title:
Indirect probes of the trilinear Higgs coupling: $gg \to h$ and $h \to
  \gamma \gamma$

abstract:
  In the framework of the Standard Model effective field theory, we examine the
indirect constraints on the trilinear Higgs coupling $\lambda$ that arise from
Higgs production in gluon-gluon-fusion and diphoton Higgs decays. We calculate
2-loop contributions to the $gg \to h$ and $h \to \gamma \gamma$ amplitudes
that are affected by modifications of the trilinear Higgs-boson vertex. This
calculation involves both the computation of anomalous dimensions and finite
matching corrections. Based on our new results, we analyse the sensitivity of
present and future measurements of the $hgg$ and $h \gamma \gamma$ couplings to
shifts in $\lambda$. Under the assumption that $O_6 = - \lambda \left
(H^\dagger H \right )^3$ is the only dimension-6 operator that alters the
trilinear Higgs interactions, we find that at present the considered loop-level
probes provide stronger constraints than $pp \to 2h$. At future high-energy
colliders indirect ${\cal O} (5)$ determinations of the trilinear Higgs
coupling may be possible, making precision measurements of $gg \to h$ and $h
\to \gamma \gamma$ a useful addition to direct extractions of $\lambda$ through
double-Higgs production.


title: Truncated $\gamma$-exponential models for tidal stellar systems

abstract:
  We introduce a parametric family of models to characterize the properties of
astrophysical systems in a quasi-stationary evolution under the incidence
evaporation. We start from an one-particle distribution
$f_{\gamma}\left(\mathbf{q},\mathbf{p}|\beta,\varepsilon_{s}\right)$ that
considers an appropriate deformation of Maxwell-Boltzmann form with inverse
temperature $\beta$, in particular, a power-law truncation at the scape energy
$\varepsilon_{s}$ with exponent $\gamma>0$. This deformation is implemented
using a generalized $\gamma$-exponential function obtained from the
\emph{fractional integration} of ordinary exponential. As shown in this work,
this proposal generalizes models of tidal stellar systems that predict
particles distributions with \emph{isothermal cores and polytropic haloes},
e.g.: Michie-King models. We perform the analysis of thermodynamic features of
these models and their associated distribution profiles. A nontrivial
consequence of this study is that profiles with isothermal cores and polytropic
haloes are only obtained for low energies whenever deformation parameter
$\gamma<\gamma_{c}\simeq 2.13$.


title: Causal inference to detect selection bias in road safety epidemiology

abstract:
  In the field of road safety, it is common to use responsibility analyses to
assess the effect of a given factor on the risk of being responsible for an
accident, among drivers involved in an accident only. Even if this design is
now widely adopted in the field, the question of selection bias is often
raised. The structural Causal Model framework now provides valuable tools to
assess causal effects from observational data and identify selection bias. In
this article, we briefly review recent results regarding the recoverability of
causal effects from selection biased data, and apply them to the case of
responsibility analyses. Our objective is to formally determine whether causal
effects can be unbiasedly estimated through this type of analyses, when
available data are restricted to severe accidents, as it is commonly the case
in practice. However, because speed has a direct effect on the severity of the
accident, we show that causal odds-ratios are not estimable from responsibility
analyses. We present numerical results to illustrate our argument, the
magnitude of the bias and to discuss recent results from real data.


title: Constraining non-commutative space-time from GW150914

abstract:
  The gravitational wave signal GW150914, recently detected by LIGO and Virgo
collaborations, is used to place a bound on the scale of quantum fuzziness of
non-commutative space-time. We show that the leading non-commutative correction
to the phase of the gravitational waves produced by a binary system appears at
the 2nd order of the post- Newtonian expansion. This correction is proportional
to $\Lambda^2 \equiv |\theta^{0i}|^2/(l_P t_P)^2$, where $\theta^{\mu \nu}$ is
the antisymmetric tensor of non-commutativity. To comply with GW150914 data, we
find that $\sqrt{\Lambda} \lesssim 6$, namely less than one order of magnitude
above the Planck scale. This is the most stringent bound on non-commutative
scale, exceeding the previous constraints from particle physics processes by
$\sim 15$ orders of magnitude.


title:
Symmetric Interior Penalty Discontinuous Galerkin Discretisations and
  Block Preconditioning for Heterogeneous Stokes Flow

abstract:
  Provable stable arbitrary order symmetric interior penalty discontinuous
Galerkin (SIP) discretisations of variable viscosity, incompressible Stokes
flow utilising $Q^2_k$--$Q_{k-1}$ elements and hierarchical Legendre basis
polynomials are developed and investigated.For solving the resulting linear
system, a block preconditioned iterative method is proposed. The nested viscous
problem is solved by a $hp$-multilevel preconditioned Krylov subspace method.
For the $p$-coarsening, a twolevel method utilising element-block Jacobi
preconditioned iterations as a smoother is employed. Piecewise bilinear
($Q^2_1$) and piecewise constant ($Q^2_0$) $p$-coarse spaces are considered.
Finally, Galerkin $h$-coarsening is proposed and investigated for the two
$p$-coarse spaces considered. Through a number of numerical experiments, we
demonstrate that utilising the $Q^2_1$ coarse space results in the most robust
$hp$-multigrid method for variable viscosity Stokes flow. Using this $Q^2_1$
coarse space we observe that the convergence of the overall Stokes solver
appears to be robust with respect to the jump in the viscosity and only mildly
depending on the polynomial order $k$. It is demonstrated and supported by
theoretical results that the convergence of the SIP discretisations and the
iterative methods rely on a sharp choice of the penalty parameter based on
local values of the viscosity.


title:
Gamma-ray upper limits on magnetars with 6 years of Fermi-LAT
  observations

abstract:
  We report on the search for gamma-ray emission from 20 magnetars using 6
years of Fermi, Large Area Telescope (LAT) observations. No significant
evidence for gamma-ray emission from any of the currently-known magnetars is
found. We derived the most stringent upper limits to date on the 0.1--10 GeV
emission of Galactic magnetars, which are estimated between
$\sim10^{-12}-10^{-11}$ erg s$^{-1}$ cm$^{-2}$. Gamma-ray pulsations were
searched for the four magnetars having reliable ephemerides over the observing
period, but none were detected. On the other hand, we also studied the
gamma-ray morphology and spectra of seven Supernova Remnants associated or
adjacent to the magnetars.


title:
Primordial Gravitational Waves and Rescattered Electromagnetic Radiation
  in the Cosmic Microwave Background

abstract:
  Understanding the interaction of primordial gravitational waves (GWs) with
the Cosmic Microwave Background (CMB) plasma is important for observational
cosmology. In this article, we provide an analysis of an effect apparently
overlooked as yet. We consider a single free electric charge and suppose that
it can be agitated by primordial GWs propagating through the CMB plasma,
resulting in periodic, regular motion along particular directions. Light
reflected by the charge will be partially polarized, and this will imprint a
characteristic pattern on the CMB. We study this effect by considering a simple
model in which anisotropic incident electromagnetic (EM) radiation is
rescattered by a charge sitting in spacetime perturbed by GWs and becomes
polarized. As the charge is driven to move along particular directions, we
calculate its dipole moment to determine the leading-order rescattered EM
radiation. The Stokes parameters of the rescattered radiation exhibit a net
linear polarization. We investigate how this polarization effect can be
schematically represented out of the Stokes parameters. We work out the
representations of gradient modes (E-modes) and curl modes (B-modes) to produce
polarization maps. Although the polarization effect results from GWs, we find
that its representations, the E- and B-modes, do not practically reflect the GW
properties such as strain amplitude, frequency and polarization states.


title: A Vector Space for Distributional Semantics for Entailment

abstract:
  Distributional semantics creates vector-space representations that capture
many forms of semantic similarity, but their relation to semantic entailment
has been less clear. We propose a vector-space model which provides a formal
foundation for a distributional semantics of entailment. Using a mean-field
approximation, we develop approximate inference procedures and entailment
operators over vectors of probabilities of features being known (versus
unknown). We use this framework to reinterpret an existing
distributional-semantic model (Word2Vec) as approximating an entailment-based
model of the distributions of words in contexts, thereby predicting lexical
entailment relations. In both unsupervised and semi-supervised experiments on
hyponymy detection, we get substantial improvements over previous results.


title:
Probing the Dynamics of Superradiant Quantum Phase Transition in a
  Single Trapped-Ion

abstract:
  We demonstrate that the quantum phase transition (QPT) of the Rabi model and
critical dynamics near the QPT can be probed in the setup of a single trapped
ion. We first show that there exists equilibrium and non-equilibrium universal
functions of the Rabi model by finding a proper rescaling of the system
parameters and observables. We then propose a scheme that can faithfully
realize the Rabi model in the limit of a large ratio of the effective atomic
transition frequency to the oscillator frequency using a single trapped-ion and
therefore the QPT. It is demonstrated that the predicted universal functions
can indeed be observed based on our scheme. Finally, the effects of realistic
noise sources on probing the universal functions in experiments are examined.


title: Sympathetic laser-cooling of graphene with Casimir-Polder forces

abstract:
  We propose a scheme to actively cool the fundamental flexural (out-of-plane)
mode of a graphene sheet via vacuum forces. Our setup consists in a cold atom
cloud placed close to a graphene sheet at distances of a few micrometers. The
atoms couple to the graphene membrane via Casimir-Polder forces. By deriving a
self-consistent set of equations governing the dynamics of the atomic gas and
the flexural modes of the graphene, we show to be possible to cool graphene
from room temperatures by actively (laser) cooling an atomic gas. By choosing
the right set of experimental parameter we are able to cool a graphene sheet
down to ~ 60 microkelvin.


title:
Statistical thermodynamic basis in drug-receptor interactions: double
  annihilation and double decoupling alchemical theories, revisited

abstract:
  Alchemical theory is emerging as a promising tool in the context of molecular
dynamics simulations for drug discovery projects. In this theoretical
contribution, I revisit the statistical mechanics foundation of non covalent
interactions in drug-receptor systems, providing a unifying treatment that
encompasses the most important variants in the alchemical approaches, from the
seminal Double Annihilation Method by Jorgensen and Ravimohan [W.L. Jorgensen
and C. Ravimohan, J. Chem. Phys. 83,3050, 1985], to the Gilson's Double
Decoupling Method [M. K. Gilson and J. A. Given and B. L. Bush and J. A.
McCammon, Biophys. J. 72, 1047 1997] and the Deng and Roux alchemical theory
[Y. Deng and B. Roux, J. Chem. Theory Comput., 2, 1255 2006]. Connections and
differences between the various alchemical approaches are highlighted and
discussed, and finally placed into the broader context of nonequilibrium
thermodynamics.


title:
The 1/c expansion of nonminimally coupled curvature-matter gravity model
  and constraints from planetary precession

abstract:
  The effects of a nonminimally coupled curvature-matter model of gravity on a
perturbed Minkowski metric are presented. The action functional of the model
involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$.
This work expands upon previous results, extending the framework developed
there to compute corrections up to order $O(1/c^4)$ of the $00$ component of
the metric tensor. It is shown that additional contributions arise due to both
the non-linear form $f^1(R)$ and the nonminimal coupling $f^2(R)$, including
exponential contributions that cannot be expressed as an expansion in powers of
$1/r$. Some possible experimental implications are assessed with application to
perihelion precession.


title:
Application of Convolutional Neural Network for Image Classification on
  Pascal VOC Challenge 2012 dataset

abstract:
  In this project we work on creating a model to classify images for the Pascal
VOC Challenge 2012. We use convolutional neural networks trained on a single
GPU instance provided by Amazon via their cloud service Amazon Web Services
(AWS) to classify images in the Pascal VOC 2012 data set. We train multiple
convolutional neural network models and finally settle on the best model which
produced a validation accuracy of 85.6% and a testing accuracy of 85.24%.


title:
Distributed Event Localization via Alternating Direction Method of
  Multipliers

abstract:
  This paper addresses the problem of distributed event localization using
noisy range measurements with respect to sensors with known positions. Event
localization is fundamental in many wireless sensor network applications such
as homeland security, law enforcement, and environmental studies. However, most
existing distributed algorithms require the target event to be within the
convex hull of the deployed sensors. Based on the alternating direction method
of multipliers (ADMM), we propose two scalable distributed algorithms named
GS-ADMM and J-ADMM which do not require the target event to be within the
convex hull of the deployed sensors. More specifically, the two algorithms can
be implemented in a scenario in which the entire sensor network is divided into
several clusters with cluster heads collecting measurements within each cluster
and exchanging intermediate computation information to achieve localization
consistency (consensus) across all clusters. This scenario is important in many
applications such as homeland security and law enforcement. Simulation results
confirm effectiveness of the proposed algorithms.


title:
How to obtain lattices from (f,sigma,delta)-codes via a generalization
  of Construction A

abstract:
  We show how cyclic $(f,\sigma,\delta)$-codes over finite rings canonically
induce a $\mathbb{Z}$-lattice in $\mathbb{R}^N$ by using certain quotients of
orders in nonassociative division algebras defined using the skew polynomial
$f$. This construction generalizes the one using certain $\sigma$-constacyclic
codes by Ducoat and Oggier, which used quotients of orders in non-commutative
associative division algebras defined by $f$, and can be viewed as a
generalization of the classical Construction A for lattices from linear codes.
It has the potential to be applied to coset coding, in particular to wire-tap
coding. Previous results by Ducoat and Oggier are obtained as special cases.


title: Weak convergence of multivariate partial maxima processes

abstract:
  For a strictly stationary sequence of $\mathbb{R}_{+}^{d}$--valued random
vectors we derive functional convergence of partial maxima stochastic processes
under joint regular variation and weak dependence conditions. The limit process
is an extremal process and the convergence takes place in the space of
$\mathbb{R}_{+}^{d}$--valued c\`{a}dl\`{a}g functions on $[0,1]$, with the
Skorohod weak $M_{1}$ topology. We also show that this topology in general can
not be replaced by the stronger (standard) $M_{1}$ topology. The theory is
illustrated on three examples, including the multivariate squared GARCH process
with constant conditional correlations.


title:
Unconventional quantized edge transport in the presence of inter-edge
  coupling in intercalated graphene

abstract:
  It is generally believed that the inter-edge coupling destroys the quantum
spin Hall (QSH) effect along with the gap opening at the Dirac points. Using
first-principles calculations, we find that the quantized edge transport
persists in the presence of inter-edge coupling in Ta intercalated epitaxial
graphene on SiC(0001), being a QSH insulator with the non-trivial gap of 81
meV. In this case, the band is characterized by two perfect Dirac cones with
different Fermi velocities, yet only one maintains the edge state feature. We
attribute such an anomalous behavior to the orbital-dependent decay of edge
states into the bulk, which allows the inter-edge coupling just between one
pair of edge states rather than two.


title:
On the finiteness of the classifying space for the family of virtually
  cyclic subgroups

abstract:
  Given a group G, we consider its classifying space for the family of
virtually cyclic subgroups. We show for many groups, including for example,
one-relator groups, acylindrically hyperbolic groups, 3-manifold groups and
CAT(0) cube groups, that they do not admit a finite model for this classifying
space unless they are virtually cyclic. This settles a conjecture due to
Juan-Pineda and Leary for these classes of groups.


title: Improved Approximation for Weighted Tree Augmentation with Bounded Costs

abstract:
  The Weighted Tree Augmentation Problem (WTAP) is a fundamental well-studied
problem in the field of network design. Given an undirected tree $G=(V,E)$, an
additional set of edges $L \subseteq V\times V$ disjoint from $E$ called
\textit{links}, and a cost vector $c\in \mathbb{R}_{\geq 0}^L$, WTAP asks to
find a minimum-cost set $F\subseteq L$ with the property that $(V,E\cup F)$ is
$2$-edge connected. The special case where $c_\ell = 1$ for all $\ell\in L$ is
called the Tree Augmentation Problem (TAP). Both problems are known to be
NP-hard.
  For the class of bounded cost vectors, we present a first improved
approximation algorithm for WTAP since more than three decades. Concretely, for
any $M\in \mathbb{Z}_{\geq 1}$ and $\epsilon > 0,$ we present an LP based
$(\delta+\epsilon)$-approximation for WTAP restricted to cost vectors $c$ in
$[1,M]^L$ for $\delta \approx 1.96417$. For the special case of TAP we improve
this factor to $\frac{5}{3}+\epsilon$.
  Our results rely on a new LP, that significantly differs from existing LPs
achieving improved bounds for TAP. We round a fractional solution in two
phases. The first phase uses the fractional solution to decompose the tree and
its fractional solution into so-called $\beta$-simple pairs losing only an
$\epsilon$-factor in the objective function. We then show how to use the
additional constraints in our LP combined with the $\beta$-simple structure to
round a fractional solution in each part of the decomposition.


title: Kernel Density Estimation for Dynamical Systems

abstract:
  We study the density estimation problem with observations generated by
certain dynamical systems that admit a unique underlying invariant Lebesgue
density. Observations drawn from dynamical systems are not independent and
moreover, usual mixing concepts may not be appropriate for measuring the
dependence among these observations. By employing the $\mathcal{C}$-mixing
concept to measure the dependence, we conduct statistical analysis on the
consistency and convergence of the kernel density estimator. Our main results
are as follows: First, we show that with properly chosen bandwidth, the kernel
density estimator is universally consistent under $L_1$-norm; Second, we
establish convergence rates for the estimator with respect to several classes
of dynamical systems under $L_1$-norm. In the analysis, the density function
$f$ is only assumed to be H\"{o}lder continuous which is a weak assumption in
the literature of nonparametric density estimation and also more realistic in
the dynamical system context. Last but not least, we prove that the same
convergence rates of the estimator under $L_\infty$-norm and $L_1$-norm can be
achieved when the density function is H\"{o}lder continuous, compactly
supported and bounded. The bandwidth selection problem of the kernel density
estimator for dynamical system is also discussed in our study via numerical
simulations.


title:
Emergence of the giant weak-component in directed random graphs with
  arbitrary degree distributions

abstract:
  The weak component generalizes the idea of connected components to directed
graphs. In this paper, an exact criterion for existence of the giant weak
component is derived for directed graphs with arbitrary bivariate degree
distributions. In addition we consider a random process for evolving directed
graphs with bounded degrees. The bounds are not the same for different vertices
but satisfy a pre-defined distribution. The analytic expression obtained for
the evolving degree distribution is then combined with the weak-component
criterion to obtain the exact time of the phase transition. The
phase-transition time is obtained as a function of the distribution that bounds
the degrees. Remarkably, when viewed from the step polymerization formalism,
the new results yield Flory-Stockmayer gelation theory and generalize it to a
broader scope.


title: Effect of memory in non-Markovian Boolean networks

abstract:
  One successful model of interacting biological systems is the Boolean
network. The dynamics of a Boolean network, controlled with Boolean functions,
is usually considered to be a Markovian (memory-less) process. However, both
self organizing features of biological phenomena and their intelligent nature
should raise some doubt about ignoring the history of their time evolution.
Here, we extend the Boolean network Markovian approach: we involve the effect
of memory on the dynamics. This can be explored by modifying Boolean functions
into non-Markovian functions, for example, by investigating the usual
non-Markovian threshold function, - one of the most applied Boolean functions.
By applying the non-Markovian threshold function on the dynamical process of a
cell cycle network, we discover a power law memory with a more robust dynamics
than the Markovian dynamics.


title: A Hybrid Dynamical Extension of Averaging

abstract:
  We extend a smooth dynamical systems averaging technique to a class of hybrid
systems with a limit cycle that is particularly relevant to the synthesis of
stable legged gaits. After introducing a definition of hybrid averageability
sufficient to recover the classical result, we provide a simple illustration of
its applicability to legged locomotion and conclude with some rather more
speculative remarks concerning the prospects for further generalization of
these ideas.


title: Polarization Sensitive Multi-Chroic MKIDs

abstract:
  We report on the development of scalable prototype microwave kinetic
inductance detector (MKID) arrays tailored for future multi-kilo-pixel
experiments that are designed to simultaneously characterize the polarization
properties of both the cosmic microwave background (CMB) and Galactic dust
emission. These modular arrays are composed of horn-coupled,
polarization-sensitive MKIDs, and each pixel has four detectors: two
polarizations in two spectral bands between 125 and 280 GHz. A horn is used to
feed each array element, and a planar orthomode transducer, composed of two
waveguide probe pairs, separates the incoming light into two linear
polarizations. Diplexers composed of resonant-stub band-pass filters separate
the radiation into 125 to 170 GHz and 190 to 280 GHz pass bands. The
millimeter-wave power is ultimately coupled to a hybrid co-planar waveguide
microwave kinetic inductance detector using a novel, broadband circuit
developed by our collaboration. Electromagnetic simulations show the expected
absorption efficiency of the detector is approximately 90%. Array fabrication
will begin in the summer of 2016.


title: Bi-connected Gravity Fields

abstract:
  I describe a bi-connection formalism of General relativity based on the dual
role of the Weitzenb\"{o}ck connection defining the parallelism at a distance
and the concomitant Levi-Civita connection derived from the Riemannian metric.
A more explicit tensor writing of the geodesic and loxodromic equations
clarifies their joint meaning.


title: A theory of semiprimitive groups

abstract:
  A transitive permutation group is semiprimitive if each of its normal
subgroups is transitive or semiregular. Interest in this class of groups is
motivated by two sources: problems arising in universal algebra related to
collapsing monoids and the graph-restrictive problem for permutation groups.
Here we develop a theory of semiprimitive groups which encompasses their
structure, their quotient actions and a method by which all finite
semiprimitive groups are constructed. We also extend some results from the
theory of primitive groups to semiprimitive groups, and conclude with open
problems of a similar nature.


title:
Molecular Polymorphism: Microwave Spectra, Equilibrium Structures, and
  an Astronomical Investigation of the HNCS Isomeric Family

abstract:
  The rotational spectra of thioisocyanic acid (HNCS), and its three energetic
isomers (HSCN, HCNS, and HSNC) have been observed at high spectral resolution
by a combination of chirped-pulse and Fabry-P\'{e}rot Fourier-transform
microwave spectroscopy between 6 and 40~GHz in a pulsed-jet discharge
expansion. Two isomers, thiofulminic acid (HCNS) and isothiofulminic acid
(HSNC), calculated here to be 35-37~kcal/mol less stable than the ground state
isomer HNCS, have been detected for the first time. Precise rotational,
centrifugal distortion, and nitrogen hyperfine coupling constants have been
determined for the normal and rare isotopic species of both molecules; all are
in good agreement with theoretical predictions obtained at the coupled cluster
level of theory. On the basis of isotopic spectroscopy, precise molecular
structures have been derived for all four isomers by correcting experimental
rotational constants for the effects of rotation-vibration calculated
theoretically. Formation and isomerization pathways have also been
investigated; the high abundance of HSCN relative to ground state HNCS, and the
detection of strong lines of SH using CH$_3$CN and H$_2$S, suggest that HSCN is
preferentially produced by the radical-radical reaction HS + CN. A radio
astronomical search for HSCN and its isomers has been undertaken toward the
high-mass star-forming region Sgr B2(N) in the Galactic Center with the 100 m
Green Bank Telescope. While we find clear evidence for HSCN, only a tentative
detection of HNCS is proposed, and there is no indication of HCNS or HSNC at
the same rms noise level. HSCN, and tentatively HNCS, displays clear deviations
from a single-excitation temperature model, suggesting weak masing may be
occurring in some transitions in this source.


title: Moser stability for volume forms on noncompact fiber bundles

abstract:
  We prove a stability result for volume forms on fiber bundles with compact
base and noncompact fibers. This generalizes the classical results of Moser and
Greene--Shiohama, and recent work by the authors.


title:
Superfluid density in cuprates: hints on gauge compositeness of the
  holes

abstract:
  We show that several features (the three-dimensional XY universality for
moderate underdoping, the almost-BCS behaviour for moderate overdoping and the
critical exponent) of the superfluid density in hole-doped cuprates hint at a
composite structure of the holes. This idea can be implemented in a spin-charge
gauge approach to the $t - t' - J$ model and provides indeed good agreement
with available experimental data.


title: Continuous-time Marginal Pricing of Power Trajectories in Power Systems

abstract:
  In this paper we formulate of the Economic Dispatch (ED) problem in Power
Systems in continuous time and include in it ramping constraints to derive an
expression of the price that reflects some important inter-temporal constraints
of the power units. The motivation for looking at this problem is the scarcity
of ramping resources and their increasing importance motivated by the
variability of power resources, particularly due to the addition of solar
power, which exacerbates the need of fast ramping units in the early morning
and early evening hours. We show that the solution for the marginal price can
be found through Euler-Lagrange equations and we argue that this price signal
better reflects the market value of power in the presence of significant ramps
in net-load.


title: Current Noise in Tunnel Junctions

abstract:
  We study current fluctuations in tunnel junctions driven by a voltage source.
The voltage is applied to the tunneling element via an impedance providing an
electromagnetic environment of the junction. We use circuit theory to relate
the fluctuations of the current flowing in the leads of the junction with the
voltage fluctuations generated by the environmental impedance and the
fluctuations of the tunneling current. The spectrum of current fluctuations is
found to consist of three parts: a term arising from the environmental
Johnson-Nyquist noise, a term due to the shot noise of the tunneling current
and a third term describing the cross-correlation between these two noise
sources. Our phenomenological theory reproduces previous results based on the
Hamiltonian model for the dynamical Coulomb blockade and provides a simple
understanding of the current fluctuation spectrum in terms of circuit theory
and properties of the average current. Specific results are given for a tunnel
junction driven through a resonator.


title:
Noise-tunable nonlinearity in a dispersively coupled diffusion-resonator
  system using superconducting circuits

abstract:
  The harmonic oscillator is one of the most widely used model systems in
physics: an indispensable theoretical tool in a variety of fields. It is well
known that otherwise linear oscillators can attain novel and nonlinear features
through interaction with another dynamical system. We investigate such an
interacting system: a superconducting LC-circuit dispersively coupled to a
superconducting quantum interference device (SQUID). We find that the SQUID
phase behaves as a classical two-level system, whose two states correspond to
one linear and one nonlinear regime for the LC-resonator. As a result, the
circuit's response to forcing can become multistable. The strength of the
nonlinearity is tuned by the level of noise in the system, and increases with
decreasing noise. This tunable nonlinearity could potentially find application
in the field of sensitive detection, whereas increased understanding of the
classical harmonic oscillator is relevant for studies of the
quantum-to-classical crossover of Jaynes-Cummings systems.


title: Well-distributed great circles on S^2

abstract:
  Let $C_1, \dots, C_n$ denote the $1/n-$neighborhood of $n$ great circles on
$\mathbb{S}^2$. We are interested in how much these areas have to overlap and
prove the sharp bounds $$ \sum_{i, j = 1 \atop i \neq j}^{n}{|C_i \cap C_j|^s}
\gtrsim_s \begin{cases} n^{2 - 2s} \qquad &\mbox{if}~0 \leq s < 2 \\ n^{-2}
\log{n} \qquad &\mbox{if}~s = 2\\ n^{1- 3s/2} \qquad &\mbox{if}~s > 2.
\end{cases} .$$ For $s=1$ there are arrangements for which the sum of mutual
overlap is uniformly bounded (for the analogous problem in $\mathbb{R}^2$ the
lower bound is $\gtrsim \log{n}$) and there are strong connections to minimal
energy configurations of $n$ charged electrons on $\mathbb{S}^2$ (the J. J.
Thomson problem).


title:
Sunspot Rotation as a Driver of Major Solar Eruptions in NOAA Active
  Region 12158

abstract:
  We studied the developing conditions of sigmoid structure under the influence
of magnetic non-potential characteristics of a rotating sunspot in the active
region (AR) 12158. Vector magnetic field measurements from Helioseismic
Magnetic Imager and coronal EUV observations from Atmospheric Imaging Assembly
reveal that the erupting inverse-S sigmoid had roots in the location of the
rotating sunspot. Sunspot rotates at a rate of 0-5deg/h with increasing trend
in the first half followed by a decrease. Time evolution of many non-potential
parameters had a well correspondence with the sunspot rotation. The evolution
of the AR magnetic structure is approximated by a time series of force free
equilibria. The NLFFF magnetic structure around the sunspot manifests the
observed sigmoid structure. Field lines from the sunspot periphery constitute
the body of the sigmoid and those from interior overly the sigmoid similar to a
fluxrope structure. While the sunspot is being rotating, two major CME
eruptions occurred in the AR. During the first (second) event, the coronal
current concentrations enhanced (degraded) consistent with the photospheric net
vertical current, however the magnetic energy is released during both the
cases. The analysis results suggest that the magnetic connections of the
sigmoid are driven by slow motion of sunspot rotation, which transforms to a
highly twisted flux rope structure in a dynamical scenario. An exceeding
critical twist in the flux rope probably leads to the loss of equilibrium and
thus triggering the onset of two eruptions.


title: Shifted Symplectic and Poisson Structures on Spaces of Framed Maps

abstract:
  We examine shifted symplectic and Poisson structures on spaces of framed
maps. We prove some results about shifted Poisson structures analogous to those
in existing ones about symplectic structures. Then, we consider the space
Map(X,D,Y) of maps from X to Y framed along a divisor D. We give conditions
under which this space has a shifted symplectic or Poisson structure. Classical
examples of symplectic and Poisson structures are provided with this theorem.


title:
The ALMA Frontier Fields survey I: 1.1 mm continuum detections in Abell
  2744, MACSJ0416.1-2403 and MACSJ1149.5+2223

abstract:
  Dusty star-forming galaxies are among the most prodigious systems at high
redshift (z>1), characterized by high star formation rates and huge dust
reservoirs. The bright end of this population has been well characterized in
recent years, but considerable uncertainties remain for fainter dusty
star-forming galaxies, which are responsible for the bulk of star formation at
high redshift and thus play a key role in galaxy growth and evolution.
  In this first paper of our series, we describe our methods for finding high
redshift faint dusty galaxies using millimeter observations with ALMA. We
obtained ALMA 1.1 mm mosaic images for three strong-lensing galaxy clusters
from the Frontier Fields survey. The 2'x2' mosaics overlap with the deep HST
WFC3/IR footprints and encompass the high magnification regions of each
cluster. The combination of extremely high ALMA sensitivity and the
magnification power of these clusters allows us to systematically probe the
sub-mJy population of dusty star-forming galaxies over a large surveyed area.
  We present a description of the reduction and analysis of the ALMA continuum
observations for the galaxy clusters Abell 2744 (z=0.308), MACSJ0416.1-2403
(z=0.396) and MACSJ1149.5+2223 (z=0.543), for which we reach observed rms
sensitivities of 55, 59 and 71 $\mu$Jy beam$^{-1}$ respectively. We detect 12
dusty star-forming galaxies at S/N>5.0 across the three clusters, all of them
presenting coincidence with NIR detected counterparts in the HST images. None
of the sources fall close to the lensing caustics, thus they are not strongly
lensed. The observed 1.1 mm flux densities for the total sample of galaxies
range from 0.41 to 2.82 mJy, with observed effective radii spanning <0.05" to
0.37"$\pm$0.21". The lensing-corrected sizes of the detected sources appear to
be in the same range as those measured in brighter samples, albeit with
possibly larger dispersion.


title:
On the number of representations by certain octonary quadratic forms
  with coefficients 1, 2, 3, 4 and 6

abstract:
  In this paper, we find formulas for the number of representations of certain
diagonal octonary quadratic forms with coefficients $1,2,3,4$ and $6$. We
obtain these formulas by constructing explicit bases of the space of modular
forms of weight $4$ on $\Gamma_0(48)$ with character.


title: On the Algebraic Representation of One-Tape Deterministic Turing Machine

abstract:
  An algebraic representation of the Turing machines is given, where the
configurations of Turing machines are represented by 4 order tensors, and the
transition functions by 8 order tensors. Two types of tensor product are
defined, one is to model the evolution of the Turing machines, and the other is
to model the compositions of transition functions. It is shown that the two
types of tensor product are harmonic in the sense that the associate law is
obeyed.


title:
Comparison of magnetic properties in a magnetic cloud and its solar
  source on April 11-14 2013

abstract:
  In the context of Sun-Earth connection of coronal mass ejections and magnetic
flux ropes (MFRs), we studied the solar active region (AR) and the magnetic
properties of magnetic cloud (MC) event during April 14-15, 2013. We use
in-situ observations from the Advanced Composition Explorer and source AR
measurements from the Solar Dynamic Observatory. The MCs magnetic structure is
reconstructed from the Grad-Shafranov method which reveals a northern component
of the axial field with left-handed helicity. The MC invariant axis is highly
inclined to the ecliptic plane pointing northward and is rotated by $117^o$
with respect to the source region PIL. The net axial flux and current in the MC
are comparatively higher than from the source region. Linear force-free alpha
distribution ($10^{-7}-10^{-6}$ m$^{-1}$) at the sigmoid leg matches the range
of twist number in the MC of 1-2 AU MFR. The MFR is non-linear force-free with
decreasing twist from the axis (9 turns/AU) towards the edge. Therefore
Gold-Hoyle (GH) configuration, assuming a constant twist, is more consistent
with the MC structure than the Lundquist configuration of increasing twist from
the axis to boundary. As an indication to that, the GH configuration yields
better fitting to the global trend of in-situ magnetic field components, in
terms of rms, than the Lundquist model. These cylindrical configurations
improved the MC fitting results when considered the effect of self-similar
expansion of MFR. For such twisting behaviour, this study suggests an
alternative fitting procedure to better characterise the MC magnetic structure
and its source region links.


title:
Electrostatic Interactions and Electro-osmotic Properties of
  Semipermeable Surfaces

abstract:
  We consider two charged semipermeable membranes, which bound bulk electrolyte
solutions and are separated by a thin film of salt-free liquid. Small
counter-ions permeate into the gap, which leads to a steric charge separation
in the system. To quantify the problem, we define an effective surface charge
density of imaginary impermeable surface, which mimics an actual semipermeable
membrane and greatly simplify analysis. The effective charge depends on
separation, generally differ from the real one, and could even be of the
opposite sign. From the exact and asymptotic solutions of the nonlinear
Poisson-Boltzmann equation, we obtain the distribution of the potential and of
counter-ions in the system. We then derive explicit formulae for the disjoining
pressure in the gap and electro-osmotic velocity, and show that both are
controlled by the effective surface charge.


title:
Measuring topological invariants from generalized edge states in
  polaritonic quasicrystals

abstract:
  We investigate the topological properties of Fibonacci quasicrystals using
cavity polaritons. Composite structures made of the concatenation of two
Fibonacci sequences allow investigating generalized edge states forming in the
gaps of the fractal energy spectrum. We employ these generalized edge states to
determine the topological invariants of the quasicrystal. When varying a
structural degree of freedom (phason) of the Fibonacci sequence, the edge
states spectrally traverse the gaps, while their spatial symmetry switches: the
periodicity of this spectral and spatial evolution yields direct measurements
of the gap topological numbers. The topological invariants that we determine
coincide with those assigned by the gap-labeling theorem, illustrating the
direct connection between the fractal and topological properties of Fibonacci
quasicrystals.


title:
The structure of Deitmar Schemes, II. Zeta functions and automorphism
  groups

abstract:
  We provide a coherent overview of a number of recent results obtained by the
authors in the theory of schemes defined over the field with one element.
Essentially, this theory encompasses the study of a functor which maps certain
geometries including graphs to Deitmar schemes with additional structure, as
such introducing a new zeta function for graphs. The functor is then used to
determine automorphism groups of the Deitmar schemes and base extensions to
fields.


title:
Homotopy Smoothing for Non-Smooth Problems with Lower Complexity than
  $O(1/\epsilon)$

abstract:
  In this paper, we develop a novel {\bf ho}moto{\bf p}y {\bf s}moothing (HOPS)
algorithm for solving a family of non-smooth problems that is composed of a
non-smooth term with an explicit max-structure and a smooth term or a simple
non-smooth term whose proximal mapping is easy to compute. The best known
iteration complexity for solving such non-smooth optimization problems is
$O(1/\epsilon)$ without any assumption on the strong convexity. In this work,
we will show that the proposed HOPS achieved a lower iteration complexity of
$\widetilde O(1/\epsilon^{1-\theta})$\footnote{$\widetilde O()$ suppresses a
logarithmic factor.} with $\theta\in(0,1]$ capturing the local sharpness of the
objective function around the optimal solutions. To the best of our knowledge,
this is the lowest iteration complexity achieved so far for the considered
non-smooth optimization problems without strong convexity assumption. The HOPS
algorithm employs Nesterov's smoothing technique and Nesterov's accelerated
gradient method and runs in stages, which gradually decreases the smoothing
parameter in a stage-wise manner until it yields a sufficiently good
approximation of the original function. We show that HOPS enjoys a linear
convergence for many well-known non-smooth problems (e.g., empirical risk
minimization with a piece-wise linear loss function and $\ell_1$ norm
regularizer, finding a point in a polyhedron, cone programming, etc).
Experimental results verify the effectiveness of HOPS in comparison with
Nesterov's smoothing algorithm and the primal-dual style of first-order
methods.


title: On the lower bound of the inner radius of nodal domains

abstract:
  We discuss the asymptotic lower bound on the inner radius of nodal domains
that arise from Laplacian eigenfunctions $ \phi_\lambda $ on a closed
Riemannian manifold $ (M,g) $. First, in the real-analytic case we present an
improvement of the currently best known bounds, due to Mangoubi (\cite{Man1}).
Furthermore, using recent results of Hezari (\cite{Hezari}, \cite{Hezari2}) we
obtain $ \log $-type improvements in the case of negative curvature and
improved bounds for $ (M,g) $ possessing an ergodic geodesic flow. Second, we
discuss the relation between the distribution of the $ L^2 $ norm of an
eigenfunction $ \phi_\lambda $ and the inner radius of the corresponding nodal
domains. In the spirit of the works of Colding-Minicozzi and Jakobson-Mangoubi,
we consider a covering of good cubes and show that, if a nodal domain is
sufficiently well covered by good cubes, then its inner radius is large.


title:
Is the observability of sterile neutrino masses consistent with
  $\nu-$oscillations?

abstract:
  It is shown that a 1980 proposal to search for heavy sterile neutrinos by
observing the energy of the associated lepton in weak decays rests on an
questionable assumption, and that the possibility of such a detection might be
inconsistent with the observability of neutrino oscillations.


title:
Using Simulations of Black Holes to Study General Relativity and the
  Properties of Inner Accretion Flow

abstract:
  While Albert Einstein's theory of General Relativity (GR) has been tested
extensively in our solar system, it is just beginning to be tested in the
strong gravitational fields that surround black holes. As a way to study the
behavior of gravity in these extreme environments I have used and added to a
ray-tracing code that simulates the X-ray emission from the accretion disks
surrounding black holes. In particular, the observational channels which can be
simulated include the thermal and reflected spectra, polarization, and
reverberation signatures. These calculations can be performed assuming GR as
well as four alternative spacetimes. These results can be used to see if it is
possible to determine if observations can test the No-Hair theorem of GR which
states that stationary, astrophysical black holes are only described by their
mass and spin. Although it proves difficult to distinguish between theories of
gravity it is possible to exclude a large portion of the possible deviations
from GR using observations of rapidly spinning stellar mass black holes such as
Cygnus X-1. The ray-tracing simulations can furthermore be used to study the
inner regions of black hole accretion flows. I examined the dependence of X-ray
reverberation observations on the ionization of the disk photosphere. My
results show that X-ray reverberation and X-ray polarization provides a
powerful tool to constrain the geometry of accretion disks which are too small
to be imaged directly. The second part of my thesis describes the work on the
balloon-borne X-Calibur hard X-ray polarimetry mission and on the space-borne
PolSTAR polarimeter concept.


title: On the Chen Conjecture regarding the complexity of QCSPs

abstract:
  Let A be an idempotent algebra on a finite domain. We combine results of Chen
2008 and Zhuk 2015 to argue that if Inv(A) satisfies the polynomially generated
powers property (PGP), then QCSP(Inv(A)) is in NP. We then use the result of
Zhuk to prove a converse, that if Inv(A) satisfies the exponentially generated
powers property (EGP), then QCSP(Inv(A)) is co-NP-hard. Since Zhuk proved that
only PGP and EGP are possible, we derive a full dichotomy for the QCSP,
justifying the moral correctness of what we term the Chen Conjecture.


title:
Generalized Laguerre Polynomials with Position-Dependent Effective Mass
  Visualized via Wigner's Distribution Functions

abstract:
  We construct, analytically and numerically, the Wigner distribution functions
for the exact solutions of position-dependent effective mass Schr\"odinger
equation for two cases belonging to the generalized Laguerre polynomials. Using
a suitable quantum canonical transformation, expectation values of position and
momentum operators can be obtained analytically in order to verify the
universality of the Heisenberg's uncertainty principle.


title: Truthfulness with Value-Maximizing Bidders

abstract:
  In markets such as digital advertising auctions, bidders want to maximize
value rather than payoff. This is different to the utility functions typically
assumed in auction theory and leads to different strategies and outcomes. We
refer to bidders who maximize value as value bidders. While simple
single-object auction formats are truthful, standard multi-object auction
formats allow for manipulation. It is straightforward to show that there cannot
be a truthful and revenue-maximizing deterministic auction mechanism with value
bidders and general valuations. Approximation has been used as a means to
achieve truthfulness, and we study which approximation ratios we can get from
truthful approximation mechanisms. We show that the approximation ratio that
can be achieved with a deterministic and truthful approximation mechanism with
$n$ bidders and $m$ items cannot be higher than 1/n for general valuations. For
randomized approximation mechanisms there is a framework with a ratio of
O(sqrt(m)). We provide better ratios for environments with restricted
valuations.


title:
Feature Extraction and Automated Classification of Heartbeats by Machine
  Learning

abstract:
  We present algorithms for the detection of a class of heart arrhythmias with
the goal of eventual adoption by practicing cardiologists. In clinical
practice, detection is based on a small number of meaningful features extracted
from the heartbeat cycle. However, techniques proposed in the literature use
high dimensional vectors consisting of morphological, and time based features
for detection. Using electrocardiogram (ECG) signals, we found smaller subsets
of features sufficient to detect arrhythmias with high accuracy. The features
were found by an iterative step-wise feature selection method. We depart from
common literature in the following aspects: 1. As opposed to a high dimensional
feature vectors, we use a small set of features with meaningful clinical
interpretation, 2. we eliminate the necessity of short-duration
patient-specific ECG data to append to the global training data for
classification 3. We apply semi-parametric classification procedures (in an
ensemble framework) for arrhythmia detection, and 4. our approach is based on a
reduced sampling rate of ~ 115 Hz as opposed to 360 Hz in standard literature.


title: Symmetry-preserving contact interaction model for heavy-light mesons

abstract:
  We use a symmetry-preserving regularization method of ultraviolet divergences
in a vector-vector contact interac- tion model for low-energy QCD. The contact
interaction is a representation of nonperturbative kernels used Dyson-Schwinger
and Bethe-Salpeter equations. The regularization method is based on a
subtraction scheme that avoids standard steps in the evaluation of divergent
integrals that invariably lead to symmetry violation. Aiming at the study of
heavy-light mesons, we have implemented the method to the pseudoscalar pion and
Kaon mesons. We have solved the Dyson-Schwinger equation for the u, d and s
quark propagators, and obtained the bound-state Bethe-Salpeter amplitudes in a
way that the Ward-Green-Takahashi identities reflecting global symmetries of
the model are satisfied for arbitrary routing of the momenta running in loop
integrals.


title: The shrinkage type of knots

abstract:
  We study spectral gaps of cellular differentials for finite cyclic coverings
of knot complements. Their asymptotics can be expressed in terms of
irrationality exponents associated with ratios of logarithms of algebraic
numbers determined by the first two Alexander polynomials. From this point of
view it is natural to subdivide all knots into three different types. We show
that examples of all types abound and discuss what happens for twist and torus
knots as well as knots with few crossings.


title:
On the origin of inner coma structures observed by Rosetta during a
  diurnal rotation of comet 67P/Churyumov-Gerasimenko

abstract:
  The Rosetta probe around comet 67P/Churyumov-Gerasimenko (67P) reveals an
anisotropic dust distribution of the inner coma with jet-like structures. The
physical processes leading to jet formation are under debate, with most models
for cometary activity focusing on localised emission sources, such as cliffs or
terraced regions. Here we suggest, by correlating high-resolution simulations
of the dust environment around 67P with observations, that the anisotropy and
the background dust density of 67P originate from dust released across the
entire sunlit surface of the nucleus rather than from few isolated sources. We
trace back trajectories from coma regions with high local dust density in space
to the non-spherical nucleus and identify two mechanisms of jet formation:
areas with local concavity in either two dimensions or only one. Pits and
craters are examples of the first case, the neck region of the bilobed nucleus
of 67P for the latter one. The conjunction of multiple sources in addition to
dust released from all other sunlit areas results in a high correlation
coefficient (~0.8) of the predictions with observations during a complete
diurnal rotation period of 67P.


title: Absolute $\mathcal F$-Borel classes

abstract:
  We investigate and compare $\mathcal F$-Borel classes and absolute $\mathcal
F$-Borel classes. We provide precise examples distinguishing these two
hierarchies. We also show that for separable metrizable spaces, $\mathcal
F$-Borel classes are automatically absolute.


title: The KIT Motion-Language Dataset

abstract:
  Linking human motion and natural language is of great interest for the
generation of semantic representations of human activities as well as for the
generation of robot activities based on natural language input. However, while
there have been years of research in this area, no standardized and openly
available dataset exists to support the development and evaluation of such
systems. We therefore propose the KIT Motion-Language Dataset, which is large,
open, and extensible. We aggregate data from multiple motion capture databases
and include them in our dataset using a unified representation that is
independent of the capture system or marker set, making it easy to work with
the data regardless of its origin. To obtain motion annotations in natural
language, we apply a crowd-sourcing approach and a web-based tool that was
specifically build for this purpose, the Motion Annotation Tool. We thoroughly
document the annotation process itself and discuss gamification methods that we
used to keep annotators motivated. We further propose a novel method,
perplexity-based selection, which systematically selects motions for further
annotation that are either under-represented in our dataset or that have
erroneous annotations. We show that our method mitigates the two aforementioned
problems and ensures a systematic annotation process. We provide an in-depth
analysis of the structure and contents of our resulting dataset, which, as of
October 10, 2016, contains 3911 motions with a total duration of 11.23 hours
and 6278 annotations in natural language that contain 52,903 words. We believe
this makes our dataset an excellent choice that enables more transparent and
comparable research in this important area.


title: In memoriam: Dmitri Ivanenko

abstract:
  Dmitri Ivanenko, professor of Moscow State University, was one of the great
theoreticians of XX century, an author of the proton-neutron model of atomic
nucleus. In honor of the 110th Year Anniversary.


title:
Implications of the 750 GeV gamma-gamma Resonance as a Case Study for
  the International Linear Collider

abstract:
  If the gamma-gamma resonance at 750 GeV suggested by 2015 LHC data turns out
to be a real effect, what are the implications for the physics case and upgrade
path of the International Linear Collider? Whether or not the resonance is
confirmed, this question provides an interesting case study testing the
robustness of the ILC physics case. In this note, we address this question with
two points: (1) Almost all models proposed for the new 750 GeV particle require
additional new particles with electroweak couplings. The key elements of the
500 GeV ILC physics program---precision measurements of the Higgs boson, the
top quark, and 4-fermion interactions---will powerfully discriminate among
these models. This information will be important in conjunction with new LHC
data, or alone, if the new particles accompanying the 750 GeV resonance are
beyond the mass reach of the LHC. (2) Over a longer term, the energy upgrade of
the ILC to 1 TeV already discussed in the ILC TDR will enable experiments in
gamma-gamma and e+e- collisions to directly produce and study the 750 GeV
particle from these unique initial states.


title:
Distributed Clock Skew and Offset Estimation in Wireless Sensor
  Networks: Asynchronous Algorithm and Convergence Analysis

abstract:
  In this paper, we propose a fully distributed algorithm for joint clock skew
and offset estimation in wireless sensor networks based on belief propagation.
In the proposed algorithm, each node can estimate its clock skew and offset in
a completely distributed and asynchronous way: some nodes may update their
estimates more frequently than others using outdated message from neighboring
nodes. In addition, the proposed algorithm is robust to random packet loss.
Such algorithm does not require any centralized information processing or
coordination, and is scalable with network size. The proposed algorithm
represents a unified framework that encompasses both classes of synchronous and
asynchronous algorithms for network-wide clock synchronization. It is shown
analytically that the proposed asynchronous algorithm converges to the optimal
estimates with estimation mean-square-error at each node approaching the
centralized Cram\'er-Rao bound under any network topology. Simulation results
further show that {the convergence speed is faster than that corresponding to a
synchronous algorithm}.


title: Further Evidence For Zero Crossing On The Three Gluon Vertex

abstract:
  The three gluon one particle irreducible function is investigated using
lattice QCD simulations over a large region of momentum in the Landau gauge for
four dimensional pure Yang-Mills equations and the SU(3) gauge group. The
results favor a zero crossing of the gluon form factor for momenta in the range
$220 - 260$ MeV. This zero crossing is required to happen in order to have a
properly defined set of Dyson-Schwinger equations. It is also shown that in the
high momentum region the lattice results are compatible with the predictions of
renormalisation group improved perturbation theory.


title:
Uniqueness of the group Fourier transform on certain nilpotent Lie
  groups

abstract:
  In this article, we prove that if the group Fourier transform of certain
integrable functions on the Heisenberg motion group (or step two nilpotent Lie
groups) is of finite rank, then the function is identically zero. These results
can be thought as an analogue to the Benedicks theorem that dealt with the
uniqueness of the Fourier transform of integrable functions on the Euclidean
spaces.


title: Some contributions to many-body quantum mathematics

abstract:
  The results summarized here are intended as rigorous mathematical statements
on various physical models coming from condensed matter physics, statistical
mechanics (classical and quantum), quantum field theory and cold atoms physics.
The main tools are mostly those of the mathematical analyst: partial
differential equations, functional analysis, spectral theory, calculus of
variations, with some incursions into probability theory. A running thread is
the construction, by rigorous asymptotic analysis most of the time, of bridges
between different levels of mathematical modeling of physical phenomena.
  This is the manuscript for the author's habilitation thesis, summarizing
results obtained between 2011 and 2016, in collaboration with: Michele
Correggi, Mathieu Lewin, Douglas Lundholm, Phan Th\`anh Nam, Robert Seiringer,
Sylvia Serfaty and Jakob Yngvason.

categories: math-ph cond-mat.quant-gas math.AP math.MP quant-ph


title: Twisted sigma-model solitons on the quantum projective line

abstract:
  On the configuration space of projections in a noncommutative algebra, and
for an automorphism of the algebra, we use a twisted Hochschild cocycle for an
action functional, and a twisted cyclic cocycle for a topological term. The
latter is Hochschild-cohomologous to the former and positivity in twisted
Hochschild cohomology results into a lower bound for the action functional.
While the equations for the critical points are rather complicate, the use of
the positivity and the bound by the topological term leads to self-duality
equations (thus yielding twisted noncommutative sigma-model solitons, or
instantons). We present explicit non trivial solutions on the quantum
projective line.


title:
Limiting the Effective Mass and New Physics Parameters from
  $0\nu\beta\beta$

abstract:
  In the light of the recent result from KamLAND-Zen (KLZ) and GERDA Phase-II,
we update the bounds on the effective mass and the new physics parameters,
relevant for neutrinoless double beta decay ($0\nu \beta \beta$). In addition
to the light Majorana neutrino exchange, we analyze beyond standard model
contributions that arise in Left-Right symmetry and R-Parity violating
supersymmetry. The improved limit from KLZ constrains the effective mass of
light neutrino exchange down to sub-eV mass regime 0.06 eV. Using the
correlation between the $^{136}\rm{Xe}$ and $^{76}\rm{Ge}$ half-lives, we show
that the KLZ limit individually rules out the positive claim of observation of
$0\nu\beta\beta$ for all nuclear matrix element compilation. For the Left-Right
symmetry and R-parity violating supersymmetry, the KLZ bound implies a factor
of 2 improvement of the effective mass and the new physics parameters. The
future ton scale experiments such as, nEXO will further constrain these models,
in particular, will rule out standard as well as Type-II dominating LRSM
inverted hierarchy scenario.


title:
A Sufficient Condition for Graphic Sequences with Given Largest and
  Smallest Entries, Length, and Sum

abstract:
  We give a sufficient condition for a degree sequence to be graphic based on
its largest and smallest elements, length, and sum. This bound generalizes a
result of Zverovich and Zverovich.


title: Four paradoxes about the special theory of relativity

abstract:
  Various paradoxes about the relativity theory have been developed since the
birth of this theory. Each paradox somewhat shows people's query about the
relativity theory, and solving of each paradox demonstrates the correctness of
relativity theory once again. In this paper, four paradoxes about the special
theory of relativity are brought forward: displacement paradox, electromagnetic
transformation paradox, Doppler paradox and magnetic force paradox. We hope
some researchers can reasonably explain these paradoxes, and then knowledge of
the relativity theory will become more abundant.


title:
STARlight: A Monte Carlo simulation program for ultra-peripheral
  collisions of relativistic ions

abstract:
  Ultra-peripheral collisions (UPCs) have been a significant source of study at
RHIC and the LHC. In these collisions, the two colliding nuclei interact
electromagnetically, via two-photon or photonuclear interactions, but not
hadronically; they effectively miss each other. Photonuclear interactions
produce vector meson states or more general photonuclear final states, while
two-photon interactions can produce lepton or meson pairs, or single mesons. In
these interactions, the collision geometry plays a major role. We present a
program, STARlight, that calculates the cross-sections for a variety of UPC
final states and also creates, via Monte Carlo simulation, events for use in
determining detector efficiency.


title:
On the local integrability of almost-product structures defined by
  space-time metrics

abstract:
  The splitting of the tangent bundle of space-time into temporal and spatial
sub-bundles defines an almost-product structure. In particular, any space-time
metric can be locally expressed in time-orthogonal form, in such a way that
whether or not that almost-product structure is locally generated by a
coordinate chart is a matter of the integrability of the Pfaff equation that
the temporal 1-form of that expression for the metric defines. When one applies
that analysis to the known exact solutions to the Einstein field equations, one
finds that many of the common ones are completely-integrable, although some of
the physically-interesting ones are not.


title: Green's function for chordal SLE curves

abstract:
  For a chordal SLE$_\kappa$ ($\kappa\in(0,8)$) curve in a domain $D$, the
$n$-point Green's function valued at distinct points $z_1,\dots,z_n\in D$ is
defined to be $$G(z_1,\dots,z_n)=\lim_{r_1,\dots,r_n\downarrow 0} \prod_{k=1}^n
r_k^{d-2} \mathbb{P}[\mbox{dist}(\gamma,z_k)<r_k,1\le k\le n],$$ where
$d=1+\frac{\kappa}{8}$ is the Hausdorff dimension of SLE$_\kappa$, provided
that the limit converges. In this paper, we will show that such Green's
functions exist for any finite number of points. Along the way we provide the
rate of convergence and modulus of continuity for Green's functions as well.
Finally, we give up-to-constant bounds for them.


title: Pollicott-Ruelle resonances via kinetic Brownian motion

abstract:
  The kinetic Brownian motion on the cosphere bundle of a Riemannian manifold
$\mathbb{M}$ is a stochastic process that models the geodesic equation
perturbed by a random white force of size $\varepsilon$. When $\mathbb{M}$ is
compact with negative curvature we show that the $L^2$-spectrum of the
infinitesimal generator of this process converges to the Pollicott--Ruelle
resonances of $\mathbb{M}$ as $\varepsilon \rightarrow 0$.


title: Safe Policy Improvement by Minimizing Robust Baseline Regret

abstract:
  An important problem in sequential decision-making under uncertainty is to
use limited data to compute a safe policy, i.e., a policy that is guaranteed to
perform at least as well as a given baseline strategy. In this paper, we
develop and analyze a new model-based approach to compute a safe policy when we
have access to an inaccurate dynamics model of the system with known accuracy
guarantees. Our proposed robust method uses this (inaccurate) model to directly
minimize the (negative) regret w.r.t. the baseline policy. Contrary to the
existing approaches, minimizing the regret allows one to improve the baseline
policy in states with accurate dynamics and seamlessly fall back to the
baseline policy, otherwise. We show that our formulation is NP-hard and propose
an approximate algorithm. Our empirical results on several domains show that
even this relatively simple approximate algorithm can significantly outperform
standard approaches.


title:
Reconnection-Driven Magnetohydrodynamic Turbulence in a Simulated
  Coronal-Hole Jet

abstract:
  Extreme-ultraviolet and X-ray jets occur frequently in magnetically open
coronal holes on the Sun, especially at high solar latitudes. Some of these
jets are observed by white-light coronagraphs as they propagate through the
outer corona toward the inner heliosphere, and it has been proposed that they
give rise to microstreams and torsional Alfv\'{e}n waves detected in situ in
the solar wind. To predict and understand the signatures of coronal-hole jets,
we have performed a detailed statistical analysis of such a jet simulated with
an adaptively refined magnetohydrodynamics model. The results confirm the
generation and persistence of three-dimensional, reconnectiondriven magnetic
turbulence in the simulation. We calculate the spatial correlations of magnetic
fluctuations within the jet and find that they agree best with the M\"{u}ller -
Biskamp scaling model including intermittent current sheets of various sizes
coupled via hydrodynamic turbulent cascade. The anisotropy of the magnetic
fluctuations and the spatial orientation of the current sheets are consistent
with an ensemble of nonlinear Alfv\'{e}n waves. These properties also reflect
the overall collimated jet structure imposed by the geometry of the
reconnecting magnetic field. A comparison with Ulysses observations shows that
turbulence in the jet wake is in quantitative agreement with that in the fast
solar wind.


title:
Gate-Variable Mid-Infrared Optical Transitions in a
  $(Bi_{1-x}Sb_x)_2Te_3$ Topological Insulator

abstract:
  We report mid-infrared spectroscopy measurements of an electrostatically
gated topological insulator, in which we observe several percent modulation of
transmittance and reflectance of (Bi1-xSbx)2Te3 films as gating shifts the
Fermi level. Infrared transmittance measurements of gated (Bi1-xSbx)2Te3 films
were enabled by use of an epitaxial lift-off method for large-area transfer of
topological insulator films from infrared-absorbing SrTiO3 growth substrates to
thermal oxidized silicon substrates. We combine these optical experiments with
transport measurements and angle-resolved photoemission spectroscopy to
identify the observed spectral modulation as a gate-driven transfer of spectral
weight between both bulk and topological surface channels and interband and
intraband channels. We develop a model for the complex permittivity of gated
(Bi1-xSbx)2Te3, and find a good match to our experimental data. These results
open the path for layered topological insulator materials as a new candidate
for tunable infrared optics and highlight the possibility of switching
topological optoelectronic phenomena between bulk and spin-polarized surface
regimes.


title:
Frequentist model comparison tests of sinusoidal variations in
  measurements of Newton's gravitational constant

abstract:
  Anderson et al have claimed to find evidence for periodic sinusoidal
variations (period=5.9 years) in measurements of Newton's Gravitational
constant. These claims have been disputed by Pitkin. Using Bayesian model
comparison, he argues that a model with an unknown Gaussian noise component is
favored over any periodic variations by more than $e^{30}$. We re-examine the
claims of Anderson et al using frequentist model comparison tests, both with
and without errors in the measurement times. Our findings lend support to
Pitkin's claim that a constant term along with an unknown systematic offset
provides a better fit to the measurements of Newton's constant, compared to any
sinusoidal variations.


title: Dyson's Partition Ranks and their Multiplicative Extensions

abstract:
  We study the Dyson rank function $N(r,3;n)$, the number of partitions of $n$
with rank $\equiv r \pmod 3$. We investigate the convexity of these functions.
We extend $N(r,3;n)$ multiplicatively to the set of partitions, and we
determine the maximum value when taken over all partitions of size $n$.


title:
A Method to Produce Intense Positron Beams via Electro Pair Production
  on Electrons

abstract:
  Intense positron beams can be prepared via electro production with the
reaction $e^{-} + e^{-} \rightarrow e^{-}+e^{+}+e^{-}+e^{-}$ due to the
availability of high current electron beams. Head on collisions inside of a
magnetic field of a solenoid are used to produce unpolarized/polarized
positrons via $e^{-}-e^{+}$ - pair production. A flux of unpolarized positrons,
$N_{positron}=6.55 \cdot 10^{11} s^{-1}$, has been obtained as a result of
calculations for a special case of parameters with beam currents for both
electron beams of $I_{e}$=10 mA and beam momenta of $p_{beam 1}$=0.63 MeV/c and
$p_{beam 2}$=10.0 MeV/c. Intensities are an order of magnitude smaller in the
case of polarized positrons due to a reduced current of one of the electron
beams. Suitable cuts on momenta of the positrons allow to achieve a
polarization transfer from electrons to positrons of $\geq $ 85\% reducing,
however, the intensity to 27\%


title: Periodicity of identifying codes in strips

abstract:
  An identifying code in a graph is a subset of vertices having a nonempty and
distinct intersection with the closed neighborhood of every vertex. We prove
that the infimum density of any identifying code in $S_k$ (an infinite strip of
$k$ rows in the square grid) can always be achieved by a periodic identifying
code with pattern length at most $2^{4k}$. Assisted by a compute program
implementing Karp's algorithm for minimum cycle mean, we find a periodic
identifying code in $S_4$ with the minimum density $11/28$, and a periodic
identifying code in $S_5$ with the minimum density $19/50$.


title: Fitting a Simplicial Complex using a Variation of k-means

abstract:
  We give a simple and effective two stage algorithm for approximating a point
cloud $\mathcal{S}\subset\mathbb{R}^m$ by a simplicial complex $K$. The first
stage is an iterative fitting procedure that generalizes k-means clustering,
while the second stage involves deleting redundant simplices. A form of
dimension reduction of $\mathcal{S}$ is obtained as a consequence.


title: Structural Transitions in Dense Networks

abstract:
  We introduce an evolving network model in which a new node attaches to a
randomly selected target node and also to each of its neighbors with
probability $p$. The resulting network is sparse for $p<\frac{1}{2}$ and dense
(average degree increasing with number of nodes $N$) for $p\geq \frac{1}{2}$.
In the dense regime, individual networks realizations built by this copying
mechanism are disparate and not self-averaging. Further, there is an infinite
sequence of structural anomalies at $p=\frac{2}{3}$, $\frac{3}{4}$,
$\frac{4}{5}$, etc., where the dependences on $N$ of the number of triangles
(3-cliques), 4-cliques, undergo phase transitions. When linking to second
neighbors of the target can occur, the probability that the resulting graph is
complete---where all nodes are connected---is non-zero as $N\to\infty$.


title: The quintic NLS on perturbations of $\mathbf{R}^3$

abstract:
  Consider the defocusing quintic nonlinear Schr\"{o}dinger equation on
$\mathbf{R}^3$ with initial data in the energy space. This problem is
"energy-critical" in view of a certain scale-invariance, which is a main source
of difficulty in the analysis of this equation. It is a nontrivial fact that
all finite-energy solutions scatter to linear solutions. We show that this
remains true under small compact deformations of the Euclidean metric. Our main
new ingredient is a long-time microlocal weak dispersive estimate that accounts
for the refocusing of geodesics.


title:
Elliptic Boundary Value Problems with Fractional Regularity Data: The
  First Order Approach

abstract:
  We study well-posedness of boundary value problems of Dirichlet and Neumann
type for elliptic systems on the upper half-space with coefficients independent
of the transversal variable, and with boundary data in fractional
Besov-Hardy-Sobolev (BHS) spaces. Our approach uses minimal assumptions on the
coefficients, and in particular does not require De Giorgi-Nash-Moser
estimates. Our results are completely new for the Hardy-Sobolev case, and in
the Besov case they extend results recently obtained by Barton and Mayboroda.
  First we develop a theory of BHS spaces adapted to operators which are
bisectorial on $L^2$, with bounded $H^\infty$ functional calculus on their
ranges, and which satisfy $L^2$ off-diagonal estimates. In particular, this
theory applies to perturbed Dirac operators $DB$. We then prove that for a
nontrivial range of exponents (the identification region) the BHS spaces
adapted to $DB$ are equal to those adapted to $D$ (which correspond to
classical BHS spaces).
  Our main result is the classification of solutions of the elliptic system
$\operatorname{div} A \nabla u = 0$ within a certain region of exponents. More
precisely, we show that if the conormal gradient of a solution belongs to a
weighted tent space (or one of their real interpolants) with exponent in the
classification region, and in addition vanishes at infinity in a certain sense,
then it has a trace in a BHS space, and can be represented as a semigroup
evolution of this trace in the transversal direction. As a corollary, any such
solution can be represented in terms of an abstract layer potential operator.
Within the classification region, we show that well-posedness is equivalent to
a certain boundary projection being an isomorphism. We derive various
consequences of this characterisation, which are illustrated in various
situations, including in particular that of the Regularity problem for real
equations.


title:
HD 24355 observed by the Kepler K2 mission: A rapidly oscillating Ap
  star pulsating in a distorted quadrupole mode

abstract:
  We present an analysis of the first Kepler K2 mission observations of a
rapidly oscillating Ap (roAp) star, HD 24355 ($V=9.65$). The star was
discovered in SuperWASP broadband photometry with a frequency of 224.31
d$^{-1}$, (2596.18 $\mu$Hz; $P = 6.4$ min) and an amplitude of 1.51 mmag, with
later spectroscopic analysis of low-resolution spectra showing HD 24355 to be
an A5 Vp SrEu star. The high precision K2 data allow us to identify 13
rotationally split sidelobes to the main pulsation frequency of HD 24355. This
number of sidelobes combined with an unusual rotational phase variation show
this star to be the most distorted quadrupole roAp pulsator yet observed. In
modelling this star, we are able to reproduce well the amplitude modulation of
the pulsation, and find a close match to the unusual phase variations. We show
this star to have a pulsation frequency higher than the critical cut-off
frequency. This is currently the only roAp star observed with the Kepler
spacecraft in Short Cadence mode that has a photometric amplitude detectable
from the ground, thus allowing comparison between the mmag amplitude
ground-based targets and the $\mu$mag spaced-based discoveries. No further
pulsation modes are identified in the K2 data, showing this star to be a
single-mode pulsator.


title:
The Partially Observable Hidden Markov Model and its Application to
  Keystroke Dynamics

abstract:
  The partially observable hidden Markov model is an extension of the hidden
Markov Model in which the hidden state is conditioned on an independent Markov
chain. This structure is motivated by the presence of discrete metadata, such
as an event type, that may partially reveal the hidden state but itself
emanates from a separate process. Such a scenario is encountered in keystroke
dynamics whereby a user's typing behavior is dependent on the text that is
typed. Under the assumption that the user can be in either an active or passive
state of typing, the keyboard key names are event types that partially reveal
the hidden state due to the presence of relatively longer time intervals
between words and sentences than between letters of a word. Using five public
datasets, the proposed model is shown to consistently outperform other anomaly
detectors, including the standard HMM, in biometric identification and
verification tasks and is generally preferred over the HMM in a Monte Carlo
goodness of fit test.


title: Estimating trends in the global mean temperature record

abstract:
  Given uncertainties in physical theory and numerical climate simulations, the
historical temperature record is often used as a source of empirical
information about climate change. Many historical trend analyses appear to
deemphasize physical and statistical assumptions: examples include regression
models that treat time rather than radiative forcing as the relevant covariate
and time series methods that account for internal variability
nonparametrically. However, given a limited record and the presence of internal
variability, estimating radiatively forced historical temperature trends
necessarily requires assumptions. Ostensibly empirical methods can involve an
inherent conflict in assumptions: they require data records that are short
enough for naive trend models to apply but long enough for internal variability
to be accounted for. In the context of global mean temperatures, methods that
deemphasize assumptions can therefore produce misleading inferences, because
the twentieth century trend is complex and the scale of correlation is long
relative to the data length. We illustrate how a simple but physically
motivated trend model can provide better-fitting and more broadly applicable
trend estimates and can address a wider array of questions. The model allows
one to distinguish, within a single framework, between uncertainties in the
shorter-term versus longer-term response to radiative forcing, with
implications not only on historical trends but also on uncertainties in future
projections. We also investigate the consequence on inferred uncertainties of
the choice of a statistical description of internal variability. While
nonparametric methods may seem to avoid making explicit assumptions, we
demonstrate how even misspecified parametric methods, if attuned to important
characteristics of internal variability, can result in more accurate statements
about trend uncertainty.


title:
Deep Structured-Output Regression Learning for Computational Color
  Constancy

abstract:
  Computational color constancy that requires esti- mation of illuminant colors
of images is a fundamental yet active problem in computer vision, which can be
formulated into a regression problem. To learn a robust regressor for color
constancy, obtaining meaningful imagery features and capturing latent
correlations across output variables play a vital role. In this work, we
introduce a novel deep structured-output regression learning framework to
achieve both goals simultaneously. By borrowing the power of deep convolutional
neural networks (CNN) originally designed for visual recognition, the proposed
framework can automatically discover strong features for white balancing over
different illumination conditions and learn a multi-output regressor beyond
underlying relationships between features and targets to find the complex
interdependence of dif- ferent dimensions of target variables. Experiments on
two public benchmarks demonstrate that our method achieves competitive
performance in comparison with the state-of-the-art approaches.


title:
Parallel electric fields are inefficient drivers of energetic electrons
  in magnetic reconnection

abstract:
  We present two-dimensional kinetic simulations, with a broad range of initial
guide fields, that isolate the role of parallel electric fields ($E_\parallel$)
in energetic electron production during collisionless magnetic reconnection. In
the strong guide field regime, $E_\parallel$ drives essentially all of the
electron energy gain, yet fails to generate an energetic component. We suggest
that this is due to the weak energy scaling of particle acceleration from
$E_\parallel$ compared to that of a Fermi-type mechanism responsible for
energetic electron production in the weak guide-field regime. This result has
important implications for energetic electron production in astrophysical
systems and reconnection-driven dissipation in turbulence.


title: BCS theory of driven superconductivity

abstract:
  We study the impact of a time-dependent external driving of the lattice
phonons in a minimal model of a BCS superconductor. Upon evaluating the
driving-induced vertex corrections of the phonon-mediated electron-electron
interaction, we show that parametric phonon driving can be used to elevate the
critical temperature $T_c$, while a dipolar phonon drive has no effect. We
provide simple analytic expressions for the enhancement factor of $T_c$.
Furthermore, a mean-field analysis of a nonlinear phonon-phonon interaction
also shows that phonon anharmonicities further amplify $T_c$. Our results hold
universally for the large class of normal BCS superconductors.


title:
Disorder and wetting transition: the pinned harmonic crystal in
  dimension three or larger

abstract:
  We consider the Lattice Gaussian free field in $d+1$ dimensions, $d=3$ or
larger, on a large box (linear size $N$) with boundary conditions zero. On this
field two potentials are acting: one, that models the presence of a wall,
penalizes the field when it enters the lower half space and one, the
{\guillemotleft}pinning potential{\guillemotright} , that rewards visits to the
proximity of the wall. The wall can be soft, i.e. the field has a finite
penalty to enter the lower half plane, or hard when the penalty is infinite. In
general the pinning potential is disordered and it gives on average a reward h
in $\mathbb{R}$ (a negative reward is a penalty): the energetic contribution
when the field at site x visits the pinning region is $\beta \omega_x+h$,
$\{\omega_x\}_{x \in \mathbb{Z}^d}$ are IID centered and exponentially
integrable random variables of unit variance and $\beta\ge 0$. In [E.
Bolthausen, J.-D. Deuschel and O. Zeitouni, J. Math. Phys. 41 (2000),
1211-1223] it is shown that, when $\beta=0$ (that is, in the non disordered
model), a delocalization-localization transition happens at $h=0$, in
particular the free energy of the system is zero for $h \le 0$ and positive for
$h>0$. We show that, for $\beta\neq 0$, the transition happens at
$h=h_c(\beta):=- \log \mathbb{E} \exp(\beta \omega_x)$ and we find the precise
asymptotic behavior of the logarithm of the free energy density of the system
when $h \searrow h_c(\beta)$. In particular, we show that the transition is of
infinite order in the sense that the free energy is smaller than any power of
$h-h_c(\beta)$ in the neighborhood of the critical point and that disorder does
not modify at all the nature of the transition. We also provide results on the
behavior of the paths of the random field in the limit $N \to \infty$.


title: Multishifts on Directed Cartesian Product of Rooted Directed Trees

abstract:
  We systematically develop the multivariable counterpart of the theory of
weighted shifts on rooted directed trees. Capitalizing on the theory of product
of directed graphs, we introduce and study the notion of multishifts on
directed Cartesian product of rooted directed trees. This framework unifies the
theory of weighted shifts on rooted directed trees and that of classical
unilateral multishifts. Moreover, this setup brings into picture some new
phenomena such as the appearance of system of linear equations in the
eigenvalue problem for the adjoint of a multishift. In the first half of the
paper, we focus our attention mostly on the multivariable spectral theory and
function theory including finer analysis of various joint spectra and wandering
subspace property for multishifts. In the second half, we separate out two
special classes of multishifts, which we refer to as torally balanced and
spherically balanced multishifts. The classification of these two classes is
closely related to toral and spherical polar decompositions of multishifts.
Furthermore, we exhibit a family of spherically balanced multishifts on
$d$-fold directed Cartesian product $\mathscr T$ of rooted directed trees.
These multishifts turn out be multiplication $d$-tuples $\mathscr M_{z, a}$ on
certain reproducing kernel Hilbert spaces $\mathscr H_a$ of vector-valued
holomorphic functions defined on the unit ball $\mathbb B^d$ in $\mathbb C^d$,
which can be thought of as tree analogs of the multiplication $d$-tuples acting
on the reproducing kernel Hilbert spaces associated with the kernels
$\frac{1}{(1-\langle{z},{{w}\rangle})^a}~(z, w \in \mathbb B^d, a \in \mathbb
N).$


title:
A High Reliability Survey of Discrete Epoch of Reionization Foreground
  Sources in the MWA EoR0 Field

abstract:
  Detection of the Epoch of Reionization HI signal requires a precise
understanding of the intervening galaxies and AGN, both for instrumental
calibration and foreground removal. We present a catalogue of 7394
extragalactic sources at 182 MHz detected in the RA=0 field of the Murchison
Widefield Array Epoch of Reionization observation programme. Motivated by
unprecedented requirements for precision and reliability we develop new methods
for source finding and selection. We apply machine learning methods to
self-consistently classify the relative reliability of 9490 source candidates.
A subset of 7466 are selected based on reliability class and signal-to-noise
ratio criteria. These are statistically cross-matched to four other radio
surveys using both position and flux density information. We find 7369 sources
to have confident matches, including 90 partially resolved sources that split
into a total of 192 sub-components. An additional 25 unmatched sources are
included as new radio detections. The catalogue sources have a median spectral
index of -0.85. Spectral flattening is seen toward lower frequencies with a
median of -0.71 predicted at 182 MHz. The astrometric error is 7 arcsec.
compared to a 2.3 arcmin. beam FWHM. The resulting catalogue covers
approximately 1400 sq. deg. and is complete to approximately 80 mJy within half
beam power. This provides the most reliable discrete source sky model available
to date in the MWA EoR0 field for precision foreground subtraction.


title:
On the existence of aggregation functions with given super-additive and
  sub-additive transformations

abstract:
  In this note we study restrictions on the recently introduced super-additive
and sub-additive transformations, $A\mapsto A^*$ and $A\mapsto A_*$, of an
aggregation function $A$. We prove that if $A^*$ has a slightly stronger
property of being strictly directionally convex, then $A=A^*$ and $A_*$ is
linear; dually, if $A_*$ is strictly directionally concave, then $A=A_*$ and
$A^*$ is linear. This implies, for example, the existence of pairs of functions
$f\le g$ sub-additive and super-additive on $[0,\infty[^n$, respectively, with
zero value at the origin and satisfying relatively mild extra conditions, for
which there exists no aggregation function $A$ on $[0,\infty[^n$ such that
$A_*=f$ and $A^*=g$.


title: On the Fermat's Last Theorem and the Dirac equation

abstract:
  In the present paper we study, in a mathematically non-formal way, the
validity of the Fermat's Last Theorem (FLT) by generalizing the usual procedure
of extracting the square root of non convenient objects initially introduced by
P. A. M. Dirac in the study of the linear relativistic wave equation.


title: Covariant-differential formulation of Lagrangian field theory

abstract:
  Building on the Utiyama principle we formulate an approach to Lagrangian
field theory in which exterior covariant differentials of vector-valued forms
replace partial derivatives, in the sense that they take up the role played by
the latter in the usual jet bundle formulation. Actually a natural Lagrangian
can be written as a density on a suitable "covariant prolongation bundle"; the
related momenta turn out to be natural vector-valued forms, and the field
equations can be expressed in terms of covariant exterior differentials of the
momenta. Currents and energy-tensors naturally also fit into this formalism.
The examples of bosonic fields and spin one-half fields, interacting with
non-Abelian gauge fields, are worked out. The "metric-affine" description of
the gravitational field is naturally included, too.


title: Remarks on groups of bundle automorphisms over the Riemann sphere

abstract:
  A geometric characterization of the structure of the group of automorphisms
of an arbitrary Birkhoff-Grothendieck bundle splitting $\bigoplus_{i=1}^{r}
\mathcal(m_{i})$ over $\mathbb{C}\mathbb{P}^{1}$ is provided, in terms of its
action on a suitable space of generalized flags in the fibers over a finite
subset $S\subset\mathbb{C}\mathbb{P}^{1}$. The relevance of such
characterization derives from the possibility of constructing geometric models
for diverse moduli spaces of stable objects in genus 0, such as parabolic
bundles, parabolic Higgs bundles, and logarithmic connections, as collections
of orbit spaces of parabolic structures and compatible geometric data
satisfying a given stability criterion, under the actions of the different
splitting types' automorphism groups, that are glued in a concrete fashion. We
illustrate an instance of such idea, on the existence of several natural
representatives for the induced actions on the corresponding vector spaces of
(orbits of) logarithmic connections with residues adapted to a parabolic
structure.


title: Practical optimization of Steiner Trees via the cavity method

abstract:
  The optimization version of the cavity method for single instances, called
Max-Sum, has been applied in the past to the Minimum Steiner Tree Problem on
Graphs and variants. Max-Sum has been shown experimentally to give
asymptotically optimal results on certain types of weighted random graphs, and
to give good solutions in short computation times for some types of real
networks. However, the hypotheses behind the formulation and the cavity method
itself limit substantially the class of instances on which the approach gives
good results (or even converges). Moreover, in the standard model formulation,
the diameter of the tree solution is limited by a predefined bound, that
affects both computation time and convergence properties. In this work we
describe two main enhancements to the Max-Sum equations to be able to cope with
optimization of real-world instances. First, we develop an alternative 'flat'
model formulation, that allows to reduce substantially the relevant
configuration space, making the approach feasible on instances with large
solution diameter, in particular when the number of terminal nodes is small.
Second, we propose an integration between Max-Sum and three greedy heuristics.
This integration allows to transform Max-Sum into a highly competitive
self-contained algorithm, in which a feasible solution is given at each step of
the iterative procedure. Part of this development participated on the 2014
DIMACS challenge on Steiner Problems, and we report the results here.


title: Modelling extragalactic extinction through gamma-ray burst afterglows

abstract:
  We analyze extragalactic extinction profiles derived through gamma-ray burst
afterglows, using a dust model specifically constructed on the assumption that
dust grains are not immutable but respond time-dependently to the local
physics. Such a model includes core-mantle spherical particles of mixed
chemical composition (silicate core, sp2 and sp3 carbonaceous layers), and an
additional molecular component, in the form of free-flying polycyclic aromatic
hydrocarbons. We fit most of the observed extinction profiles. Failures occur
for lines of sight presenting remarkable rises blueward the bump. We find a
tendency in the carbon chemical structure to become more aliphatic with the
galactic activity, and to some extent with increasing redshifts. Moreover, the
contribution of the moleclar component to the total extinction is more
important in younger objects. The results of the fitting procedure (either
successes and failures) may be naturally interpreted through an evolutionary
prescription based on the carbon cycle in the interstellar medium of galaxies.


title:
Classical Neumann Problems for Hessian equations and
  Alexandrov-Fenchel's inequalities

abstract:
  Recently, the first named author together with Xinan Ma \cite{ma2015neumann},
have proved the existence of the Neumann problems for Hessian equations. In
this paper, we proceed further to study classical Neumann problems for Hessian
equations. We prove here the existence of classical Neumann problems under the
uniformly convex domain in R^n. As an application, we use the solution of the
classical Neumann problem to give a new proof of a family of Alexandrov-Fenchel
inequalities arising from convex geometry. This geometric application is
motivated from Reilly \cite{Reilly1980}.


title: A direct Proof for Quadratic Convergence of the Geometric Newton Method

abstract:
  We consider the problem of numerically computing a critical point of a
functional $J\colon M\rightarrow R$ where $M$ is a Riemannian manifold. Due to
local quadratic convergence a popular choice to solve this problem is the
geometric Newton method. The proofs for quadratic convergence either use
computations in a chart or require additional geometric quantities such as
parallel translation. In this short note we provide a direct proof for
quadratic convergence.


title: Endohedrally confined hydrogen atom with a moving nucleus

abstract:
  We studied the hydrogen atom as a system of two quantum particles in
different confinement conditions; a spherical-impenetrable-wall cavity and a
fullerene molecule cage. The motion is referred to the center of spherical
cavities, and the Schr\"{o}dinger equation solved by means of a Generalized
Sturmian Function expansion in spherical coordinates. The solutions present
different properties from the ones described by the many models in the
literature, where the proton is fixed in space and only the electron is
considered as a quantum particle. Our results show that the position of the
proton (i.e. the center of mas of the H atom) is very sensitive to the
confinement condition, and could vary substantially from one state to another,
from being sharply centered to being localized outside the fullerene molecule.
Interchange of the localization characteristics between the states when varying
the strength of the fullerene cage and mass occurred through crossing
phenomena.


title: Eigenvalue tunnelling and decay of quenched random networks

abstract:
  We consider the canonical ensemble of $N$-vertex Erd\H{o}s-R\'enyi (ER)
random topological graphs with quenched vertex degree, and with fugacity $\mu$
for each closed triple of bonds. We claim complete defragmentation of large-$N$
graphs into the collection of $[p^{-1}]$ almost full subgraphs (cliques) above
critical fugacity, $\mu_c$, where $p$ is the ER bond formation probability.
Evolution of the spectral density, $\rho(\lambda)$, of the adjacency matrix
with increasing $\mu$ leads to the formation of two-zonal support for
$\mu>\mu_c$. Eigenvalue tunneling from one (central) zone to the other means
formation of a new clique in the defragmentation process. The adjacency matrix
of the ground state of a network has the block-diagonal form where number of
vertices in blocks fluctuate around the mean value $Np$. The spectral density
of the whole network in this regime has triangular shape. We interpret the
phenomena from the viewpoint of the conventional random matrix model and
speculate about possible physical applications.


title:
Surface state dominated spin-charge current conversion in topological
  insulator/ferromagnetic insulator heterostructures

abstract:
  We report the observation of ferromagnetic resonance-driven spin pumping
signals at room temperature in three-dimensional topological insulator thin
films -- Bi2Se3 and (Bi,Sb)2Te3 -- deposited by molecular beam epitaxy on
yttrium iron garnet thin films. By systematically varying the Bi2Se3 film
thickness, we show that the spin-charge conversion efficiency, characterized by
the inverse Rashba-Edelstein effect length (lambda_IREE), increases
dramatically as the film thickness is increased from 2 quintuple layers,
saturating above 6 quintuple layers. This suggests a dominant role of surface
states in spin and charge interconversion in topological insulator/ferromagnet
heterostructures. Our conclusion is further corroborated by studying a series
of YIG/(BiSb)2Te3 heterostructures. Finally, we use the ferromagnetic resonance
linewidth broadening and the inverse Rashba-Edelstein signals to determine the
effective interfacial spin mixing conductance and lambda_IREE.