title: Planar algebras, cabling and the Drinfeld double

abstract:
  We produce an explicit embedding of the planar algebra of the Drinfeld double
of a finite-dimensional, semisimple and cosemisimple Hopf algebra $H$ into the
two-cabling of the planar algebra of the dual Hopf algebra $H^*$ and
characterise the image.


title: Second-order virial expansion for an atomic gas in a harmonic waveguide

abstract:
  The virial expansion for cold two-component Fermi and Bose atomic gases is
considered in the presence of a waveguide and in the vicinity of a Feshbach
resonance. The interaction between atoms and the coupling with the Feshbach
molecules is modeled using a quantitative separable two-channel model. The
scattering phase-shift in an atomic waveguide is defined. This permits us to
extend the Beth-Uhlenbeck formula for the second-order virial coefficient to
this inhomogeneous case.


title: Searching for high-$K$ isomers in the proton-rich $A\sim80$ mass region

abstract:
  Configuration-constrained potential-energy-surface calculations have been
performed to investigate the $K$ isomerism in the proton-rich $A\sim80$ mass
region. An abundance of high-$K$ states are predicted. These high-$K$ states
arise from two and four-quasi-particle excitations, with $K^{\pi}=8^{+}$ and
$K^{\pi}=16^{+}$, respectively. Their excitation energies are comparatively
low, making them good candidates for long-lived isomers. Since most nuclei
under studies are prolate spheroids in their ground states, the oblate shapes
of the predicted high-$K$ states may indicate a combination of $K$ isomerism
and shape isomerism.


title: Integral automorphisms of affine spaces over finite fields

abstract:
  A permutation of the point set of the affine space $AG(n,q)$ is called an
integral automorphism if it preserves the integral distance defined among the
points. In this paper, we complete the classification of the integral
automorphisms of $AG(n,q)$ for $n\ge 3$.


title:
Algebraic method for constructing singular steady solitary waves: A case
  study

abstract:
  This article describes the use of algebraic methods in a phase plane analysis
of ordinary differential equations. The method is illustrated by the study of
capillary-gravity steady surface waves propagating in shallow water. We
consider the (fully nonlinear, weakly dispersive) Serre-Green-Naghdi equations
with surface tension, because it provides a tractable model that, in the same
time, is not too simple so the interest of the method can be emphasised. In
particular, we analyse a special class of solutions, the solitary waves, which
play an important role in many fields of Physics. In capillary-gravity regime,
there are two kinds of localised infinitely smooth travelling wave solutions --
solitary waves of elevation and of depression. However, if we allow the
solitary waves to have an angular point, the "zoology" of solutions becomes
much richer and the main goal of this study is to provide a complete
classification of such singular localised solutions using the methods of the
effective Algebraic Geometry.

categories: physics.class-ph math.AG math.AP math.CA nlin.SI


title:
Fabricating Highly Ordered Nanofiber Assemblies by Controlled Shear Flow
  and Solvent Evaporation

abstract:
  Fabrication of highly ordered and dense nanofibers assemblies is of key
importance in designing high-performance and multi-functional materials. In
this work, we design an experimental approach in silico, combining shear flow
and solvent evaporation to establish nanofiber alignment and densification of
the assemblies. We demonstrate the feasibility of this approach by performing
dissipative particle dynamics simulations, where the hydrodynamic and thermal
fluctuation effects are fully modeled. We find that the microstructural order
of assembled nanofibers can be established within a specific range of the
Peclet number and evaporation flux. The underlying mechanism is elucidated by
considering the competition between hydrodynamic coupling and fluctuating
dynamics of nanofibers. Based on these understandings, we outline a practical
setup to fabricate highly ordered and dense nanofiber assemblies.


title: The mixing angle as a function of neutrino mass ratio

abstract:
  In the quark sector, we experience a correlation between the mixing angles
and the mass ratios. A partial realization of the similar tie-up in the
neutrino sector helps to constrain the parametrization of masses and mixing,
and hints for a predictive framework. We derive five hierarchy dependent
textures of neutrino mass matrix with minimum number of parameters ($\leq\,4$),
following a model-independent strategy.


title: Fine-scale Surface Normal Estimation using a Single NIR Image

abstract:
  We present surface normal estimation using a single near infrared (NIR)
image. We are focusing on fine-scale surface geometry captured with an
uncalibrated light source. To tackle this ill-posed problem, we adopt a
generative adversarial network which is effective in recovering a sharp output,
which is also essential for fine-scale surface normal estimation. We
incorporate angular error and integrability constraint into the objective
function of the network to make estimated normals physically meaningful. We
train and validate our network on a recent NIR dataset, and also evaluate the
generality of our trained model by using new external datasets which are
captured with a different camera under different environment.


title:
Multi-Photon Multi-Channel Interferometry for Quantum Information
  Processing

abstract:
  This thesis reports advances in the theory of design, characterization and
simulation of multi-photon multi-channel interferometers. I advance the design
of interferometers through an algorithm to realize an arbitrary discrete
unitary transformation on the combined spatial and internal degrees of freedom
of light. This procedure effects an arbitrary $n_{s}n_{p}\times n_{s}n_{p}$
unitary matrix on the state of light in $n_{s}$ spatial and $n_{p}$ internal
modes.
  I devise an accurate and precise procedure for characterizing any multi-port
linear optical interferometer using one- and two-photon interference. Accuracy
is achieved by estimating and correcting systematic errors that arise due to
spatiotemporal and polarization mode mismatch. Enhanced accuracy and precision
are attained by fitting experimental coincidence data to a curve simulated
using measured source spectra. The efficacy of our characterization procedure
is verified by numerical simulations.
  I develop group-theoretic methods for the analysis and simulation of linear
interferometers. I devise a graph-theoretic algorithm to construct the boson
realizations of the canonical SU$(n)$ basis states, which reduce the canonical
subgroup chain, for arbitrary $n$. The boson realizations are employed to
construct $\mathcal{D}$-functions, which are the matrix elements of arbitrary
irreducible representations, of SU$(n)$ in the canonical basis. I show that
immanants of principal submatrices of a unitary matrix $T$ are a sum of the
diagonal $\mathcal{D}(\Omega)$-functions of group element $\Omega$ over $t$
determined by the choice of submatrix and over the irrep $(\lambda)$ determined
by the immanant under consideration. The algorithm for $\mathrm{SU}(n)$
$\mathcal{D}$-function computation and the results connecting these functions
with immanants open the possibility of group-theoretic analysis and simulation
of linear optics.


title: Uniform convergence of penalized time-inhomogeneous Markov processes

abstract:
  We provide an original and general sufficient criterion ensuring the
exponential contraction of Feynman-Kac semi-groups of penalized processes. This
criterion is applied to time-inhomogeneous one-dimensional diffusion processes
conditioned not to hit 0 and to penalized birth and death processes evolving in
a quenched random environment.


title:
Discrete approximations of determinantal point processes on continuous
  spaces: tree representations and tail triviality

abstract:
  We prove tail triviality of determinantal point processes $ \mu $ on
continuous spaces. Tail triviality had been proved for such processes only on
discrete spaces, and hence we have generalized the result to continuous spaces.
To do this, we construct tree representations, that is, discrete approximations
of determinantal point processes enjoying a determinantal structure. There are
many interesting examples of determinantal point processes on continuous spaces
such as zero points of the hyperbolic Gaussian analytic function with Bergman
kernel, and the thermodynamic limit of eigenvalues of Gaussian random matrices
for Sine$_2 $, Airy$_2 $, Bessel$_2 $, and Ginibre point processes. Tail
triviality of $ \mu $ plays a significant role in proving the uniqueness of
solutions of infinite-dimensional stochastic differential equations (ISDEs)
associated with $ \mu $. For particle systems in $ \R $ arising from random
matrix theory, there are two completely different constructions of natural
stochastic dynamics. One is given by stochastic analysis through ISDEs and
Dirichlet form theory, and the other is an algebraic method based on space-time
correlation functions. Tail triviality is used crucially to prove the
equivalence of these two stochastic dynamics.


title:
Global persistence of geometrical structures for the boussinesq equation
  with no diffusion

abstract:
  Here we investigate the so-called temperature patch problem for the
incompressible Boussinesq system with partial viscosity, in the whole space
$\mathbb{R}^N$ $(N \geq 2)$, where the initial temperature is the
characteristic function of some simply connected domain with $C^{1,
\varepsilon}$ H{\"o}lder regularity. Although recent results in [1, 15] ensure
that an initially $C^1$ patch persists through the evolution, whether higher
regularity is preserved has remained an open question. In the present paper, we
give a positive answer to that issue globally in time, in the 2-D case for
large initial data and in the higher dimension case for small initial data.


title: Density matrix of radiation of black hole with fluctuating horizon

abstract:
  The density matrix of Hawking radiation is calculated in the model of black
hole with fluctuating horizon. Quantum fluctuations smear the classical horizon
of black hole and modify the density matrix of radiation producing the
off-diagonal elements. The off-diagonal elements may store information of
correlations between radiation and black hole. The smeared density matrix was
constructed by convolution of the density matrix calculated with the
instantaneous horizon with the Gaussian distribution over the instantaneous
horizons. The distribution has the extremum at the classical radius of the
black hole and the width of order of the Planck length. Calculations were
performed in the model of black hole formed by the thin collapsing shell which
follows a trajectory which is a solution of the matching equations connecting
the interior and exterior geometries.


title: Serving by local consensus in the public service location game

abstract:
  We discuss the issue of distributed and cooperative decision-making in a
network game of public service location. Each node of the network can choose to
be a provider of service which is accessible to the provider itself and also to
all the neighboring nodes. A node may also choose only to be a consumer, and
then it has to pay a tax, and the collected tax is evenly distributed to all
the service providers to remedy their cost. If nodes do not communicate with
each other but make individual best-response decisions, the system will be
trapped in an inefficient situation of high tax level. In this work we
investigate a decentralized local-consensus selection mechanism, according to
which nodes in need of service recommend their neighbors of highest local
impact as candidate servers, and a node may become a server only if all its
non-server neighbors give their assent. We demonstrate that this
local-consensus mechanism, although only involving information exchange among
neighboring nodes, leads to socially efficient solutions with tax level
approaching the lowest possible value. Our results may help in understanding
and improving collective problem-solving in various networked social systems
and robotic systems.


title:
Interplay between magnetism and energetics in FeCr alloys from a
  predictive non-collinear magnetic tight-binding model

abstract:
  Magnetism is a key driving force controlling several thermodynamic and
kinetic properties of Fe-Cr systems. We present a newly-developed TB model for
Fe-Cr, where magnetism is treated beyond the usual collinear approcimation. A
major advantage of this model consists in a rather simple fitting procedure. In
particular, no specific properties of the binary system is explicitly required
in the fitting database. The present model is proved to be accurate and highly
transfer-able for electronic, magnetic and energetic properties of a large
variety of structural and chemical environments: surfaces, interfaces, embedded
clusters, and the whole compositional range of the binary alloy. The occurence
of non-collinear magnetic configurations caused by magnetic frustrations is
successfully predicted. The present TB approach can apply for other binary
magnetic transition-metal alloys. It is expected to be particularly promissing
if the size difference between the alloying elements is rather small and the
electronic properties prevail.


title:
Three-body model for an isoscalar spin-triplet neutron-proton pair in
  $^{102}{\rm Sb}$

abstract:
  We discuss the isoscalar $T=0, S=1$ pairing correlation in the low-lying
states of $^{102}{\rm Sb}={}^{100}{\rm Sn}+p+n$ nucleus. To this end, we employ
${\rm core}+p+n$ three-body model with the model space constructed by
self-consistent mean-field calculations. The model is developed with both
non-relativistic and relativistic effective interactions, the latter of which
are found to be more realistic for the present case due to the pseudo-spin
symmetry. It turns out that the $(L,S,T)=(0,1,0)$ pairing scheme is strongly
hindered in $^{102}$Sb with the relativistic model because of the near
degeneracy of the $g_{7/2}$ and $d_{5/2}$ orbitals in the valence space. This
pair-breaking effect is clearly seen in the charge-exchange Gamow-Teller-type
transitions rather than in the binding energies of $T=0$ and $T=1$ states.


title: A Classical Realizability Model for a Semantical Value Restriction

abstract:
  We present a new type system with support for proofs of programs in a
call-by-value language with control operators. The proof mechanism relies on
observational equivalence of (untyped) programs. It appears in two type
constructors, which are used for specifying program properties and for encoding
dependent products. The main challenge arises from the lack of expressiveness
of dependent products due to the value restriction. To circumvent this
limitation we relax the syntactic restriction and only require equivalence to a
value. The consistency of the system is obtained semantically by constructing a
classical realizability model in three layers (values, stacks and terms).


title: Simple Does It: Weakly Supervised Instance and Semantic Segmentation

abstract:
  Semantic labelling and instance segmentation are two tasks that require
particularly costly annotations. Starting from weak supervision in the form of
bounding box detection annotations, we propose a new approach that does not
require modification of the segmentation training procedure. We show that when
carefully designing the input labels from given bounding boxes, even a single
round of training is enough to improve over previously reported weakly
supervised results. Overall, our weak supervision approach reaches ~95% of the
quality of the fully supervised model, both for semantic labelling and instance
segmentation.


title:
Attraction-induced dynamical stability of a Bose-Einstein condensate in
  a nonlinear lattice

abstract:
  We study multiple-period Bloch states of a Bose-Einstein condensate with
spatially periodic interactomic interaction. Solving the Gross-Pitaevskii
equation for the continuum model, and also using a simplified discrete version
of it, we investigate the energy-band structures and the corresponding
stability properties. We observe a new "attraction-induced dynamical stability"
mechanism caused by the localization of the density distribution in the
attractive domains of the system and the isolation of these higher-density
regions. This makes the superfluid stable near the zone boundary, and also
enhances the stability of higher-periodic states if the nonlinear interaction
strength is sufficiently high.


title: The Matrix Sequence in terms of bi-periodic Fibonacci numbers

abstract:
  In this paper, we define the bi-periodic Fibonacci matrix sequence that
represent bi-periodic Fibonacci numbers. Then, we investigate generating
function, Binet formula and summations of bi-periodic Fibonacci matrix
sequence. After that, we say that some behaviours of bi-periodic Fibonacci
numbers also can be obtained by considering properties of this new matrix
sequence. Finally, we express that well-known matrix sequences, such as
Fibonacci, Pell, $k$-Fibonacci matrix sequences are special cases of this
generalized matrix sequence.


title: Conic Martingales from Stochastic Integrals

abstract:
  In this paper we introduce the concept of conic martingales}. This class
refers to stochastic processes having the martingale property, but that evolve
within given (possibly time-dependent) boundaries. We first review some results
about the martingale property of solution to driftless stochastic differential
equations. We then provide a simple way to construct and handle such processes.
Specific attention is paid to martingales in $[0,1]$. One of these martingales
proves to be analytically tractable. It is shown that up to shifting and
rescaling constants, it is the only martingale (with the trivial constant,
Brownian motion and Geometric Brownian motion) having a separable coefficient
$\sigma(t,y)=g(t)h(y)$ and that can be obtained via a time-homogeneous mapping
of Gaussian diffusions. The approach is exemplified to the modeling of
stochastic conditional survival probabilities in the univariate (both
conditional and unconditional to survival) and bivariate cases.


title: Modular Curves with many Points over Finite Fields

abstract:
  We compute the number of points over finite fields of some classes of modular
curves, namely $X_0(N)$, $X_0^+(N)$, without using explicit equations. In this
way we could improve many lower bounds for the maximum number of points of a
curve over finite fields.


title: Landweber-Kaczmarz method in Banach spaces with inexact inner solvers

abstract:
  In recent years Landweber(-Kaczmarz) method has been proposed for solving
nonlinear ill-posed inverse problems in Banach spaces using general convex
penalty functions. The implementation of this method involves solving a
(nonsmooth) convex minimization problem at each iteration step and the existing
theory requires its exact resolution which in general is impossible in
practical applications. In this paper we propose a version of
Landweber-Kaczmarz method in Banach spaces in which the minimization problem
involved in each iteration step is solved inexactly. Based on the
$\varepsilon$-subdifferential calculus we give a convergence analysis of our
method. Furthermore, using Nesterov's strategy, we propose a possible
accelerated version of Landweber-Kaczmarz method. Numerical results on computed
tomography and parameter identification in partial differential equations are
provided to support our theoretical results and to demonstrate our accelerated
method.


title:
The C(3P) + NH3 reaction in interstellar chemistry: II. Low temperature
  rate constants and modeling of NH, NH2 and NH3 abundances in dense
  interstellar clouds

abstract:
  A continuous supersonic flow reactor has been used to measure rate constants
for the C + NH3 reaction over the temperature range 50 to 296 K. C atoms were
created by the pulsed laser photolysis of CBr4. The kinetics of the title
reaction were followed directly by vacuum ultra-violet laser induced
fluorescence (VUV LIF) of C loss and through H formation. The experiments show
unambiguously that the reaction is rapid at 296 K, becoming faster at lower
temperatures, reaching a value of 1.8 10-10 cm3 molecule-1 s-1 at 50 K. As this
reaction is not currently included in astrochemical networks, its influence on
interstellar nitrogen hydride abundances is tested through a dense cloud model
including gas-grain interactions. In particular, the effect of the
ortho-to-para ratio of H2 which plays a crucial role in interstellar NH3
synthesis is examined.


title:
Light scattering by fractal dust aggregates: I. Angular dependence of
  scattering

abstract:
  In protoplanetary disks, micron-sized dust grains coagulate to form highly
porous dust aggregates. Because the optical properties of these aggregates are
not completely understood, it is important to investigate how porous dust
aggregates scatter light. In this study, the light scattering properties of
porous dust aggregates were calculated using a rigorous method, the T-matrix
method, and the results were then compared with those obtained using the
Rayleigh-Gans-Debye (RGD) theory and Mie theory with the effective medium
approximation (EMT). The RGD theory is applicable to moderately large
aggregates made of nearly transparent monomers. This study considered two types
of porous dust aggregates, ballistic cluster-cluster agglomerates (BCCAs) and
ballistic particle-cluster agglomerates (BPCAs). First, the angular dependence
of the scattered intensity was shown to reflect the hierarchical structure of
dust aggregates; the large-scale structure of the aggregates is responsible for
the intensity at small scattering angles, and their small-scale structure
determines the intensity at large scattering angles. Second, it was determined
that the EMT underestimates the backward scattering intensity by multiple
orders of magnitude, especially in BCCAs, because the EMT averages the
structure within the size of the aggregates. It was concluded that the RGD
theory is a very useful method for calculating the optical properties of BCCAs.


title: Semiparametric Copula Quantile Regression for Complete or Censored Data

abstract:
  When facing multivariate covariates, general semiparametric regression
techniques come at hand to propose flexible models that are unexposed to the
curse of dimensionality. In this work a semiparametric copula-based estimator
for conditional quantiles is investigated for complete or right-censored data.
In spirit, the methodology is extending the recent work of Noh et al. (2013)
and Noh et al. (2015), as the main idea consists in appropriately defining the
quantile regression in terms of a multivariate copula and marginal
distributions. Prior estimation of the latter and simple plug-in lead to an
easily implementable estimator expressed, for both contexts with or without
censoring, as a weighted quantile of the observed response variable. In
addition, and contrary to the initial suggestion in the literature, a
semiparametric estimation scheme for the multivariate copula density is
studied, motivated by the possible shortcomings of a purely parametric approach
and driven by the regression context. The resulting quantile regression
estimator has the valuable property of being automatically monotonic across
quantile levels, and asymptotic normality for both complete and censored data
is obtained under classical regularity conditions. Finally, numerical examples
as well as a real data application are used to illustrate the validity and
finite sample performance of the proposed procedure.


title:
Asymmetric Fuglede Putnam's Theorem for operators reduced by their
  eigenspaces

abstract:
  Fuglede-Putnam Theorem have been proved for a considerably large number of
class of operators. In this paper by using the spectral theory, we obtain a
theoretical and general framework from which Fuglede-Putnam theorem may be
promptly established for many classes of operators.


title: Quantum-classical transition in the Caldeira-Leggett model

abstract:
  The quantum-classical transition in the Caldeira-Leggett model is
investigated in the framework of the functional renormalization group method.
It is shown that a divergent quadratic term arises in the action due to the
heat bath in the model. By removing the divergence with a frequency cutoff we
considered the critical behavior of the model. The critical exponents belonging
to the susceptibility and the correlation length are determined and their
independence of the frequency cutoff and the renormalization scheme is shown.


title:
The inverse problem of a mixed Li\'enard type nonlinear oscillator
  equation from symmetry perspective

abstract:
  In this paper, we discuss the inverse problem for a mixed Li\'enard type
nonlinear oscillator equation $\ddot{x}+f(x)\dot{x}^2+g(x)\dot{x}+h(x)=0$,
where $f(x),\,g(x)$ and $h(x)$ are arbitrary functions of $x$. Very recently,
we have reported the Lie point symmetries of this equation. By exploiting the
interconnection between Jacobi last multiplier, Lie point symmetries and
Prelle-Singer procedure we construct a time independent integral for the case
exhibiting maximal symmetry from which we identify the associated conservative
non-standard Lagrangian and Hamiltonian functions. The classical dynamics of
the nonlinear oscillator is also discussed and certain special properties
including isochronous oscillations are brought out.


title: On permutable meromorphic functions

abstract:
  We study the class $\mathcal{M}$ of functions meromorphic outside a countable
closed set of essential singularities. We show that if a function in
$\mathcal{M}$, with at least one essential singularity, permutes with a
non-constant rational map $g$, then $g$ is a M\"{o}bius map that is not
conjugate to an irrational rotation. For a given function $ f \in\mathcal{M}$
which is not a M\"{o}bius map, we show that the set of functions in
$\mathcal{M}$ that permute with $ f $ is countably infinite. Finally, we show
that there exist transcendental meromorphic functions $f: \mathbb{C} \to
\mathbb{C}$ such that, among functions meromorphic in the plane, $f$ permutes
only with itself and with the identity map.


title: Fluctuations of the competition interface in presence of shocks

abstract:
  We consider last passage percolation (LPP) models with exponentially
distributed random variables, which are linked to the totally asymmetric simple
exclusion process (TASEP). The competition interface for LPP was introduced and
studied by Ferrari and Pimentel in [Ann. Probab. 33 (2005), 1235-1254] for
cases where the corresponding exclusion process had a rarefaction fan. Here we
consider situations with a shock and determine the law of the fluctuations of
the competition interface around its deterministic law of large number
position. We also study the multipoint distribution of the LPP around the
shock, extending our one-point result of [Probab. Theory Relat. Fields 61
(2015), 61-109].


title: Low-temperature quantum transport in CVD-grown single crystal graphene

abstract:
  Chemical vapor deposition (CVD) has been proposed for large-scale graphene
synthesis for practical applications. However, the inferior electronic
properties of CVD graphene are one of the key problems to be solved. In this
study, we present a detailed study on the electronic properties of high-quality
single crystal monolayer graphene. The graphene is grown by CVD on copper using
a cold-wall reactor and then transferred to Si/SiO2. Our low-temperature
magneto-transport data demonstrate that the characteristics of the measured
single-crystal CVD graphene samples are superior to those of polycrystalline
graphene and have a quality which is comparable to that of exfoliated graphene
on Si/SiO2. The Dirac point in our best samples is located at back-gate
voltages of less than 10V, and their mobility can reach 11000 cm2/Vs. More than
12 flat and discernible half-integer quantum Hall plateaus have been observed
in high magnetic field on both the electron and hole side of the Dirac point.
At low magnetic field, the magnetoresistance shows a clear weak localization
peak. Using the theory of McCann et al., we find that the inelastic scattering
length is larger than 1 {\mu}m in these samples even at the charge neutrality
point.


title: Recognizing projections of rational curves

abstract:
  Given two rational, properly parametrized space curves ${\mathcal C}_1$ and
${\mathcal C}_2$, where $\CCC_2$ is contained in some plane $\Pi$, we provide
an algorithm to check whether or not there exist perspective or parallel
projections mapping $\CCC_1$ onto $\CCC_2$, i.e. to recognize $\CCC_2$ as the
projection of $\CCC_1$. In the affirmative case, the algorithm provides the eye
point(s) of the perspective transformation(s), or the direction(s) of the
parallel projection(s). The problem is mainly discussed from a symbolic point
of view, but an approximate algorithm is also included.


title: Measures and fibers

abstract:
  We study measures on compact spaces by analyzing the properties of fibers of
continuous mappings into 2^omega. We show that if a compact zerodimensional
space K carries a measure of uncountable Maharam type, then such a mapping has
a non-scattered fiber and, if we assume additionally a weak version of Martin's
Axiom, such a mapping has a fiber carrying a measure of uncountable Maharam
type. Also, we prove that every compact zerodimensional space which supports a
strictly positive measure and which can be mapped into 2^omega by a
finite-to-one function is separable.


title:
Energy solutions to one-dimensional singular parabolic problems with
  $BV$ data are viscosity solutions

abstract:
  We study one-dimensional very singular parabolic equations with periodic
boundary conditions and initial data in $BV$, which is the energy space. We
show existence of solutions in this energy space and then we prove that they
are viscosity solutions in the sense of Giga-Giga.


title: Dirac quantum time mirror

abstract:
  Both metaphysical and practical considerations related to time inversion have
intrigued scientists for generations. Physicists have strived to devise and
implement time-inversion protocols, in particular different forms of "time
mirrors" for classical waves. Here we propose an instantaneous time mirror for
quantum systems, i.e., a controlled time discontinuity generating wave function
echoes with high fidelities. This concept exploits coherent particle-hole
oscillations in a Dirac spectrum in order to achieve population reversal, and
can be implemented in systems such as (real or artificial) graphene.


title: A General Framework for Estimating Graphlet Statistics via Random Walk

abstract:
  Graphlets are induced subgraph patterns and have been frequently applied to
characterize the local topology structures of graphs across various domains,
e.g., online social networks (OSNs) and biological networks. Discovering and
computing graphlet statistics are highly challenging. First, the massive size
of real-world graphs makes the exact computation of graphlets extremely
expensive. Secondly, the graph topology may not be readily available so one has
to resort to web crawling using the available application programming
interfaces (APIs). In this work, we propose a general and novel framework to
estimate graphlet statistics of "any size". Our framework is based on
collecting samples through consecutive steps of random walks. We derive an
analytical bound on the sample size (via the Chernoff-Hoeffding technique) to
guarantee the convergence of our unbiased estimator. To further improve the
accuracy, we introduce two novel optimization techniques to reduce the lower
bound on the sample size. Experimental evaluations demonstrate that our methods
outperform the state-of-the-art method up to an order of magnitude both in
terms of accuracy and time cost.


title:
Effect of electronic correlations on the metal-insulator transition of
  $\alpha$-(BEDT-TTF)$_2$I$_3$: theoretical and experimental investigations of
  its optical properties

abstract:
  The organic salt $\alpha$-(BEDT-TTF)$_2$I$_3$ is considered a model system
for metal-insulator transition due to electronic charge ordering at $T_{\rm
CO}=135$~K. The optical properties obtained from polarized reflection
measurements above and below $T_{\rm CO}$ can be well described by calculations
based on first-principle density-functional theory (DFT). We discuss the effect
of electronic correlations on the metal-insulator transition.


title:
Separated spin evolution quantum hydrodynamics of degenerated electrons
  with spin-orbit interaction and extraordinary wave spectrum

abstract:
  To consider a contribution of the spin-orbit interaction in the extraordinary
wave spectrum we derive a generalization of the separate spin evolution quantum
hydrodynamics. Applying corresponding nonlinear Pauli equation we include Fermi
spin current contribution in the spin evolution. We find that the spectrum of
extraordinary waves consists of three branches: two of them are well-known
extraordinary waves and the third one is the spin-electron acoustic wave
(SEAW). Earlier SEAWs have been considered in the electrostatic limit. Here we
include the electromagnetic effects in their spectrum at the propagation
perpendicular to the external magnetic field. We find that the SEAW spectrum
considerably changes at the account of transverse part of electric field. We
obtain that the separate spin evolution modifies spectrum of the well-known
extraordinary waves either. A change of the extraordinary wave spectrum due to
the spin-orbit interaction is obtained as well.


title: Relativistic Mirrors in Laser Plasmas (Analytical Methods)

abstract:
  Relativistic flying mirrors in plasmas are realized as thin dense electron
(or electron-ion) layers accelerated by high-intensity electromagnetic waves to
velocities close to the speed of light in vacuum. The reflection of an
electromagnetic wave from the relativistic mirror results in its energy and
frequency changing. In a counter-propagation configuration, the frequency of
the reflected wave is multiplied by the factor proportional to the Lorentz
factor squared. This scientific area promises the development of sources of
ultrashort X-ray pulses in the attosecond range. The expected intensity will
reach the level at which the effects predicted by nonlinear quantum
electrodynamics start to play a key role.


title: Entanglement and coherence in quantum state merging

abstract:
  Understanding the resource consumption in distributed scenarios is one of the
main goals of quantum information theory. A prominent example for such a
scenario is the task of quantum state merging where two parties aim to merge
their parts of a tripartite quantum state. In standard quantum state merging,
entanglement is considered as an expensive resource, while local quantum
operations can be performed at no additional cost. However, recent developments
show that some local operations could be more expensive than others: it is
reasonable to distinguish between local incoherent operations and local
operations which can create coherence. This idea leads us to the task of
incoherent quantum state merging, where one of the parties has free access to
local incoherent operations only. In this case the resources of the process are
quantified by pairs of entanglement and coherence. Here, we develop tools for
studying this process, and apply them to several relevant scenarios. While
quantum state merging can lead to a gain of entanglement, our results imply
that no merging procedure can gain entanglement and coherence at the same time.
We also provide a general lower bound on the entanglement-coherence sum, and
show that the bound is tight for all pure states. Our results also lead to an
incoherent version of Schumacher compression: in this case the compression rate
is equal to the von Neumann entropy of the diagonal elements of the
corresponding quantum state.


title: Pseudo B-Fredholm Operators and Spectral Theory

abstract:
  In this paper, we show that every pseudo B-Fredholm operator is a pseudo
Fredholm operator. Afterwards, we prove that the pseudo B-Weyl spectrum is
empty if and only if the pseudo B-Fredholm spectrum is empty. Also, we study a
symmetric difference between some parts of the spectrum.


title:
New axiomatizable classes of Banach spaces via disjointness-preserving
  isometries

abstract:
  Let C be an axiomatizable class of order continuous real or complex Banach
lattices, that is, this class is closed under isometric vector lattice
isomorphisms and ultraproducts, and the complementary class is closed under
ultrapowers. We show that if linear isometric embeddings of members of C in
their ultrapowers preserve disjointness, the class C^B of Banach spaces
obtained by forgetting the Banach lattice structure is still axiomatizable.
Moreover if C coincides with its "script class" SC, so does C^B with SC^B. This
allows us to give new examples of axiomatizable classes of Banach spaces,
namely certain Musielak-Orlicz spaces, Nakano spaces, and mixed norm spaces.


title:
Statistical modelling of individual animal movement: an overview of key
  methods and a discussion of practical challenges

abstract:
  With the influx of complex and detailed tracking data gathered from
electronic tracking devices, the analysis of animal movement data has recently
emerged as a cottage industry amongst biostatisticians. New approaches of ever
greater complexity are continue to be added to the literature. In this paper,
we review what we believe to be some of the most popular and most useful
classes of statistical models used to analyze individual animal movement data.
Specifically we consider discrete-time hidden Markov models, more general
state-space models and diffusion processes. We argue that these models should
be core components in the toolbox for quantitative researchers working on
stochastic modelling of individual animal movement. The paper concludes by
offering some general observations on the direction of statistical analysis of
animal movement. There is a trend in movement ecology toward what are arguably
overly-complex modelling approaches which are inaccessible to ecologists,
unwieldy with large data sets or not based in mainstream statistical practice.
Additionally, some analysis methods developed within the ecological community
ignore fundamental properties of movement data, potentially leading to
misleading conclusions about animal movement. Corresponding approaches, e.g.
based on L\'evy walk-type models, continue to be popular despite having been
largely discredited. We contend that there is a need for an appropriate balance
between the extremes of either being overly complex or being overly simplistic,
whereby the discipline relies on models of intermediate complexity that are
usable by general ecologists, but grounded in well-developed statistical
practice and efficient to fit to large data sets.


title:
Strengthened Reeh-Schlieder Property and Scattering in Quantum Field
  Theories without Mass Gaps

abstract:
  We develop Haag-Ruelle scattering theory for Wigner particles in local
relativistic Quantum Field Theory without assuming mass gaps or any other
restrictions on the spectrum of the mass operator near the particle masses. Our
approach is based on the Reeh-Schlieder property of the vacuum state. It is
shown that a strengthened variant of this property, concerning the relative
approximation error for single-particle states, implies the existence of
scattering states.


title: Achievable DoF Regions of MIMO Networks with Imperfect CSIT

abstract:
  We focus on a two-receiver Multiple-Input-Multiple-Output (MIMO) Broadcast
Channel (BC) and Interference Channel (IC) with an arbitrary number of antennas
at each node. We assume an imperfect knowledge of local Channel State
Information at the Transmitters (CSIT), whose error decays with the
Signal-to-Noise-Ratio. With such configuration, we characterize the achievable
Degrees-of-Freedom (DoF) regions in both BC and IC, by proposing a
Rate-Splitting approach, which divides each receiver's message into a common
part and a private part. Compared to the RS scheme designed for the symmetric
MIMO case, this scheme is suitable for the general asymmetric deployment with
an arbitrary number of antennas at each node. In BC, the proposed block 1)
employs an unequal power allocation to the private messages of the two
receivers, 2) exploits the benefit of having an extra spatial dimension at one
receiver, and 3) is carried out with a Space-Time transmission. These features
enable the scheme to yield a greater DoF region than trivially extending the
scheme designed for the symmetric case. In IC, we modify the scheme proposed
for the BC case by applying a linear transformation to the channel matrices.
Such a linear transformation allows us to identify the signal space where the
two transmitted signals interfere with each other and propose a proper power
allocation policy. The achievable DoF regions are shown to be optimal for some
antenna configurations.


title: Two-loop five-point all plus helicity Yang-Mills amplitude

abstract:
  We re-compute the recently derived two-loop five-point all plus Yang-Mills
amplitude using Unitarity and Recursion. Recursion requires augmented recursion
to determine the sub-leading pole. Using these methods the simplicity of this
amplitude is understood.


title:
The use of discrete gradient methods for total variation type
  regularization problems in image processing

abstract:
  Discrete gradient methods are well-known methods of Geometric Numerical
Integration, which preserve the dissipation of gradient systems. The
preservation of the dissipation of a system is an important feature in numerous
image processing tasks. We promote the use of discrete gradient methods in
image processing by exhibiting experiments with nonlinear total variation (TV)
deblurring, denoising, and inpainting.


title:
Direct Observation in 3d of Structural Crossover in Binary Hard Sphere
  Mixtures

abstract:
  For binary fluid mixtures of spherical particles in which the two species are
sufficiently different in size, the dominant wavelength of oscillations of the
pair correlation functions is predicted to change from roughly the diameter of
the large species to that of the small species along a sharp crossover line in
the phase diagram [C. Grodon, M. Dijkstra, R. Evans & R. Roth, J.Chem.Phys.
121, 7869 (2004)]. Using particle-resolved colloid experiments in 3d we
demonstrate that crossover exists and that its location in the phase diagram is
in quantitative agreement with the results of both theory and our Monte-Carlo
simulations. In contrast with previous work [J. Baumgartl, R. Dullens, M.
Dijkstra, R. Roth & C. Bechinger, Phys.Rev.Lett. 98, 198303 (2007)], where a
correspondence was drawn between crossover and percolation of both species, in
our 3d study we find that structural crossover is unrelated to percolation.


title: Resonances for homoclinic trapped sets

abstract:
  We study semiclassical resonances generated by homoclinic trapped sets.
First, under some general assumptions, we prove that there is no resonance in a
region below the real axis. Then, we obtain a quantization rule and the
asymptotic expansion of the resonances when there is a finite number of
homoclinic trajectories. The same kind of results is proved for homoclinic sets
of maximal dimension. Next, we generalize to the case of
homoclinic/heteroclinic trajectories and we study the three bump case. In all
these settings, the resonances may either accumulate on curves or form clouds.
We also describe the corresponding resonant states.


title: Strange Quark Stars as Probe of Dark Matter

abstract:
  We demonstrate that the observation of old strange quark stars (SQSs) can set
important limits on the scattering cross sections $\sigma_q$ between the light
quarks and the non-interacting scalar dark matter (DM). By analyzing a set of
1403 of solitary pulsarlike compact stars in the Milky Way, we find the old
solitary pulsar PSR J1801-0857D can set the most stringent upper limits on
$\sigma_q$ or the DM-proton scattering cross sections $\sigma_p$. By converting
$\sigma_q$ into $\sigma_p$ based on effective operator analyses, we show the
resulting $\sigma_p$ limit by assuming PSR J1801-0857D to be a SQS could be
comparable with that of the current direct detection experiments but much
weaker (by several orders of magnitude) than that obtained by assuming PSR
J1801-0857D to be a neutron star (NS), which requires an extremely small
$\sigma_p$ far beyond the limits of direct detection experiments. Our findings
imply that the old pulsars are favored to be SQSs rather than NSs if the scalar
DM were observed by future terrestrial experiments.

categories: nucl-th astro-ph.CO astro-ph.SR hep-ph nucl-ex


title:
Angular distribution of cosmological parameters as a probe of
  inhomogeneities: a kinematic parametrisation

abstract:
  We use a kinematic parametrisation of the luminosity distance to measure the
angular distribution on the sky of time derivatives of the scale factor, in
particular the Hubble parameter H_0, the deceleration parameter q_0, and the
jerk parameter j_0. We apply a recently published method to complement probing
the inhomogeneity of the large-scale structure by means of the inhomogeneity in
the cosmic expansion. This parametrisation is independent of the cosmological
equation of state, which renders it adequate to test interpretations of the
cosmic acceleration alternative to the cosmological constant. For the same
analytical toy model of an inhomogeneous ensemble of homogenous pixels, we
derive the backreaction term in j_0 due to the fluctuations of {H_0,q_0} and
measure it to be of order 10^{-2} times the corresponding average over the
pixels in the absence of backreaction. In agreement with that computed using a
Lambda CDM parametrisation of the luminosity distance, the backreaction effect
on q_0 remains below the detection threshold. Although the backreaction effect
on j_0 is about ten times that on q_0, it is also below the detection
threshold. Hence backreaction remains unobservable both in q_0 and in j_0.


title:
Cubic Perturbations of Symmetric elliptic Hamiltonians of degree four in
  a Complex domain

abstract:
  We consider arbitrary one-parameter cubic deformations of the Duffing
oscillator $x"=x-x^3$. In the case when the first Melnikov function $M_1$
vanishes, but $M_2\neq 0$ we compute the general form of $M_2$ and study its
zeros in a suitable complex domain.


title: Some invariant properties of quasi-M\"obius maps

abstract:
  We investigate properties which remain invariant under the action of
quasi-M\"obius maps of quasi-metric spaces. A metric space is called doubling
with constant D if every ball of finite radius can be covered by at most D
balls of half the radius. It is shown that the doubling property is an
invariant property for (quasi-)M\"obius spaces. Additionally it is shown that
the property of uniform disconnectedness is an invariant for (quasi-)M\"obius
spaces as well.


title:
On homoclinic solutions for a second order difference equation with
  p-Laplacian

abstract:
  In this paper, we obtain conditions under which the difference equation
$-\Delta \left( a(k)\phi _{p}(\Delta u(k-1))\right) +b(k)\phi_{p}(u(k))=\lambda
f(k,u(k)),\quad k\in \mathbb{Z}$, has infinitely many homoclinic solutions. A
variant of the fountain theorem is utilized in the proof of our theorem. It
improves the results in [L.Kong, homoclinic solutions for a second order
difference equation with $p-$Laplacian, \textit{Appl. Math. Comput}.,
\textbf{247} (2014), 1113--1121], where the set of conditions imposed on
nonlinearity is inconsistent.


title: On the number of solutions in random hypergraph 2-colouring

abstract:
  We determine the limiting distribution of the logarithm of the number of
satisfying assignments in the random $k$-uniform hypergraph 2-colouring problem
in a certain density regime for all $k\ge 3$ . As a direct consequence we
obtain that in this regime the random colouring model is contiguous wrt. the
planted model, a result that helps simplifying the transfer of statements
between these two models.


title: A Trust Model for Data Sharing in Smart Cities

abstract:
  The data generated by the devices and existing infrastructure in the Internet
of Things (IoT) should be shared among applications. However, data sharing in
the IoT can only reach its full potential when multiple participants contribute
their data, for example when people are able to use their smartphone sensors
for this purpose. We believe that each step, from sensing the data to the
actionable knowledge, requires trust-enabled mechanisms to facilitate data
exchange, such as data perception trust, trustworthy data mining, and reasoning
with trust related policies. The absence of trust could affect the acceptance
of sharing data in smart cities. In this study, we focus on data usage
transparency and accountability and propose a trust model for data sharing in
smart cities, including system architecture for trust-based data sharing, data
semantic and abstraction models, and a mechanism to enhance transparency and
accountability for data usage. We apply semantic technology and defeasible
reasoning with trust data usage policies. We built a prototype based on an air
pollution monitoring use case and utilized it to evaluate the performance of
our solution.


title: The quenched SU(2) fundamental scalar propagator in minimal Landau gauge

abstract:
  It is a long-standing question whether the confinement of matter fields in
QCD has an imprint in the (gauge-dependent) correlation functions, especially
the propagators. As the analytic structure plays an important role in this
question, high-precision data is necessary for lattice investigations. Also, it
is interesting how this depends on the dimensionality of the theory. To make a
study over a wide range of parameters possible this suggests to use scalar
particles. This is done here: The propagator of a fundamental scalar is studied
in two, three, and four dimensions in quenched SU(2) Yang-Mills theory in
minimal Landau gauge, both in momentum space and position space. Particular
emphasis is put on the effects of renormalization. The results suggest a quite
intricate volume dependence and the presence of an intrinsic mass scale, but no
obvious connection to confinement.


title:
Self-energies of ground-state octet and decuplet baryon states due to
  the coupling to the baryon-meson continuum

abstract:
  We present an unquenched quark model calculation of the mass shifts of
ground-state octet and decuplet baryons due to the coupling to the meson-baryon
continuum. The $q\bar{q}$ pair-creation effects are taken explicitly into
account through a microscopic, QCD-inspired, quark-antiquark pair- creation
mechanism.


title:
Experience with wavefront sensor and deformable mirror interfaces for
  wide-field adaptive optics systems

abstract:
  Recent advances in adaptive optics (AO) have led to the implementation of
wide field-of-view AO systems. A number of wide-field AO systems are also
planned for the forthcoming Extremely Large Telescopes. Such systems have
multiple wavefront sensors of different types, and usually multiple deformable
mirrors (DMs).
  Here, we report on our experience integrating cameras and DMs with the
real-time control systems of two wide-field AO systems. These are CANARY, which
has been operating on-sky since 2010, and DRAGON, which is a laboratory
adaptive optics real-time demonstrator instrument. We detail the issues and
difficulties that arose, along with the solutions we developed. We also provide
recommendations for consideration when developing future wide-field AO systems.


title:
Occupation times of generalized Ornstein-Uhlenbeck processes with
  two-sided exponential jumps

abstract:
  For an Ornstein-Uhlenbeck process driven by a double exponential jump
diffusion process, we obtain formulas for the joint Laplace transform of it and
its occupation times. The approach used is remarkable and can be extended to
investigate the occupation times of an Ornstein-Uhlenbeck process driven by a
more general Levy process.


title: Low-cost approximate reconstructing of heterogeneous microstructures

abstract:
  We propose an approximate reconstruction of random heterogeneous
microstructures using the two-exponent power-law (TEPL). This rule originates
from the entropic descriptor (ED) that is a multi-scale measure of spatial
inhomogeneity for a given microstructure. A digitized target sample is a cube
of linear size L in voxels. Then, a number of trial configurations can be
generated by a model of overlapping spheres of a fixed radius, which are
randomly distributed on a regular lattice. The TEPL describes the averaged
maximum of the ED as a function of the phase concentration and the radius.
Thus, it can be used to determine the radius. The suggested approach is tested
on surrogate samples of ceramic and carbonate. In each of the cases, fifty
low-cost trials provided a few good enough candidates to a selection of the
optimal reconstruction. When a better accuracy is planned, the final
reconstructions can serve as the starting configurations. Then, the resulting
reconstructions should be competitive indeed to those starting with random
configurations.


title:
Ab initio Investigation of Vibrational, Thermodynamic, and Optical
  properties of Sc2AlC MAX compound

abstract:
  The structural, vibrational, thermodynamical and optical properties of
technologically important, weakly coupled MAX compound, Sc2AlC are calculated
using density functional theory (DFT). The structural properties of Sc2AlC are
compared with results reported earlier. The vibrational, thermodynamical, and
optical properties are theoretically estimated for the first time. The phonon
dispersion curve has been calculated and the dynamical stability of this
compound has been investigated. The optical and acoustic modes are observed
clearly. We have calculated the Helmholtz free energy (F), internal energy (E),
entropy (S) and specific heat capacity (Cv) from the phonon density of states.
Various optical parameters have also been calculated. The reflectance spectrum
shows that it this compound has the potential to be used as a solar reflector.


title: Global solutions to folded concave penalized nonconvex learning

abstract:
  This paper is concerned with solving nonconvex learning problems with folded
concave penalty. Despite that their global solutions entail desirable
statistical properties, they lack optimization techniques that guarantee global
optimality in a general setting. In this paper, we show that a class of
nonconvex learning problems are equivalent to general quadratic programs. This
equivalence facilitates us in developing mixed integer linear programming
reformulations, which admit finite algorithms that find a provably global
optimal solution. We refer to this reformulation-based technique as the mixed
integer programming-based global optimization (MIPGO). To our knowledge, this
is the first global optimization scheme with a theoretical guarantee for folded
concave penalized nonconvex learning with the SCAD penalty [J. Amer. Statist.
Assoc. 96 (2001) 1348-1360] and the MCP penalty [Ann. Statist. 38 (2001)
894-942]. Numerical results indicate a significant outperformance of MIPGO over
the state-of-the-art solution scheme, local linear approximation and other
alternative solution techniques in literature in terms of solution quality.


title: A Short Note on P-Value Hacking

abstract:
  We present the expected values from p-value hacking as a choice of the
minimum p-value among $m$ independents tests, which can be considerably lower
than the "true" p-value, even with a single trial, owing to the extreme
skewness of the meta-distribution.
  We first present an exact probability distribution (meta-distribution) for
p-values across ensembles of statistically identical phenomena. We derive the
distribution for small samples $2<n \leq n^*\approx 30$ as well as the limiting
one as the sample size $n$ becomes large. We also look at the properties of the
"power" of a test through the distribution of its inverse for a given p-value
and parametrization.
  The formulas allow the investigation of the stability of the reproduction of
results and "p-hacking" and other aspects of meta-analysis.
  P-values are shown to be extremely skewed and volatile, regardless of the
sample size $n$, and vary greatly across repetitions of exactly same protocols
under identical stochastic copies of the phenomenon; such volatility makes the
minimum $p$ value diverge significantly from the "true" one. Setting the power
is shown to offer little remedy unless sample size is increased markedly or the
p-value is lowered by at least one order of magnitude.


title:
Sampling measures, Muckenhoupt Hamiltonians, and triangular
  factorization

abstract:
  Let $\mu$ be an even measure on the real line $\mathbb{R}$ such that $$c_1
\int_{\mathbb{R}}|f|^2\,dx \le \int_{\mathbb{R}}|f|^2\,d\mu \le
c_2\int_{\mathbb{R}}|f|^2\,dx$$ for all functions $f$ in the Paley-Wiener space
$\mathrm{PW}_{a}$. We prove that $\mu$ is the spectral measure for the unique
Hamiltonian $\mathcal{H}=\left(w&00&\frac{1}{w}\right)$ on $[0,a]$ generated by
a weight $w$ from the Muckenhoupt class $A_2[0,a]$. As a consequence of this
result, we construct Krein's orthogonal entire functions with respect to $\mu$
and prove that every positive, bounded, invertible Wiener-Hopf operator on
$[0,a]$ with real symbol admits triangular factorization.


title: Web Data Knowledge Extraction

abstract:
  A constantly growing amount of information is available through the web.
Unfortunately, extracting useful content from this massive amount of data still
remains an open issue. The lack of standard data models and structures forces
developers to create adhoc solutions from the scratch. The figure of the expert
is still needed in many situations where developers do not have the correct
background knowledge. This forces developers to spend time acquiring the needed
background from the expert. In other directions, there are promising solutions
employing machine learning techniques. However, increasing accuracy requires an
increase in system complexity that cannot be endured in many projects. In this
work, we approach the web knowledge extraction problem using an expertcentric
methodology. This methodology defines a set of configurable, extendible and
independent components that permit the reutilisation of large pieces of code
among projects. Our methodology differs from similar solutions in its
expert-driven design. This design, makes it possible for subject-matter expert
to drive the knowledge extraction for a given set of documents. Additionally,
we propose the utilization of machine assisted solutions that guide the expert
during this process. To demonstrate the capabilities of our methodology, we
present a real use case scenario in which public procurement data is extracted
from the web-based repositories of several public institutions across Europe.
We provide insightful details about the challenges we had to deal with in this
use case and additional discussions about how to apply our methodology.


title:
In-plane Topological p-n Junction in the Three-Dimensional Topological
  Insulator Bi$_{2-x}$Sb$_x$Te$_{3-y}$Se$_y$

abstract:
  A topological p-n junction (TPNJ) is an important concept to control spin and
charge transport on a surface of three dimensional topological insulators
(3D-TIs). Here we report successful fabrication of such TPNJ on a surface of
3D-TI Bi$_{2-x}$Sb$_x$Te$_{3-y}$Se$_y$ thin films and experimental observation
of the electrical transport. By tuning the chemical potential of n-type
topological Dirac surface of BSTS on its top half by employing
tetrafluoro-7,7,8,8-tetracyanoquinodimethane as an organic acceptor molecule, a
half surface can be converted to p-type with leaving the other half side as the
opposite n-type, and consequently TPNJ can be created. By sweeping the
back-gate voltage in the field effect transistor structure, the TPNJ was
controlled both on the bottom and the top surfaces. A dramatic change in
electrical transport observed at the TPNJ on 3D-TI thin films promises novel
spin and charge transport of 3D-TIs for future spintronics.


title:
Viscoelasticity with time-dependent memory kernels. Part II: asymptotic
  behavior of solutions

abstract:
  We continue the analysis on the model equation arising in the theory of
viscoelasticity $$ \partial_{tt} u(t)-\big[1+k_t(0)\big]\Delta u(t)
-\int_0^\infty k'_t(s)\Delta u(t-s) d s + f(u(t)) = g $$ in the presence of a
(convex, nonnegative and summable) memory kernel $k_t(\cdot)$ explicitly
depending on time. Such a model is apt to describe, for instance, the dynamics
of aging viscoelastic materials. The earlier paper [4] was concerned with the
correct mathematical setting of the problem, and provided a well-posedness
result within the novel theory of dynamical systems acting on time-dependent
spaces, recently established by Di Plinio {\it et al.}\ [14] In this second
work, we focus on the asymptotic properties of the solutions, proving the
existence and the regularity of the time-dependent global attractor for the
dynamical process generated by the equation. In addition, when $k_t$ approaches
a multiple $m\delta_0$ of the Dirac mass at zero as $t\to\infty$, we show that
the asymptotic dynamics of our problem is close to the one of its formal limit
$$\partial_{tt} u(t)-\Delta u(t) -m\Delta\partial_t u(t)+ f(u(t)) = g$$
describing viscoelastic solids of Kelvin-Voigt type.


title:
The local structure of electrically stressed liquid water and
  implications for modelling of dielectric relaxation

abstract:
  In a floating water bridge the total radiation scattering of water stressed
by a moderately strong electric field (1mV/nm) was compared to water without an
applied electric field using X-ray and small angle neutron scattering.
Structure refinement was carried out using the EPSR method and the TIP4P/2005
water model. These results did not reveal a significant difference in the local
static structure of water however analysis of the simulation indicated that the
modeled local potential energy surface reveals a departure between electrically
stressed and unstressed water. The observed differences show that the local
environment is changed by the applied electric field although weak relative to
the intermolecular coulombic field. When discussing the results we show that
the current methods used to simulate the pair potentials are still insufficient
to treat such non-equilibrium systems and further simulation techniques have to
be developed to properly reconstruct the microscopic dielectric relaxation
process.


title: Certifying Spoofing-Protection of Firewalls

abstract:
  We present an algorithm to certify IP spoofing protection of firewall
rulesets. The algorithm is machine-verifiably proven sound and its use is
demonstrated in real-world scenarios.


title: Cooperative strings in glassy nanoparticles

abstract:
  Motivated by recent experimental results on glassy polymer nanoparticles, we
develop a minimal theoretical framework for the glass transition in spherical
confinement. This is accomplished using our cooperative-string model for
supercooled dynamics, that was successful at recovering the bulk phenomenology
and describing the thin-film anomalies. In particular, we obtain predictions
for the mobile-layer thickness as a function of temperature, and for the
effective glass-transition temperature as a function of the radius of the
spherical nanoparticle - including the existence of a critical particle radius
below which vitrification never occurs. Finally, we compare the theoretical
results to experimental data on polystyrene from the recent literature, and we
discuss the latter.

categories: cond-mat.stat-mech cond-mat.dis-nn cond-mat.mes-hall cond-mat.soft physics.chem-ph


title: A multiscale mathematical model of tumour invasive growth

abstract:
  Known as one of the hallmarks of cancer [30], cancer cell invasion of human
body tissue is a complicated spatio-temporal multiscale process which enables a
localised solid tumour to transform into a systemic, metastatic and fatal
disease. This process explores and takes advantage of the reciprocal relation
that solid tumours establish with the extracellular matrix (ECM) components and
other multiple distinct cell types from the surrounding microenvironment.
Through the secretion of various proteolytic enzymes such as matrix
metalloproteinases (MMP) or the urokinase plasminogen activator (uPA), the
cancer cell population alters the configuration of the surrounding ECM
composition and overcomes the physical barriers to ultimately achieve local
cancer spread into the surrounding tissue. The active interplay between the
tissue-scale tumour dynamics and the molecular mechanics of the involved
proteolytic enzymes at the cell-scale underlines the biologically multiscale
character of invasion, and raises the challenge of modelling this process with
an appropriate multiscale approach. In this paper, we present a new two-scale
moving boundary model of cancer invasion that explores the tissue scale tumour
dynamics in conjunction with the molecular dynamics of the urokinase
plasminogen activation system. Building on the multiscale moving boundary
method proposed in [58], the modelling that we propose here allows us to study
the changes in tissue scale tumour morphology caused by the cell-scale uPA
micro-dynamics occurring along the invasive edge of the tumour. Our
computational simulation results demonstrate a range of heterogeneous dynamics
which are qualitatively similar to the invasive growth patterns observed in a
number of different types of cancer, such as the tumour infiltrative growth
patterns discussed in [33].


title:
Position-aided Large-scale MIMO Channel Estimation for High-Speed
  Railway Communication Systems

abstract:
  We consider channel estimation for high-speed railway communication systems,
where both the transmitter and the receiver are equipped with large-scale
antenna arrays. It is known that the throughput of conventional training
schemes monotonically decreases with the mobility. Assuming that the moving
terminal employs a large linear antenna array, this paper proposes a
position-aided channel estimation scheme whereby only a portion of the transmit
antennas send pilot symbols and the full channel matrix can be well estimated
by using these pilots together with the antenna position information based on
the joint spatial-temporal correlation. The relationship between mobility and
throughput/DoF is established. Furthermore, the optimal selections of transmit
power and time interval partition between the training and data phases as well
as the antenna size are presented accordingly. Both analytical and simulation
results show that the system throughput with the position-aided channel
estimator does not deteriorate appreciably as the mobility increases, which is
sharply in contrast with the conventional one.


title:
Self-adjoint boundary conditions for the prolate spheroid differential
  operator

abstract:
  We consider the formal prolate spheroid differential operator on a finite
symmetric interval and describe all its self-adjoint boundary conditions. Only
one of these boundary conditions corresponds to a self-adjoint differential
operator which commute with the Fourier operator truncated on the considered
finite symmetric interval.


title: Foliations, solvability and global injectivity

abstract:
  Let $F: \mathbb{R}^n\to \mathbb{R}^n$ be a $C^{\infty}$ map such that $DF(x)$
is invertible for every $x\in \mathbb{R}^n$. Although being a local
diffeomorphism, $F$ is not necessarily globally injective if $n\geq2$. In this
note we discuss some additional assumptions implying the global injectivity of
$F$ for $n\geq 2$, as well as relations between them.


title: Interplay of Coulomb interaction and spin-orbit coupling

abstract:
  We employ the Gutzwiller variational approach to investigate the interplay of
Coulomb interaction and spin-orbit coupling in a three-orbital Hubbard model.
Already in the paramagnetic phase we find a substantial renormalization of the
spin-orbit coupling that enters the effective single-particle Hamiltonian for
the quasi-particles. Only close to half band-filling and for sizable Coulomb
interaction we observe clear signatures of Hund's atomic rules for spin,
orbital, and total angular momentum. For a finite local Hund's-rule exchange
interaction we find a ferromagnetically ordered state. The spin-orbit coupling
considerably reduces the size of the ordered moment, it generates a small
ordered orbital moment, and it induces a magnetic anisotropy. To investigate
the magnetic anisotropy energy, we use an external magnetic field that tilts
the magnetic moment away from the easy axis $(1,1,1)$.


title:
Space CoBot: modular design of an holonomic aerial robot for indoor
  microgravity environments

abstract:
  This paper presents the design of a small aerial robot for inhabited
microgravity environments, such as orbiting space stations (e.g., ISS). In
particular, we target a fleet of robots, called Space CoBots, for collaborative
tasks with humans, such as telepresence and cooperative mobile manipulation.
The design is modular, comprising an hexrotor based propulsion system, and a
stack of modules including batteries, cameras for navigation, a screen for
telepresence, a robotic arm, space for extension modules, and a pair of docking
ports. These ports can be used for docking and for mechanically attaching two
Space CoBots together. The kinematics is holonomic, and thus the translational
and the rotational components can be fully decoupled. We employ a
multi-criteria optimization approach to determine the best geometric
configuration for maximum thrust and torque across all directions. We also
tackle the problem of motion control: we use separate converging controllers
for position and attitude control. Finally, we present simulation results using
a realistic physics simulator. These experiments include a sensitivity
evaluation to sensor noise and to unmodeled dynamics, namely a load
transportation.


title:
Method for observing robust and tunable phonon blockade in a
  nanomechanical resonator coupled to a charge qubit

abstract:
  Phonon blockade is a purely quantum phenomenon, analogous to Coulomb and
photon blockades, in which a single phonon in an anharmonic mechanical
resonator can impede the excitation of a second phonon. We propose an
experimental method to realize phonon blockade in a driven harmonic
nanomechanical resonator coupled to a qubit, where the coupling is proportional
to the second-order nonlinear susceptibility $\chi^{(2)}$. This is in contrast
to the standard realizations of phonon and photon blockade effects in Kerr-type
$\chi^{(3)}$ nonlinear systems. The nonlinear coupling strength can be adjusted
conveniently by changing the coherent drive field.As an example, we apply this
model to predict and describe phonon blockade in a nanomechanical resonator
coupled to a Cooper-pair box (i.e., a charge qubit) with a linear longitudinal
coupling. By obtaining the solutions of the steady state for this composite
system, we give the conditions forobserving strong antibunching and
sub-Poissonian phonon-number statistics in this induced second-order nonlinear
system. Besides using the qubit to produce phonon blockade states, the qubit
itself can also be employed to detect blockade effects by measuring its states.
Numerical simulations indicate that the robustness of the phonon blockade, and
the sensitivity of detecting it, will benefit from this strong induced
nonlinear coupling.


title:
Persistent paramagnons deep in the metallic phase of
  Sr$_{2-x}$La$_x$IrO$_4$

abstract:
  We have studied the magnetic excitations of electron-doped
Sr$_{2-x}$La$_x$IrO$_4$ ($0 \leq x \leq 0.10$) using resonant inelastic x-ray
scattering (RIXS) at the Ir L$_3$-edge. The long range magnetic order is
rapidly lost with increasing $x$, but two-dimensional short-range order (SRO)
and dispersive magnon excitations with nearly undiminished spectral weight
persist well into the metallic part of the phase diagram. The magnons in the
SRO phase are heavily damped and exhibit anisotropic softening. Their
dispersions are well described by a pseudospin-1/2 Heisenberg model with
exchange interactions whose spatial range increases with doping. We also find a
doping-independent high-energy magnetic continuum, which is not described by
this model. The spin-orbit excitons arising from the pseudospin-3/2 manifold of
the Ir ions broaden substantially in the SRO phase, but remain largely
separated from the low-energy magnons. Pseudospin-1/2 models are therefore a
good starting point for the theoretical description of the low-energy magnetic
dynamics of doped iridates.


title: Modulation instability and solitons in two-color nematic crystals

abstract:
  The conditions under which stable evolution of two nonlinear interacting
waves are derived within the context of nematic crystals. Two cases are
considered: plane waves and solitons. In the first case, the modulation
instability analysis reveals that while the nonlocal term suppresses the growth
rates, substantially, the coupled system exhibits significantly higher growth
rates than its scalar counterpart. In the soliton case, the necessary
conditions are derived that lead the solitons to exhibit stable, undistorted
evolution, suppressing any breathing behavior and radiation, leading to soliton
mutual guiding.


title:
Application of the Finite Element Method in a Quantitative Imaging
  technique

abstract:
  We present the Finite Element Method (FEM) for the numerical solution of the
multidimensional coefficient inverse problem (MCIP) in two dimensions. This
method is used for explicit reconstruction of the coefficient in the hyperbolic
equation using data resulted from a single measurement. To solve our MCIP we
use approximate globally convergent method and then apply FEM for the resulted
equation. Our numerical examples show quantitative reconstruction of the sound
speed in small tumor-like inclusions.


title:
Composite Topological Excitations in Ferromagnet-Superconductor
  Heterostructures

abstract:
  We investigate the formation of a new type of composite topological
excitation -- the skyrmion-vortex pair (SVP) -- in hybrid systems consisting of
coupled ferromagnetic and superconducting layers. Spin-orbit interaction in the
superconductor mediates a magnetoelectric coupling between the vortex and the
skyrmion, with a sign (attractive or repulsive) that depends on the topological
indices of the constituents. We determine the conditions under which a bound
SVP is formed, and characterize the range and depth of the effective binding
potential through analytical estimates and numerical simulations. Furthermore,
we develop a semiclassical description of the coupled skyrmion-vortex dynamics
and discuss how SVPs can be controlled by applied spin currents.


title: Electron Diffraction by Plasmon Waves

abstract:
  An electron beam traversing a structured plasmonic field is shown to undergo
diffraction with characteristic angular patterns of both elastic and inelastic
outgoing electron components. In particular, a plasmonic {\it grating} (e.g., a
standing wave formed by two counter-propagating plasmons in a thin film)
produces diffraction orders of the same parity as the net number of exchanged
plasmons. Large diffracted beam fractions are predicted to occur for realistic
plasmon intensities in attainable geometries due to a combination of phase and
amplitude changes locally imprinted on the passing electron wave. Our study
opens new vistas in the study of multiphoton exchanges between electron beams
and evanescent optical fields with unexplored effects related to the
transversal component of the electron wave function.


title: A Novel Approach to Extra Dimensions

abstract:
  Four-dimensional spacetime, together with a natural generalisation to extra
dimensions, is obtained through an analysis of the structures and symmetries
deriving from possible arithmetic expressions for one-dimensional time. On
taking the infinitesimal limit this simple one-dimensional structure can be
consistently equated with a homogeneous form of arbitrary dimension possessing
both spacetime and more general symmetries. An extended 4-dimensional manifold,
with the associated spacetime symmetry, provides a natural breaking mechanism
for a higher-dimensional form and symmetry of time. It will be described how
this symmetry breaking leads to a series of distinct properties of the Standard
Model of particle physics, deriving directly from the natural mathematical
development of the theory.


title: On double Poisson structures on commutative algebras

abstract:
  Double Poisson structures (a la Van den Bergh) on commutative algebras are
studied; the main result shows that there are no non-trivial such structures on
polynomial algebras of Krull dimension greater than one. For a general
commutative algebra A, this places significant restrictions on possible double
Poisson structures. Exotic double Poisson structures are exhibited by the case
of the polynomial algebra on a single generator, previously considered by Van
den Bergh.


title:
Approximate Capacity of the Gaussian Interference Channel with Noisy
  Channel-Output Feedback

abstract:
  In this paper, an achievability region and a converse region for the two-user
Gaussian interference channel with noisy channel-output feedback (G-IC-NOF) are
presented. The achievability region is obtained using a random coding argument
and three well-known techniques: rate splitting, superposition coding and
backward decoding. The converse region is obtained using some of the existing
perfect-output feedback outer-bounds as well as a set of new outer-bounds that
are obtained by using genie-aided models of the original G-IC-NOF. Finally, it
is shown that the achievability region and the converse region approximate the
capacity region of the G-IC-NOF to within a constant gap in bits per channel
use.


title:
Mosco convergence for H(curl) spaces, higher integrability for Maxwell's
  equations, and stability in direct and inverse EM scattering problems

abstract:
  This paper is concerned with the scattering problem for time-harmonic
electromagnetic waves, due to the presence of scatterers and of inhomogeneities
in the medium.
  We prove a sharp stability result for the solutions to the direct
electromagnetic scattering problem, with respect to variations of the scatterer
and of the inhomogeneity, under minimal regularity assumptions for both of
them. The stability result leads to uniform bounds on solutions to the
scattering problems for an extremely general class of admissible scatterers and
inhomogeneities.
  The uniform bounds are a key step to tackle the challenging stability issue
for the corresponding inverse electromagnetic scattering problem. In this paper
we establish two optimal stability results of logarithmic type for the
determination of polyhedral scatterers by a minimal number of electromagnetic
scattering measurements.
  In order to prove the stability result for the direct electromagnetic
scattering problem, we study two fundamental issues in the theory of Maxwell
equations: Mosco convergence for H(curl) spaces and higher integrability
properties of solutions to Maxwell equations in nonsmooth domains.


title:
The interplay between conformity and anticonformity and its polarizing
  effect on society

abstract:
  Simmering debates leading to polarization are observed in many domains.
Although empirical findings show a strong correlation between this phenomenon
and modularity of a social network, still little is known about the actual
mechanisms driving communities to conflicting opinions. In this paper, we used
an agent-based model to check if the polarization may be induced by a
competition between two types of social response: conformity and
anticonformity. The proposed model builds on the q-voter model (Castellano et
al. 2009b) and uses a double-clique topology in order to capture segmentation
of a community. Our results indicate that the interplay between intra-clique
conformity and inter-clique anticonformity may indeed lead to a polarized state
of the entire system. We have found a dynamic phase transition controlled by
the fraction $L$ of cross-links between cliques. In the regime of small values
of $L$ system is able to reach the total positive consensus. If the values of
$L$ are large enough, anticonformity takes over and the system always ends up
in a polarized stated. Putting it the other way around, the segmentation of the
network is not a sufficient condition for the polarization to appear. A
suitable level of antagonistic interactions between segments is namely required
to arrive at a polarized steady state within our model.


title:
A geometric proof of Wilbrink's characterization of even order classical
  unitals

abstract:
  Using geometric methods and without invoking deep results from group theory,
we prove that a classical unital of even order $n\geq4$ is characterized by two
conditions (I) and (II): (I) is the absence of O'Nan configurations of four
distinct lines intersecting in exactly six distinct points; (II) is a notion of
parallelism. This was previously proven by Wilbrink (1983), where the proof
depends on the classification of finite groups with a split BN-pair of rank 1.


title:
Can we obtain a "new femtoscopy" on the basis of electromagnetic
  effects?

abstract:
  We review our studies of spectator-induced electromagnetic (EM) effects on
charged pion emission in ultrarelativistic heavy ion collisions. These effects
are found to consist in the electromagnetic {charge splitting} of pion directed
flow as well as very large distortions in spectra and ratios of produced
charged particles. As it emerges from our analysis, they offer sensitivity to
the actual distance $d_E$ between the pion formation zone at freeze-out and the
spectator matter. As a result, this gives a new possibility of studying the
space-time evolution of dense and hot matter created in the course of the
collision. Having established that $d_E$ traces the longitudinal evolution of
the system and therefore rapidly decreases as a function of pion rapidity, we
investigate the latter finding in view of pion feed-over from intermediate
resonance production. As a result we obtain a first estimate of the pion
decoupling time from EM effects which we compare to existing HBT data. We
conclude that spectator-induced EM interactions can serve as a new tool for
studying the space-time characteristics and longitudinal evolution of the
system.


title: Optimal large-scale quantum state tomography with Pauli measurements

abstract:
  Quantum state tomography aims to determine the state of a quantum system as
represented by a density matrix. It is a fundamental task in modern scientific
studies involving quantum systems. In this paper, we study estimation of
high-dimensional density matrices based on Pauli measurements. In particular,
under appropriate notion of sparsity, we establish the minimax optimal rates of
convergence for estimation of the density matrix under both the spectral and
Frobenius norm losses; and show how these rates can be achieved by a common
thresholding approach. Numerical performance of the proposed estimator is also
investigated.


title:
Likewise theta functions of rank $r$ on $\mathbb{R}^d$: analytic
  properties and associated Segal-Bargmann transform

abstract:
  We introduce and study the Hilbert space of $(L^2,\Gamma,\chi)$-likewise
theta functions on $\mathbb{R}^d$ with respect to a given discrete subgroup
$\Gamma$ of arbitrary rank and a character $\chi$ of $\Gamma$. A concrete
description is given and an orthonormal basis is then constructed. Its range by
the classical Segal-Bargmann transform is also characterized and leads to the
so-called theta-Bargmann Fock space.


title:
Saturation properties of nuclear matter in the presence of strong
  magnetic field

abstract:
  Different saturation properties of cold symmetric nuclear matter in the
strong magnetic field have been considered. We have seen that for magnetic
fields about $B> 3 \times 10 ^ {17}\ G$, {for both cases with and without
nucleon anomalous magnetic moments}, the saturation density and saturation
energy grow by increasing the magnetic field. It is indicated that the magnetic
susceptibility of symmetric nuclear matter becomes negative showing the
diamagnetic response especially at $B< 3 \times 10 ^ {17}\ G$. We have found
that for the nuclear matter, the magnitude of orbital magnetization reaches the
higher values comparing to the spin magnetization. Our results for the
incompressibility show that at high enough magnetic fields, i.e. $B> 3 \times
10 ^ {17}\ G$, {the softening of equation of state caused by Landau
quantization is overwhelmed by stiffening due to the magnetization of nuclear
matter.} We have shown that the effects of strong magnetic field on nuclear
matter may affect the constraints on the equation of state of symmetric nuclear
matter obtained applying the experimental observable.


title:
Characterization of the size and position of electron-hole puddles at a
  graphene p-n junction

abstract:
  The effect of an electron-hole puddle on the electrical transport when
governed by snake states in a bipolar graphene structure is investigated. Using
numerical simulations we show that information on the size and position of the
electron-hole puddle can be obtained using the dependence of the conductance on
magnetic field and electron density of the gated region. The presence of the
scatterer disrupts snake state transport which alters the conduction pattern.
We obtain a simple analytical formula that connects the position of the
electron-hole puddle with features observed in the conductance. Size of the
electron-hole puddle is estimated from the magnetic field and gate potential
that maximizes the effect of the puddle on the electrical transport.


title: Hooked flare ribbons and flux-rope related QSL footprints

abstract:
  We studied the magnetic topology of active region 12158 on 2014 September 10
and compared it with the observations before and early in the flare which
begins at 17:21 UT (SOL2014-09-10T17:45:00). Our results show that the
sigmoidal structure and flare ribbons of this active region observed by SDO/AIA
can be well reproduced from a Grad-Rubin non linear force free field
extrapolation method. Various inverse-S and -J shaped magnetic field lines,
that surround a coronal flux rope, coincide with the sigmoid as observed in
different extreme ultraviolet wavelengths, including its multi-threaded curved
ends. Also, the observed distribution of surface currents in the magnetic
polarity where it was not prescribed is well reproduced. This validates our
numerical implementation and set-up of the Grad-Rubin method. The modeled
double inverse-J shaped Quasi-Separatrix Layer (QSL) footprints match the
observed flare ribbons during the rising phase of the flare, including their
hooked parts. The spiral-like shape of the latter may be related to a complex
pre-eruptive flux rope with more than one turn of twist, as obtained in the
model. These ribbon-associated flux-rope QSL-footprints are consistent with the
new standard flare model in 3D, with the presence of a hyperbolic flux tube
located below an inverse tear drop shaped coronal QSL. This is a new step
forward forecasting the locations of reconnection and ribbons in solar flares,
and the geometrical properties of eruptive flux ropes.


title: Transition of thermal rectification in silicon nanocones

abstract:
  Current understanding of thermal rectification asserts that the rectification
ratio (R), which measures the relative heat flux between two ends of a
nanostructure, is determined by its geometric asymmetry. The higher the
asymmetry, the higher the R. However, by using nonequilibrium molecular
dynamics method we have calculated thermal transport in Si nanocones as an
example, the results show that such an understanding may be incorrect and R may
not increase monotonically with geometric asymmetry. Rather, R exhibits a sharp
reverse when the vertex angle ({\theta}) of the nanocone is approximately
90{\deg}. In other words, when {\theta} > 90{\deg}, R decreases, rather than
increasing. We show that this abnormal behavior is originated from a change in
the thermal transport mechanism. At small {\theta}s, phonon transport is
dominated by localized modes, especially for transport from tip to bottom. At
large {\theta}s, however, these localized modes disappear, leading to R
decrease.


title:
Challenges and prospects for better measurements of the CMB intensity
  spectrum

abstract:
  Spectral distortions of the Cosmic Microwave Background (CMB) offer the
possibility of probing processes which occurred during the evolution of our
Universe going back up to Z$\simeq 10^7$. Unfortunately all the attempts so far
carried out for detecting distortions failed. All of them were based on
comparisons among absolute measurements of the CMB temperature at different
frequencies. We suggest a different approach: measurements of the frequency
derivative of the CMB temperature over large frequency intervals instead of
observations of the absolute temperature at few, well separated, frequencies as
frequently done in the past, and, direct measurements of the foregrounds which
hinder bobservations, at the same site and with the same radiometer prepared
for the search of CMB distortions. We discuss therefore the perspectives of new
observations in the next years from the ground, at very special sites, or in
space as independent missions or part of other CMB projects


title:
Zeros of a cross-product of the Coulomb wave and Tricomi hypergeometric
  functions

abstract:
  Motivated by a problem related to conditions for the existence of clines in
genetics, in this note our aim is to show that the positive zeros of a
cross-product of the regular Coulomb wave function and the Tricomi
hypergeometric function are increasing with respect to the order. In
particular, this implies that the eigenvalues of a boundary value problem are
increasing with the dimension.


title:
Dynamics, Control, and Estimation for Aerial Robots Tethered by Cables
  or Bars

abstract:
  We consider the problem of controlling an aerial robot connected to the
ground by a passive cable or a passive rigid link. We provide a thorough
characterization of this nonlinear dynamical robotic system in terms of
fundamental properties such as differential flatness, controllability, and
observability. We prove that the robotic system is differentially flat with
respect to two output pairs: elevation of the link and attitude of the vehicle;
elevation of the link and longitudinal link force (e.g., cable tension, or bar
compression). We show the design of an almost globally convergent nonlinear
observer of the full state that resorts only to an onboard accelerometer and a
gyroscope. We also design two almost globally convergent nonlinear controllers
to track any sufficiently smooth time-varying trajectory of the two output
pairs. Finally we numerically test the robustness of the proposed method in
several far-from-nominal conditions: nonlinear cross-coupling effects,
parameter deviations, measurements noise and non ideal actuators.


title:
Limits on the Neutrino Velocity, Lorentz Invariance, and the Weak
  Equivalence Principle with TeV Neutrinos from Gamma-Ray Bursts

abstract:
  Five TeV neutrino events weakly correlated with five gamma-ray bursts (GRBs)
were detected recently by IceCube. This work is an attempt to show that if the
GRB identifications are verified, the observed time delays between the TeV
neutrinos and gamma-ray photons from GRBs provide attractive candidates for
testing fundamental physics with high accuracy. Based on the assumed
associations between the TeV neutrinos and GRBs, we find that the limiting
velocity of the neutrinos is equal to that of photons to an accuracy of
$\sim1.9\times10^{-15}-2.5\times10^{-18}$, which is about $10^{4}-10^{7}$ times
better than the constraint obtained with the neutrino possibly from a blazar
flare. In addition, we set the most stringent limits up to date on the energy
scale of quantum gravity for both the linear and quadratic violations of
Lorentz invariance, namely $E_{\rm QG, 1}>6.3\times10^{18}-1.5\times10^{21}$
GeV and $E_{\rm QG, 2}>2.0\times10^{11}-4.2\times10^{12}$ GeV, which are
essentially as good as or are an improvement of one order of magnitude over the
results previously obtained by the GeV photons of GRB 090510 and the PeV
neutrino from a blazar flare. Assuming that the Shapiro time delay is caused by
the gravitational potential of the Laniakea supercluster of galaxies, we also
place the tightest limits to date on Einstein's weak equivalence principle
through the relative differential variations of the parameterized
post-Newtonian parameter $\gamma$ values for two different species of particles
(i.e., neutrinos and photons), yielding $\Delta\gamma \sim 10^{-11}-10^{-13}$.
However, it should be emphasized again that these limits here obtained are at
best forecast of what could be achieved if the GRB/neutrino correlations would
be finally confirmed.


title: Black holes and information: A new take on an old paradox

abstract:
  Interest in the black hole information paradox has recently been catalyzed by
the newer "firewall" argument. The crux of the updated argument is that
previous solutions which relied on observer complementarity are in violation of
the quantum condition of monogamy of entanglement; with the prescribed remedy
being to discard the equivalence principle in favor of an energy barrier (or
firewall) at the black hole horizon. Differing points of view have been put
forward, including the "ER=EPR" counterargument and the final-state solution,
both of which can be viewed as potential resolutions to the apparent conflict
between quantum monogamy and Einstein equivalence. After reviewing these recent
developments, this paper argues that the ER=EPR and final-state solutions can
-- thanks to observer complementarity -- be seen as the same resolution of the
paradox but from two different perspectives: inside and outside the black hole.


title: Online Ramsey Games for more than two colors

abstract:
  Consider the following one-player game played on an initially empty graph
with $n$ vertices. At each stage a randomly selected new edge is added and the
player must immediately color the edge with one of $r$ available colors. Her
objective is to color as many edges as possible without creating a
monochromatic copy of a fixed graph $F$.
  We use container and sparse regularity techniques to prove a tight upper
bound on the typical duration of this game with an arbitrary, but fixed, number
of colors for a family of $2$-balanced graphs. The bound confirms a conjecture
of Marciniszyn, Sp\"ohel and Steger and yields the first tight result for
online graph avoidance games with more than two colors.


title: Gauge aspect of tetrad field in gravity

abstract:
  In general relativity, an inertial frame can only be established in a small
region of spacetime, and a locally inertial frame is mathematically represented
by a tetrad field in gravity. The tetrad field is not unique due to the freedom
to perform a local Lorentz transformation in an inertial frame, and there
exists freedom to choose the locally inertial frame at each spacetime. The
local Lorentz transformations are known as non-Abelian gauge transformations
for the tetrad field, and to fix the gauge freedom, corresponding to the
Lorentz gauge $\partial^\mu\mathcal{A}_\mu=0$ and Coulomb gauge
$\partial^i\mathcal{A}_i=0$ in electrodynamics, the Lorentz gauge and Coulomb
gauge for the tetrad field are proposed in the present work. Moreover,
properties of the Lorentz gauge and Coulomb gauge for tetrad field are
discussed, which show the similarities to those in electromagnetic field.


title: Observational signatures of Higgs inflation

abstract:
  We investigate the dependency of Higgs inflation on the non-renormalisable
matching between the low energy Standard Model limit and the inflationary
regime at high energies. We show that for the top mass range $m_t \gtrsim
171.8$ GeV the scenario robustly predicts the spectral index $n_s \simeq 0.97$
and the tensor-to-scalar ratio $r\simeq 0.003$. The matching is however
non-trivial, even the best-fit values $m_h=125.09$ GeV and $m_t=173.21$ GeV
require a jump $\delta \lambda \sim 0.01$ in the Higgs coupling below the
inflationary scale. For $m_t\lesssim 171.8$ GeV, the matching may generate a
feature in the inflationary potential. In this case the predicted values of
$n_s$ and $r$ vary but the model is still falsifiable. For example, a detection
of negative running of spectral index at level $\alpha_s \lesssim -0.01$ would
rule out Higgs inflation.


title:
Statistical inference for the mean outcome under a possibly non-unique
  optimal treatment strategy

abstract:
  We consider challenges that arise in the estimation of the mean outcome under
an optimal individualized treatment strategy defined as the treatment rule that
maximizes the population mean outcome, where the candidate treatment rules are
restricted to depend on baseline covariates. We prove a necessary and
sufficient condition for the pathwise differentiability of the optimal value, a
key condition needed to develop a regular and asymptotically linear (RAL)
estimator of the optimal value. The stated condition is slightly more general
than the previous condition implied in the literature. We then describe an
approach to obtain root-$n$ rate confidence intervals for the optimal value
even when the parameter is not pathwise differentiable. We provide conditions
under which our estimator is RAL and asymptotically efficient when the mean
outcome is pathwise differentiable. We also outline an extension of our
approach to a multiple time point problem. All of our results are supported by
simulations.


title:
The Derivation of the Linear Boltzmann Equation from a Rayleigh Gas
  Particle Model

abstract:
  A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the
deterministic dynamics of many interacting particles with random initial data.
We study a Rayleigh gas where a tagged particle is undergoing hard-sphere
collisions with background particles, which do not interact among each other.
In the Boltzmann-Grad scaling, we derive the validity of a linear Boltzmann
equation for arbitrary long times under moderate assumptions on higher moments
of the initial distributions of the tagged particle and the possibly
non-equilibrium distribution of the background. The convergence of the empiric
dynamics to the Boltzmann dynamics is shown using Kolmogorov equations for
associated probability measures on collision histories.