title:
Enhanced capital-asset pricing model for the reconstruction of bipartite
  financial networks

abstract:
  Reconstructing patterns of interconnections from partial information is one
of the most important issues in the statistical physics of complex networks. A
paramount example is provided by financial networks. In fact, the spreading and
amplification of financial distress in capital markets is strongly affected by
the interconnections among financial institutions. Yet, while the aggregate
balance sheets of institutions are publicly disclosed, information on single
positions is mostly confidential and, as such, unavailable. Standard approaches
to reconstruct the network of financial interconnection produce unrealistically
dense topologies, leading to a biased estimation of systemic risk. Moreover,
reconstruction techniques are generally designed for monopartite networks of
bilateral exposures between financial institutions, thus failing in reproducing
bipartite networks of security holdings (\eg, investment portfolios). Here we
propose a reconstruction method based on constrained entropy maximization,
tailored for bipartite financial networks. Such a procedure enhances the
traditional {\em capital-asset pricing model} (CAPM) and allows to reproduce
the correct topology of the network. We test this ECAPM method on a dataset,
collected by the European Central Bank, of detailed security holdings of
European institutional sectors over a period of six years (2009-2015). Our
approach outperforms the traditional CAPM and the recently proposed MECAPM both
in reproducing the network topology and in estimating systemic risk due to
fire-sales spillovers. In general, ECAPM can be applied to the whole class of
weighted bipartite networks described by the fitness model.


title:
Small Chimera States without Multistability in a Globally Delay-Coupled
  Network of Four Lasers

abstract:
  We present results obtained for a network of four delay-coupled lasers
modelled by Lang-Kobayashi-type equations. We find small chimera states
consisting of a pair of synchronized lasers and two unsynchronized lasers. One
class of these small chimera states can be understood as intermediate steps on
the route from synchronization to desynchronization and we present the entire
chain of bifurcations giving birth to them. This class of small chimeras can
exhibit limit-cycle or quasiperiodic dynamics. A second type of small chimera
states exists apparently disconnected from any region of synchronization,
arising from pair synchronization inside the chaotic desynchronized regime. In
contrast to previously reported chimera states in globally coupled networks, we
find that the small chimera state is the only stable solution of the system for
certain parameter regions, i.e. we do not need to specially prepare initial
conditions.


title:
Gamblets for opening the complexity-bottleneck of implicit schemes for
  hyperbolic and parabolic ODEs/PDEs with rough coefficients

abstract:
  Implicit schemes are popular methods for the integration of time dependent
PDEs such as hyperbolic and parabolic PDEs. However the necessity to solve
corresponding linear systems at each time step constitutes a complexity
bottleneck in their application to PDEs with rough coefficients. We present a
generalization of gamblets introduced in \cite{OwhadiMultigrid:2015} enabling
the resolution of these implicit systems in near-linear complexity and provide
rigorous a-priori error bounds on the resulting numerical approximations of
hyperbolic and parabolic PDEs. These generalized gamblets induce a
multiresolution decomposition of the solution space that is adapted to both the
underlying (hyperbolic and parabolic) PDE (and the system of ODEs resulting
from space discretization) and to the time-steps of the numerical scheme.


title: Enforcing Termination of Interprocedural Analysis

abstract:
  Interprocedural analysis by means of partial tabulation of summary functions
may not terminate when the same procedure is analyzed for infinitely many
abstract calling contexts or when the abstract domain has infinite strictly
ascending chains. As a remedy, we present a novel local solver for general
abstract equation systems, be they monotonic or not, and prove that this solver
fails to terminate only when infinitely many variables are encountered. We
clarify in which sense the computed results are sound. Moreover, we show that
interprocedural analysis performed by this novel local solver, is guaranteed to
terminate for all non-recursive programs --- irrespective of whether the
complete lattice is infinite or has infinite strictly ascending or descending
chains.


title: Anharmonic effects in the optical and acoustic bending modes of graphene

abstract:
  The out-of-plane fluctuations of carbon atoms in a graphene sheet have been
studied by means of classical molecular dynamic simulations with an empirical
force-field as a function of temperature. The Fourier analysis of the
out-of-plane fluctuations often applied to characterize the acoustic bending
mode of graphene is extended to the optical branch, whose polarization vector
is perpendicular to the graphene layer. This observable is inaccessible in a
continuous elastic model of graphene but it is readily obtained by the
atomistic treatment. Our results suggest that the long-wavelength limit of the
acoustic out-of-plane fluctuations of a free layer without stress is
qualitatively similar to that predicted by a harmonic model under a tensile
stress. This conclusion is a consequence of the anharmonicity of both in-plane
and out-of-plane vibrational modes of the lattice. The most striking anharmonic
effect is the presence of a linear term, $\omega_{A}=v_{A}k$, in the dispersion
relation of the acoustic bending band of graphene at long wavelengths
($k\rightarrow0$). This term implies a strong reduction of the amplitude of
out-of-plane oscillations in comparison to a flexural mode with a
$k^{2}$-dependence in the long-wavelength limit. Our simulations show an
increase of the sound velocity associated to the bending mode, as well as an
increase of its bending constant, $\kappa,$ as the temperature increases.
Moreover, the frequency of the optical bending mode, $\omega_{O}(\Gamma)$, also
increases with the temperature. Our results are in agreement with recent
analytical studies of the bending modes of graphene using either perturbation
theory or an adiabatic approximation in the framework of continuous layer
models.


title:
Probing Higgs-radion mixing in warped models through complementary
  searches at the LHC and the ILC

abstract:
  We consider the Higgs-radion mixing in the context of warped space extra
dimensional models with custodial symmetry and investigate the prospects of
detecting the mixed radion. Custodial symmetries allow the Kaluza-Klein
excitations to be lighter, and protect Zbb to be in agreement with experimental
constraints. We perform a complementary study of discovery reaches of the
Higgs-radion mixed state at the 13 and 14 TeV LHC and at the 500 and 1000 GeV
ILC. We carry out a comprehensive analysis of the most significant production
and decay modes of the mixed radion in the 80 GeV - 1 TeV mass range, and
indicate the parameter space that can be probed at the LHC and the ILC. There
exists a region of the parameter space which can be probed, at the LHC, through
the diphoton channel even for a relatively low luminosity of 50 fb^{-1}. The
reach of the 4-lepton final state, in probing the parameter space is also
studied in the context of 14 TeV LHC, for a luminosity of 1000 fb^{-1}. At the
ILC, with an integrated luminosity of 500 fb^{-1}, we analyze the Z-radion
associated production and the WW fusion production, followed by the radion
decay into bb and W+W-. The WW fusion production is favored over the Z-radion
associated channel in probing regions of the parameter space beyond the LHC
reach. The complementary study at the LHC and the ILC is useful both for the
discovery of the radion and the understanding of its mixing sector.


title: The floating body in real space forms

abstract:
  We carry out a systematic investigation on floating bodies in real space
forms. A new unifying approach not only allows us to treat the important
classical case of Euclidean space as well as the recent extension to the
Euclidean unit sphere, but also the new extension of floating bodies to
hyperbolic space.
  Our main result establishes a relation between the derivative of the volume
of the floating body and a certain surface area measure, which we called the
floating area. In the Euclidean setting the floating area coincides with the
well known affine surface area, a powerful tool in the affine geometry of
convex bodies.


title:
Topological quantum phase transition driven by anisotropic spin-orbit
  coupling in trinuclear organometallic coordination crystals

abstract:
  We show how quasi-one-dimensional correlated insulating states arise at
two-thirds filling in organometallic multinuclear coordination complexes
described by layered decorated honeycomb lattices. The interplay of spin-orbit
coupling and electronic correlations leads to pseudospin-1 moments arranged in
weakly coupled chains with highly anisotropic exchange and a large trigonal
splitting. This leads to a quantum phase transition from a Haldane phase to a
topologically trivial phase as the relative strength of the spin-orbit coupling
increases.


title: W-Markov measures, transfer operators, wavelets and multiresolutions

abstract:
  In a general setting we solve the following inverse problem: Given a positive
operators $R$, acting on measurable functions on a fixed measure space
$(X,\mathcal B_X)$, we construct an associated Markov chain. Specifically,
starting with a choice of $R$ (the transfer operator), and a probability
measure $\mu_0$ on $(X, \mathcal B_X)$, we then build an associated Markov
chain $T_0, T_1, T_2,\ldots$, with these random variables (r.v) realized in a
suitable probability space $(\Omega,\mathcal F, \mathbb P)$, and each r.v.
taking values in $X$, and with $T_0$ having the probability $\mu_0$ as law. We
further show how spectral data for $R$, e.g., the presence of $R$-harmonic
functions, propagate to the Markov chain. Conversely, in a general setting, we
show that every Markov chain is determined by its transfer operator. In a range
of examples we put this correspondence into practical terms: $(i)$ iterated
function systems (IFS), $(ii)$ wavelet multiresolution constructions, and
$(iii)$ IFSs with random control.


title:
Cosmic ray interactions in the solar system: The Gerasimova-Zatsepin
  effect

abstract:
  The Gerasimova-Zatsepin effect of collisions of ultra-high-energy cosmic ray
nuclei with photons emitted by the sun may cause two simultaneous air showers
on Earth. This effect is simulated using the full energy spectrum of solar
photons, ray tracing through the interplanetary magnetic field and upper limit
values for the iron and oxygen cosmic ray fluxes. Only the most abundant
interactions in which a single proton is emitted from the nucleus are
considered. For the first time the distributions of distances between the
individual showers at Earth as a function of the distance of the primary cosmic
ray to the Sun are shown. These distributions are used to estimate the
capabilities of current detector arrays to measure the Gerasimova-Zatsepin
effect and to show that a dedicated array is capable of measuring this effect.


title: Wave-scattering from a gently curved surface

abstract:
  We study wave scattering from a gently curved surface. We show that the
recursive relations, implied by shift invariance, among the coefficients of the
perturbative series for the scattering amplitude allow to perform an infinite
resummation of the perturbative series to all orders in the amplitude of the
corrugation. The resummed series provides a derivative expansion of the
scattering amplitude in powers of derivatives of the height profile, which is
expected to become exact in the limit of quasi-specular scattering. We discuss
the relation of our results with the so-called small-slope approximation
introduced some time ago by Voronovich.


title: Fully DNN-based Multi-label regression for audio tagging

abstract:
  Acoustic event detection for content analysis in most cases relies on lots of
labeled data. However, manually annotating data is a time-consuming task, which
thus makes few annotated resources available so far. Unlike audio event
detection, automatic audio tagging, a multi-label acoustic event classification
task, only relies on weakly labeled data. This is highly desirable to some
practical applications using audio analysis. In this paper we propose to use a
fully deep neural network (DNN) framework to handle the multi-label
classification task in a regression way. Considering that only chunk-level
rather than frame-level labels are available, the whole or almost whole frames
of the chunk were fed into the DNN to perform a multi-label regression for the
expected tags. The fully DNN, which is regarded as an encoding function, can
well map the audio features sequence to a multi-tag vector. A deep pyramid
structure was also designed to extract more robust high-level features related
to the target tags. Further improved methods were adopted, such as the Dropout
and background noise aware training, to enhance its generalization capability
for new audio recordings in mismatched environments. Compared with the
conventional Gaussian Mixture Model (GMM) and support vector machine (SVM)
methods, the proposed fully DNN-based method could well utilize the long-term
temporal information with the whole chunk as the input. The results show that
our approach obtained a 15% relative improvement compared with the official
GMM-based method of DCASE 2016 challenge.


title: Radial segregation driven by axial convection

abstract:
  We experimentally study the mixing of binary granular systems in a horizontal
rotating cylinder. When materials have the same size and differ by dynamic
angle of repose only, we observe an axial transport of matter that generates
transient radial segregation. The system then evolves towards homogeneity. If
materials differ by density also radial segregation becomes steady. A mechanism
is suggested where radial segregation is promoted by axial differences of
dynamic angle of repose. This differs from the free surface segregation
suggested so far to explain radial segregation.


title:
Non-Fermi-liquid behavior in quantum impurity models with
  superconducting channels

abstract:
  We study how the non-Fermi-liquid nature of the overscreened multi-channel
Kondo impurity model affects the response to a BCS pairing term that, in the
absence of the impurity, opens a gap $\Delta$. We find that non-Fermi liquid
features do persist even at finite $\Delta$: the local density of states lacks
coherence peaks, the states in the continuum above the gap are unconventional,
and the boundary entropy is a non-monotonic function of temperature. Even more
surprisingly, we also find that the low-energy spectrum in the limit $\Delta\to
0$ actually does not correspond to the spectrum strictly at $\Delta=0$. In
particular, the $\Delta\to 0$ ground state is an orbitally degenerate
spin-singlet, while it is an orbital singlet with a residual spin degeneracy at
$\Delta=0$. In addition, there are fractionalized spin-1/2 sub-gap excitations
whose energy in units of $\Delta$ tends towards a finite and universal value
when $\Delta\to 0$; as if the universality of the anomalous power-law exponents
that characterise the overscreened Kondo effect turned into universal energy
ratios when the scale invariance is broken by $\Delta\not=0$. This intriguing
phenomenon can be explained by the renormalisation flow towards the
overscreened fixed point and the gap cutting off the orthogonality catastrophe
singularities.


title:
Computing reconstructions from nonuniform Fourier samples: Universality
  of stability barriers and stable sampling rates

abstract:
  We study the problem of recovering an unknown compactly-supported
multivariate function from samples of its Fourier transform that are acquired
nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction
problems of this kind arise in various imaging applications, where Fourier
samples are taken along radial lines or spirals for example.
  Specifically, we consider finite-dimensional reconstructions, where a limited
number of samples is available, and investigate the rate of convergence of such
approximate solutions and their numerical stability. We show that the
proportion of Fourier samples that allow for stable approximations of a given
numerical accuracy is independent of the specific sampling geometry and is
therefore universal for different sampling scenarios. This allows us to relate
both sufficient and necessary conditions for different sampling setups and to
exploit several results that were previously available only for very specific
sampling geometries.
  The results are obtained by developing: (i) a transference argument for
different measures of the concentration of the Fourier transform and Fourier
samples; (ii) frame bounds valid up to the critical sampling density, which
depend explicitly on the sampling set and the spectrum.
  As an application, we identify sufficient and necessary conditions for stable
and accurate reconstruction of algebraic polynomials or wavelet coefficients
from nonuniform Fourier data.


title: Gravitating vortices and the Einstein--Bogomol'nyi equations

abstract:
  In this work we consider the gravitating vortex equations. These equations
couple a metric over a compact Riemann surface with a hermitian metric over a
holomorphic line bundle equipped with a fixed global section --- the Higgs
field ---, and have a symplectic interpretation as moment-map equations. As a
particular case of the gravitating vortex equations on $\mathbb{P}^1$, we find
the Einstein--Bogomol'nyi equations, previously studied in the theory of cosmic
strings in physics. We prove two main results in this paper. Our first main
result gives a converse to an existence theorem of Y. Yang for the
Einstein--Bogomol'nyi equations, establishing in this way a correspondence with
Geometric Invariant Theory for these equations. In particular, we prove a
conjecture by Y. Yang about the non-existence of cosmic strings on
$\mathbb{P}^1$ superimposed at a single point. Our second main result is an
existence and uniqueness result for the gravitating vortex equations in genus
greater than one.

categories: math.DG gr-qc hep-th math-ph math.AG math.MP


title: Spintronic nano-devices for bio-inspired computing

abstract:
  Bio-inspired hardware holds the promise of low-energy, intelligent and highly
adaptable computing systems. Applications span from automatic classification
for big data management, through unmanned vehicle control, to control for
bio-medical prosthesis. However, one of the major challenges of fabricating
bio-inspired hardware is building ultra-high density networks out of complex
processing units interlinked by tunable connections. Nanometer-scale devices
exploiting spin electronics (or spintronics) can be a key technology in this
context. In particular, magnetic tunnel junctions are well suited for this
purpose because of their multiple tunable functionalities. One such
functionality, non-volatile memory, can provide massive embedded memory in
unconventional circuits, thus escaping the von-Neumann bottleneck arising when
memory and processors are located separately. Other features of spintronic
devices that could be beneficial for bio-inspired computing include tunable
fast non-linear dynamics, controlled stochasticity, and the ability of single
devices to change functions in different operating conditions. Large networks
of interacting spintronic nano-devices can have their interactions tuned to
induce complex dynamics such as synchronization, chaos, soliton diffusion,
phase transitions, criticality, and convergence to multiple metastable states.
A number of groups have recently proposed bio-inspired architectures that
include one or several types of spintronic nanodevices. In this article we show
how spintronics can be used for bio-inspired computing. We review the different
approaches that have been proposed, the recent advances in this direction, and
the challenges towards fully integrated spintronics-CMOS (Complementary metal -
oxide - semiconductor) bio-inspired hardware.


title: Holonomy classification of Lorentz-K\"ahler manifolds

abstract:
  The classification problem for holonomy of pseudo-Riemannian manifolds is
actual and open. In the present paper, holonomy algebras of Lorentz-K\"ahler
manifolds are classified. A simple construction of a metric for each holonomy
algebra is given. Complex Walker coordinates are introduced and described using
the potential. Complex pp-waves are characterized in terms of the curvature,
holonomy and the potential. Classification of Lorentz-K\"ahler symmetric spaces
is reviewed.


title: Optimal adaptation for early stopping in statistical inverse problems

abstract:
  For linear inverse problems $Y=\mathsf{A}\mu+\xi$, it is classical to recover
the unknown signal $\mu$ by iterative regularisation methods $(\widehat
\mu^{(m)}, m=0,1,\ldots)$ and halt at a data-dependent iteration $\tau$ using
some stopping rule, typically based on a discrepancy principle, so that the
weak (or prediction) squared-error $\|\mathsf{A}(\widehat
\mu^{(\tau)}-\mu)\|^2$ is controlled. In the context of statistical estimation
with stochastic noise $\xi$, we study oracle adaptation (that is, compared to
the best possible stopping iteration) in strong squared-error $E[\|\hat
\mu^{(\tau)}-\mu\|^2]$.
  For a residual-based stopping rule oracle adaptation bounds are established
for general spectral regularisation methods. The proofs use bias and variance
transfer techniques from weak prediction error to strong $L^2$-error, as well
as convexity arguments and concentration bounds for the stochastic part.
Adaptive early stopping for the Landweber method is studied in further detail
and illustrated numerically.


title:
Intrinsic Lipschitz graphs and vertical $\beta$-numbers in the
  Heisenberg group

abstract:
  The purpose of this paper is to introduce and study some basic concepts of
quantitative rectifiability in the first Heisenberg group $\mathbb{H}$. In
particular, we aim to demonstrate that new phenomena arise compared to the
Euclidean theory, founded by G. David and S. Semmes in the 90's. The theory in
$\mathbb{H}$ has an apparent connection to certain nonlinear PDEs, which do not
play a role with similar questions in $\mathbb{R}^{3}$.
  Our main object of study are the intrinsic Lipschitz graphs in $\mathbb{H}$,
introduced by B. Franchi, R. Serapioni and F. Serra Cassano in 2006. We claim
that these $3$-dimensional sets in $\mathbb{H}$, if any, deserve to be called
quantitatively $3$-rectifiable. Our main result is that the intrinsic Lipschitz
graphs satisfy a weak geometric lemma with respect to vertical $\beta$-numbers.
Conversely, extending a result of David and Semmes from $\mathbb{R}^{n}$, we
prove that a $3$-Ahlfors-David regular subset in $\mathbb{H}$, which satisfies
the weak geometric lemma and has big vertical projections, necessarily has big
pieces of intrinsic Lipschitz graphs.


title: Lyapunov exponents and eigenvalues of products of random matrices

abstract:
  Let $X_1,X_2, \ldots $ be a sequence of $i.i.d$ real (complex) $d \times d $
invertible random matrices with common distribution $\mu$ and $\sigma_1(n),
\sigma_2(n), \ldots , \sigma_d(n)$ be the singular values, $\lambda_1(n),
\lambda_2(n), \ldots , \lambda_d(n)$ be the eigenvalues of $X_nX_{n-1}\cdots
X_1$ in the decreasing order of their absolute values for every $n$. It is
known that if $\mathbb{E}(\log^{+}\|X_1\|)< \infty$, then with probability one
for all $1 \leq p \leq d$, $$
  \lim_{n \to \infty} \frac{1}{n}\log \sigma_p(n)=\gamma_p, $$ where
${\gamma_1,\gamma_2 \ldots \gamma_d}$ are the Lyapunov exponents associated
with $\mu$. In this paper we show that under certain support and moment
conditions on $\mu$, the absolute values of eigenvalues also exhibit the same
asymptotic behaviour. In fact, a stronger asymptotic relation holds between the
singular values and the eigenvalues $i.e.$ for any $r>0$ with probability one
for all $1 \leq p \leq d$, $$ \lim_{n \to \infty} \frac{1}{n^r}\log
\left(\frac{|\lambda_p(n)|}{\sigma_p(n)}\right)= 0, $$ which implies that the
fluctuations of the eigenvalues have the same asymptotic distribution as that
of the corresponding singular values. Isotropic random matrices and also random
matrices with $i.i.d$ real elements, which have some finite moment and bounded
density whose support contains an open set, are shown to satisfy the moment and
support conditions under which the above relations hold.


title:
Criteria for extensional necking instability in complex fluids and soft
  solids. Part II imposed tensile stress and force protocols

abstract:
  We study the necking of a filament of complex fluid or soft solid subject to
uniaxial tensile stretching, under conditions of constant imposed stress and
force, by means of linear stability analysis and nonlinear simulations. We
demonstrate necking to be a flow instability that is an unavoidable consequence
of the constitutive behaviour of essentially any viscoelastic material. We
derive criteria for the onset of necking that can be reported in terms of
characteristic signatures in the shapes of the experimentally measured material
functions, and that should therefore apply universally to all materials. To
confirm their generality, we show them to hold numerically in six constitutive
models. Under conditions of constant stress, we find two distinct dynamical
regimes as a function of time. In the first regime the strain rate quickly
attains a value prescribed by the fluid's underlying homogeneous constitutive
curve, at the given stress. In this first regime, no appreciable necking
arises. A second regime then ensues in which the homogeneous flow destabilises
to form a neck. This necking instability can occur via two distinct modes. The
first mode is relatively gentle and arises in any regime where the slope of the
constitutive curve is positive. It has a rate of necking per accumulated strain
unit set by the inverse of the slope of the constitutive curve. The second mode
sets in when a carefully defined `elastic derivative' of the tensile force
first slopes down as a function of the time. We discuss the way in which these
modes of instability manifest themselves in entangled polymeric fluids,
demonstrating four distinct regimes of necking behaviour as a function of
stress. Under conditions of constant imposed force, typically the flow sweeps
up the underlying constitutive curve of the fluid in question, with instability
to necking in any regime where that curve is positively sloping.


title:
Geometry and Topology of the space of K\"ahler metrics on singular
  varieties

abstract:
  Let $Y$ be a compact K\"ahler normal space and $\alpha \in
H^{1,1}(Y,\mathbb{R})$ a K\"ahler class. We study metric properties of the
space $\mathcal{H}_\alpha$ of K\"ahler metrics in $\alpha$ using Mabuchi
geodesics. We extend several results by Calabi, Chen, Darvas previously
established when the underlying space is smooth. As an application we
analytically characterize the existence of K\"ahler-Einstein metrics on
$\mathbb{Q}$-Fano varieties, generalizing a result of Tian, and illustrate
these concepts in the case of toric varieties.


title: Collective Semi-Supervised Learning for User Profiling in Social Media

abstract:
  The abundance of user-generated data in social media has incentivized the
development of methods to infer the latent attributes of users, which are
crucially useful for personalization, advertising and recommendation. However,
the current user profiling approaches have limited success, due to the lack of
a principled way to integrate different types of social relationships of a
user, and the reliance on scarcely-available labeled data in building a
prediction model. In this paper, we present a novel solution termed Collective
Semi-Supervised Learning (CSL), which provides a principled means to integrate
different types of social relationship and unlabeled data under a unified
computational framework. The joint learning from multiple relationships and
unlabeled data yields a computationally sound and accurate approach to model
user attributes in social media. Extensive experiments using Twitter data have
demonstrated the efficacy of our CSL approach in inferring user attributes such
as account type and marital status. We also show how CSL can be used to
determine important user features, and to make inference on a larger user
population.


title: Stochastic modelling of thermal effects on a ferromagnetic nano particle

abstract:
  In this work, we are interested in the behaviour of a single ferromagnetic
mono--domain particle submitted to an external field with a stochastic
perturbation. This model is a step toward the mathematical understanding of
thermal effects on ferromagnets. In a first part, we discuss modelling issues
and propose several ways to integrate a random noise in the deterministic
model. Then, among all these approaches, we focus on the more natural one and
study its long time behaviour. We prove that the system converges to the unique
stable equilibrium of the deterministic model and make precise the L^p rate of
the convergence. Finally, we illustrate the theoretical results by numerical
simulations.


title: The Niceness of Unique Sink Orientations

abstract:
  Random Edge is the most natural randomized pivot rule for the simplex
algorithm. Considerable progress has been made recently towards fully
understanding its behavior. Back in 2001, Welzl introduced the concepts of
\emph{reachmaps} and \emph{niceness} of Unique Sink Orientations (USO), in an
effort to better understand the behavior of Random Edge. In this paper, we
initiate the systematic study of these concepts. We settle the questions that
were asked by Welzl about the niceness of (acyclic) USO. Niceness implies
natural upper bounds for Random Edge and we provide evidence that these are
tight or almost tight in many interesting cases. Moreover, we show that Random
Edge is polynomial on at least $n^{\Omega(2^n)}$ many (possibly cyclic) USO. As
a bonus, we describe a derandomization of Random Edge which achieves the same
asymptotic upper bounds with respect to niceness and discuss some algorithmic
properties of the reachmap.


title: A structure theorem for abelian quasi-ordered groups

abstract:
  We introduce a notion of compatible quasi-ordered groups which unifies valued
and ordered abelian groups. It was proved in a paper by Fakhruddin that a
compatible quasi-order on a field is always either an order or a valuation. We
show here that the group case is more complicated than the field case and
describe the general structure of a compatible quasi-ordered abelian group. We
also develop a notion of quasi-order-minimality and establish a connection with
C-minimality, thus answering a question of F.Delon.


title: A Game-Theoretic Approach to Word Sense Disambiguation

abstract:
  This paper presents a new model for word sense disambiguation formulated in
terms of evolutionary game theory, where each word to be disambiguated is
represented as a node on a graph whose edges represent word relations and
senses are represented as classes. The words simultaneously update their class
membership preferences according to the senses that neighboring words are
likely to choose. We use distributional information to weigh the influence that
each word has on the decisions of the others and semantic similarity
information to measure the strength of compatibility among the choices. With
this information we can formulate the word sense disambiguation problem as a
constraint satisfaction problem and solve it using tools derived from game
theory, maintaining the textual coherence. The model is based on two ideas:
similar words should be assigned to similar classes and the meaning of a word
does not depend on all the words in a text but just on some of them. The paper
provides an in-depth motivation of the idea of modeling the word sense
disambiguation problem in terms of game theory, which is illustrated by an
example. The conclusion presents an extensive analysis on the combination of
similarity measures to use in the framework and a comparison with
state-of-the-art systems. The results show that our model outperforms
state-of-the-art algorithms and can be applied to different tasks and in
different scenarios.


title: Macroscopic superpositions as quantum ground states

abstract:
  We study the question of what kind of a macroscopic superposition can(not)
naturally exist as a ground state of some gapped local many-body Hamiltonian.
We derive an upper bound on the energy gap of an arbitrary physical Hamiltonian
provided that its ground state is a superposition of two well-distinguishable
macroscopic "semi-classical" states. For a large class of macroscopic
superposition states we show that the gap vanishes in the macroscopic limit.
This in turn shows that preparation of such states by simple cooling to the
ground state is not experimentally feasible and requires different strategy.
Our approach is very general and can be used to rule out a variety of quantum
states, some of which do not even exhibit macroscopic quantum properties.
Moreover, our methods and results can be used for addressing quantum marginal
related problems.


title: Solving the time-dependent Schr\"odinger equation via Laplace transform

abstract:
  We show how the Laplace transform can be used to give a solution of the
time-dependent Schr\"odinger equation for an arbitrary initial wave packet if
the solution of the stationary equation is known. The solution is obtained
without summing up eigenstates nor do we need the path integral. We solve the
initial value problem for three characteristic piecewise constant potentials.
The results give an intuitive picture of the wave packet dynamics, reproducing
explicitly all possible reflection and transmission processes. We investigate
classical and quantum properties of the evolution and determine the reflection
and transmission probabilities.


title:
Tate Conjecture and Higher Brauer Groups of Abelian Varieties in
  Characteristic Zero

abstract:
  Let $A$ be an abelian variety over a field finitely generated over
$\mathbb{Q}$. We show that the finiteness of the $\ell$-primary torsion
subgroup of the higher Brauer group is a sufficient criterion for the Tate
conjecture to hold. Furthermore, we extend methods for computations of
transcendental Brauer groups to higher Brauer groups.


title: Boundedness of varieties of log general type

abstract:
  We survey recent results on the boundedness of the moduli functor of stable
pairs


title: On absolute nonshadowability of transitive maps

abstract:
  We study shadowing property for random infinite pseudotrajectories of a
continuous map $f$ of a compact metric space. For the cases of transitive maps
and transitive attractors we prove a dichotomy: either $f$ satisfies shadowing
property or random pseudotrajectory is shadowable with probability 0.


title:
Comprehensive Reactive Receiver Modeling for Diffusive Molecular
  Communication Systems: Reversible Binding, Molecule Degradation, and Finite
  Number of Receptors

abstract:
  This paper studies the problem of receiver modeling in molecular
communication systems. We consider the diffusive molecular communication
channel between a transmitter nano-machine and a receiver nano-machine in a
fluid environment. The information molecules released by the transmitter
nano-machine into the environment can degrade in the channel via a first-order
degradation reaction and those that reach the receiver nano-machine can
participate in a reversible bimolecular reaction with receiver receptor
proteins. Thereby, we distinguish between two scenarios. In the first scenario,
we assume that the entire surface of the receiver is covered by receptor
molecules. We derive a closed-form analytical expression for the expected
received signal at the receiver, i.e., the expected number of activated
receptors on the surface of the receiver. Then, in the second scenario, we
consider the case where the number of receptor molecules is finite and the
uniformly distributed receptor molecules cover the receiver surface only
partially. We show that the expected received signal for this scenario can be
accurately approximated by the expected received signal for the first scenario
after appropriately modifying the forward reaction rate constant. The accuracy
of the derived analytical results is verified by Brownian motion particle-based
simulations of the considered environment, where we also show the impact of the
effect of receptor occupancy on the derived analytical results.


title:
Fading Coronal Structure and the Onset of Turbulence in the Young Solar
  Wind

abstract:
  Above the top of the solar corona, the young slow solar wind transitions from
low-beta, magnetically structured flow dominated by radial structures, to
high-beta, less structured flow dominated by hydrodynamics. This transition,
long inferred via theory, is readily apparent in the sky region close to 10
degrees from the Sun, in processed, background-subtracted solar wind images. We
present image sequences collected by the STEREO/HI1 instrument in 2008 Dec,
covering apparent distances from approximately 4 to 24 degrees from the center
of the Sun and spanning this transition in large-scale morphology of the wind.
We describe the observation and novel techniques to extract evolving image
structure from the images, and we use those data and techniques to present and
quantify the clear textural shift in the apparent structure of the corona and
solar wind in this altitude range. We demonstrate that the change in apparent
texture is due both to anomalous fading of the radial striae that characterize
the corona, and to anomalous relative brightening of locally dense puffs of
solar wind that we term "flocculae;" and show that these phenomena are
inconsistent with smooth radial flow, but consistent with onset of hydrodynamic
or MHD instabilities leading to a turbulent cascade in the young solar wind.


title: Boson/Fermion Janus Particles

abstract:
  Thermodynamically, bosons and fermions differ by their statistics only. A
general entropy functional is proposed by superposition of entropic terms,
typical for different quantum gases. The statistical properties of the
corresponding Janus particles are derived by variation of the weight of the
boson/fermion fraction. It is shown that di-bosons and anti-fermions separate
in gas and liquid phases, while three-phase equilibrium appears for
poly-boson/fermion Janus particles.


title:
Epitaxial graphene homogeneity and quantum Hall effect in
  millimeter-scale devices

abstract:
  Quantized magnetotransport is observed in 5.6 x 5.6 mm^2 epitaxial graphene
devices, grown using highly constrained sublimation on the Si-face of SiC(0001)
at high temperature (1900 {\deg}C). The precise quantized Hall resistance of
Rxy = h/2e^2 is maintained up to record level of critical current Ixx = 0.72 mA
at T = 3.1 K and 9 T in a device where Raman microscopy reveals low and
homogeneous strain. Adsorption-induced molecular doping in a second device
reduced the carrier concentration close to the Dirac point(n ~ 1E10 (1/cm^2)),
where mobility of 43700 cm^2/Vs is measured over an area of 10 mm^2. Atomic
force, confocal optical, and Raman microscopies are used to characterize the
large-scale devices, and reveal improved SiC terrace topography and the
structure of the graphene layer. Our results show that the structural
uniformity of epitaxial graphene produced by face-to-graphite processing
contributes to millimeter-scale transport homogeneity, and will prove useful
for scientific and commercial applications.


title:
Mapping the kinetic Sunyaev-Zel'dovich effect toward MACS J0717.5+3745
  with NIKA

abstract:
  Measurement of the gas velocity distribution in galaxy clusters provides
insight into the physics of mergers, through which large scale structures form
in the Universe. Velocity estimates within the intracluster medium (ICM) can be
obtained via the Sunyaev-Zel'dovich (SZ) effect, but its observation is
challenging both in term of sensitivity requirement and control of systematic
effects, including the removal of contaminants. In this paper we report
resolved observations, at 150 and 260 GHz, of the SZ effect toward the triple
merger MACS J0717.5+3745 (z=0.55), using data obtained with the NIKA camera at
the IRAM 30m telescope. Assuming that the SZ signal is the sum of a thermal
(tSZ) and a kinetic (kSZ) component and by combining the two NIKA bands, we
extract for the first time a resolved map of the kSZ signal in a cluster. The
kSZ signal is dominated by a dipolar structure that peaks at -5.1 and +3.4
sigma, corresponding to two subclusters moving respectively away and toward us
and coincident with the cold dense X-ray core and a hot region undergoing a
major merging event. We model the gas electron density and line-of-sight
velocity of MACS J0717.5+3745 as four subclusters. Combining NIKA data with
X-ray observations from XMM-Newton and Chandra, we fit this model to constrain
the gas line-of-sight velocity of each component, and we also derive, for the
first time, a velocity map from kSZ data (i.e. that is model-dependent). Our
results are consistent with previous constraints on the merger velocities, and
thanks to the high angular resolution of our data, we are able to resolve the
structure of the gas velocity. Finally, we investigate possible contamination
and systematic effects with a special care given to radio and submillimeter
galaxies. Among the sources that we detect with NIKA, we find one which is
likely to be a high redshift lensed submillimeter galaxy.


title: Neural Network Based Next-Song Recommendation

abstract:
  Recently, the next-item/basket recommendation system, which considers the
sequential relation between bought items, has drawn attention of researchers.
The utilization of sequential patterns has boosted performance on several kinds
of recommendation tasks. Inspired by natural language processing (NLP)
techniques, we propose a novel neural network (NN) based next-song recommender,
CNN-rec, in this paper. Then, we compare the proposed system with several NN
based and classic recommendation systems on the next-song recommendation task.
Verification results indicate the proposed system outperforms classic systems
and has comparable performance with the state-of-the-art system.


title: Logical synchronization: how evidence and hypotheses steer atomic clocks

abstract:
  A clock steps a computer through a cycle of phases. For the propagation of
logical symbols from one computer to another, each computer must mesh its
phases with arrivals of symbols from other computers. Even the best atomic
clocks drift unforeseeably in frequency and phase; feedback steers them toward
aiming points that depend on a chosen wave function and on hypotheses about
signal propagation. A wave function, always under-determined by evidence,
requires a guess. Guessed wave functions are coded into computers that steer
atomic clocks in frequency and position---clocks that step computers through
their phases of computations, as well as clocks, some on space vehicles, that
supply evidence of the propagation of signals. Recognizing the dependence of
the phasing of symbol arrivals on guesses about signal propagation elevates
`logical synchronization.' from its practice in computer engineering to a
discipline essential to physics. Within this discipline we begin to explore
questions invisible under any concept of time that fails to acknowledge the
unforeseeable. In particular, variation of spacetime curvature is shown to
limit the bit rate of logical communication.


title:
Sign-changing tower of bubbles for a sinh-Poisson equation with
  asymmetric exponents

abstract:
  Motivated by the statistical mechanics description of stationary
2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity,
we construct a concentrating solution sequence in the form of a tower of
singular Liouville bubbles, each of which has a different degeneracy exponent.
The asymmetry parameter $\gamma\in(0,1]$ corresponds to the ratio between the
intensity of the negatively rotating vortices and the intensity of the
positively rotating vortices. Our solutions correspond to a superposition of
highly concentrated vortex configurations of alternating orientation; they
extend in a nontrivial way some known results for $\gamma=1$. Thus, by
analyzing the case $\gamma\neq1$ we emphasize specific properties of the
physically relevant parameter $\gamma$ in the vortex concentration phenomena.


title:
Prospects for constraining the spin of the massive black hole at the
  Galactic center via the relativistic motion of a surrounding star

abstract:
  In this paper, we investigate the quality of constraining the spin of the
massive black hole (MBH) at the Galactic center (GC) by using full general
relativistic simulations of the motion of a surrounding star. We obtain the
dependence mapping of the spin-induced signals on any spin direction of the MBH
for given example stars, which indicates the feasibility to test whether the
spin direction is the same as the normal of the young stellar disk located at
the GC, and, further to provide insights into the assembly history of the MBH.
We demonstrate the quality of constraining the MBH spin that may be achieved,
given any set of the astrometric and the redshift precisions of observational
facilities. We find that in the ranges of the astrometric and the velocity
precisions with 1--30$\mu$as and 0.1--10 km/s, an improvement in astrometric
precision would be more effective at improving the quality of constraining the
spin than an improvement in velocity precision. We obtain the parameter space
of the semimajor axis and the eccentricity for the orbit of the target star
that a high-precision constraint on the GC MBH spin can be obtained via the
motion of the star. Our results show that the spin of the GC MBH can be
constrained with 1-sigma error <~0.1 or even >~0.02 by monitoring the orbital
motion of a star, if existing as expected, with semimajor axis <~300AU and
eccentricity >~0.95 over a period shorter than a decade through future
facilities.


title: Reorganization of a granular medium around a localized transformation

abstract:
  Physical and chemical transformation processes in reactive granular media
involve the reorganization of the structure. In this paper, we study
experimentally the rearrangements of a two-dimensional (2D) granular packing
undergoing a localized transformation. We track the position and evolution of
all the disks that constitute the granular packing when either a large intruder
shrinks in size or is pulled out of the granular structure. In the two
situations the displacements at long time are similar to 2D quasistatic silo
flows whereas the short-time dynamic is heterogeneous in both space and time.
We observe an avalanchelike behavior with power-law distributed events
uncorrelated in time. In addition, the instantaneous evolutions of the local
solid fraction exhibit self-similar distributions. The averages and the
standard deviations of the solid fraction variations can be rescaled,
suggesting a single mechanism of rearrangement.


title: Products of two proportional primes

abstract:
  In RSA cryptography numbers of the form $pq$, with $p$ and $q$ two distinct
proportional primes play an important role. For a fixed real number $r>1$ we
formalize this by saying that an integer $pq$ is an RSA-integer if $p$ and $q$
are primes satisfying $p<q\le rp$. Recently Dummit, Granville and Kisilevsky
showed that substantially more than a quarter of the odd integers of the form
$pq$ up to $x$, with $p, q$ both prime, satisfy $p\equiv q\equiv 3\pmod{4}$. In
this paper we investigate this phenomenon for RSA-integers. We establish an
analogue of a strong form of the prime number theorem with the logarithmic
integral replaced by a variant. From this we derive an asymptotic formula for
the number of RSA-integers $\le x$ which is much more precise than an earlier
one derived by Decker and Moree in 2008.


title: Groups of piecewise isometric permutations of lattice points

abstract:
  Let M denote either Euclidean or hyperbolic n-space, and let G be a discrete
group of isometries of M, with the property that G respects and acts
tile-transitively on a convex-polyhedral tesselation of M. Given an arbitrary
base point p in M, we consider the orbit Gp in M and define a notion of
"G-polyhedral pieces" S in Gp. The objects of our interest are the groups pi(S)
of all piecewise G-isometric permutations on S.
  In this paper we merely present the two most basic examples, and these play
rather different roles: The case when G = PSL(2,Z) acting on the hyperbolic
plane reveals that the "piecewise hyperbolic" groups phi(Gp) here have
prominent relatives: they are closely related to Richard Thompson's group V.
And in the Euclidean case when G = Isom(Z^n) we find that the "piecewise
Euclidean" groups pei(S) - as well as the corresponding "piecewise translation"
groups pet(S) - have divers but to some extent accessible finiteness
properties.


title: On Lossless Feedback Delay Networks

abstract:
  Lossless Feedback Delay Networks (FDNs) are commonly used as a design
prototype for artificial reverberation algorithms. The lossless property is
dependent on the feedback matrix, which connects the output of a set of delays
to their inputs, and the lengths of the delays. Both, unitary and triangular
feedback matrices are known to constitute lossless FDNs, however, the most
general class of lossless feedback matrices has not been identified. In this
contribution, it is shown that the FDN is lossless for any set of delays, if
all irreducible components of the feedback matrix are diagonally similar to a
unitary matrix. The necessity of the generalized class of feedback matrices is
demonstrated by examples of FDN designs proposed in literature.


title: Comments on fake supersymmetry

abstract:
  Flat domain walls and spherical black holes are solutions to coupled
second-order ODE's of the Hamiltonian form. Hamilton-Jacobi theory then implies
that first-order flow equations always exist (possibly up to isolated
submanifolds). If the first-order equations factorise in a specific way, they
take a form that has been named fake supersymmetry. We point out that this
factorisation is always possible at zero temperature. We therefore propose a
less generic definition of fake supersymmetry, which involves the boundary
conditions in a non-trivial way, and we analyse its physical relevance. For
instance attractor flows are necessarily fake supersymmetric in our restricted
sense. To illustrate the definition we provide new analytic solutions for
axion-dilaton domain walls with fake superpotentials that were argued not to
exist.


title:
On the continuous dependence on the coefficients of evolutionary
  equations

abstract:
  In an abstract Hilbert space setting, we discuss many linear phenomena of
mathematical physics. The functional analytic framework presented is used to
address continuous dependence of the solution operators
$\mathcal{S}(\mathcal{M})$ of certain (linear partial differential) equations
on the coefficients $\mathcal{M}$. For this, we introduce a particular class of
coefficients $\mathcal{M}$ and study the (nonlinear) mapping
$\mathcal{M}\mapsto \mathcal{S}(\mathcal{M})$. We provide criteria that
guarantee the continuity of $\mathcal{S}(\cdot)$ under the norm, the strong,
and the weak operator topology. We exemplify our findings in non-autonomous
electro-magnetic theory, thermodynamics and acoustics.


title:
Simulation and experiments of Stacks of High Temperature Superconducting
  Coated Conductors Magnetized by Pulsed Field Magnetization with Multi-Pulse
  Technique

abstract:
  High temperature superconducting (HTS) bulks or stacks of coated conductors
(CCs) can be magnetized to become trapped field magnets (TFMs). The magnetic
fields of such TFMs can break the limitation of conventional magnets (<2 T), so
they show potential for improving the performance of many electrical
applications that use permanent magnets like rotating machines. Towards
practical or commercial use of TFMs, effective in situ magnetization is one of
the key issues. The pulsed field magnetization (PFM) is among the most
promising magnetization methods in virtue of its compactness, mobility and low
cost. However, due to the heat generation during the magnetization, the trapped
field and flux acquired by PFM usually cannot achieve the full potential of a
sample (acquired by the field cooling or zero field cooling method). The
multi-pulse technique was found to effectively improve the trapped field by PFM
in practice. In this work, a systematic study on the PFM with successive pulses
is presented. A 2D electromagnetic-thermal coupled model with comprehensive
temperature dependent parameters is used to simulate a stack of CCs magnetized
by successive magnetic pulses. An overall picture is built to show how the
trapped field and flux evolve with different pulse sequences and the evolution
patterns are analyzed. Based on the discussion, an operable magnetization
strategy of PFM with successive pulses is suggested to provide more trapped
field and flux. Finally, experimental results of a stack of CCs magnetized by
typical pulse sequences are presented for demonstration.


title:
Revisiting perfect fluid dark matter: Observational constraints from our
  galaxy

abstract:
  We revisit certain features of an assumed spherically symmetric perfect fluid
dark matter halo in the light of the observed data of our galaxy


title:
Explicit solutions and multiplicity results for some equations with the
  $p$-Laplacian

abstract:
  We derive explicit ground state solutions for several equations with the
$p$-Laplacian in $R^n$, including (here $\varphi (z)=z|z|^{p-2}$, with $p>1$)
\[ \varphi \left(u'(r)\right)' +\frac{n-1}{r} \varphi
\left(u'(r)\right)+u^M+u^Q=0 \,. \] The constant $M>0$ is assumed to be below
the critical power, while $Q=\frac{M p-p+1}{p-1}$ is above the critical power.
This explicit solution is used to give a multiplicity result, similarly to C.S.
Lin and W.-M. Ni [11]. We also give the $p$-Laplace version of G. Bratu's
solution [3].
  In another direction, we present a change of variables which removes the
non-autonomous term $r^{\alpha}$ in \[ \varphi \left(u'(r)\right)'
+\frac{n-1}{r} \varphi \left(u'(r)\right)+r^{\alpha} f(u)=0 \,, \] while
preserving the form of this equation. In particular, we study singular
equations, when $\alpha <0$. The Coulomb case $\alpha=-1$ turned out to give
the critical power.


title:
Riccati observers for position and velocity bias estimation from either
  direction or range measurements

abstract:
  This paper revisits the problems of estimating the position of an object
moving in $n$ ($\geq 2$)-dimensional Euclidean space using velocity
measurements and either direction or range measurements of one or multiple
source points. The proposed solutions exploit the Continuous Riccati Equation
(CRE) to calculate observer gains yielding global exponential stability of zero
estimation errors, even in the case where the measured velocity is biased by an
unknown constant perturbation. These results are obtained under persistent
excitation (p.e.) conditions depending on the number of source points and body
motion that ensure both uniform observability and good conditioning of the CRE
solutions. With respect to prior contributions on these subjects some of the
proposed solutions are entirely novel while others are adapted from existing
ones with the preoccupation of stating simpler and more explicit conditions
under which uniform exponential stability is achieved. A complementary
contribution, related to the delicate tuning of the observers gains, is the
derivation of a lower-bound of the exponential rate of convergence specified as
a function of the amount of persistent excitation. Simulation results
illustrate the performance of the proposed observers.


title: Issues in evaluating semantic spaces using word analogies

abstract:
  The offset method for solving word analogies has become a standard evaluation
tool for vector-space semantic models: it is considered desirable for a space
to represent semantic relations as consistent vector offsets. We show that the
method's reliance on cosine similarity conflates offset consistency with
largely irrelevant neighborhood structure, and propose simple baselines that
should be used to improve the utility of the method in vector space evaluation.


title: Effective field theory approach to heavy quark fragmentation

abstract:
  Using an approach based on Soft Collinear Effective Theory (SCET) and Heavy
Quark Effective Theory (HQET) we determine the $b$-quark fragmentation function
from electron-positron annihilation data at the $Z$-boson peak at
next-to-next-to leading order, with next-to-next-to leading log resummation of
DGLAP logarithms, and next-to-next-to-next-to leading log resummation of
endpoint logarithms. This analysis improves, by one order, the previous
extraction of the $b$-quark fragmentation function. We find that while the
addition of the next order in the calculation does not much shift the extracted
form of the fragmentation function, it does reduce theoretical errors
indicating that the expansion is converging. Using an approach based on
effective field theory allows us to systematically control theoretical errors.
While the fits of theory to data are generally good, the fits seem to be
hinting that higher order correction from HQET may be needed to explain the
$b$-quark fragmentation function at smaller values of momentum fraction.


title:
Finite-dimensional approximation and non-squeezing for the cubic
  nonlinear Schr\"odinger equation on $\R^2$

abstract:
  We prove symplectic non-squeezing (in the sense of Gromov) for the cubic
nonlinear Schr\"odinger equation on $\R^2$. This is the first symplectic
non-squeezing result for a Hamiltonian PDE in infinite volume. As the
underlying symplectic Hilbert space is $L^2(\R^2)$, this requires working with
initial data in this space. This space also happens to be scaling-critical for
this equation. Thus, we also obtain the first unconditional symplectic
non-squeezing result in such a critical setting.
  More generally, we show that solutions of this PDE can be approximated by a
finite-dimensional Hamiltonian system, despite the wealth of non-compact
symmetries: scaling, translation, and Galilei boosts. This approximation result
holds uniformly on bounded sets of initial data. Complementing this
approximation result, we show that all solutions of the finite-dimensional
Hamiltonian system can be approximated by the full PDE.
  A key ingredient in these proofs is the development of a general methodology
for obtaining uniform global space-time bounds for suitable Fourier truncations
of dispersive PDE models.


title: Symmetries of the Space of Linear Symplectic Connections

abstract:
  There is constructed a family of Lie algebras that act in a Hamiltonian way
on the symplectic affine space of linear symplectic connections on a symplectic
manifold. The associated equivariant moment map is a formal sum of the
Cahen-Gutt moment map, the Ricci tensor, and a translational term. The critical
points of a functional constructed from it interpolate between the equations
for preferred symplectic connections and the equations for critical symplectic
connections. The commutative algebra of formal sums of symmetric tensors on a
symplectic manifold carries a pair of compatible Poisson structures, one
induced from the canonical Poisson bracket on the space of functions on the
cotangent bundle polynomial in the fibers, and the other induced from the
algebraic fiberwise Schouten bracket on the symmetric algebra of each fiber of
the cotangent bundle. These structures are shown to be compatible, and the
required Lie algebras are constructed as central extensions of their linear
combinations restricted to formal sums of symmetric tensors whose first order
term is a multiple of the differential of its zeroth order term.


title:
Inhomogeneous quasi-adiabatic driving of quantum critical dynamics in
  weakly disordered spin chains

abstract:
  We introduce an inhomogeneous protocol to drive a weakly disordered quantum
spin chain quasi-adiabatically across a quantum phase transition and minimize
the residual energy of the final state. The number of spins that simultaneously
reach the critical point is controlled by the length scale in which the
magnetic field is modulated, introducing an effective size that favors
adiabatic dynamics. The dependence of the residual energy on this length scale
and the velocity at which the magnetic field sweeps out the chain is shown to
be nonmonotonic. We determine the conditions for an optimal suppression of the
residual energy of the final state and show that inhomogeneous driving can
outperform conventional adiabatic schemes based on homogeneous control fields
by several orders of magnitude.


title:
The Hanle and Zeeman polarization signals of the solar Ca II 8542 \AA\
  line

abstract:
  We highlight the main results of a three-dimensional (3D) multilevel
radiative transfer investigation about the solar disk-center polarization of
the Ca {\sc ii} 8542 \AA\ line. First, we investigate the linear polarization
due to the atomic level polarization produced by the absorption and scattering
of anisotropic radiation in a 3D model of the solar atmosphere, taking into
account the symmetry breaking effects caused by its thermal, dynamic and
magnetic structure. Second, we study the contribution of the Zeeman effect to
the linear and circular polarization. Finally, we show examples of the Stokes
profiles produced by the joint action of atomic level polarization and the
Hanle and Zeeman effects. We find that the Zeeman effect tends to dominate the
linear polarization signals only in the localized patches of opposite magnetic
polarity where the magnetic field is relatively strong and slightly inclined,
while outside such very localized patches the linear polarization is often
dominated by the contribution of atomic level polarization. We demonstrate that
a correct modeling of this last contribution requires taking into account the
symmetry breaking effects caused by the thermal, dynamic and magnetic structure
of the solar atmosphere, and that in the 3D model used the Hanle effect in
forward-scattering geometry (disk center observation) mainly reduces the
polarization corresponding to the zero-field case. We emphasize that, in
general, a reliable modeling of the linear polarization in the Ca {\sc ii} 8542
\AA\ line requires taking into account the joint action of atomic level
polarization and the Hanle and Zeeman effects.


title:
A kinetic regime of hydrodynamic fluctuations and long time tails for a
  Bjorken expansion

abstract:
  We develop a set of kinetic equations for hydrodynamic fluctuations which are
equivalent to nonlinear hydrodynamics with noise. The hydro-kinetic equations
can be coupled to existing second order hydrodynamic codes to incorporate the
physics of these fluctuations. We first show that the kinetic response
precisely reproduces the renormalization of the shear viscosity and the
fractional power ($\propto \omega^{3/2}$) which characterizes equilibrium
correlators of energy and momentum for a static fluid. Then we use the
hydro-kinetic equations to analyze thermal fluctuations for a Bjorken
expansion, evaluating the contribution of thermal noise from the earliest
moments and at late times. In the Bjorken case, the solution to the kinetic
equations determines the coefficient of the first fractional power of the
gradient expansion ($\propto 1/(\tau T)^{3/2}$) for the expanding system.
Numerically, we find that the contribution to the longitudinal pressure from
hydrodynamic fluctuations is larger than second order hydrodynamics for typical
medium parameters used to simulate heavy ion collisions.


title:
Orbital stability of coplanar two-planet exosystems with high
  eccentricities

abstract:
  The long-term stability of the evolution of two-planet systems is considered
by using the general three body problem (GTBP). Our study is focused on the
stability of systems with adjacent orbits when at least one of them is highly
eccentric. In these cases, in order for close encounters, which destabilize the
planetary systems, to be avoided, phase protection mechanisms should be
considered. Additionally, since the GTBP is a non-integrable system, chaos may
also cause the destabilization of the system after a long time interval. By
computing dynamical maps, based on Fast Lyapunov Indicator, we reveal regions
in phase space with stable orbits even for very high eccentricities (e>0.5).
Such regions are present in mean motion resonances (MMR). We can determine the
position of the exact MMR through the computation of families of periodic
orbits in a rotating frame. Elliptic periodic orbits are associated with the
presence of apsidal corotation resonances (ACR). When such solutions are
stable, they are associated with neighbouring domains of initial conditions
that provide long-term stability. We apply our methodology so that the
evolution of planetary systems of highly eccentric orbits is assigned to the
existence of such stable domains. Particularly, we study the orbital evolution
of the extrasolar systems HD 82943, HD 3651, HD 7449, HD 89744 and HD 102272
and discuss the consistency between the orbital elements provided by the
observations and the dynamical stability.


title: On some links between quantum physics and gravitation

abstract:
  It is widely believed that quantum gravity effects are negligible in a
conventional laboratory experiment because quantum gravity should play its role
only at a distance of about Planck's length ($\sim10^{-33}$ cm). Sometimes that
is not the case as shown in this article. We discuss two new ideas about
quantum physics connections with gravity. First, the Hong-Ou-Mandel effect
relation to quantum gravity is examined. Second, it is shown that the very
existence of gravitons is a consequence of quantum statistics. Moreover, since
the Bose-Einstein statistics is a special case of Compound Poisson
Distribution, it predicts the existence of an infinite family of high-spin
massless particles.


title:
Interstellar Gas and X-rays toward the Young Supernova Remnant RCW 86;
  Pursuit of the Origin of the Thermal and Non-Thermal X-ray

abstract:
  We have analyzed the atomic and molecular gas using the 21 cm HI and 2.6/1.3
mm CO emissions toward the young supernova remnant (SNR) RCW 86 in order to
identify the interstellar medium with which the shock waves of the SNR
interact. We have found an HI intensity depression in the velocity range
between $-46$ and $-28$ km s$^{-1}$ toward the SNR, suggesting a cavity in the
interstellar medium. The HI cavity coincides with the thermal and non-thermal
emitting X-ray shell. The thermal X-rays are coincident with the edge of the HI
distribution, which indicates a strong density gradient, while the non-thermal
X-rays are found toward the less dense, inner part of the HI cavity. The most
significant non-thermal X-rays are seen toward the southwestern part of the
shell where the HI gas traces the dense and cold component. We also identified
CO clouds which are likely interacting with the SNR shock waves in the same
velocity range as the HI, although the CO clouds are distributed only in a
limited part of the SNR shell. The most massive cloud is located in the
southeastern part of the shell, showing detailed correspondence with the
thermal X-rays. These CO clouds show an enhanced CO $J$ = 2-1/1-0 intensity
ratio, suggesting heating/compression by the shock front. We interpret that the
shock-cloud interaction enhances non-thermal X-rays in the southwest and the
thermal X-rays are emitted by the shock-heated gas of density 10-100 cm$^{-3}$.
Moreover, we can clearly see an HI envelope around the CO cloud, suggesting
that the progenitor had a weaker wind than the massive progenitor of the
core-collapse SNR RX J1713.7$-$3949. It seems likely that the progenitor of RCW
86 was a system consisting of a white dwarf and a low-mass star with
low-velocity accretion winds.


title: Casimir free energy and pressure for magnetic metal films

abstract:
  We examine the Casimir free energy and pressure of magnetic metal films,
which are free-standing in vacuum, sandwiched between two dielectric plates,
and deposited on either nonmagnetic or magnetic metallic plates. All
calculations are performed using both the Drude and plasma model approaches to
the Lifshitz theory. According to our results, the Casimir free energies and
pressures calculated using both theoretical approaches are significantly
different in the magnitude and sign even for thin films of several tens of
nanometers thickness. Thus, for the Ni film of 47\,nm thickness deposited on a
Fe plate the obtained magnitudes of the Casimir free energy differ by the
factor of 5866. We show that the Casimir free energy and pressure of a magnetic
film calculated using the plasma model approach do not possess the classical
limit, but exponentially fast drop to zero with increasing film thickness. If
the Drude model approach is used, the classical limit is reached for magnetic
films of about 150\,nm thickness, but the Casimir free energy remains nonzero
in the limit of ideal metal, contrary to expectations. For the plasma model
approach the Casimir free energy of a film vanishes in this case. Numerical
computations are performed for the magnetic films made of Ni, nonmagnetic
plates made of Cu and Al, and magnetic plates made of Fe using the tabulated
optical data for the complex indexes of refraction of all metals. The obtained
results can be used for a discrimination between the plasma and Drude model
approaches in the Casimir physics and in the investigation of stability of thin
films.


title:
Magneto-oscillations of the mobility edge in Coulomb frustrated bosons
  and fermions

abstract:
  We study the crossover from strong to weak localization of hard-core bosons
on a two dimensional honeycomb lattice in a magnetic field, as motivated by
recent experiments on structured films. Taking into account long range Coulomb
interactions among the bosons, an effective mobility edge in the excitation
spectrum of the insulating Bose glass is identified as the (intensive) energy
scale at which excitations become nearly delocalized. Within the forward
scattering approximation in the bosonic hopping we find the effective mobility
edge $\epsilon_c$ to oscillate periodically with the magnetic flux per
plaquette, $\phi$. We find non-analytic cusps in $\epsilon_c(\phi)$ at integer
or half-integer flux. The bosonic magneto-oscillations start with an increase
of the mobility edge (and thus of resistance) with applied flux, in contrast to
the equivalent fermionic problem. The amplitude of the oscillations is much
more substantial in bosons than in fermions. Bosons exhibit a single hump per
flux period, while fermion characteristics undergo two humps. Those are
identical for non-interacting fermions, but Coulomb correlations are shown to
lead to systematic deviations from this statistical period doubling. Our theory
reproduces several key features observed in the activated magneto-transport in
structured films.


title:
Global Properties of Nested Network Model with Application to
  Multi-Epitope HIV/CTL Dynamics

abstract:
  Mathematical modeling and analysis can provide insight on the dynamics of
ecosystems which maintain biodiversity in the face of competitive and
prey-predator interactions. Of primary interests are the underlying structure
and features which stabilize diverse ecological networks. Recently Korytowski
and Smith [17] proved that a perfectly nested infection network, along with
appropriate life history trade-offs, leads to coexistence and persistence of
bacteria-phage communities in a chemostat model. In this article, we generalize
their model in order to apply it to the within-host dynamics virus and immune
response, in particular HIV and CTL (Cytotoxic T Lymphocyte) cells. Our model
can produce a diverse hierarchy of viral and immune populations, built through
sequential viral escape from dominant immune responses and rise in subdominant
immune responses, consistent with observed patterns of HIV/CTL evolution. We
find a Lyapunov function for the system which leads to rigorous
characterization of persistent viral and immune variants, and informs upon
equilibria stability and global dynamics. Results are interpreted in the
context of within-host HIV/CTL evolution and numerical simulations are
provided.


title:
Semiparametrically Efficient Estimation of Euclidean Parameters under
  Equality Constraints

abstract:
  Assume a (semi)parametrically efficient estimator is given of the Euclidean
parameter in a (semi)parametric model. A submodel is obtained by constraining
this model in that a continuously differentiable function of the Euclidean
parameter vanishes. We present an explicit method to construct
(semi)parametrically efficient estimators of the Euclidean parameter in such
equality constrained submodels and prove their efficiency. Our construction is
based solely on the original efficient estimator and the constraining function.
  Only the parametric case of this estimation problem and a nonparametric
version of it have been considered in literature.


title: Self-Reciprocal Polynomials and Coterm Polynomials

abstract:
  We classify all self-reciprocal polynomials arising from reversed Dickson
polynomials over $\mathbb{Z}$ and $\mathbb{F}_p$, where $p$ is prime. As a
consequence, we also obtain coterm polynomials arising from reversed Dickson
polynomials.


title: Beltrami equations in the plane and Sobolev regularity

abstract:
  New results regarding the Sobolev regularity of the principal solution of the
linear Beltrami equation $\bar{\partial} f = \mu \partial f + \nu
\overline{\partial f}$ for discontinuous Beltrami coefficients $\mu$ and $\nu$
are obtained, using Kato-Ponce commutators, obtaining that $\overline \partial
f$ belongs to a Sobolev space with the same smoothness as the coefficients but
some loss in the integrability parameter. A conjecture on the cases where the
limitations of the method do not work is raised.


title:
Global exponential stabilisation for the Burgers equation with localised
  control

abstract:
  We consider the 1D viscous Burgers equation with a control localised in a
finite interval. It is proved that, for any $\varepsilon>0$, one can find a
time $T$ of order $\log\varepsilon^{-1}$ such that any initial state can be
steered to the $\varepsilon$-neighbourhood of a given trajectory at time $T$.
This property combined with an earlier result on local exact controllability
shows that the Burgers equation is globally exactly controllable to
trajectories in a finite time. We also prove that the approximate
controllability to arbitrary targets does not hold even if we allow infinite
time of control.


title: Analogues of Jacobi's derivative formula III

abstract:
  In this paper, we realize high-level versions of Jacobi's derivative formula
to all the rational characteristics corresponding to level $k \,\,(k=3,4,5,6).$
For this purpose, we propose the method to obtain derivative formulas by means
of the residue theorem. We believe that this method can be also applied to all
the rational characteristics corresponding to level $k\ge 7.$


title: Infinite J-matrices and a matrix moment problem

abstract:
  This is a translation of a paper that appeared (in Russian) in Dokl. Akad.
Nauk SSSR 69, nr 2 (1949), 125-128.


title:
Improved Finite Difference Method with a Compact Correction Term for
  Solving Poisson's Equations

abstract:
  An improved finite difference method with compact correction term is proposed
to solve the Poisson equations. The compact correction term is developed by a
coupled high-order compact and low-order classical finite difference
formulations. The numerical solutions obtained by the classical finite
difference method are considered as fundamental solutions with lower accuracy,
whereas compact correction term is added into source term of classical discrete
formulation to improve the accuracy of numerical solutions. The proposed method
can be extended from two- to multi-dimensional cases straightforwardly.
Numerical experiments are carried out to verify the accuracy and efficiency of
this method.


title: Anisotropic Long-Range Spin Systems

abstract:
  We consider anisotropic long-range interacting spin systems in $d$
dimensions. The interaction between the spins decays with the distance as a
power law with different exponents in different directions: we consider an
exponent $d_{1}+\sigma_1$ in $d_1$ directions and another exponent
$d_{2}+\sigma_2$ in the remaining $d_2\equiv d-d_1$ ones. We introduce a low
energy effective action with non analytic power of the momenta. As a function
of the two exponents $\sigma_1$ and $\sigma_2$ we show the system to have three
different regimes, two where it is actually anisotropic and one where the
isotropy is finally restored. We determine the phase diagram and provide
estimates of the critical exponents as a function of the parameters of the
system, in particular considering the case of one of the two $\sigma$'s fixed
and the other varying. A discussion of the physical relevance of our results is
also presented.


title:
A Taxonomy and Library for Visualizing Learned Features in Convolutional
  Neural Networks

abstract:
  Over the last decade, Convolutional Neural Networks (CNN) saw a tremendous
surge in performance. However, understanding what a network has learned still
proves to be a challenging task. To remedy this unsatisfactory situation, a
number of groups have recently proposed different methods to visualize the
learned models. In this work we suggest a general taxonomy to classify and
compare these methods, subdividing the literature into three main categories
and providing researchers with a terminology to base their works on.
Furthermore, we introduce the FeatureVis library for MatConvNet: an extendable,
easy to use open source library for visualizing CNNs. It contains
implementations from each of the three main classes of visualization methods
and serves as a useful tool for an enhanced understanding of the features
learned by intermediate layers, as well as for the analysis of why a network
might fail for certain examples.


title:
Excess magneto-resistance in multiband superconductors due to the
  viscous flow of composite vortices

abstract:
  By using the time-dependent Ginzburg-Landau theory, we show that extremely
diverse experimental data on flux-flow resistivity in multiband superconductors
can be qualitatively explained by a composite nature of Abrikosov vortices
consisting of elementary fractional vortices in different bands. In composite
vortices, the ratio of a core size to electric field relaxation length is found
to vary in wide limits depending on system parameters. As a result, the
flux-flow magneto-resistance can strongly exceed the single-component
Bardeen-Stephen estimation provided that moving vortices generate electric
field stretching strongly outside the vortex cores.


title:
The performance of the jet trigger for the ATLAS detector during 2011
  data taking

abstract:
  The performance of the jet trigger for the ATLAS detector at the LHC during
the 2011 data taking period is described. During 2011 the LHC provided
proton-proton collisions with a centre-of-mass energy of 7 TeV and heavy ion
collisions with a 2.76 TeV per nucleon-nucleon collision energy. The ATLAS
trigger is a three level system designed to reduce the rate of events from the
40 MHz nominal maximum bunch crossing rate to the approximate 400 Hz which can
be written to offline storage. The ATLAS jet trigger is the primary means for
the online selection of events containing jets. Events are accepted by the
trigger if they contain one or more jets above some transverse energy
threshold. During 2011 data taking the jet trigger was fully efficient for jets
with transverse energy above 25 GeV for triggers seeded randomly at Level 1.
For triggers which require a jet to be identified at each of the three trigger
levels, full efficiency is reached for offline jets with transverse energy
above 60 GeV. Jets reconstructed in the Event Filter and corresponding to
offline jets with transverse energy greater than 60 GeV, are reconstructed with
a resolution in transverse energy of better than 4% in the central region and
better than 2.5% in the forward direction.


title:
Polynomial-Time Key Recovery Attack on the Faure-Loidreau Scheme based
  on Gabidulin Codes

abstract:
  Encryption schemes based on the rank metric lead to small public key sizes of
order of few thousands bytes which represents a very attractive feature
compared to Hamming metric-based encryption schemes where public key sizes are
of order of hundreds of thousands bytes even with additional structures like
the cyclicity. The main tool for building public key encryption schemes in rank
metric is the McEliece encryption setting used with the family of Gabidulin
codes. Since the original scheme proposed in 1991 by Gabidulin, Paramonov and
Tretjakov, many systems have been proposed based on different masking
techniques for Gabidulin codes. Nevertheless, over the years all these systems
were attacked essentially by the use of an attack proposed by Overbeck.
  In 2005 Faure and Loidreau designed a rank-metric encryption scheme which was
not in the McEliece setting. The scheme is very efficient, with small public
keys of size a few kiloBytes and with security closely related to the
linearized polynomial reconstruction problem which corresponds to the decoding
problem of Gabidulin codes. The structure of the scheme differs considerably
from the classical McEliece setting and until our work, the scheme had never
been attacked. We show in this article that this scheme like other schemes
based on Gabidulin codes, is also vulnerable to a polynomial-time attack that
recovers the private key by applying Overbeck's attack on an appropriate public
code. As an example we break concrete proposed $80$ bits security parameters in
a few seconds.


title: On D-modules related to the b-function and Hamiltonian flow

abstract:
  Let f be a quasi-homogeneous polynomial with an isolated singularity. We
compute the length of the D-modules $Df^c/Df^{c+1}$ generated by complex powers
of f in terms of the Hodge filtration on the top cohomology of the Milnor
fiber. For 1/f we obtain one more than the reduced genus of the singularity. We
conjecture that this holds without the quasi-homogeneous assumption. We also
deduce that the aforementioned quotient is nonzero when c is a root of the
b-function of f (which Saito recently showed fails to hold in the inhomogeneous
case). We obtain these results by comparing these D-modules to those defined by
Etingof and the second author which represent invariants under Hamiltonian
flow.


title:
Active Matter in Lateral Parabolic Confinement: From Subdiffusion to
  Superdiffusion

abstract:
  In this work we studied the diffusive behavior of active brownian particles
under lateral parabolic confinement. The results showed that we go from
subdiffusion to ballistic motion as we vary the angular noise strength and
confinement intensity. We argued that the subdiffusion regimes appear as
consequence of the restricted space available for diffusion (achieved either
through large confinement and/or large noise); we saw that when there are large
confinement and noise intensity, a similar configuration to single file
diffusion appears; on the other hand, normal and superdiffusive regimes may
occur due to low noise (longer persistent motion), either through exploring a
wider region around the potential minimum in the transverse direction (low
confinement), or by forming independent clusters (high confinement).


title:
Mixing for the Burgers equation driven by a localised two-dimensional
  stochastic forcing

abstract:
  We consider the one-dimensional Burgers equation perturbed by a stochastic
forcing, which is assumed to be white in time and localised and low-dimensional
in space. We establish a mixing property for the Markov process associated with
the problem in question. The proof is based on a general criterion for mixing
and a recent result on global approximate controllability to trajectories for
damped conservation laws.


title: Updated determination of $\alpha_s(m_\tau^2)$ from tau decays

abstract:
  Using the most recent release of the ALEPH $\tau$ decay data, we present a
very detailed phenomenological update of the $\alpha_s(m_\tau^2)$
determination. We have exploited the sensitivity to the strong coupling in many
different ways, exploring several complementary methodologies. All
determinations turn out to be in excellent agreement, allowing us to extract a
very reliable value of the strong coupling. We find
$\alpha_{s}^{(n_f=3)}(m_\tau^2) = 0.328 \pm 0.012$ which implies
$\alpha_{s}^{(n_f=5)}(M_Z^{2}) = 0.1197\pm 0.0014$. We critically revise
previous work, and point out the problems flawing some recent analyses which
claim slightly smaller values.


title:
The Clausius-Mossotti formula for dilute random media of perfectly
  conducting inclusions

abstract:
  We consider a large number of randomly dispersed spherical, identical,
perfectly conducting inclusions (of infinite conductivity) in a bounded domain.
The host medium's conductivity is finite and can be inhomogeneous. In the
dilute limit, with some boundedness assumption on a large number (proportional
to the global volume fraction raised to the power of -1/2) of marginal
probability densities, we prove convergence in H^1 norm of the expectation of
the solution of the steady state heat equation, to the solution of an effective
medium problem, where the conductivity is given by the Clausius-Mossotti
formula. Error estimates are provided as well.


title: Charge density wave modulation and gap measurements in CeTe$_3$

abstract:
  We present a study of charge density wave (CDW) ordering in CeTe$_3$ at room
temperature using a scanning tunneling microscope and Raman spectroscopy. Two
characteristic CDW ordering wavevectors obtained from the Fourier analysis are
assessed to be $|{\bf \textbf{c}}^\ast-{\bf q}|=4.19\,{\rm nm}^{-1}$ and $|{\bf
q}|=10.26\,{\rm nm}^{-1}$ where $|{\bf c}^\ast| = 2\pi/c$ is the reciprocal
lattice vector. The scanning tunneling spectroscopy measurements, along with
inelastic light (Raman) scattering measurements, show a CDW gap $\Delta_{\rm
max}$ of approximately 0.37 eV. In addition to the CDW modulation, we observe
an organization of the Te sheet atoms in an array of alternating V- and N-
groups along the CDW modulation, as predicted in the literature.


title:
Sampling-based Gradient Regularization for Capturing Long-Term
  Dependencies in Recurrent Neural Networks

abstract:
  Vanishing (and exploding) gradients effect is a common problem for recurrent
neural networks with nonlinear activation functions which use backpropagation
method for calculation of derivatives. Deep feedforward neural networks with
many hidden layers also suffer from this effect. In this paper we propose a
novel universal technique that makes the norm of the gradient stay in the
suitable range. We construct a way to estimate a contribution of each training
example to the norm of the long-term components of the target function s
gradient. Using this subroutine we can construct mini-batches for the
stochastic gradient descent (SGD) training that leads to high performance and
accuracy of the trained network even for very complex tasks. We provide a
straightforward mathematical estimation of minibatch s impact on for the
gradient norm and prove its correctness theoretically. To check our framework
experimentally we use some special synthetic benchmarks for testing RNNs on
ability to capture long-term dependencies. Our network can detect links between
events in the (temporal) sequence at the range approx. 100 and longer.


title: Non-Equilibrium Random Matrix Theory : Transition Probabilities

abstract:
  In this letter we present an analytic method for calculating the transition
probability between two random Gaussian matrices with given eigenvalue spectra
in the context of Dyson Brownian motion. We show that in the Coulomb gas
language, in large $N$ limit, memory of the initial state is preserved in the
form of a universal linear potential acting on the eigenvalues. We compute the
likelihood of any given transition as a function of time, showing that as
memory of the initial state is lost, transition probabilities converge to those
of the static ensemble.

categories: cond-mat.stat-mech hep-th math-ph math.MP


title: How to estimate epidemic risk from incomplete contact diaries data?

abstract:
  Social interactions shape the patterns of spreading processes in a
population. Techniques such as diaries or proximity sensors allow to collect
data about encounters and to build networks of contacts between individuals.
The contact networks obtained from these different techniques are however
quantitatively different. Here, we first show how these discrepancies affect
the prediction of the epidemic risk when these data are fed to numerical models
of epidemic spread: low participation rate, under-reporting of contacts and
overestimation of contact durations in contact diaries with respect to sensor
data determine indeed important differences in the outcomes of the
corresponding simulations {with for instance an enhanced sensitivity to initial
conditions}. Most importantly, we investigate if and how information gathered
from contact diaries can be used in such simulations in order to yield an
accurate description of the epidemic risk, assuming that data from sensors
represent the ground truth. The contact networks built from contact sensors and
diaries present indeed several structural similarities: this suggests the
possibility to construct, using only the contact diary network information, a
surrogate contact network such that simulations using this surrogate network
give the same estimation of the epidemic risk as simulations using the contact
sensor network. We present and {compare} several methods to build such
surrogate data, and show that it is indeed possible to obtain a good agreement
between the outcomes of simulations using surrogate and sensor data, as long as
the contact diary information is complemented by publicly available data
describing the heterogeneity of the durations of human contacts.


title: Captioning Images with Diverse Objects

abstract:
  Recent captioning models are limited in their ability to scale and describe
concepts unseen in paired image-text corpora. We propose the Novel Object
Captioner (NOC), a deep visual semantic captioning model that can describe a
large number of object categories not present in existing image-caption
datasets. Our model takes advantage of external sources -- labeled images from
object recognition datasets, and semantic knowledge extracted from unannotated
text. We propose minimizing a joint objective which can learn from these
diverse data sources and leverage distributional semantic embeddings, enabling
the model to generalize and describe novel objects outside of image-caption
datasets. We demonstrate that our model exploits semantic information to
generate captions for hundreds of object categories in the ImageNet object
recognition dataset that are not observed in MSCOCO image-caption training
data, as well as many categories that are observed very rarely. Both automatic
evaluations and human judgements show that our model considerably outperforms
prior work in being able to describe many more categories of objects.


title: On the number of periodic geodesics in rank 1 surfaces

abstract:
  We consider the geodesic flow of a compact connected rank 1 surface. We prove
a formula for the topological pressure as the exponential growth rate of rank 1
periodic geodesics generalizing a previous result of K. Gelfert and B. Schapira
[12].


title: The emotional arcs of stories are dominated by six basic shapes

abstract:
  Advances in computing power, natural language processing, and digitization of
text now make it possible to study a culture's evolution through its texts
using a "big data" lens. Our ability to communicate relies in part upon a
shared emotional experience, with stories often following distinct emotional
trajectories and forming patterns that are meaningful to us. Here, by
classifying the emotional arcs for a filtered subset of 1,327 stories from
Project Gutenberg's fiction collection, we find a set of six core emotional
arcs which form the essential building blocks of complex emotional
trajectories. We strengthen our findings by separately applying Matrix
decomposition, supervised learning, and unsupervised learning. For each of
these six core emotional arcs, we examine the closest characteristic stories in
publication today and find that particular emotional arcs enjoy greater
success, as measured by downloads.


title: Higgs sector with spontaneous CP violation in $S(3)$ Standard Model

abstract:
  Conditions for spontaneous Charge-Parity (CP) violation in the scalar
potential sector of general $S(3)$ Higgs-doublet model (3HDM) are analyzed. An
analysis of the Higgs sector of the minimal $S(3)$-invariant extension of the
Standard Model including CP violation arising from the spontaneous breaking of
the electroweak symmetry is presented. This extended Higgs sector with three
SU(2) doublets Higgs fields with complex vev's provides an interesting scenario
to analyze the Higgs masses spectrum, trilinear self-couplings and CP
violation. We present how the spontaneous electroweak symmetry breaking, coming
from three $S(3)$ Higgs fields, gives an interesting scenario with nine
physical Higgs and three Goldstone bosons, when spontaneous CP violation arises
from the Higgs field $S(3)$ singlet $H_S$.


title: Temporal multimode storage of entangled photon pairs

abstract:
  Multiplexed quantum memories capable of storing and processing entangled
photons are essential for the development of quantum networks. In this context,
we demonstrate the simultaneous storage and retrieval of two entangled photons
inside a solid-state quantum memory and measure a temporal multimode capacity
of ten modes. This is achieved by producing two polarization entangled pairs
from parametric down conversion and mapping one photon of each pair onto a
rare-earth-ion doped (REID) crystal using the atomic frequency comb (AFC)
protocol. We develop a concept of indirect entanglement witnesses, which can be
used as Schmidt number witness, and we use it to experimentally certify the
presence of more than one entangled pair retrieved from the quantum memory. Our
work puts forward REID-AFC as a platform compatible with temporal multiplexing
of several entangled photon pairs along with a new entanglement certification
method useful for the characterisation of multiplexed quantum memories.


title: How van der Waals interactions determine the unique properties of water

abstract:
  While the interactions between water molecules are dominated by strongly
directional hydrogen bonds (HBs), it was recently proposed that relatively
weak, isotropic van der Waals (vdW) forces are essential for understanding the
properties of liquid water and ice. This insight was derived from ab initio
computer simulations, which provide an unbiased description of water at the
atomic level and yield information on the underlying molecular forces. However,
the high computational cost of such simulations prevents the systematic
investigation of the influence of vdW forces on the thermodynamic anomalies of
water. Here we develop efficient ab initio-quality neural network potentials
and use them to demonstrate that vdW interactions are crucial for the formation
of water's density maximum and its negative volume of melting. Both phenomena
can be explained by the flexibility of the HB network, which is the result of a
delicate balance of weak vdW forces, causing e.g. a pronounced expansion of the
second solvation shell upon cooling that induces the density maximum.

categories: physics.comp-ph cond-mat.other cond-mat.stat-mech physics.chem-ph


title: Ultra-thin metamaterial for perfect and omnidirectional sound absorption

abstract:
  Using the concepts of slow sound and of critical coupling, an ultra-thin
acoustic metamaterial panel for perfect and omnidirectional absorption is
theoretically and experimentally conceived in this work. The system is made of
a rigid panel with a periodic distribution of thin closed slits, the upper wall
of which is loaded by Helmholtz Resonators (HRs). The presence of resonators
produces a slow sound propagation shifting the resonance frequency of the slit
to the deep sub-wavelength regime ($\lambda/88$). By controlling the geometry
of the slit and the HRs, the intrinsic visco-thermal losses can be tuned in
order to exactly compensate the energy leakage of the system and fulfill the
critical coupling condition to create the perfect absorption of sound in a
large range of incidence angles due to the deep subwavelength behavior.


title:
Action selection in growing state spaces: Control of Network Structure
  Growth

abstract:
  The dynamical processes taking place on a network depend on its topology.
Influencing the growth process of a network therefore has important
implications on such dynamical processes. We formulate the problem of
influencing the growth of a network as a stochastic optimal control problem in
which a structural cost function penalizes undesired topologies. We approximate
this control problem with a restricted class of control problems that can be
solved using probabilistic inference methods. To deal with the increasing
problem dimensionality, we introduce an adaptive importance sampling method for
approximating the optimal control. We illustrate this methodology in the
context of formation of information cascades, considering the task of
influencing the structure of a growing conversation thread, as in Internet
forums. Using a realistic model of growing trees, we show that our approach can
yield conversation threads with better structural properties than the ones
observed without control.