title: By-passing the Kohn-Sham equations with machine learning

abstract:
  Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of
density functional theory to solve electronic structure problems in a wide
variety of scientific fields, ranging from materials science to biochemistry to
astrophysics. Machine learning holds the promise of learning the kinetic energy
functional via examples, by-passing the need to solve the Kohn-Sham equations.
This should yield substantial savings in computer time, allowing either larger
systems or longer time-scales to be tackled, but attempts to machine-learn this
functional have been limited by the need to find its derivative. The present
work overcomes this difficulty by directly learning the density-potential and
energy-density maps for test systems and various molecules. Both improved
accuracy and lower computational cost with this method are demonstrated by
reproducing DFT energies for a range of molecular geometries generated during
molecular dynamics simulations. Moreover, the methodology could be applied
directly to quantum chemical calculations, allowing construction of density
functionals of quantum-chemical accuracy.

categories: physics.comp-ph cs.LG physics.chem-ph stat.ML


title: Complex Geometry of Nuclei and Atoms

abstract:
  We propose a new geometrical model of matter, in which neutral atoms are
modelled by compact, complex algebraic surfaces. Proton and neutron numbers are
determined by a surface's Chern numbers. Equivalently, they are determined by
combinations of the Hodge numbers, or the Betti numbers. Geometrical
constraints on algebraic surfaces allow just a finite range of neutron numbers
for a given proton number. This range encompasses the known isotopes.


title: Mass extinctions and supernova explosions

abstract:
  A nearby supernova (SN) explosion could have negatively influenced life on
Earth, maybe even been responsible for mass extinctions. Mass extinction poses
a significant extinction of numerous species on Earth, as recorded in the
paleontologic, paleoclimatic, and geological record of our planet. Depending on
the distance between the Sun and the SN, different types of threats have to be
considered, such as ozone depletion on Earth, causing increased exposure to the
Sun's ultraviolet radiation, or the direct exposure of lethal x-rays. Another
indirect effect is cloud formation, induced by cosmic rays in the atmosphere
which result in a drop in the Earth's temperature, causing major glaciations of
the Earth. The discovery of highly intensive gamma ray bursts (GRBs), which
could be connected to SNe, initiated further discussions on possible
life-threatening events in Earth's history. The probability that GRBs hit the
Earth is very low. Nevertheless, a past interaction of Earth with GRBs and/or
SNe cannot be excluded and might even have been responsible for past extinction
events.


title: Network Psychometrics

abstract:
  This chapter provides a general introduction of network modeling in
psychometrics. The chapter starts with an introduction to the statistical model
formulation of pairwise Markov random fields (PMRF), followed by an
introduction of the PMRF suitable for binary data: the Ising model. The Ising
model is a model used in ferromagnetism to explain phase transitions in a field
of particles. Following the description of the Ising model in statistical
physics, the chapter continues to show that the Ising model is closely related
to models used in psychometrics. The Ising model can be shown to be equivalent
to certain kinds of logistic regression models, loglinear models and
multi-dimensional item response theory (MIRT) models. The equivalence between
the Ising model and the MIRT model puts standard psychometrics in a new light
and leads to a strikingly different interpretation of well-known latent
variable models. The chapter gives an overview of methods that can be used to
estimate the Ising model, and concludes with a discussion on the interpretation
of latent variables given the equivalence between the Ising model and MIRT.


title: Low-complexity method for hybrid MPC with local guarantees

abstract:
  Model predictive control problems for constrained hybrid systems are usually
cast as mixed-integer optimization problems (MIP). However, commercial MIP
solvers are designed to run on desktop computing platforms and are not suited
for embedded applications which are typically restricted by limited
computational power and memory. To alleviate these restrictions, we develop a
novel low-complexity, iterative method for a class of non-convex, non-smooth
optimization problems. This class of problems encompasses hybrid model
predictive control problems where the dynamics are piece-wise affine (PWA). We
give conditions such that the proposed algorithm has fixed points and show
that, under practical assumptions, our method is guaranteed to converge locally
to local minima. This is in contrast to other low-complexity methods in the
literature, such as the non-convex alternating directions method of multipliers
(ADMM), for which no such guarantees are known for this class of problems. By
interpreting the PWA dynamics as a union of polyhedra we can exploit the
problem structure and develop an algorithm based on operator splitting
procedures. Our algorithm departs from the traditional MIP formulation, and
leads to a simple, embeddable method that only requires matrix-vector
multiplications and small-scale projections onto polyhedra. We illustrate the
efficacy of the method on two numerical examples, achieving good closed-loop
performance with computational times several orders of magnitude smaller
compared to state-of-the-art MIP solvers. Moreover, it is competitive with ADMM
in terms of suboptimality and computation time, but additionally provides local
optimality and local convergence guarantees.


title: Do nuclear collisions create a locally equilibrated quark-gluon plasma?

abstract:
  Experimental results on azimuthal correlations in high energy nuclear
collisions (nucleus-nucleus, proton-nucleus and proton-proton) seem to be well
described by viscous hydrodynamics. It is often argued that this agreement
implies either local thermal equilibrium or at least local isotropy. In this
note, I present arguments why this is not the case. Neither local
near-equilibrium nor near-isotropy are required in order for hydrodynamics to
offer a successful and accurate description of experimental results. However, I
predict the breakdown of hydrodynamics at momenta of order seven times the
temperature, corresponding to a smallest possible QCD liquid drop size of 0.15
fm.


title:
Coherent destruction of tunneling in graphene irradiated by elliptically
  polarized lasers

abstract:
  Photo-induced transition probabilities in graphene are studied theoretically
from the viewpoint of Floquet theory. Conduction band populations are computed
for a strongly, periodically driven graphene sheet under linear, circular, and
elliptic polarization. Features of the momentum spectrum of excited
quasi-particles can be directly related to the avoided crossing of the Floquet
quasi-energy levels. In particular, the impact of the ellipticity and the
strength of the laser excitation on the avoided crossing structure -- and on
the resulting transition probabilities -- is studied. It is shown that the
ellipticity provides an additional control parameter over the phenomenon of
coherent destruction of tunneling in graphene, allowing one to selectively
suppress multiphoton resonances.


title: The GALAH Survey: Observational Overview and Gaia DR1 companion

abstract:
  The Galactic Archaeology with HERMES (GALAH) Survey is a massive
observational project to trace the Milky Way's history of star formation,
chemical enrichment, stellar migration and minor mergers. Using high-resolution
(R$\simeq$28,000) spectra taken with the High Efficiency and Resolution
Multi-Element Spectrograph (HERMES) instrument at the Anglo-Australian
Telescope (AAT), GALAH will determine stellar parameters and abundances of up
to 29 elements for up to one million stars. Selecting targets from a
colour-unbiased catalogue built from 2MASS, APASS and UCAC4 data, we expect to
observe dwarfs at 0.3 to 3 kpc and giants at 1 to 10 kpc. This enables a
thorough local chemical inventory of the Galactic thin and thick disks, and
also captures smaller samples of the bulge and halo. In this paper we present
the plan, process and progress as of early 2016 for GALAH survey observations.
In our first two years of survey observing we have accumulated the largest
high-quality spectroscopic data set at this resolution, over 200,000 stars. We
also present the first public GALAH data catalogue: stellar parameters (Teff,
log(g), [Fe/H], [alpha/Fe]), radial velocity, distance modulus and reddening
for 10680 observations of 9860 Tycho-2 stars that may be included in the first
Gaia data release.


title:
Strongly coupled near-field radiative and conductive heat transfer
  between planar objects

abstract:
  We study the interplay of conductive and radiative heat transfer (RHT) in
planar geometries and predict that temperature gradients induced by radiation
can play a significant role on the behavior of RHT with respect to gap sizes,
depending largely on geometric and material parameters and not so crucially on
operating temperatures. Our findings exploit rigorous calculations based on a
closed-form expression for the heat flux between two plates separated by vacuum
gaps $d$ and subject to arbitrary temperature profiles, along with an
approximate but accurate analytical treatment of coupled conduction--radiation
in this geometry. We find that these effects can be prominent in typical
materials (e.g. silica and sapphire) at separations of tens of nanometers, and
can play an even larger role in metal oxides, which exhibit moderate
conductivities and enhanced radiative properties. Broadly speaking, these
predictions suggest that the impact of RHT on thermal conduction, and vice
versa, could manifest itself as a limit on the possible magnitude of RHT at the
nanoscale, which asymptotes to a constant (the conductive transfer rate when
the gap is closed) instead of diverging at short separations.


title: Pfaffian Correlation Functions of Planar Dimer Covers

abstract:
  The Pfaffian structure of the boundary monomer correlation functions in the
dimer-covering planar graph models is rederived through a combinatorial /
topological argument. These functions are then extended into a larger family of
order-disorder correlation functions which are shown to exhibit Pfaffian
structure throughout the bulk. Key tools involve combinatorial switching
symmetries which are identified through the loop-gas representation of the
double dimer model, and topological implications of planarity.


title: Track Facial Points in Unconstrained Videos

abstract:
  Tracking Facial Points in unconstrained videos is challenging due to the
non-rigid deformation that changes over time. In this paper, we propose to
exploit incremental learning for person-specific alignment in wild conditions.
Our approach takes advantage of part-based representation and cascade
regression for robust and efficient alignment on each frame. Unlike existing
methods that usually rely on models trained offline, we incrementally update
the representation subspace and the cascade of regressors in a unified
framework to achieve personalized modeling on the fly. To alleviate the
drifting issue, the fitting results are evaluated using a deep neural network,
where well-aligned faces are picked out to incrementally update the
representation and fitting models. Both image and video datasets are employed
to valid the proposed method. The results demonstrate the superior performance
of our approach compared with existing approaches in terms of fitting accuracy
and efficiency.


title: A graph for which the inertia bound is not tight

abstract:
  The inertia bound gives an upper bound on the independence number of a graph
by considering the inertia of matrices corresponding to the graph. The bound is
known to be tight for graphs on 10 or fewer vertices as well as for all perfect
graphs. The question has been asked as to whether the bound is always tight. We
show that the bound is not tight for the Paley graph on 17 vertices as well as
for the graph obtained from Paley 17 by deleting a vertex.


title: Uniform Asymptotic Expansion for the Incomplete Beta Function

abstract:
  In [Temme N.M., Special functions. An introduction to the classical functions
of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons,
Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the
incomplete beta function was derived. It was not obvious from those results
that the expansion is actually an asymptotic expansion. We derive a remainder
estimate that clearly shows that the result indeed has an asymptotic property,
and we also give a recurrence relation for the coefficients.


title:
Fast flow asymptotics for stochastic incompressible viscous fluids in
  $\mathbb{R}^2$ and SPDEs on graphs

abstract:
  Fast advection asymptotics for a stochastic reaction-diffusion-advection
equation are studied in this paper. To describe the asymptotics, one should
consider a suitable class of SPDEs defined on a graph, corresponding to the
stream function of the underlying incompressible flow.


title: Informing the structure of complex Hadamard matrix spaces using a flow

abstract:
  The defect of a complex Hadamard matrix $H$ is an upper bound for the
dimension of a continuous Hadamard orbit stemming from $H$. We provide a new
interpretation of the defect as the dimension of the center subspace of a
gradient flow and apply the Center Manifold Theorem of dynamical systems theory
to study local structure in spaces of complex Hadamard matrices. Through
examples, we provide several applications of our methodology including the
construction of affine families of Hadamard matrices.


title: Quantum Cosmology and the Evolution of Inflationary Spectra

abstract:
  We illustrate how it is possible to calculate the quantum gravitational
effects on the spectra of primordial scalar/tensor perturbations starting from
the canonical, Wheeler-De Witt, approach to quantum cosmology. The composite
matter-gravity system is analysed through a Born-Oppenheimer approach in which
gravitation is associated with the heavy degrees of freedom and matter (here
represented by a scalar field) with the light ones. Once the independent
degrees of freedom are identified the system is canonically quantised. The
differential equation governing the dynamics of the primordial spectra with its
quantum-gravitational corrections is then obtained and is applied to diverse
inflationary evolutions. Finally, the analytical results are compared to
observations through a Monte Carlo Markov Chain technique and an estimate of
the free parameters of our approach is finally presented and the results
obtained are compared with previous ones.


title: Nanosurveyor: a framework for real-time data processing

abstract:
  Scientists are drawn to synchrotrons and accelerator based light sources
because of their brightness, coherence and flux. The rate of improvement in
brightness and detector technology has outpaced Moore's law growth seen for
computers, networks, and storage, and is enabling novel observations and
discoveries with faster frame rates, larger fields of view, higher resolution,
and higher dimensionality. Here we present an integrated software/algorithmic
framework designed to capitalize on high throughput experiments, and describe
the streamlined processing pipeline of ptychography data analysis. The pipeline
provides throughput, compression, and resolution as well as rapid feedback to
the microscope operators.


title:
Earth-abundant and Non-toxic SiX (X=S, Se) Monolayers as Highly
  Efficient Thermoelectric Materials

abstract:
  Current thermoelectric (TE) materials often have low performance or contain
less abundant and/or toxic elements, thus limiting their large-scale
applications. Therefore, new TE materials with high efficiency and low cost are
strongly desirable. Here we demonstrate that, SiS and SiSe monolayers made from
non-toxic and earth-abundant elements intrinsically have low thermal
conductivities arising from their low-frequency optical phonon branches with
large overlaps with acoustic phonon modes, which is similar to the
state-of-the-art experimentally demonstrated material SnSe with a layered
structure. Together with high thermal power factors due to their
two-dimensional nature, they show promising TE performances with large figure
of merit (ZT) values exceeding 1 or 2 over a wide range of temperatures. We
establish some basic understanding of identifying layered materials with low
thermal conductivities, which can guide and stimulate the search and study of
other layered materials for TE applications.


title: On the generalized restricted sumsets in abelian groups

abstract:
  Suppose that $A$, $B$ and $S$ are non-empty subsets of a finite abelian group
$G$. Then the generalized restricted sumset $$ A\stackrel{S}+B:=\{a+b:\,a\in
A,\ b\in B,\ a-b\not\in S\} $$ contains at least $$ \min\{|A|+|B|-3|S|,p(G)\}
$$ elements, where $p(G)$ is the least prime factor of $|G|$. Further, we also
have $$ |A\stackrel{S}+B|\geq \min\{|A|+|B|-|S|-2,p(G)\}, $$ provided that both
$|A|$ and $|B|$ are large with respect to $|S|$.


title:
The Source of Solar Energy, ca. 1840-1910: From Meteoric Hypothesis to
  Radioactive Speculations

abstract:
  Why does the Sun shine? Today we know the answer to the question and we also
know that earlier answers were quite wrong. The problem of the source of solar
energy became an important part of physics and astronomy only with the
emergence of the law of energy conservation in the 1840s. The first theory of
solar heat based on the new law, due to J. R. Mayer, assumed the heat to be the
result of meteors or asteroids falling into the Sun. A different and more
successful version of gravitation-to-heat energy conversion was proposed by H.
Helmholtz in 1854 and further developed by W. Thomson. For more than forty
years the once so celebrated Helmholtz-Thomson contraction theory was accepted
as the standard theory of solar heat despite its prediction of an age of the
Sun of only 20 million years. In between the gradual demise of this theory and
the radically different one based on nuclear processes there was a period in
which radioactivity was considered a possible alternative to gravitational
contraction. The essay discusses various pre-nuclear ideas of solar energy
production, including the broader relevance of the question as it was conceived
in the Victorian era.


title:
Joint Optimization of Energy Efficiency and Data Compression in
  TDMA-Based Medium Access Control for the IoT - Extended Version

abstract:
  Energy efficiency is a key requirement for the Internet of Things, as many
sensors are expected to be completely stand-alone and able to run for years
without battery replacement. Data compression aims at saving some energy by
reducing the volume of data sent over the network, but also affects the quality
of the received information. In this work, we formulate an optimization problem
to jointly design the source coding and transmission strategies for
time-varying channels and sources, with the twofold goal of extending the
network lifetime and granting low distortion levels. We propose a scalable
offline optimal policy that allocates both energy and transmission parameters
(i.e., times and powers) in a network with a dynamic Time Division Multiple
Access (TDMA)-based access scheme.


title:
A Cut Finite Element Method for the Bernoulli Free Boundary Value
  Problem

abstract:
  We develop a cut finite element method for the Bernoulli free boundary
problem. The free boundary, represented by an approximate signed distance
function on a fixed background mesh, is allowed to intersect elements in an
arbitrary fashion. This leads to so called cut elements in the vicinity of the
boundary. To obtain a stable method, stabilization terms is added in the
vicinity of the cut elements penalizing the gradient jumps across element
sides. The stabilization also ensures good conditioning of the resulting
discrete system. We develop a method for shape optimization based on moving the
distance function along a velocity field which is computed as the $H^1$ Riesz
representation of the shape derivative. We show that the velocity field is the
solution to an interface problem and we prove an a priori error estimate of
optimal order, given the limited regularity of the velocity field across the
interface, for the the velocity field in the $H^1$ norm. Finally, we present
illustrating numerical results.


title: The Manin-Peyre conjecture for a certain biprojective cubic threefold

abstract: The conjectures of Manin and Peyre are confirmed for a certain threefold.


title:
Non-umbilical quaternionic contact hypersurfaces in hyper-K\"ahler
  manifolds

abstract:
  We show that any compact quaternionic contact (qc) hypersurfaces in a
hyper-K\"ahler manifold which is not totally umbilical has an induced qc
structure, locally qc homothetic to the standard 3-Sasakian sphere. We also
show that any nowhere umbilical qc hypersurface in a hyper-K\"ahler manifold is
endowed with an involutive 7-dimensional distribution whose integral leafs are
locally qc-conformal to the standard 3-Sasakian sphere.


title:
Where is the Goldmine? Finding Promising Business Locations through
  Facebook Data Analytics

abstract:
  If you were to open your own cafe, would you not want to effortlessly
identify the most suitable location to set up your shop? Choosing an optimal
physical location is a critical decision for numerous businesses, as many
factors contribute to the final choice of the location. In this paper, we seek
to address the issue by investigating the use of publicly available Facebook
Pages data---which include user check-ins, types of business, and business
locations---to evaluate a user-selected physical location with respect to a
type of business. Using a dataset of 20,877 food businesses in Singapore, we
conduct analysis of several key factors including business categories,
locations, and neighboring businesses. From these factors, we extract a set of
relevant features and develop a robust predictive model to estimate the
popularity of a business location. Our experiments have shown that the
popularity of neighboring business contributes the key features to perform
accurate prediction. We finally illustrate the practical usage of our proposed
approach via an interactive web application system.


title: Spherical $\Pi$-type Operators in Clifford Analysis and Applications

abstract:
  The $\Pi$-operator (Ahlfors-Beurling transform) plays an important role in
solving the Beltrami equation. In this paper we define two $\Pi$-operators on
the n-sphere. The first spherical $\Pi$-operator is shown to be an $L^2$
isometry up to isomorphism. To improve this, with the help of the spectrum of
the spherical Dirac operator, the second spherical $\Pi$ operator is
constructed as an isometric $L^2$ operator over the sphere. Some analogous
properties for both $\Pi$-operators are also developed. We also study the
applications of both spherical $\Pi$-operators to the solution of the spherical
Beltrami equations.


title:
Earliest stages of the non-equilibrium in axially symmetric,
  self-gravitating, dissipative fluids

abstract:
  We report a study on axially and reflection symmetric dissipative fluids,
just after its departure from hydrostatic and thermal equilibrium, at the
smallest time scale at which the first signs of dynamic evolution appear. Such
a time scale is smaller than the thermal relaxation time, the thermal
adjustment time and the hydrostatic time. It is obtained that the onset of
non--equilibrium will critically depend on a single function directly related
to the time derivative of the vorticity. Among all fluid variables (at the time
scale under consideration), only the tetrad component of the anisotropic tensor
in the subspace orthogonal to the four--velocity and the Killing vector of
axial symmetry, shows signs of dynamic evolution. Also, the first step toward a
dissipative regime begins with a non--vanishing time derivative of the heat
flux component along the meridional direction. The magnetic part of the Weyl
tensor vanishes (not so its time derivative), indicating that the emission of
gravitational radiation will occur at later times. Finally, the decreasing of
the effective inertial mass density, associated to thermal effects, is clearly
illustrated.


title: Undersampled Phase Retrieval via Majorization-Minimization

abstract:
  In the undersampled phase retrieval problem, the goal is to recover an
$N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity
measurements without phase information. This problem has drawn a lot of
attention to reduce the number of required measurements since a recent theory
established that $M\approx4N$ intensity measurements are necessary and
sufficient to recover a generic signal $\mathbf{x}$. In this paper, we propose
to exploit the sparsity in the original signal and develop low-complexity
algorithms with superior performance based on the majorization-minimization
(MM) framework. The proposed algorithms are preferred to existing benchmark
methods since at each iteration a simple surrogate problem is solved with a
closed-form solution that monotonically decreases the original objective
function. Experimental results validate that our algorithms outperform existing
up-to-date methods in terms of recovery probability and accuracy, under the
same settings.


title: Theory of electron-plasmon coupling in semiconductors

abstract:
  The ability to manipulate plasmons is driving new developments in
electronics, optics, sensing, energy, and medicine. Despite the massive
momentum of experimental research in this direction, a predictive
quantum-mechanical framework for describing electron-plasmon interactions in
real materials is still missing. Here, starting from a many-body Green's
function approach, we develop an ab initio approach for investigating
electron-plasmon coupling in solids. As a first demonstration of this
methodology, we show that electron-plasmon scattering is the primary mechanism
for the cooling of hot carriers in doped silicon, it is key to explain measured
electron mobilities at high doping, and it leads to a quantum zero-point
renormalization of the band gap in agreement with experiment.


title: Lie supergroups vs. super Harish-Chandra pairs: a new equivalence

abstract:
  It is known that there exists a natural functor $\Phi$ from Lie supergroups
to super Harish-Chandra pairs. A functor going backwards, that associates a Lie
supergroup with each super Harish-Chandra pair, yielding an equivalence of
categories, was found by Koszul [18]; this result was later extended by other
authors, to different levels of generality, but always elaborating on Koszul's
original idea.
  In this paper, I provide two new backwards equivalences, i.e. two different
functors $\Psi^\circ$ and $\Psi^e$ that construct a Lie supergroup (thought of
as a special group-valued functor) out of a given super Harish-Chandra pair, so
that any Lie supergroup is recovered from its naturally associated super
Harish-Chandra pair; more precisely, both $\Psi^\circ$ and $\Psi^e$ are
quasi-inverse to the functor $\Phi$.


title:
Distributed Online Optimization in Dynamic Environments Using Mirror
  Descent

abstract:
  This work addresses decentralized online optimization in non-stationary
environments. A network of agents aim to track the minimizer of a global
time-varying convex function. The minimizer evolves according to a known
dynamics corrupted by an unknown, unstructured noise. At each time, the global
function can be cast as a sum of a finite number of local functions, each of
which is assigned to one agent in the network. Moreover, the local functions
become available to agents sequentially, and agents do not have a prior
knowledge of the future cost functions. Therefore, agents must communicate with
each other to build an online approximation of the global function. We propose
a decentralized variation of the celebrated Mirror Descent, developed by
Nemirovksi and Yudin. Using the notion of Bregman divergence in lieu of
Euclidean distance for projection, Mirror Descent has been shown to be a
powerful tool in large-scale optimization. Our algorithm builds on Mirror
Descent, while ensuring that agents perform a consensus step to follow the
global function and take into account the dynamics of the global minimizer. To
measure the performance of the proposed online algorithm, we compare it to its
offline counterpart, where the global functions are available a priori. The gap
between the two is called dynamic regret. We establish a regret bound that
scales inversely in the spectral gap of the network, and more notably it
represents the deviation of minimizer sequence with respect to the given
dynamics. We then show that our results subsume a number of results in
distributed optimization. We demonstrate the application of our method to
decentralized tracking of dynamic parameters and verify the results via
numerical experiments.


title:
Dialogue manager domain adaptation using Gaussian process reinforcement
  learning

abstract:
  Spoken dialogue systems allow humans to interact with machines using natural
speech. As such, they have many benefits. By using speech as the primary
communication medium, a computer interface can facilitate swift, human-like
acquisition of information. In recent years, speech interfaces have become ever
more popular, as is evident from the rise of personal assistants such as Siri,
Google Now, Cortana and Amazon Alexa. Recently, data-driven machine learning
methods have been applied to dialogue modelling and the results achieved for
limited-domain applications are comparable to or outperform traditional
approaches. Methods based on Gaussian processes are particularly effective as
they enable good models to be estimated from limited training data.
Furthermore, they provide an explicit estimate of the uncertainty which is
particularly useful for reinforcement learning. This article explores the
additional steps that are necessary to extend these methods to model multiple
dialogue domains. We show that Gaussian process reinforcement learning is an
elegant framework that naturally supports a range of methods, including prior
knowledge, Bayesian committee machines and multi-agent learning, for
facilitating extensible and adaptable dialogue systems.


title:
Mapping axonal density and average diameter using non-monotonic
  time-dependent gradient-echo MRI

abstract:
  This paper presents a novel method for quantifying axonal density and
diameter using simple multiple gradient echo (MGE) MRI


title: Critical behavior of dissipative two-dimensional spin lattices

abstract:
  We explore critical properties of two-dimensional lattices of spins
interacting via an anisotropic Heisenberg Hamiltonian and subject to incoherent
spin flips. We determine the steady-state solution of the master equation for
the density matrix via the corner-space renormalization method. We investigate
the finite-size scaling and critical exponent of the magnetic linear
susceptibility associated to a dissipative ferromagnetic transition. We show
that the Von Neumann entropy increases across the critical point, revealing a
strongly mixed character of the ferromagnetic phase. Entanglement is witnessed
by the quantum Fisher information which exhibits a critical behavior at the
transition point, showing that quantum correlations play a crucial role in the
transition even though the system is in a mixed state.


title: Master equations and the theory of stochastic path integrals

abstract:
  This review provides a pedagogic and self-contained introduction to master
equations and to their representation by path integrals. We discuss analytical
and numerical methods for the solution of master equations, keeping our focus
on methods that are applicable even when stochastic fluctuations are strong.
The reviewed methods include the generating function technique and the Poisson
representation, as well as novel ways of mapping the forward and backward
master equations onto linear partial differential equations (PDEs). Spectral
methods, WKB approximations, and a variational approach have been proposed for
the analysis of the PDE obeyed by the generating function. After outlining
these methods, we solve the derived PDEs in terms of two path integrals. The
path integrals provide distinct exact representations of the conditional
probability distribution solving the master equations. We exemplify both path
integrals in analysing elementary chemical reactions. Furthermore, we review a
method for the approximation of rare event probabilities and derive path
integral representations of Fokker-Planck equations. To make our review
accessible to a broad community, we have used the language of probability
theory rather than quantum (field) theory. The probabilistic structures
underpinning various technical concepts, such as coherent states, the
Doi-shift, and normal-ordered observables, are thereby made explicit.


title:
Logarithmic Black Hole Entropy Corrections and Holographic R\'enyi
  Entropy

abstract:
  The entanglement and R\'{e}nyi entropies for spherical entangling surfaces in
CFTs with gravity duals can be explicitly calculated by mapping these entropies
first to the thermal entropy on hyperbolic space and then, using the AdS/CFT
correspondence, to the Wald entropy of topological black holes. Here we extend
this idea by taking into account corrections to the Wald entropy. Using the
method based on horizon symmetries and the asymptotic Cardy formula, we
calculate corrections to the Wald entropy and find that these corrections are
proportional to the logarithm of horizon area. With the corrected black hole
entropy expression, we then find corrections to the R\'{e}nyi entropies. We
calculate these corrections for both Einstein as well as Gauss-Bonnet gravity
duals. Corrections with logarithmic dependence on the area of the entangling
surface naturally occur at the order $G_{D}^0$ and it seems to be a general
feature of entanglement and R\'{e}nyi entropies for CFTs with gravity duals. In
particular, there is a logarithmic correction to the entropy in odd boundary
spacetime dimensions as well.


title:
Efficient deterministic giant photon phase shift from a single charged
  quantum dot

abstract:
  Solid-state quantum emitters have long been recognised as the ideal platform
to realize integrated quantum photonic technologies. We use a self-assembled
negatively charged QD in a low Q-factor photonic micropillar to demonstrate for
the first time a key figure of merit for deterministic switching and
spin-photon entanglement: a shift in phase of an input single photon of
$>90^{o}$ with values of up to $2\pi/3$ ($120^{o}$) demonstrated. This $>\pi/2$
($90^{o}$) measured value represents an important threshold: above this value
input photons interact with the emitter deterministically. A deterministic
photon-emitter interaction is the only viable scalable means to achieve several
vital functionalities not possible in linear optics such as quantum switches
and entanglement gates. Our experimentally determined value is limited by mode
mismatch between the input laser and the cavity, QD spectral fluctuations and
spin relaxation. We determine that up to $80\%$ of the collected photons have
interacted with the QD and undergone a phase shift of $\pi$.


title: On rings of differential operators derived from automorphic forms

abstract:
  We study linear ordinary differential equations which are analytically
parametrized on Hermitian symmetric spaces and invariant under the action of
symplectic groups. They are generalizations of the classical Lam\'e equation.
Our main result gives a closed relation between such differential equations and
automorphic forms for symplectic groups. Our study is based on techniques
concerning with the monodromy of complex differential equations, the
Baker-Akhiezer functions and algebraic curves attached to rings of differential
operators.


title: 2-Segal sets and the Waldhausen construction

abstract:
  It is known by results of Dyckerhoff-Kapranov and of
G\'alvez--Carrillo-Kock-Tonks that the output of the Waldhausen S.-construction
has a unital 2-Segal structure. Here, we prove that a certain S.-functor
defines an equivalence between the category of augmented stable double
categories and the category of unital 2-Segal sets. The inverse equivalence is
described explicitly by a path construction. We illustrate the equivalence for
the known examples of partial monoids, cobordism categories with genus
constraints and graph coalgebras.


title:
Contiguity and non-reconstruction results for planted partition models:
  the dense case

abstract:
  We consider the two block stochastic block model on $n$ nodes with
asymptotically equal cluster sizes. The connection probabilities within and
between cluster are denoted by $p_n:=\frac{a_n}{n}$ and $q_n:=\frac{b_n}{n}$
respectively. Mossel et al.(2012) considered the case when $a_n=a$ and $b_n=b$
are fixed. They proved the probability models of the stochastic block model and
that of Erd{\"o}s-R{\'e}nyi graph with same average degree are mutually
contiguous whenever $(a-b)^2<2(a+b)$ and are asymptotically singular whenever
$(a-b)^2>2(a+b)$. Mossel et al.(2012) also proved that when $(a-b)^2<2(a+b)$ no
algorithm is able to find an estimate of the labeling of the nodes which is
positively correlated with the true labeling. It is natural to ask what happens
when $a_n$ and $b_n$ both grow to infinity. We prove that their results extend
to the case when $a_n=o(n)$ and $b_n=o(n)$. We also consider the case when
$\frac{a_n}{n} \to p \in (0,1)$ and $(a_n-b_n)^2= \Theta(a_n+b_n)$. Observe
that in this case $\frac{b_n}{n} \to p$ also. We show that here the models are
mutually contiguous if $(a_n-b_n)^2< 2(1-p)(a_n+b_n)$ and they are
asymptotically singular if $(a_n-b_n)^2 > 2(1-p)(a_n+b_n)$. Further we also
prove it is impossible find an estimate of the labeling of the nodes which is
positively correlated with the true labeling whenever $(a_n-b_n)^2<
2(1-p)(a_n+b_n)$. The results of this paper justify the negative part of a
conjecture made in Decelle et al.(2011) for dense graphs.


title: Complexity Regularization and Local Metric Entropy

abstract:
  In the context of Structural Risk Minimization, one is presented a sequence
of classes $\{\mathcal{G}_j\}$ from which, given a random sample $(X_i,Y_i)$
one wants to choose a strongly consistent estimator. For certain types of
classes of functions, we present a criterion to choose an estimator, based on
the minimization of the sum of empirical error and a complexity penalty
$r(n,j)$ over each class $\G_j$.
  We present also several other results together with important results found
on current literature on the subject, in an attempt to present and unify the
theory in the context of regression estimation. In particular we present a
generalization of the consistency of Structural Risk Minimization in the
context of regression estimation which are all new results found on Chapter 5.


title: Intermittent gravity-driven flow of grains through narrow pipes

abstract:
  Grain flows through pipes are frequently found in various settings, such as
in pharmaceutical, chemical, petroleum, mining and food industries. In the case
of size-constrained gravitational flows, density waves consisting of
alternating high- and low-compactness regions may appear. This study
investigates experimentally the dynamics of density waves that appear in
gravitational flows of fine grains through vertical and slightly inclined
pipes. The experimental device consisted of a transparent glass pipe through
which different populations of glass spheres flowed driven by gravity. Our
experiments were performed under controlled ambient temperature and relative
humidity, and the granular flow was filmed with a high-speed camera.
Experimental results concerning the length scales and celerities of density
waves are presented, together with a one-dimensional model and a linear
stability analysis. The analysis exhibits the presence of a long-wavelength
instability, with the most unstable mode and a cut-off wavenumber whose values
are in agreement with the experimental results.


title:
Efimov-van-der-Waals universality for ultracold atoms with positive
  scattering lengths

abstract:
  We study the universality of the three-body parameters for systems relevant
for ultracold quantum gases with positive $s$-wave two-body scattering lengths.
Our results account for finite-range effects and their universality is tested
by changing the number of deeply bound diatomic states supported by our
interaction model. We find that the physics controlling the values of the
three-body parameters associated with the ground and excited Efimov states is
constrained by a variational principle and can be strongly affected by $d$-wave
interactions that prevent both trimer states from merging into the atom-dimer
continuum. Our results enable comparisons to current experimental data and they
suggest tests of universality for atomic systems with{positive scattering
lengths.


title: The size function for cyclic cubic fields

abstract:
  The size function for a number field is an analogue of the dimension of the
Riemann-Roch spaces of divisors on an algebraic curve. It was conjectured to
attain its maximum at the trivial class of Arakelov divisors. This conjecture
was proved for many number fields with unit groups of rank one. Our research
confirms that the conjecture also holds for cyclic cubic fields, which have
unit groups of rank two.


title:
Spectral energy distribution simulations of a possible ring structure
  around the young, red brown dwarf G196-3B

abstract:
  The origin of the very red optical and infrared colours of intermediate-age
($\sim$10 - 500 Myr) L-type dwarfs remains unknown. It has been suggested that
low-gravity atmospheres containing large amounts of dust may account for the
observed reddish nature. We explored an alternative scenario by simulating
protoplanetary and debris discs around G196-3B, which is an L3 young brown
dwarf with a mass of $\sim 15$ $M_{\rm Jup}$ and an age in the interval 20 -
300 Myr. The best-fit solution to G196-3B's photometric spectral energy
distribution from optical wavelengths through 24 $\mu$m corresponds to the
combination of an unreddened L3 atmosphere ($T_{\rm eff} \approx 1870$~K) and a
warm ($\approx$ 1280 K), narrow ($\approx$ 0.07 - 0.11 R$_{\odot}$) debris disc
located at very close distances ($\approx$ 0.12 - 0.20 R$_{\odot}$) from the
central brown dwarf. This putative, optically thick, dusty belt, whose presence
is compatible with the relatively young system age, would have a mass $\ge
7\times 10^{-10}$ M$_{\oplus}$ comprised of sub-micron/micron characteristic
dusty particles with temperatures close to the sublimation threshold of
silicates. Considering the derived global properties of the belt and the
disc-to-brown dwarf mass ratio, the dusty ring around G196-3B may resemble the
rings of Neptune and Jupiter, except for its high temperature and thick
vertical height ($\approx 6 \times 10^3$ km). Our inferred debris disc model is
able to reproduce G196-3B's spectral energy distribution to a satisfactory
level of achievement.


title: Mixed convection in turbulent channels with unstable stratification

abstract:
  We study turbulent flows in planar channels with unstable thermal
stratification, using direct numerical simulations in a wide range of Reynolds
and Rayleigh numbers and reaching flow conditions which are representative of
asymptotic developed turbulence. The combined effect of forced and free
convection produces a peculiar pattern of quasi--streamwise rollers occupying
the full channel thickness with aspect--ratio considerably higher than unity;
it has been observed that they have an important redistributing effect on
temperature and momentum. The mean values and the variances of the flow
variables do not appear to follow Prandtl's scaling in the flow regime near
free convection, except for the temperature and vertical velocity fluctuations,
which are more affected by turbulent plumes. Nevertheless, we find that the
Monin--Obukhov theory still yields a useful representation of the main flow
features. In particular, the widely used Businger--Dyer relationships provide a
convenient way of accounting for the bulk effects of shear and buoyancy,
although individual profiles may vary widely from the alleged trends.
Significant deviations are found in DNS with respect to the commonly used
parametrization of the mean velocity in the light-wind regime, which may have
important practical impact in models of atmospheric dynamics. Finally, for
modelling purposes, we devise a set of empirical predictive formulas for the
heat flux and friction coefficients which can be used with about $10\%$ maximum
error in a wide range of flow parameters.


title: Structure of the pairing gap from orbital nematic fluctuations

abstract:
  We study superconducting instability from orbital nematic fluctuations in a
minimal model consisting of the $d_{xz}$ and $d_{yz}$ orbitals, and choose
model parameters which capture the typical Fermi surface geometry observed in
iron-based superconductors. We solve the Eliashberg equations down to low
temperatures with keeping the renormalization function and a full momentum
dependence of the pairing gap. When superconductivity occurs in the tetragonal
phase, we find that the pairing gap exhibits a weak momentum dependence over
the Fermi surfaces. The superconducting instability occurs also inside the
nematic phase. When the $d_{xz}$ orbital is occupied more than the $d_{yz}$
orbital in the nematic phase, a larger (smaller) gap is realized on the
Fermi-surface parts, where the $d_{xz}$ ($d_{yz}$) orbital component is
dominant, leading to a substantial momentum dependence of the pairing gap on
the hole Fermi surfaces. On the other hand, the momentum dependence of the gap
is weak on the electron Fermi surfaces. We also find that while the leading
instability is the so-called $s_{++}$-wave symmetry, the second leading one is
$d_{x^2-y^2}$-wave symmetry. In particular, these two states are nearly
degenerate in the tetragonal phase whereas such quasi-degeneracy is lifted in
the nematic phase and the $d_{x^2-y^2}$-wave symmetry changes to highly
anisotropic $s$-wave symmetry.


title: Measurements of open heavy-flavour production with ALICE at the LHC

abstract:
  In ALICE, open heavy-flavour production is studied through the measurements
of the leptons (electrons and muons) from heavy-flavour hadron decays at
central and forward rapidity and via the reconstruction of D-meson hadronic
decays at mid-rapidity. An overview of the open heavy-flavour production with
ALICE in pp ($\sqrt{s}$ = 2.76 TeV and 7 TeV), p--Pb ($\sqrt {s_{\rm NN}}$ =
5.02 TeV) and Pb--Pb ($\sqrt {s_{\rm NN}}$ = 2.76 TeV) collisions will be
presented. We will discuss the production cross sections, modifications of the
transverse momentum distributions, azimuthal anisotropic emissions and
correlations with hadrons in comparison with various theoretical predictions.


title:
Modes and exceptional points in waveguides with impedance boundary
  conditions

abstract:
  A planar waveguide with impedance boundary, composed of non-perfect metallic
plates, and with passive or active dielectric filling is considered. We show
the possibility of selective mode guiding and amplification when homogeneous
pump is added to the dielectric, and analyze differences in TE and TM mode
propagation. Such a non-conservative system is also shown to feature
exceptional points, for specific and experimentally tunable parameters, which
are described for a particular case of transparent dielectric.

categories: physics.optics math-ph math.MP physics.class-ph


title:
Asteroseismology of hybrid $\delta$ Scuti--$\gamma$ Doradus pulsating
  stars

abstract:
  Hybrid $\delta$ Scuti-$\gamma$ Doradus pulsating stars show acoustic ($p$)
oscillation modes typical of $\delta$ Scuti variable stars, and gravity ($g$)
pulsation modes characteristic of $\gamma$ Doradus variable stars
simultaneously excited. Observations from space missions like MOST, CoRoT, and
\emph{Kepler} have revealed a large number of hybrid $\delta$ Scuti-$\gamma$
Doradus pulsators, thus paving the way for a exciting new channel for
asteroseismic studies. We perform a detailed asteroseismological modeling of
five hybrid $\delta$ Scuti-$\gamma$ Doradus stars. We employ a grid-based
modeling approach to sound the internal structure of the target stars by
employing a huge grid of stellar models from the zero-age main sequence to the
terminal-age main sequence, varying parameters like stellar mass, effective
temperature, metallicity and core overshooting. We compute their adiabatic
radial ($\ell= 0$) and non-radial ($\ell= 1, 2, 3$) $p$ and $g$ mode periods.
We employ two model-fitting procedures to searching for the models that best
reproduce the observed pulsation spectra of each target star, that is, the
asteroseismological models. We derive the fundamental parameters and the
evolutionary status of five hybrid $\delta$ Scuti-$\gamma$ Doradus variable
stars recently observed with the CoRoT and \emph{Kepler} space missions: CoRoT
105733033, CoRoT 100866999, KIC 11145123, KIC 9244992, and HD 49434. The
asteroseismological model for each star results from different criteria of
model selection, in which we take full advantage of the richness of periods
that characterizes the pulsation spectra of this kind of stars.


title: Classifying locally compact semitopological polycyclic monoids

abstract:
  We present a complete classification of Hausdorff locally compact polycyclic
monoids up to a topological isomorphism. A {\em polycyclic monoid} is an
inverse monoid with zero, generated by a subset $\Lambda$ such that $xx^{-1}=1$
for any $x\in\Lambda$ and $xy^{-1}=0$ for any distinct $x,y\in\Lambda$. We
prove that any non-discrete Hausdorff locally compact topology with continuous
shifts on a polycyclic monoid $M$ coincides with the topology of one-point
compactification of the discrete space $M\setminus\{0\}$.


title: Suppression of blow-up in Patlak-Keller-Segel via shear flows

abstract:
  In this paper we consider the parabolic-elliptic Patlak-Keller-Segel models
in $\mathbb T^d$ with $d=2,3$ with the additional effect of advection by a
large shear flow. Without the shear flow, the model is $L^1$ critical in two
dimensions with critical mass $8\pi$; solutions with mass less than $8\pi$ are
global and solutions with mass larger than $8 \pi$ with finite second moment,
all blow up in finite time. In three dimensions, the model is $L^{3/2}$
critical and $L^1$ supercritical; there exists solutions with arbitrarily small
mass which blow up in finite time arbitrarily fast. We show that the additional
shear flow, if it is chosen sufficiently large, suppresses one dimension of the
dynamics and hence can suppress blow-up. In two dimensions, the problem becomes
effectively $L^1$ subcritical and so all solutions are global in time (if the
shear flow is chosen large). In three dimensions, the problem is effectively
$L^1$ critical, and solutions with mass less than $8\pi$ are global in time
(and for all mass larger than $8\pi$, there exists solutions which blow up in
finite time).


title: Canonical Supermartingale Couplings

abstract:
  Two probability distributions $\mu$ and $\nu$ in second stochastic order can
be coupled by a supermartingale, and in fact by many. Is there a canonical
choice? We construct and investigate two couplings which arise as optimizers
for constrained Monge-Kantorovich optimal transport problems where only
supermartingales are allowed as transports. Much like the Hoeffding-Fr\'echet
coupling of classical transport and its symmetric counterpart, the antitone
coupling, these can be characterized by order-theoretic minimality properties,
as simultaneous optimal transports for certain classes of reward (or cost)
functions, and through no-crossing conditions on their supports; however, our
two couplings have asymmetric geometries. Remarkably, supermartingale optimal
transport decomposes into classical and martingale transport in several ways.


title: Principles of Differential Geometry

abstract:
  The present text is a collection of notes about differential geometry
prepared to some extent as part of tutorials about topics and applications
related to tensor calculus. They can be regarded as continuation to the
previous notes on tensor calculus as they are based on the materials and
conventions given in those documents. They can be used as a reference for a
first course on the subject or as part of a course on tensor calculus.


title:
Finite size scaling analysis of a nonequilibrium phase transition in the
  naming game model

abstract:
  We realize an extensive numerical study of the Naming Game model with a noise
term which accounts for perturbations. This model displays a non-equilibrium
phase transition between an absorbing ordered consensus state, which occurs for
small noise, and a disordered phase with fragmented clusters characterized by
heterogeneous memories, which emerges at strong noise levels. The nature of the
phase transition is studied by means of a finite-size scaling analysis of the
moments. We observe a scaling behavior typical of a discontinuous transition
and we are able to estimate the thermodynamic limit. The scaling behavior of
the clusters size seems also compatible with this kind of transition.


title: Groups whose Fourier algebra and Rajchman algebra coincide

abstract:
  We study locally compact groups for which the Fourier algebra coincides with
the Rajchman algebra. In particular, we show that there exist uncountably many
non-compact groups with this property. Generalizing a result of Hewitt and
Zuckerman, we show that no non-compact nilpotent group has this property,
whereas non-compact solvable groups with this property are known to exist.
  We provide several structural results on groups whose Fourier and Rajchman
algebras coincide as well as new criteria for establishing this property.
  Finally, we study the relation between groups with completely reducible
regular representation and groups whose Fourier and Rajchman algebras coincide.
For unimodular groups with completely reducible regular representation, we show
that the Fourier algebra may in general be strictly smaller than the Rajchman
algebra.


title: On hamiltonian colorings of block graphs

abstract:
  A hamiltonian coloring c of a graph G of order p is an assignment of colors
to the vertices of G such that $D(u,v)+|c(u)-c(v)|\geq p-1$ for every two
distinct vertices u and v of G, where D(u,v) denoted the detour distance
between u and v. The value hc(c) of a hamiltonian coloring c is the maximum
color assigned to a vertex of G. The hamiltonian chromatic number, denoted by
hc(G), is the min{hc(c)} taken over all hamiltonian coloring c of G. In this
paper, we present a lower bound for the hamiltonian chromatic number of block
graphs and give a sufficient condition to achieve the lower bound. We
characterize symmetric block graphs achieving this lower bound. We present two
algorithms for optimal hamiltonian coloring of symmetric block graphs.


title:
Higgs portal dark matter and neutrino mass and mixing with a doubly
  charged scalar

abstract:
  We consider an extension of the Standard Model involving two new scalar
particles around the TeV scale: a singlet neutral scalar $\phi$, to be
eventually identified as the Dark Matter candidate, plus a doubly charged
$SU(2)_L$ singlet scalar, $S^{++}$, that can be the source for the
non-vanishing neutrino masses and mixings. Assuming an unbroken $Z_2$ symmetry
in the scalar sector, under which only the additional neutral scalar $\phi$ is
odd, we write the most general (renormalizable) scalar potential. The model may
be regarded as a possible extension of the conventional Higgs portal Dark
Matter scenario which also accounts for neutrino mass and mixing. This
framework cannot completely explain the observed positron excess. However a
softening of the discrepancy observed in conventional Higgs portal framework
can be obtained, especially when the scale of new physics responsible for
generating neutrino masses and lepton number violating processes is around 2
TeV.


title:
A Generalised uniqueness theorem and the graded ideal structure of
  Steinberg algebras

abstract:
  Given an ample, Hausdorff groupoid $\mathcal{G}$, and a unital commutative
ring $R$, we consider the Steinberg algebra $A_R(\mathcal {G})$. First we prove
a uniqueness theorem for this algebra and then, when $\mathcal{G}$ is graded by
a cocycle, we study graded ideals in $A_R(\mathcal {G})$. Applications are
given for two classes of ample groupoids, namely those coming from actions of
groups on graphs, and also to groupoids defined in terms of Boolean dynamical
systems.


title: Topographical coloured plasmonic coins

abstract:
  The use of metal nanostructures for colourization has attracted a great deal
of interest with the recent developments in plasmonics. However, the current
top-down colourization methods based on plasmonic concepts are tedious and time
consuming, and thus unviable for large-scale industrial applications. Here we
show a bottom-up approach where, upon picosecond laser exposure, a full colour
palette independent of viewing angle can be created on noble metals. We show
that colours are related to a single laser processing parameter, the total
accumulated fluence, which makes this process suitable for high throughput
industrial applications. Statistical image analyses of the laser irradiated
surfaces reveal various distributions of nanoparticle sizes which control
colour. Quantitative comparisons between experiments and large-scale
finite-difference time-domain computations, demonstrate that colours are
produced by selective absorption phenomena in heterogeneous nanoclusters.
Plasmonic cluster resonances are thus found to play the key role in colour
formation.


title: Proof of a Null Penrose Conjecture using a new Quasi-local Mass

abstract:
  We define an explicit quasi-local mass functional which is non-decreasing
along all foliations (satisfying a convexity assumption) of null cones. We use
this new functional to prove the null Penrose conjecture under fairly generic
conditions.


title:
Collective excitations using a room-temperature gas of 3-level atoms in
  a cavity

abstract:
  We theoretically investigate an ensemble of three-level room-temperature
atoms in a two-mode optical cavity, focusing on the case of counterpropagating
light fields. We find that in the limit of large detunings the problem admits
relatively simple and intuitive solutions. When a classical field drives one of
the transitions, the system becomes equivalent to an ensemble of two-level
atoms with suppressed Doppler broadening. In contrast, when the same transition
is driven with a single photon, the system collectively behaves like a single
two-level atom. This latter result is particularly relevant in the context of
quantum nonlinear optics.


title:
Quantum phase gate Based on Electromagnetically Induced Transparency in
  Optical Cavities

abstract:
  We theoretically investigate the implementation of a quantum phase gate in a
system constituted by a single atom inside an optical cavity, based on the
electromagnetically induced transparency effect. Firstly we show that a probe
pulse can experience a $\pi$ phase shift due to the presence or absence of a
classical control field. Considering the interplay of the cavity-EIT effect and
the quantum memory process, we demonstrated a controlled phase gate between two
single photons. To this end, firstly one needs to store a (control) photon in
the ground atomic states. In the following, a second (target) photon must
impinge on the atom-cavity system. Depending on the atomic state, this second
photon will be either transmitted or reflected, acquiring different phase
shifts. This protocol can then be easily extended to multiphoton systems, i.e.,
keeping the control photon stored, it may induce phase shifts in several single
photons, thus enabling the generation of multipartite entangled states. We
explore the relevant parameter space in the atom-cavity system that allows the
implementation of quantum phase gates using the recent technologies. In
particular we have found a lower bound for the cooperativity of the atom-cavity
system which enables the implementation of phase shift on single photons. The
induced shift on the phase of a photonic qubit and the controlled phase gate
between single photons, combined with optical devices, enable to perform
universal quantum computation.


title: Hydrogen atom wave function and eigen energy in the Rindler space

abstract:
  We study the hydrogen atom eigenstate energy and wave function in the Rindler
space. The probability distribution is tilted because the electric field of the
nucleus is no longer spherically symmetric. The hydrogen atom therefore cannot
be treated exactly in the same way as what it is in an inertial frame. We also
find that if the external force accelerates only the nucleus and then the
nucleus accelerates its surrounding electrons through electromagnetic force,
the electrons can tunnel through the local energy gap and split the hydrogen
atom into an ion. This is similar to what one expects from the Stark effect.
However, the critical acceleration is about $3\times 10^{22} m/s^2$. It is well
beyond the gravitational acceleration on a regular star surface.


title:
Elementary recursive quantifier elimination based on Thom encoding and
  sign determination

abstract:
  We describe a new quantifier elimination algorithm for real closed fields
based on Thom encoding and sign determination. The complexity of this algorithm
is elementary recursive and its proof of correctness is completely algebraic.
In particular, the notion of connected components of semialgebraic sets is not
used.


title:
Two-color above threshold ionization of atoms and ions in XUV Bessel
  beams and combined with intense laser light

abstract:
  The two-color above-threshold ionization (ATI) of atoms and ions is
investigated for a vortex Bessel beam in the presence of a strong near-infrared
(NIR) light field. While the photoionization is caused by the photons from the
weak but extreme ultra-violet (XUV) vortex Bessel beam, the energy and angular
distribution of the photoelectrons and their sideband structure are affected by
the plane-wave NIR field. We here explore the energy spectra and angular
emission of the photoelectrons in such two-color fields as a function of the
size and location of the target (atoms) with regard to the beam axis. In
addition, analogue to the circular dichroism in typical two-color ATI
experiments with circularly polarized light, we define and discuss seven
different dichroism signals for such vortex Bessel beams that arise from the
various combinations of the orbital and spin angular momenta of the two light
fields. For localized targets, it is found that these dichroism signals
strongly depend on the size and position of the atoms relative to the beam. For
macroscopically extended targets, in contrast, three of these dichroism signals
tend to zero, while the other four just coincide with the (standard) circular
dichroism, similar as for Bessel beams with small opening angle. Detailed
computations of the dichroism are performed and discussed for the $4s$
valence-shell photoionization of Ca$^+$ ions.


title: Latest Results from VERITAS: Gamma 2016

abstract:
  The VERITAS imaging atmospheric Cherenkov telescope array has been observing
the northern TeV sky with four telescopes since summer 2007. Over 50 gamma-ray
sources have been studied, including active and starburst galaxies, pulsars and
their nebulae, supernova remnants and Galactic binary systems. We review here
some of the most recent VERITAS results, and discuss the status and prospects
for collaborative work with other gamma-ray instruments, and with
multimessenger observatories.


title:
Second order differential equations for bosons with spin j > 1 and in
  the bases of general tensor-spinors of rank-2j

abstract:
  A boson of spin-j>1 can be described in one of the possibilities within the
Bargmann-Wigner framework by means of one sole differential equation of order
twice the spin, which however is known to be inconsistent as it allows for
non-local, ghost and acausally propagating solutions, all problems which are
difficult to tackle. The other possibility is provided by the Fierz-Pauli
framework which is based on the more comfortable to deal with second order
Klein-Gordon equation, but it needs to be supplemented by an auxiliary
condition. Although the latter formalism avoids some of the pathologies of the
high-order equations, it still remains plagued by some inconsistencies such as
the acausal propagation of the wave fronts of the (classical) solutions within
an electromagnetic environment. We here suggest a method alternative to the
above two that combines their advantages while avoiding the related
difficulties. Namely, we suggest one sole strictly (j,0)+ (0,j) representation
specific second order differential equation, which is derivable from a
Lagrangian and whose solutions do not violate causality. The equation under
discussion presents itself as the product of the Klein-Gordon operator with a
momentum independent projector on Lorentz irreducible representation spaces
constructed from one of the Casimir invariants of the spin-Lorentz group. The
basis used is that of general tensor-spinors of rank-2j.


title:
A Category Theoretical Investigation of the Type Hierarchy for
  Heterogeneous Sensor Integration

abstract:
  Consider the case of many sensors, each returning very different types of
data (e.g., a camera returning images, a thermometer returning probability
distributions, a newspaper returning articles, a traffic counter returning
numbers). Additionally we have a set of questions, or variables, that we wish
to use these sensors to inform (e.g., temperature, location, crowd size,
topic). Rather than using one sensor to inform each variable we wish to
integrate these sources of data to get more robust and complete information.
The problem, of course, is how to inform a variable, e.g., crowd size, using a
number, a newspaper article, and an image. How do we integrate these very
different types of information? Michael Robinson proposes that sheaf theory is
the canonical answer. Moreover, one of the axioms in Robinson's paper which
makes sheaf theory work for data integration is that all data sources have the
structure of a vector space. Therefore, the motivating question for everything
in this report is "How do we interpret arbitrary sensor output as a vector
space with the intent to integrate?"


title:
On the accuracy of the MB-pol many-body potential for water: Interaction
  energies, vibrational frequencies, and classical thermodynamic and dynamical
  properties from clusters to liquid water and ice

abstract:
  The MB-pol many-body potential has recently emerged as an accurate molecular
model for water simulations from the gas to the condensed phase. In this study,
the accuracy of MB-pol is systematically assessed across the three phases of
water through extensive comparisons with experimental data and high-level ab
initio calculations. Individual many-body contributions to the interaction
energies as well as vibrational spectra of water clusters calculated with
MB-pol are in excellent agreement with reference data obtained at the coupled
cluster level. Several structural, thermodynamic, and dynamical properties of
the liquid phase at atmospheric pressure are investigated through classical
molecular dynamics simulations as a function of temperature. The structural
properties of the liquid phase are in nearly quantitative agreement with X-ray
diffraction data available over the temperature range from 268 to 368 K. The
analysis of other thermodynamic and dynamical quantities emphasizes the
importance of explicitly including nuclear quantum effects in the simulations,
especially at low temperature, for a physically correct description of the
properties of liquid water. Furthermore, both densities and lattice energies of
several ice phases are also correctly reproduced by MB-pol. Following a recent
study of DFT models for water, a score is assigned to each computed property,
which demonstrates the high and, in many respects, unprecedented accuracy of
MB-pol in representing all three phases of water.


title:
Nonlinear waves in stratified Taylor--Couette flow. Part 1. Layer
  formation

abstract:
  This paper is the first part of a two-fold study of mixing, i.e. the
formation of layers and upwelling of buoyancy, in axially stratified
Taylor--Couette flow, with fixed outer cylinder. Using linear analysis and
direct numerical simulation, we show the critical role played by
non-axisymmetric instability modes, despite the fact that the flow is
centrifugally unstable in the sense of Rayleigh's criterion. Interactions
between helical modes of opposite handedness leads to the formation of
nonlinear coherent structures: (mixed)-ribbons and (mixed)-cross-spirals. These
give birth to complex density interface patterns, seemingly appearing and
disappearing periodically as the coherent structure slowly rotates around the
annulus. These coherent structures seem to be responsible for the formation of
layers reported in a recent experiment by Oglethorpe et al. (2013). We
distinguish `dynamic layering', instantaneous, localized and caused by the
vortical motions, from `static layering' corresponding to the formation of a
`staircase profile' in the adiabatically sorted background density. The latter
only occurs at large enough Schmidt number, revealing the significant impact of
the Schmidt number in the layering process.


title:
Nonlinear waves in stratified Taylor--Couette flow. Part 2. Buoyancy
  flux

abstract:
  This paper is the second part of a two-fold study of mixing, i.e. the
formation of layers and upwelling of buoyancy, in axially stratified
Taylor--Couette flow, with fixed outer cylinder. In a first paper, we showed
that the dynamics of the flow was dominated by coherent structures made of a
superposition of nonlinear waves. (Mixed)-ribbons and (mixed)-cross-spirals are
generated by interactions between a pair of linearly unstable helical modes of
opposite `handedness', and appear to be responsible for the formation of
well-mixed layers and sharp density interfaces. In this paper, we show that
these structures are also fully accountable for the upwards buoyancy flux in
the simulations. The mechanism by which this occurs is a positive coupling
between the density and vertical velocity components of the most energetic
waves. This coupling is primarily caused by diffusion of density at low Schmidt
number Sc, but can also be a nonlinear effect at larger Sc. Turbulence was
found to contribute negatively to the buoyancy flux at Sc=1,10,16, which lead
to the conclusion that mass upwelling is a consequence of chaotic advection,
even at large Reynolds number. Artificially isolating the coherent structure
therefore leads to excellent estimates of the flux Richardson numbers Ri_f from
the DNS. We also used the theoretical framework of Winters et al. (1995) to
analyse the energetics of mixing in an open control volume, shedding light on
the influence of end effects in the potential energy budget. The potential
connection with the buoyancy flux measurements made in the recent experiment of
Oglethorpe et al. (2013) is also discussed.


title:
The connection between supernova remnants and the Galactic magnetic
  field: An analysis of quasi-parallel and quasi-perpendicular cosmic ray
  acceleration for the axisymmetric sample

abstract:
  The mechanism for acceleration of cosmic rays in supernova remnants (SNRs) is
an outstanding question in the field. We model a sample of 32 axisymmetric SNRs
using the quasi-perpendicular and quasi-parallel cosmic-ray-electron (CRE)
acceleration cases. The axisymmetric sample is defined to include SNRs with a
double-sided, bilateral morphology, and also those with a one-sided morphology
where one limb is much brighter than the other. Using a coordinate
transformation technique, we insert a bubble-like model SNR into a model of the
Galactic magnetic field. Since radio emission of SNRs is dominated by
synchrotron emission and since this emission depends on the magnetic field and
CRE distribution, we are able to simulate the SNRs emission and compare this to
data. We find that the quasi-perpendicular CRE acceleration case is much more
consistent with the data than the quasi-parallel CRE acceleration case, with
G327.6+14.6 (SN1006) being a notable exception. We propose that SN1006 may be a
case where both quasi-parallel and quasi-perpendicular acceleration are
simultaneously at play in a single SNR.


title: On the Power of Statistical Zero Knowledge

abstract:
  We examine the power of statistical zero knowledge proofs (captured by the
complexity class SZK) and their variants. First, we give the strongest known
relativized evidence that SZK contains hard problems, by exhibiting an oracle
relative to which SZK (indeed, even NISZK) is not contained in the class UPP,
containing those problems solvable by randomized algorithms with unbounded
error. This answers an open question of Watrous from 2002 [Aar]. Second, we
"lift" this oracle separation to the setting of communication complexity,
thereby answering a question of G\"o\"os et al. (ICALP 2016). Third, we give
relativized evidence that perfect zero knowledge proofs (captured by the class
PZK) are weaker than general zero knowledge proofs. Specifically, we exhibit
oracles relative to which SZK is not contained in PZK, NISZK is not contained
in NIPZK, and PZK is not equal to coPZK. The first of these results answers a
question raised in 1991 by Aiello and H{\aa}stad (Information and Computation),
and the second answers a question of Lovett and Zhang (2016). We also describe
additional applications of these results outside of structural complexity.
  The technical core of our results is a stronger hardness amplification
theorem for approximate degree, which roughly says that composing the
gapped-majority function with any function of high approximate degree yields a
function with high threshold degree.


title:
Vacuum polarization and classical self-action near higher-dimensional
  defects

abstract:
  We analyze the gravity-induced effects associated with a massless scalar
field in a higher-dimensional spacetime being the tensor product of
$(d-n)$-dimensional Minkowski space and $n$-dimensional
spherically/cylindrically-symmetric space with a solid/planar angle deficit.
These spacetimes are considered as simple models for a multidimensional global
monopole (if \mbox{$n\geqslant 3$}) or cosmic string (if $n=2$) with $(d-n-1)$
flat extra dimensions. Thus, we refer to them as conical backgrounds. In terms
of the angular deficit value, we derive the perturbative expression for the
scalar Green's function, valid for any $d\geqslant 3$ and $2\leqslant
n\leqslant d-1$, and compute it to the leading order. With the use of this
Green's function we compute the renormalized vacuum expectation value of the
field square $\langle \phi^{2}(x)\rangle_{\mathrm{ren}}$ and the renormalized
vacuum averaged of the scalar-field's energy-momentum tensor $\langle T_{M
N}(x)\rangle_{\mathrm{ren}}$ for arbitrary $d$ and $n$ from the interval
mentioned above and arbitrary coupling constant to the curvature $\xi$. In
particular, we revisit the computation of the vacuum polarization effects for a
non-minimally coupled massless scalar field in the spacetime of a straight
cosmic string. The same Green's function enables to consider the old purely
classical problem of the gravity-induced self-action of a classical pointlike
scalar or electric charge, placed at rest at some fixed point of the space
under consideration. To deal with divergences, which appear in consideration of
the both problems, we apply the dimensional-regularization technique, widely
used in quantum field theory (QFT). The explicit dependence of the results upon
the dimensionalities of both the bulk and conical submanifold, is discussed.


title: Eigenvalue inequalities for the Laplacian with mixed boundary conditions

abstract:
  Inequalities for the eigenvalues of the (negative) Laplacian subject to mixed
boundary conditions on polyhedral and more general bounded domains are
established. The eigenvalues subject to a Dirichlet boundary condition on a
part of the boundary and a Neumann boundary condition on the remainder of the
boundary are estimated in terms of either Dirichlet or Neumann eigenvalues. The
results complement several classical inequalities between Dirichlet and Neumann
eigenvalues due to P\'{o}lya, Payne, Levine and Weinberger, Friedlander, and
others.


title: Langevin dynamics with general kinetic energies

abstract:
  We study Langevin dynamics with a kinetic energy different from the standard,
quadratic one in order to accelerate the sampling of Boltzmann-Gibbs
distributions. In particular, this kinetic energy can be non-globally
Lipschitz, which raises issues for the stability of discretizations of the
associated Langevin dynamics. We first prove the exponential convergence of the
law of the continuous process to the Boltzmann-Gibbs measure by a hypocoercive
approach, and characterize the asymptotic variance of empirical averages over
trajectories. We next develop numerical schemes which are stable and of weak
order two, by considering splitting strategies where the discretizations of the
fluctuation/dissipation are corrected by a Metropolis procedure. We use the
newly developped schemes for two applications: optimizing the shape of the
kinetic energy for the so-called adaptively restrained Langevin dynamics (which
considers perturbations of standard quadratic kinetic energies vanishing around
the origin); and reducing the metastability of some toy models using
non-globally Lipschitz kinetic energies.


title:
An Analyst's Traveling Salesman Theorem for sets of dimension larger
  than one

abstract:
  In his 1990 Inventiones paper, P. Jones characterized subsets of rectifiable
curves in the plane via a multiscale sum of $\beta$-numbers. These
$\beta$-numbers are geometric quantities measuring how far a given set deviates
from a best fitting line at each scale and location. Jones' result is a
quantitative way of saying that a curve is rectifiable if and only if it has a
tangent at almost every point. Moreover, computing this square sum for a curve
returns the length of the curve up to multiplicative constant. K. Okikiolu
extended his result from subsets of the plane to subsets of Euclidean space. G.
David and S. Semmes extended the discussion to include sets of (integer)
dimension larger than one, under the assumption of Ahlfors regularity and using
a variant of Jones' $\beta$ numbers. In this paper we give a version of P.
Jones' theorem for sets of arbitrary (integer) dimension lying in Euclidean
space. We estimate the $d$-dimensional Hausdorff measure of a set in terms of
an analogous sum of $\beta$-type numbers. There is no assumption of Ahlfors
regularity, but rather, only of a lower bound on the Hausdorff content. We
adapt David and Semmes' version of Jones' $\beta$-numbers by redefining them
using a Choquet integral. A key tool in the proof is G. David and T. Toro's
parametrization of Reifenberg flat sets (with holes).


title: Emergent computation in simple model of neural activity

abstract:
  We investigate the dynamics of a network consisting of an array of identical
cortical units with nearest neighbor interactions under periodic arousal. Each
unit consists of two interconnected populations of neurons tuned to a state in
which many nonlinear resonances are available. The network is critically
balanced due to short-ranged antisymmetric connections between units. For wide
ranges of the network parameters, the patterns of activity resemble the
dynamics of cellular automata. It is argued that these dynamical states may
provide a template in which computation can be implemented.


title:
Measurement of long-range angular correlations and azimuthal
  anisotropies in high-multiplicity $p$$+$Au collisions at
  $\sqrt{s_{_{NN}}}=200$ GeV

abstract:
  We present the first measurements of long-range angular correlations and the
transverse momentum dependence of elliptic flow $v_2$ in high-multiplicity
$p$$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV. A comparison of these
results with previous measurements in high-multiplicity $d$$+$Au and $^3{\rm
He}$$+$Au collisions demonstrates a relation between $v_2$ and the initial
collision eccentricity $\varepsilon_2$, suggesting that the observed
momentum-space azimuthal anisotropies in these small systems have a collective
origin and reflect the initial geometry. Good agreement is observed between the
measured $v_2$ and hydrodynamic calculations for all systems, and an argument
disfavoring theoretical explanations based on momentum-space domain
correlations is presented. The set of measurements presented here allows us to
leverage the distinct intrinsic geometry of each of these systems to
distinguish between different theoretical descriptions of the long-range
correlations observed in small collision systems.


title: Bellman functions and $L^p$ estimates for paraproducts

abstract:
  We give an explicit formula for one possible Bellman function associated with
the $L^p$ boundedness of dyadic paraproducts regarded as bilinear operators or
trilinear forms. Then we apply the same Bellman function in various other
settings, to give self-contained alternative proofs of the estimates for
several classical operators. These include the martingale paraproducts of
Ba\~{n}uelos and Bennett and the paraproducts with respect to the heat flows.


title: Nonlinear resonances and multi-stability in simple neural circuits

abstract:
  This article describes a numerical procedure designed to tune the parameters
of periodically-driven dynamical systems to a state in which they exhibit rich
dynamical behavior. This is achieved by maximizing the diversity of subharmonic
solutions available to the system within a range of the parameters that define
the driving. The procedure is applied to a problem of interest in computational
neuroscience: a circuit composed of two interacting populations of neurons
under external periodic forcing. Depending on the parameters that define the
circuit, such as the weights of the connections between the populations, the
response of the circuit to the driving can be strikingly rich and diverse. The
procedure is employed to find circuits that, when driven by external input,
exhibit multiple stable patterns of periodic activity organized in complex
tuning diagrams and signatures of low dimensional chaos.


title: Fermionic Matrix Product Operators and Topological Phases of Matter

abstract:
  We introduce the concept of fermionic matrix product operators, and show that
they provide a natural representation of fermionic fusion tensor categories.
This allows for the classification of two dimensional fermionic topological
phases in terms of matrix product operator algebras. Using this approach we
give a classification of fermionic symmetry protected topological phases with
respect to a group $G$ in terms of three cohomology groups:
$H^1(G,\mathbb{Z}_2)$, describing which matrix product operators are of
Majorana type, $H^2(G,\mathbb{Z}_2)$, describing the fermionic nature of the
fusion tensors that arise when two matrix product operators are multiplied, and
the supercohomolgy group $\bar{H}^3(G,U(1))$ which corresponds to the
associator that changes the order of fusion. We also generalize the tensor
network description of the string-net ground states to the fermionic setting,
yielding simple representations of a class that includes the fermionic toric
code.


title: A Linear-Time Variational Integrator for Multibody Systems

abstract:
  We present an efficient variational integrator for multibody systems.
Variational integrators reformulate the equations of motion for multibody
systems as discrete Euler-Lagrange (DEL) equations, transforming forward
integration into a root-finding problem for the DEL equations. Variational
integrators have been shown to be more robust and accurate in preserving
fundamental properties of systems, such as momentum and energy, than many
frequently used numerical integrators. However, state-of-the-art algorithms
suffer from $O(n^3)$ complexity, which is prohibitive for articulated multibody
systems with a large number of degrees of freedom, $n$, in generalized
coordinates. Our key contribution is to derive a recursive algorithm that
evaluates DEL equations in $O(n)$, which scales up well for complex multibody
systems such as humanoid robots. Inspired by recursive Newton-Euler algorithm,
our key insight is to formulate DEL equation individually for each body rather
than for the entire system. Furthermore, we introduce a new quasi-Newton method
that exploits the impulse-based dynamics algorithm, which is also $O(n)$, to
avoid the expensive Jacobian inversion in solving DEL equations. We demonstrate
scalability and efficiency, as well as extensibility to holonomic constraints
through several case studies.


title: Low scale left-right-right-left symmetry

abstract:
  We propose an effective left-right-right-left model with a parity breaking
scale around a few TeV. One of the main achievements of the model is that the
mirror fermions as well as the mirror gauge sector simultaneously could be at
TeV scale. It is shown that the most dangerous quadratic divergence of the SM
Higgs boson involving the top quark in the loop is naturally suppressed, and
begins at three loop. The model postpones the fine-tuning of the mass of the SM
Higgs boson up to a sufficiently high scale. The model explains the smallness
of the neutrino masses whether they are Dirac or Majorana. Furthermore, the
strong $CP$ phase is zero in this model.


title: Controlling collective spontaneous emission with plasmonic waveguides

abstract:
  We demonstrate a plasmonic route to control the collective spontaneous
emission of two-level quantum emitters. Superradiance and subradiance effects
are observed over distances comparable to the operating wavelength inside
plasmonic nanochannels. These plasmonic waveguides can provide an effective
epsilon-near-zero operation in their cut-off frequency and Fabry-Perot
resonances at higher frequencies. The related plasmonic resonant modes are
found to efficiently enhance the constructive (superradiance) or destructive
(subradiance) interference between different quantum emitters located inside
the waveguides. By increasing the number of emitters located in the elongated
plasmonic channel, the superradiance effect is enhanced at the
epsilon-near-zero operation, leading to a strong coherent increase in the
collective spontaneous emission rate. In addition, the separation distance
between neighboring emitters and their emission wavelengths can be changed to
dynamically control the collective emission properties of the plasmonic system.
It is envisioned that the dynamic modification between quantum superradiant and
subradiant modes will find applications in quantum entanglement of qubits,
low-threshold nanolasers and efficient sensors.


title: Rapid Mixing of Geodesic Walks on Manifolds with Positive Curvature

abstract:
  We introduce a Markov chain for sampling from the uniform distribution on a
Riemannian manifold $\mathcal{M}$, which we call the $\textit{geodesic walk}$.
We prove that the mixing time of this walk on any manifold with positive
sectional curvature $C_{x}(u,v)$ bounded both above and below by $0 <
\mathfrak{m}_{2} \leq C_{x}(u,v) \leq \mathfrak{M}_2 < \infty$ is
$\mathcal{O}^*\left(\frac{\mathfrak{M}_2}{\mathfrak{m}_2}\right)$. In
particular, this bound on the mixing time does not depend explicitly on the
dimension of the manifold. In the special case that $\mathcal{M}$ is the
boundary of a convex body, we give an explicit and computationally tractable
algorithm for approximating the exact geodesic walk. As a consequence, we
obtain an algorithm for sampling uniformly from the surface of a convex body
that has running time bounded solely in terms of the curvature of the body.


title:
Polaron spin echo envelope modulations in an organic semiconducting
  polymer

abstract:
  Theoretical treatment of the electron spin echo envelope modulation (ESEEM)
spectra from polarons in a semiconducting $\pi$- conjugated polymer is
presented. The contact hyperfine coupling and the dipolar interaction between
the polaron and proton spins are found to have distinct contributions in the
ESEEM spectra. However, since the two contributions are spaced very closely,
and the dipolar contribution is dominant, the detection of the contact
hyperfine interaction is difficult. To resolve this problem, a recipe of
probing the contact hyperfine and dipolar interactions selectively is proposed,
and a method for detecting the polaron contact hyperfine interaction is
formulated. The ESEEM decay due to the polaron random hopping is analyzed, and
the robustness of the method against this decay is verified. Moreover, this
decay is linked to the transport properties of polarons, providing an auxiliary
probe for the polaron transport.


title:
On the origin of perpendicular magnetic anisotropy in strained Fe-Co(-X)
  films

abstract:
  Very high magnetic anisotropies have been theoretically predicted for
strained Fe-Co(-X) and indeed several experiments on epitaxial thin films
seemed to confirm strain induced anisotropy enhancement. This study presents a
critical analysis of the different contributions to perpendicular anisotropy:
volume, interface and surface anisotropies. Tracing these contributions,
thickness series of single layer films as well as multilayers with Au-Cu
buffers/interlayers of different lattice parameters have been prepared. The
analysis of their magnetic anisotropy reveals a negligible influence of the
lattice parameter of the buffer. Electronic effects, originating from both, the
Au-Cu interface and the film surface, outrange the elastic effects. Surface
anisotropy, however, exceeds the interface anisotropy by more than a factor of
three. A comparison with results from Density Functional Theory suggests, that
the experimentally observed strong perpendicular surface anisotropy originates
from a deviation from an ideal oxide-free surface. Accordingly, tailored
Fe-Co-X/oxide interfaces may open a route towards high anisotropy in rare-earth
free materials.


title: Strong parameter renormalization from optimum lattice model orbitals

abstract:
  We revisit the old problem of which is the best single particle basis to
express a Hubbard-like lattice model. A rigorous variational solution of this
problem leads to equations in which the answer depends in a self-consistent
manner on the solution of the lattice model itself. Contrary to naive
expectations, for arbitrary small interactions, the optimized orbitals differ
from the non-interacting ones, leading also to substantial changes in the model
parameters as shown analytically and in an explicit numerical solution for a
simple double-well one-dimensional case. At strong coupling, we obtain the
direct exchange interaction with a very large renormalization with important
consequences for the explanation of ferromagnetism with model hamiltonians.
Moreover, in the case of two atoms and two fermions we show that the
optimization equations are closely related to reduced density matrix functional
theory thus establishing an unsuspected correspondence between continuum and
lattice approaches.


title:
Signature of magnetic-dependent gapless odd frequency states at
  superconductor/ferromagnet interfaces

abstract:
  The theory of superconductivity developed by Bardeen, Cooper and Schrieffer
(BCS) explains the stabilization of electron pairs into a spin-singlet, even
frequency, state by the formation of an energy gap within which the density of
states is zero. At a superconductor interface with an inhomogeneous
ferromagnet, a gapless odd frequency superconducting state is predicted, in
which the Cooper pairs are in a spin-triplet state. Although indirect evidence
for such a state has been obtained, the gap structure and pairing symmetry have
not so far been determined. Here we report scanning tunnelling spectroscopy of
Nb superconducting films proximity coupled to epitaxial Ho. These measurements
reveal pronounced changes to the Nb subgap superconducting density of states on
driving the Ho through a metamagnetic transition from a helical
antiferromagnetic to a homogeneous ferromagnetic state for which a BCS-like gap
is recovered. The results prove odd frequency spin-triplet superconductivity at
superconductor/inhomogeneous magnet interfaces.


title:
Robust Spectral Detection of Global Structures in the Data by Learning a
  Regularization

abstract:
  Spectral methods are popular in detecting global structures in the given data
that can be represented as a matrix. However when the data matrix is sparse or
noisy, classic spectral methods usually fail to work, due to localization of
eigenvectors (or singular vectors) induced by the sparsity or noise. In this
work, we propose a general method to solve the localization problem by learning
a regularization matrix from the localized eigenvectors. Using matrix
perturbation analysis, we demonstrate that the learned regularizations suppress
down the eigenvalues associated with localized eigenvectors and enable us to
recover the informative eigenvectors representing the global structure. We show
applications of our method in several inference problems: community detection
in networks, clustering from pairwise similarities, rank estimation and matrix
completion problems. Using extensive experiments, we illustrate that our method
solves the localization problem and works down to the theoretical detectability
limits in different kinds of synthetic data. This is in contrast with existing
spectral algorithms based on data matrix, non-backtracking matrix, Laplacians
and those with rank-one regularizations, which perform poorly in the sparse
case with noise.


title: Semi-Supervised Classification with Graph Convolutional Networks

abstract:
  We present a scalable approach for semi-supervised learning on
graph-structured data that is based on an efficient variant of convolutional
neural networks which operate directly on graphs. We motivate the choice of our
convolutional architecture via a localized first-order approximation of
spectral graph convolutions. Our model scales linearly in the number of graph
edges and learns hidden layer representations that encode both local graph
structure and features of nodes. In a number of experiments on citation
networks and on a knowledge graph dataset we demonstrate that our approach
outperforms related methods by a significant margin.


title: The Gaussian streaming model and Lagrangian effective field theory

abstract:
  We update the ingredients of the Gaussian streaming model (GSM) for the
redshift-space clustering of biased tracers using the techniques of Lagrangian
perturbation theory, effective field theory (EFT) and a generalized Lagrangian
bias expansion. After relating the GSM to the cumulant expansion, we present
new results for the real-space correlation function, mean pairwise velocity and
pairwise velocity dispersion including counter terms from EFT and bias terms
through third order in the linear density, its leading derivatives and its
shear up to second order. We discuss the connection to the Gaussian peaks
formalism. We compare the ingredients of the GSM to a suite of large N-body
simulations, and show the performance of the theory on the low order multipoles
of the redshift-space correlation function and power spectrum. We highlight the
importance of a general biasing scheme, which we find to be as important as
higher-order corrections due to non-linear evolution for the halos we consider
on the scales of interest to us.


title:
$8\pi$-periodic dissipationless ac Josephson effect on a quantum
  spin-Hall edge via a Quantum magnetic impurity

abstract:
  Time-reversal invariance places strong constraints on the properties of the
quantum spin Hall edge. One such restriction is the inevitability of
dissipation in a Josephson junction between two superconductors formed on such
an edge without the presence of interaction. Interactions and spin-conservation
breaking are key ingredients for the realization of dissipationless ac
Josephson effect on such quantum spin Hall edges. We present a simple quantum
impurity model that allows to create a dissipationless fractional Josephson
effect on a quantum spin Hall edge. We then use this model to substantiate a
general argument that shows that any such non-dissipative Josephson effect must
necessarily by $8\pi$-periodic.


title: Orthogonality Catastrophes in Quantum Electrodynamics

abstract:
  The insertion of a small polarizable particle in an arbitrarily large optical
cavity significantly alters the quantum-mechanical state of the electromagnetic
field in that the photon ground state of the empty cavity and that of the
cavity with the particle become mutually orthogonal and, thus, cannot be
connected adiabatically in the infinite limit. The photon problem can be mapped
exactly onto that of a many-body system of fermions, which is known to exhibit
an orthogonality catastrophe when a finite-range local potential is introduced.
We predict that the motion of polarizable objects inside a cavity, no matter
how slow, as well as their addition and removal from the cavity, will generate
a macroscopic, diverging number of low-energy photons. The significance of
these results in regard to the quantum measurement problem and the dynamical
Casimir effect are also discussed.


title:
Entropy of the Sum of Two Independent, Non-Identically-Distributed
  Exponential Random Variables

abstract:
  In this letter, we give a concise, closed-form expression for the
differential entropy of the sum of two independent, non-identically-distributed
exponential random variables. The derivation is straightforward, but such a
concise entropy has not been previously given in the literature. The usefulness
of the expression is demonstrated with examples.