prompt stringlengths 15 200 | answer stringlengths 0 425k |
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\section{Introduction}
\label{intro}
The central goal of the beam energy scan (BES) program at RHIC is to seek
evidence for the existence of a critical point in the phase
diagram of strong-interaction | matter. The hope is to detect this
postulated second order
phase transition point through the analysis of higher order cumulants
of net charge fluctuations. Maxima of cumulants of net charge fluctuations,
e.g. the $2^{nd}$ and $4^{th}$ order cumulants, trace the chiral
crossover transition line at small values of th... |
\section{Introduction}
Establishing causal relations between variables from observation of their behaviour in time is central to scientific investigation and it is at the core of data-science where th | ese causal relations are the basis for the construction of useful models and tools capable of prediction.
The capability to predict (future) outcomes from the analytics of (past) input data is crucial in modeling and it should be the main property to take into consideration in model selection, when the validity and m... |
\section{Introduction}
There are many examples of dissipative systems that can be derived from conservative ones. The derivation can be
done in many different ways, for example by adding a very stro | ng friction term or by homogenization techniques
or by properly rescaling the time variable by a small
parameter (through the so-called ``parabolic scaling"). In the recent work of the author and Y. Brenier \cite{BD}, we suggested a very straightforward idea: just perform the
quadratic change of time
$t\rightarrow \the... |
\section{Introduction}
A classical problem in grammatical inference is to find, i.e.\ \emph{learn}, a regular language from a set of examples of that language.
When this set is divided into positive | examples (belonging to the language) and negative examples (not belonging to the language), the problem is typically solved by searching for the smallest deterministic finite automaton (DFA) that accepts the positive examples, and rejects the negative ones.
Provided with sufficiently many examples, there exist algorith... |
\section{Introduction}
\IEEEPARstart{S}{pectral} analysis techniques are among the most important tools for extracting information from time series data recorded {from} naturally occurring processes. | Examples include speech \cite{Quatieri:08}, images \cite{lim1990two}, electroencephalography (EEG) \cite{Buzsaki:09}, oceanography \cite{emery2001data}, climatic time series \cite{ghil2002advanced} and seismic data \cite{Yilmaz:01}. Due to the exploratory nature of most of these applications, non-parametric techniques... |
\section{INTRODUCTION}\label{sec1}
Recent observations in the $\gamma$-ray\xspace band ($\geq 100$ MeV) show that the extragalactic $\gamma$-ray\xspace sky is dominated by emission from blazars - an e | xtreme class of Active Galactic Nuclei (AGNs) which have jets that are forming a small angle with respect to the line of sight \citep{urry}. Blazars are known to emit electromagnetic radiation in almost all frequencies that are currently being observed, ranging from radio to Very High Energy (VHE; $>$ 100 GeV) $\gamma$... |
\section{Introduction}
Recently, character composition models have shown great success in many NLP tasks, mainly because of their robustness in dealing with out-of-vocabulary (OOV) words by capturing | sub-word informations. Among the character composition models, bidirectional long short-term memory (LSTM) models and convolutional neural networks (CNN) are widely applied in many tasks, e.g. part-of-speech (POS) tagging \citep{Santos:2014, Plank:2016}, named entity recognition \citep{Santos:2015}, language modeling ... |
\section{Introduction}
\label{sec:Intro}
In the last few years Recurrent Neural Networks (RNNs) \cite{jordan-serial,Elman90findingstructure,Hochreiter-1997-LSTM} have proved very effective in several | Natural Language Processing (NLP) tasks such as Part-of-Speech tagging (POS tagging), chunking, Named Entity Recognition (NER), Spoken Language Understanding (SLU), machine translation and even more \cite{RNN-Mikolov-Interspeech-2010,RNNExtensions_Mikolov-ICASSP-2011,Collobert-2008-UAN-1390156.1390177,Collobert-2011-N... |
\section{Introduction}
Flows in suspensions are often characterized by transport phenomena that
originate from the interaction of the particles among themselves and with the flow.
In dilute suspens | ions, the particle interactions are
mediated by hydrodynamic forces. In more concentrated suspensions,
the contribution from direct contact of the particles is dominant.
Effective diffusivities greatly exceeding the values expected from
molecular effects are often observed, even in the absence of turbulence
\cite{ru... |
\section{Introduction}\label{Intro}
Write $G$ for the the random graph $G_{n,1/2}$ and
$f(k)$ ($=f_n(k)$) for the expected number of
$k$-cliques in $G$; that is,
$f(k)=\C{n}{k}2^{-\C{k}{2}}$.
S | et
\[
k_0 = k_0(n) = \min \{k:f(k)<1\}
\]
and temporarily (through Conjecture~\ref{ASConj})
set $k=k(n) =k_0-4$.
It is easy to see that $k \sim 2\log_2n$ and that $f(k)$ is at least about
$n^3$ (precisely, $f(k)=\tilde{\gO}(n^3)$, where, as usual, $\tilde{\gO}$ ignores log factors).
We will call a collection ... |
\section{Introduction}
\label{sec:intro}
The one-point probability distribution function (PDF) of the matter
density field in the universe, and its related statistics the distribution
of galaxy count | s, have a long and somewhat patchy history in cosmology
and extragalactic astronomy. It was Edwin Hubble almost a century ago
who found that the counts of about $44,000$ extra-galactic nebulae
distributed over a large area of the sky have a probability
distribution that is not Gaussian but can be approximated by a
log-... |
\section{Introduction}
\label{Intro}
Disc galaxies with spiral arms, including the Milky Way, occupy a large fraction of galaxies in the current Universe although the fraction depends on mass and colo | ur \citep[e.g.][and references therein]{bst:88}. Such spiral galaxies generally have relatively smooth stellar distribution, and their star clusters in the discs are small: $M_{\rm cl}\lsim10^3~{\rm M_\odot}$ \citep[e.g.][]{ll:03}. Their spiral arms are considered to drive the formation of such star clusters.
In the h... |
\section{Introduction}\label{sec:intro}
Electron spin resonance (ESR) and its variants in magnetically ordered systems - ferromagnetic and antiferromagnetic resonances -
represent one of the most pr | ecise and frequently used spectroscopic probes of excitations of magnetic media. The essence of the magnetic resonance technique consists in measuring
absorption of electromagnetic radiation (usually in the microwave range of frequencies) by a sample material which is (typically) subjected to an external static magneti... |
\section{Introduction}\label{section:Introduction}
\indent \myparagraph{Subspace Clustering} Over the past fifteen years the model of a union of linear subspaces, also called a \emph{subspace arrang | ement} \citep{Derksen:JPAA07}, has gained significant popularity in pattern recognition and computer vision \citep{Vidal:SPM11-SC}, often replacing the classical model of a single linear subspace, associated to the well-known Principal Component Analysis (PCA) \citep{Hotelling-1933,Pearson-1901,Jolliffe-2002}. This has... |
\section{Introduction}
Given two smooth projective varieties $X$ and $Y$ related by a Fourier-Mukai transform $\Phi : D^b(X) \to D^b(Y)$, it is usually not the case that a slope stable coherent sheaf | $E$ on $X$ is taken by $\Phi$ to a slope stable coherent sheaf on $Y$. It is therefore natural to ask: under what circumstances does this happen?
Yoshioka gave examples and counterexamples to the above question on Abelian and K3 surfaces \cite{YosNote}. On threefolds, Bridgeland-Maciocia showed in \cite[Theorem 1.... |
\section{Introduction}
\label{sec_introduction}
Generalized linear mixed models (GLMMs) are generalized linear models
with random terms in the linear predictor. The random effects in the
GLMM can acc | ommodate for overdispersion often present in non-Gaussian
data, and dependence among correlated observations arising from
longitudinal or repeated measures studies. GLMM is one of the most
frequently used statistical models. Here, we consider a popular Bayesian
GLMM for binary data, namely, the probit linear mixed mode... |
\section{INTRODUCTION}
\label{sec:Intro}
In the past decade, fast-developing non-targeted supernova (SN) survey
programs have discovered a new class of unusual SNe whose peak absolute
magnitud | es $M_{\mathrm{peak}}$ at all bands are brighter than $-21$ mag.
These very luminous SNe are called \textquotedblleft superluminous
supernovae (SLSNe)" \citep{Qiu2011,Gal2012}.
It appears that SLSNe can be simply divided into two categories, SLSNe I and
II. SLSNe I have spectra around the peaks that are lack of h... |
\section{Introduction}
\label{sec_Intro}
Let $\PG(N,q)$ be the $N$-dimensional projective space over the
Galois field $\mathbb{F}_q$ of order $q$. A $k$-cap in $\PG(N,q)$ is a
set of $k$ points | no three of which are collinear. A $k$-cap $\K$
is complete if it is not contained in a $(k+1)$-cap or, equivalently, if every point of $\PG(N,q) \setminus
\K$ is collinear with two points of $\K$.
Caps in $\PG(2,q)$ are also called arcs and they have been
widely studied by many authors in the past decades, see
... |
\section{Introduction} \label{sec:intro}
Crystals exposing a face bearing a net charge are intrinsically unstable if, in addition, the unit cell also has a net dipole moment perpendicular to the surf | ace. Such a termination is referred to as a type III polar surface in the classification by Tasker\cite{Tasker1979}. Tasker explained the instability of type III surfaces by showing that the energy diverges with increasing thickness of the crystal (polar catastrophe). Yet, surfaces with type III orientations do occur i... |
\section{Introduction}\label{sec:intro}
Credit card frauds, a concept included in the wider notion of financial frauds \cite{ngai2011application, west2016intelligent}, is a topic attracting an increa | sing attention from the scientific community. This is due, on the one hand, to the raising costs that they generate for the system, reaching billions of dollars in yearly losses and a percentage loss of revenues equal to the $1.4\%$ of online payments \cite{bhatla2003understanding}. On the other hand, credit card fraud... |
\section{Introduction}
Innovative industries invest resources (e.g., money and time for research and development) to construct new systems and to improve the performance of the previously-deployed one | s. To generate revenue and offset the cost of research, they ideally want to capitalize on their achievements. This is sometimes done by restricting the use of their ideas through patents or by hiding the features of their systems as trade secrets.
When opting for trade secrets, reverse engineering techniques can be us... |
\section{Introduction}
\label{sec:intro}
A pure superfluid in the zero temperature limit has no viscosity. The superfluid is formed by atoms which have condensed into the ground state. The condensate | atoms behave collectively and are described by a coherent macroscopic wavefunction. In liquid $^3$He and dilute Fermi gases, the condensate is formed by pairs of atoms known as Cooper pairs. For most superfluids, including $^3$He-B, the superfluid velocity {\bf {v}}\, is proportional to the gradient of the phase of t... |
\section{Introduction}
\subsection{Mahler's conjecture for the volume product}
A {\it convex body} in $\R^n$ is a compact convex set in $\R^n$ with nonempty interior.
Denote by $\K^n$ the se | t of all convex bodies in $\R^n$.
A convex body $K \in \K^n$ is said to be {\it centrally symmetric} if it satisfies $K=-K$.
We denote by $\K^n_0$ the set of all $K \in \K^n$ which are centrally symmetric.
Let $K \in \K^n$ be a convex body.
The interior of $K$ is denoted by $\interior K$.
For $z \in \interior K$... |
\section{Introduction}
Energy injection by supernova explosions can lead to strong outflows from
star forming galaxies.
These supernovae (SNe) driven galactic outflows could eject a significant
frac | tion of the interstellar medium (ISM) along with metals
into their circum-galactic medium (CGM) and the general
intergalactic medium (IGM).
Feedback due to starburst driven outflows are also invoked in galaxy formation
models to get correct shape of the galaxy luminosity functions.
It is well demonstrated that a high... |
\section{Introduction} %
Iterative Learning Control (ILC) enables significant performance improvements for batch-to-batch control applications, by generating a command signal that compensates for rep | etitive disturbances through learning from previous iterations, also called batches or trials. Theoretical and implementation aspects, including convergence, causality, and robustness, have been addressed in, e.g., \cite{BristowThaAll2006}, \cite{AhnMooChe2007}, \cite{RogersGalOwe2007}, \cite{Owens2016}, \cite{Pipeleer... |
\section{Introduction}
\vspace{2mm}
Glitches are sudden jumps of amplitude $\Delta\Omega$ in the angular velocity $\Omega$ of some isolated pulsars
with fractional increases that span the range $\Del | ta\Omega/\Omega \sim 10^{-11} \div 10^{-5}$
in otherwise steadily spinning-down neutron stars (NSs).
According to the Jodrell Bank Glitch Catalog\footnote{Glitch data are extracted from the database www.jb.man.ac.uk/pulsar/glitches.html.},
more than four hundred glitches have been observed, in more than a hundred obje... |
\section{Introduction}\label{sec:introduction}}
\IEEEPARstart{S}{ensor} Networks and Wireless Sensor Networks (WSN) are two main components involved in the development of the
Internet of Things (I | oT). Security and privacy handling for Sensor Networks present new issues due to specific constraints. Low resources on computation, hardware functionalities and energy consumption in WSNs. We can divide research work into two categories: security and privacy for the data being sent over the network on one side, and no... |
\section{Introduction}
\subsection{Motivation and history}
There is an intimate relationship between special functions and group theory.
It consists of a very fruitful cross-fertilization which has | been
exploited in several directions.
Typically, matrix coefficients of compact or complex groups are related to polynomials in various forms.
In this paper, we explore this relationship further and we discuss multivariable matrix-valued
orthogonal polynomials related to the representation theory of compact groups.... |
\section{Introduction}
\label{sec:intro}
Inflation~\cite{Starobinsky:1980te, Sato:1980yn, Guth:1980zm, Linde:1981mu, Albrecht:1982wi, Linde:1983gd} describes a phase of accelerated expansion in the ea | rly Universe, during which vacuum quantum fluctuations of the gravitational and matter fields were amplified to cosmological perturbations~\cite{Starobinsky:1979ty, Mukhanov:1981xt, Hawking:1982cz, Starobinsky:1982ee, Guth:1982ec, Bardeen:1983qw}. These primordial fluctuations later seeded the cosmic microwave backgro... |
\section{The Higher Order $G$-Transformation} \label{se1}
The $G$-transformation was designed by Gray and Atchison
\cite{Gray:1967:NTR} as an extrapolation method for
evaluating infinite
integrals of | the form $\int^{\infty}_a f(t)\,dt\equiv I[f]$.
It was later
generalized in different ways in Atchison and Gray
\cite{Atchison:1968:NTR} and Gray and Atchison
\cite{Gray:1968:GT}, the ultimate generalization being given in
Gray, Atchison, and McWilliams \cite{Gray:1971:HOT}. This generalization
was denoted the higher-o... |
\section{Introduction}
It is well accepted nowadays that the Universe underwent a period of strong and extremely quick accelerated expansion, namely the inflation stage, immediately after its origin | (usually termed as the Big Bang singularity). From the very first proposal of the inflationary paradigm in 1981, by Guth~\cite{Guth} and Sato~\cite{Sato}, several attempts to describe this early-time acceleration have been carried out (see Refs.~\cite{infrev}, for some reviews).
Moreover, cosmological data~\cite{Planc... |
\section{Introduction}
In the foundations of quantum mechanics, the status of the wavefunction is one of the most debated issues. Associating a wavefunction with each system, QM provides very accura | te predictions about the possible measurement outcomes. However, the axioms of QM are silent about the nature of the wavefunction, i.e., these axioms are logically consistent with several different ontological statuses of the wavefunction.
The Ontological Models Framework (OMF) introduced by Harrigan and Spekkens \cit... |
\section{Introduction}
An emergent class of transient objects defined by unusually strong
calcium line emissions that develop in optical spectra months after
explosion has garnered considerable atten | tion in the last
decade. These have been referred to as ``Ca-rich,''
\citep{Filippenko03}, SN\,2005E-like \citep{Perets10}, and ``Ca-rich
gap'' transients \citep{Kasliwal12}. Here we adopt the broad
classification of ``Ca-rich transient.''
During the early photospheric stages, Ca-rich transients have distinct
He lines... |
\section{Introduction}
The strong coupling \as\ is one of the fundamental parameters of the
standard model of particle physics thus its precise determination is mandatory.
Nowadays, event shapes an | d jet rates measured in three-jet formation in
electron-positron annihilation are still among the most precise tools used
for accurate extractions of \as\ from data. In these analyses, the measurement
of \as\ involves fitting theoretical predictions for a given observable and
collider energy to observations. Hence ... |
\section{Introduction}
Blue compact dwarf galaxies (BCDs) are low-mass systems characterized by active star formation in compact regions and strong narrow emission lines superposed on a flat stella | r continuum \citep[e.g.,][]{salzer89,kehrig04}. They were originally considered as either nascent or immature galaxies that had recently undergone intense bursts of star formation \citep{searle73}. However, it turns out that they also contain stellar populations older than $\sim$1~Gyr as shown by a number of optical an... |
\section{Introduction}
The energy transfer in the light-harvesting antenna complex (LHC) takes place via exciton propagation among pigments bound to the LHC proteins \cite{book1}. The exciton is cr | eated by resonant photo-absorption on an antenna pigment, leading to electron excitation from the ground to the excited energy level, $\gamma +E_0 \to E_1$, Fig.~\ref{fig1}. Due to the dipole-dipole interaction, $V$, the exciton then propagates between neighboring pigments to the reaction center (RC), while all, excit... |
\section{Introduction}\label{sec:intro}
Very high energy gamma rays (VHE; E $>$ 100\,GeV) are messengers of the most energetic phenomena in the Universe. A number of pulsars, pulsar wind nebulae, supe | rnova remnants and micro-quasars in our own Galaxy have been detected to emit such energetic radiation. Outside the Milky Way, VHE gamma rays have been seen from ultra-relativistic jets of particles escaping super-massive black holes and from galaxies with an exceptional rate of star formation. The VHE sky counts nowad... |
\section{Introduction}
\label{sec:1}
Diffusion MRI is a powerful non-invasive imaging technique widely used to explore white matter in the human brain.
Diffusion Tensor Imaging (DTI)~\citep{Basser19 | 94} is used to reconstruct a tensor field from diffusion weighted images (DWIs).
High Angular Resolution Diffusion Imaging~\citep{TuchMRM2002,frank_MRM2002,Descoteaux2007,tournier_NI2007,Cheng_PDF_MICCAI2010,cheng_MICCAI2015,cheng_NI2014,ozarslan_NI13},
which makes no assumption of a 3D Gaussian distribution of the d... |
\section{Introduction}
Cloud radio access network (C-RAN) \cite{CRAN2011} is a promising and flexible architecture to accommodate the exponential growth of mobile data traffic in the next-generation | cellular network. In a C-RAN, all~the base-band signal processing is shifted to a single base-band unit (BBU) pool \cite{Shi2015}. The conventional base-stations (BSs), however, are replaced by geographically distributed remote antenna ports (RAPs) with only antenna elements and power amplifiers, which are connected to... |
\section{Introduction}
Let $(X,\rho)$ be a metric space. For a compact subset $K$ of $X$, $b_{(X,\rho)}(K)$ denotes the \textit{Borsuk number} of $K$, that is, the minimal number of parts of $K$ of s | maller diameter necessary to partition $K$. The \textit{Borsuk number} of $(X,\rho)$ is defined to be $B(X,\rho)=\max _{K}b_{X,\rho}(K)$. If $\Omega(\rho)$ denotes the set of metrics on $X$ equivalent to $\rho$, then the \textit{topological Borsuk number} of $(X,\rho)$ is defined by $B(X)=\min_{\tau\in\Omega(\rho)}B(X,... |
\section{Introduction}
\input{intro1}
\input{content1}
\end{docum | ent}
\section{Plant Model and Network-System Architecture}
\label{s:problem setup}
Throughout this work, we shall focus on a single-loop multi-variable control architecture with an unreliable input communication channel.
Consider a linear time-invariant control system with additive process noise and controlled... |
\section{Introduction}
Our motivation to work with massive spin-2 particles in a curved
background is twofold. On one hand, they can represent massive
gravitons at the linearized approximation, on th | e other hand, they
can be understood as elementary massive spin-2 particles in a
given gravitational background.
Regarding the motivation for massive gravitons, they lead to an
weaker gravitational interaction at large distances, which could
contribute to the observed \cite{super1,super2} accelerated
expansion of the ... |
\section{Introduction and summary}
Scattering amplitudes are central for understanding the structure of superstring theory. Their low-energy ($\alpha'$) expansion exhibits many deep mathematical stru | ctures. For instance, the four-graviton scattering amplitude of type II string theory in $10-d$ space-time dimensions is expected to be invariant under the string U-duality group $E_{d+1}(\mathbb{Z})$~\cite{Hull:1994ys} order by order in $\alpha'$~\cite{Sen:1994fa,Green:1997tv}. This can be used together with supersymm... |
\section{Introduction}
\label{Sec:Intro}
The so-called Wigner distribution is known to provide maximally detailed information on quantum systems describing the distribution of particles in phase spac | e.
In the case of hadron structure, the QCD Wigner distribution~\cite{Ji:2003ak,Belitsky:2003nz,Lorce:2011kd}, or its Fourier transform, the Generalized Transverse Momentum
Dependent Distribution (GTMD) \cite{Meissner:2009ww,Hatta:2011ku,Lorce:2013pza,Echevarria:2016mrc}, provides multidimensional partonic imaging of... |
\section{Introduction}
\subsection{} The setting of finite groups acting on categories is a well-studied ground, see e.g. \cite{Deligne, Sosna, GK, E1, E2} and
references therein. A useful way to def | ine the action is to require for every $g \in G$ an autoequivalence $\rho_g\colon \mathcal C \to \mathcal C$
together with a choice of isomorphisms $\rho_g \rho_h \simeq \rho_{gh}$ satisfying a cocycle condition, see \ref{def-action}.
One would then study the category of equivariant objects $\mathcal C^G$, see \ref{def... |
\section{Introduction}
\label{sec1}
Last few years have witnessed a massive growth in consumer interest in smart devices [1]. These include smartphones, smart TVs, and recently smartwatches. Becau | se of their increased penetration, smartwatches have claimed a handsome market share. A typical smartwatch contains a heart rate monitor, GPS, thermometer, camera and accelerometer. Thus, it can provide a variety of services. These services include temperature and pulse measurements and the number of calories consumed ... |
\section{Introduction}\label{sec:introduction}
A wide variety of decision making problems in engineering, physical, or economic systems can be formulated as convex quadratic programs of the form
\beg | in{equation}
\label{eq:QCQP}
\begin{array}{clll}
\displaystyle\textnormal{minimize}&\displaystyle \norm{\bm A (\bm x) \bm \xi}^2 + \bm b(\bm x)^\top\bm \xi + c (\bm x)\\
\textnormal{subject to}& \displaystyle {\bm x\in\mathcal X}.
\end{array}
\end{equation}
Here, $\mathcal X\subseteq\mathbb{R}^D$ is the feasible set... |
\section{Introduction and statement of the results} \label{sec:intro}
We consider dynamical systems defined by the iteration of a meromorphic function
\[
f: \mathbb C \to \widehat{\C},
\]
on the com | plex plane, especially those with an essentially singularity at infinity (transcendental). Motivating examples of such maps are given by root-finding algorithms like, for instance, Newton's method applied to any entire transcendental map.
In this setting the Riemann sphere $\widehat{\C}$ splits into two invariant s... |
\section{Introduction}
Spin squeezed states of atomic ensembles have many applications as resources for quantum enhanced metrology~\cite{wineland2,andre,johannes1,leroux2010,Hosten2}, continuous varia | ble quantum information processing~\cite{rev123}, and multipartite entanglement~\cite{anders2,korbicz,briegel1}. Various methods for generating spin squeezed states in atomic ensembles have been proposed~\cite{thorne,anders1,leroux2012,torre,monika5} and realized experimentally~\cite{eugene1,eugene2,muessel,monika1,ler... |
\section{\label{sec:level}Introduction\protect}
The two most important methods to obtain reliable quantitative spectral information about the electronic properties of a superconductor are Giaever tun | neling \cite{Wolf2011} and point contact Andreev spectroscopy \cite{Blonder1982b, Daghero2010}. In tunnel spectroscopy two metal thin films are weakly coupled by an insulating tunnel barrier, leading to a current-voltage characteristic which is controlled by the unperturbed superconducting densities of states in both m... |
\section{Introduction}
Quasi-periodic pulsations (QPPs) are usually observed in the light
curves of solar flares
\citep{Nakariakov09,Inglis16,Pugh16,Van16,Zhang16a}. They typically
display regular and | periodic peaks from the total flux based on the
time-series analysis. The observations of QPPs can cover almost all
the wavelengths, such as soft/hard X-rays (SXR/HXR)
\citep{Lipa78,Ning14a,Aschwanden98,Dolla12,Tan16},
extreme-ultraviolet (EUV/UV)
\citep{Nakariakov99,Ning14b,Liu11,Kumar16,Lil16} and radio
\citep{Aschw... |
\section{Introduction}
\label{sec:intro}
Conversational agents can seamlessly integrate into our lives by offering a natural language interface for complex tasks.
However, the complexity of conversa | tions with current slot-filling dialogue systems is limited.
One limitation is that the user usually cannot refer back to an earlier state in the dialogue, which is essential \textit{e.g.}, when comparing alternatives or researching a complex subject.
The recently published Frames dataset \citep{el_asri_frames_2017} p... |
\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus -.2ex}{2.3 ex plus .2ex}{\centering\large\bf}{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus -.2ex}{2.3 ex plus .2ex}{\centering\large\ | bf}}
\usepackage{amsmath, amssymb}
\usepackage{amsthm}
\usepackage{braket}
\usepackage{mathtools}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\usepackage{latexsym}
\def\hfill $\Box${\hfill $\Box$}
\usepackage{cases}
\makeatletter
\renewcommand{\theequation}{
\thesection.\arabic{equation}}
\@addtores... |
\section{Introduction}
Heusler alloys, a vast family of ternary compounds, are often considered an ideal platform for engineering
and designing novel functional materials. Such class includes both me | tals and insulators, and among them
superconductors, topological insulators, thermoelectric alloys, and both optical and magnetic
materials~\cite{felser_basics_2015, graf_heusler_2011}. As such, the possibility of using alloys of this family for
fine tuning and controlling the electronic structure and the magnetic o... |
\section{Introduction}
The cosmic microwave background (CMB) observation and potentially the large-scale structure (LSS) observation in the future offer exciting opportunities to test high energy phy | sics whose energy scale is far beyond what other types of experiments can achieve. In particular the oscillatory features of those observations can in principle constrain the possible ``ultra-violet complete'' theories of gravity. Such theories are needed in order to fully understand inflation, which is currently the m... |
\section{\\Modelled EIG properties}
\label{App:ModelledEIG_Properties}
The SFH, dust attenuation and stellar mass of the EIGs were estimated by fitting a model to their UV-to-near-IR SEDs as describe | d section \ref{sec:ResultsModel}.
Figure \ref{f:ResGalMC_1D} shows, for each of the modelled EIGs, the marginalized posterior distributions of $Age_{1}$, $\tau^{-1}$, \EBV, $\ifmmode M \else $M$ \fi_{2}$ and {\Mstar}.
The extreme $\tau^{-1}$ values where $\left| \tau \right| \ll Age_{1}$ ... |
\section{Introduction}
Quantum correlations are intrinsically related to quantum information theory,
as resources for quantum information protocols \cite{mother}. The quantification of quantum
inf | ormation rates is performed by a quantum version of entropic measures, especially by von Neumann entropy
\begin{equation}
S(\rho) = - \text{Tr}(\rho \log \rho),
\end{equation}
and its related measures \cite{wildebook},
although there are generalizations of von Neumann entropy, and its related measures, by means
of ... |
\section{Introduction}
\label{sec:intr}
The proton and neutron density distributions generated in the course of a heavy-ion collision, especially at a total density exceeding its normal value ($\rho_{ | \rm 0}$ = 0.16 fm$^{\rm -3}$), are among the main points of interest of theorists, experimentalists and observers, within the communities of low and medium-energy nuclear physics and of astrophysics of compact objects. The relative asymmetry of these distributions pertains to the determination of the Equation of State... |
\section{Introduction}
The present investigation is motivated by the problem of erosion and deposition
of sediment at the bottom of fluvial and estuarine environments as well as along hill slopes,
w | hich result from the action of the surface water flow.
The ultimate goal is to understand the morphological evolution of the sediment bed.
Other applications of channel flows can be found in chemistry, biological fluid
dynamics and industrial engineering.
Providing reliable predictions of the river-bed evolution re... |
\section{Introduction} The development of lasers has revitalized
atomic, molecular, chemical, and optical physics. The interaction of
intense laser pulses with matter gives rise to a wealth of phenom | ena that are nonlinear in both the laser intensity and the number of photons involved, examples being multiphoton ionization (MPI), above-threshold
ionization (ATI), or tunneling ionization (see, e.g.,
\cite{Milosevic2006} for a review). While for weak laser fields MPI
could still be tackled in a perturbative fashion w... |
\section{Introduction}
The usual way of studying the geometry of curves is by means of the well known Frenet frame. Such a frame is rich in geometric informations \cite{Kreyszig1991,Kuhnel2010}, but | since its principal normal always points to the center of curvature, it may result in unnecessary rotation and then making its use unsuitable in some contexts. In this respect, the consideration of \emph{rotation minimizing frames} $\{\mathbf{t},\mathbf{n}_1,\mathbf{n}_2\}$ (RM frames, for short) is of special interest... |
\section{Introduction}
Theory of isomonodromic deformation and Painlev{\'e} equations
has long been a subject of intensive study, with many applications both in
mathematics and in physics.
Recent | discovery of the isomonodromy/CFT correspondence
\cite{GIL}, \cite{GIL1}, \cite{ILTy}
opened up a new perspective to this domain.
In a nutshell, it states that the Painlev{\'e}
tau functions are Fourier transform of conformal blocks at $c=1$.
The AGT relation allows one to write a combinatorial
formula for the lat... |
\section{Introduction}\label{section:Introduction}
Motivated partially by the findings of~\cite{HilBauWey13}, in
particular by our difficulties in evolving gravitational wave data
close to the critic | al threshold of black hole formation with the
moving puncture gauge, we turned to an alternative formulation and a
more accurate numerical method. We implemented the generalized
harmonic formulation in a pseudospectral code, \texttt{bamps}, which
was recently described in detail
in~\cite{HilWeyBru15,BugDieBer15,HilHarB... |
\section{Introduction}
\subsection{Problem Statement}
We consider the problem of recovering a function $u$
from finite dimensional data $y$ where
\begin{equation}
\label{eq:basiceq}
y=Ku +\varepsil | on^c\eta.
\end{equation}
Here $y\in \mathbb R^J$ denotes a finite number of observations corrupted by noise $\varepsilon^c\eta$ of size $\varepsilon^c$ and where we assume that
$\eta$ is a centred Gaussian
$\mathsf{N}(0,\Sigma).$ We suppose that the function $u \in BV_{\rm binary}$ where
$BV_{\rm binary}(D)=\{\psi\i... |
\section{Introduction}
An optimization problem principal to machine learning and statistics is that of finite sums:
\begin{align} \label{opt:fsm}
\min_{\bw\in\reals^d} F(\bw) \coloneqq \frac1n\sum_ | {i=1}^n f_i(\bw),
\end{align}
where the individual functions $f_i$ are assumed to possess some favorable analytical properties, such as Lipschitz-continuity, smoothness or strong convexity (see \cite{nesterov2004introductory} for details). We measure the \emph{iteration complexity} of a given optimization algorithm b... |
\section{Introduction}
\label{intro}
A Salem number is a real algebraic integer $\tau > 1$ of degree at least four,
conjugate to $\tau ^{-1}$, all of whose conjugates, excluding $\tau$ and $\ta | u ^{-1}$, are unimodal i.e., lie on $|z| = 1$.
The corresponding minimal polynomial $P(x)$ of degree $d$
of these numbers, called a Salem polynomial, is (self-)reciprocal, that is $x^d P(1/x) = P(x)$. Since $P(x)$ is self-reciprocal and irreducible it must have even degree.
It is well known \cite{Smy} that $\tau^n$ s... |
\section{Introduction}
Let $S$ be an orientable surface of finite type. Let $\text{Mod}(S)$
be the mapping class group of orientation preserving diffeomorphisms
of $S$ modulo isotopy. Let ${\mathca | l T}(S)$ be the Teichm{\"u}ller{ } space of
marked conformal structures on $S$, and the moduli space
$\mathcal{M}(S)$ of Riemann surfaces is the quotient ${\mathcal T}(S)/
\text{Mod}(S)$. Let $\mathcal{Q}(S)$ be the space of unit area
quadratic differentials, which may be identified with the unit
cotangent bundle of ${... |
\section{Introduction}
\vskip 0.5cm \ \ \ On May 24, 2000, the Clay Mathematics Institute
(CMI for short) announced that it would award prizes of 1 million
dollars each for solutions to seven mathe | matics problems. These
seven problems are
\begin{enumerate}[label=Problem \arabic{enumi}.,itemsep=6pt,leftmargin=*]
\item The ``P versus NP" Problem
\item The Riemann Hypothesis
\item The Poincar{\'e} Conjecture
\item The Hodge Conjecture
\item The Birch-Swinnerton-Dyer Conjecture (briefly, the BSD conjecture)
\item T... |
\section{Introduction}
Closed, unparametrized plane curves are used to represent the outline or shape of objects and as such they arise naturally in shape analysis and its applications~\cite{Srivasta | va2016}; these include medical imaging, computer animation, geometric morphometry and other fields. Analysis of shapes and their differences relies on the notion of distance between shapes. To define such a distance, we start from a Riemannian metric on the space of curves and compute its induced geodesic distance.
We... |
\section{Introduction}
\IEEEPARstart{T}{he} most noticeable developments foreseen in the near future in power systems involve Distribution Networks (DNs). Future DNs are expected to host a big percen | tage of Renewable Energy Sources (RES) and other Distributed Energy Resources (electric vehicles, flexible loads, fuel cells, batteries, etc.). Moreover, it is expected that DNs will be called upon to actively support the bulk Transmission Network (TN) participating in ancillary services with the help of Information an... |
\section*{Introduction}
\label{sect:introduction}
Let $k$ be a field of characteristic $\neq 2$ and $\bar{k}/k$ an algebraic closure of $k$.
Let $E$ be an elliptic curve over $k$, presented as a d | ouble cover
$$
\pi: E\rightarrow {\mathbb P}^1,
$$
ramified in 4 points, and
$E[\infty]\subset E(\bar{k})$ the set of its torsion points. In \cite{BT-small} we proved:
\begin{thm}
If $E_1, E_2$ are nonisomorphic elliptic curves over $\bar{{\mathbb Q}}$, then
$$
\pi_1(E_1[\infty]) \cap \pi_2(E_2[\infty])
$$
is f... |
\section{Introduction}
\label{intro}
When a polycrystalline material is deformed, its microstructure generally experiences a reorientation of the crystal lattices of each grain towards a preferential | distribution of orientations known as \emph{crystallographic texture}. The study of texture evolution is important because textured metals typically exhibit plastic anisotropy, which plays a significant role on mechanical properties.
Predicting the evolution of deformation-induced texture and the accompanying plastic ... |
\section{Introduction}
Although the double-helix structure of DNA stores genetic information linearly as a sequence of bases at the molecular level, entropy randomizes the three-dimensional conformati | ons of DNA polymers in free solution, making accessing genomic information from long polymers exceedingly challenging.
To manipulate and study DNA, physical approaches have been developed to spatially arrange DNA in a controlled format, including magnetic and optical traps~\cite{bustamante00,bustamante03}, microfluidi... |
\section{INTRODUCTION}\label{intro}
Coronal rain refers to cool and dense elongated plasma blobs or thread segments, which suddenly
appear in the low corona, falling along coronal loops all the way | down to the solar surface.
This phenomenon was first recorded and classified as coronal sunspot prominences, commonly originating
in coronal space and pouring down to spot regions \citep{Pettit43}, and was later observed
and clarified as ``coronal rain'' by its characteristic feature of rapid brightening when
approa... |
\section{Introduction}
There exist several classes of non-associative algebras (baric,
evolution, Bernstein, train, stochastic, etc.), whose investigation
has provided a number of significant con | tributions to theoretical
population genetics \cite{R,WB}. Such classes have been defined
different times by several authors, and all algebras belonging to
these classes are generally called \textit{genetic}. In \cite{Eth}
it was introduced the formal language of abstract algebra to the
study of the genetics. Note... |
\section{Introduction}\label{sec:intro}
\subsection{Background}
A \defn{hypergraph} $G$ is a pair $(V,E)$, where $V=V(G)$ is the vertex set of $G$ and the edge set $E$ is a set of subsets of $V$. | We often identify $G$ with $E$, in particular, we let $|G|:=|E|$. We say that $G$ is an \defn{$r$-graph} if every edge has size $r$. We let $\krq{r}{n}$ denote the complete $r$-graph on $n$ vertices.
Let $G$ and $F$ be $r$-graphs. An \defn{$F$-decomposition of $G$} is a collection $\cF$ of copies of $F$ in $G$ such... |
\section{Introduction}\label{sec:intro}
Adiabatic quantum computation (AQC) has been proposed as a successful technique for solving certain classes of optimization problems (see \cite{albash2016,farhi | 01,McGeoch2013,optimization_AQO}). In particular, quantum annealers (QA) such as the ones manufactured by D-Wave Systems Inc. \cite{DwaveNature} approximate the adiabatic evolution in the presence of various sources of noise and finite temperature to solve Ising models of the form
\begin{equation} \label{Ising_def} \t... |
\section{Introduction}
\label{seq1}
Nowadays, Cloud computing allows data owners to use massive data storage and large computation capabilities at a very low costs. Despite these benefits, such a da | ta outsourcing induces important security challenges. Indeed, data owners lose the control over the pieces of information they outsource. To protect data in terms of confidentiality and privacy from unauthorized users as well as from the cloud, one common solution consists in encrypting data. However, if using encrypti... |
\section{Concluding comments}
\label{sec:conclusion}
In this paper, we have studied an optimal dividend problem where the profitability of the firm is stochastic.
In this context, we have given a comp | arison result for general dynamics as well as outlined a numerical algorithm to compute the solution.
The convergence of the numerical method is a consequence of the comparison result.
The numerical solution indicates that the problem exhibits both barrier and band structure, depending on the current profitability.
Th... |
\section{Introduction}\label{s:intro}
Let $G$ be a reductive algebraic group defined over an algebraically closed field $K$ of characteristic $p$ (possibly equal to 0), $C$ be a conjugacy class of | $G$ and $u$ be a positive integer. In 2007 Guralnick \cite{Guralnick} proved the following result:
\begin{theorem}\cite[Theorem 1.1]{Guralnick}.
Given a reductive algebraic group $G$, a conjugacy class $C$ of $G$ and a positive integer $u$, the set $\{g \in G: g^u\in C\}$ is a finite union of conjugacy classes of $... |
\section{\@startsection {section}{1}{\z@
{-5.5ex \@plus -1ex \@minus -.2ex
{2.3ex \@plus.2ex
{\ | normalfont\large\bfseries}}
\renewcommand\subsection{\@startsection{subsection}{2}{\z@
{-3.25ex\@plus -1ex \@minus -.2ex
{1.5ex \@plus .2ex
{\normalfont\normalsize\bfseries}}
\renewcommand\thesection {\@arab... |
\section{Introduction}
\label{sec:intro}
The nature of Type Ia supernova (SN Ia) progenitors remains one of the enduring mysteries of astrophysics (for recent reviews, see \citealt{hill13a} and \cit | ealt{maoz14a}). For decades, many researchers favored a scenario involving a C/O white dwarf (WD) whose mass approaches the Chandrasekhar limit via stable hydrogen-rich accretion from a non-degenerate companion \citep{wi73,nomo82a} or in an unstable merger with another C/O WD \citep{it84,webb84}. Carbon fusion at the... |
\section*{Abstract (Not appropriate in this style!)}%
\else \small
\begin{center}{\bf Abstract\vspace{-.5em}\vspace{\z@}}\end{center}%
\quotation
\fi
}%
}{%
}%
\@ifundefined{endabstr | act}{\def\endabstract
{\if@twocolumn\else\endquotation\fi}}{}%
\@ifundefined{maketitle}{\def\maketitle#1{}}{}%
\@ifundefined{affiliation}{\def\affiliation#1{}}{}%
\@ifundefined{proof}{\def\proof{\noindent{\bfseries Proof. }}}{}%
\@ifundefined{endproof}{\def\endproof{\mbox{\ \rule{.1in}{.1in}}}}{}%
\@ifundefined{newfi... |
\section{Introduction} \label{sec:intro}
It is now widely accepted that quasars are powered by accretion of material onto supermassive black holes (SMBHs). The continuum emission and the broad emissi | on lines (BELs) often show aperiodic variations (e.g., \citealt{FitchEtAl1967}; \citealt{AndrillatEtAl1968}). Theoretically, the BEL fluxes are supposed to vary in response to the variations of the ionizing continuum with a lag of about light travelling time. Hence, via the cross correlation analysis of the BELs and th... |
\section{Example: A Secure Cloud Server}
\label{sec:example}
\begin{figure}
\small
\[
\begin{array}{l}
Server \equiv \\\new{usage}{ \arrayType{\Int}_{\bot}}{\{0,0,0\}};\\
\new{blocked}{ \arrayType{\ | Int}_{\bot}}{\{0,0,0\}};\\
\new{nextID}{ \Int_{\bot}}{0};\\
RegisterUsers ~|~CheckUsag
\\[4mm]
RegisterUsers \equiv \\
!~\acceptPub{\mathit{newUsers}}{\chanTypePub{\arrayType{\pubKeyType}_{\bot}}};\\
~~\inputChanII{newUsers}{client1Client2};\\
~~\letk{client1}{client1Client2[0]} \\
~~\letk{client2}{client1Client2[1]} ... |
\section{Minimum Kantorovitch Estimators}
\paragraph{MKE.} Given some empirical distribution $\nu \eqdef \frac{1}{n}\sum_{j=1}^n \de_{y_j}$ where $y_j \in \Xx\subset\RR^p$, and a parametric family of | probability distributions $(\mu_\th)_{\th\in\Theta} \subset \Pp(\Xx)$, $\Theta\subset \mathbb{R}^q$, a Minimum Kantorovitch Estimator (MKE)~\cite{bassetti2006minimum,montavon2016wasserstein,bernton2017inference} for $\th$ is defined as any solution of the problem
\eql{\label{eq-fitting-energy-orig}\tag{MKE}
\umin{\th... |
\section{Introduction}
In relativistic mechanics, we describe a geometric perspective of dynamics. This means that
we start by describing pseudo-Riemannian spaces via metrics $(M, g)$ by which w | e shall measure
infinitesimal arc lengths in such spaces. Dynamical trajectories or geodesics between any two
chosen fixed points are the shortest path in terms of integrated length in between. We are
familiar with the usage of infinitesimal arc length in special relativity for flat spaces.
\begin{equation}
\la... |
\section{Introduction}\label{sec:1}
Let $C$ be a (binary) singly even self-dual code.
All codes in this note are binary.
Let $C_0$ denote the
subcode of $C$ consisting of
codewords having weight $\e | quiv0\pmod4$.
The {\em shadow} $S$ of $C$ is defined to be $C_0^\perp \setminus C$.
Shadows for self-dual codes were introduced by Conway and
Sloane~\cite{C-S}
in order to derive new upper bounds for the minimum weight of
singly even self-dual codes, and to provide
restrictions on the weight enumerators of
singly even... |
\section{Introduction}
It is well known that solutions $u$ of the $p$-Laplace equation, for
$1<p<\infty$, can be characterized as local minimizers of the $L^p$-norm of $|\nabla u|$.
This formulation | has the advantage that it can be generalized to
a metric measure space, by replacing $|\nabla u|$ with
the minimal $p$-weak upper gradient $g_u$; see Section \ref{preliminaries}
for definitions and notation.
The study of such $p$-minimizers is a starting point for nonlinear potential theory,
which is now well developed... |
\section{Introduction} \label{introduction}
With the explosive growth of informal electronic communications such as email, social media, web comments, etc., colloquial languages that were historicall | y unwritten are starting to be written for the first time. For these languages, there are extremely limited (approximately zero) resources available, not even large amounts of monolingual text data or possibly not even small amounts of monolingual text data. Even when audio resources are available, difficulties arise w... |
\section{Introduction}
Summarization of large texts is still an open problem in language processing. People nowadays have lesser time and patience to go through large pieces of text which make automat | ic summarization important. Automatic summarization has significant applications in summarizing large texts like stories, journal papers, news articles and even larger texts like books.
Existing methods for summarization can be broadly categorized into two categories \textit{Extractive} and \textit{Abstractive}. Extra... |
\section{Abstract}
The influence of elastic strain on the lithium vacancy formation and migration in bulk LiCoO$_2$
is evaluated by means of first-principles calculations within density functional the | ory (DFT). Strain dependent energies are determined directly from defective cells and also within linear elasticity theory from the elastic dipole tensor ($G_{ij}$) for ground state and saddle point configurations.
We analyze finite size-effects in the calculation of $G_{ij}$, compare the predictions of the linear el... |
\section{Introduction}
In the standard cosmological model,
the accelerated expansion of the universe is attributed
to the cosmological constant $\Lambda$.
However, to match the observed expansion, |
$\Lambda$ must be of the order of $10^{-122}$ in Planck units,
which raises a fine-tuning problem.
A possible alternative is to modify general relativity (GR) at large distances or low momenta.
A massive spin-2 field theory, known as the dRGT theory~\cite{dRGT,HasanRosen},
is a theoretically well-motivated modifi... |
\section{Introduction and Summary}
Energy conditions are indispensable in understanding classical and quantum gravity. The weakest but most commonly used of the standard energy conditions is the null | energy condition (NEC), which states that \(T_{kk} \equiv T_{ab}k^{a}k^{b} \geq 0\) where \(T_{ab}\) is the stress tensor of the matter coupled to gravity and \(k^{a}\) is any null vector. It is sufficiently weak to be satisfied by familiar classical field theories, yet strong enough to prove the second law of black h... |
\section{Introduction}
Nowadays deep laser cooling of neutral atoms is routinely used for
broad range of modern quantum physics researches including
metrology, atom optics, and quantum degeneracy s | tudies. The
well-known techniques for laser cooling below the Doppler limit,
like sub-Doppler polarization gradient cooling \cite{Dalibard1989},
velocity selective coherent population trapping
\cite{Aspect1994,Adams1995} or Raman cooling
\cite{Kasevich1992,ctannoudji1995} are restricted to atoms with
degenerated ... |
\section{Introduction}\label{intro}
Let $d$ be a positive integer. If $X$ is a subspace of $L^1 (\mathbb{T}^d)$, then we denote by $\mathcal{M}_{X \rightarrow L^2 (\mathbb{T}^d)}$ the class of all mul | tipliers from $X$ to $L^2 (\mathbb{T}^d)$, namely the class $\mathcal{M}_{X \rightarrow L^2 (\mathbb{T}^d)}$ consists of all functions $m: \mathbb{Z}^d \rightarrow \mathbb{C}$ such that for every $f \in X$ one has $\sum_{(k_1, \cdots, k_d) \in \mathbb{Z}^d} |m( k_1, \cdots, k_d) \widehat{f} (k_1, \cdots, k_d)|^2 < \in... |
\section{Introduction}
\vspace{-0.10cm}
\todo{Need motivating sentence.}
Chemical space is huge: it is estimated to contain over $10^{60}$ molecules.
Among these, fewer than 100 million compounds ca | n be found in public
repositories or databases \cite{Reymond_2012}. This discrepancy between
\textit{known} compounds and \textit{possible} compounds
indicates the potential for discoverying many new compounds with highly desirable functionality
(e.g., new energy materials, pharmaceuticals, dyes, etc.). While the
vast ... |
\section*{References}}
\makeatletter
\def\ps@pprintTitle{%
\let\@oddhead\@empty
\let\@evenhead\@empty
\let\@oddfoot\@empty
\let\@evenfoot\@oddfoot
}
\makeatother
\usepackage[usenames,dvip | snames]{color}
\usepackage[backref=page]{hyperref}
\hypersetup{
colorlinks,
citecolor=green,
linkcolor=blue,
urlcolor=Blue}
\newcommand{\riccardo}[1]{{\color{red}{Riccardo: #1}}}
\newcommand{\Riccardo}[1]{{\color{blue}{Riccardo: #1}}}
\newcommand{\Giulio}[1]{{\color{magenta}{Giulio: #1}}}
\newcommand{\Robert}... |
\section{Introduction and Statement of Results}\label{s1}
The smallest parts function ${\mathrm{spt}}(n)$ of Andrews is defined for any integer $n\geq1$ as the number of
smallest parts among the int | eger partitions of size $n$. For example, the partitions of $n=4$ are (with the smallest parts underlined):
\begin{align*}
&\underline{4},\\
&3+\underline{1},\\
&\underline{2}+\underline{2},\\
&2+\underline{1}+\underline{1},\\
&\underline{1}+\underline{1}+\underline{1}+\underline{1},
\end{align*}
and so ${\mathrm{spt}... |
\section{Introduction}\label{sec1:Intro}
\red{
\subsection{Coupling functions, their nature and uses}\label{sec12:CF_Intro}
}
\noindent Interacting dynamical systems abound in science and technology | , with examples ranging from physics and chemistry, through biology and population dynamics, to communications and climate \cite{Kuramoto:84,Winfree:80,Pikovsky:01,Strogatz:03b,Haken:83}.
The interactions are defined by two main aspects: structure and function. The structural links determine the connections and commu... |
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