in $N_f=8$ one-family model.


title: Probing the Source of Proton Mass by"Unbreaking" Scale-Chiral Symmetry

abstract:
  I describe a possible scenario for the origin of proton mass in terms of
Cheshire Cat, half-skyrmions, topology change and interplay between hidden
chiral-scale symmetry and induced local symmetry. This differs from the
standard constituent-quark scenario. As the baryonic matter density is
increased toward the vector manifestation (VM) fixed-point at which the $\rho$
mass is to vanish, the effective in-medium mass ratio $m^*_\rho/m^*_N$ is to
tend to zero proportionally to $g^*_\rho$ where $g^*_\rho$ is the in-medium
hidden gauge coupling constant. I develop the thesis that the intricacy
involved in the mass generation could be decoded from experiments at RIB
accelerators and massive compact stars.


title:
Discrete Boltzmann modeling of Rayleigh-Taylor instability in
  two-component compressible flows

abstract:
  A discrete Boltzmann model (DBM) is proposed to probe the Rayleigh-Taylor
instability (RTI) in two-component compressible flows. Each species has a
flexible specific heat ratio and is described by one discrete Boltzmann
equation (DBE). Independent discrete velocities are adopted for the two DBEs.
The collision and force terms in the DBE account for the molecular collision
and external force, respectively. Two types of force terms are exploited. In
addition to recovering the modified Navier-Stokes equations in the hydrodynamic
limit, the DBM has the capability of capturing detailed nonequilibrium effects.
Furthermore, we use the DBM to investigate the dynamic process of the RTI. The
invariants of tensors for nonequilibrium effects are presented and studied. For
low Reynolds numbers, both global nonequilibrium manifestations and the growth
rate of the entropy of mixing show three stages (i.e., the reducing,
increasing, and then decreasing trends) in the evolution of the RTI. On the
other hand, the early reducing tendency is suppressed and even eliminated for
high Reynolds numbers. Relevant physical mechanisms are analyzed and discussed.


title:
The Local Bubble in the interstellar medium and the origin of the low
  energy cosmic rays

abstract:
  An analysis of the energy spectra of cosmic rays and particularly the precise
data from the AMS-02 experiment support the view about the important role of
the Local Bubble in the nearby interstellar medium. It is suggested that the
bulk of cosmic rays below about 200 GV of rigidity (momentum/charge ratio)
comes from the modest number of supernova remnants in the Local Bubble which
appear to have occurred some $10^6$ years ago and contributed to its formation.
At higher rigidities the contribution from a 'Local Source', a single supernova
remnant generated some $10^5$ years ago seems to dominate up to, at least 1000
GV.


title: On the IceCube spectral anomaly

abstract:
  Recently it was noted that different IceCube datasets are not consistent with
the same power law spectrum of the cosmic neutrinos: this is the IceCube
spectral anomaly, that suggests that they observe a multicomponent spectrum. In
this work, the main possibilities to enhance the description in terms of a
single extragalactic neutrino component are examined. The hypothesis of a
sizable contribution of Galactic high-energy neutrino events distributed as
$E^{-2.7}$ [ApJ 826, 185 (2016)] is critically analyzed and its natural
generalization is considered. The stability of the expectations is studied by
introducing free parameters, motivated by theoretical considerations and
observational facts. The upgraded model here examined has 1)~a Galactic
component with different normalization and shape $E^{- 2.4}$; 2)~an
extragalactic neutrino spectrum based on new data; 3)~a non-zero prompt
component of atmospheric neutrinos. The two key predictions of the model
concern the `high-energy starting events' collected from the Southern sky. The
Galactic component produces a softer spectrum and a testable angular
anisotropy. A second, radically different class of models, where the second
component is instead isotropic, plausibly extragalactic and with a relatively
soft spectrum, is disfavored instead by existing observations of muon neutrinos
from the Northern sky and below few 100 TeV.


title: Bergman kernel and hyperconvexity index

abstract:
  Let $\Omega\subset {\mathbb C}^n$ be a bounded domain with the hyperconvexity
index $\alpha(\Omega)>0$. Let $\varrho$ be the relative extremal function of a
fixed closed ball in $\Omega$ and set $\mu:=|\varrho|(1+|\log|\varrho||)^{-1}$,
$\nu:=|\varrho|(1+|\log|\varrho||)^n$. We obtain the following estimates for
the Bergman kernel: (1) For every $0<\alpha<\alpha(\Omega)$ and $2\le
p<2+\frac{2\alpha(\Omega)}{2n-\alpha(\Omega)}$, there exists a constant $C>0$
such that $\int_\Omega |\frac{K_\Omega(\cdot,w)}{\sqrt{K_\Omega(w)}}|^{p}\le C
|\mu(w)|^{-\frac{(p-2) n}\alpha}$ for all $w\in \Omega$. (2) For every $0<r<1$,
there exists a constant $C>0$ such that $
  \frac{|K_\Omega(z,w)|^2}{K_\Omega(z)K_\Omega(w)}\le C
(\min\{\frac{\nu(z)}{\mu(w)},\frac{\nu(w)}{\mu(z)}\})^r $ for all $z,w\in
\Omega$. Various application of these estimates are given.


title: Next Generation Muon g-2 Experiment at FNAL

abstract:
  The precise measurement of the muon anomalous magnetic moment
$a_\mathrm{\mu}$ has stimulated much theoretical and experimental efforts over
more than six decades. The last experiment at Brookhaven National Laboratory,
Upton, NY, USA obtained a value more than three standard deviations larger than
predicted by the Standard Model of particle physics, and is one of the
strongest hints for physics beyond the Standard Model. A new experiment at
Fermi National Accelerator Laboratory, Batavia, IL, USA to measure
$a_\mathrm{\mu}$ with fourfold increased precision to $140\,\mathrm{ppb}$ is
currently in its commissioning phase. While the new experiment will reuse the
$1.45\,\mathrm{T}$ superconducting muon storage ring which was shipped from
Brookhaven National Laboratory, most of the other instrumentation of the
experiment will be new. This will allow the experiment to make efficient use of
the significantly higher number of muons available at the new muon campus. We
discuss the general status of the experiment and in particular focus on the
improved tools available to homogenize and determine the magnetic field in the
muon storage ring.


title: P_3-Games on Chordal Bipartite Graphs

abstract:
  Let G=(V,E) be a connected graph. A set U subseteq V is convex if G[U] is
connected and all vertices of V\U have at most one neighbor in U. Let sigma(W)
denote the unique smallest convex set that contains W subseteq V. Two players
play the following game. Consider a convex set U and call it the `playground.'
Initially, U = emptyset. When U=V, the player to move loses the game.
Otherwise, that player chooses a vertex x in V\U which is at distance at most
two from U. The effect of the move is that the playground U changes into
sigma(U cup {x}) and the opponent is presented with this new playground.
  A graph is chordal bipartite if it is bipartite and has no induced cycle of
length more than four. In this paper we show that, when G is chordal bipartite,
there is a polynomial-time algorithm that computes the Grundy number of the
P_3-game played on G. This implies that there is an efficient algorithm to
decide whether the first player has a winning strategy.


title:
On Ground States and Phase Transitions of $\lambda$-Model on the Cayley
  Tree

abstract:
  In the paper, we consider the $\lambda$-model with spin values $\{1, 2, 3\}$
on the Cayley tree of order two. We first describe ground states of the model.
Moreover, we also proved the existence of translation-invariant Gibb measures
for the $\lambda$-model which yield the existence of the phase transition.
Lastly, we established the exitance of 2-periodic Gibbs measures for the model.


title:
High performance THz emitters based on ferromagnetic/nonmagnetic
  heterostructures

abstract:
  We report a THz emitter with excellent performances based on nonmagnetic (NM)
and ferromagnetic (FM) heterostructures. The spin currents are first excited by
the femtosecond laser beam in the NM/FM bilayer, and then transient charge
currents are generated by inverse spin Hall effect, leading to THz emission out
of the structure. The broadband THz waves emitted from our film stacks have a
peak intensity exceeding 500 um thick ZnTe crystals (standard THz emitters).
Our device is insensitive to the polarization of an incident laser beam which
indicates the noise resistive feature. In contrast, the polarization of THz
waves is fully controllable by an external magnetic field. We have also
fabricated the devices on flexible substrates with a great performance, and
demonstrated that the devices can be driven by low power lasers. Together with
the low cost and mass productive sputtering growth method for the film stacks,
the proposed THz emitters can be readily applied to a wide range of THz
equipment. Our study also points towards an alternative approach to
characterize spintronic devices with NM/FM bilayers.


title:
Controlled assembly of single colloidal crystals using electro-osmotic
  micro-pumps

abstract:
  We assemble charged colloidal spheres at deliberately chosen locations on a
charged unstructured glass substrate utilizing ion exchange based
electro-osmotic micro-pumps. Using microscopy, a simple scaling theory and
Brownian Dynamics simulations, we systematically explore the control parameters
of crystal assembly and the mechanisms through which they depend on the
experimental boundary conditions. We demonstrate that crystal quality depends
crucially on the assembly distance of the colloids. This is understood as
resulting from the competition between inward transport by the electro-osmotic
pump flow and the electro-phoretic outward motion of the colloids. Optimized
conditions include substrates of low and colloids of large electro-kinetic
mobility. Then a sorting of colloids by size is observed in binary mixtures
with larger particles assembling closer to the ion exchanger beads. Moreover,
mono-sized colloids form defect free single domain crystals which grow outside
a colloid-free void with facetted inner crystal boundaries centred on the ion
exchange particle. This works remarkably well, even with irregularly formed ion
exchange resin splinters.


title:
Spin orbit torques and Dzyaloshinskii-Moriya interaction in
  dual-interfaced Co-Ni multilayers

abstract:
  We study the spin orbit torque (SOT) and Dzyaloshinskii-Moriya interaction
(DMI) in the dual-interfaced Co-Ni perpendicular multilayers. Through the
combination of top and bottom layer materials (Pt, Ta, MgO and Cu), SOT and DMI
are efficiently manipulated due to an enhancement or cancellation of the top
and bottom contributions. However, SOT is found to originate mostly from the
bulk of a heavy metal (HM), while DMI is more of interfacial origin. In
addition, we find that the direction of the domain wall (DW) motion can be
either along or against the electron flow depending on the DW tilting angle
when there is a large DMI. Such an abnormal DW motion induces a large assist
field required for hysteretic magnetization reversal. Our results provide
insight into the role of DMI in SOT driven magnetization switching, and
demonstrate the feasibility of achieving desirable SOT and DMI for spintronic
devices.


title: Giant nonreciprocal emission of spin waves in Ta/Py bilayers

abstract:
  Spin waves are propagating disturbances in the magnetization of magnetic
materials. One of their interesting properties is the nonreciprocity,
exhibiting that their amplitude depends on the magnetization direction.
Nonreciprocity in spin waves is of great interest in both fundamental science
and applications, as it offers an extra knob to control the flow of waves for
the technological fields of logics and switch applications. We show a high
nonreciprocity in spin waves from Ta/Py bilayer systems with out-of-plane
magnetic fields. The nonreciprocity depends on the thickness of Ta underlayer
which is found to induce an interfacial anisotropy. The origin of observed high
nonreciprocity is twofold; different polarities of the in-plane magnetization
due to different angles of canted out-of-plane anisotropy and the spin pumping
effect at the Ta/Py interface. Our findings provide an opportunity to engineer
highly efficient nonreciprocal spin wave based applications such as
nonreciprocal microwave devices, magnonic logic gates, and information
transports.


title: Understanding Sea Ice Melting via Functional Data Analysis

abstract:
  In this article, we considered the problem of sea ice cover is melting.
Considering the `satellite passive microwave remote sensing data' as functional
data, we studied daily observation of sea ice cover of each year as a smooth
continuous function of time. We investigated the mean function for the sea ice
area for following decades and computed the corresponding $95\%$ bootstrap
confidence interval for the both Arctic and Antarctic Oceans. We found the mean
function for the sea ice area dropped statistically significantly in recent
decades for the Arctic Ocean. However, no such statistical evidence was found
for the Antarctic ocean. Essentially, the mean function for sea ice area in the
Antarctic Ocean is unchanged. Additional evidence of the melting of sea ice
area in the Arctic Ocean is provided by three types of phase curve (namely,
Area vs. Velocity, Area vs. Acceleration, and Velocity Vs. Acceleration). In
the Arctic Ocean, during the summer, the current decades is observing the size
of the sea ice area about $30\%$ less, than what it used to be during the first
decade. In this article, we have taken a distribution-free approach for our
analysis, except the data generating process, belongs to the Hilbert space.


title:
Helicity dependent photovoltaic effect in Bi2Se3 under normal incident
  light

abstract:
  Topological insulators (TIs) form a new class of materials with insulating
bulk and surface conduction ensured by topologically protected surface states
(TPSS). We investigate the impact of the helicity of a normally incident laser
beam on the photovoltaic effect in the TI Bi2Se3. The observation of a helicity
dependent photovoltaic effect for normally incident light indicates the
presence of out-of-plane spin components for some TPSSs due to the hexagonal
warping. In addition, fluctuations in the electrostatic potential at the
surface locally break the rotational symmetry of the film allowing the helicity
dependent photovoltaic effect. Our result suggests that engineering local
electrostatic potentials in Bi2Se3 would allow the control of optically
generated spin currents, which may be useful for applications in
spin-optoelectronics.


title: New Types of Convergence on Time Scales

abstract:
  This paper is discussing about the notion of some new types of convergences
namely $I$-convergence and $I^*$-convergence of a $\Delta$-measurable function
$f$ on time scales $T$ by considering ideal on time scales $T$. This idea is
further extended to the notion of statistical convergence of a
$\Delta$-measurable function $f$ on time scales $T$.


title: Ergodic maximum principle for stochastic systems

abstract:
  We present a version of the stochastic maximum principle (SMP) for ergodic
control problems. In particular we give necessary (and sufficient) conditions
for optimality for controlled dissipative systems in finite dimensions. The
strategy we employ is mainly built on duality techniques. We are able to
construct a dual process for all positive times via the analysis of a suitable
class of perturbed linearized forward equations. We show that such a process is
the unique bounded solution to a Backward SDE on infinite horizon from which we
can write a version of the SMP.


title: Techniques for multifractal spectrum estimation in financial time series

abstract:
  Multifractal analysis is one of the important approaches that enables us to
measure the complexity of various data via the scaling properties. We compare
the most common techniques used for multifractal exponents estimation from both
theoretical and practical point of view. Particularly, we discuss the methods
based on estimation of R\'enyi entropy, which provide a powerful tool
especially in presence of heavy-tailed data. To put some flesh on bare bones,
all methods are compared on various real financial datasets, including daily
and high-frequency data.


title:
A characterization of connected self-affine fractals arising from
  collinear digits

abstract:
  Let $A$ be an expanding integer matrix with characteristic polynomial
$f(x)=x^{2}+px+q$, and let $\mathcal{D}=\{0,1,\dots,|q|-2,|q|+m\}\mathbf{v}$ be
a collinear digit set where $m\geqslant 0, {\mathbf v}\in {\mathbb Z}^2$. It is
well known that there exists a unique self-affine fractal $T$ satisfying
$AT=T+\mathcal{D}$. In this paper, we give a complete characterization on the
connected $T$. That generalizes the previous result of $|q|=3$.


title: Windings of planar processes, Exponential Functionals and Asian options

abstract:
  Motivated by a common Mathematical Finance topic, we discuss the reciprocal
of the exit time from a cone of planar Brownian motion which also corresponds
to the exponential functional of an associated Brownian motion. We prove a
conjecture by Vakeroudis and Yor (2012) concerning infinite divisibility
properties of this random variable and we present a novel simple proof of De
Blassie's result (1987-1988) about the asymptotic behaviour of the distribution
of the Bessel clock appearing in the skew-product representation of planar
Brownian motion, for t large. Similar issues for the exponential functional of
a Levy process are also discussed. We finally use the findings obtained by the
windings approach in order to get results for quantities associated to the
pricing of Asian options.


title:
Exercise Motion Classification from Large-Scale Wearable Sensor Data
  Using Convolutional Neural Networks

abstract:
  The ability to accurately identify human activities is essential for
developing automatic rehabilitation and sports training systems. In this paper,
large-scale exercise motion data obtained from a forearm-worn wearable sensor
are classified with a convolutional neural network (CNN). Time-series data
consisting of accelerometer and orientation measurements are formatted as
images, allowing the CNN to automatically extract discriminative features. A
comparative study on the effects of image formatting and different CNN
architectures is also presented. The best performing configuration classifies
50 gym exercises with 92.1% accuracy.


title:
Anisotropic $L^{2}$-weighted Hardy and $L^{2}$-Caffarelli-Kohn-Nirenberg
  inequalities

abstract:
  We establish sharp remainder terms of the $L^{2}$-Caffarelli-Kohn-Niren\-berg
inequalities on homogeneous groups, yielding the inequalities with best
constants. Our methods also give new sharp Caffarelli-Kohn-Nirenberg type
inequalities in $\mathbb{R}^{n}$ with arbitrary quasi-norms. We also present
explicit examples to illustrate our results for different weights and in
abelian cases.


title: LambdaDL: Syntax and Semantics (Preliminary Report)

abstract:
  Semantic data fuels many different applications, but is still lacking proper
integration into programming languages. Untyped access is error-prone while
mapping approaches cannot fully capture the conceptualization of semantic data.
In this paper, we present $\lambda_{DL}$,a $\lambda$-calculus with a modified
type system to provide type-safe integration of semantic data. This is achieved
by the integration of description logics into the $\lambda$-calculus for typing
and data access. It is centered around several key design principles. Among
these are (1) the usage of semantic conceptualizations as types, (2) subtype
inference for these types, and (3) type-checked query access to the data by
both ensuring the satisfiability of queries as well as typing query results
precisely in $\lambda_{DL}$. The paper motivates the use of a modified type
system for semantic data and it provides the theoretic foundation for the
integration of description logics as well as the core formal specifications of
$\lambda_{DL}$ including a proof of type safety.


title:
Study of Tomlinson-Harashima Precoding Strategies for Physical-Layer
  Security in Wireless Networks

abstract:
  In this paper, we propose novel non-linear precoders for the downlink of a
multi-user MIMO system with the existence of multiple eavesdroppers. The
proposed non-linear precoders are designed to improve the physical-layer
secrecy rate. Specifically, we combine the non-linear successive optimization
Tomlinson-Harashima precoding (SO-THP) with generalized matrix inversion (GMI)
technique to maximize the physical-layer secrecy rate. For the purpose of
comparison, we examine different traditional precoders with the proposed
algorithm in terms of secrecy rate as well as BER performance. We also
investigate simplified generalized matrix inversion (S-GMI) and
lattice-reduction (LR) techniques in order to efficiently compute the
parameters of the precoders. We further conduct computational complexity and
secrecy rate analysis of the proposed and existing algorithms. In addition, in
the scenario without knowledge of channel state information (CSI) to the
eavesdroppers, a strategy of injecting artificial noise (AN) prior to the
transmission is employed to enhance the physical-layer secrecy rate. Simulation
results show that the proposed non-linear precoders outperform existing
precoders in terms of BER and secrecy rate performance.


title:
Amplified-reflection plasmon instabilities in grating-gate plasmonic
  crystals

abstract:
  We identify a possible mechanism of the plasmon instabilities in periodically
gated two-dimensional electron systems with a modulated electron density
(plasmonic crystals) under direct current. The instability occurs due to the
amplified reflection of the small density perturbations from the gated/ungated
boundaries under the proper phase matching conditions between the crystal unit
cells. Based on the transfer-matrix formalism, we derive the generic dispersion
equation for the travelling plasmons in these structures. Its solution in the
hydrodynamic limit shows that the threshold drift velocity for the instability
can be tuned below the plasmon phase and carrier saturation velocities, and the
plasmon increment can exceed the collisional damping rate typical to III-V
semiconductors at 77 K and graphene at room temperature.


title: On the stability for Alexandrov's Soap Bubble theorem

abstract:
  Alexandrov's Soap Bubble theorem dates back to $1958$ and states that a
compact embedded hypersurface in $\mathbb{R}^N$ with constant mean curvature
must be a sphere. For its proof, A.D. Alexandrov invented his reflection
priciple. In $1982$, R. Reilly gave an alternative proof, based on integral
identities and inequalities, connected with the torsional rigidity of a bar. In
this article we study the stability of the spherical symmetry: the question is
how much a hypersurface is near to a sphere, when its mean curvature is near to
a constant in some norm. We present a stability estimate that states that a
compact hypersurface $\Gamma\subset\mathbb{R}^N$ can be contained in a
spherical annulus whose interior and exterior radii, say $\rho_i$ and $\rho_e$,
satisfy the inequality $$ \rho_e - \rho_i \le C \Vert H - H_0
\Vert^{\tau_N}_{L^1 (\Gamma)}, $$ where $\tau_N=1/2$ if $N=2, 3$, and
$\tau_N=1/(N+2)$ if $N\ge 4$. Here, $H$ is the mean curvature of $\Gamma$,
$H_0$ is some reference constant and $C$ is a constant that depends on some
geometrical and spectral parameters associated with $\Gamma$. This estimate
improves previous results in the literature under various aspects. We also
present similar estimates for some related overdetermined problems.


title:
A class of Weiss-Weinstein bounds and its relationship with the
  Bobrovsky-Mayer-Wolf-Zakai bounds

abstract:
  A fairly general class of Bayesian "large-error" lower bounds of the
Weiss-Weinstein family, essentially free from regularity conditions on the
probability density functions support, and for which a limiting form yields a
generalized Bayesian Cramer-Rao bound (BCRB), is introduced. In a large number
of cases, the generalized BCRB appears to be the Bobrovsky-Mayer-Wolf-Zakai
bound (BMZB). Interestingly enough, a regularized form of the Bobrovsky-Zakai
bound (BZB), applicable when the support of the prior is a constrained
parameter set, is obtained. Modified Weiss-Weinstein bound and BZB which
limiting form is the BMZB are proposed, in expectation of an increased
tightness in the threshold region. Some of the proposed results are exemplified
with a reference problem in signal processing: the Gaussian observation model
with parameterized mean and uniform prior.


title:
Certified Roundoff Error Bounds using Bernstein Expansions and Sparse
  Krivine-Stengle Representations

abstract:
  Floating point error is an inevitable drawback of embedded systems
implementation. Computing rigorous upper bounds of roundoff errors is
absolutely necessary to the validation of critical software. This problem is
even more challenging when addressing non-linear programs. In this paper, we
propose and compare two new methods based on Bernstein expansions and sparse
Krivine-Stengle representations, adapted from the field of the global
optimization to compute upper bounds of roundoff errors for programs
implementing polynomial functions. We release two related software package
FPBern and FPKiSten, and compare them with state of the art tools. We show that
these two methods achieve competitive performance, while computing accurate
upper bounds by comparison with other tools.


title:
On the homotopy classification of proper Fredholm maps into a Hilbert
  space

abstract:
  We classify the homotopy classes of proper Fredholm maps from an infinite
dimensional Hilbert manifold into its model space in terms of a suitable
version of framed cobordism. Our construction is an alternative approach to the
classification introduced by Elworthy and Tromba in 1970 and does not make use
of further structures on the ambient manifold, such as Fredholm structures. In
the special case of index zero, we obtain a complete classification involving
the Caccioppoli-Smale mod 2 degree and the absolute value of the oriented
degree.


title: Massive Corrections to Entanglement in Minimal E8 Toda Field Theory

abstract:
  In this letter we study the exponentially decaying corrections to saturation
of the second R\'enyi entropy of one interval of length L in minimal E8 Toda
field theory. It has been known for some time that the entanglement entropy of
a massive quantum field theory in 1+1 dimensions saturates to a constant value
for m1 L <<1 where m1 is the mass of the lightest particle in the spectrum.
Subsequently, results by Cardy, Castro-Alvaredo and Doyon have shown that there
are exponentially decaying corrections to this behaviour which are
characterised by Bessel functions with arguments proportional to m1 L. For the
von Neumann entropy the leading correction to saturation takes the precise
universal form -K0(2m1 L)/8 whereas for the R\'enyi entropies leading
corrections which are proportional to K0(m1 L) are expected. Recent numerical
work by P\'almai for the second R\'enyi entropy of minimal E8 Toda has found
next-to-leading order corrections decaying as exp(-2m1 L) rather than the
expected exp(-m1 L). In this paper we investigate the origin of this result and
show that it is incorrect. An exact form factor computation of correlators of
branch point twist fields reveals that the leading corrections are proportional
to K0(m1 L) as expected.


title:
Unified Reasoning about Robustness Properties of Symbolic-Heap
  Separation Logic

abstract:
  We introduce heap automata, a formalism for automatic reasoning about
robustness properties of the symbolic heap fragment of separation logic with
user-defined inductive predicates. Robustness properties, such as
satisfiability, reachability, and acyclicity, are important for a wide range of
reasoning tasks in automated program analysis and verification based on
separation logic. Previously, such properties have appeared in many places in
the separation logic literature, but have not been studied in a systematic
manner. In this paper, we develop an algorithmic framework based on heap
automata that allows us to derive asymptotically optimal decision procedures
for a wide range of robustness properties in a uniform way. We implemented a
protoype of our framework and obtained promising results for all of the
aforementioned robustness properties. Further, we demonstrate the applicability
of heap automata beyond robustness properties. We apply our algorithmic
framework to the model checking and the entailment problem for symbolic-heap
separation logic.


title: Finite $p$-groups having Schur multiplier of maximum order

abstract:
  Let $G$ be a non-abelian $p$-group of order $p^n$ and $M(G)$ denote the Schur
multiplier of $G$. Niroomand proved that $|M(G)| \leq
p^{\frac{1}{2}(n+k-2)(n-k-1)+1}$ for non-abelian $p$-groups $G$ of order $p^n$
with derived subgroup of order $p^k$. Recently Rai classified $p$-groups $G$ of
nilpotency class $2$ for which $|M(G)|$ attains this bound. In this article we
show that there is no finite $p$-group $G$ of nilpotency class $c \geq 3$ for
$p\neq3$ such that $|M(G)|$ attains this bound. Hence $|M(G)| \leq
p^{\frac{1}{2}(n+k-2)(n-k-1)}$ for $p$-groups $G$ of class $c \geq 3$ where $p
\neq 3$. We also construct a $p$-group $G$ for $p=3$ such that $|M(G)|$ attains
the Niroomand's bound.


title: The Log Convex Density Conjecture in Hyperbolic Space

abstract:
  The isoperimetric problem with a density or weighting seeks to enclose
prescribed weighted area with minimum weighted perimeter. According to
Chambers' recent proof of the Log Convex Density Conjecture, for many densities
on $\mathbb{R}^n$ the answer is a sphere about the origin. We generalize his
results from $\mathbb{R}^n$ to $\mathbb{H}^n$ with related but different volume
and perimeter densities.


title: Evidence of Two Resonant Structures in $e^+ e^- \to \pi^+ \pi^- h_c$

abstract:
  The cross sections of $e^{+}e^{-}\to\pi^{+}\pi^{-}h_c$ at center-of-mass
energies from 3.896 to 4.600 GeV are measured using data samples collected with
the BESIII detector operating at the Beijing Electron Positron Collider. The
cross sections are found to be of the same order of magnitude as those of
$e^{+}e^{-}\to\pi^{+}\pi^{-}J/\psi$ and $e^{+}e^{-}\to\pi^{+}\pi^{-}\psi(2S)$,
but the line shape is inconsistent with the $Y$ states observed in the latter
two modes. Two structures are observed in the $e^{+}e^{-}\to\pi^{+}\pi^{-}h_c$
cross sections around 4.22 and 4.39 GeV/$c^{2}$, which we call $Y(4220)$ and
$Y(4390)$, respectively. A fit with a coherent sum of two Breit-Wigner
functions results in a mass of $(4218.4^{+5.5}_{-4.5}\pm0.9)$ MeV/$c^{2}$ and a
width of $(66.0^{+12.3}_{-8.3}\pm0.4)$ MeV for the $Y(4220)$, and a mass of
$(4391.6^{+6.3}_{-6.8}\pm1.0)$ MeV/$c^{2}$ and a width of
$(139.5^{+16.2}_{-20.6}\pm0.6)$ MeV for the $Y(4390)$, where the first
uncertainties are statistical and the second ones systematic. The statistical
significance of $Y(4220)$ and $Y(4390)$ is 10$\sigma$ over one structure
assumption.


title:
pg-Causality: Identifying Spatiotemporal Causal Pathways for Air
  Pollutants with Urban Big Data

abstract:
  Many countries are suffering from severe air pollution. Understanding how
different air pollutants accumulate and propagate is critical to making
relevant public policies. In this paper, we use urban big data (air quality
data and meteorological data) to identify the \emph{spatiotemporal (ST) causal
pathways} for air pollutants. This problem is challenging because: (1) there
are numerous noisy and low-pollution periods in the raw air quality data, which
may lead to unreliable causality analysis, (2) for large-scale data in the ST
space, the computational complexity of constructing a causal structure is very
high, and (3) the \emph{ST causal pathways} are complex due to the interactions
of multiple pollutants and the influence of environmental factors. Therefore,
we present \emph{p-Causality}, a novel pattern-aided causality analysis
approach that combines the strengths of \emph{pattern mining} and
\emph{Bayesian learning} to efficiently and faithfully identify the \emph{ST
causal pathways}. First, \emph{Pattern mining} helps suppress the noise by
capturing frequent evolving patterns (FEPs) of each monitoring sensor, and
greatly reduce the complexity by selecting the pattern-matched sensors as
"causers". Then, \emph{Bayesian learning} carefully encodes the local and ST
causal relations with a Gaussian Bayesian network (GBN)-based graphical model,
which also integrates environmental influences to minimize biases in the final
results. We evaluate our approach with three real-world data sets containing
982 air quality sensors, in three regions of China from 01-Jun-2013 to
19-Dec-2015. Results show that our approach outperforms the traditional causal
structure learning methods in time efficiency, inference accuracy and
interpretability.


title:
Cat-state generation and stabilization for a nuclear spin through
  electric quadrupole interaction

abstract:
  Spin cat states are superpositions of two or more coherent spin states (CSSs)
that are distinctly separated over the Bloch sphere. Additionally, the nuclei
with angular momenta greater than 1/2 possess a quadrupolar charge
distribution. At the intersection of these two phenomena, we devise a simple
scheme for generating various types of nuclear spin cat states. The native
biaxial electric quadrupole interaction that is readily available in strained
solid-state systems plays a key role here. However, the fact that built-in
strain cannot be switched off poses a challenge for the stabilization of target
cat states once they are prepared. We remedy this by abruptly diverting via a
single rotation pulse the state evolution to the neighborhood of the fixed
points of the underlying classical Hamiltonian flow. Optimal process parameters
are obtained as a function of electric field gradient biaxiality and nuclear
spin angular momentum. The overall procedure is seen to be robust under 5%
deviations from optimal values. We show that higher level cat states with four
superposed CSS can also be formed using three rotation pulses. Finally, for
open systems subject to decoherence we extract the scaling of cat state
fidelity damping with respect to the spin quantum number. This reveals rates
greater than the dephasing of individual CSSs. Yet, our results affirm that
these cat states can preserve their fidelities for practically useful durations
under the currently attainable decoherence levels.


title:
Convergence of the Euler-Maruyama method for multidimensional SDEs with
  discontinuous drift and degenerate diffusion coefficient

abstract:
  We prove strong convergence of order $1/4-\epsilon$ for arbitrarily small
$\epsilon>0$ of the Euler-Maruyama method for multidimensional stochastic
differential equations (SDEs) with discontinuous drift and degenerate diffusion
coefficient. The proof is based on estimating the difference between the
Euler-Maruyama scheme and another numerical method, which is constructed by
applying the Euler-Maruyama scheme to a transformation of the SDE we aim to
solve.


title:
Hermite-Birkhoff Interpolation on Arbitrarily Distributed Data on the
  Sphere and Other Manifolds

abstract:
  We consider the problem of interpolating a function given on scattered points
using Hermite-Birkhoff formulas on the sphere and other manifolds. We express
each proposed interpolant as a linear combination of basis functions, the
combination coefficients being incomplete Taylor expansions of the interpolated
function at the interpolation points. The basis functions have the following
features: (i) depend on the geodesic distance; (ii) are orthonormal with
respect to the point-evaluation functionals; and (iii) have all derivatives
equal zero up to a certain order at the interpolation points. Moreover, the
construction of such interpolants, which belong to the class of partition of
unity methods, takes advantage of not requiring any solution of linear systems.


title: Yang-Mills Instanton Sheaves with Higher Topological Charges

abstract:
  We explicitly construct SL(2,C) Yang-Mills (weakly) three and four instanton
sheaves on CP^3. These results extend the previous construction of Yang-Mills
(weakly) instanton sheaves with topological charge two [18].


title: RBF-PU Interpolation with Variable Subdomain Sizes and Shape Parameters

abstract:
  In this paper, we deal with the challenging computational issue of
interpolating large data sets, with eventually non-homogeneous densities. To
such scope, the Radial Basis Function Partition of Unity (RBF-PU) method has
been proved to be a reliable numerical tool. However, there are not available
techniques enabling us to efficiently select the sizes of the local PU
subdomains which, together with the value of the RBF shape parameter, greatly
influence the accuracy of the final fit. Thus here, by minimizing an \emph{a
priori} error estimate, we propose a RBF-PU method by suitably selecting
variable shape parameters and subdomain sizes. Numerical results and
applications show performaces of the interpolation technique.


title:
The multiple soliton and peakon solutions of the Dullin-Gottwald-Holm
  equation

abstract:
  Explicit multi-soliton and multi-peakon solutions of the Dullin-Gottwald-Holm
equation are constructed via Darboux transformation and direct computation,
respectively. To this end we first map the Dullin-Gottwald-Holm equation to a
negative order KdV equation by a reciprocal transformation. Then we use the
Darboux matrix approach to derive multi-soliton solutions of the
Dullin-Gottwald-Holm equation from the solutions of the negative order KdV
equation. Finally, we find multi-peakon solutions of the Dullin-Gottwald-Holm
equation in weak sense. For $\alpha=\frac{1}{2}$ and $\alpha\neq \frac{1}{2}$,
several types of two-peakon solutions are discussed in detail. Moreover, the
dynamic behaviors of the obtained solutions are illustrated through some
figures.


title: Measuring Coherence with Entanglement Concurrence

abstract:
  Quantum coherence is a fundamental manifestation of the quantum superposition
principle. Recently, Baumgratz \emph{et al}. [Phys. Rev. Lett. \textbf{113},
140401 (2014)] presented a rigorous framework to quantify coherence from the
view of theory of physical resource. Here we propose a new valid quantum
coherence measure which is a convex roof measure, for a quantum system of
arbitrary dimension, essentially using the generalized Gell-Mann matrices.
Rigorous proof shows that the proposed coherence measure fulfills all the
requirements dictated by the resource theory of quantum coherence measures.
Moreover, strong links between the resource frameworks of coherence concurrence
and entanglement concurrence is derived, which shows that any degree of
coherence with respect to some reference basis can be converted to entanglement
via incoherent operations. Our work provides a clear quantitative and
operational connection between coherence and entanglement based on two kinds of
concurrence. This new coherence measure, coherence concurrence, may be
beneficial to the study of quantum coherence.


title: Event reweighting with the NuWro neutrino interaction generator

abstract:
  Event reweighting has been implemented in the NuWro neutrino event generator
for a number of free theory parameters in the interaction model. Event
reweighting is a key analysis technique, used to efficiently study the effect
of neutrino interaction model uncertainties. This opens up the possibility for
NuWro to be used as a primary event generator by experimental analysis groups.
A preliminary model tuning to ANL and BNL data of quasi-elastic and single pion
production events was performed to validate the reweighting engine.


title: The effect of delay on contact tracing

abstract:
  We consider a model for an infectious disease in the onset of an outbreak. We
introduce contact tracing incorporating a tracing delay. The effect of
randomness in the delay and the effect of the length of this delay in
comparison to the infectious period of the disease respectively to a latency
period on the effect of tracing, given e.g. by the change of the reproduction
number, is analyzed. We focus particularly on the effect of randomness in the
tracing delay.


title:
Computation of Kazhdan-Lusztig polynomials and some applications to
  finite groups

abstract:
  We discuss a practical algorithm to compute parabolic Kazhdan-Lusztig
polynomials. As an application we compute Kazhdan-Lusztig polynomials which are
needed to evaluate a character formula for reductive groups due to Lusztig.
  Some coefficients of these polynomials have interesting interpretations for
certain finite groups. We find examples of finite dimensional modules for
finite groups with much higher dimensional first cohomology group than in all
previously known cases.
  Some of these examples lead to the construction of finite groups with many
maximal subgroups, contradicting an old conjecture by G.~E.~Wall.


title: UY Puppis - A New Anomalous Z Cam Type Dwarf Nova

abstract:
  The defining characteristic of Z Cam stars are standstills in their light
curves. Some Z Cams exhibit atypical behaviour by going into outburst from a
standstill. It has previously been suggested that UY Pup had been a Z Cam star,
but it was ruled out due to its long-term light curve. However, in December
2015 UY Pup went into outburst and unexpectedly entered into a short standstill
instead of returning to quiescence. Furthermore, UY Pup exhibited additional
unusual behaviour with two outbursts detected during its standstill. After this
standstill UY Pup made a brief excursion to a quiescence state and slowly rose
to a longer and well-defined standstill, where it again went into another
outburst. Through comparative analysis, research, and observational data of UY
Pup it is evident and thus concluded that it is indeed a Z Cam star, in which
renders it to be one of only four known anomalous Z Cam stars.


title: The Chern-Simons invariants for the double of a compression body

abstract:
  Given a 3-manifold that can be written as the double of a compression body,
we compute the Chern-Simons critical values for arbitrary compact connected
structure groups. We also show that the moduli space of flat connections is
connected when there are no reducibles.


title: A Hecke algebra attached to mod 2 modular forms of level 5

abstract:
  Let $F$ be the element $\sum_{n\ \mathit{odd},\ n>0}x^{n^{2}}$ of $Z/2[[x]]$.
Set $G=F(x^{5})$, $D=F(x)+F(x^{25})$. For $k>0$, $(k,10)=1$, define $D_{k}$ as
follows. $D_{1}=D$, $D_{3}=D^{8}/G$, $D_{7}=D^{2}G$, $D_{9}=D^{4}G$;
furthermore $D_{k+10}=G^{2}D_{k}$.
  Using modular forms of level $\Gamma_{0}(5)$ we show that the space $W$
spanned by the $D_{k}$ is stabilized by the formal Hecke operators
$T_{p}:Z/2[[x]]\rightarrow Z/2[[x]]$, $p\ne 2$ or $5$. And we determine the
structure of the (completed) shallow Hecke algebra attached to $W$. This
algebra proves to be a power series ring in $T_{3}$ and $T_{7}$ with an element
of square $0$ adjoined. As Hecke module, $W$ identifies with a certain
subquotient of the space of mod~2 modular forms of level $\Gamma_{0}(5)$, and
our Hecke algebra result parallels findings in level 1 (by J.-L. Nicolas and
J.-P. Serre) and in level $\Gamma_{0}(3)$ by us.


title:
30 years, some 700 integrals, and 1 dessert, or: Electroweak two-loop
  corrections to the Zbb vertex

abstract:
  The one-loop corrections to the weak mixing angle $\sin^2\theta_{eff}^b$
derived from the $Z{\bar b}b$ vertex, are known since 1985. It took another 30
years to calculate the complete electroweak two-loop corrections to
$\sin^2\theta_{eff}^b$. The main obstacle was the calculation of the O(700)
bosonic two-loop vertex integrals with up to three mass scales, at $s=M_Z^2$.
We did not perform the usual integral reduction and master evaluation, but
chose a completely numerical approach, using two different calculational
chains. One method relies on publicly available sector decomposition
implementations. Further, we derived Mellin-Barnes (MB) representations,
exploring the publicly available MB suite. We had to supplement the MB suite by
two new packages: AMBRE~3, a Mathematica program, for the efficient treatment
of non-planar integrals and MBnumerics for advanced numerics in the Minkowskian
space-time. Our preliminary result for LL2016, the "dessert", for the
electroweak bosonic two-loop contributions to $\sin^2\theta_{eff}^b$ is:
$\Delta \sin^2\theta_{eff}^{b(\alpha^2,\rm bos)} = \sin^2\theta_W ~
\Delta\kappa_b^{(\alpha^2,bos)}$, with $\Delta\kappa_b^{(\alpha^2,bos)} =
-1.0276 x 10^{-4}$. This contribution is about a quarter of the corresponding
fermionic corrections and of about the same magnitude as several of the known
higher-order QCD corrections. The $\sin^2\theta_{eff}^b$ is now predicited in
the Standard Model with a relative error of $10^{-4}$ [1].


title:
On the nature and correction of the spurious S-wise spiral galaxy
  winding bias in Galaxy Zoo 1

abstract:
  The Galaxy Zoo 1 catalog displays a bias towards the S-wise winding direction
in spiral galaxies which has yet to be explained. The lack of an explanation
confounds our attempts to verify the Cosmological Principle, and has spurred
some debate as to whether a bias exists in the real universe. The bias
manifests not only in the obvious case of trying to decide if the universe as a
whole has a winding bias, but also in the more insidious case of selecting
which galaxies to include in a winding direction survey. While the former bias
has been accounted for in a previous image-mirroring study, the latter has not.
Furthermore, the bias has never been {\em corrected} in the GZ1 catalog, as
only a small sample of the GZ1 catalog was re-examined during the mirror study.
We show that the existing bias is a human {\em selection} effect rather than a
human chirality bias. In effect, the excess S-wise votes are spuriously
"stolen" from the elliptical and edge-on-disk categories, not the Z-wise
category. Thus, when selecting a set of spiral galaxies by imposing a threshold
$T$ so that $\max(P_S,P_Z) > T$ or $P_S+P_Z>T$, we spuriously select more
S-wise than Z-wise galaxies. We show that when a provably unbiased machine
selects which galaxies are spirals independent of their chirality, the S-wise
surplus vanishes, even if humans are still used to determine the chirality.
Thus, when viewed across the entire GZ1 sample (and by implication, the Sloan
catalog), the winding direction of arms in spiral galaxies as viewed from Earth
is consistent with the flip of a fair coin.


title:
$C^3$-index: A PageRank based multi-faceted metric for authors'
  performance measurement

abstract:
  Ranking scientific authors is an important but challenging task, mostly due
to the dynamic nature of the evolving scientific publications. The basic
indicators of an author's productivity and impact are still the number of
publications and the citation count (leading to the popular metrics such as
h-index, g-index etc.). H-index and its popular variants are mostly effective
in ranking highly-cited authors, thus fail to resolve ties while ranking
medium-cited and low-cited authors who are majority in number. Therefore, these
metrics are inefficient to predict the ability of promising young researchers
at the beginning of their career. In this paper, we propose $C^3$-index that
combines the effect of citations and collaborations of an author in a
systematic way using a weighted multi-layered network to rank authors. We
conduct our experiments on a massive publication dataset of Computer Science
and show that - (i) $C^3$-index is consistent over time, which is one of the
fundamental characteristics of a ranking metric, (ii) $C^3$-index is as
efficient as h-index and its variants to rank highly-cited authors, (iii)
$C^3$-index can act as a conflict resolution metric to break ties in the
ranking of medium-cited and low-cited authors, (iv) $C^3$-index can also be
used to predict future achievers at the early stage of their career.


title: Recovering lost 21 cm radial modes via cosmic tidal reconstruction

abstract:
  21 cm intensity mapping has emerged as a promising technique to map the
large-scale structure of the Universe, at redshifts $z$ from 1 to 10.
Unfortunately, many of the key cross-correlations with the cosmic microwave
background and photo-$z$ galaxies have been thought to be impossible due to the
foreground contamination for radial modes with small wave numbers. In this
paper, we apply tidal reconstruction to the simulated 21 cm fields and recover
the lost large-scale radial modes successfully. We estimate the detectability
of the cross-correlation signals and find they can be detected at high
significance with current 21 cm experiments. The tidal field reconstruction
method opens up a new set of possibilities to probe the Universe and is
extremely valuable not only for 21 cm surveys but also for cosmic microwave
background and photometric-redshift observations.


title:
Extended skyrmion lattice scattering and long-time memory in the chiral
  magnet Fe$_{1-x}$Co$_x$Si

abstract:
  Small angle neutron scattering measurements on a bulk single crystal of the
doped chiral magnet Fe$_{1-x}$Co$_x$Si with $x$=0.3 reveal a pronounced effect
of the magnetic history and cooling rates on the magnetic phase diagram. The
extracted phase diagrams are qualitatively different for zero and field cooling
and reveal a metastable skyrmion lattice phase outside the A-phase for the
latter case. These thermodynamically metastable skyrmion lattice correlations
coexist with the conical phase and can be enhanced by increasing the cooling
rate. They appear in a wide region of the phase diagram at temperatures below
the $A$-phase but also at fields considerably smaller or higher than the fields
required to stabilize the A-phase.


title:
Hierarchical DSSC structures based on single walled TiO2 nanotube arrays
  reach back-side illumination solar light conversion efficiency of 8%

abstract:
  In the present work we introduce a path to the controlled construction of
DSSCs based on hierarchically structured single walled, self-organized TiO2
layers. In a first step we describe a simple approach to selectively remove the
inner detrimental shell of anodic TiO2 nanotubes (NTs). This then allows
controlled well-defined layer-by-layer decoration of these TiO2-NT walls with
TiO2 nanoparticles (this in contrast to conventional TiO2 nanotubes). We show
that such defined multiple layered decoration can be optimized to build dye
sensitized solar cells that (under back-side illumination conditions) can yield
solar light conversion efficiencies in the range of 8 %. The beneficial effects
observed can be ascribed to a combination of three factors : 1) improved
electronic properties of the single walled tubes themselves, 2) a further
improvement of the electronic properties by the defined TiCl4 treatment, and 3)
a higher specific dye loading that becomes possible for the layer-by-layer
decorated single walled tubes.


title: On derivatives of Siegel-Eisenstein series over global function fields

abstract:
  The aim of this article is to study the derivative of "incoherent"
Siegel-Eisenstein series on symplectic groups over function fields. By the
Siegel-Weil formula for "coherent" Siegel-Eisenstein series, we can relate the
non-singular Fourier coefficients of the derivative in question to the
arithmetic of quadratic forms. Restricting to the special case when the
incoherent quadratic space has dimension 2, we explicitly compute all the
Fourier coefficients, and connect the derivative with the special cycles on the
coarse moduli schemes of rank 2 Drinfeld modules with "complex multiplication."


title:
DSValidator: An Automated Counterexample Reproducibility Tool for
  Digital Systems (Tool Demonstration)

abstract:
  An automated counterexample reproducibility tool based on MATLAB is
presented, called DSValidator, with the goal of reproducing counterexamples
that refute specific properties related to digital systems. We exploit
counterexamples generated by the Digital System Verifier (DSVerifier), which is
a model checking tool based on satisfiability modulo theories for digital
systems. DSValidator reproduces the execution of a digital system, relating its
input with the counterexample, in order to establish trust in a verification
result. We show that DSValidator can validate a set of intricate
counterexamples for digital controllers used in a real quadrotor attitude
system within seconds and also expose incorrect verification results in
DSVerifier. The resulting toolbox leverages the potential of combining
different verification tools for validating digital systems via an exchangeable
counterexample format.


title: The planar $L_p$-Minkowski problem for $0< p<1$

abstract:
  Necessary and sufficient conditions for the existence of solutions to the
asymmetric $L_p$ Minkowski problem in $\mathbb{R}^2$ are established for $0 < p
< 1$.


title: Nonlinear Sturm Oscillation: from the interval to a star

abstract:
  The Sturm oscillation property, i.e. that the $n$-th eigenfunction of a
Sturm-Liouville operator on an interval has $n -1$ zeros (nodes), has been well
studied. This result is known to hold when the interval is replaced by a metric
(quantum) tree graph. We prove that the solutions of the real stationary
nonlinear Schr\"odinger equation on an interval satisfy a nonlinear version of
the Sturm oscillation property. However, we show that unlike the linear theory,
the nonlinear version of the Sturm oscillation breaks down already for a star
graph. We point out conditions under which this violation can be assured.


title:
Hawking radiation of scalar and vector particles from 5D Myers-Perry
  black holes

abstract:
  In the present paper we explore the Hawking radiation as a quantum tunneling
effect from a rotating 5 dimensional Myers-Perry black hole (5D-MPBH) with two
independent angular momentum components. First, we investigate the Hawking
temperature by considering the tunneling of massive scalar particles and spin-1
vector particles from the 5D-MPBH in the Painlev\'{e} coordinates and then in
the corotating frames. More specifically, we solve the Klein-Gordon and Proca
equations by applying the WKB method and Hamilton-Jacobi equation in both
cases. Finally, we recover the Hawking temperature and show that coordinates
systems do not affect the Hawking temperature.


title: Creep and fluidization in thermal amorphous solids

abstract:
  When submitted to a constant mechanical load, many amorphous solids display
power law creep followed by fluidization. A fundamental understanding of these
processes is still far from being achieved. Here, we characterize creep and
fluidization on the basis of a mesoscopic viscoplastic model that includes
thermally activated yielding events and a broad distribution of energy
barriers, which may be lowered under the effect of a local deformation. We
relate the creep exponent observed before fluidization to the width of barrier
distribution and to the specific form of stress redistribution following
yielding events. We show that Andrade creep is accompanied by local
strain-hardening driven by stress redistribution and find that the fluidization
depends exponentially on the applied stress. The simulation results are
interpreted in the light of a mean-field analysis, and should help in
rationalizing the creep phenomenology of amorphous solids.


title:
Fabrication and Analysis of Three-Layer All-Silicon Interference Optical
  Filter with Sub-Wavelength Structure toward High Performance Terahertz Optics

abstract:
  We propose an all-silicon multi-layer interference filter composed solely of
silicon with sub-wavelength structure (SWS) in order to realize high
performance optical filters operating in the THz frequency region with
robustness against cryogenic thermal cycling and mechanical damage. We
demonstrate fabrication of a three-layer prototype using well-established
common micro-electro-mechanical systems (MEMS) technologies as a first step
toward developing practical filters. The measured transmittance of the
three-layer filter agrees well with the theoretical transmittances calculated
by a simple thin-film calculation with effective refractive indices as well as
a rigorous coupled-wave analysis simulation. We experimentally show that SWS
layers can work as homogeneous thin-film interference layers with effective
refractive indices even if there are multiple SWS layers in a filter.


title: Complexity Issues in Computing Spectra, Pseudospectra and Resolvents

abstract:
  We display methods that allow for computations of spectra, pseudospectra and
resolvents of linear operators on Hilbert spaces and also elements in unital
Banach algebras. The paper considers two different approaches, namely,
pseudospectral techniques and polynomial numerical hull theory. The former is
used for Hilbert space operators whereas the latter can handle the general case
of elements in a Banach algebra. This approach leads to multicentric
holomorphic calculus. We also discuss some new types of pseudospectra and the
recently defined Solvability Complexity Index


title:
Imbalanced magnetohydrodynamic turbulence modified by velocity shear in
  the solar wind

abstract:
  We study incompressible imbalanced magnetohydrodynamic turbulence in the
presence of background velocity shears. Using scaling arguments, we show that
the turbulent cascade is significantly accelerated when the background velocity
shear is stronger than the velocity shears in the subdominant Alfv% \'{e}n
waves at the injection scale. The spectral transport is then controlled by the
background shear rather than the turbulent shears and the Tchen spectrum with
spectral index $-1$ is formed. This spectrum extends from the injection scale
to the scale of the spectral break where the subdominant wave shear becomes
equal to the background shear. The estimated spectral breaks and power spectra
are in good agreement with those observed in the fast solar wind. The proposed
mechanism can contribute to enhanced turbulent cascades and modified $-1$
spectra observed in the fast solar wind with strong velocity shears. This
mechanism can also operate in many other astrophysical environments where
turbulence develops on top of non-uniform plasma flows.


title: Numerical and analytical results for the two disks capacitor problem

abstract:
  In this paper we study the two disks capacitor, for equal and different
radii. The new results obtained allow a complete characterization of capacity
coefficients and forces at short distances. An extensive numerical calculation
confirms the theoretical results. The study shows the existence of a hierarchy
in the divergent behavior of the capacitance coefficients and this implies some
unusual behavior of the forces, strictly related to the dimensionality of the
near-contact zone between electrodes.


title:
Equivalence of Weighted Anchored and ANOVA Spaces of Functions with
  Mixed Smoothness of Order one in $L_p$

abstract:
  We consider $\gamma$-weighted anchored and ANOVA spaces of functions with
mixed first order partial derivatives bounded in a weighted $L_p$ norm with $1
\leq p \leq \infty$. The domain of the functions is $D^d$, where $D \subseteq
\mathbb{R}$ is a bounded or unbounded interval. We provide conditions on the
weights $\gamma$ that guarantee that anchored and ANOVA spaces are equal (as
sets of functions) and have equivalent norms with equivalence constants
uniformly or polynomially bounded in $d$. Moreover, we discuss applications of
these results to integration and approximation of functions on $D^d$.


title:
On one-dimensional compressible Navier-Stokes equations for a reacting
  mixture in unbounded domains

abstract:
  In this paper we consider the one-dimensional Navier-Stokes system for a
heat-conducting, compressible reacting mixture which describes the dynamic
combustion of fluids of mixed kinds on unbounded domains. This model has been
discussed on bounded domains by Chen (SIAM Jour. Math. Anal., 23 (1992),
609--634) and Chen-Hoff-Trivisa (Arch. Rat. Mech. Anal. 166 (2003), 321--358)
among others, in which the reaction rate function is a discontinuous function
obeying the Arrhenius Law. We prove the global existence of weak solutions to
this model on one-dimensional unbounded domains with large initial data in
$H^1$. Moreover, the large-time behaviour of the weak solution is identified
and proved. In particular, the uniform-in-time bounds for the temperature and
specific volume have been established via energy estimates. For this purpose we
utilise techniques developed by Kazhikhov and coauthors ({\it cf.} Siber. Math.
Jour. 23 (1982), 44--49; Jour. Appl. Math. Mech., 41 (1977), 273--282), as well
as a crucial estimate in the recent work by Li-Liang (Arch. Rat. Mech. Anal.
220 (2016), 1195--1208). Several new estimates are also established, in order
to treat the unbounded domain and the reacting terms.


title: The cycle structure of a Markoff automorphism over finite fields

abstract:
  We begin an investigation of the action of pseudo-Anosov elements of
$\mathrm{Out}(\mathbf{F}_{2})$ on the Markoff-type varieties \[
\mathbb{X}_{\kappa}:\:x^{2}+y^{2}+z^{2}=xyz+2+\kappa \] over finite fields
$\mathbb{F}_{p}$ with $p$ prime. We first make a precise conjecture about the
permutation group generated by $\mathrm{Out}(\mathbf{F}_{2})$ on
$\mathbb{X}_{-2}(\mathbb{F}_{p})$ that shows there is no obstruction at the
level of the permutation group to a pseudo-Anosov acting `generically'. We
prove that this conjecture is sharp. We show that for a fixed pseudo-Anosov
$g\in\mathrm{Out}(\mathbf{F}_{2})$, there is always an orbit of $g$ of length
$\geq C\log p+O(1)$ on $\mathbb{X}_{\kappa}(\mathbb{F}_{p})$ where $C>0$ is
given in terms of the eigenvalues of $g$ viewed as an element of
$\mathrm{GL}_{2}(\mathbf{Z})$. This improves on a result of Silverman (2007)
that applies to general morphisms of quasi-projective varieties. We have
discovered that the asymptotic $(p\to\infty)$ behavior of the longest orbit of
a fixed pseudo-Anosov $g$ acting on $\mathbb{X}_{-2}(\mathbb{F}_{p})$ is
dictated by a dichotomy that we describe both in combinatorial terms and in
algebraic terms related to Gauss's ambiguous binary quadratic forms, following
Sarnak. This dichotomy is illustrated with numerics, based on which we
formulate a precise conjecture.


title: Polar Coordinates and Noncommutative Phase Space

abstract:
  The so-called Weyl transform is a linear map from a commutative algebra of
functions to a noncommutative algebra of linear operators, characterized by an
action on Cartesian coordinate functions of the form $(x, y) \mapsto (X, Y)$
such that $XY -YX = i\epsilon I$, i.e. the defining relation for the Heisenberg
Lie algebra. Study of this transform has been expansive. We summarize many
important results from the literature. The primary goal of this work is to
prove the final result: the realization of the polar transformation $(\rho,
e^{i\theta}) \mapsto (R, e^{i\Theta})$ in terms of explicit orthogonal function
expansions, while starting from elementary principles and utilizing minimal
machinery. Our results are not strictly original but their presentation here is
intended to simplify introduction to these subjects in a novel manner.


title: On the topology of the Lorenz system

abstract:
  We present a new paradigm for three dimensional chaos, and specifically for
the Lorenz equations. The main difficulty in these equations and for a generic
flow in dimension three is the existence of singularities. We show how to use
knot theory as a way to remove the singularities. Specifically, we claim:
  (1) For certain parameters, the Lorenz system has an invariant one
dimensional curve, which is a trefoil knot. The knot is a union of invariant
manifolds of the singular points.
  (2) The flow is topologically equivalent to an Anosov flow on the complement
of this curve, and even to a geodesic flow.
  (3) When varying the parameters, the system exhibits topological phase
transitions, i.e. for special parameter values, it will be topologically
equivalent to an Anosov flow on a knot complement, and different knots appear
for different parameter values.
  The steps of a mathematical proof of these statements are at different
stages. Some have been proven, for some we present numerical evidence and some
are still conjectural.


title:
An Alternating Automaton for First-Order Linear Temporal Logic--Tech
  Report

abstract:
  In this paper we give automata-based representation of LTL-FO$^+$ properties.
LTL-FO$^+$ is an extension of LTL that includes first-order quantification over
bounded variable, thus greatly increasing the expressivity of the language. An
automata representation of this formalism allows greater ease in writing and
understanding properties, as well as in performing manipulations, such as
negation or emptiness checking. The automata representation of an LTL-FO$^+$
formula has finite size regardless of the domain of quantified variables, and
the number of states that is linear in the size of the property.


title:
The limits of weak selection and large population size in evolutionary
  game theory

abstract:
  Evolutionary game theory is a mathematical approach to studying how social
behaviors evolve. In many recent works, evolutionary competition between
strategies is modeled as a stochastic process in a finite population. In this
context, two limits are both mathematically convenient and biologically
relevant: weak selection and large population size. These limits can be
combined in different ways, leading to potentially different results. We
consider two orderings: the wN limit, in which weak selection is applied before
the large population limit, and the Nw limit, in which the order is reversed.
Formal mathematical definitions of the Nw and wN limits are provided. Applying
these definitions to the Moran process of evolutionary game theory, we obtain
asymptotic expressions for fixation probability and conditions for success in
these limits. We find that the asymptotic expressions for fixation probability,
and the conditions for a strategy to be favored over a neutral mutation, are
different in the Nw and wN limits. However, the ordering of limits does not
affect the conditions for one strategy to be favored over another.