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\section{Introduction and statement of main results - Smile
of the Cheshire Cat$^*$}
Structural stability and
the persistence of coherent structures under perturbations of a
dynamical system are fundamental issues in dynamical
systems theory with implications in many fields of application.
In the context of discrete, finite dimensional Hamiltonian systems,
this issue is addressed by the celebrated KAM theorem
\cite{kn:KAM}, which guarantees the persistence of most invariant tori
of the unperturbed dynamics under small Hamiltonian perturbations.
For infinite dimensional systems, defined by Hamiltonian partial
differential equations (PDEs), KAM type methods have recently been used
to obtain results on the persistence of periodic and quasiperiodic
solutions, in the case where
solutions are defined on compact spatial domains with appropriate
boundary conditions \cite{kn:Bgn}, \cite{kn:CW}, \cite{kn:Kuk}.
Variational methods have also been used to study this problem; see,
for example, \cite{kn:Bz}.
The compactness of the spatial domain ensures discreteness of the
spectrum associated with the unperturbed dynamics.
Therefore this situation is the generalization of the finite
dimensional case to systems with an infinite number of discrete
oscillators and frequencies.
In this paper we consider these questions in the context of Hamiltonian
systems for which the unperturbed dynamics has associated with it
discrete {\it and} continuous spectrum.
This situation arises in the study of Hamiltonian PDEs governing
functions defined on unbounded spatial domains or, more generally,
extended systems.
The physical picture is that of a system which can
be viewed as an interaction between one or more discrete oscillators
and a field or continuous medium.
In contrast to the KAM theory, where nonresonance implies persistence, we
find here that resonant nonlinear interaction
between discrete (bound state) modes and continuum (dispersive
radiation) modes
leads to {\it energy transfer} from the discrete to continuum modes.
This mechanism is responsible for the eventual time-decay and
nonpersistence of trapped
states. The rate of time-decay, however, is very slow and hence such a
trapped state can be thought of as a {\it metastable state}.
The methods we develop are applicable to
a large class of problems which can be viewed schematically in
terms of
"particle-field interactions".
In the present work,
we have not attempted to present general results under
weak hypotheses but rather have endeavored to illustrate, by way
of example, this widely occurring phenomenon and clearly present the
strategy for its analysis. A more general point of view will be
taken up in future work. The approach we use was motivated and in
part developed in the context of
our study of a class of nonlinear Schr\"odinger equations with
multiple
nonlinear bound states and the
quantum resonance problem \cite{kn:SW1bs},
\cite{kn:SWseco}, \cite{kn:SWGAFA}, \cite{kn:SW2bs}.
See also \cite{kn:BP1},\cite{kn:BP2} and \cite{kn:PW}.
Related problems are also considered in \cite{kn:LPS} and
\cite{kn:Nier}.
We begin with a linear dispersive Hamiltonian
PDE for a function $u(x,t)$, $x\in {\rm \rlap{I}\,\bf R}^n$ and $t>0$. Suppose that this
system has spatially localized and time-periodic solutions. Such
solutions are often called {\it bound
states}.
A typical solution to such a linear system consists of (i) a non-decaying part,
expressible as a linear combination of bound states, plus
(ii) a part which
decays to zero in suitable norms (dispersion). This paper is devoted
to the study of the following questions:
\medskip
\noindent{\bf(1)} Do small amplitude spatially localized and
time-periodic solutions persist for
typical nonlinear and Hamiltonian perturbations?
\noindent{\bf (2)} What is the character of general small amplitude solutions to
the perturbed dynamics?
\noindent{\bf (3)} How are the structures of the unperturbed dynamics manifested
in the perturbed dynamics?
\medskip
Representative of the class of equations of interest is the nonlinear
Klein-Gordon equation:
\begin{equation} \partial_t^2\ u\ =\ \left(\Delta - V(x) - m^2\right)u + \lambda f(u),\
\lambda\in{\rm \rlap{I}\,\bf R}
\label{eq:nlkg}
\end{equation}
with $f(u)$ real-valued, smooth in a neighborhood of $u=0$ and
having an expansion:
\begin{equation} f(u) = u^3 + {\cal O}(u^4) . \label{eq:nonlin}\end{equation}
Here, $u:(x,t)\mapsto u(x,t)\in{\rm \rlap{I}\,\bf R}$, $x\in {\rm \rlap{I}\,\bf R}^3$, and $t>0$.
We shall restrict our large time asymptotic analysis to the case $f(u)=u^3$.
The more general case
(\ref{eq:nonlin}) can be treated by the technique of this paper
by making suitable modification of $W^{s,p}$ norms used.
We consider (\ref{eq:nlkg}) with Cauchy data:
\begin{equation}
u(x,0)\ =\ u_0(x),\ {\rm and }\ \partial_t u(x,0)\ =\ u_1(x).
\nonumber\end{equation}
Equation (\ref{eq:nlkg}) is a Hamiltonian system with energy:
\begin{equation}
{\cal E}[u,\partial_tu]\ \equiv\
{1\over2}\ \int (\partial_tu)^2\ +\ |\nabla u|^2\ +\ m^2u^2\ +\ V(x)u^2\
dx\ +\ \lambda \int\ F(u)\ dx,
\label{eq:energy}
\end{equation}
where $F'(u)=f(u)$ and $F(0)=0$.
In the context of equations of type (\ref{eq:nlkg}), we have found the
following answers to questions (1), (2) and (3).
\noindent{\bf (A1)} In a small open neighborhood of the origin, there are no
periodic or quasiperiodic solutions; Corollary 1.1.
\noindent{\bf (A2)} All solutions in this neighborhood tend to zero (radiate)
as $t\to\infty$; Theorem 1.1.
\noindent{\bf (A3)} The time decay of solutions is anomalously slow$^*$, {\it i.e.}
a rate which is slower than the free dispersive rate; Theorem 1.1.
\bigskip
Dynamical systems of the type we analyze appear
in a number of physical settings. Consider
a nonlinear medium in which waves can propagate. If the medium has local
inhomogeneities, defects or impurities, these arise in the mathematical
model as a spatially dependent coefficient in the equation
({\it e.g.} localized potential). Such perturbations of the original
homogeneous (translation invariant) dynamics introduce new modes
into the system ({\it impurity modes}) which can trap some of the
energy and affect
the time evolution of the system; see
\cite{kn:MS}, \cite{kn:KM}, \cite{kn:ZKMV}.
\bigskip
Let $\langle K\rangle\ =\ \left( 1\ +\ |K|^2\right)^{1\over2}$.
For the nonlinear Klein-Gordon equation, (\ref{eq:nlkg}), we prove
the following result.
\begin{theo}
Let $V(x)$ be real-valued and such that
\medskip
\noindent {\bf (V1)} For $\delta>5$ and $|\alpha |\le2$,
$|\partial^\alpha V(x)|\le C_\alpha\langle x\rangle^{-\delta}$.
\noindent {\bf (V2)}
$(-\Delta +1)^{-1}\left( (x\cdot\nabla)^l V(x)\right)(-\Delta +1)^{-1}$ is
bounded on $L^2$ for $|l|\le N_*$ with $N_*\ge10$.
\noindent {\bf (V3)} Zero is not a {\it resonance} of the operator $-\Delta +V$; see
\cite{kn:JK}, \cite{kn:Y}.
Assume the operator
\begin{equation} B^2= - \Delta + V(x) + m^2 \label{eq:Bdef}\end{equation}
has continuous spectrum, $\sigma_{cont}(H)= [m^2,\infty)$, and
a unique strictly positive simple eigenvalue, $\Omega^2<m^2$ with
associated normalized eigenfunction, $\varphi$:
\begin{equation} B^2\varphi = \Omega^2\varphi.\nonumber\end{equation}
Correspondingly,
the linear Klein-Gordon equation (\ref{eq:nlkg}), with $\lambda=0$, has
a two-parameter family of spatially localized and time-periodic
solutions of the form:
\begin{equation} u(x,t)\ = \ R\ \cos(\Omega t + \theta)\ \varphi(x).\label{eq:exact}\end{equation}
Assume the resonance condition
\begin{equation}
\Gamma\equiv
{\pi\over3\Omega}\ \left({\bf P_c}\varphi^3,\delta(B-3\Omega){\bf P_c}\varphi^3\right)
\equiv\ {\pi\over3\Omega}\ \left|\left({\cal F}_c\varphi^3\right)(3\Omega)\right|^2
> 0.\label{eq:nlfgr}\end{equation}
Here, ${\bf P_c}$ denotes the projection onto the continuous spectral
part of $B$ and ${\cal F}_c$ denotes the Fourier transform relative to the
continuous spectral part of $B$.
Assume that the initial data $u_0$, $u_1$ are such that
the norms $\|u_0\|_{W^{2,2}\cap W^{2,1}}$ and
$\|u_1\|_{W^{1,2}\cap W^{1,1}}$ are sufficiently
small.
Then, the solution of the
initial value problem for (\ref{eq:nlkg}),
with $\lambda\ne0$ and $f(u)=u^3$ decays as $t\to\pm\infty$.
The solution $u(x,t)$ has the following expansion as $t\to\pm\infty$:
\begin{equation} u(x,t)\ =\
R(t)\ \cos\left(\Omega t +
\theta (t)
\right)\ \varphi(x)\ +\ \eta(x,t), \nonumber
\end{equation}
where
\begin{equation}
R(t) = {\cal O}(|t|^{-{1\over4}})\ ,
\theta (t) = {\cal O}(|t|^{1\over2}),\ {\rm and}\
\| \eta(\cdot ,t) \|_8 = {\cal O}(|t|^{-{3\over4}}).
\label{eq:uasymp}
\end{equation}
More precisely,
\begin{eqnarray}
R\ &=&\ \tilde R\ +\ {\cal O}(|\tilde R|^2),\ (
\ |\tilde R| \ {\rm small})
\nonumber\\
\tilde R\ &=&\
2^{1\over4}\tilde R_0\
({1+{3\over4}\tilde R_0^4\ \Omega^{-1}\ \lambda^2\ \Gamma\ |t|})^{-{1\over4}}
\cdot\left( 1+{\cal O}(|t|^{-\delta})\right),\ \delta >0\nonumber\\
R(0)\ &=&\ R_0,\ R_0^2\ =\ \left|\left(\varphi,u_0\right)\right|^2
\ +\ \Omega^{-2}\left|\left(\varphi,
u_1\right)\right|^2\nonumber
\end{eqnarray}
\end{theo}
\begin{cor}
Under the hypotheses of Theorem 1.1,
there are no periodic or quasiperiodic orbits of the flow $t\mapsto
\left( u(t),\partial_tu(t)\right)$ defined by (\ref{eq:nlkg}) in a
sufficiently small neighborhood of the origin in the space
$\left( W^{2,1}\cap W^{2,2}\right) \times \left( W^{1,2}\cap W^{1,1}\right)$.
\end{cor}
It is interesting to contrast our results with those known for
Hamiltonian partial differential equations for a function $u(x,t)$,
where $x$ varies over a
compact spatial domain, {\it e.g.} periodic or Dirichlet boundary
conditions \cite{kn:Bgn}, \cite{kn:CW}, \cite{kn:Kuk}.
For nonlinear wave equations of the
form,
(\ref{eq:nlkg}), with {\it periodic boundary conditions} in $x$,
KAM type results have been proved; invariant tori, associated with
a
{\it nonresonance} condition persist under
small perturbations.
The {\it nonresonance}
hypotheses of such results fail in the current context
, a consequence of
the continuous spectrum associated with unbounded spatial
domains.
In our situation, non-vanishing {\it resonant coupling} (condition
(\ref{eq:nlfgr}))
provides the mechanism for the radiative decay and
therefore
nonpersistence of
localized periodic solutions.
\noindent
{\bf Remarks:}
\noindent{(1)}
The condition (\ref{eq:nlfgr}) is a {\it nonlinear variant of
the Fermi golden rule} arising in quantum mechanics; see, for example,
\cite{kn:CFKS},
\cite{kn:SWGAFA}.
This condition holds generically in the space of potentials satisfying
the hypothesis of the theorem.
Note that the condition (\ref{eq:nlfgr}) implies that
\begin{equation} 3\Omega\in \sigma_{cont}(B) \label{eq:hrc}\end{equation}
{\it i.e.} the frequency, $3\Omega$,
generated by the cubic nonlinearity lies in the continuous spectrum of
$B$.
The hypothesis (\ref{eq:nlfgr}) ensures a nonvanishing coupling to the
continuous spectrum.
\noindent {(2)} The regularity and decay hypotheses on $V(x)$ are related to the
techniques we use to obtain suitable decay estimates on the linear evolution in
$L^2(\langle x\rangle^{-\sigma} dx)$ and $L^p$; see section 2.
\noindent (3) {\it Persistence of dynamically
stable bound states for special perturbations:}
There are nonlinear perturbations of the linear Klein-Gordon equation,
(\ref{eq:nlkg}) with $\lambda =0$, for which
there is a persistence of time-periodic and spatially
localized
solutions. Suppose we extend our considerations to the class of
complex-valued
solutions: $u:{\rm \rlap{I}\,\bf R}^n\times{\rm \rlap{I}\,\bf R}\to \C$, and study the perturbed
equation:
\begin{equation}
\left(\ \partial_t^2\ -\ \Delta\ +\ V(x)\ +\ \lambda |u|^{p-1}\
\right)u\ =\ 0,\ \label{eq:complex-nlkg}
\end{equation}
where $1<p<\infty$ for $n=1,2$ and $1<p< {{n+2}\over{n-2}}$ for
$n\ge3$. Unlike (\ref{eq:nlkg}), equation (\ref{eq:complex-nlkg})
has the symmetry $u\mapsto ue^{i\gamma}$ and it has been shown \cite{kn:RW}
that
(\ref{eq:complex-nlkg})
has time periodic and spatially localized solutions of
the form
$e^{i\omega t}\Phi(x;\omega)$ with $\Phi\in H^1$, which
bifurcate
from the zero solution at the point eigenvalue of
$-\Delta + V(x) -\omega^2$, by global variational
\cite{kn:PLL}, \cite{kn:strauss} and local bifurcation methods
\cite{kn:Nirenberg}. There are numerous other examples of equations for
which the persistence of coherent structures under perturbations is
linked to the perturbation respecting a certain symmetry of the
unperturbed problem.
The stability of small amplitude bifurcating
states of (\ref{eq:complex-nlkg}) can be proved using the methods of
\cite{kn:GSS}, \cite{kn:MIW86}. An asymptotic
stability and
scattering theory has been developed for
nonlinear Schr\"odinger dynamics (NLS) in
\cite{kn:SW1bs}. If the
potential $V(x)$ supports more than one bound
state, the above methods
can be used to show the persistence of
{\it nonlinear excited states}. However, it is
shown in \cite{kn:SW2bs} that
the NLS excited states are unstable, due to a
resonant mechanism of the
type studied here for (\ref{eq:nlkg}).
\noindent{(4)}
In contrast with the time-decay rates associated with linear dispersive
equations, the time-decay rates
of typical solutions described by Theorem 1.1 is anomalously slow. See
section 8 for a discussion of this point.
\bigskip
We now present an outline of the ideas behind our analysis.
For $\lambda=0$, solutions of equation (\ref{eq:nlkg}) are naturally
decomposed into their discrete and continuous spectral components:
\begin{equation} u(x,t)\ =\ a(t)\varphi(x)\ +\ \eta(x,t),
\quad \left(\varphi,\eta(\cdot,t)\right)\ =\ 0, \label{eq:decomp}\end{equation}
where $(f,g)$ denotes the usual complex inner product on $L^2$.
The functions $a(t)$ and
$\eta(x,t)$ satisfy system of {\it decoupled} equations:
\begin{eqnarray}
a'' + \Omega^2\ a &=& 0, \\
\partial_t^2\ \eta\ +\ B^2\eta &=& 0,
\end{eqnarray}
with initial data
\begin{eqnarray}
a(0)\ &=&\ \left(\varphi,u_0\right),\ \quad a'(0)\ =\
\left(\varphi,u_1\right)\nonumber\\
\eta(x,0)\ &=&\ {\bf P_c} u_0,\ \quad \partial_t\ \eta(x,0)\ =\ {\bf P_c} u_1
\label{eq:aetadata}
\end{eqnarray}
For $\lambda\ne0$, and for small amplitude initial conditions, we use
the same decomposition, (\ref{eq:decomp}). Now the discrete and the
continuum modes are coupled and the dynamics are qualitatively described
by the following {\it model system}:
\begin{eqnarray}
a'' + \Omega^2\ a &=&
3\lambda a^2\left(\chi,\eta(\cdot ,t)\right) \label{eq:modelcce1} \\
\partial_t^2\ \eta -\ \Delta \eta + m^2\eta &=& \lambda\ a^3\chi
\label{eq:modelcce2}.
\end{eqnarray}
Here, $\chi(x)$ is a localized function of $x$; in particular,
$\chi={\varphi^{3}}$, and we assume (see (\ref{eq:nlfgr})) $3\Omega > m$.
In selecting the model problem (\ref{eq:modelcce1}-\ref{eq:modelcce2}),
we have replaced $B^2$, restricted to its continuous spectral part, by
$B_0^2=-\Delta + m^2$, which intuitively should lead to the same
qualtitative result.
The system (\ref{eq:modelcce1}-\ref{eq:modelcce2})
can be interpreted as a system
governing the dynamics of discrete oscillator, with amplitude $a(t)$
and natural frequency $\Omega$, coupled
to a continuous medium in which waves, of amplitude $\eta(x,t)$, propagate,
or as an oscillating particle coupled to a field.
\footnote{A related example is a model introduced in 1900 by H. Lamb
\cite{kn:Lamb}, governing the
oscillations of mass-spring-string system. See also
\cite{kn:BK}, \cite{kn:FKM}, \cite{kn:SDG}, \cite{kn:JP}.}
The system (\ref{eq:modelcce1}-\ref{eq:modelcce2})
is a Hamiltonian system with conserved
total energy functional:
\begin{eqnarray} \tilde{\cal E}[\ \eta,\partial_t\eta, a,a'\ ] &\equiv&
\frac{1}{2}\int\ (\partial_t\eta)^2+|\nabla\eta |^2\ +\ m^2 \eta^2\ dx\ +\
\frac{1}{2}\left({a'}^2 + \Omega^2 a^2 \right)
\nonumber \\
&-&\lambda a^3\int\chi(x)\eta(x,t)\ dx \label{eq:conserve}\end{eqnarray}
We now solve (\ref{eq:modelcce2}) and substitute the result into
(\ref{eq:modelcce1}).
Note that, to leading order, solutions of (\ref{eq:modelcce1})
oscillate with frequency $\Omega$. Therefore the $a^3$ term
in (\ref{eq:modelcce2}) acts as an external driving force with a $3\Omega$
frequency component.
Since $9\Omega^2$\ is larger than $m^2$, a nonlinear
resonance of the oscillator with the continuum takes place.
To calculate the effect of this resonance requires a careful analysis
involving (i) a study of
singular limits of
resolvents as an eigenvalue parameter approaches the continuous
spectrum (see section 4) and (ii) and the derivation of a normal form which is
natural for an infinite dimensional conservative system with
dispersion
(see section 5).
This leads to an equation of the following type for $a(t)$ (or rather some
near-identity transform of it):
\begin{equation} a'' + \left(\Omega^2 + {\cal O}(\vert a\vert^2)
\right)a =
-\Gamma\ r^4\ a',\ \ t>0\label{eq:dosc}\end{equation}
where $ r = {\cal O}(|a|)$, and $\Gamma>0$ is the positive number
given in (\ref{eq:nlfgr}). For the model system (\ref{eq:modelcce2}),
${\cal F}_c$ in (\ref{eq:nlfgr}) is replaced by the usual Fourier
transform.
This is the equation of a nonlinearly damped oscillator:
\begin{equation} {d\over dt}\left((a')^2 + [\Omega^2 + {\cal O}(|a|^2)] a^2\right) =
-2\Gamma r^4 (a')^2\ <0,\ {\rm for\ } \ t>0\nonumber\end{equation}
Therefore, nonlinear resonance is responsible for {\it internal damping}
in the system; energy is lost or rather transferred
from the discrete oscillator into the field or
continuous medium, where it is propagated to infinity as dispersive
waves. Solutions of
(\ref{eq:dosc}) decay with a rate ${\cal O}(t^{-1/4})$, and it follows
that $\|\eta(\cdot ,t)\|_\infty = {\cal O}(t^{-3/4}).$ Note, however
that the
total energy of the system, an $H^1$ type quantity, is conserved.
In (\ref{eq:dosc}), we have neglected
higher order effects coming from the continuous spectral part of $H$. These, it
turns out, has a small effect and can be treated perturbatively.
Aspects of the analysis are related to our recent treatment of the
quantum resonance problem \cite{kn:SWseco}, \cite{kn:SWGAFA}.
The situation with quantum
resonances can be summarized briefly as follows. Let $H_0$ be
a self-adjoint operator having an eigenvalue, $\lambda_0$, embedded in
its continuous spectrum, with corresponding normalized eigenfunction $\psi_0$.
Let $W$ be a small localized symmetric perturbation,
satisfying the (generically valid) Fermi golden rule resonance condition:
\begin{equation} \Gamma_0\ \equiv\ \pi\left(W\psi_0,\delta(H_0-\lambda_0) {\bf P_c} W\psi_0\right)\ne0.
\label{eq:fgr}\end{equation}
Then in a neighborhood of $\lambda_0$, we show that the spectrum of
$H=H_0+W$ is
absolutely continuous by proving that all solutions of the Schr\"odinger
equation:
\begin{equation}
i\ \partial_t \psi\ =\ H \psi\ =\ (H_0 + W) \psi, \label{eq:ls}
\end{equation}
with initial data which is spectrally localized (with
respect to $H$) in a neighborhood of
$\lambda_0$, decay to zero in a local energy norm as $t\to\pm\infty$.
Such solutions are characterized by exponential time-decay for an
initial transient period, and then algebraic (dispersive decay)
thereafter. During this transient period, $A(t)$, the projection onto the mode
$\psi_0$, is governed by the equation:
\begin{equation} {A'}(t) = (i\lambda_* - \Gamma_0)A(t),\ \ t>0 \label{eq:linA}\end{equation}
where $\lambda_* \sim \lambda_0 + \left(\psi_0,W\psi_0\right)$, and
by (\ref{eq:fgr}), $\Gamma_0>0$.
In the class of nonlinear problems under consideration, if we express
the amplitude, $a(t)$, as
\begin{equation}
a(t)\ =\ A(t)\ e^{i\Omega t} + \overline A (t)\ e^{-i\Omega t}
\label{eq:aA}
\end{equation}
then we find after a near-identity transformation an equation of the
form:
\begin{equation} A' = ic_{21}|A|^2A\ +\ (ic_{32} - {3\over4}{\lambda^2\over\Omega}\Gamma)|A|^4A,\quad t>0.\label{eq:Aosc}\end{equation}
From this, the ${\cal O}(t^{-1/4})$ behavior is evident.
Equations (\ref{eq:aA}-\ref{eq:Aosc}) lead to (\ref{eq:dosc}).
As in (\ref{eq:dosc}), we have in (\ref{eq:linA}) and (\ref{eq:Aosc})
neglected the higher order
coupling to the continuous spectral (radiation) component
of the solution. These contributions are treated perturbatively.
\noindent {\bf Remarks:}
\noindent{(1)} {\it Lamb shift}:\
Note that in the nonlinear problem, asymptotically there is no {\it Lamb
shift} type correction to the frequency; the frequency shift is ${\cal
O}(|A|^2)={\cal O}(t^{-1/2})$ as $t\to\pm\infty$.
\noindent{(2)}
{\it Emergence of irreversible behavior from reversible dynamics;
dissipation through dispersion}:\
Being Hamiltonian, the underlying equation of motion,
(\ref{eq:nlkg}), is time reversible. In particular, the equation has
the invariance: $u(x,t)\mapsto u(x,-t)$. Yet, the equation in
(\ref{eq:Aosc}) is clearly not time-reversible. This apparent paradox
is related to the "$\varepsilon$-{\it prescription}" discussed in section
4 and Proposition 2.1; the singular limit
\begin{equation} \lim_{\varepsilon\downarrow 0}\ \exp(i\sqrt{-\Delta + m^2}\ t)(-\Delta +m^2 -
E \pm i \varepsilon)^{-1}\end{equation}
satisfies a local decay estimate as $t\to\pm\infty$. For $t<0$, the
corresponding equation for $A(t)$ would have $-\Gamma$ replaced by
$+\Gamma$; {\it cf.} \cite{kn:AB}, \cite{kn:BP2}, \cite{kn:SWseco},
\cite{kn:SWGAFA}.
\bigskip
\bigskip
The nonpersistence of
small amplitude spatially localized and time-periodic
or quasiperiodic
solutions to (\ref{eq:nlkg}) has been studied in
\cite{kn:sigalcmp},\cite{kn:sigjapan}. In this work, the phenomenon of
nonpersistence is
formulated as a question concerning the instability of embedded eigenvalues of a
suitable {\it linear} self-adjoint operator.
A result on structural instability is proved;
under the hypothesis (\ref{eq:nlfgr}),
time-periodic or quasiperiodic solutions of the linear problem equation
($\lambda = 0$) do not continue to nearby solutions of the nonlinear
problem ($\lambda\ne0$).
The question of nonpersistence of periodic solutions has
also been considered extensively in the context of
the sine-Gordon equation
\begin{equation} \partial_t^2 u = \partial_x^2 u - \sin u. \label{eq:sg}\end{equation}
Spatially localized and time-periodic
solutions of the sine-Gordon equation are called {\it breathers} and the
question of their persistence under small Hamiltonian perturbations in the
dynamics has been the subject of extensive investigations. See, for
example, \cite{kn:SK},
\cite{kn:C}, \cite{kn:CP}
\cite{kn:WeA},
\cite{kn:BMW}, \cite{kn:Bnr},
\cite{kn:D},
\cite{kn:Kich},
\cite{kn:PS}, \cite{kn:St}, \cite{kn:McSh}.
Analytical, formal asymptotic and numerical studies
strongly suggest that for
typical Hamiltonian perturbations of the sine-Gordon equation, for
example, the $\phi^4$ model:
\begin{equation} \partial_t^2\ u = \partial_x^2 u - u + u^3, \label{eq:phi4}\end{equation}
no small amplitude breathers exist and that solutions obtained from
spatially localized initial data {\it radiate}
to zero
very slowly as $t$ tends to infinity.
\footnote{ In \cite{kn:MA}, breather type solutions have been
constructed for the discrete
sine-Gordon equation, where $\partial_x^2$, is replace by its discretization
on a sufficiently coarse lattice. Also, a generalization of
the notion of breather
has been considered in the geometric context of {\it
wave maps} \cite{kn:SS}.}
We believe this is related to the mechanism for slow radiative decay, as
explained by Theorem 1.1 in the context of (\ref{eq:nlkg}).
Finally, we wish to comment on the connection between our work and
the approach taken
in \cite{kn:sigalcmp}, \cite{kn:BMW}, \cite{kn:D}, and
\cite{kn:Kich}.
As in the continuation theory of periodic solutions of ordinary
differential equations \cite{kn:CL}, it is natural to
seek a periodic solution of (\ref{eq:nlkg}) for
$\lambda\ne0$ which behaves, as the amplitude $a$ tends to zero, like
a solution (\ref{eq:exact}) of the linear limit problem.
The equation is {\it autonomous} with respect to time, so we seek a
$2\pi\Omega_a^{-1}$-periodic solution for $\lambda\ne0$ with an
amplitude dependent period. Since we do not know the period {\it \'a priori},
it is convenient to define
\begin{equation}
u(x,t)\ =\ U_a(x,s), \quad\ s=\Omega_a t
\nonumber\end{equation}
and require that $U_a(x,s)$ be $2\pi$ periodic in $s$. Thus
(\ref{eq:nlkg}) becomes
\begin{equation}
\left( \Omega_a^2\ \partial_s^2\ +\ B^2\ \right)\ U_a\ =\ \lambda\ U_a^3.
\label{eq:s-nlkg}
\end{equation}
We formally expand the solution and frequency:
\begin{eqnarray}
U_a\ &=&\ aU_1\ +\ a^3\ U_3\ +\ ...\nonumber\\
\Omega_a &=&\ \Omega\ +\ a^2\ \Omega_2\ +\ ...\ .
\label{eq:Ua}\end{eqnarray}
Substitution of (\ref{eq:Ua}) into (\ref{eq:s-nlkg}) and
assembling terms according to their order in $a$, one gets a hierarchy of
equations beginning with
\begin{eqnarray}
{\cal O}(a^1):\qquad
\left( \Omega^2\partial_s^2\ +\ B^2\ \right)\ U_1\ &=&\ 0\label{eq:U1}\\
{\cal O}(a^3):\qquad
\left( \Omega^2\partial_s^2\ +\ B^2\ \right)\ U_3\ &=&\
\lambda U_1^3\ -\ 2\Omega\Omega_2\partial_s^2U_1
\label{eq:U3}
\end{eqnarray}
Equation (\ref{eq:U1}) has a solution
\begin{equation} U_1(x,s)\ =\ \cos{s}\ \varphi(x).\nonumber\end{equation}
Substitution into (\ref{eq:U3}) gives the following explicit equation
for $U_3$:
\begin{equation}
\left( \Omega^2\partial_s^2\ +\ B^2\ \right)\ U_3\ =\
\left( {3\lambda\over4}\varphi^3\ +\ 2\Omega\Omega_2\varphi\ \right)\
\cos{s}\ + {\lambda\over4}\varphi^3\cos{3s}
\label{eq:U3a}
\end{equation}
We now express $U_3$ in the form $U_3=U_3^{(1)} + U_3^{(2)}$, where
\begin{eqnarray}
\left( \Omega^2\partial_s^2\ +\ B^2\ \right)\ U_3^{(1)}\ &=&\
\left( {3\lambda\over4}\varphi^3\ +\ 2\Omega\Omega_2\varphi\ \right)\
\cos{s}\label{eq:U3i}\\
\left( \Omega^2\partial_s^2\ +\ B^2\ \right)\ U_3^{(2)}\ &=&\
{\lambda\over4}\varphi^3\cos{3s}.\label{eq:U3ii}
\end{eqnarray}
Since the inhomogeneous term in (\ref{eq:U3i}) is nonresonant with the
continuous spectrum of $B^2$, one can find a $2\pi$-periodic solution
$U_3^{(1)}$ provided the right hand side is
$L^2(S^1_{2\pi}\times{\rm \rlap{I}\,\bf R}^3)$ - orthogonal to the adjoint zero mode:
$\cos{s}\ \varphi(x)$. This latter condition uniquely determines $\Omega_2$.
Note however that the right hand side of
(\ref{eq:U3ii}) is resonant with the continuous spectrum of $B^2$ if
$3\Omega > m$. To compute the obstruction to solvability, seek
a solution of (\ref{eq:U3ii}) of the form
$U_3^{(2)}\ =\ \cos{3s}\ F$. Then,
\begin{equation}
\left(\ B^2\ -\ 9\Omega^2\ \right)F\ =\ {\lambda\over4}\varphi^3\nonumber
\end{equation}
and thus we expect to find $F\in L^2$ if and only if the component of
$\varphi^3$ in the direction of the generalized eigenfunction at
frequency $3\Omega$ of the operator $B$ vanishes. Therefore, if the
nonlinear Fermi golden rule (\ref{eq:nlfgr}) holds, our formal expansion
in $L^2(S^1_{2\pi}\times{\rm \rlap{I}\,\bf R}^3)$ breaks down.
The relation with our work is that we
prove that this obstruction to solvability, in fact, implies
the radiative behavior of solutions
described in our main theorem.
\bigskip
\noindent{\bf Acknowledgments:}
The problem studied in this paper was raised by T.C. Spencer in
lectures and informal discussions in the late 1980's.
M.I.W. learned of this problem from T.C. Spencer and A.S. from I.M. Sigal.
The authors wish to thank them for their insights and continued
interest.
The authors also wish
to thank B. Birnir for stimulating
discussions, and R. Pyke and J.B. Rauch for their careful reading
of and thoughtful comments on the manuscript.
This research was carried out while MIW was on sabbatical
leave in the Program in Applied and Computational Mathematics at
Princeton University. MIW would like to thank Phil Holmes for his
hospitality and for providing a stimulating research environment.
This research was supported in part by NSF grant DMS-9401777 and an
FAS-Rutgers grant award (AS) and by NSF grant
DMS-9500997 (MIW).
\section{Linear Analysis}
\bigskip
In this section we summarize the tools of linear analysis
employed in this paper.
\subsection{ Estimates for the (free) Klein Gordon equation}
We begin by considering the Cauchy problem for the linear Klein-Gordon
equation for a function $u(x,t),\ x\in {\rm \rlap{I}\,\bf R}^n,\ t\ne0$.
\begin{eqnarray}
\partial_t^2 u\ &=&\ (\Delta-m^2)u=-B_0^2 u\label{eq:lkg}\\
u(x,0)\ &=&\ u_0(x),\ \ \partial_t u(x,0)=u_1(x)\ .\label{eq:lkgdata}
\end{eqnarray}
There exist operators $E_0^{(0)}(t)$ and $E_1^{(0)}(t)$ such that
\begin{equation}
u(x,t)\ =\ E_0^{(0)}(t)\ u_0\ +\ E_1^{(0)}(t)\ u_1. \label{eq:lkgsoln}
\end{equation}
We write
\begin{eqnarray} E_0^{(0)}(t) f &=&\ \cos B_0t\ f\ , \rm{and} \nonumber\\
E_1^{(0)}(t) g\ &=&\ {\sin B_0t\over B_0} g\ ,\label{eq:3.4}
\end{eqnarray}
where ($\omega(k)\ =\ \sqrt{m^2+k^2}$):
\begin{eqnarray}
E_0^{(0)}(t) f\ &=&\ \int\ \cos\omega(k)t\ \hat f(k)\ e^{ik\cdot x}\ dk\nonumber\\
E_1^{(0)}(t) g\ &=&\ \int\ {\sin\omega(k)t\over\omega(k)}\ \hat g(k)\ e^{ik\cdot
x}\ dk.
\label{eq:ezeo}
\end{eqnarray}
The first result we cite is proved using stationary phase methods; see
\cite{kn:Br}. See \cite{kn:Kl} for another approach to decay estimates
for (\ref{eq:lkg}).
Let $W^{s,p}({\rm \rlap{I}\,\bf R}^n)$ denote the Sobolev space of functions with
derivatives of order $\le s$ in $L^p$.
\begin{theo}
Let $1<p\le 2$,\ ${1\over p}+{1\over p'}=1$,\ $\delta\equiv
{1\over2}-{1\over p'}$ and $0\le\theta\le1$. Then,
\noindent (a)\ if $\delta(n+1+\theta)\le \nu +s$, we have for $\nu=0,1$:
\begin{eqnarray}
\|\ E_\nu^{(0)} g\|_{p'}\ &\le&\ K(t)\ \|g\|_{s,p}\ ,\ t\ge0,\
{\rm where } \label{eq:eozest}
\\
K(t)\ &=&\ C t^{-(n-1-\theta)\delta},\ 0<t\le1,\nonumber\\
&=&\ C t^{-(n-1+\theta)\delta}, \ t\ge1.
\label{eq:ezzest}
\end{eqnarray}
\noindent (b)
If $s\ge (1/2-1/p')(n+2)-1$, then for $t\ge1$ the (Schr\"odinger-like) $L^{p'}$
decay rate,
$t^{-n({1\over2}-{1\over p'})}$, holds in (\ref{eq:ezzest}).
\end{theo}
In subsequent sections, we shall use some specific consequences of this
result.
\begin{cor}
Consider the linear Klein Gordon equation (\ref{eq:lkg}) in dimension
$n=3$. Then,
\begin{eqnarray}
||E_1^{(0)}(t) g||_8 &\le& C\ t^{-{9\over 8}}\ ||g||_{1,{8\over7}}\
\ t\ge 1 \label{eq:eoztge1}\\
||E_1^{(0)}(t) g||_8\ &\le&\ C\ t^{-{3\over 8}}\ ||g||_{1,{8\over7}}\
0<t\le 1
\label{eq:eoztle1}\\
|| E^{(0)}_\nu (t) g||_4\ &\le&\ C\ t^{-{1\over 2}}\ ||g||_{1,{4\over3}},\
\ t > 0,\
\nu\ =\ 0,1.
\label{eq:ezjtge1}
\end{eqnarray}
\end{cor}
\noindent {\it proof:} Estimates (\ref{eq:eoztge1}) and (\ref{eq:eoztle1})
follow from the theorem
with the choice of parameters: $p'=8$,\ $s=1$,\ $n=3$, and $\theta
=1$. Estimate (\ref{eq:ezjtge1}) follows from the theorem with the choice of
parameters:
\ $p'=4$,\ $s=1$, $n=3$\ and $\theta=0$.
\bigskip
\subsection{Estimates for the Klein Gordon equation with a
potential}
\medskip
We now consider the Cauchy problem for the linear
Klein-Gordon equation with a potential
\begin{equation}
\partial^2_t u\ =\ (\Delta-m^2-V(x))u\ =\ -B^2u
\label{eq:lkgv}
\end{equation}
where $B^2$ is positive and self-adjoint.
We write the solution to the initial value problem for (\ref{eq:lkgv})
with initial data (\ref{eq:lkgdata}) as:
\begin{eqnarray}
u(x,t)\ =\ E_0(t) u_0 &+& E_1(t) u_1\ ,\ {\rm where} \\
\smallskip
E_0(t) f\ &=&\ \cos(Bt)f\ ,\ \rm{and}\\
E_1(t) g\ &=&\ {\sin (Bt)\over B} g\ .\nonumber
\end{eqnarray}
One expects that estimates of the type appearing in Theorem 2.1 and
Corollary 2.1 will hold as well for $E_0(t)$ and $E_1(t)$ restricted to ${\bf P_c}
L^2$, the
continuous spectral part of $H = B^2$. One can relate functions of the
operator $H$, on its continuous spectral part, to functions of $H_0\ =\
B_0^2$
using {\it wave operators}. Let
\begin{equation}
W_+\ =\ {\rm strong}\ -\ \lim_{t\to\infty}\ e^{itH}e^{-itH_0}.
\label{eq:waveop}
\end{equation}
Wave operators relate $H_0$ to $H$ on ${\bf P_c} L^2$ via the intertwining property:
\begin{equation}
H\ = W_+\ H_0\ W_+^*\quad {\rm on }\ {\bf P_c} L^2.
\label{eq:intertwine}
\end{equation}
K. Yajima \cite{kn:Y} has proved the $W^{k,p}({\rm \rlap{I}\,\bf R}^n)$
boundedness of wave operators for the
Schr\"odinger equation. A consequence of this work is the following
result for spatial dimension $n=3$:
\begin{theo}
Let $H=-\Delta+V$,
where $V(x)$ be real-valued function on ${\rm \rlap{I}\,\bf R}^3$
satisfying the following hypotheses, which are satisfied by smooth and
sufficiently rapidly decaying
potentials:
\noindent For any $|\alpha|\le\ell$ there is a constant $C_\alpha$ such that
$$\bigg|{\partial^\alpha V\over\partial x^\alpha}(x)\bigg|\ \le\ C_\alpha\langle x\rangle^{-\delta}\
,\quad \delta> 5\ .$$
Additionally, assume that $0$ is neither an eigenvalue nor a {\it resonance} of
$H$; see \cite{kn:Y}, \cite{kn:JK}.
If $0\le k,k'\le l$ and $1\le p,p'\le\infty$, then there exists a constant $C>0$ such
that for any Borel function $f$ on ${\bf R}^1$ we have
$$C^{-1}\ ||f(H_0)||_{B(W^{k,p}, W^{k',p'})}\
\le\ ||f(H){\bf P_c}(H)||_{B(W^{k,p}, W^{k',p'})}\ \le\
C\ ||f(H_0)||_{B(W^{k,p}, W^{k',p'})}.$$
Here,
${\bf P_c}(H)$ denotes the projection onto the continuous spectral part of
the operator $H$.
\end{theo}
\noindent {\bf Remark:} In our applications, we shall use Theorem 2.2 with
$|l|\le2$.
Theorem 2.2 implies that the dispersive estimates for the free
Klein Gordon group carry over to the operators $E_0(t)$ and $E_1(t)$ restricted
to the continuous spectral part of $B$.
\begin{theo}
If $g\in \ \hbox{\rm Range}\ {\bf P_c}(H)$, then each of the estimates of Theorem 2.1 and Corollary 2.1 hold with
$E^{(0)}_j$ replaced by $E_j$.
\end{theo}
\subsection{ Singular resolvents and time decay}
As discussed in the introduction, the damping term in the effective nonlinear
oscillator (\ref{eq:Aosc}), is related to the evaluation of a singular limit
of the resolvent as the eigenvalue parameter approaches the continuous
spectrum. To ensure that the correction terms to the nonlinear
oscillator (\ref{eq:Aosc}) can be treated perturbatively, we require
local decay estimates for the operator
$e^{iBt}(B-\Lambda\pm i0)^{-1}$, where
$\Lambda$ is a point in the interior of the continuous spectrum
of $B$ ($\Lambda >m$).
Such estimates are analogous to those used by the authors in recent
work on a time dependent approach to the quantum resonance problem
\cite{kn:SWGAFA}.
We begin with a proposition, which is essentially a restatement of
Theorem 2.3 for $E_j(t)$, and is proved the same way.
\begin{prop} ({\it $W^{s,p}$ estimates for $e^{iBt}$})
Assume that $V(x)$ satisfies the hypotheses of Theorem 2.2 ($n=3$);
see \cite{kn:Y} for hypotheses for general space dimension, $n\ge3$.
Let $p$ and $p'$ be as in Theorem 2.1 and let $l\ge s\ge
({1\over2}-{1\over p'})(n+2)$, where $l$ is as in Theorem 2.2. Then,
\begin{equation}
\|\ e^{iBt}\
{\bf P_c}\ \psi\|_{p'}
\ \le\
C|t|^{-n({1\over2}-{1\over p'})}\ \|\psi\|_{s,p},\ t\ne0,
\label{eq:Wsp}
\end{equation}
\end{prop}
The next proposition is the "singular" resolvent estimate we shall
require in section 7. Let $\sigma_*(n)=\max\{{n\over2},2+{2n\over
n+2}\}$.
\begin{prop} Assume the hypotheses of Proposition 2.1. Additionally, assume
that $V(x)$ satisfies hypothesis {\bf (V2)} of Theorem 1.1. Also, let
$\sigma>\sigma_*(n)$.
Then, for any point $\Lambda$ ($\Lambda
> m$) in the continuous spectrum of $B$ we have for $l=0,1,2$:
\begin{eqnarray}
\|\langle x\rangle^{-\sigma}\ e^{iBt}\ \left(B-\Lambda +
i0\right)^{-l}\ {\bf P_c}\ \langle x\rangle^{-\sigma}\ \psi\|_{2}
\ &\le&\
C\ \langle t\rangle^{-{2n\over n+2}}\ \|\psi\|_{1,2},\ t>0,\nonumber\\
\|\ \langle x\rangle^{-\sigma}\ e^{iBt}\ \left(B-\Lambda -
i0\right)^{-l}\ {\bf P_c}\ \langle x\rangle^{-\sigma} \psi\|_{2}
\ &\le&\
C\ \langle t\rangle^{-{2n\over n+2}}\ \|\psi\|_{1,2},\ t<0,
\label{eq:ld2}
\end{eqnarray}
\end{prop}
\noindent{\it proof}: We prove the estimate (\ref{eq:ld2}) for the case of
the $t>0$. For the case, $t<0$,
the same argument with simple modifications applies.
Let $g_\Delta = g_\Delta(B)$
denote a smooth
characteristic functions of an open interval, $\Delta$
which contains
$\Lambda$ and is contained in the continuous spectrum of $B$.
Also, let
${\overline g}_\Delta\equiv 1 - g_\Delta$. We then
write, for $l=1,2$:
\begin{eqnarray}
e^{iBt}\ \left( B - \Lambda + i\varepsilon\right)^{-l}{\bf P_c}\ &=&\
e^{iBt}\ g_\Delta(B)\ \left( B - \Lambda + i\varepsilon\right)^{-l}{\bf P_c}\
+\ e^{iBt}\ \overline g_\Delta(B)\ \left( B - \Lambda +
i\varepsilon\right)^{-l}{\bf P_c}\nonumber \\
&\equiv&\ S_1^\varepsilon(t) \ +\ S_2^\varepsilon(t).\label{eq:s1s2}
\end{eqnarray}
We now estimate the operators $S_j\equiv \lim_{\varepsilon\to0}S_j^\varepsilon$,
$j=1,2$ individually.
\bigskip
\centerline{\it Estimation of $S_1(t)$:}
\medskip
Consider the case $l=2$; the case $l=1$ is simpler.
First, we note that:
\begin{eqnarray}
&&\langle x\rangle^{-\sigma}\ S_1^\varepsilon(t)\ \langle x\rangle^{-\sigma}\ \nonumber\\
\ \ \ &=&\ -e^{it(\Lambda -i\varepsilon)}\ \int_t^\infty \ ds\ \int_s^\infty\
d\tau\
\langle x\rangle^{-\sigma}\ e^{i\tau(B-\Lambda +i\varepsilon)}\
g_\Delta(B){\bf P_c}\ \langle x\rangle^{-\sigma}\ \label{eq:integralrep}
\end{eqnarray}
Now we claim that the operator in the integrand satisfies the estimate:
\begin{equation}
\| \langle x\rangle^{-\sigma}\ e^{i\tau(B-\Lambda +i\varepsilon)}\
g_\Delta(B){\bf P_c}\ \langle x\rangle^{-\sigma}\|_{{\cal B}(L^2)}\ \le\
C\ {e^{-\varepsilon\tau}\over{\langle \tau\rangle^{r}}},
\label{eq:2.20}\end{equation}
for $r<\sigma$. The desired estimate on $S_1^\varepsilon$
then follows by use of (\ref{eq:2.20}) in
(\ref{eq:integralrep}) and that $\sigma>\sigma_*(n)$.
It is simple to see that (\ref{eq:2.20}) is
expected. For, suppose that instead of $B{\bf P_c}$ we had $B_0$. Let
$\omega(k) = \sqrt{m^2+k^2}$, the dispersion relation of $B_0$.
Then, setting $L= \left(i\partial_{k_j}\omega\right)^{-1}\partial_{k_j}$,
and using that
$|\nabla_k\omega|\ne0$ on the support of
$g_\Delta$,
we get
\begin{eqnarray}
e^{iB_0t}g_\Delta(B_0) f\ &=&\ \int\ e^{i\omega(k)t}\ e^{ik\cdot x}g_\Delta(k)
\hat f(k)\ dk
\nonumber\\
&=&\ t^{-r}\ \int\ L^r\left( e^{i\omega(k)t}\right) \ e^{ik\cdot
x}\ g_\Delta(k) \hat f(k)\ dk\nonumber\\
&=&\ t^{-r}\ \int\ e^{i\omega(k)t} \left(L^{\dagger}\right)^{r} \
\left(e^{ik\cdot x} g_\Delta(k) \hat f(k)\right)\ dk.
\label{eq:express} \end{eqnarray}
Estimation of $\langle x\rangle^{-\sigma} e^{iB_0t}g_\Delta(B_0) f$ in $L^2$ by
Fourier transform methods, using that
$|\nabla \omega|$ is bounded away from zero on the
support of
$g_\Delta$,
we have that if $\sigma >\max\{ {n\over2},2\}$ and $r<\sigma$, then
\begin{equation}
\|\langle x\rangle^{-\sigma}e^{iB_0t}g_\Delta(B_0)f\|_2\ \le\ C\langle
t\rangle^{-r}\|\langle x\rangle^\sigma f\|_2.
\label{eq:B0variant1}\end{equation}
Use of this estimate, in the above expression for $S_1^\varepsilon$ (with
$B$ replaced by $B_0$) gives, for $l=0,1,2$:
\begin{equation}
\|\langle x\rangle^{-\sigma}e^{iB_0t}\left(B_0-\Lambda+i0\right)^{-l}\langle
x\rangle^{-\sigma}\|_{{\cal B}(L^2)}\le C\langle t\rangle^{-r+l}.
\label{eq:B0variant2}\end{equation}
Two approaches to proving
an estimate of the type (\ref{eq:B0variant1}) and
(\ref{eq:B0variant2}) for $e^{iBt}g_\Delta(B){\bf P_c}$ are as follows:
\noindent (a) One can "map" the estimate for $B_0$ to that for
$B{\bf P_c}$ using the wave operator $W_+$. In this approach we would
need to derive estimates for $W_+g_\Delta(B_0)$ in weighted $L^2$
spaces, or alternatively
\noindent (b) One can use the approach based on the "Mourre estimate",
developed in quantum
scattering theory. This approach is more in the spirit of energy
estimates for partial differential equations and does not require
the use of wave operators.
Here, we shall follow the latter approach. Time decay estimates like
(\ref{eq:B0variant1}) are a consequence of an approach to {\it minimal velocity
estimates} of Sigal and Soffer \cite{kn:SigSof}, which were proved using
the ideas of Mourre \cite{kn:Mourre}; see also Perry, Sigal \& Simon
\cite{kn:PSS}. For our
application to the the operator $e^{-iBt}g_\Delta(B)$, we shall refer to
special cases of results
stated in Skibsted \cite{kn:Skibsted} and Debi\'evre, Hislop \&
Sigal
\cite{kn:DHS}.
We first introduce some definitions and assumptions:.
\noindent {\bf (A0)}\
\ (a) Let $N\ge2$ and $g_\Delta\in C_0^\infty$, be a smooth
characteristic function which is equal to one on the open interval $\Delta$.
\ (b) Let $H$ and $A$ denote self adjoint operators on a Hilbert
space ${\cal H}$. Assume $H$ is bounded below.
Let ${\cal D}$ denote the domain of $A$ and
${\cal D}(H)$ the domain of $H$. Assume ${\cal D}\cap{\cal D}(H)$ is
dense in ${\cal D}(H)$, and
let $\langle A\rangle\equiv (I+|A|^2)^{1\over2}$.
\medskip
\noindent {\bf (A1)}\ Let ${\rm ad}_A^0(H)=H$. For $1\le k\le N_*$, define
iteratively the commutator form
\begin{equation} i^k{\rm ad}_A^k(H)\ =\ i\left[\ i^{k-1}{\rm ad}_A^{k-1}(H)\ ,\ A\ \right]\nonumber
\end{equation}
on ${\cal D}\cap{\cal D}(H)$. Assume that for $1\le k\le N_*$, $i^k{\rm
ad}_A^k(H)$ extends
to a symmetric operator with domain ${\cal D}(H)$,
where $N_*=\left[ N+{3\over2} \right]+1$.
\medskip
\noindent {\bf (A2)}\ For $|s|<1$,\ $e^{iAs} : {\cal D}(H)\ \rightarrow
{\cal D}(H)$ and $\sup_{|s|<1}\|\ He^{iAs}\psi\ \|_{\cal H}\ <\ \infty,$
for any $\psi\in {\cal D}(H)$.
\medskip
\noindent {\bf (A3)}\ {\it Mourre estimate}:
\begin{equation}
g_\Delta (H)\ i[H,A]\ g_\Delta (H)\ \ge \theta\ g_\Delta(H)^2\
\label{eq:mourre}
\end{equation}
for some $\theta>0$.
\bigskip
Under the above assumptions, we have, via Theorem 2.4 of
\cite{kn:Skibsted}, the following:
\begin{theo}\ Assume conditions (A0)-(A3). Then,
for all $\varepsilon_1 >0$ and $t>0$
\begin{equation}
\|\ F\left({A\over t}<\theta\right)\ e^{-iHt}\ g_\Delta (H)
\langle A\rangle^{-{N\over2}}\psi\
\|_{\cal H}
\ \le\ C \langle t\rangle^{ -{N\over2}+\varepsilon_1 }\ \|\ \psi\ \|_{\cal
H},
\label{eq:mvb}
\end{equation}
where $\theta$ is as in (\ref{eq:mourre}).
\end{theo}
\medskip
To prove this theorem we set $A(\tau)\ =\ A\ -\ b\tau$, where $\tau\equiv t+1$.
Then, for any $b<\theta$, we have by
(\ref{eq:mourre}) that the Heisenberg derivative,
$DA(\tau)\ \equiv \partial_tA(\tau) + i[H,A(\tau)]$,
satisfies
\begin{equation}
g_\Delta\ DA(\tau)\ g_\Delta\ =\
g_\Delta\ \left( i[H,A] - b \right) g_\Delta\ \ge \left(\theta\ -\
b\right)g_\Delta^2.
\nonumber \end{equation}
The result now follows by an application of Theorem 2.4 of
\cite{kn:Skibsted}.
\noindent {\bf Remark:} The hypotheses of Theorem 2.4 can be relaxed \cite{kn:HSS}
to the following two conditions:
(i) the operator $g_\Delta(H)\ {\rm ad}_A^n(H)\ g_\Delta(H)$ can be extended to a
bounded operator on ${\cal H}$ for $n=0,1,2...,\left[{N\over2}+1\right]+1$, and
(ii) the Mourre estimate, (\ref{eq:mourre}).
\bigskip
We shall apply Theorem 2.4 for the case $H = B = \sqrt{-\Delta + m^2
+V(x)}$, $A=\left(x\cdot p\ +\ p\cdot x\right)/2$, $p=-i\nabla_x$ and ${\cal H} = L^2$.
Before verifying the hypotheses of Theorem 2.4,
we show how this
theorem is used to
derive the desired estimates on $e^{iBt}g_\Delta(B)$.
With the application of Theorem 2.4 in mind, we estimate the
norm of $\langle x\rangle^{-\sigma} e^{iBt}g_\Delta(B)$
by decomposing it into the
spectral sets on which $A/t$ is less than and greater than or equal to
$\theta$. Let $\Delta_1$ denote an interval containing $\Delta$ and denote by
${\cal C}$ the operator that associates to a function $f$ its complex
conjugate ${\overline f}$. Furthermore, note
that $e^{iBt} \ =\ {\cal C}\ e^{-iBt}\ {\cal
C}$ and ${\cal C}\ g(B)\ =\ g(B)\ {\cal C}$, if $g$ is real-valued on
the spectrum of $B$. Then
we find,
\begin{eqnarray}
\|\ \langle x\rangle^{-\sigma}\ e^{iBt}g_\Delta(B)\psi\ \|_2
\ &=& \|\ \langle x\rangle^{-\sigma}\ g_{\Delta_1}(B)\ e^{iBt}\ g_\Delta(B)\psi\ \|_2
\nonumber\\
&=& \|\ \langle x\rangle^{-\sigma}g_{\Delta_1}(B) {\cal C}\
e^{-iBt}\ {\cal C}\ g_\Delta(B)\psi\|_2
\nonumber\\
\ &=&
\|\ \langle x\rangle^{-\sigma}g_{\Delta_1}(B)\ \langle A\rangle^\sigma\cdot
\langle A\rangle^{-\sigma}
\ e^{-iBt}\ g_\Delta(B){\overline\psi}\ \|_2\nonumber\\
&\le&\
\|\ \langle x\rangle^{-\sigma}g_{\Delta_1}(B)\ \langle A\rangle^\sigma\|_{{\cal B}(L^2)}
\cdot
\|\ \langle A\rangle^{-\sigma}
\ e^{-iBt}\ g_\Delta(B){\overline \psi}\ \|_2\nonumber\\
&\le&\ C\ \|\ \langle A\rangle^{-\sigma}
\ e^{-iBt}\ g_\Delta(B) {\overline\psi}\ \|_2\nonumber\\
&\le&\ C_1 \|\ F\left({A\over t} <\theta\right)\ \langle
A\rangle^{-\sigma}
\ e^{-iBt}\ g_\Delta(B){\overline\psi}\ \|_2\ \nonumber\\
&&\ +\ C_2\|\ F\left({A\over t}\ge \theta\ \right) \langle
A\rangle^{-\sigma}
\ e^{-iBt}\ g_\Delta(B){\overline\psi}\ \|_2
\label{eq:split}
\end{eqnarray}
We have used here that, with $A$ defined as above, the $L^2$ operator norm
of $\langle x\rangle^{-\sigma}g_{\Delta_1}(B) \langle A\rangle^\sigma$ is bounded; see
\cite{kn:PSS}.
By Theorem 2.4, the first term on the right hand side of (\ref{eq:split}) can
be
estimated from above by:
\begin{eqnarray}
&&C_1 \|\ F\left({A\over t} <\theta\right)\ \langle A\rangle^{-\sigma}
\ e^{-iBt}\ g_\Delta(B) g_{\Delta_1}(B) {\overline\psi}\ \|_2\
\le\nonumber\\
&&\ \ \ \ C_1 C\langle t\rangle^{-{N\over2}+\varepsilon_1}
\|\ \langle A\rangle^{N\over2}g_{\Delta_1}(B)\langle x\rangle^{-{N\over2}}\|_{{\cal
B}(L^2)}\
\|\langle x\rangle^{N\over2}\psi\|_2.\label{eq:term1}
\end{eqnarray}
Since $\theta t>0$, the second term is bounded as follows:
\begin{equation}
C_2\|\ F\left({A\over t}\ge \theta\ \right) \langle
A\rangle^{-\sigma}
\ e^{-iBt}\ g_\Delta(B) {\overline \psi}\ \|_2\
\le\ C\langle t\rangle^{-\sigma}\
\|\psi\|_2.
\label{eq:term2}\end{equation}
From (\ref{eq:split}), (\ref{eq:term1}) and (\ref{eq:term2}), we have
\begin{equation}
\|\langle x\rangle^{-\sigma}e^{iBt}g_\Delta(B)\psi\|_2\ \le\
C\left( \langle t\rangle^{-\sigma}\ +\ \langle
t\rangle^{-{N\over2}+\varepsilon_1}\right)\
\|\langle x\rangle^{N\over2} \psi\|_2.
\label{eq:S1nearsingularity}
\end{equation}
Use of (\ref{eq:S1nearsingularity}) in a direct
estimation of
(\ref{eq:integralrep}) gives:
\begin{equation}
\|\langle x\rangle^{-\sigma} S^\varepsilon_1(t)\langle
x\rangle^{-\sigma}\|_{{\cal B}(L^2)}\le
C\ \left(\ \langle t\rangle^{-{N\over2}+2+\varepsilon_1}\ +\ \langle t\rangle^{-\sigma +2} \right).
\label{eq:S1nearsingularityA}\end{equation}
We make the final choice of $N$ and $\sigma$ after estimation of
$S_2^\varepsilon(t)$.
\bigskip
To complete the estimation of $S_1^\varepsilon(t)$, it
remains to verify hypotheses (A0)-(A3).
These hypotheses are known to hold for the operator
$H=B^2=-\Delta+V +m^2$; see \cite{kn:CFKS}. Hypothesis (A0) holds $H=B$ with domain
$W^{1,2}({\rm \rlap{I}\,\bf R}^n)$. Clearly hypothesis (A2) holds for $H=B$ since it holds for
$H=B^2$. Hypothesis
(A1) can be reduced to its verification for $B^2$
using the Kato square root formula \cite{kn:RS1}: for any $\psi\in{\cal D}(B^2)$:
\begin{equation}
B\psi =\ \pi^{-1}\ \int_0^\infty\ w^{-1/2}\ B^2\ (B^2 + w)^{-1}\ \psi\ dw.
\label{eq:Katosqrt1}
\end{equation}
To verify (A1) for the case $k=1$ we must show that $[A,B]\ B^{-1}$
is a bounded operator on $L^2$.
Using (\ref{eq:Katosqrt1}) we have:
\begin{equation}
[A,B]\ B^{-1}\ =\ \pi^{-1}\
\int_0^\infty\ w^{1\over2}\ (B^2+w)^{-1}\ [A,B^2]\
B^{-1}\ (B^2+w)^{-1}\ dw
\label{eq:AB}
\end{equation}
Since
\begin{equation}
\left[ B^2,iA\right]\ =\ 2B^2\ -x\cdot\nabla V\ -2\left( V\ +\ m^2 \right),
\nonumber\end{equation}
we have
that
\begin{equation}
[B^2,iA]\ B^{-1}\ =\ 2 B\ -\ \left( x\cdot\nabla V + 2V
\right)
\ B^{-1}\
-\ 2m^2B^{-1}.\nonumber\end{equation}
Substitution into (\ref{eq:AB}) we get:
\begin{eqnarray}
[A,B]\ B^{-1}\ &=&\ {2\over\pi}\ \int_0^\infty\ w^{1\over2}\ B\ (B^2+w)^{-2}\
dw\nonumber\\
\ &-&\ {1\over\pi}\ \int_0^\infty\ (B^2+w)^{-1}\ \left(x\cdot\nabla V\ +2V -
2m^2\right)
B^{-1} (B^2+w)^{-1}\ dw\nonumber\\
&\equiv&\ J_1\ +\ J_2.
\end{eqnarray}
The term $J_1$ can be rewritten as
\begin{equation} J_1\ =\ -{2\over\pi}\ \int_0^\infty\ w^{1\over2}\ {d\over dw}
(B^2+w)^{-1}\ dw\ B\nonumber\\
=\ I,\nonumber\end{equation}
which follows from integration by parts and the formula (\ref{eq:Katosqrt1})
with $\psi$ replaced by $B^{-1}\psi$.
Using that $\|(B^2+w)^{-1}\|\le (\Omega^2+w)^{-1}$,
\begin{equation}
\|\ \left(x\cdot\nabla V\ +2V - 2m^2\right) B^{-1}\ \|\ \le\ \|x\cdot\nabla
V\ +2V - 2m^2\|_\infty\
\|B^{-1}\|_{{\cal B}(L^2)},\nonumber\end{equation}
and the hypotheses on $V$ we have that
for some constant $C$ dependent on $V$,
\begin{equation}
|J_2|\ \le\ C\int_0^\infty\ w^{1\over2}\ (\Omega^2+w)^{-2}\ dw\ <\ \infty.
\nonumber\end{equation}
The higher order commutators are handled in a similar manner; they are even
simpler because each successive commutator results in an extra factor of
$(B^2+w)^{-1}$.
This leaves us with verification of the Mourre estimate (A3) for $H=B$. Proposition
2.2 of \cite{kn:DHS} says that under hypotheses on $B^2$, verified in \cite{kn:CFKS},
that (A3) holds for $B$ as well.
\bigskip
\centerline{\it Estimation of $S_2$:}
\medskip
In $S_2(t)$, the energy is localized away from $\Lambda$ so we seek to
use the $W^{k,s}$ estimates of Proposition 2.1. Note that of the
cases $l=1$ and $l=2$, the case $l=1$ is "worse" because ${\overline g}_\Delta$
localizes the energy away from the singularity at $\Lambda$, and the
$l=1$ term has slower decay for large energy. We therefore carry out the
estimation for $l=1$.
Let $q^{-1}+p'^{-1}=1/2$ and $p'^{-1} + p^{-1}=1$.
Since $\sigma > {n\over2}$, $\langle x\rangle^{-\sigma}\in L^q$ and therefore:
\begin{eqnarray}
&&\| \langle x\rangle^{-\sigma}\ S_2^\varepsilon(t)\ \langle x\rangle^{-\sigma}\ f \|_2
\ \le\
C\|\langle x\rangle^{-\sigma}\|_{{\cal B}(L^{p'},L^2)}\
\|e^{iB_0t}(B_0-\Lambda+i0)^{-1}{\overline g}_\Delta(B_0)\ W_+^*
\langle x\rangle^{-\sigma} f\|_{p'}\nonumber\\
&& \ \ \le\ C\|e^{iB_0t}B_0^{-1}\|_{{\cal B}(W^{1,p},L^{p'})} \
\| {\overline g}_\Delta(B_0)(B_0-\Lambda+i0)^{-1} B_0 W_+^*
\langle x\rangle^{-\sigma}\ f \|_{1,p}\nonumber\\
&&\ \ \le\
C\|e^{iB_0t}B_0^{-1}\|_{{\cal B}(W^{1,p},L^{p'})} \
\| {\overline g}_\Delta(B_0)(B_0-\Lambda+i0)^{-1}B_0\cdot B_0 W_+^*
\langle x\rangle^{-\sigma}\ f \|_p\nonumber\\
&& \ \ \le\ C\|e^{iB_0t}B_0^{-1}\|_{{\cal B}(W^{1,p},L^{p'})} \
\| {\overline g}_\Delta(B_0)(B_0-\Lambda+i0)^{-1}B_0 \|_{{\cal
B}(L^p)}
\|B_0 W_+^* \langle x\rangle^{-\sigma}\ f \|_p
\label{eq:S2estimate}
\end{eqnarray}
The three factors in (\ref{eq:S2estimate}) are estimated as follows:
(i) By part (a) of Theorem 2.1,
\begin{equation}
\|e^{iB_0t}B_0^{-1}\|_{{\cal B}(W^{1,p},L^{p'})}\ \le\
C\ |t|^{-{2n\over n+2}},
\end{equation}
where $p=2-8/(n+6)$ and $p'= 2 (n+2)/(n-2)$.
(ii) $\| {\overline g}_\Delta(B_0)(B_0-\Lambda+i0)^{-1}B_0 \|_{{\cal
B}(L^p)}$
is bounded because ${\overline g}_\Delta(\mu)(\mu-\Lambda+i0)^{-1}\mu$
is a multiplier on $L^p$ \cite{kn:Stein}.
\noindent
Using the boundedness of $W_+$ on $W^{2,p}$ and that
$\sigma>\max\{ {n\over2},2 \}$, we have
\begin{eqnarray}
\|B_0 W_+^* \langle x\rangle^{-\sigma}\ f \|_p\ &\le&\ \|W_+^* \langle
x\rangle^{-\sigma}\ f \|_{1,p} \nonumber\\
&\le&\ \| W_+^*\|_{{\cal B}(W^{2,p})}\ \| \langle x\rangle^{-\sigma}\ f\|_{1,p}\nonumber\\
&\le&\ C\| f\|_{1,2}.
\nonumber\end{eqnarray}
Therefore,
\begin{equation}
\| \langle x\rangle^{-\sigma} S_2^\varepsilon \langle x\rangle^{-\sigma} \psi\|_2\ \le\
C\langle t\rangle^{-{2n\over{n+2}}}\ \|\psi\|_{1,2}.
\label{eq:S2awayfromsingularityA}
\end{equation}
We now combine the estimates of $S_j^\varepsilon(t),\ j=1,2$ to complete the proof.
Combining (\ref{eq:S1nearsingularityA}) and
(\ref{eq:S2awayfromsingularityA}) and taking $\varepsilon\downarrow 0$ yields
\begin{equation}
\| \langle x\rangle^{-\sigma}\ e^{iBt}\ \left( B-\Lambda + i0\right)^{-l}\
{\bf P_c}\ \langle x\rangle^{-\sigma}\ \psi \|_2
\ \le\
C\ \left( \langle t\rangle^{-{N\over2} + 2 +\varepsilon_1}\ +\ \langle t\rangle^{-\sigma +2}\ +\
\langle t\rangle^{ -{2n\over n+2} }\
\right) \|\psi\|_{1,2}.
\nonumber\end{equation}
The estimates (\ref{eq:ld2}) now follows by taking $N$
and $\sigma$ such that
\begin{eqnarray}
\sigma\ &\ge&\ 2\ +\ {2n\over n+2}\nonumber\\
\sigma\ &>&\ \max\{ {n\over2},2 \}\nonumber\\
{N\over2}\ &\ge&\ 2\ +\ {2n\over n+2}\ +\ \varepsilon_1\nonumber
\end{eqnarray}
The constraints on $\sigma$ are implied by the hypothesis $\sigma>\sigma_*(n)$.
The remaining constraint holds if $N\ >\ 8$. Since we have applied Theorem 2.4
in our estimation of $S_1^\varepsilon$, we need that (A1) hold with $N_*=\left[
N+{3\over2}\right]+1\ge10$.
This completes the proof of Proposition 2.2.
\section{Existence theory}
In this section we outline an existence theory for (\ref{eq:nlkg})
with initial conditions $u(x,0) = u_0\in W^{2,2}({\rm \rlap{I}\,\bf R}^3)$ and $\partial_tu(x,0) = u_1\in
W^{1,2}({\rm \rlap{I}\,\bf R}^3)$.
We first reformulate the initial value problem and then introduce the
hypotheses
on the operator $H$.
Regarding (\ref{eq:nlkg})
as a perturbation of a linear constant coefficient equation, we first
write the initial value problem as:
\begin{eqnarray}
\partial_t^2 u\ +\ B_0^2 u\ &=&\ -Vu \ +\ \lambda f(u).\label{eq:ivpnlkg1}\\
u(x,0)\ &=&\ u_0(x)\nonumber\\
\partial_tu(x,0)\ &=&\ u_1(x)\nonumber
\end{eqnarray}
Let
\begin{eqnarray}
{\bf u}\ &=&\ \pmatrix{ u\cr v},\ \ U(t)\ =\ \pmatrix{ \cos(B_0t) & \sin(B_0t)/B_0\cr
-B_0\sin(B_0t) &\ \cos(B_0t) },\nonumber\\
{\bf u}_0\ &=&\ \pmatrix{ u_0 \cr u_1},\ \
{\bf F}({\bf u})\ =\ \pmatrix{0 \cr -V u\ +\ \lambda f(u)}.\nonumber
\end{eqnarray}
Then, the initial value problem can be reformulated as a system of first order
equations:
\begin{equation}
\partial_t{\bf u}\ =\ \pmatrix{0&1\cr-B_0^2&0}{\bf u}\ +\ {\bf F}({\bf u}).\nonumber
\end{equation}
We now follow the strategy of reformulating the problem of finding a
solution of the initial value problem
as the problem of finding a fixed
point ${\bf u}$ of an appropriate mapping. In particular, we seek ${\bf u}$ in the space
\begin{equation}
{\bf X}_0\ =\ W^{2,2}({\rm \rlap{I}\,\bf R}^3)\ \times\ W^{1,2}({\rm \rlap{I}\,\bf R}^3)
\label{eq:Xzspace}
\end{equation}
satisfying
\begin{equation}
{\cal A}\ {\bf u} \ =\ {\bf u}, \label{eq:integral-equation}
\end{equation}
where
\begin{equation}
{\cal A}{\bf u}(t)\ \equiv\ U(t){\bf u}_0\ +\ \int_0^t U(t-s)\ F({\bf u})\ ds. \label{eq:Adef}
\end{equation}
\medskip
\noindent
For a discussion of
the existence and low energy scattering for the case $V\equiv 0$, see
\cite{kn:GV}, \cite{kn:strauss}, \cite{kn:Kl} and references
cited therein.
\bigskip
\noindent\ \ {\bf Hypotheses of H\ =\ $-\Delta +V$}
\noindent {\bf (H1)}\ $V\in W^{1,\infty}$
\noindent {\bf (H2)}\ $ H=B^2 $ is a positive and self-adjoint operator
\noindent {\bf (H3)}\ The semi-infinite interval, $[m^2,\infty)$, consists of
absolutely continuous spectrum of $H$.
\noindent {\bf (H4)}\ $H$ has exactly
one (simple)
eigenvalue $\Omega^2$ satisfying $0\ <\ \Omega^2\ <\ m^2$,
with corresponding eigenfunction $\varphi\in
L^2,\
||\varphi||_2=1.$
\noindent {\bf (N)}\ $f(u)\ =\ u^3\ +\ f_4(u),\ f_4(u)\ =\ {\cal O}(u^4)$
and $f(u)$ is smooth in a neighborhood of $u=0$.
These hypotheses are by no means the least stringent, but are
sufficient for the present purposes.
\begin{theo} ({\bf Local existence theory})
\noindent
Consider the Cauchy problem for the nonlinear Klein Gordon equation
(\ref{eq:nlkg}) with
initial data, ${\bf u}_0$ of class ${\bf X}_0$.
\item{(a)} There exists strictly positive
numbers,
$T_{max}$ and $T^{max}$ (forward and backward
maximal times of existence) which depend on the ${\bf X}_0$ norm of the
initial data, such that the initial value problem has a
unique solution of class
$C^0\left((-T^{max},+T_{max}); {\bf X}_0\right)$ in the sense of the integral
equation (\ref{eq:integral-equation}).
\item{(b)} For $t\in (-T^{max},+T_{max})$ conservation of
energy holds: ${\cal E}[u(\cdot,t), \partial_t u(\cdot,t)]\ =\
{\cal E}[u_0, u_1]$, where ${\cal E}$ is defined in equation
(\ref{eq:energy}).
\item{(c)} Either $T_{max}$ is finite or $T_{max}$ is infinite. If
$T_{max}$ is finite, then
\begin{equation}
\lim_{t \uparrow T_{max}}\ \| {\bf u}(\cdot,t)\|_{{\bf X}_0}\ =\ \infty.
\label{eq:Xz-controls}
\end{equation}
The analogous statement holds with $T_{max}$ replaced by $T^{max}$ and
$\lim_{t\uparrow T_{max}}$ replaced by $\lim_{t\downarrow -T^{max}}$ .
\end{theo}
We now sketch a proof of Theorem 3.1. We restrict our attention to the case
$t\ge0$; the proof is identical for $t\le0$. Furthermore,
we shall, for simplicity, consider the
case of the cubic nonlinearity: $f(u)=u^3$.
Using hypothesis (H1) on $V$,
it is simple to show,
using the estimates of Corollary 2.1,
that for $T>0$ sufficiently
small and depending essentially on the ${\bf X}_0$ norm of ${\bf u}_0$,
the mapping
${\cal A}$ maps a closed ball in $C^0\left( [0,T);{\bf X}_0\right)$
to itself, and is a strict contraction. This ensures the existence of
a unique fixed point, which is a $C^0\left( [0,T);{\bf X}_0\right)$ solution
of the initial value problem (\ref{eq:ivpnlkg1})
in the sense of the integral equation (\ref{eq:integral-equation}).
That the ${\bf X}_0$ norm must blow up if $T_{max}$ is finite is a standard
continuation argument based on the fixed point proof of part (a).
In section 7, we study the asymptotic behavior of solutions as
$t\to\pm\infty$. A consequence of this analysis and the argument below
is that if ${\bf u}_0$ satisfies
the more stringent hypothesis that the norm $\|{\bf u}_0\|_{{\bf X}}$ is sufficiently
small, where
\begin{equation}
{{\bf X}}\ \equiv\ \left( W^{2,2}\cap W^{2,1}\right)\ \times
\ \left(W^{1,2}\cap
W^{1,1} \right),\label{eq:bX}
\end{equation}
then $T_{max}=T^{max}=\infty$ and the solution decays to zero
as dilineated in the statement of Theorem 1.1.
We reason as follows. A unique solution, ${\bf u}(t)$,
exists locally
in time and is continuous in $t$ with values in ${\bf X}_0$.
It follows that for $|t|<T$, the $W^{1,4}$ and $L^8$ norms
of $u(\cdot,t)$ are finite. Moreover, the solution satisfies energy
conservation and therefore $\|u(t)\|_{W^{1,2}}+\|v(t)\|_2$ is
bounded uniformly by a
constant which is independent of $T$, and depends only on $\|u_0\|_{W^{1,2}}+
\|v_0\|_2$.
To ensure that the quantities estimated continue to be well defined and satisfy
the {\it 'a priori} estimates of section 7 it suffices to show that
$\|{\bf u}(t)\|_{{\bf X}_0}$ remains bounded as $t\uparrow T$.
A direct and elementary estimation of the integral equation
(\ref{eq:integral-equation}) yields the estimate:
\begin{eqnarray}
\|{\bf u}(t)\|_{{\bf X}_0}\ &\le& C\left(\|u_0\|_{W^{2,2}}\ +\ \|u_1\|_{W^{1,2}}\right)\ \nonumber\\
&+&\
C\left(\|V\|_{W^{1,\infty}},\lambda\right)\
\int_0^t\ \left( \|u(s)\|_{W^{1,2}}\ +\ \|u(s)\|_{W^{1,2}}^3\ +\
\|u^2(s)\nabla u(s)\|_2\ \right) ds.\nonumber\\
&&\label{eq:H2ap}
\end{eqnarray}
The main tool used in obtaining (\ref{eq:H2ap}) is the bound
$\|E_1^{(0)}(t)\partial_i\|_{{\cal B}(L^2)}\le m^{-1}$.
A simple consequence of the {\it 'a priori} bound (\ref{eq:aprioriest}) and
the decomposition of $u(t,\cdot)$ is
that
\begin{equation}
\|\nabla u(t)\|_4\ +\ \| u(t)\|_8\ \le\ {\tilde C},
\ |t|<T.
\label{eq:bound}
\end{equation}
The constant $\tilde C$, depends on the norm $\| {\bf u}_0\|_{{\bf X}}$.
The first two terms in the integrand of (\ref{eq:H2ap}) are uniformly bounded
by conservation of energy.
Furthermore, this energy bound together with (\ref{eq:bound})
implies a bound on the last term in the integrand
of the estimate (\ref{eq:H2ap}). It follows that $\|{\bf u}(t)\|_{{\bf X}_0}$ remains
bounded as $t\uparrow T$. Therefore, given the estimates of section 7 we
have $T_{max} =\infty$, and the decay of solutions.
A further consequence of the proof is:
\begin{cor}
Under the hypotheses of Theorem 1.1, the solution of the initial value problem
exists globally in $W^{2,2}({\rm \rlap{I}\,\bf R}^3)$ and satisfies the estimate:
\begin{equation} \|u(t)\|_{W^{2,2}}\le C\ \langle t\rangle.\nonumber\end{equation}
\end{cor}
\section{ Isolation of the key resonances and formulation as coupled
finite and infinite dimensional dynamical system}
Using the notation (\ref{eq:Bdef}), the initial value problem for
(\ref{eq:nlkg}) can be rewritten as
\begin{eqnarray}
&&\partial^2_t\ u\ +\ B^2\ u\ =\ \lambda\ f(u),\ \ f(u)=u^3\label{eq:nlkg1} \\
&&u(x,0)\ =\ u_0(x),\ \partial_t\ u(x,0)\ =\ u_1(x).\nonumber
\end{eqnarray}
For small amplitude solutions,
it is natural to decompose the solution as follows:
\begin{eqnarray}
u(x,t)\ &=&\ a(t)\varphi (x)+\eta (x,t),
\label{eq:ansatz}\\
\left( \eta(\cdot,t),\varphi\right)\ &=&\ 0 \quad \hbox{\rm for
all}\ \ t\
.
\label{eq:orthog}
\end{eqnarray}
Substitution of (\ref{eq:ansatz}) into (\ref{eq:nlkg1}) gives
\begin{equation}
a''\varphi\ +\ \partial^2_t\eta\ +\ \Omega^2 a\varphi\ +\ B^2\eta\
=\ \lambda\ f(a\varphi\ +\ \eta)
\label{eq:a1}
\end{equation}
We now implement (\ref{eq:orthog}). Taking the inner product of
(\ref{eq:a1}) with $\varphi$ gives
\begin{equation}
a''\ +\ \Omega^2 a\ =\ \lambda(\varphi,f(a\varphi+\eta)).
\label{eq:aeqn}
\end{equation}
Let ${\bf P_c}$ denote the projection onto the continuous spectral part
of
$B^2$, i.e.
\begin{equation}
{\bf P_c}\ v\equiv
v-(\varphi,v)\varphi. \label{eq:Pc}
\end{equation}
Then, since $\eta = {\bf P_c}\eta$, we have
\begin{equation}
\partial^2_t\eta\ +\ B^2\eta=\lambda {\bf P_c} f(a\varphi+\eta)
\label{eq:etaeqn}
\end{equation}
Equations (\ref{eq:aeqn})-(\ref{eq:etaeqn}) comprise a coupled dynamical
system
for the bound state and continuous
spectral components (relative to $H=B^2$) of the solution $u$.
The initial conditions for this system are given by
(\ref{eq:aetadata}).
Expansion of the cubic terms in (\ref{eq:aeqn}-\ref{eq:etaeqn})
gives the system
\begin{eqnarray}
a''\ +\ \Omega^2a\ &=&\ \lambda\
\left[\ a^3\int\varphi^4\ +\ 3a^2\int\varphi^3\eta\ +\ 3a\int
\varphi^2\eta^2\ +\ \int\varphi\eta^3\ \right]\
\label{eq:aeqn2}\\
\partial_t^2\ \eta\ +\ B^2\ \eta\ &=&\ \lambda {\bf P_c}\ \left(
a^3\varphi^3\ +\ 3a^2\varphi^2\eta
\ +\ 3a\varphi\eta^2\ +\ \eta^3\ \right) ,\label{eq:etaeqn2}
\end{eqnarray}
with initial conditions
\begin{eqnarray}
a(0)&=&(\varphi,u_0)\ ,\quad a'(0)=(\varphi,u_1)\ \nonumber\\
\eta(x,0)\ &=&\ {\bf P_c} u_0\ ,\quad\partial_t\eta(x,0)\ =\ {\bf P_c} u_1
\label{eq:data}
\end{eqnarray}
We now locate the source of the resonance. Equation (\ref{eq:aeqn2})
has a homogeneous solution which
oscillates with frequencies $\pm\Omega$. Thus, to leading order, $\eta$ solves a driven wave
equation containing the driving frequencies $\pm 3\Omega$. If $9\Omega^2>m^2$, then by $(H3)$, we expect a
resonant interaction with radiation modes of energy
$3\Omega\in\sigma_{cont}(H)$.
This resonant part of $\eta$, has its dominant effect on the $a$-oscillator
in the term of (\ref{eq:aeqn2}),
which is linear in $\eta$. Our goal is to derive from
(\ref{eq:aeqn2}-\ref{eq:etaeqn2}) an equivalent dynamical system
which is of the type described in the introduction, but which is corrected by terms which decay sufficiently
rapidly with time and which can therefore be treated perturbatively.
We first write
\begin{equation}
\eta=\eta_1+\eta_2+\eta_3\ ,
\label{eq:eta123}
\end{equation}
where $\eta_1(t)$ satisfies the {\it linear dynamics} with the given initial data:
\begin{equation}
\partial^2_t\ \eta_1\ +\ B^2\eta_1\ =\ 0\ ,\quad\eta_1(x,0)\ =\ {\bf P_c} u_0\ ,\
\partial_t\ \eta_1(x,0)\ =\ {\bf P_c}\ u_1,\
\label{eq:eta1eqn}
\end{equation}
and $\eta_2(t)$ is the leading order {\it response}
\begin{equation}
\partial^2_t\ \eta_2\ +\ B^2\eta_2\ =\ \lambda\ a^3\ {\bf P_c}\ \varphi^3;\
\eta_2(x,0)=0,\
\partial_t\ \eta_2(x,0)=0\ .
\label{eq:eta2eqn}
\end{equation}
Equation (\ref{eq:aeqn2}) can now be written in an expanded form.
\begin{eqnarray}
a''\ +\ \Omega^2\ a\ &=&\ \lambda\left[\
a^3\int\varphi^4+3a^2\int\varphi^3\ \left(\ \eta_1+\eta_2+\eta_3\ \right)
+3a\int\varphi^2
\eta^2+\int\varphi
\eta^3\ \right]\nonumber\\
&\equiv&\ F(a,\eta)
\label{eq:aeqn3}
\end{eqnarray}
We expect the function $a(t)$ to consist of "fast oscillations",
coming from the natural frequency $\Omega$ and its nonlinearly generated
harmonics, and slow variations due to its small amplitude.
We next extract from $a(t)$ the dominant "fast" oscillations of frequency
$\Omega$:
\begin{equation}
a(t)\ =\ A\ e^{i\Omega t}+\overline A\ e^{-i\Omega t}\ .
\label{eq:aA1}
\end{equation}
We then substitute (\ref{eq:aA1}) into (\ref{eq:aeqn3}) and impose the
constraint:
\begin{equation}
A' e^{i\Omega t}\ +\ {\overline A}'e^{-i\Omega t}\ =\ 0
\nonumber\end{equation}
Equation (\ref{eq:aeqn3}) then is reduced to the first order equation:
\begin{equation}
A'\ =\ (2i\Omega)^{-1}\ e^{-i\Omega t}\ F(a,\eta)\ ,
\label{eq:Aeqn}
\end{equation}
where $F(a,\eta)=F(A,\overline A,\eta,t)$.
From (\ref{eq:aeqn3}) we have that $F(a,\eta)$ is the sum of the following terms:
\begin{eqnarray}
F_1(a)& =&\ \lambda a^3\int\varphi^4\nonumber\\
F_2(a,\eta_j)&=&\ 3\lambda a^2\int\varphi^3\eta_j\ , \quad j=1,2,3\nonumber\\
F_3(a,\eta)&=&\ 3\lambda a\int\varphi^2\eta^2\nonumber\\
F_4(\eta)&=&\ \lambda\int\varphi\eta^3\ .\ \label{eq:F1234}
\end{eqnarray}
The remainder of this section is primarily devoted to an (involved)
expansion of
$F_2(a,\eta_2)$. The terms of this expansion are of several types:
(a) the resonant damping term, (b) terms of the same order
whose net
effect is a nonlinear phase correction and (c) higher order
terms which are to be treated perturbatively in the asymptotic analysis
as $t\to\pm\infty$.
\smallskip
\centerline{\it Computation of $F_2(a,\eta_2)$}
We first break $\eta_2$ into a part containing the key resonance $\eta^r_2$ and nonresonant part
$\eta^{nr}_2$.
\smallskip
\begin{prop}
$$\eta_2=\eta^r_2 +\eta^{nr}_2\ ,\label{eq:4.16}$$
where
\begin{equation}
\eta^r_2={\lambda\over 2iB} e^{iBt}\int^t_0 e^{-is(B-3\Omega)} A^3(s)\
ds\ {\bf P_c}\varphi^3\
,\label{eq:eta-r2}
\end{equation}
and
\begin{eqnarray}
\eta^{nr}_2&=&\ {\lambda\over 2iB} \e{iBt}\bigg\lbrack 3\int^t_0 \e{-is(B-\Omega)}
A^2(s)\overline A(s)ds\nonumber\\
&+&\ 3\int^t_0 \e{-is(B+\Omega)}\ \overline A^2(s)A(s)\ ds\nonumber\\
&+&\ \int^t_0\e{-is(B+3\Omega)}\ \overline A^3(s)\ ds\bigg\rbrack\ {\bf P_c}\varphi^3\nonumber\\
&-&\ {\lambda\over 2iB} \e{-iBt}\bigg\lbrack\int^t_0 \e{is(B+3\Omega)}\
A^3(s)\ ds\nonumber\\
&+&\ 3\int^t_0 \e{is(B+\Omega)}\ A^2(s)\overline A(s)\ ds+3\int^t_0 \e{is(B-\Omega)}\overline A^2(s) A(s)\ ds\nonumber\\
&+&\ \int^t_0\e{is(B-3\Omega)}\ \overline A^3(s)\ ds\bigg\rbrack\ {\bf P_c}\varphi^3\nonumber\\
&\equiv&\ \sum^7_{j=1} \eta^{nr}_{2j}\nonumber\\ \
\label{eq:eta-nr2}
\end{eqnarray}
\end{prop}
The superscripts $r$ and $nr$ denote respectively a resonant contribution
and nonresonant
contribution.
\medskip
\noindent{\it Proof:}
The solution of (\ref{eq:eta2eqn}) can be expressed, using the
variation of constants formula, as:
\begin{equation}
\eta_2\ =\ \lambda\int^t_0{\sin B(t-s)\over B} a^3(s)\ ds\ {\bf P_c}\varphi^3,\nonumber
\end{equation}
Substitution of (\ref{eq:aA1}) for $a(s)$ and using the expansion
of $\sin\left(B(t-s)\right)$ in terms of the operators $\exp\left(\pm iB(t-s)\right)$
leads to an expression for $\eta_2$ which is a sum of eight terms. The
term
$\eta_2^r$, as defined above, is anticipated to be the most important.
The other seven terms are lumped together in $\eta_2^{nr}$.
\medskip
We now focus on $\eta_2^r$.
In order to study $\eta^r_2$ near the resonant point $3\Omega$ in the continuous spectrum of
$B$, we first introduce a regularization of $\eta^r_2$. For
$\varepsilon>0$, let
\begin{equation}
\eta^r_{2\varepsilon}\equiv{\lambda\over 2iB}\e{iBt}\int^t_0\e{-is(B-3\Omega+i\varepsilon)} A^3(s)\
ds\ {\bf P_c}\varphi^3\
\label{eq:eta-2eps}
\end{equation}
Note that $\eta^r_2=\lim_{\varepsilon\to0}\eta^r_{2\varepsilon}$.
The following result, proved using integration by parts, isolates the
key (local in $t$) resonant term.
\smallskip
\begin{prop} For $\varepsilon\ge0$,
\begin{eqnarray}
\eta^r_{2\varepsilon}&=&\ {\lambda\over 2} \Big\lbrack B(B-3\Omega+i\varepsilon)
\Big\rbrack^{-1}
\e{3i\Omega t}A^3(t)\ e^{\varepsilon t} {\bf P_c}\varphi^3\nonumber\\
&-&\ {\lambda\over 2}A_0^3 \Big\lbrack B(B-3\Omega+i\varepsilon)\Big\rbrack^{-1}
\e{iB t}\ {\bf P_c}\varphi^3\nonumber\\
&-&\ {3\over 2}\lambda \Big\lbrack B(B-3\Omega+i\varepsilon)\Big\rbrack^{-1}
\e{iB t}\int^t_0 \e{-is(B-3\Omega +i\varepsilon )}A^2A'\ ds\ {\bf P_c}\varphi^3\nonumber\\
&=&\ \eta^r_{*\varepsilon}+\eta^{nr1}_{*\varepsilon}+\eta^{nr2}_{*\varepsilon}
\label{eq:eta-2eps1}
\end{eqnarray}
\end{prop}
\noindent{\bf Remark:} The choice $+i\varepsilon$ in (\ref{eq:eta-2eps})
is motivated by the fact that the operator \
\begin{equation} (B-3\Omega+i0)^{-1}e^{iBt} \nonumber\end{equation}
satisfies appropriate
decay estimates as $t\rightarrow \infty$; see Proposition 2.1.
It follows that
the limit as $\varepsilon\to0^+$ of the last two terms in (\ref{eq:eta-2eps1})
decay in time like $\la t\ra^{-1-\alpha}(\alpha>0)$; see section 7.
We now use the above computation to obtain an expression for $F_2(a,\eta_2)$. First, from
Proposition 4.1 we have
\begin{eqnarray}
F_2(a,\eta_2)\ &=&\ F_2(a,\eta^r_2)+F_2(a,\eta^{nr}_2)\nonumber\\
&=&\ \lim_{\varepsilon\to0} F_2(a,\eta^r_{*\varepsilon})\ +\
\lim_{\varepsilon\to0} F_2(a,\eta^{nr1}_{*\varepsilon} +
\eta^{nr2}_{*\varepsilon})+F_2(a,\eta_2^{nr})\ ,\nonumber\\
&\equiv&\ F_2(a,\eta^r_*)\ +\ F_2(a,\eta^{nr1}_*\ +\ \eta^{nr2}_*)\
+\ F_2(a,\eta_2^{nr})
\label{eq:F2}
\end{eqnarray}
where $F_2(a,\cdot)$ is defined in (\ref{eq:F1234}). We begin with
the contribution to (\ref{eq:Aeqn}) coming from
$F_2(a,\eta^r_*)$. What follows now is a detailed expansion of the term
$F_2(a,\eta^r_*)$ and
$F_2(a,\eta_2^{nr})$. The terms $F_2(a,\eta_*^{nr1}+\eta_*^{nr2})$ can be
treated
perturbatively by estimation of its magnitude; see section 5.
\smallskip
\centerline{\it Computation of $F_2(a,\eta^r_*)$}
Let
\begin{eqnarray}
\Lambda\ &\equiv&\
\lim_{\varepsilon\rightarrow 0}\left(\ {\bf P_c}\varphi^3, {1\over B}\ {B-3\Omega\over
(B-3\Omega)^2+\varepsilon^2} {\bf P_c}\varphi^3\ \right)
\label{eq:Lambda}\\
&=&\ \left(\ {\bf P_c}\varphi^3, {1\over B} {\rm P.V.} {1\over
B-3\Omega}\ {\bf P_c}\varphi^3\ \right),\ {\rm and}\
\nonumber\end{eqnarray}
\begin{eqnarray}
\Gamma&\equiv&\ \lim_{\varepsilon\rightarrow 0}\ \left(\ {\bf P}_c\varphi^3,
{1\over B}\ {\varepsilon\over
(B-3\Omega)^2+\varepsilon^2} {\bf P_c}\ \varphi^3\ \right)\nonumber\\
&=&\ {\pi\over 3\Omega} \left( {\bf P_c}\ \varphi^3,\delta(B-3\Omega) {\bf P_c}\ \varphi^3\right)\nonumber\\
&=&\ {\pi\over3\Omega}\ \left|\ {\cal F}_c[\varphi^3](3\Omega)\ \right|^2 .
\label{eq:Gamma}
\end{eqnarray}
By hypothesis (\ref{eq:nlfgr}), $\Gamma>0$.
We now substitute the expression for $\eta_{*\varepsilon}^r$, given in
(\ref{eq:eta-2eps1}) into the definition
of $F_2(a, \eta_{*\varepsilon}^r)$ in (\ref{eq:F1234}). Passage to the limit,
$\varepsilon\to0$, and use of the distributional identity:
\begin{equation}
(x\pm i0)^{-1}\ \equiv\ \lim_{\varepsilon\to0}\ (x\pm
i\varepsilon)^{-1}\ =\ {\rm P.V.}\ x^{-1}\ \mp i\pi\delta(x)
\nonumber\end{equation}
yields:
\smallskip
\begin{prop}
\begin{eqnarray}
F_2(a,\eta^r_*)&=&\ \lim_{\varepsilon\rightarrow 0}F_2(a,\eta^r_{*\varepsilon})\nonumber\\
&=& {3\over 2}\lambda^2 \left(
\Lambda-i\Gamma\right) \Big\lbrack|A|^4 Ae^{i\Omega t}
+A^5 e^{5i\Omega t}+2|A|^2 A^3 e^{3i\Omega t}\Big\rbrack\label{eq:4.23}
\end{eqnarray}
\end{prop}
We have completed the evaluation of the first term in (\ref{eq:F2}). \
To calculate the contribution of
(\ref{eq:4.23}) to the amplitude equation (\ref{eq:Aeqn}) we need only multiply (\ref{eq:4.23}) by
$(2i\Omega)^{-1}
e^{-i\Omega t}$. This gives
\smallskip
\begin{prop}
\begin{equation}
(2i\Omega)^{-1}\ e^{-i\Omega t}\ F_2(a,\eta^r_*)\
=\ -{3\over 4}{\lambda^2\over \Omega}\ (i\Lambda+\Gamma)\Big\lbrack |A|^4 A+A^5 e^{4i\Omega t}+2|A|^2A^3
e^{2i\Omega t}\Big\rbrack\label{eq:4.24}
\end{equation}
\end{prop}
The term $-{3\over 4}{\lambda^2\over \Omega}\ \Gamma |A|^4 A$ plays the role of a nonlinear damping; it drives
the decay of $A$ and, in turn, that of $\eta$; see the discussion in the introduction.
\medskip
\centerline{\it Computation of $F_2(a,\eta_2^{nr})$:}
We now focus on $F_2(a,\eta_2^{nr})$, the third term in (\ref{eq:F2}).
This requires a rather extensive, expansion of
$\eta_2^{nr}=\sum_j\eta^{nr}_{2j}$; see (\ref{eq:eta-nr2}).
From Proposition 4.3, we expect the dominant
terms to be
$ {\cal O}(|A|^5)$.
Our approach
is now to make explicit all terms which are formally
$ {\cal O}(|A|^5)$ (anticipating that $A'\ =\ {\cal O}(|A|^3)$, $A''\
=\ {\cal O}(|A|^5)$ and $(|A|^2)'\
=\ {\cal O}(|A|^6)$ ) and to treat the remainder
as a perturbation which we shall later estimate to be of higher order.
This expansion of
$\eta_2^{nr}$ is presented in the following proposition which we prove
using repeated integration by parts. As written, these expressions are
formal. By the definition of $F_2(a,\eta_2^{nr})$ we require that they
hold when integrating against a rapidly decaying function, {\it i.e.}
$\varphi^3$.
\smallskip
\begin{prop} The following expansions hold in ${\cal S}'$:
\begin{eqnarray}
\eta^{nr}_{21}&=&\ {\lambda\over 2B(B-\Omega)} |A|^2 A e^{it\Omega}\ {\bf P_c}\varphi^3
+{3\lambda\over 2iB (B-\Omega)^2} e^{it\Omega}(|A|^2A)'\ {\bf P_c}\varphi^3\nonumber\\
&+&\ {3\lambda e^{iBt}\over 2B(B-\Omega)}\Big\lbrack
|A_0|^2A_0+(|A|^2A)'\big|_{t=0}\Big\rbrack\ {\bf P_c}\varphi^3\nonumber\\
&-&\ {3\lambda\over 2iB(B-\Omega)^2} e^{iBt}\int^t_0 e^{-is(B-\Omega)}\ (|A|^2 A)''\
ds
\ {\bf P_c}\varphi^3\label{eq:4.25}
\end{eqnarray}
\begin{eqnarray}
\eta^{nr}_{22}&=&\ {3\lambda\over 2B(B+\Omega)}|A|^2\overline A e^{-it\Omega} {\bf P_c}\varphi^3 +{3\lambda\over
2iB(B+\Omega)^2}e^{-it\Omega} (\overline A^2 A'+2{\overline A}' |A|^2){\bf P_c}\varphi^3\nonumber\\
&+&\ e^{iBt}\Big\lbrack-{3\over 2}\ {\lambda\over 2B(B+\Omega)}|A_0|^2\overline A -{3\lambda\over 2B(B+\Omega)}
(|A|^2A)'\big|_{t=0}\Big\rbrack {\bf P_c}\varphi^3\nonumber\\
&-&\ {3\lambda\over 2iB(B+\Omega)^2} e^{iBt}\int^t_0 e^{-is(B+\Omega)}(|A|^3\overline A)''(s)\ ds\
{\bf P_c}\varphi^3
\label{eq:4.26}
\end{eqnarray}
\smallskip
\begin{eqnarray}
\eta^{nr}_{23}&=&\ {\lambda\overline A (t)^3\over 2B(B+3\Omega)} e^{-3it\Omega}\ {\bf P_c}\varphi^3
+{3\lambda\over 2iB(B+3\Omega)^2} e^{-it3\Omega} (\overline A(t)^3)'\ {\bf P_c}\varphi^3\nonumber\\
&-&\ {3\over 2}\lambda{e^{iBt}\over B(B+3\Omega)}\Big\lbrack\overline A^3_0+(\overline A^3)'\big|_{t=0}\Big\rbrack
{\bf P_c}\varphi^3\nonumber\\
&-&\ {3\over 2}\ {\lambda\over iB(B+3\Omega)^2}e^{iBt}\int^t_0 e^{-is (B+3\Omega)}(\overline A(s)^2)''\ ds\ {\bf P_c}\varphi^3\nonumber\\
\label{eq:4.27}
\end{eqnarray}
\smallskip
\begin{eqnarray}
\eta^{nr}_{24}&=&\ {\lambda\over 2B(B+3\Omega)} A^3(t) e^{3it\Omega}{\bf P_c}\varphi^3
-{3\lambda\over 2iB(B+3\Omega)^2} e^{3it\Omega} (A^3)'\ {\bf P_c}\varphi^3\nonumber\\
&-&\ {3\over 2}\lambda{e^{-iBt}\over B(B+3\Omega)}\Big\lbrack A^3_0+(A^3)'\big|_{t=0}\Big\rbrack
{\bf P_c}\varphi^3\nonumber\\
&+&\ {3\lambda\over 2 iB(B+3\Omega)^2}e^{-iBt}\int^t_0 e^{is (B+3\Omega)}(A^3(s))''\
ds\ {\bf P_c}\varphi^3\nonumber\\
\label{eq:4.28}
\end{eqnarray}
\smallskip
\begin{eqnarray}
\eta^{nr}_{25}&=&\ {3\lambda\over 2B(B+\Omega)} |A|^2 A\ e^{it\Omega}\ {\bf P_c}\varphi^3
-{3\lambda\over 2iB(B+\Omega)^2} e^{it\Omega} (|A|^2 A)'{\bf P_c}\varphi^3\nonumber\\
&-&\ {3\over 2}\lambda{e^{-iBt}\over B(B+\Omega)}\Big\lbrack |A_0|^2 A_0+(|A|^2 A)'
\big|_{t=0}\Big\rbrack
{\bf P_c}\varphi^3\nonumber\\
&+&\ {3\lambda\over 2 iB(B+\Omega)^2}e^{-iBt}\int^t_0 e^{is (B+\Omega)}(|A|^2 A)''\
ds\ {\bf P_c}\varphi^3\nonumber\\
\label{eq:4.29}
\end{eqnarray}
\smallskip
\begin{eqnarray}
\eta^{nr}_{26}&=&\ {3\lambda\over 2B(B-\Omega)} |A|^2 \overline A \ e^{-it\Omega}\ {\bf P_c}\varphi^3
-{3\lambda\over 2iB(B-\Omega)^2} e^{-it\Omega} (|A|^2 \overline A)'\ {\bf P_c}\varphi^3\nonumber\\
&-&\ {3\over 2}\lambda{e^{-iBt}\over B(B-\Omega)}\Big\lbrack |A_0|^2 \overline A_0+(|A|^2 \overline A)'
\big|_{t=0}\Big\rbrack\ {\bf P_c}\varphi^3\nonumber\\
&+&\ {3\over 2 i}\lambda {1\over B(B-\Omega)^2}e^{iBt}\int^t_0 e^{is(B-\Omega)}(|A|^2 \overline A )''\ ds\ {\bf P_c}\varphi^3\nonumber\\
\label{eq:4.30}
\end{eqnarray}
\smallskip
\begin{eqnarray}
\eta^{nr}_{27}&=&\ {\lambda\overline A^3(t)\ e^{-3it\Omega}\over 2B(B-3\Omega-i0)}\ {\bf P_c}\varphi^3
-{3\lambda\over 2iB(B-3\Omega -i0)^2} e^{-3it\Omega}(\overline A^3)'\ {\bf P_c}\varphi^3\nonumber\\
&-&\ {3\over 2}\lambda {e^{-iBt}\over B (B-3\Omega - i0)}
\Big\lbrack\overline A_0^3+(\overline A^3)'\big|_{t=0}\Big\rbrack\ {\bf P_c}\varphi^3 \nonumber\\
&+& {3\lambda\over
2iB(B-3\Omega-i0)^2} e^{-iBt}\int^t_0 e^{is(B-3\Omega)} (\overline A^3)''ds\ {\bf P_c}\varphi^3
\label{eq:4.31}
\end{eqnarray}
\end{prop}
Recall that our goal is to elucidate the structure of the amplitude
equation: $A'\ =\ (2i\Omega)^{-1}e^{-i\Omega t}F$, in (\ref{eq:Aeqn}),
where we first focused on the contribution: $(2i\Omega)^{-1}e^{-i\Omega
t}F_2$. From (\ref{eq:F2}) and Proposition 4.4 we see now that we need
to obtain convenient expressions for
\begin{eqnarray}
(2i\Omega)^{-1} e^{-i\Omega t} F_2(a,\eta^{nr}_2)\ &=&\
\sum^7_{j=1}(2i\Omega)^{-1} e^{-i\Omega t}\ F_2(a,\eta^{nr}_{2j})\nonumber\\
&=&\ 3\lambda(2i\Omega)^{-1} a^2 e^{-i\Omega t}\sum^7_{j=1}\int\varphi^3\eta^{nr}_{2j}\
.\label{eq:4.32}
\end{eqnarray}
Each of the seven terms contributing to $\eta_2^{nr}$
is expressed as a part which is ${\cal O}(|A|^5)$
plus an error term
which is estimated in magnitude in section 5.
The $ {\cal O}(|A|^5)$ part and error terms are displayed
in the following two propositions.
\smallskip
\begin{prop}
Let
\begin{equation}
\rho(\zeta)\equiv({\bf P_c}\varphi^3, B^{-1}(B-\zeta)^{-1}{\bf P_c}\varphi^3).
\label{eq:rhoeqn}
\end{equation}
Then,
\begin{eqnarray}
&&(2i\Omega)^{-1} e^{-i\Omega t} F_2(a,\eta^{nr}_{21})\nonumber\\
&=&\ {\lambda^2\over\Omega} \rho(\Omega) \Big\lbrack {3\over 4i} |A|^2A^3 e^{2i\Omega t} +{3\over
2i} |A|^4A+ {3\over 4i} |A|^4\overline A e^{-2i\Omega t}\Big\rbrack
+E^{nr}_{21}\label{eq:4.33}
\end{eqnarray}
\smallskip
\begin{eqnarray}
&&(2i\Omega)^{-1} e^{-i\Omega t} F_2(a,\eta^{nr}_{22})\nonumber\\
&=&\ {\lambda^2\over\Omega}\rho(-\Omega) \Big\lbrack{9\over 4i}|A|^4A+{9\over 2i}|A|^4\overline A
e^{-2i\Omega t}+{9\over 4i}|A|^2\overline A^3 e^{-4i\Omega t}\Big\rbrack
+E^{nr}_{22}\label{eq:4.34}
\end{eqnarray}
\smallskip
\begin{eqnarray}
&&(2i\Omega)^{-1} e^{-i\Omega t} F_2(a,\eta^{nr}_{23})\nonumber\\
&=&\ {\lambda^2\over\Omega}\rho(-3\Omega) \Big\lbrack{3\over 4i}|A|^4\overline A e^{-2i\Omega t}+{3\over 2}
|A|^2\overline A^3
e^{-4i\Omega t}+{3\over 4}\overline A^5 e^{-6i\Omega t}\Big\rbrack
+E^{nr}_{23}\label{eq:4.35}
\end{eqnarray}
\smallskip
\begin{eqnarray}
&&(2i\Omega)^{-1} e^{-i\Omega t} F_2(a,\eta^{nr}_{24})\nonumber\\
&=&\ {\lambda^2\over\Omega}\rho(-3\Omega) \Big\lbrack{3\over 4}A^5 e^{4i\Omega t}+{3\over 4}
A^3 |A|^2
e^{2i\Omega t}+{3\over 4}|A|^4 A \Big\rbrack
+E^{nr}_{24}\label{eq:4.36}
\end{eqnarray}
\smallskip
\begin{eqnarray}
&&(2i\Omega)^{-1} e^{-i\Omega t} F_2(a,\eta^{nr}_{25})\nonumber\\
&=&\ {\lambda^2\over\Omega}\rho(-\Omega) \Big\lbrack{9\over 4i}|A|^2 A^3 e^{2i\Omega t}+{9\over 2i}
|A|^4 A+{9\over 4i}|A|^4\overline A
e^{-2i\Omega t} \Big\rbrack
+E^{nr}_{25}\label{eq:4.37}
\end{eqnarray}
\smallskip
\begin{eqnarray}
&&(2i\Omega)^{-1} e^{-i\Omega t} F_2(a,\eta^{nr}_{26})\nonumber\\
&=&\ {\lambda^2\over\Omega}\rho(\Omega) \Big\lbrack{9\over 4i}|A|^4 A +{9\over 2i}|A|^4\overline A
e^{-2i\Omega t}+{9\over 4i}
|A|^2 \overline A^3
e^{-4i\Omega t} \Big\rbrack
+E^{nr}_{26}\label{eq:4.38}
\end{eqnarray}
\smallskip
\begin{eqnarray}
&&(2i\Omega)^{-1} e^{-i\Omega t} F_2(a,\eta^{nr}_{27})\nonumber\\
&=&\ {\lambda^2\over\Omega}\rho(3\Omega +i0) \Big\lbrack{3\over 4i}|A|^4 \overline A
e^{-2i\Omega t}+{3\over 2i}
|A|^2 \overline A^3
e^{-4i\Omega t} +\overline A^5 e^{-6i\Omega t}\Big\rbrack
+E^{nr}_{27}\label{eq:4.39}
\end{eqnarray}
\end{prop}
\smallskip
In our analysis of the large time behavior ($t\to\pm\infty$), we shall
require an upper bound of the error terms $E_{2j}^{nr}$ given in:
\begin{prop}
\begin{eqnarray}
&&|E^{nr}_{2j}\ |\le\ C_\varphi\
|\lambda|^2\ |A|^2\Big\lbrace\ |A|^2 |A'|\ +\
\|\langle x\rangle^{-\sigma} (B-\zeta_j)^{-1}\ e^{iBt}\ {\bf P_c} \varphi^3 \|_2\nonumber\\
&+&\ \|\langle x\rangle^{-\sigma} (B-\zeta_j)^{-2}\
\ \int^t_0 e^{iB(t-s)}\ {\cal O}\left((|A|^3)''\right)\ ds\
{\bf P_c}\varphi^3 \|_2\ \Big\rbrace
,\label{eq:4.40}
\end{eqnarray}
where $\zeta_1=\zeta_6=\Omega,\ \zeta_2=\zeta_5=-\Omega,\ \zeta_3=\zeta_4=-3\Omega,$ and
$\zeta_7=3\Omega+i0$.
\end{prop}
In section 7, we shall estimate this expression using the decay
estimates of section 2, in particular Proposition 2.2.
\medskip
The desired form of the $A$-equation is now emerging.
Use of Propositions 4.4 and 4.6 in (\ref{eq:Aeqn}) yields:
\begin{prop}
The amplitude $A(t)$ satisfies the
equation (see Proposition 4.6 for the definition of $\rho(\zeta)$):
\begin{eqnarray}
A'&=&\ {-i\lambda\over 2\Omega}\ \|\varphi\|_4^4\ (\ 3|A|^2A\ +\ A^3 e^{2i\Omega t}\ +\
3|A|^2\overline A \
e^{-2i\Omega t}\ +\ \overline A^3 e^{-4i\Omega t}\ )\nonumber\\
&&\ -{3\over 4}\ {\lambda^2\over\Omega}\ \Gamma|A|^4A\ -\ {3i\over 4\Omega}\
\lambda^2\ \Big\lbrack
\Lambda\ -\ 5\rho(\Omega)\ +\ 3\rho(-\Omega)\ +\ \rho(-3\Omega)\ \Big\rbrack |A|^4A\nonumber\\
&&\ -{3\lambda^2\over 4\Omega} A^5\ e^{4i\Omega t}\ \Big\lbrack
i\Lambda\ +\ \Gamma\ -\ \rho(-3\Omega)\ \Big\rbrack\nonumber\\
&&\ -{3i\lambda^2\over 4\Omega}\ |A|^2A^3\ e^{2i\Omega t}\ \Big\lbrack
-2\ \Lambda\ +\ 2i\Gamma\ +\ \rho(\Omega)\ +\ i\rho(-3\Omega)\ +\
3\rho(-\Omega)\
\Big\rbrack\nonumber\\
&&\ -{3i\lambda^2\over 4\Omega}\ |A|^4\overline A\ e^{-2i\Omega t}\ \Big\lbrack
\ 7\rho(\Omega)\ +\ 9\rho(-\Omega)\ +\ \rho(-3\Omega)\ +\ \rho(3\Omega+i0)\
\Big\rbrack\nonumber\\
&&\ -{3i\lambda^2\over 4\Omega} |A|^2\overline A^3\ e^{-4i\Omega t}\ \Big\lbrack
\ 3\rho(-\Omega)\ -\ 2i\rho(-3\Omega)\ +\ \rho(3\Omega+i0)\ +\ 3\rho(\Omega)\
\Big\rbrack\nonumber\\
&&\ -{3i\lambda^2\over 4\Omega}\ \overline A^5\ e^{-6i\Omega
t}\ \Big\lbrack\ i\rho(-3\Omega)\ -\ {4\over3}i\rho(3\Omega+i0)\ \Big\rbrack\ +\ {\bf E}\nonumber\\
\label{eq:4.41}
\end{eqnarray}
where
\begin{eqnarray}
{\bf E} &=&\ (2i\Omega)^{-1} e^{i\Omega t}\ 3\lambda a\int\varphi\eta^2\nonumber\\
&+&\ (2i\Omega)^{-1}\lambda e^{-i\Omega t}\int\varphi \eta^3\nonumber\\
&+&\ \sum^7_{j=1} E^{nr}_{2j}\nonumber\\
&+&\ (2i\Omega)^{-1} e^{-i\Omega t}\Big\lbrack F_2(a,\eta_1)+F_2(a,\eta_3)\Big\rbrack\nonumber\\
&+&\ F_2(a,\eta^{nr1}_* +\eta_*^{nr2})\label{eq:4.42}
\end{eqnarray}
\end{prop}
Here, $F_2(a,\eta_j)$ is given by (\ref{eq:F1234}).
In the next section we show how to rewrite
(\ref{eq:4.41}) in a manner which makes explicit which terms
determine the large time behavior of the amplitude and phase of $A(t)$.
\section{Dispersive Hamiltonian normal form}
To analyze the asymptotic behavior of $A(t)$ (or equivalently $a(t)$)
and $\eta(t,x)$ as
$t\rightarrow\infty$ it is useful to use the idea of
normal forms \cite{kn:KAM}, \cite{kn:GH}, \cite{kn:SV} from dynamical
systems theory. We derive a perturbed normal form which makes
the anticipated large time behavior of solutions transparent.
\smallskip
\begin{prop}
There exists a smooth near-identity change of variables, $A\mapsto \tilde A$
with the following properties:
\begin{eqnarray}
\tilde A\ &=&\ A\ +\ h(A,t)\nonumber\\
h( A,t)\ &=&\ O(|A|^3),\quad |A|\to0\nonumber\\
h(A,t)\ &=&\ h(A,t+2\pi\Omega^{-1}),\label{eq:cov}
\end{eqnarray}
and such that in terms of $\tilde A$ equation (\ref{eq:4.41}) becomes:
\begin{eqnarray}
{\tilde A}'&=&\ i\lambda c_{21} |\tilde A|^2\tilde A +\lambda^2
d_{32}|\tilde
A|^4\tilde A+i\lambda^2 c_{32}|\tilde A|^4\tilde A\nonumber\\
&+&\ O(|\tilde A|^7)+{\bf \tilde E}\ ,
\label{eq:tildeAeqn}
\end{eqnarray}
where $\lambda^2 d_{32} =-{3\over4}{\lambda^2\over\Omega} \Gamma<0$.
The constants $c_{21}$ and $c_{32}$ are real
numbers, explicitly calculable in terms of the coefficients appearing in
(\ref{eq:4.41}). The remainder term $|\tilde{\bf E}|$ is estimable in
terms of
$|{\bf E}|$ for $|\tilde A|<1$ (equivalently
$|A|<1)$.
\end{prop}
\noindent{\bf Remarks:}
\noindent The point of this proposition is that in the new
variables the dynamics evidently have a dissipative aspect. Specifically,
neglecting the perturbation to the normal form one has:
\begin{equation}
\partial_t\ |\tilde A|^2\ =\ -{3\over8}\ {\lambda^2\over\Omega}\ \Gamma\
|\tilde A|^6\ <\ 0
\nonumber\end{equation}
We therefore refer to
(\ref{eq:tildeAeqn}) as a {\it dispersive Hamiltonian
normal form}. In finite dimensional Hamiltonian systems, the normal form
associated with a one degree of freedom Hamiltonian system is an
equation like
(\ref{eq:tildeAeqn}), but with all the coefficients of the terms
$|A|^{2m}A$ being purely imaginary. Here we find that resonant coupling to
an infinite dimensional dispersive wave field can lead to a normal form
with general complex coefficients, which in our context implies the
internal damping effect described above. See section 8 for further
discussion.
\bigskip
We now present an elementary derivation of the change of variables
(\ref{eq:cov}) leading to (\ref{eq:tildeAeqn}).
Equation (\ref{eq:4.41}) is of
the form:
\begin{equation}
A'\ =\ \sum_{j\in\{3,5\}}\ \sum_{k+l=j}\ \alpha_{kl}\ A^k\
{\overline A}^l\ e^{i(k-l-1)\Omega t}\ +\ {\bf E},
\label{eq:prepnf1}
\end{equation}
where the coefficients $\alpha_{kl}$ can be read off (\ref{eq:4.41}).
The proof we present is quite general and shows, in particular, that
the normal
form for equations like (\ref{eq:prepnf1}) is (\ref{eq:tildeAeqn})
\begin{prop}
There is a change of variables, as in (\ref{eq:cov}), such that
equation (\ref{eq:prepnf1}) is mapped to:
\begin{eqnarray}
\tilde A'\ &=&\ k_{21} |\tilde A|^2\tilde A
+ k_{32}|\tilde A|^4\tilde A\nonumber\\
&+&\ {\cal O}( |\tilde A|^7)+{\bf \tilde E}\ ,\ {\rm where}
\label{eq:generaltildeAeqn}
\end{eqnarray}
\begin{eqnarray}
{\bf \tilde E}\ &=&\ {\bf E}\circ (I+h),\nonumber\\
k_{21}\ &=&\ \alpha_{21}\nonumber\\
k_{32}\ &=&\ \alpha_{32}\ +\ (2i\Omega)^{-1}\left[\
{3\over2}|\alpha_{03}|^2\ -\ 2\alpha_{30}\alpha_{12}\ +\
2 |\alpha_{12}|^2\ \right]\label{eq:kij}
\end{eqnarray}
\end{prop}
The conclusion in Proposition 5.1 concerning the "damping
coefficient" $d_{32}$
depends on the particular properties of the coefficients in
(\ref{eq:Aeqn}). In particular we have from (\ref{eq:Aeqn}) and
(\ref{eq:prepnf1}) that:
\begin{eqnarray}
\alpha_{21}\ &=&\ \alpha_{12}\ =\
{3\lambda\over 2i\Omega}\|\varphi\|_4^4,\nonumber\\
\alpha_{03}\ &=&\ {\lambda\over 2i\Omega}\|\varphi\|_4^4,\nonumber\\
\alpha_{32}\ &=&\ -{3\lambda^2\over4\Omega}\Gamma\ -\
{3i\lambda^2\over 4\Omega}\ \left[ \Lambda\ -\ 5\rho(\Omega)\ +
\ 3\rho(-\Omega)\ +\ \rho(-3\Omega)\ \right].
\label{eq:alphaij}
\end{eqnarray}
From these formulae, we have $\lambda^2 d_{32}$ is given by the real part of
$\alpha_{32}$, the "singular" Fermi golden rule contribution.
\noindent{\bf Remark:}
The construction of the map $A\mapsto {\tilde A}$ can
be applied as well to equations of the form (\ref{eq:prepnf1}) where
the right hand side is an
arbitrary expansion in powers of $A$ and ${\overline A}$.
\medskip
To make the structure clear we write out the equation with
a particular ordering of terms:
\begin{eqnarray}
A'\ &=&\ \alpha_{21}\ |A|^2A\ +\ \alpha_{32}\ |A|^4A\ +\
O_3(A)\ +\ O_5(A)\ +\ {\bf E},
\label{eq:prenfm2}\\
\quad&&{\rm\ where\ }\nonumber\\
\ O_3(A)\ &=&\ \alpha_{30}\ A^3\ e^{2i\Omega t}\ +\ \alpha_{12}\
A{\overline A}^2\ e^{-2i\Omega t}\ +\ \alpha_{03}\ {\overline A}^3\
e^{-4i\Omega t},\quad {\rm and\ }\label{eq:O3}\\
\ O_5(A)\ &=&\ \alpha_{50}\ A^5\ e^{4i\Omega t}\ +\
\alpha_{41}\ A^4 {\overline A} \ e^{2i\Omega t}\ +\
\alpha_{23}\ A^2 {\overline A}^3 \ e^{-2i\Omega t}\nonumber\\
\quad &+&\ \alpha_{14}\ A {\overline A}^4 \ e^{-4i\Omega t}\ +\
\alpha_{05}\ {\overline A}^5 \ e^{-6i\Omega t}\
\label{eq:O5}
\end{eqnarray}
Note that each term in $O_3(A)$ and $O_5(A)$ is of the
form: oscillatory function of $t$ times order ${\cal O}(|A|^3)$
or ${\cal O}(|A|^5)$.
The computations that follow, though elementary, are rather lengthy so
we first outline the strategy of our proof.
Integration of (\ref{eq:prenfm2}) gives
\begin{equation}
A\ =\ A_0\ +\ \int_0^t\ \alpha_{21}\ |A|^2A\ +\ \alpha_{32}\ |A|^4A\ +\
O_3(A)\ +\ O_5(A)\ +\ {\bf E}\ ds.
\label{eq:Aint}
\end{equation}
The idea is that terms with explicit periodic oscillations average to
zero and can be neglected in
determining the large time behavior of the solution.
Our strategy is now to expand the explicitly oscillatory terms using
repeated
integrations by parts and to make explicit all terms up to and including order
$|A|^5$. The computation has two stages. In stage one, after repeated
integration by parts the equation (\ref{eq:Aint}) is expressed in the
equivalent form:
\begin{eqnarray}
A(t)\ -\ H_1(A(t),t)\ &=&\ A_0\ -\ H_1(A_0,0)\nonumber\\
&+&\ \int_0^t\ {\rm \ "resonant"\ terms\ like\ }\ |A|^2A\ ,\ |A|^4A\
ds\nonumber\\
&+&\ \int_0^t\ {\rm terms\ of\ type }\ O_5(A)\ ds\ +\ {\rm higher\ order\ corrections}
\label{eq:Aint1}
\end{eqnarray}
This suggests the change of variables $A\mapsto A_1=A(t)\ -\
H_1(A(t),t)$, giving
\begin{eqnarray}
A_1(t)\ &=&\ A_{10}\
+\ \int_0^t\ {\rm terms\ like\ }\ |A_1|^2A_1\ ,\ |A_1|^4A_1\
ds\nonumber\\
&+&\ {\rm terms\ of\ type }\ O_5(A_1)\ +\ {\rm higher\ order\ corrections}.
\label{eq:Aint2}
\end{eqnarray}
The latter equation is equivalent to a differential equation
of the form:
\begin{eqnarray}
A_1'(t)\ &=&\ \ {\rm terms\ like\ }\ |A_1|^2A_1\ ,\
|A_1|^4A_1\nonumber\\
&+&\ {\rm terms\ of\ type\ } O_5(A_1)\ +\ {\rm higher\ order\
corrections}.
\label{eq:Aint1diff}
\end{eqnarray}
which is a step closer to the form of the equation we seek. A second
iteration of this process yields the result.
\medskip
We now embark on the details of the proof.
\medskip
\noindent{\it Expansion of} $\int_0^t\ O_3(A)\ ds$:
\medskip
Integration of the expression in (\ref{eq:O3}) gives
\begin{eqnarray}
\int_0^t\ O_3(A)\ ds\ &=&\ h_3(A(t),t)\ -\ h_3(A_0,0)\nonumber\\
&-&\ {3\alpha_{30}\over 2i\Omega}\ \int_0^t\ e^{2i\Omega s}A^2\ A'\ ds\
+\ {\alpha_{12}\over 2i\Omega}\ \int_0^t\ e^{-2i\Omega s}\ \left( A\ {\overline
A}^2\right) '\ ds\nonumber\\
&+&\ {\alpha_{03}\over 4i\Omega}\ \int_0^t\ e^{-4i\Omega s} \left( {\overline A}^3 \right)'
\ ds,
\label{eq:intO3-1}
\end{eqnarray}
where
\begin{equation}
h_3(A,t)\ =\ {\alpha_{30}\over 2i\Omega}\ A^3\ e^{2i\Omega t}
\ -\ {\alpha_{12}\over 2i\Omega}\ A\ {\overline A}^2\ e^{-2i\Omega t}
\ -\ {\alpha_{03}\over 4i\Omega}\ {\overline A}^3\ e^{-4i\Omega t}
\label{eq:h3}
\end{equation}
We now replace $A'$ in (\ref{eq:intO3-1}) by
its abbreviated expression given in
(\ref{eq:prenfm2}).
Thus we have:
\begin{eqnarray}
\int_0^t\ O_3(A)\ ds\ &=&\ h_3(A(t),t)\ -\ h_3(A_0,0)\nonumber\\
&-& {3\alpha_{30}\over 2i\Omega}\ \int_0^t\ e^{2i\Omega s}A^2\
\left[ \alpha_{21}\ |A|^2A\ +\
O_3(A)\ +\ {\cal O}(|A|^5)\ +\ {\bf E}\ \right]\ ds\nonumber\\
&+& {\alpha_{12}\over 2i\Omega}\ \int_0^t\ e^{-2i\Omega s}{\overline A}^2\
\left[ \alpha_{21}\ |A|^2 A\ +\ O_3(A)\ +\
{\cal O}(|A|^5)\ +\ {\bf E}\ \right]\ ds\nonumber\\
&+& {\alpha_{12}\over 2i\Omega}\ \int_0^t\ e^{-2i\Omega s}
\ 2|A|^2\
\left[ {\overline \alpha}_{21}\ |A|^2{\overline A}\ +\ {\overline O}_3(A)\
+\ {\cal O}(|A|^5)\ +\ \overline{{\bf E}}\ \right]\ ds\nonumber\\
&+& {3\alpha_{03}\over 4i\Omega}\ \int_0^t\ e^{-4i\Omega s}{\overline
A}^2\
\left[ {\overline \alpha}_{21}\ |A|^2{\overline A}\ +\ {\overline O}_3(A)\
+\ {\cal O}(|A|^5)\ +\ \overline{\bf E}\ \right]\ ds
\label{eq:intO3}
\end{eqnarray}
Substitution of (\ref{eq:O3}) into (\ref{eq:intO3}) and integrating by
parts, we arrive at the
following expression:
\begin{eqnarray}
\int_0^t\ O_3(A)\ ds\ &=&\ h_3(A(t),t)\ +\ h_{3a}(A(t),t)\ -
h_3(A_0,0)\ -\ h_{3a}(A_0,0)\nonumber\\
&+&\ {1\over 2i\Omega}\ \left( {3\over2}\
|\alpha_{03}|^2\ -\ 2\alpha_{30}\alpha_{12}\ +\ 2|\alpha_{12}|^2
\right)\ \int_0^t\ |A|^4A\
ds\nonumber\\
&+&\ \int_0^t\ {\cal O}\left( |A|^2(|A|^5+|{\bf E}|)\right)\ ds,
\label{eq:intO3a}
\end{eqnarray}
where
\begin{eqnarray}
h_{3a}(A,t)\ &=&\ \left[\ -{\alpha_{12}{\overline \alpha}_{03}\over2\Omega^2}\
+\ {3\alpha_{30}\alpha_{21}\over 4\Omega^2}\ \right]
A^4{\overline A}\ e^{2i\Omega t}\ -\
{3\alpha_{30}^2\over 8\Omega^2}\
A^5\ e^{4i\Omega t}\nonumber\\
&+&\ {1\over 4\Omega^2}\ \left(\ \alpha_{21}\alpha_{12}\ +\
{3\over2}\alpha_{03}{\overline \alpha}_{12}\ -\ 3\alpha_{30}\alpha_{03}\
+\ 2\alpha_{12}\overline\alpha_{21}\right)\
A^2{\overline A}^3\ e^{-2i\Omega t}\nonumber\\
&+&\ {1\over 8\Omega^2}\ \left(\ \alpha_{12}^2\ +\
{3\over2}\alpha_{03}{\overline \alpha}_{21}\ +\
2\alpha_{12}\overline\alpha_{30}\ \right)\
\ A{\overline A}^4\ e^{-4i\Omega t}\nonumber\\
&+&\ {1\over 4\Omega^2}\ \left(\ {1\over3}\alpha_{03}\alpha_{12}\ +\
{1\over2}\alpha_{03}{\overline \alpha}_{30}\ \right)\
{\overline A}^5\ e^{-6i\Omega t}.
\label{eq:h3a}
\end{eqnarray}
\medskip
Referring back to (\ref{eq:prenfm2}), we see we must now obtain an
\medskip
\noindent{\it Expansion of} $\int_0^t\ O_5(A)\ ds$:
\medskip
From (\ref{eq:O5}) we have, after integration by parts:
\begin{eqnarray}
\int_0^t\ O_5(A)\ ds\ &=& \ h_{3b}(A(t),t)\ -\ h_{3b}(A_0,0)\nonumber\\
&+&\ \int_0^t\ {\cal O}\left(\ |A|^4(|A|^3\ +\ |{\bf E}|)\
\right)\ ds,
\label{eq:intO5}
\end{eqnarray}
where
\begin{eqnarray}
h_{3b}(A,t)\ &=&\ {\alpha_{50}\over 4i\Omega}\ A^5\ e^{4i\Omega t}\ +\
{\alpha_{41}\over 2i\Omega}\ A^4 {\overline A}\ e^{2i\Omega t}\ -\
{\alpha_{23}\over 2i\Omega}\ A^2\ {\overline A}^3\ e^{-2i\Omega t}\nonumber\\
&-&\ {\alpha_{14}\over 4i\Omega}\ A {\overline A}^4\ e^{-4i\Omega t}\ -\
{\alpha_{05}\over 6i\Omega}\ {\overline A}^5\ e^{-6i\Omega t}.
\label{eq:h5}
\end{eqnarray}
Therefore from (\ref{eq:Aint}) and our computations we have:
\begin{eqnarray}
&&\ A\ -\ h_3(A,t)\ -\ h_{3a}(A,t)\ -\ h_{3b}(A,t)\ \nonumber\\
&&\ =\ A_0\ -\ h_3(A_0,0)\ -\ h_{3a}(A_0,0)\ -\ h_{3b}(A_0,0)\nonumber\\
&+& \int_0^t\ \alpha_{21}\ |A|^2A\ +\ \alpha_{32}\ |A|^4A\
ds\nonumber\\
&+&\ {1\over 2i\Omega}\ \left(\
{3\over2}|\alpha_{03}|^2\ -\ 2\alpha_{30}\alpha_{12}\ +\
2|\alpha_{12}|^2\ \right)\ \int_0^t\
|A|^4A\ ds\ +\ \int_0^t\ {\bf E}\ ds\nonumber\\
&+&\ \int_0^t\ {\cal O}\left(\ |A|^4 (|A|^3\ + |{\bf E}|)\ \right)\
+\ {\cal O}\left(\ |A|^2 (|A|^5\ + |{\bf E}|)\ \right)\ ds.
\label{eq:pre-cov}
\end{eqnarray}
This suggests the change of variables:
\begin{eqnarray}
A_1\ &\equiv&\ A\ -\ H_1(A,t),\quad {\rm where}\nonumber\\
H_1(A,t)\ &=&\ h_3(A,t)\ +\ h_{3a}(A,t)\ +\ h_{3b}(A,t),
\label{eq:A1}
\end{eqnarray}
which for small $|A|$, is a near-identity change of variables.
Using this change of variables we have that (\ref{eq:pre-cov}) becomes
\begin{eqnarray}
A_1\ &=&\ A_{10}\ +\ \int_0^t\ \alpha_{21}\ |A_1|^2A_1\ +\ \alpha_{32}\ |A_1|^4A_1\
ds\nonumber\\
&+&\ {1\over 2i\Omega}\ \left(\
{3\over2}|\alpha_{03}|^2\ -\ 2\alpha_{30}\alpha_{12}\ +\
2|\alpha_{12}|^2\ \right)\ \int_0^t\
|A_1|^4A_1\ ds\nonumber\\
&+&\ \int_0^t\ \left(\ 2\alpha_{21}\ |A_1|^2\ H_1(A_1,s)\ + A_1^2\
{\overline H_1}(A_1,s)\ \right)\ ds\
+\ \int_0^t\ {\bf E_1}\ ds\nonumber\\
&+&\ \int_0^t\ {\cal O}\left(\ |A_1|^4 (|A_1|^3\ + |{\bf E_1}|)\ \right) \
+\ {\cal O}\left(\ |A_1|^2 (|A_1|^5\ + |{\bf E_1}|) \right)\ ds.
\label{eq:A1eqn}
\end{eqnarray}
We expand the terms involving $H_1(A,t)$. Using integration by parts, as
above, we obtain:
\begin{equation}
2\alpha_{21}\int_0^t\ |A_1|^2\ H_1\ ds\ = h_{5a}(A_1,t)\ -\ h_{5a}(A_{10},0)\
+\ \int_0^t\ {\cal O}\left(\ |A_1|^4 (|A_1|^3\ + |{\bf E_1}|)\ \right)\
ds,
\label{eq:intH1a}
\end{equation}
and
\begin{equation}
\alpha_{21}\int_0^t\ A_1^2\ {\overline H}_1\ ds\ = h_{5b}(A_1,t)\ -\
h_{5b}
(A_{10},0)\
+\ \int_0^t\ {\cal O}\left(\ |A_1|^4 (|A_1|^3\ + |{\bf E_1}|)\ \right)\
ds,
\label{eq:intH1b}
\end{equation}
where
\begin{eqnarray}
h_{5a}(A,t)\ &=&\ -{\alpha_{21}\alpha_{30}\over2\Omega^2}\
e^{2i\Omega t}\ A_1^4\ {\overline A_1}\ -\
{\alpha_{21}\alpha_{12}\over 2\Omega^2}\
e^{-2i\Omega t}\ A_1^2\ {\overline A_1}^3\nonumber\\
&-&\ {\alpha_{21}\alpha_{03}\over 8\Omega^2}\
e^{-4i\Omega t}\ A_1\ {\overline A_1}^4 \label{eq:h5a}\\
h_{5b}(A,t)\ &=&\
-{\alpha_{21}{\overline \alpha}_{30}\over 4\Omega^2}\
e^{-2i\Omega t}\ A_1^2\ {\overline A_1}^3\ -\
{\alpha_{21}{\overline \alpha}_{12}\over 4\Omega^2}\
e^{2i\Omega t}\ A_1^4\ {\overline A_1}\nonumber\\
&-&\ {\alpha_{21}{\overline \alpha}_{30}\over 16\Omega^2}\
e^{4i\Omega t}\ A_1^5
\nonumber\\
H_{5}(A,t)\ &=&\ h_{5a}(A,t)\ +\ h_{5b}(A,t)
\label{eq:H5ab}
\end{eqnarray}
Thus
\begin{eqnarray}
A_1\ -\ H_5(A_1(t),t)\ &=&\ A_{10}\ -\ H_5(A_{10},0)\nonumber\\
&+&\ \int_0^t\ \alpha_{21}\ |A_1|^2A_1\ +\ \alpha_{32}\ |A_1|^4A_1\
ds\nonumber\\
&+&\ {1\over 2i\Omega}\ \left(\
{3\over2}|\alpha_{03}|^2\ -\ 2\alpha_{30}\alpha_{12}\ +\
2|\alpha_{12}|^2\ \right)\ \int_0^t\
|A_1|^4A_1\ ds\nonumber\\
&+&\ \int_0^t\ {\cal O}\left(\ |A_1|^7\ +\ |A_1|^2 |{\bf E_1}|\ +\
|{\bf E_1}| \right)\ ds.
\nonumber\\
\label{eq:preA2eqn}
\end{eqnarray}
Now define
\begin{equation}
\tilde A\ \equiv\ A_1\ -\ H_5(A_1,t).
\label{eq:tAdef}
\end{equation}
In terms of this new variable we have:
\begin{eqnarray}
\tilde A\ &=&\ \tilde A_0\ +\ \int_0^t\ \alpha_{21}\ |\tilde A|^2\tilde
A\ +\
\alpha_{32}\ |\tilde A|^4\tilde A\
ds\nonumber\\
&+&\ {1\over 2i\Omega}\ \left(\
{3\over2}|\alpha_{03}|^2\ -\ 2\alpha_{30}\alpha_{12}\ +\
2|\alpha_{12}|^2\ \right)\ \int_0^t\
|\tilde A|^4\tilde A\ ds\nonumber\\
&+&\ \int_0^t\ {\cal O}\left(\ |\tilde A|^7\ +\ |{\bf \tilde
E}|\ \right)\ ds,
\label{eq:tAeqn}
\end{eqnarray}
where $|{\bf \tilde E}|$ is estimable in terms of $|{\bf E}|$ for
$|A|<1$.
This completes the proof.
\bigskip
\section{Large $t$ behavior of solutions to the perturbed normal form
equations}
\medskip
We now consider the large time behavior of solutions to the
ordinary differential equations of the form (\ref{eq:tildeAeqn}).
In particular, we compare the behavior of solutions
of (\ref{eq:tildeAeqn})
to those of the equation with $\tilde{\bf E}$ set equal to zero.
Thus we consider the equations:
\begin{eqnarray}
\beta'\ &=&\ ic_{21}|\beta|^2\beta\
+\ (ic_{32}-\gamma)\ |\beta |^4\beta\
+\ {\bf
Q}(t),
\label{eq:pnfm}\\
\alpha'\ &=&\ ic_{21}|\alpha|^2\alpha\ +\ (ic_{32}-\gamma)\
|\alpha|^4\alpha,
\label{eq:nfm}
\end{eqnarray}
where $\gamma>0$.
We first consider the unperturbed equation, (\ref{eq:nfm}).
Multiplication of (\ref{eq:nfm}) by $\overline\alpha$
and taking the real part of
the resulting equation yields the equation:
\begin{equation}
r'\ =\ -2\ \gamma\ r^3,\qquad r\ =\ |\alpha|^2.
\label{eq:amp2}
\end{equation}
Integration of (\ref{eq:amp2}) yields:
\begin{equation}
r^2(t)\ =\ r_0^2\ \left( 1\ +\ 4\ \gamma\ r_0^2\ t \right)^{-1}.
\nonumber\end{equation}
To prove the above lemma, we begin by multiplying (\ref{eq:pnfm}) by
$\overline \beta$ and taking the real part of the resulting equation. This
gives:
\begin{equation}
r'(t)\ =\ -2\ \gamma\ r^3(t)\ +\ {\bf Q}(t)\overline \beta(t)\ +\ \overline
{\bf Q}(t)\
\beta(t),\nonumber
\end{equation}
which implies the differential inequality:
\begin{equation}
r'(t)\ \le\ -2\ \gamma\ r^3(t)\ +\ 2\ |{\bf Q}(t)|\ r^{1\over2}(t).
\label{eq:ineq}
\end{equation}
We now prove
\begin{lem}
Suppose $r(t)\ =\ |\beta(t)|^2$ satisfies (\ref{eq:ineq}) with:
\begin{equation}
|{\bf Q}(t)|\ \le\ Q_0\ \langle t\rangle^{-{5\over4}-\delta},\quad \delta\ge0.
\label{eq:Qbound}
\end{equation}
Then,
\begin{equation}
|\beta(t)|^4\ \le\ \left( 1+4|\beta_0|^4\gamma t\right)^{-1}\
\left(\ 2|\beta_0|^4\ +\ {\ m_*^2\ Q_0^{8\over5}\over
\gamma^{3\over5}\ \langle t\rangle^{{8\over3}\delta} }\ \right),
\label{eq:Aest}
\end{equation}
where $m_*\ =\ \max\{1,4\gamma |\beta_0|^4\}$.
\end{lem}
\noindent{\it proof:}
Use of (\ref{eq:Qbound}) in (\ref{eq:ineq}) gives the inequality
\begin{equation}
r'(t)\ \le\ -2\gamma r^3(t)\ +\ 2Q_0\ \langle t\rangle^{-{5\over4}-\delta}\
r^{1\over2}(t).\nonumber
\end{equation}
Multiplication by $r(t)$ gives:
\begin{equation}
z'(t)\ \le -4\gamma\ z^2(t)\ +\ 4Q_0\ \langle t\rangle^{-{5\over4}-\delta}\
z^{3\over4}(t),\quad {\rm where}\ z(t)\ =\ r^2(t).
\label{eq:zeqn}\end{equation}
Note that the equation
\begin{equation} \zeta'(t)\ =\ -4\gamma\ \zeta^2(t), \quad \zeta(0)\ =\ z_0\ =\
|\beta_0|^4\nonumber\end{equation}
has solutions:
\begin{equation} \zeta(t)\ =\ \ z_0\ \left( 1\ +\ 4\ z_0\gamma t\right)^{-1}.
\nonumber\end{equation}
Anticipating this as the dominant behavior for large $t$, we define:
\begin{equation} z(t)\ \equiv\ \zeta(t)\ R(t).\label{eq:zR}\end{equation}
Substitution into (\ref{eq:zeqn}) and simplifying gives:
\begin{equation}
R'(t)\ \le\
{-4\gamma z_0\over 1\ +\ 4\ z_0\gamma t}\ R\ (R-1)\ +\
C\ {Q_0\over |z_0|^{1\over4}}\ \left( 1 + 4z_0\gamma t\right)^{1\over4}
\langle t\rangle^{-{5\over4}-\delta}\ R^{3\over4}(t).\label{eq:Reqn1}
\end{equation}
We now consider the last term in (\ref{eq:Reqn1}). Noting that
\begin{equation}
(1+t)^{-1}\le m_*\ (1+4\gamma z_0 t)^{-1},\quad
m_*\ =\ \max\{1,4\gamma z_0\},
\nonumber\end{equation}
we have for any $\varepsilon > 0$:
\begin{eqnarray}
C\ {Q_0\over |z_0|^{1\over4}}\ { \left( 1 + 4z_0\gamma
t\right)^{1\over4}\over
\langle t\rangle^{{5\over4}+\delta} }\ R^{3\over4}(t)\ &\le&\
C\ {Q_0\over |z_0|^{1\over4}}\ { m_*^{1\over4}\over \langle
t\rangle^{1+\delta} } \ R^{3\over4}\nonumber\\
&\le&\ C\ {Q_0\ m_*^{5\over8} \over \varepsilon\ |z_0|^{1\over4}
\langle t\rangle^{{5\over8} + \delta}}\
\times {\varepsilon\ R^{3\over4}(t)\over (1 + 4z_0\gamma t)^{3\over8}}\nonumber\\
&\le&\ C_1\ { Q_0^{8\over5}\ m_*^{3\over5} \over \varepsilon^{8\over5}\
z_0^{2\over5}\ \langle t\rangle^{1+{8\over5}\delta} }\ +\
C_2\ { \varepsilon^{8\over3}\ R^2(t) \over (1 + 4z_0\gamma t)}.
\nonumber
\end{eqnarray}
The last inequality follows from the inequality: $ab\le p^{-1}(\varepsilon a)^p+q^{-1}(b/\varepsilon)^q,\quad p^{-1} + q^{-1}=1$, for the choice $p={8\over3}$ and
$q={8\over5}$.
This last estimate can now be used in (\ref{eq:Reqn1}) and implies:
\begin{eqnarray}
R'\ &\le&\ {-4\gamma z_0 + C_2 \varepsilon^{8\over3}\over 1 + 4z_0\gamma t}\
R^2(t)\ +\ {4\gamma z_0\over 1 + 4z_0\gamma t}\ R(t)\ +\
C_1\ { Q_0^{8\over5}\ m_*^{3\over5} \over \varepsilon^{8\over5}\
z_0^{2\over5}\ \langle t\rangle^{1+{8\over5}\delta} }\nonumber\\
&& {\rm \ which\ when\ setting}\ C_2\varepsilon^{8\over3}=2\gamma z_0,\ {\rm
\ is\ }\nonumber\\
&\le&\ -{2\gamma z_0 \over 1 + 4z_0\gamma t}\ R\ (R-2)\ +\
C {Q_0^{8\over5}\ m_*\over \gamma^{3\over5}z_0 \langle
t\rangle^{1+{8\over3}\delta}}.
\label{eq:Reqn3}
\end{eqnarray}
Now set $R\ =\ 2\ +\ S$. Since the term proportional to $S^2$ is
negative, we obtain
\begin{equation}
S'\ \le\ {-4\gamma z_0\over 1\ +\ 4\ z_0\gamma t}\ S \ +\
C {Q_0^{8\over5}\ m_*\over \gamma^{3\over5}z_0 \langle
t\rangle^{1+{8\over5}\delta}}.
\label{eq:Seqn1}\end{equation}
Multiplication by $1 + 4\ z_0\gamma t$ yields:
\begin{eqnarray}
\partial_t\left[\ (1\ +\ 4\ z_0\gamma t)\ S(t)\ \right]
\ &\le&\ C {Q_0^{8\over5}\ m_*\over \gamma^{3\over5}z_0}\
{1 + 4\ z_0\gamma t\over (1 + t)}\ {1\over \langle t\rangle^{{8\over5}\delta}}\nonumber\\
&\le&\ C {Q_0^{8\over5}\ m_*^2\over \gamma^{3\over5}z_0}\
{ 1\over \langle t\rangle^{{8\over5}\delta} }.
\label{eq:Seqn2}
\end{eqnarray}
Integration of (\ref{eq:Seqn2}) from $0$ to $t$ implies:
\begin{equation}
S(t)\ \le\ C\ {Q_0^{8\over5}\ m_*^2\over \gamma^{3\over5}z_0}\
{1\over \langle t\rangle^{{8\over5}\delta}}.
\label{eq:Sest}
\end{equation}
The Lemma now follows from (\ref{eq:Sest}) and the relation:
\begin{equation}
|\beta(t)|^4\ \equiv z(t)\ \equiv \zeta(t)\ R(t)\ \equiv\ \zeta(t)\
\left(\ 2\ +\ S(t)\ \right).
\nonumber
\end{equation}
\section{ Asymptotic behavior of solutions to the nonlinear Klein-
Gordon equation}
In \S2 we proved that local in time solutions, ${\bf u}(t)$,
exist in the space $C^0(-T^*,T_*;{\bf X}_0)$, for some $T_*, T^* >0$.
We now study obtain the required {\it 'a priori} bounds to ensure
(a) persistence of the solution, ${\bf u}(t)$, as a continuous function with values
in ${\bf X}_0$ ($T^*=T_*=\infty$) and
(b) the decay of solutions as $t\to\pm\infty$ in
suitable norms. Due to the linear estimates
of section 2, we require more stringent hypotheses on
$u_0$ and $u_1$. These linear estimates require finiteness of $W^{1,4/3}$ and
$W^{1,8/7}$ norms which, by interpolation, are controlled under the assumption
${\bf u}_0\in{\bf X}$ (see
section 2). Specifically, $u_0\in W^{2,2}\cap W^{2,1}$ and $u_1\in
W^{1,2}\cap W^{1,1}.$
Using the results of the previous section, the original dynamical
systems (\ref{eq:nlkg1}) can now be rewritten as:
\begin{eqnarray}
u(x,t) &=& a(t)\ \varphi(x) + \eta(x,t),\nonumber \\
\eta(x,t) &=& \eta_1(x,t) + \eta_2(x,t) + \eta_3(x,t),\nonumber \\
a(t) &=& A(t)\ e^{i\Omega t} + {\bar A}(t)\ e^{-i\Omega t},\nonumber \\
A(t) &=& \tilde A(t) + h(\tilde A(t),t),\label{eq:decomposition}
\end{eqnarray}
Here, $h(\tilde A,t)$ is a smooth periodic function of $t$, cubic in $\tilde A$ for $\tilde A
\to0$, $\eta_1$ and $\eta_2$ are defined by (\ref{eq:eta1eqn})-
(\ref{eq:eta2eqn}), and $\tilde A(t)$ satisfies the perturbed normal form equation:
\begin{equation} \tilde A'\ =
\ i\lambda c_{21}\ |\tilde A|^2\tilde A\ -\ \gamma\ |\tilde A|^4\tilde A \ +\
i\lambda^2c_{32}|\tilde A|^4\tilde A\ +\ {\cal O}(|\tilde A |^7)\ +\ {\tilde
{\bf E}}(t,a,\eta). \label{eq:taeqn}\end{equation}
Here $\tilde {\bf E} = {\bf E}\circ (I+h)$,
with ${\bf E}$ given by (\ref{eq:4.42}).
\bigskip
In (\ref{eq:taeqn}),
\begin{equation} \gamma\ =\ {3\over4}\ {\lambda^2\over\Omega}\ \Gamma,\qquad
\Gamma\ \equiv\ {\pi\over3\Omega}\ \left( {\bf P_c}\varphi^3,\delta(B-3\Omega) {\bf P_c}\varphi^3\right)>0.
\label{eq:constants}\end{equation}
The constants $c_{21}$ and $c_{32}$ are real numbers which are
computable by the algorithm presented in section 5.
\medskip
The above definitions of $A$, $\tilde A$, and $h$, together with the
estimates proved below, can be used to verify in a straightforward
manner the assertions of Theorem 1.1 concerning $R(t)\equiv |A(t)|$,
and $\theta(t)\equiv \arg{A(t)}$.
To proceed with a study of the $t\to\infty$ behavior, recall that:
\begin{eqnarray} &&\left(\partial_t^2 + B^2\right)\eta_1 = 0,\qquad\qquad
\eta_1(x,0)\ = \ {\bf P_c} u_0,\ \partial_t\eta_1(x,0)=\ {\bf P_c} u_1, \label{eq:eta1} \\
&&\left(\partial_t^2 + B^2\right)\eta_2 = \lambda
a^3\ {\bf P_c}\varphi^3,\qquad
\eta_2(x,0)=0,\ \partial_t\eta_2(x,0)=0, \label{eq:eta2} \\
&&\left(\partial_t^2 + B^2\right)\eta_3 =
\lambda {\bf P_c}\left( 3a^2\varphi^2\eta +3a\varphi\eta^2
+\eta^3 \right),\quad
\eta_3(x,0)\ =\ \partial_t\eta_3(x,0)=0. \label{eq:eta3}
\end{eqnarray}
To motivate the strategy, we
first argue heuristically. Since $\gamma > 0$, if $\tilde{\bf E}$
is negligible, then $|\tilde A|\sim \la t\ra^{-1/4}$ as $t\to\infty$,
and therefore by (\ref{eq:aA}), $a\sim \la t\ra^{-1/4}$, as
$t\to\infty$. It then follows from (\ref{eq:eta2}) that, in
appropriate norms, that $\eta_2\sim \la t\ra^{-3/4}$ and
$\eta_3\sim \la t\ra^{-1+\delta}$ for some $\delta>0$.
To make all this precise requires {\it \'a priori} estimates on the
system the above equations.
We now recall Lemma 6.1 concerning equations of the
form (\ref{eq:taeqn}). This result gives conditions ensuring that $\tilde A$
behaves like the solution of the equation obtained by setting $\tilde{\bf E}$
to zero.
Our next task is to obtain an upper bound on $\tilde{\bf E}(t)$
in (\ref{eq:4.42}) of the form (\ref{eq:Qbound}). Since the equation for
$\tilde A(t)$ is coupled to that of $\eta$, the factor $Q_0$ in
(\ref{eq:Qbound})
will depend on $\eta$ and $\tilde A$. The next proposition, together with
Proposition 4.7, provides estimates for the individual terms in
$\tilde{\bf E}$.
It is convenient to introduce the notation:
\begin{equation}
[A]_\alpha(T)\ = \ \sup_{0\le t\le T}\la t\ra^\alpha |A(t)|
\label{eq:norm1}
\end{equation}
\begin{equation} [ \eta ]_{p,\alpha}(T)\ = \
\sup_{0\le t\le T}\la t\ra^\alpha
||\eta(t)||_p. \label{eq:norm2}
\end{equation}
To avoid cumbersome notation, where it should cause no confusion, we
shall abbreviate expressions like $[\cdot\cdot\cdot](T)$ by
$[\cdot\cdot\cdot]$, until it is necessary to make the dependence on
$T$ explicit. In the estimates below, we shall often use the notation $C_\varphi$
to denote a constant depending on some $W^{k,p}$ norm of the bound state,
$\varphi$. Under our hypotheses, $\varphi$ is a sufficiently smooth and
exponentially decaying function for which these norms are finite; see
\cite{kn:Agmon}.
Because of Proposition 5.1,
we need only estimate the terms of ${\bf E}$,
given in (\ref{eq:4.42}).
The following proposition is the main step toward the estimate on
${\bf E}$.
\bigskip
\begin{prop} {\it Estimates on the terms in ${\bf E}(t)$:}
For $0\le s\le t$, the terms of ${\bf E}(s)$, as defined in
(\ref{eq:4.42}), are estimated as follows:
\begin{eqnarray}
{\rm (i)}\ \left|\lambda a\int\varphi \eta^2\right| &\le&
|\lambda|\ C_\varphi\
[A]_{1/4}\ [\eta]_{8,3/4}^2\ \la t\ra^{-7/4}, \label{eq:e1}\\
{\rm (ii)}\ \left|\lambda\int\varphi \eta^3\right| &\le&
|\lambda|\ C_\varphi\ [\eta]_{8,3/4}^3\ \la t\ra^{-9/4}, \label{eq:e2}\\
{\rm (iii)}\ \left| F_2(a,\eta_1)\right|&\le& |\lambda|\
[A]_{1/4}^2\ \|{\bf u}_0\|_{{\bf X}}\ \la t\ra^{-13/8}, \label{eq:e3}\\
{\rm (iv)}\ \left| F_2(a,\eta_3)\right| &\le&
C_\varphi\ |\lambda|\ [A]_{1/4}^2\ C\left(\
[A]_{1/4},[\eta]_{8,3/4},[B\eta_3]_{4,1/4+\sigma_0},
\|{\bf u}_0\|_{{\bf X}}\ \right)
\ \la t\ra^{-5/4-\sigma_0}, \nonumber\\
\label{eq:e4}\\
{\rm (v)}\ \left| F_2(a,\eta_*^{nr1})\right|&\le&
C_\varphi\ |\lambda|^2\ |A_0|^2\ [A]_{1/4}^2\ \la t\ra^{-2},
\label{eq:e5}\\
{\rm (vi)}\ \left| F_2(a,\eta_*^{nr2})\right| &\le&
C_\varphi\ |\lambda|^2\ [A]_{1/4}^2\ [|A|^2|A'|]_{5/4}\ \la t\ra^{-7/4},
\label{eq:e6}\\
{\rm (vii)}\ \left| E_{2j}^{nr}\right| &\le& |\lambda|\ C_\varphi\
\left([|A|^4|A'|]_{7/4}\ + \ [A]_{1/4}^2\ +\ [|A|^2|(A^3)''|]_{7/4}\right)\
\ \la t\ra^{-13/8}\nonumber\\
\label{eq:e7}.
\end{eqnarray}
In (iv), $C(r_1,r_2,r_3,r_4)$ is bounded for $\sum_j|r_j|$ bounded and tends to
zero as $\sum_j|r_j|$ tends to zero; see Proposition 7.4.
\end{prop}
\bigskip
\noindent We now embark on the proof of this proposition.
Parts (i) and (ii) follow by H\"older's inequality. To prove part (iii), apply
H\"older's inequality and the linear propagator estimates of Theorem 2.3.
We now focus on (iv)-(vi).
\medskip
\centerline{\it Estimation of $ F_2(a, \eta_3)$}
Recall (see \ref{eq:F1234}) that
\begin{equation}
F_2(a, \eta_3) = 3\lambda a^2\int\varphi^3\eta_3.
\nonumber\end{equation}
We start by estimating $||\eta_3||_8$.
We first express $\eta_3$, defined in (\ref{eq:eta3}), as
\begin{equation} \eta_3(t) =\lambda\ \sum_{j=1}^3\
\int_{I_j}E_1(t-s){\bf P_c}\left(3a^2\varphi^2\eta\ +\ 3a\varphi\eta^2\ +\
\eta^3\right)\ ds, \label{eq:eta3a}
\end{equation}
where
\begin{equation} I_1=[0,t/2],\ I_2=[t/2,t-1],\ {\rm and }\ I_3=[t-1,t].\nonumber\end{equation}
We estimate each integral separately.
\begin{equation}
||\eta_3(t)||_8\le |\lambda|\sum_{j=1}^3\ \int_{I_j}
||E_1(t-s){\bf P_c}\left(3a^2\varphi^2\eta\ +\ 3a\varphi\eta^2\ +\
\eta^3\right)||_8\ ds.\nonumber
\end{equation}
The integrands are estimated as follows using the linear estimates
of Corollary 2.1:
\begin{eqnarray}
\int_{I_1}||E_1(t-s){\bf P_c}\{ \cdot\cdot\cdot\}||_8\ ds &\le&
C\int_0^{t/2} |t-s|^{-9/8}\ ||\{ \cdot\cdot\cdot\}||_{1,8/7}\ ds,
\nonumber\\
\int_{I_2}||E_1(t-s){\bf P_c}\{ \cdot\cdot\cdot\}||_8\ ds &\le&
C\int_{t/2}^{t-1} |t-s|^{-9/8}\ ||\{ \cdot\cdot\cdot\}||_{1,8/7}\ ds,
\nonumber\\
\int_{I_3}||E_1(t-s){\bf P_c}\{ \cdot\cdot\cdot\}||_8\ ds &\le&
C\int_{t-1}^t |t-s|^{-3/8}\ ||\{ \cdot\cdot\cdot\}||_{1,8/7}\ ds,
\label{eq:eta3b}
\end{eqnarray}
where
\begin{equation} ||\{ \cdot\cdot\cdot\}||_{1,8/7}\le\
C\left(|A|^2\ ||\varphi^2\eta||_{1,8/7}\ +\
|A|\ ||\varphi\eta^2||_{1,8/7}\ +\
||\eta^3||_{1,8/7}\right).
\end{equation}
\medskip
\begin{prop}
\begin{eqnarray}
&&(i)\ |A|^2\ ||\varphi^2\eta||_{1,8/7}\ \le \ C_\varphi\ |A|^2\
\left(||\eta||_8\ +\ ||B\eta||_4\right),\nonumber\\
&&(ii)\ |A|\ ||\varphi\eta^2||_{1,8/7}\ \le\
C_\varphi\ |A|\ \left(||\eta||_8^2\ + \ ||B\eta||_4\
||\eta||_8\right),\nonumber\\
&&(iii)\ ||\eta^3||_{1,8/7}\ \le\ C\left(||\eta||_{2,1},\varphi\right)\
||\eta||_8^{5/3}
\label{eq:eta3c}
\end{eqnarray}
\end{prop}
\bigskip
\noindent{\it proof:} We prove part (i). The estimates (ii) and (iii) follows
similarly.
\begin{eqnarray} ||\varphi^2\eta||_{1,8/7}\ &\le&\
C\left(||\varphi^2\eta||_{8/7}\ +\
||\varphi\partial\varphi\eta||_{8/7}\ +\
||\varphi^2\partial\eta||_{8/7}\right)\nonumber \\
&\le&\
C\left(||\varphi^2||_{4/3}\ ||\eta||_8\ +\
||\varphi\partial\varphi||_{4/3}\ ||\eta||_8\ +\
||\varphi^2||_{8/5}\ ||\partial\eta||_4\right),
\label{eq:db0}
\end{eqnarray}
by H\"older's inequality.
To express the right hand side of (\ref{eq:db0}) in terms of $||B\eta||_4$,
and thereby completing the proof of part (i), it suffices to show that:
\begin{equation}
||\partial\eta||_4\ \le\ C ||B\eta||_4.\nonumber\end{equation}
This follows if we show that the operator
$\partial_iB^{-1}$ is bounded on $L^p$ (with $p=4$).
\bigskip
To prove the $L^p$ boundedness of $\partial_iB^{-1}$, we can apply the results
on the wave operator, $W_*$ in \S2.2. Indeed, for any $g\in L^p$, we
have using the boundedness of the wave operators on $W^{1,p}$, for $p\ge1$,
that
\begin{eqnarray}
\|\partial_iB^{-1}g\|_p\ &=&\ \|\partial_i W_+ B_0^{-1}W_+^*g\|_p\nonumber\\
&\le&\ C\| W_+ B_0^{-1}W_+^*g\|_{W^{1,p}}\nonumber\\
&\le&\ C\|B_0^{-1}W_+^*g\|_{W^{1,p}}\nonumber\\
&\le&\ C\|W_+^*g\|_p\ \le\ C\|g\|_p.
\nonumber\end{eqnarray}
\noindent{\bf Remark:} We offer here an alternative proof which does not make
use of the wave operators, and therefore applies under weaker hypotheses
on $V$.
We begin with the
square root formula see \cite{kn:RS1} and (\ref{eq:Katosqrt1}):
\noindent For any $\psi\in{\cal D}(B^2)$:
\begin{equation}
B^{-1}\ =\ \pi^{-1}\ \int_0^\infty\ w^{-1/2}(B^2 + w)^{-1}\ dw.
\label{eq:Katosqrt}
\end{equation}
By (\ref{eq:Katosqrt}) and the second resolvent formula we have:
\begin{equation}
\partial_i B^{-1}\ =\ \partial_i B_0^{-1}
\ +\ \pi^{-1}\ \int_0^\infty\ w^{-1/2}\ \partial_i (B_0^2 + w)^{-1}\ V\
(B^2 + w)^{-1}\ dw.
\label{eq:Kato2}
\end{equation}
The boundedness in $L^p$ ($p\ge1$) of the operator $\partial_i B_0^{-1}$ holds because
$\xi_i(|\xi|^2 +m^2)^{-1/2}$ is a multiplier on $L^p$; see \cite{kn:Stein}.
Similarly, $\partial_i (B_0^2 + w)^{-1}$ is bounded on $L^p$ for any $w>0$ and
estimation of the second term in (\ref{eq:Kato2}) is reduced to estimation
of the norm of the operator $V\ (B^2 + w)^{-1}$.
Note that:
\begin{equation}
(B^2 + w)^{-1}\ =\ \int_0^\infty e^{-t(B^2+w)}\ dt\label{eq:heatrep}
\end{equation}
Since $\inf\sigma(B^2)=\Omega^2>0$,
\begin{equation}
\| e^{-t(B^2-\Omega^2/2)} \|_{{\cal B}(L^p)}\ \le\ C\nonumber
\end{equation}
and therefore
\begin{equation}
\|(B^2 + w)^{-1}\|_{ {\cal B}(L^p)}\ \le\ C\ \int_0^\infty e^{-t(\Omega^2/2 +w)}
\ \le\ C'(1+w)^{-1}.\nonumber\end{equation}
Boundedness in $L^p$ of $\partial_i B^{-1}$ now follows. Namely,
\begin{equation}
\|\partial_i B^{-1}\|_{{\cal B}(L^p)}\ \le\
\|\partial_i B_0^{-1}\|_{{\cal B}(L^p)}\
+\ C'\|\partial_i (B_0^2 + w)^{-1}\|_{{\cal B}(L^p)}\ \|V\|_\infty\ \int_0^\infty
w^{-1/2}(1+w)^{-1}\ dw\ < \infty.\nonumber
\end{equation}
\medskip
From (\ref{eq:eta3c}) we see that $||B\eta||_4$ must be estimated.
Recall that
\begin{equation} B\eta\ =\ B\eta_1\ +\ B\eta_2\ +\ B\eta_3.\end{equation}
By (\ref{eq:eta1})
\begin{equation} B\eta_1\ =\ E_0(t)B{\bf P_c} u_0\ +\ E_1(t)B{\bf P_c} u_1,\end{equation}
and so
\begin{equation} ||B\eta_1(t)||_4\ \le\ C\la t\ra^{-1/2}\ \|{\bf u}_0\|_{{\bf X}};
\label{eq:beta1}\end{equation}
see (\ref{eq:bX}) for definition of $\|{\bf u}_0\|_{{\bf X}}$.
By (\ref{eq:eta2})
\begin{equation}
B\eta_2\ =\ \lambda\int_0^t E_1(t-s)\ a^3(s)\ B {\bf P_c}\varphi^3\ ds,
\end{equation}
which can by Theorem 2.3 be estimated as
\begin{equation}
||B\eta_2(t)||_4\ \le\ C|\lambda|\int_0^t|t-s|^{-3/4}\ |A(s)|^3\
\|{\bf P_c}\varphi^3\|_{4/3}\ ds\ \le \ C_\varphi |\lambda|\ [A]_{1/4}^3\
\la t\ra^{-1/2}.
\label{eq:Beta2}
\end{equation}
The estimation of $||B\eta_3(t)||_4$ is more involved. By
(\ref{eq:eta3}),
\begin{equation}
B\eta_3\ =\ \lambda\int_0^t\ \sin B(t-s)\ {\bf P_c}
\left[ 3a^2\ \varphi^2\ \eta\ +\ 3a\ \varphi\eta^2\ +\ \eta^3\
\right]\ ds.
\end{equation}
By Theorem 2.3,
\begin{equation}
||B\eta_3(t)||_4\ \le\ C|\lambda|\int_0^t|t-s|^{-1/2}
\left[\ |A|^2\ ||\varphi^2\eta||_{1,4/3}\ +\
|A|\ ||\varphi\eta^2||_{1,4/3}\ +\
||\eta^3||_{1,4/3}\ \right]\ ds.\label{eq:beta3}
\end{equation}
The following proposition provides estimates for the integrand. It is
proved in the same manner as Proposition 7.2.
\begin{prop}
\begin{eqnarray}
|A|^2\ ||\varphi^2\eta ||_{1,4/3}\ &\le&\
C_\varphi\ |A|^2\ \left( ||\eta ||_8\ +\ ||B\eta_1 ||_4\ +\ ||B\eta_2 ||_4\
+\ ||B\eta_3 ||_4\right) , \nonumber\\
|A|\ ||\varphi\eta^2 ||_{1,4/3}\ &\le&\
C_\varphi\ |A|\ \left( ||\eta ||_8^2\ +\ ||\eta ||_8\
||B\eta ||_4\ \right)
\nonumber\\
||\eta^3 ||_{1,4/3}\ &\le&\ 3\ ||\eta ||_8^2\ ||\partial\eta ||_2.
\end{eqnarray}
\end{prop}
\bigskip
Anticipating the behavior
$$|A(t)|\sim t^{-1/4},\ ||\eta(t)||_8\sim\ t^{-3/4},$$
and using (\ref{eq:beta1}), we find that $B\eta_3$
is driven by terms which are formally of order $\la t\ra^{-1}$.
Estimation in
$L^4$ will lead to convolution of $\la t\ra^{-1}$ with
$\la t\ra^{-1/2}$ giving a rate of $\la t\ra^{-1/2 + \delta_0}$,
for any $\delta_0>0$.
\bigskip
For $0\le t\le T$, with $T$ fixed and arbitrary, we have:
\begin{eqnarray}
|A|^2\ ||\varphi^2\eta||_{4/3,1}\ &\le&\
C_\varphi\ [A]_{1/4}^2\ \left([\eta ]_{8,3/4}\la t\ra^{-5/4}\
+\ [B\eta_1]_{4,1/2}\la t\ra^{-1}\right.\nonumber\\
&+&\ \left.
[B\eta_2]_{4,1/2}\la t\ra^{-1}\ +\
[B\eta_3]_{4,1/2-\delta_0} \la t\ra^{-1+\delta_0}\right),
\nonumber
\end{eqnarray}
where $\delta_0$ is positive and arbitrary.
Also,
\begin{eqnarray}
|A|\ ||\varphi\eta^2||_{1,4/3}\ &\le&
C_\varphi\ [A]_{1/4}\left(\ [\eta ]_{8,3/4}^2\la t\ra^{-7/4}\
+\ [\eta ]_{8,3/4}[B\eta_1]_{4,0}\la t\ra^{-1}\ \right)
\nonumber\\
||\eta^3||_{1,4/3}\ &\le&\ ||\eta ||_{1,2}\ [\eta ]_{8,3/4}^2\
\la t\ra^{-3/2}.
\nonumber
\end{eqnarray}
It follows that for $0\le t\le T$
\begin{equation}
||B\eta_3 ||_4\ \le\ C_\varphi |\lambda|\
\int_0^t\ |t-s|^{-1/2}\ ds \la t\ra^{-1+\delta_0}\
G(A,\eta,T),\nonumber
\end{equation}
where
\begin{eqnarray}
G(A,\eta,T)\ &\equiv&\
[A]_{1/4}^2\ \left(\ [\eta ]_{8,3/4}\ +\ [B\eta_1]_{4,1/2}\ +\
[B\eta_2]_{4,1/2}\ +\ [B\eta_3]_{4,1/2-\delta_0}\
\right)\nonumber\\
&+& [A]_{1/4}\ \left(\ [\eta ]_{8,3/4}^2\ +\ [\eta ]_{8,3/4}\
[B\eta_1]_{4,0}\ \right)\ + ||\eta ||_{1,2}\ [\eta ]_{8,3/4}^2.
\nonumber
\end{eqnarray}
Therefore, for $0\le t\le T$:
\begin{equation}
||B\eta_3(t) ||_4\ \le\ C_\varphi |\lambda|\ G(A,\eta,T)\
\la t\ra^{-1/2 +\delta_0},\
\label{eq:b3est}
\end{equation}
for any $\delta_0>0$.
We now use the estimate (\ref{eq:b3est}) in (\ref{eq:eta3c}) in order to
obtain a bound on $||\eta_3(t) ||_8$. First, a consequence of
(\ref{eq:eta3c}), (\ref{eq:beta1}), (\ref{eq:Beta2}) and
(\ref{eq:b3est}) is that for $0\le t\le T$:
\begin{eqnarray}
|A|^2\ ||\varphi^2\eta||_{1,8/7}\ &\le&\
C_\varphi\ [A]_{1/4}^2\ \left(\ [\eta ]_{8,3/4}\ +\
\|{\bf u}_0\|_{{\bf X}}\ +\ [A]_{1/4}^3\ +\ [B\eta_3 ]_{4,1/2-\delta_0}\
\right) \ \la t\ra^{-1+\delta_0} ,\nonumber\\
|A|\ ||\varphi\eta^2||_{1,8/7}\ &\le&\
C_\varphi\ [A]_{1/4}\ \left(\ [\eta ]_{8,3/4}^2\ +\
\{\|{\bf u}_0\|_{{\bf X}}\ +\ [B\eta_3]_{4,1/2-\delta_0}\
+\ [A]_{1/4}^3 \}\ [\eta ]_{8,3/4}\ \right) \
\la t\ra^{-1+\delta_0},\nonumber\\
||\eta^3||_{1,8/7}\ &\le&\ C_\varphi\left( ||\eta||_{1,2}\right) \
[\eta ]_{8,3/4}^{5/3}\ \la t\ra^{-5/4}.
\label{eq:b3estA}
\end{eqnarray}
Substitution of (\ref{eq:b3estA}) into (\ref{eq:eta3a}-\ref{eq:eta3b})
leads to an estimate for $||\eta_3(t) ||_8$.
For $0\le t\le T$:
\begin{eqnarray}
||\eta_3(t) ||_8\ &\le&\ |\lambda|\ C_\varphi\ \la t\ra^{-1+\delta_0}\
\left( \right.
[A]_{1/4}^2
\{
[\eta ]_{8,3/4}\ +\ \|{\bf u}_0\|_{{\bf X}} +\ [A]_{1/4}^3\
+\ [B\eta_3 ]_{4,1/2-\delta_0}
\} \nonumber\\
&+& [A]_{1/4}\
\{\ [\eta ]_{8,3/4}^2\ +\ \left[\
\|{\bf u}_0\|_{{\bf X}} +\
[B\eta_3]_{4,1/2-\delta_0}\ +\ [A]_{1/4}^3\ \right]\
[\eta ]_{8,3/4}\
\}\nonumber\\
&+& \ C\left(||\eta||_{1,2},\varphi\right)\
[\eta ]_{8,3/4}^{5/3}\ \left. \right),
\label{eq:eta3A}
\end{eqnarray}
where $\delta_0$ is arbitary.
Finally we can now estimate $F_2(a,\eta_3)$ using
(\ref{eq:F1234}) and (\ref{eq:eta3A}). Choosing $\delta_0$ so that
$$-1+\delta_0\ =\ -3/4 -\sigma_0,\ {\rm with}\ \sigma_0>0,$$
we have
\begin{prop}
\begin{eqnarray}
\left| F_2(a,\eta_3)\right|\
\ &\le&\ C_\varphi |\lambda |\ [A]_{1/4}^2\
\left(\ [A]_{1/4}^2\{\ [\eta ]_{8,3/4}\ +\ \|{\bf u}_0|_{{\bf X}}\ +\
[A]_{1/4}^3\ +\ [B\eta_3 ]_{4,1/4+\sigma_0}\ \}\right. \nonumber\\
&+& [A]_{1/4}\ \{\ [\eta ]_{8,3/4}^2\ +\
\left[ \|{\bf u}_0\|_{{\bf X}}\ +\
[A]_{1/4}^3\ +\ [B\eta_3 ]_{4,1/4+\sigma_0}\ \right]\ [\eta ]_{8,3/4}
\}\ \nonumber\\
&+&\left.\ \ C\left(||\eta||_{1,2},\varphi\right)\
[\eta ]_{8,3/4}^{5/3}\ \right)\
\la t\ra^{-5/4-\sigma_0}.
\label{eq:eta3B}
\end{eqnarray}
\end{prop}
\bigskip
\centerline{\it Estimation of $ F_2(a,\eta_*^{nr1})$ and
$F_2(a,\eta_*^{nr2})$ }
\bigskip
By (\ref{eq:eta-2eps1})
\begin{eqnarray}
\eta_*^{nr1}\ &=&\ -{\lambda\over2} A_0^3\ B^{-1}(B-3\Omega +i0)^{-1}\
e^{iBt}\ {\bf P_c}\ \varphi^3,\ {\rm and}\ \nonumber\\
\eta_*^{nr2}\ &=& -{3\lambda\over2}\ B^{-1}(B-3\Omega +i0)^{-1}\
\int_0^te^{iB(t-s)}\ e^{i3\Omega s}\ A^2A'\ ds {\bf P_c}\varphi^3
\nonumber
\end{eqnarray}
Estimation using Proposition 2.2 gives:
\begin{eqnarray}
\left|F_2(a,\eta_*^{nr1})\right|\ &=&\ 3\ |\lambda|\ |a|^2\
\left|\int\varphi^3\eta_*^{nr1}\right|\nonumber\\
&=&\ C|\lambda|^2\ |A_0|^3 |A|^2\
\left|\ \int\ \varphi^3\ \left[ B(B-3\Omega +i0 )\right]^{-1}\
e^{iBt}\ {\bf P_c}\ \varphi^3\ \right| \nonumber\\
&\le&\ C|\lambda|^2\ |A_0|^3 |A|^2\ \|\
\langle x\rangle^\sigma\varphi^3\ \|_2\ \|\langle x\rangle^{-\sigma}
(B-3\Omega +i0)^{-1}\ e^{iBt}\
{\bf P_c} B^{-1} \varphi^3\|_2 \nonumber\\
&\le&\ C_{\varphi}\ |\lambda|^2\ |A_0|^2\
[A]_{1/4}^2\ \la t\ra^{-{5\over4} +\delta}.
\end{eqnarray}
Here, we have used that
$1/2 + 6/5 = 5/4 + \delta$, for some $\delta >0$.
The constant $C_\varphi$ depends on
$ \|\langle x\rangle^\sigma B^{-1} \langle x \rangle^{-\sigma}\|_{{\cal B}(L^2)}$.
It is easy to check that this norm is bounded if we replace $B^{-1}$ by
$B^{-2}$. The estimate of interest is reduced to this case using the
Kato square root formula (\ref{eq:Katosqrt}).
Similarly, we have
\begin{eqnarray}
\left| F_2(a,\eta_*^{nr2})\right| &=&\ 3|\lambda |\ |a|^2\
\left| \int\varphi^3\eta_*^{nr2}\right| \nonumber\\
&\le&\ C\ |\lambda|^2\ |A|^2\ \left|\ \int\ \varphi^3 \left[
B(B-3\Omega +i\varepsilon)\right]^{-1}\ \int_0^t\
e^{i(t-s)(B-3\Omega)}\ A^2 A'\ ds\ {\bf P_c} \varphi^3\ \right|\nonumber\\
&\le&\ C_\varphi\ |\lambda |^2\ |A|^2\
\int_0^t\langle t-s\rangle^{-{3\over2}+\mu}\
|A|^2\ |A'|\ ds\ \nonumber\\
&\le&\ C_\varphi\ |\lambda |^2\ [A]_{1/4}^2\ [|A|^2|A'|]_{5/4}\ \langle
t\rangle^{-{7\over4}},
\end{eqnarray}
where we have taken $\mu$ sufficiently small
so that the last integral $t-$ integral is
convolution with an $L^1$ function, which then preserves the decay rate
, $\langle t\rangle^{-{7\over4}}$,
which exceeds $\langle t\rangle^{-{5\over4}}$
\bigskip
\centerline{\it Estimation of $E_{2j}^{nr}$:}
\bigskip
To estimate (\ref{eq:4.40}) we use Propositions
2.1 and 2.2. Due to the singularity in the resolvent at frequency
$3\Omega$, the case $j=7$, is most difficult and we focus on it.
To treat this singularity, we use
Proposition 2.2, for $n=3$:
\begin{equation}
\| \langle x\rangle^{-\sigma}(B-\zeta_7)^{-2}e^{iB(t-s)}\langle x\rangle^{-\sigma}\psi
\|_2\ \le\ C\langle t-s\rangle^{-{6\over5}}\|\psi\|_{1,2}. \nonumber
\end{equation}
Use of this estimate in (\ref{eq:4.40}) yields
\begin{eqnarray}
&& |E_{2j}^{nr}|\ \le\nonumber\\
&&\ \ \ \ C_\varphi |\lambda |^2
\ \left(\ [|A|^4|A'|]_{7/4} \la t\ra^{-7/4}\ +\ [A]_{1/4}^2\la t\ra^{-13/8}\ +\
[|A|^4|A''| + |A|^3|A'|^2]_{9/4}\la t\ra^{-13/8}\ \right),
\nonumber
\end{eqnarray}
from which estimate (vii) of Proposition 7.1 follows. This finally
completes the proof of Proposition 7.1.
Proposition 7.1 can now be used to obtain the desired estimate for
${\bf E}(t)$ and therefore ${\bf\tilde A}(t)$, for $|A|$ sufficiently
small. Note that the right hand side of the estimates depend on
$|A'|$ and $|A''|$. These can each be estimated directly from the equation
for $A$, (\ref{eq:4.41}), and its derivative. The result is that
$|A'|$ and $|A''|$ may be estimated by $[A]_{1/4}^3\langle t\rangle^{-{3\over4}}$,
the only effect being a change in the multiplicative constants which is
independent of $A$ and $\eta$. This observation together with
Proposition 7.1 yields:
\begin{prop}
There is positive number $\delta$ such that
\begin{equation}
\left| {\bf E}(t)\right| \le\ Q_0(A,\eta)
\langle t\rangle^{-{5\over4}-\delta}
\label{eq:EQbound}
\end{equation}
where
\begin{equation}
Q_0(A,\eta)\ =\
[\eta ]_{8,3/4}^3\ +\ [A]_{1/4}\
\left(\ 1\ +\ C\left( [A]_{1/4},[\eta ]_{8,3/4},
[B\eta_3]_{4,1/4+\sigma_0}, \|{\bf u}_0\|_{{\bf X}}\
\right)\
\right)
\label{eq:Q0}
\end{equation}
\end{prop}
\medskip
It now remains to estimate $||\eta ||_8$.
\begin{eqnarray}
||\eta ||_8 &\le&\ ||\eta_1 ||_8\ +\ ||\eta_2 ||_8\ +\ ||\eta_3 ||_8\nonumber\\
&\le&\ ||E_0(t) {\bf P_c} u_0||_8\ +\ ||E_1(t) {\bf P_c} u_1||_8\ +\
|\lambda |\int_0^t ||E_1(t-s)a^3(s) {\bf P_c}\varphi^3||_8\ ds\ +\
||\eta_3 ||_8.
\nonumber
\end{eqnarray}
Using Theorem 2.3 and the bound (\ref{eq:eta3A}) we get
\begin{prop}
\begin{eqnarray}
||\eta ||_8 &\le&\ C_\varphi\ \left(\
\|{\bf u}_0\|_{{\bf X}}\ +\ [A]_{1/4}^3\right. \nonumber\\
&+&\ [A]_{1/4}^2 \{ \ [\eta ]_{8,3/4}\ +\ \|{\bf u}_0\|_{{\bf X}}\ +\
[A]_{1/4}^3\ + [B\eta_3]_{4,1/4+\sigma_0} \}\nonumber\\
&+&\ [A]_{1/4}\ \{\ [\eta ]_{8,3/4}^2\ +\
\left[ \|{\bf u}_0\|_{{\bf X}}\ +\ [A]_{1/4}^3\ +\
[B\eta_3]_{4,1/4+\sigma_0} \right]\ [\eta ]_{8,3/4}\}
\nonumber\\
&+&\ \left. C\left( ||\eta ||_{1,2},\varphi\right)\ [\eta ]_{8,3/4}^{5/3}\
\right)\ \langle t\rangle^{-3/4} .
\label{eq:eta3C}
\end{eqnarray}
\end{prop}
\bigskip
The following proposition summarizes our labors.
\begin{prop}
For any $T>0$:
\begin{eqnarray}
[\eta ]_{8,3/4}(T)
&\le&\ C_\varphi \left(\ \|{\bf u}_0\|_{{\bf X}}\ +\
[A]_{1/4}^3(T)\ +\ [B\eta_3 ]_{4,1/4+\sigma_0}^2(T)\right. \nonumber\\
&+& \left.
C_\varphi\left( ||\eta ||_{1,2}\right)\ [\eta ]_{8,3/4}^{5/3}(T)\
\right) \nonumber\\
\ [A]_{1/4}^4(T) &\le&\ \left( |A_0|^4 + Q_0(A,\eta)^{8\over5}\ \right)
\nonumber\\
\ [B\eta_3]_{4,1/4+\sigma_0}(T) &\le&\
\left( [A]_{1/4}^2(T)\ +\ [\eta ]_{8,3/4}^2(T)\ +\ [B\eta_2]_{4,1/2}^2(T)\
+\ [B\eta_3]_{4,1/4+\sigma_0}^2(T)\ \right),\nonumber\\
\sup_{0\le t\le T}||\eta(t)||_{1,2}\ &\le&\ C\ {\cal E}(u_0,u_1)\le C
\|u_0 , u_1\|_{1,2}.
\nonumber
\end{eqnarray}
\end{prop}
The first three estimates are proved above while the last follows from
conservation of energy (see section 1) and the decomposition of the
solution.
Now define
\begin{equation} M(T)\ \equiv\ [\eta ]_{8,3/4}(T)\ +\ [A]_{1/4}(T)\ +\
[B\eta_3]_{4,1/4+\sigma_0}(T).\nonumber
\end{equation}
Then, combining the estimates of the previous proposition we have, for
some $\alpha >0$:
\begin{equation}
M(T) \left(\ 1-M(T)^\alpha\ \right)\ \le\ C_\varphi\
\|{\bf u}_0\|_{{\bf X}}.
\nonumber
\end{equation}
If $M(0)$ and $\|{\bf u}_0\|_{{\bf X}}$
are sufficiently small, we have by the continuity of $M(T)$,
that there is a constant $M_*$, which
is independent of $T$, such
that for all $T$
\begin{equation} M(T)\le M_*.
\label{eq:aprioriest}
\end{equation}
This completes the proof of Theorem 1.1.
\section{ Summary and discussion}
We have considered a class of nonlinear Klein-Gordon equations,
(\ref{eq:nlkg}),
which are perturbations of a linear dispersive equation which has a
time periodic and spatially localized (bound state) solution. The
unperturbed and perturbed dynamical systems are Hamiltonian. We have shown
that if a
nonlinear resonance condition (\ref{eq:nlfgr}) holds,
then solutions with
sufficiently small initial data tend to zero as $t\to\pm\infty$. This
resonance condition is a nonlinear variant of the {\it Fermi golden rule}
(\ref{eq:fgr}). A consequence of our result is that
time-periodic and spatially localized solutions do not persist under
small Hamiltonian perturbations. Time-decay of small
amplitude solutions
is also a property of the translation invariant ($V\equiv0$)
nonlinear Klein-Gordon equation. However, the presence of a bound
state of the unperturbed problem,
causes a nonlinear resonance leading to the anomalously slow
radiative decay of solutions.
We now conclude with some further remarks on the results of this paper,
mention
directions currently under
investigation and some open problems.
\bigskip
\noindent {\bf 1.\ Anomalously slow time-decay rates:}
It is natural to compare the time-decay
rate of solutions described by Theorem 1.1 with those
of related problems.
(1a) {\it Translation invariant linear Klein-Gordon equation}\
($V\equiv
0$ and $\lambda=0$):
\noindent We shall refer to {\it free
dispersive rates of decay} as those associated with the constant
coefficient equation:
\begin{equation}
\partial_t^2 u\ -\ \Delta u\ + \ m^2u\ =\ 0.\label{eq:freeKG}
\end{equation}
Results on this are presented in \S2. Roughly speaking,
if the initial data has a sufficient number of
derivatives in $L^p,\ 1 < p\le 2$, then the solution
decays at a
rate
${\cal O}(t^{-n({1\over2}-{1\over p'})})$ in
$L^{p'}$. Here, $p^{-1} + (p')^{-1}=1$.
(1b) {\it Translation invariant nonlinear
Klein Gordon equation}\
($V\equiv 0$ and $\lambda\ne0$):\
\noindent
For small initial conditions it has
been shown that solutions decay at free dispersive rates;
see \cite{kn:strauss} and references
cited therein.
(1c) {\it Linear Klein-Gordon equation with a potential having a
bound
state, as hypothesized}
\ ($V\ne0$ and $\lambda=0$):
\medskip
\noindent By the spectral theorem, a typical solution will decompose into
a
linear superposition of (i) a bound state part, of the form:
$R_0\cos(\Omega t+\rho_0)\varphi(x)$, and (ii) a
part which disperses to zero at free
dispersive rates.
(1d) {\it Nonlinear Klein-Gordon equation with a potential having a
bound
state, as hypothesized}\ ($V\ne0$ and $\lambda\ne0$):
Whereas the decaying part of the solution in the above cases tends
to
zero at a
free dispersive rate, Theorem 1.1 implies that the decay rate is
anomalously slow. In particular, the decay rate
obtained in $L^8$ is ${\cal O}(t^{-{1\over4}})$, while the
free
dispersive rate in $L^8$ is ${\cal O}(t^{-{9\over8}})$.
This slow rate of decay, due to the nonlinear resonant
interactions
give rise to a
long-lived or {\it metastable states}.
\noindent{\bf 2. Dispersive Hamiltonian normal form}
In a finite dimensional Hamiltonian system of one degree of freedom,
the
general normal form is:
\begin{equation} A' = i\left(c_{10} + c_{21}|A|^2 + c_{32}|A|^4 +...+
c_{n+1,n}|A|^{2n}+...\right)A,
\end{equation}
where $c_{n,n+1}$ are real numbers. In the present context we
have the
{\it dispersive Hamiltonian normal form}
\begin{equation} A' = \left(k_{10} + k_{21}|A|^2 + k_{32}|A|^4
+...+ k_{n+1,n}|A|^{2n}+...\right)A,
\end{equation}
where
$$k_{n+1,n}=d_{n+1,n} + ic_{n+1,n}$$
are, in general,
numbers with real and imaginary part. Contributions to the
real parts of
coefficients come from resonances with the continuous
spectrum.
If (\ref{eq:nlfgr}) fails
there are two possibilities; either (a) $3\Omega$ does not lie in the
continuous spectrum of $B$ (it lies in the gap $(0,m)$), or (b) $3\Omega$
lies in the continuous spectrum of $B$ but we are in the non-generic
situation where the projection of $\varphi^3$ onto the generalized
(continuum) eigenmode of frequency $3\Omega$ is zero.
In either case, we expect that, typically, internal dissipation
would arise in the normal form at higher order.
More precisely, we conjecture that the leading order nonzero
$d_{n_*+1,n_*}$, which would correspond
to a resonance with the continuum of a
higher harmonic: $q_*\Omega\in\sigma_{cont}(B)$, $q_*>3$ is always
negative. (If the sign of $d_{n_*+1,n_*}$ were positive,
this would seem to be in violation
of the conservation of energy and the implied Lyapunov stability
of the zero solution.)
The corresponding
decay rate would then be slower, specifically ${\cal
O}( |t|^{-{1\over 2n_*}} )$.
From this perspective one may expect the existence of breather solutions
of integrable nonlinear flows like the sine-Gordon equation or the extremely
long-lived breather -like states of the $\phi^4$ - model as
corresponding to the case where to all orders
the coefficients $d_{n+1,n}$ are zero. Does the vanishing of all such
coefficients have an interpretation in terms of the infinitely many
time-invariants for the integrable flow?
\noindent {\bf 3. Multiple bound state problems:}
Of interest are problems
where the underlying potential, $V(x)$, supports more than
one bound state. What is the large time behavior of such systems?
Our analysis and the above remarks suggest that
a more general normal form could be developed, and the
corresponding ( in general slower) decay rates anticipated.
Is it possible that a resonance among the multiple
"discrete oscillators" can be arranged so that one gets a persistence of
nondecaying solutions, or does radiation to the continuum always win out?
\noindent {\bf 4. Relation to center manifold theory:}
Our program of decomposing the original conservative
dynamical system into a finite
dimensional dynamical system (\ref{eq:dosc}) which is weakly coupled to
an infinite dimensional dynamical system is one commonly used in
dissipative
dynamical systems. There, it is often possible using the center
manifold approach \cite{kn:Carr}, \cite{kn:VI}, to construct an invariant
center-stable manifold. The dynamics in a neighborhood of an equilibrium
point are characterized by an exponentially fast contraction on to the
stable-center manifold. The contraction is exponential because the part
of the linearized spectrum associated with the infinite dimensional
part of the dynamics is contained in the left half plane. In the
current context of conservative dynamical systems, the linearization
about the equilibrium point (here $u\equiv 0$) lies on the imaginary
axis; in particular, two complex conjugate eigenvalues $\pm i\Omega$
and continous spectrum from $\pm im$ to $\pm i\infty$.
The analogue of dissipation is the mechanism of dispersive radiation
of energy, related to the continuous spectrum, and the associated
algebraic time-decay.
There is recent work on the
application of center manifold methods to certain special
conservative dynamical systems of nonlinear Schr\"odinger type;
see the center manifold analysis of \cite{kn:PW} applied to problem studied
by the authors in \cite{kn:SW1bs}.
It would be of interest to understand whether
geometric insight on the structure of the phase space for
problems of the type
considered in this paper can be obtained using the ideas of
invariant manifold theory.
\noindent {\bf 5. Systems with disorder:}
In this paper, we have seen the effect of a single localized defect on
the wave propagation dynamics in a nonlinear system.
Of great interest would be an understanding of the effects of a
spatially random distribution of defects modeled, for example,
by random potential
$V(x)$ on the localization of energy in nonlinear systems
such as (\ref{eq:nlkg}). Related questions are studied in \cite{kn:FSW},
\cite{kn:GKSV}, \cite{kn:Bronski}.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,447 |
using System;
/*
Problem 3. Divide by 7 and 5
Write a Boolean expression that checks for given integer if it can be divided (without remainder) by 7 and 5 at the same time.
*/
class DivideBySevenAndFive
{
static void Main()
{
Console.WriteLine("Enter a number:");
int number = int.Parse(Console.ReadLine());
if (((number % 35) == 0) && (number != 0))
{
Console.WriteLine("true");
}
else
{
Console.WriteLine("false");
}
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 2,754 |
Echinobunus elegans is een hooiwagen uit de familie Sclerosomatidae.
Sclerosomatidae | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,955 |
Transcript: Bill Belichick Press Conference 8/3
BB: BB: Alright, how are we doing today? Grinding through camp here.
Q: Since you've put the pads on, we've some of the one-on-one drills between the offensive and defensive lineman. What can you learn from players in those one-on-one periods?
BB: Well, you know, all those one-on-one periods are good periods because they give the players an opportunity to just focus on the technique. There's no play, there's no down-and-distance, there' none of all the other things that come and there's no adjustments. It's just focus on individual fundamental techniques, and every play has a lot of those in them. So, various drills - long ball drills, one-on-one drills, so forth - it isolates just the technique - footwork, hand placement, leverage, so forth - and all the things that are involved without all the other components of a play that factor into a play where players don't have to think about that. You can just focus on his technique. We just coach his technique so it's part of the overall process of the good play.
Q: Do you find that those drills simulate pretty well what a player sees once you get the whole team out in 11-on-11?
BB: Again, it's that fundamental. I mean, again, there are a lot of other things that could happen, and there are other players that are involved in a play that it's not just isolated. There are times when it's just isolated, but the majority of the time, it really isn't. But your fundamentals need to be good, and if they're good in the individual one-on-one part of it, then usually those fundamentals will transfer to stunts and combination routes and so forth and so on. Again, it's just the teaching progression. I mean, if fundamentals are wrong in a basic one-on-one situation, then it's just going to go downhill from there. It's not going to get any better. So, then when other things start happening, when you start getting games or combination routes or pick routes or whatever, whatever the next part of the sequence is, then it's just going to get worse. So, you try to start with a good fundamental. You try to start doing it right, and then, if you have to make adjustments during the play or as the play extends, then those are further coaching points, which we go from one-on-one to two-on-two, and pass rush and pass protection one-on-one to two-on-two, to eventually five-on-four, to team, sometimes half-line - not half-line, but just the interior line, like seven-on-six, six-on-six in pass protection - and then we go to full team. So that's just the logical progression to put it all together.
Q: Have you found that one-on-one drills are helpful to the coaching staff to notice something about a player you might not know much about? Is it easier to see something in those drills, as opposed to the team periods?
BB: Some players are better players in one-on-one, isolated situations, and some players are better in team situations. They don't necessarily correlate directly. Some guys, when you put the other 21 guys out there, just have an instinct and a feel and better anticipate and maybe react quicker than what they would if it's just a one-on-one matchup. Some guys, in a one-on-one matchup, do better. And then when you put everybody else out there, certainly when you start to change the situations a little bit - change the formation, change the plays, change the down-and-distances - then it slows down and you don't see that same level of performance that you see in one-on-ones. Now, sometimes that changes as the player gets more experienced and gets more comfortable and can transfer his individual skills into team skills and apply - because, again, not every play is the same play- so applying certain skills in certain situations. Yeah, I mean, we definitely learn those things. It's not all equal. Each guy is different, but I think you try to take the positives and show a player, 'Look, here you are in one-on-one situations. You've got to be able to transfer that to team,' or, 'Here's how you can individually have more success by doing this technique better or that technique a little better because you're just isolated on that.' There's no I was reading this, or I got that call or something else happened. You can eliminate all of that. And the players learn from each other. You watch the other guys do it and you see another guy do something or you see him make a mistake and you understand why you can't do that or maybe you can do something that he can do. That also is a good time to experiment with a different pass rush technique or a different route technique or a different coverage technique or something that maybe you personally don't feel as confident about. Now, in a one-on-one situation, you might be more apt or we would tell the player, 'Look, here's a good time for you to use this so you can came some confidence in it,' so we would use it in a team or eventually in a game setting that he might not do if he didn't gain the confidence in a more isolated drill.
Q: How much does it complicate things when one specific position group gets pretty shallow with minor injuries in training camp?
BB: Yeah, that's part of training camp and part of just practice in general is managing your team, trying to keep everybody moving along. But sometimes, as you said, if a certain group is lower in numbers, that affects what either that side of the ball can do or maybe what the other side of the ball can do against it. Occasionally, we have to make some kind of modifications. Hopefully the train doesn't come to a complete halt and we're able to maybe do a little more of something else in order to manage the reps of a particular player or a particular group, like when Joe Cardona wasn't here at the beginning of training camp. We modified our teaching schedule a little bit there to work on a couple phases of the kicking game when he wasn't here and changed that to work on the ones where we needed a snapper. It's not an uncommon thing. We talk about that every night when we go through our practice schedule. We go through the overall where our team is, where our individual position groups are, where the individual players are and put it all together. Occasionally, we have to make a team adjustment, but usually it's more within the group of how we're going to rep the plays with the players that are there. Not an uncommon thing.
Q: Fans seemed to enjoy watching you throw blocking pads at the quarterbacks in practice on Tuesday. Do you take any particular enjoyment in that drill?
BB: Yeah, that's good. I mean, look, if they can't handle it from us, they're in a lot of trouble. They're going to get a lot bigger, stronger, faster, more explosive guys than what we have on the coaching staff. You know, we hit the receivers with bags and try to knock the ball away from them and make them catch through contact and make the quarterbacks avoid a rush and stuff like that. Look, if they can't handle us, it's going to be a long year.
Q: Tom Brady said after the Super Bowl that he has all the answers to the test. So, for someone with that wealth of experience, how can you challenge him on a daily and weekly basis?
BB: Yeah. I mean, look, there's a lot of us around here that have a lot of experience, but I don't really think that matters too much in terms of this year. We're in a new year. It's a new team, new opponents, new challenges, and we'll have to find a way to get over those hurdles, and they'll be there every day. They'll be there every week. Yeah, we've probably seen some element of it before somewhere, but not with this team we haven't. None of us have. I haven't coached this team before. None of the players on this team have played with some of the other players on the team, so we'll have to work all that out.
Q: Does it ever surprise you how long Brady has been able to play and at this level?
BB: I mean, yeah. I mean, he's had a great career, he works hard, comes to work every day. It's been like that for a long time. So, I mean, I don't want to say you take it for granted, but I mean, I wouldn't say it's like a big shock that he's going to walk in here today and be prepared and go out and perform and give us his best. That's what he's been doing, so we all expect that. He expects that out of himself. I'm sure he expects it out of me. You know, we all expect it out of each other. But, the level of consistency and the longevity of it is obviously very, very impressive.
Q: Are you guys doing anything as a team for Brady's birthday during or after practice?
BB: Like the parade? Yeah.
Q: With regards to Jimmy Garoppolo, you had to prepare him to play during training camp last year.
BB: Right, it was different.
Q: How do you go about this preparation process with him this year, and how do you think he's gone about his business as he deals with the uncertainty of it now?
BB: Well, I don't think there's uncertainty about the situation. I mean, look, it is what it is. I think he's talked about it. It's different than it was last year. Last year was last year. This year is this year. Again, that's a good example of each year's a little bit different for all of us in one way or another, no matter how much experience we have. I think he's trying to make the most of his opportunities, trying to prepare and do the best that he can in the opportunities that he has, like every other player is. It's different, but at that position, we all know that could change in five minutes. That's like 2008. It can all change in a hurry. Actually, that's true at every position, not just that position. It's true at every position. When Lonie [Paxton] tore his ACL, that changed that in one play. That's what having a good team is is everybody being ready to go and having depth and being able to handle whatever we have to handle.
Q: Do you feel like Garoppolo has been consistent enough for you in training camp thus far?
BB: Well, I mean, it's training camp. Look, I don't think any of us are where we need to be. I mean, we've been basically at this for a week, so there are things we all can do better. We all need to do better, starting with me, the coaching staff, every player - experienced, inexperienced, whatever position they play. I mean, we've all got a long way to go. We've got a lot of work to do. I don't think anybody's even close to where they need to be.
Q: When it comes to the quarterback position, how do you balance encouraging a guy to take a chance he might not take in a game situation versus wanting to be as clean as possible in practice?
BB: Well, I mean, practice is the time to do it, and that's the only way - again, if you don't execute it in practice, it's hard to execute it in the game. I'm not saying never, but not very often. Yeah, you need to find that out in practice at quarterback - I mean, at other positions, as well, but specifically at quarterback - what windows you can get it into, what windows you can't, whether you can make this throw to that player or as you could do to another player. I mean, is it different? Can you do it the same? And that's finding that out, gaining confidence or understanding, 'No, I'm not comfortable doing that. I don't want to do that in a game situation.' It's a lot better to find that out in practice than it is in the game. Of course, we don't want to go out there and make a lot of mistakes, but there's definitely an element of aggressively executing a play in practice to find out what limit you can take it to in a more competitive situation. So that's what this is for. I wouldn't say all bad plays that happen are bad plays. A lot of times those plays become good plays or good learning plays for situations going forward. The bad plays really come in the games. Look, nobody wants to go out there and - the same thing with a receiver. I mean, you might run a route to try to experiment or try something a little bit different. Not a good route, didn't work - alright, we're not going to do that again the next time, or if we do it, we're going to do it differently to do it right. Yeah, I mean, there's definitely an element of that. That's not, again, to say we want to go out there and make 22 mistakes on every play because we're just winging it around and trying to experiment and find out and all that. I mean, that's not really what we're trying to do, but there is an element of that, especially at this time of year. But, you know, sometimes that happens in the regular season, too. You put in a play and, 'Alright, here's the play,' and you throw it in practice and, 'Can I get this in there? Yeah, you can,' or maybe, 'No, I can't. OK, if I get this look in the game, then I've got to go to my secondary receiver.' That kind of thing.
Q: Do you find that there's more of that aggressiveness when there are more new players involved, specifically receivers or pass-catching options?
BB: Well, again, there's always an element of that. I thought he was going to go behind, he thought he was going to go in front, and sometimes that's - I mean, we have rules on that. We coach things a certain way, but I mean, look, it's a fluid game. Once a player gets out there and he's in the play, he's going to make the best decision he can in that particular situation. Sometimes the guidelines are just guidelines and the player's going to do what he thinks is best in that situation. It's not always maybe the same as what his teammate thought it was going to be, whether it was a quarterback throwing to a receiver, whether it's two offensive lineman passing off a pass-rush game, whether it's a couple of defenders on a certain blocking scheme. 'I thought this was the way you were going to play it. I was going to play it this way. No, you're going to play it that way. Alright, then I'll make the adjustment.' I mean, there's a lot of that. There's a lot of that in our meetings when we go through the practice film of each other understanding - I mean, there's that silent communication - but each of us understanding what our teammates are going to do. So, eventually, we get to the point where we're not thinking about it. It's not an, 'I wasn't sure. I was waiting to see,' type of thing. We can just go out there and play aggressively because I know where you're going to be, you know where I'm going to be and we've done it enough times that we're confident in it. Yeah, that comes up a lot every night.
Patriots players comment on their 17-47 loss to the Buffalo Bills on Saturday, January 15, 2022.
Transcript: Bill Belichick Press Conference 1/16
Read the full transcript from Patriots head coach Bill Belichick's press conference on Sunday, January 16, 2022.
What They're Saying: Buffalo Bills
A look at what Buffalo Bills coaches and players are saying ahead of their Wild Card Playoff game against the New England Patriots.
Read the full transcript from Patriots Head Coach Bill Belichick's press conference on Thursday, January 13, 2022.
Read the full transcript from Patriots Head Coach Bill Belichick's press conference on Wednesday, January 12, 2022.
Read the full transcript from Patriots Head Coach Bill Belichick's press conference on Monday, January 10, 2022.
New England Patriots Postgame Quotes 1/9
New England Patriots Head Coach Bill Belichick, Quarterback Mac Jones and select players comment on their 24-33 loss to the Miami Dolphins on Sunday, January 9, 2022.
Miami Dolphins Postgame Quotes 1/9
Miami Dolphins Head Coach Brian Flores, Quarterback Tua Tagovailoa and select players comment on their 33-24 win over the New England Patriots on Sunday, January 9, 2022.
Read the full transcript from Patriots Head Coach Bill Belichick's press conference on Friday, January 7, 2022.
What They're Saying: Miami Dolphins
A look at what Miami Dolphins coaches and players are saying about their upcoming game against the New England Patriots.
Transcript: Mac Jones Press Conference 1/5
Read the full transcript from Patriots Quarterback Mac Jones' video conference call on Wednesday, January 5, 2022.
Read the full transcript from Patriots Head Coach Bill Belichick's press conference from Wednesday, January 5, 2022. | {
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<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:orientation="vertical" >
<TextView
android:id="@+id/state"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_gravity="center_horizontal"
android:gravity="center_horizontal|center_vertical"
android:text="TextView"
android:textColor="@color/White"
android:textColorHint="@color/White" />
<TextView
android:id="@+id/childname"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_gravity="center"
android:text="Remote Control"
android:textColor="@color/White" />
<Button
android:id="@+id/launch_value"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_gravity="center_horizontal"
android:background="@drawable/button_config"
android:text="Launch"
android:textColor="@drawable/button_text_color"
android:textOff="Off!"
android:textOn="On!" >
</Button>
</LinearLayout>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,915 |
Taylor Swift Performs in NYC at First Public Appearance Since Scooter Braun and Big Machine Feud
Taylor Swift performed to an intimate audience in New York City at Amazon Music's Prime Day Concert
Melody Chiu
Melody Chiu is a Senior Editor for PEOPLE. She has been with the brand since 2009, editing, writing and reporting across all entertainment verticals. She oversees PEOPLE's music and events coverage and has written cover stories on Taylor Swift, Selena Gomez, Melissa McCarthy, Blake Shelton and Sandra Oh. The Los Angeles native graduated from the University of Southern California and has appeared on Extra!, The Talk, Access Hollywood and Good Morning America.
and Ale Russian
Published on July 11, 2019 01:15 AM
After spending a quiet Fourth of July in the Caribbean with her girlfriends following a drama-filled week, Taylor Swift was back on top in New York City on Wednesday at Amazon Music's Prime Day concert.
The Grammy winner, 29, performed her hits including "Welcome to New York" and also "Shake It Off" to a celeb-studded crowd.
While she did not directly address the feud between herself and Justin Bieber's manager Scooter Braun and her former record label Big Machine, she sent fans into a spin when she emphasized the "Shake It Off" line "liars and the dirty, dirty cheats of the world."
Her audience also had her back with fans handing out hearts that read, "Hold this PINK heart against your flashlight the moment Taylor Swift finishes performing her first song. #WeStandWithTaylor Follow @theSwiftie911"
Also in the audience supporting her were Gigi Hadid and Ashley Avignone, along with Justin Theroux, who took videos of Swift's set.
Other performers at the event — hosted by Jane Lynch — included Dua Lipa, SZA and Becky G.
Evan Agostini/Invision/AP/Shutterstock
Taylor Swift. Evan Agostini/Invision/AP/Shutterstock
While she did not address it Wednesday, a source close to Swift previously told PEOPLE the superstar has no qualms about speaking out against Braun, who closed a $300 million deal with her former label Big Machine, and the Nashville-based company's founder Scott Borchetta.
"She has no regrets expressing her thoughts about Scooter acquiring her music catalog," said the source. "She wanted to share her truth with her fans."
After Swift claimed she learned of the sale of Big Machine to Braun, 38, with the rest of the world and accused the manager of "manipulative bullying" over the years via a Tumblr post, it's been a game of he-said, she-said between the singer, Braun and Borchetta, 57, who first signed the singer when she was a teen to his then-fledgling label.
Braun has not commented on the situation or the singer's claims about him.
Last week, the Swift doubled down on accusations she made via her post that she "wasn't given an opportunity to buy" her "life's work."
Taylor Swift Spent Fourth of July in the Caribbean Amid Drama with Scooter Braun and Her Former Label Head Scott Borchetta
"Scott Borchetta never gave Taylor Swift an opportunity to purchase her masters, or the label, outright with a check in the way he is now apparently doing for others," her lawyer Donald Passman told PEOPLE in a statement.
A source previously told Variety that Swift had to sign a deal that would bind her to Big Machine or its new owner for another 10 years in order to buy her masters or the label.
Neither Swift nor Borchetta have commented further about their failed contract negotiations — including the specifics of any offers that were made from either side.
However, hours after Swift said she was "grossed out" by Braun's acquisition of Big Machine Label Group and her catalog, Borchetta did respond with his own lengthy statement on the label's website, essentially accusing Swift of bending the truth.
Scott Borchetta, Taylor Swift, Scooter Braun. Rick Diamond/Getty Images; Larry Busacca/Getty Images; Jeff Kravitz/FilmMagic
Taylor Swift vs. Scooter Braun: Inside the Drama Surrounding the Manager's $300 Million Purchase
In his letter, Borchetta claimed the deal he offered Swift gave her "100% of all Taylor Swift assets … to be transferred to her immediately upon signing the new agreement."
He also denied having any knowledge of bullying by Braun. "As to her comments about 'being in tears or close to it' anytime my new partner Scooter Braun's name was brought up, I certainly never experienced that," he wrote. "Scooter was never anything but positive about Taylor."
"We were working together on a new type of deal for our new streaming world that was not necessarily tied to 'albums' but more of a length of time," he added.
RELATED VIDEO: Taylor Swift's Rep Says Singer Learned of Scooter Braun's Purchase from News When She Woke Up
In her Tumblr post, Swift said the deal she was offered involved earning one album back for each "new one I turned in."
"I walked away because I knew once I signed that contract, Scott Borchetta would sell the label, thereby selling me and my future," she added. "I had to make the excruciating choice to leave behind my past."
Swift, whose new album Lover hits shelves Aug. 23, said learning that it was Braun who had ultimately purchased her masters from Borchetta was her "worst nightmare."
For more on Taylor Swift, pick up the latest issue of PEOPLE, on newsstands Friday.
Taylor Swift 'Has No Regrets' About Speaking Out Against Scooter Braun and Scott Borchetta: Source
Kelly Clarkson Advises Taylor Swift to Re-Record Her Old Songs Amid Scooter Braun Drama
Scooter Braun Jokes 'Last Couple of Weeks Have Really Taken a Toll' Amid Drama with Taylor Swift
Taylor Swift's Lawyer Says She Wasn't Given Opportunity to Buy Her Former Label or Masters Outright
Taylor Swift Reveals Plans to Re-Record First 6 Albums After Scooter Braun's Big Machine Purchase
Kelly Clarkson Says Reba McEntire Gave Her the Idea for Taylor Swift to Re-Record Her Songs
Taylor Swift Fans Celebrate as Singer Is Now Free to Re-Record Original Music
Can Taylor Swift 'Actually' Re-Record Her Old Songs Like Kelly Clarkson Suggested?
Scooter Braun Has Reached Out to Taylor Swift to Have 'a Private Conversation,' Says Source
Scooter Braun Recalls a 'Kind' Teenage Taylor Swift but Declines to Comment on Recent Drama
Taylor Swift's Former Label Head Denies Singer's Claims Scooter Braun Was 'Bullying' Her
Scooter Braun Congratulates Taylor Swift on 'Brilliant' New Album' Lover' After Drama
Taylor Swift Speaks Out After Scooter Braun Sells Her Masters for $300 Million
Taylor Swift vs. Big Machine: Why It's in Her Favor to Go Public with Their Feud
Taylor Swift's Rep Says Singer Learned of Scooter Braun's Purchase from News When She Woke Up
Taylor Swift Spent Fourth of July in Caribbean Amid Drama with Scooter Braun and Her Former Label | {
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} | 169 |
Zhuhai Cloud () is a oceanography research vessel designed for uncrewed operations in open waters and as a mother ship for uncrewed vehicles. She has been called the first "drone mothership" and the first "unmanned vehicle carrier".
The ship was built by China State Shipbuilding Corporation's Huangpu Wenchong for Sun Yat-sen University's Southern Marine Science and Engineering Guangdong Laboratory. The laboratory's goal is to surveil an underwater and above water area 50 nautical miles in diameter using a network of unmanned devices.
Zhuhai Cloud may have military applications. Timothy Heath, a RAND Corporation analyst, believes these include accurately mapping depths for submarines, and deploying smart mines.
References
Research vessels of China | {
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Plethodon shenandoah är en groddjursart som beskrevs av Richard Highton och Richard Dane Worthington 1967. Plethodon shenandoah ingår i släktet Plethodon och familjen lunglösa salamandrar. IUCN kategoriserar arten globalt som sårbar. Inga underarter finns listade i Catalogue of Life.
Källor
Externa länkar
Lunglösa salamandrar
shenandoah | {
"redpajama_set_name": "RedPajamaWikipedia"
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NCTA, cable entities come together on scheduling industry events
March 4, 2008 By Mike Robuck
Traveling to cable industry events will be a lot easier starting next year.
The National Cable & Telecommunications Association's (NCTA) board of directors announced that it has approved a plan, which was co-developed with other cable industry associations, to schedule industry meetings and events at the same time during selected weeks in the spring and fall.
The various cable industry entities will work together to ensure that their major annual events will occur during one of the two weeks each year, which will be called "Cable Connection-Spring" and "Cable Connection-Fall."
The participating groups include the NCTA, the Society of Cable Telecommunications Engineers (SCTE), The Walter Kaitz Foundation, Women in Cable Telecommunications (WICT), Cable & Telecommunications Association for Marketing (CTAM), CableLabs, the Association of Cable Communicators (ACC), the Cabletelevision Advertising Bureau (CAB), The Cable Center, Cable Positive, Cable Pioneers, and The National Association for Multi-ethnicity in Communications (NAMIC).
"The realigned schedule allows member companies, participants and exhibitors to allocate time and resources more efficiently to better support these organizations and events and to enhance the value of the shared experience of our incredibly collaborative industry," said NCTA President and CEO Kyle McSlarrow.
Starting next year, industry events such as the NCTA's The Cable Show, CableLabs' conferences and the SCTE's Conference on Emerging Technologies (ET) will be held for several days starting on April 2, 2009, in Washington, D.C.
"CableLabs will refocus and integrate our conference planning," said CableLabs President and CEO Richard Green. "We look forward to creating a comprehensive array of sessions and exhibits that will continue to advance our industry's leadership in telecommunications technology."
In the fall of 2009, CTAM Summit, SCTE Cable-Tec Expo, the Cable Center Hall of Fame Dinner and a CableLabs seminar will be among the events in Denver, beginning Oct. 25, 2009.
"The inclusion of SCTE's Conference on Emerging Technologies and Cable-Tec Expo in these two Cable Connection weeks offers great opportunities to expand the knowledge transfer in the engineering space," said SCTE President and CEO John Clark. "And the new era of 'linkage' between technology and other cable functional areas shows that these linkage opportunities are more needed than ever."
• FCC to consider phasing in DTV transition
• Analyst downgrades Cablevision due to acquisition strategy
• Insight bulks up digital tier with more HD, digital music offerings
• NCTA, cable entities come together on scheduling industry events
• Brophy, Campbell join ACA's executive committee
• AT&T, Sprint upgrade networks in select markets
• Clearwire ups sub count, operating loss in Q4
• New Cisco router based on new chip
• Japan, China, U.S. drive 2007 fiber deployments
• Number of U.S. mobile subs who recall ads increasing
• Broadband Briefs for 3/04/08 | {
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The extension integrates [payum](http://payum.forma-dev.com/documentation#Payum) into [laravel](http://laravel.com/) framework.
It already supports [+35 gateways](https://github.com/Payum/Core/blob/master/Resources/docs/supported-gateways.md).
Provide nice configuration layer, secured capture controller, storages and lots of other features.
## Resources
* [Documentation](http://payum.org/doc#PayumLaravelPackage)
* [Sandbox](https://github.com/makasim/PayumLaravelBundleSandbox)
* [Questions](http://stackoverflow.com/questions/tagged/payum)
* [Issue Tracker](https://github.com/Payum/PayumLaravelBundle/issues)
## Contributing
PayumLaravelPackage is an open source, community-driven project. Pull requests are very welcome.
## Like it? Spread the world!
Star it on [github](https://github.com/Payum/PayumLaravelPackage) or [packagist](https://packagist.org/packages/payum/payum-laravel-bundle).
You may also drop a message on Twitter.
## License
PayumLaravelPackage is released under the [MIT License](LICENSE).
| {
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} | 4,619 |
All reviews are the subjective opinions of third parties and not of the website or its owners. Reviews are placed by members of the public that have held a function or event at Totteridge Millhillians Cricket Club.
At needadisco.com we only accept reviews from confirmed clients that have booked a DJ to play at Totteridge Millhillians Cricket Club via our website, with the arrangements independently verified by both the DJ and the client before the event takes place - no "fake reviews" here!
"After a shaky start when I thought all the cricketers would still be at the venue. We had a wonderful evening. No pressure to clear up and leave, very relaxed staff. Some guests felt the bar staff were a bit slow but otherwise, no complaints. Every one enjoyed the evening. I would definitely recommend the venue for similar events."
Helpful information for DJs and entertainers visiting Totteridge Millhillians Cricket Club provided by trusted members of needadisco.com.
Information is based on enquiries and bookings handled via needadisco.com so whilst it's a great insight, if you have any questions or concerns about holding a function or event at Totteridge Millhillians Cricket Club please contact the venue.
Totteridge Millhillians Cricket Club has previously been hired as a venue for private parties such as birthday celebrations, anniversaries, engagements etc.
Totteridge Millhillians Cricket Club is in our Sports, Social & Members' Clubs category. The map below shows other local venues in the same category. | {
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{"url":"https:\/\/www.gradesaver.com\/textbooks\/math\/calculus\/calculus-3rd-edition\/chapter-5-the-integral-5-7-substitution-method-preliminary-questions-page-275\/1","text":"# Chapter 5 - The Integral - 5.7 Substitution Method - Preliminary Questions - Page 275: 1\n\n(a) and (b) .\n\n#### Work Step by Step\n\n(a) and (b) are candidates for the Substitution Method. In (a), we can use the substitution $u=x^5$ and for (b) we can use the substitution $u=\\sin x$.\n\nAfter you claim an answer you\u2019ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide\u00a0feedback.","date":"2022-08-11 02:30:45","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9391202926635742, \"perplexity\": 791.0541420265132}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-33\/segments\/1659882571232.43\/warc\/CC-MAIN-20220811012302-20220811042302-00013.warc.gz\"}"} | null | null |
Q: yii framework drop down list with condition at least 3 numbers I am new to php and yii framework. I want to do a dropdownlist with matching result. But if you want to type for example at least 3 or 4 letters to get result. If you type 3 numbers or letters the dropdownlist will open automatically and let you see all words/numbers that has the 3 letters/numbers consecutive.
I checked this site.
http://www.yiiframework.com/wiki/48/by-example-chtml/#hh5
But I dont know where I can set the condition for what I want to do. Thanks a lot.
A: In view page,
$term = CHtml::listData(Term::model()->findAll(), 'termid', 'term_name');//!< $term to select term details
echo CHtml::activeDropDownList($model, 'termid', $term, array(
'empty' => Yii::t('app','Select Term'), 'class' => "form-control",
));
A: have a look at http://yiiwheels.2amigos.us/ they have really good widgets that can help you. http://yiiwheels.2amigos.us/site/inputs#select2 will be of great help to you.
$term = CHtml::listData(Term::model()->findAll(), 'termid', 'term_name');
$this->widget('yiiwheels.widgets.select2.WhSelect2', array(
'asDropDownList' => true,
'model' => $model,
'attribute'=>'attribute'
'pluginOptions' => array(
'tags' => $term,
'placeholder' => 'type 2amigos',
'width' => '40%',
'tokenSeparators' => array(',', ' ')
)));
haven't tested it though,
| {
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{"url":"https:\/\/www.gamedev.net\/forums\/topic\/215484-i-thought-that\/","text":"#### Archived\n\nThis topic is now archived and is closed to further replies.\n\n# I thought that...\n\nThis topic is 5200 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.\n\n## Recommended Posts\n\nI''ve been working on a additive blit for a sprite engine, and soon realized that the complexity of the algorithm was O(n^2). I thought to myself that a faster way had to exist, and MMX came up as a valid solution (I think everyone with a semi-modern computer has MMX cababilities). I implemented a bit of MMX code, but the gain in FPS I get is really poor (just about 2fps). I thought MMX was supposed to accelerate code in the sense that it can do 8 operations at the same time (well... same time... you know what I mean). Am I doing something wrong, or is MMX just not a great tool? To give an example, the following shows the old additive blit pixel adding part of the code and the MMX version. Note that ATable is a 256x256 array containing each possible alpha blend values (so I don''t have to calculate it all the time).\n\/\/the header file\nstruct Pixel32\n{\nunsigned char rgbBlue;\nunsigned char rgbGreen;\nunsigned char rgbRed;\nunsigned char alpha;\n};\n\n\/\/side effect Pixel32 addition in first Parameter\nvoid BlitRGBQUADEx(Pixel32 *a, Pixel32 *b, int SourceAlpha)\n{\n\/\/CLng(.Red) + m_bytLookup(m_lngSourceAlpha, m_pxlSource.Red\na->rgbRed = ClipBytesC(a->rgbRed,ATable[SourceAlpha][b->rgbRed]);\na->rgbGreen = ClipBytesC(a->rgbGreen,ATable[SourceAlpha][b->rgbGreen]);\na->rgbBlue = ClipBytesC(a->rgbBlue,ATable[SourceAlpha][b->rgbBlue]);\n}\n\n\/\/summation of two pixels\nunsigned char ClipBytesC(unsigned char x, unsigned char y)\n{\n\/\/\/\/\/MAKE A HABIT OF USING BRACES WITH IF''s AND SUCH!!\nint tmp = x+y;\nif (tmp>255)\n{\nreturn 255;\n}\nelse\n{\nreturn tmp;\n}\n}\n\nNow, it looks like this (with MMX)\nvoidTransAlphaMMX(Pixel32 *dest, Pixel32 *src, int ALPHA)\n{\n\/\/int cap = width * height; \/\/calculate the number of iterations to go through\n\/\/int tmpcal;\n\/\/int numNext;\n\n\/\/if (ALPHA<0) \/\/prevent out of bounds error\n\/\/\tALPHA = 0;\n\/\/else if(ALPHA>255)\n\/\/\tALPHA = 255;\nPointerReturn pr;\npr.p1 = dest;\npr.p2 = src;\npr.Alpha = ALPHA;\nint r,g,b,br,bg,bb; \/\/red green blue, backred, backgreen, backblue\n\nr = dest->rgbRed; g = dest->rgbGreen; b = dest->rgbBlue;\nbr = ATable[ALPHA][src->rgbRed]; bg = ATable[ALPHA][src->rgbGreen]; bb = ATable[ALPHA][src->rgbBlue];\n\n_asm\n{\npush edi\t;Save off to restore later\npush esi\t;Save off to restore later\n\n\/\/SPAN_RUN_565: movq mm7,[edi]\t; Copy the 8 bytes pointed to by edi into mm7\n\/\/movq mm6,[esi]\t\t\t\t; Copy the 8 bytes pointed to by esi into mm6\n\n;place dest pixels\nmovq mm0, r\nmovq mm1, g\nmovq mm2, b\n\n;place source alpha pixels\nmovq mm3, br\nmovq mm4, bg\nmovq mm5, bb\n\n;add pixels, dest = dest + source\n\n;move transformed pixels to r,g,b\nmovq r, mm0\nmovq g, mm1\nmovq b, mm2\n\nemms\t\t;Clean up the MMX registers\n\n\/\/cmp eax,0\t\t\t\t\t; If eax = 0 we have set the flag\n\/\/jg SPAN_RUN_565\t\t\t\t; if flag is zero finish else loop back for more\n\npop esi\t\t;Restore esi\npop edi\t\t;Restore edi\n\n}\n\/\/store pixels transforme\ndest->rgbRed = r; dest->rgbGreen = g; dest->rgbBlue = b;\n\/\/return ALPHA;\nreturn pr;\n}\n\nThanks My signature used to suck. But it''s much better now.\n\n##### Share on other sites\nemms is a very slow instruction, try only calling it when you have done all the blends. you wont see an 8x speed improvement, your probably going to see more like 1.5x -- if you optimize it well.\nalso, amd cpu''s have femms (fast emms), not sure if newer intel processors support it aswell.\n\n##### Share on other sites\nThis is how I''d do it:\n\nWell, you seem to be just adding two arrays, right?\n\nwith SSE you can add 4 components at a time. [Don''t confuse this as being twice as fast as MMX]. Let say you''re have 1,000 RGB values that you want to add, this is what you''d do:\n\nso 1,000 RGB values (RGB = 3*4 = 12 bytes for one RGB val). So our two arrays are 12,000 bytes long. SSE can do 4 adds in one \"operation\", so we need to looop 3000 times.\n\nloop 3000 times\n{\ndo 2 moves to load 2 registers, one from src array, one from dest\nwrite the result back to memory\nincrement pointers\n}\n\nPlus, I couldn''t really see how you were taking advantage of MMX. That code load one value into one register, and another value in another register and tried to add them. What I think you want to do is load a bunch of values in one register, and bunch of values in another register and call add on them.\n\nHere''s what I use: http:\/\/www.amd.com\/us-en\/assets\/content_type\/white_papers_and_tech_docs\/26568.pdf\n\nLook up these instructions:\nMOVDQU [page 151]\n\nAlso, try not to traverse 2 arrays that are a multiple of 4k apart on AMD64s, because I think they''ll map to the same place in cache... and that''s not good.\n\n##### Share on other sites\nquote:\nOriginal post by ngill\nWell, you seem to be just adding two arrays, right?\n\nThat''s correct. It is actually a matrix, but iterating through the pointer makes it act as an array.\n\nquote:\nOriginal post by ngill\nwith SSE you can add 4 components at a time. [Don''t confuse this as being twice as fast as MMX].\n\nloop 3000 times\n{\ndo 2 moves to load 2 registers, one from src array, one from dest\nwrite the result back to memory\nincrement pointers\n}\n\nTwo things. First, I''m not quite sure how to code the pseudo code above because I am not familiar at all with SSE stuff. Also, I''m not quite sure what you mean by \"do two moves to load 2 registers,\" and \"add 2 registers\" (call me stupid, but I just don''t seem to get it). Second, coudn''t the same process be done with MMX? The idea in using MMX was to obtain a performance boost (at least to some degree considerable) without forcing users to have a newer machine. In other words, my entire game was written in order to work with older machines, and I know that MMX has been around for quite some time. I understand that SSE is indeed faster, but I am not sure it has quite as long a history as MMX. Am I correct in beleiving this, or is SSE on most semi-mordern computers nowadays? If SSE has existed for as long as MMX has and most semi- computers have it, then how would I write the code in SSE (or MMX even, since you say that I''m doing it the slow way)?\n\nThanks a million!\n\nMy signature used to suck. But it''s much better now.\n\n##### Share on other sites\nThis is a fast mmx additive blitter, doing 2 pixels (8 color components) per iteration. It can be done even faster.\n\ns is a pointer to the source, d is a pointer to destination, len is the length of the array in pixels. Preferably, s and s should be 8-byte aligned.\n\nif (len>3) {\n__asm {\nmov esi,s\nmov edi,d\nmov ebx,len\nmov ecx,len\nmov edx,ecx\nshr ecx,1\nand ebx,3\nmov len,ebx\nmovq [edi],mm0 \/\/store 2 pixels\nsub edx,2\ndec ecx\n\ncmp edx,0\nmovd mm0,[esi]\nmovd mm1,[edi]\nmovd [edi],mm0\nemms\n}\n\nthis isn''t 100% optimized but you should be getting the idea.\n\n##### Share on other sites\nquote:\nOriginal post by ageny6\nTwo things. First, I'm not quite sure how to code the pseudo code above because I am not familiar at all with SSE stuff.\n\nIt's REALLY EASY, just google for a tutorial on SSE.\n\nquote:\n\nAlso, I'm not quite sure what you mean by \"do two moves to load 2 registers,\" and \"add 2 registers\" (call me stupid, but I just don't seem to get it). Second, coudn't the same process be done with MMX?\n\nCheck out the pdf link in my earlier post, I even gave you the page numbers of the instructions. It's all there bro.\n\nIf you really want to learn, do this: write it once in MMX. Write it again in SSE. then write some code to test which one in faster. If you wrote your code correctly, i wouldn't be surprised if SSE2 is faster. Then if it's available, use the SSE2 codepath on a newer machine, and MMX on an older machine.\n\n\"SSE2 code can always be written to perform as well as MMX. Frequently better, especially with unrolling, but need to understand the machine [if you want to optimize ALOT]\"\n--Ranganathan Sudhakar [an expert in athlon64 architecture]\n\n[edited by - ngill on March 26, 2004 3:45:31 PM]\n\n##### Share on other sites\nNice! Thanks a lot\n\nI stumbled upon a program called quexal, which abstract assembly code into a nicer interface. I do, however have to pay to get a full version.\n\nDoes anyone know whether the free shareware version is worthwhile? Is there a better application out there? Is there a free application of the sort?\n\nThanks\n\nMy signature used to suck. But it''s much better now.\n\n##### Share on other sites\nI''d pay to learn SSE, not to run away from it.\n\nIf managing registers scares you, try intrinsics [which handle register allocation and scheduling for you]\n\nBut intrinsics performance sucks unless you have VS 8.0 =[. Don''t know how it is with other compilers.\n\n##### Share on other sites\nDo it with bit shifts:\n\nint blend(int surfaceColor, int newColor , int amt ) { \treturn 0xff000000 | ( ( ( amt * ( ( ( newColor ) & 0xff00ff ) - ( ( surfaceColor ) & 0xff00ff ) ) >> 8 ) + ( ( surfaceColor ) & 0xff00ff ) ) & 0xff00ff ) | ( ( amt * ( ( ( newColor ) & 0x00ff00 ) - ( ( surfaceColor ) & 0x00ff00 ) ) >> 8 ) + ( ( surfaceColor ) & 0x00ff00 ) ) & 0x00ff00 ;}\n\n1. 1\n2. 2\nRutin\n19\n3. 3\n4. 4\n5. 5\n\n\u2022 14\n\u2022 13\n\u2022 9\n\u2022 12\n\u2022 9\n\u2022 ### Forum Statistics\n\n\u2022 Total Topics\n631438\n\u2022 Total Posts\n3000074\n\u00d7","date":"2018-06-25 16:41:23","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.31203019618988037, \"perplexity\": 5877.261290453054}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-26\/segments\/1529267868135.87\/warc\/CC-MAIN-20180625150537-20180625170537-00214.warc.gz\"}"} | null | null |
\section*{Acknowledgements}
We would like to thank the teams behind the open-source packages used in this project, including AI2-THOR~\cite{kolve2017ai2}, AllenAct~\cite{weihs2020allenact}, Habitat~\cite{savva2019habitat}, \raisebox{-0.1\height}{\includegraphics[width=0.025\textwidth]{figures/huggingface.pdf}} Datasets~\cite{Lhoest2021DatasetsAC}, NumPy~\cite{harris2020array}, PyTorch~\cite{paszke2017automatic}, Pandas~\cite{mckinney2011pandas}, Wandb~\cite{wandb}, Shapely~\cite{shapely2007}, Hydra~\cite{Yadan2019Hydra}, SciPy~\cite{virtanen2020scipy}, UMAP~\cite{mcinnes2018umap-software}, NetworkX~\cite{hagberg2008exploring}, EvalAI~\cite{EvalAI}, TensorFlow~\cite{abadi2016tensorflow}, OpenAI Gym~\cite{Brockman2016OpenAIG}, Seaborn~\cite{waskom2021seaborn}, PySAT~\cite{imms-sat18}, and Matplotlib~\cite{hunter2007matplotlib}.
{
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\bibliographystyle{ieee}
\section{Introduction}
\label{sec:introduction}
Computer vision and natural language processing models have become increasingly powerful through the use of large-scale training data. Recent models such as CLIP~\cite{Radford2021LearningTV}, DALL-E~\cite{Ramesh2021ZeroShotTG}, GPT-3~\cite{Brown2020LanguageMA}, and Flamingo~\cite{flamingo} use massive amounts of task agnostic data to pre-train large neural architectures that perform remarkably well at downstream tasks, including in zero and few-shot settings. In comparison, the Embodied AI (\mbox{\sc{E-AI}}\xspace) research community predominantly trains agents in simulators with far fewer scenes~\cite{Ramakrishnan2021HabitatMatterport3D,kolve2017ai2,Deitke2020RoboTHORAO}. Due to the complexity of tasks and the need for long planning horizons, the best performing \mbox{\sc{E-AI}}\xspace models continue to overfit on the limited training scenes and thus generalize poorly to unseen environments.
In recent years, \mbox{\sc{E-AI}}\xspace simulators have become increasingly more powerful with support for physics, manipulators, object states, deformable objects, fluids, and real-sim counterparts \cite{kolve2017ai2,savva2019habitat,Shen2020iGibsonAS,Gan2020ThreeDWorldAP,xiang2020sapien}, but scaling them up to tens of thousands of scenes has remained challenging. Existing \mbox{\sc{E-AI}}\xspace environments are either designed manually \cite{kolve2017ai2,Gan2020ThreeDWorldAP} or obtained via 3D scans of real structures \cite{savva2019habitat,Ramakrishnan2021HabitatMatterport3D}. The former approach requires 3D artists to spend a significant amount of time designing 3D assets, arranging them in sensible configurations within large spaces, and carefully configuring the right textures and lighting in these environments. The latter involves moving specialized cameras through many real-world environments and then stitching the resulting images together to form 3D reconstructions of the scenes. These approaches are not scalable, and expanding existing scene repositories multiple orders of magnitude is not practical.
We present \mbox{\sc{ProcTHOR}}\xspace, a framework built off of AI2-THOR~\cite{kolve2017ai2}, to procedurally generate fully-interactive, physics-enabled environments for \mbox{\sc{E-AI}}\xspace research. Given a room specification (e.g., a house with 3 bedrooms, 3 baths, and 1 kitchen), \mbox{\sc{ProcTHOR}}\xspace can produce a large and diverse set of floorplans that meet these requirements (Fig.~\ref{fig:examples}). A large asset library of 108 object types and 1633 fully interactable instances is used to automatically populate each floorplan, ensuring that object placements are physically plausible, natural, and realistic. One can also vary the intensity and color of lighting elements (both artificial lighting and simulated skyboxes) in each scene, to simulate variations in indoor lighting and the time of the day. Assets (such as furniture and fruit) and larger structures such as walls and doors can be assigned a variety of colors and textures, sampled from sets of plausible colors and materials for each asset category. Together, the diversity of layouts, assets, placements, and lighting leads to an arbitrarily large set of environments -- allowing \mbox{\sc{ProcTHOR}}\xspace to scale orders of magnitude beyond the number of scenes currently supported by present-day simulators. In addition, \mbox{\sc{ProcTHOR}}\xspace supports dynamic material randomizations, whereby colors and materials of individual assets can be randomized each time an environment is loaded into memory for training. Importantly, in contrast to environments produced using 3D scans, scenes produced by \mbox{\sc{ProcTHOR}}\xspace contain objects that both support a variety of different object states (\emph{e.g.}\xspace open, closed, broken, \emph{etc.}\xspace) and are fully interactive so that they can be physically manipulated by agents with robotic arms. We also present \mbox{\sc{ArchitecTHOR}}\xspace, a 3D artist-designed set of 10 high quality fully interactable houses, meant to be used as a test-only environment for research within household environments. In contrast to AI2-iTHOR (single rooms) and RoboTHOR (lesser visual diversity) environments, \mbox{\sc{ArchitecTHOR}}\xspace contains larger, diverse, and realistic houses.
\begin{figure}[tp]
\centering
\vspace{-0.35in}
\makebox[\textwidth][c]{
\includegraphics[width=1\textwidth]{figures/procthor-cover.jpg}
}
\caption{We propose \mbox{\sc{ProcTHOR}}\xspace{}, a framework to procedurally generate a large variety of diverse, interactable, and customizable houses.}
\vspace{-0.2in}
\label{fig:examples}
\end{figure}
We demonstrate the ease and effectiveness of \mbox{\sc{ProcTHOR}}\xspace by sampling an environment of 10,000 houses (named \mbox{\sc{ProcTHOR-10k}}\xspace), composed of diverse layouts ranging from small 1-room houses to larger 10-room houses. We train agents with very simple neural architectures (CNN+RNN) -- \emph{without} a depth sensor, and instead only employing RGB channels, with no explicit mapping and no human task supervision -- on \mbox{\sc{ProcTHOR-10k}}\xspace and produce state-of-the-art (SoTA) models on several navigation and interaction benchmarks. As of 10am PT on June 14th, 2022 we obtain (1) \textbf{RoboTHOR ObjectNav Challenge}~\cite{robothor-challenge} -- 0-shot performance superior to the previous SoTA which uses RoboTHOR training scenes -- with fine-tuning we obtain an 8.8 point improvement in SPL over the previous SoTA; (2) \textbf{Habitat ObjectNav Challenge 2022}~\cite{habitat-challenge} -- top of the leaderboard results with a ${>}3$ point gain in SPL over the next best submission; (3) \textbf{1-phase Rearrangement Challenge 2022}~\cite{roomr-challenge} -- top of the leaderboard results with Prop Fixed Strict improving from 0.19 to 0.245; (4) \textbf{AI2-iTHOR ObjectNav} -- 0-shot numbers which already outperform a previous model that trains on AI2-iTHOR, with fine-tuning we achieve a success rate of 77.5\%; (5) \textbf{ArmPointNav}~\cite{manipulathor} -- 0-shot number that beats previous SoTA results when using RGB; and (6) \textbf{ArchitecTHOR ObjectNav} -- a large success rate improvement from 18.5\% to 31.4\%. Finally, an ablation analysis clearly shows the advantages of scaling up from 10 to 100 to 1K and finally to 10K scenes and indicates that further improvements can be obtained by invoking \mbox{\sc{ProcTHOR}}\xspace to produce even larger environments.
In summary, our contributions are (1) \mbox{\sc{ProcTHOR}}\xspace, a framework that allows for the performant procedural generation of an unbounded number of diverse, fully-interactive, simulated environments, (2) \mbox{\sc{ArchitecTHOR}}\xspace, a new, 3D artist-designed set of houses for \mbox{\sc{E-AI}}\xspace evaluation, and (3) SoTA results across six \mbox{\sc{E-AI}}\xspace benchmarks covering manipulation and navigation tasks, including strong 0-shot results.
\mbox{\sc{ProcTHOR}}\xspace will be open-sourced and the code used in this work will be released.
\section{Related Work}
\label{sec:relatedwork}
\noindent \textbf{Embodied AI platforms.} Various Embodied AI platforms have been developed over the past several years~\cite{kolve2017ai2,savva2019habitat,Shen2020iGibsonAS,xiang2020sapien,Gan2020ThreeDWorldAP,house3d}. These platforms target different design goals. AI2-THOR~\cite{kolve2017ai2} and its variants (ManipulaTHOR~\cite{manipulathor} and RoboTHOR~\cite{Deitke2020RoboTHORAO}) are built in the Unity game engine and focus on agent-object interactions, object state changes, and accurate physics simulation. Unlike AI2-THOR, Habitat~\cite{savva2019habitat} provides scenes constructed from 3D scans of houses, however, objects and scenes are not interactable. A more recent version, Habitat 2.0~\cite{szot2021habitat}, introduces object interactions at the expense of being limited to one floorplan and synthetic scenes. iGibson~\cite{Shen2020iGibsonAS} includes photo-realistic scenes, but with limited interactions such as pushing. iGibson 2.0~\cite{Li2021iGibson2O} extends iGibson by focusing on household tasks and object state changes in synthetic scenes and includes a virtual reality interface. ThreeDWorld~\cite{Gan2020ThreeDWorldAP} targets high-fidelity physics simulation such as liquid and deformable object simulation. VirtualHome~\cite{Puig2018VirtualHomeSH} is designed for simulating human activities via programs. RLBench~\cite{james2020rlbench}, RoboSuite~\cite{zhu2020robosuite} and Sapien~\cite{xiang2020sapien} target fine-grained manipulation. The main advantage of \mbox{\sc{ProcTHOR}}\xspace is that we can generate a diverse set of \emph{interactive} scenes procedurally, enabling studies of data augmentation and large-scale training in the context of Embodied AI.
\noindent \textbf{Large-scale datasets.} Large-scale datasets have resulted in major breakthroughs in different domains such as image classification~\cite{imagenet,Kuznetsova2020TheOI}, vision and language~\cite{Changpinyo2021Conceptual1P,Thomee2016YFCC100MTN}, 3D understanding~\cite{shapenet2015,Xiang2016ObjectNet3DAL}, autonomous driving~\cite{nuscenes,sun2020scalability}, and robotic object manipulation~\cite{pinto2016supersizing,mu2021maniskill}. However, there are not many interactive large-scale datasets for Embodied AI research. \mbox{\sc{ProcTHOR}}\xspace includes interactive houses generated procedurally. Hence, there are an arbitrarily large number of scenes in the framework. The closest works to ours are~\cite{Ramakrishnan2021HabitatMatterport3D,Petrenko2021MegaverseSE,li2021openrooms}. HM3D~\cite{Ramakrishnan2021HabitatMatterport3D} is a recent framework that includes 1,000 scenes generated using 3D scans of real environments. \mbox{\sc{ProcTHOR}}\xspace has a number of key distinctions: (1) unlike HM3D which includes static scenes, the scenes in \mbox{\sc{ProcTHOR}}\xspace are interactive i.e., objects can move and change state, the lighting and texture of objects can change, and a physics engine determines the future states of the scenes; (2) it is challenging to scale up HM3D as it requires scanning a house and cleaning up the data, while we can procedurally generate more houses; (3) HM3D can be used only for navigation tasks (as there is no physics simulation and object interaction), while \mbox{\sc{ProcTHOR}}\xspace can be used for tasks other than navigation. OpenRooms~\cite{li2021openrooms} is similar to HM3D in terms of the source of the data (3D scans) and dataset size. However, OpenRooms is interactive. OpenRooms is also confined to the set of scanned houses, and it takes a significant amount of time to annotate a new scene (e.g., labeling materials for one object takes 1 minute), while \mbox{\sc{ProcTHOR}}\xspace does not suffer from these issues. Megaverse~\cite{Petrenko2021MegaverseSE} is another large-scale Embodied AI platform that includes procedurally generated environments. Although it is impressive in terms of simulation speed, it includes only game-like environments with a simplified appearance. In contrast, \mbox{\sc{ProcTHOR}}\xspace mimics real-world houses in terms of the complexity of appearance, physics, and object interactions.
\noindent \textbf{Scene generation.} Indoor scene synthesis has been studied extensively in computer vision and graphics communities. \cite{Chang2015TextT3,Chang2014LearningSK,chang2014interactive} address generating 3D scenes from text descriptions. \cite{wu2019data,Hu2020Graph2PlanLF,Nauata2021HouseGANGA} learn to generate house floorplans. \cite{Ritchie2019FastAF,Zhang2020DeepGM,Chaudhuri2019LearningGM,Wang2021SceneFormerIS,keshavarzi2020scenegen,li2019grains} use generative models for indoor scene generation. \cite{zhou2019scenegraphnet,Savva2017SceneSuggestC3} propose potential objects for a query location in an indoor scene. Others have used procedural generation \cite{khalifa2020pcgrl, earle2021learning} and unsupervised learning \cite{dennis2020emergent} to synthesize grid-world environments for AI. \mbox{\sc{ProcTHOR}}\xspace is specifically designed for Embodied AI research in the sense that (1) all scenes are interactive and physics-enabled, and the placement of objects respects the physics of the world (e.g., there are no two objects that clip through each other), (2) there are various forms of scene augmentation such as randomization of object placements while following certain commonsense rules, variation in the appearance of objects and structures, and variation in lighting.
\section{\mbox{\sc{ProcTHOR}}\xspace}
\label{sec:generation}
\vspace{-0.1in}
\mbox{\sc{ProcTHOR}}\xspace is a framework to procedurally generate \mbox{\sc{E-AI}}\xspace environments. It extends \mbox{\sc{AI2-THOR}}\xspace and, thereby, inherits \mbox{\sc{AI2-THOR}}\xspace's large asset library, robotic agents, and accurate physics simulation. Just as in scenes painstakingly created by designers in \mbox{\sc{AI2-THOR}}\xspace, environments in \mbox{\sc{ProcTHOR}}\xspace are fully interactive and support navigation, object manipulation, and multi-agent interaction.
\begin{minipage}{\linewidth}
\centering
\vspace{0.05in}
\begin{overpic}[width=\textwidth]{figures/compressions/generation-3-raster.jpg}
\put(0,0){\includegraphics[width=1\textwidth]{figures/compressions/generation-3-vector.pdf}}
\end{overpic}
\captionof{figure}{Procedurally generating a house using \mbox{\sc{ProcTHOR}}\xspace.}
\label{fig:genOverview}
\end{minipage}
Fig.~\ref{fig:genOverview} shows a high-level schematic of the procedure used by \mbox{\sc{ProcTHOR}}\xspace to generate a scene. Given a room specification (\emph{e.g.}\xspace house with 1 bedroom + 1 bathroom), \mbox{\sc{ProcTHOR}}\xspace uses multi-stage conditional sampling to, iteratively, generate a floor plan, create an external wall structure, sample lighting, and doors, then sample assets including large, small and wall objects, pick colors and textures, and determine appropriate placements for assets within the scene. We refer the reader to the appendix for details regarding our procedural generation and sampling mechanism, but highlight five key characteristics of \mbox{\sc{ProcTHOR}}\xspace: \textbf{Diversity}, \textbf{Interactivity}, \textbf{Customizability}, \textbf{Scale}, and \textbf{Efficiency}.
\noindent \textbf{Diversity.}
\mbox{\sc{ProcTHOR}}\xspace enables the creation of rich and diverse environments. Mirroring the success of pre-training models with diverse data in the vision and NLP domains, we demonstrate the utility of this diversity on several \mbox{\sc{E-AI}}\xspace tasks. Scenes in \mbox{\sc{ProcTHOR}}\xspace exhibit diversity across several facets:
\noindent \emph{Diversity of floor plans.}
Given a room specification, we first employ iterative boundary cutting to obtain an external scene layout (that can range from a simple rectangle to a complex polygon). The recursive layout generation algorithm by Lopes \emph{et al.}\xspace~\cite{lopes2010constrained} is then used to divide the scene into the desired rooms. Finally, we determine connectivity between rooms using a set of user-defined constraints. These procedures result in natural room layouts (e.g., bedrooms are often connected to adjoining bathrooms via a door, bathrooms more often have a single entrance, etc). As exemplified in Fig.~\ref{fig:floorplanExamples}, \mbox{\sc{ProcTHOR}}\xspace generates hugely diverse floor plans using this procedure.
\begin{minipage}{\linewidth}
\centering
\vspace{0.05in}
\includegraphics[width=0.9\textwidth]{figures/floorplans4_1.pdf}
\captionof{figure}{\textbf{Floorplan diversity.} Examples showing the diversity of the generated floorplans. Rooms in the house are colored by \crule[bedroomColor]{2.5mm}{2.5mm} Bedroom, \crule[bathroomColor]{2.5mm}{2.5mm} Bathroom, \crule[kitchenColor]{2.5mm}{2.5mm} Kitchen, and \crule[livingRoomColor]{2.5mm}{2.5mm} Living Room.}
\label{fig:floorplanExamples}
\end{minipage}
\noindent \emph{Diversity of assets.}
\mbox{\sc{ProcTHOR}}\xspace populates scenes with small and large assets from its database of 1633 household assets across 108 categories (examples in Fig.~\ref{fig:assetsDiversity}). While many assets are inherited from \mbox{\sc{AI2-THOR}}\xspace, we also introduce new assets such as windows, doors, and countertops, hand-designed by 3D graphic designers. Asset instances are split into train/val/test subsets and are interactable, i.e. objects can be picked and placed within the scenes, some objects have multiple states (\emph{e.g.}\xspace a light can be on or off) and several objects consists of parts with rigid body motions (\emph{e.g.}\xspace door on a microwave).
\begin{minipage}{\linewidth}
\centering
\includegraphics[width=1\textwidth]{figures/assets2.jpg}
\begin{center}
\vspace{-0.05in}
{\large $\cdots$}
\vspace{-0.05in}
\end{center}
\captionof{figure}{\textbf{Object diversity.} A subset of instances for four object categories.}
\label{fig:assetsDiversity}
\end{minipage}
\noindent \emph{Diversity of materials.}
Walls can have two kinds of materials -- one of 40 solid (and popular) colors or one of 122 wall textures such as brick and tile.
We also provide 55 floor materials. The ceiling material for the entire house is sampled from the set of wall materials. \mbox{\sc{ProcTHOR}}\xspace also provides the ability to randomize materials of objects. Materials are only randomized within categories, which ensures objects still look and behave like the class they represent.
\begin{minipage}{\linewidth}
\centering
\includegraphics[width=1\textwidth]{figures/demo3.jpg}
\captionof{figure}{\textbf{Material augmentation}. Different materials for objects and structural elements like walls and floors.}
\label{fig:textureDiversity}
\end{minipage}
\noindent \emph{Diversity of object placements.}
Asset categories have several soft annotations that help place them realistically within a house. These include room assignments (\emph{e.g.}\xspace couch in a living room but not a bathroom) and location assignments (\emph{e.g.}\xspace fridge along a wall, TV not on the floor). We also develop the notion of a Semantic Asset Group (SAG) -- groups of assets that typically co-occur (\emph{e.g.}\xspace dining table with four chairs) and thus must be sampled and placed using dependent sampling. Given a layout, individual assets and SAGs that lie on the floor are sampled and placed iteratively, ensuring that rooms continue to have adequate floor space for agents to navigate and manipulate objects. Then wall objects such as windows and paintings get placed, and finally, surface objects (ones found on top of other assets) are placed (\emph{e.g.}\xspace cups on the kitchen counter). This sampling allows for a large and diverse set of object choices and placements within any layout. Fig.~\ref{fig:placementDiversity} shows such variations.
\begin{minipage}{\linewidth}
\centering
\vspace{0.05in}
\includegraphics[width=1\textwidth]{figures/pos-placement-2.jpg}
\captionof{figure}{\textbf{Object placement.} Four examples of object placement within the same room layout.}
\label{fig:placementDiversity}
\end{minipage}
\noindent \emph{Diversity of lighting.}
\mbox{\sc{ProcTHOR}}\xspace supports a single directional light (analogous to the sun) and several point lights (analogous to lightbulbs). Varying the color, intensity, and placement of these sources allows us to simulate different artificial lighting, typically observed in houses, and also at different times of the day. Lighting has a significant effect on the rendered images as seen in Fig.~\ref{fig:lightingDiversity}.
\begin{minipage}{\linewidth}
\centering
\vspace{0.05in}
\includegraphics[width=1\textwidth]{figures/lighting-small2.jpg}
\captionof{figure}{\textbf{Lighting variation}. Morning, dusk, and night lighting for an example scene.}
\label{fig:lightingDiversity}
\end{minipage}
\noindent \textbf{Interactivity.} A key property of \mbox{\sc{ProcTHOR}}\xspace is the ability to interact with objects to change their location or state (Fig.~\ref{fig:interactivity}). This capability is fundamental to many Embodied AI tasks. Datasets like HM3D~\cite{Ramakrishnan2021HabitatMatterport3D} that are created from static 3D scans do not possess this capability. \mbox{\sc{ProcTHOR}}\xspace supports agents with arms capable of manipulating objects and interacting with each other.
\begin{minipage}{\linewidth}
\centering
\vspace{0.05in}
\includegraphics[width=1\textwidth]{figures/3PanelProcTHOR_03.jpg}
\captionof{figure}{\textbf{Interactivity.} Object states can change (e.g., the laptop or the lamp in the left panel), and the agents can interact with objects and other agents (middle and right panels).}
\label{fig:interactivity}
\end{minipage}
\noindent \textbf{Customizability.} \mbox{\sc{ProcTHOR}}\xspace supports many room, asset, material, and lighting specifications. With a few simple lines of specification, one can easily generate customized environments of interest. Fig.~\ref{fig:customize} shows examples of such varied scenes (classroom, library, and office).
\begin{minipage}{\linewidth}
\centering
\vspace{0.05in}
\includegraphics[width=1\textwidth]{figures/customizability.jpg}
\captionof{figure}{\textbf{Customizability.} \mbox{\sc{ProcTHOR}}\xspace can be used to construct custom scene types such as classrooms, libraries, and offices.}
\label{fig:customize}
\end{minipage}
\noindent \textbf{Scale and Efficiency.}
\mbox{\sc{ProcTHOR}}\xspace currently uses 16 different scene specifications to seed the scene generation process. These can result in over 100 billion layouts. \mbox{\sc{ProcTHOR}}\xspace uses 18 different Semantic Asset groups and 1633 assets. These can result in roughly 20 million unique asset groups. Each of these assets can be placed in numerous locations. In addition, each house gets scaled and uses a variety of lighting. This diversity of layouts, assets, materials, placements, and lighting enables the generation of \emph{arbitrarily large} sets of houses -- either statically generated and stored as a dataset or dynamically generated at each iteration of training. Scenes are efficiently represented in a JSON specification and are loaded into \mbox{\sc{AI2-THOR}}\xspace at runtime, making the memory overhead of storing houses incredibly efficient. Moreover, the scene generation process is fully automatic and fast and \mbox{\sc{ProcTHOR}}\xspace provides high framerates for training \mbox{\sc{E-AI}}\xspace models (see Sec.~\ref{sec:analysis} for details).
\section{\mbox{\sc{\textbf{ProcTHOR}}}\xspace{}-10K}
\label{sec:analysis}
\begin{figure}[t]
\centering
\begin{subfigure}[h]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{figures/objects_per_room.pdf}
\end{subfigure}
\hfill
\begin{subfigure}[h]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{figures/house_area_distribution.pdf}
\end{subfigure}
\hfill
\begin{subfigure}[h]{0.325\textwidth}
\centering
\includegraphics[width=\textwidth]{figures/num_rooms.pdf}
\end{subfigure}
\caption{\textbf{\mbox{\sc{\textbf{ProcTHOR}}}\xspace{}-10K statistics.} \emph{Left:} distribution of the number of objects in each room; \emph{Middle:} distribution of the area of each house, bucketed into small, medium, and large houses; \emph{Right:} bar plot showing the distribution over the number of rooms that make up each house.}
\label{fig:dists}
\vspace{-0.2in}
\end{figure}
\begin{figure}[b]
\centering
\vspace{-0.2in}
\includegraphics[width=\textwidth]{figures/sec4-4.jpg}
\caption{\textbf{Example scenes} in \mbox{\sc{ProcTHOR}}\xspace{}-10K with top-down and an egocentric view.}
\label{fig:10k}
\end{figure}
We demonstrate the power and potential of \mbox{\sc{ProcTHOR}}\xspace using a sampled set of 10,000 fully interactive houses obtained by the procedural generation process described in Section~\ref{sec:generation} -- which we label \mbox{\sc{ProcTHOR}}\xspace-10K. An additional set of 1,000 validation and 1,000 testing houses are available for evaluation. Asset splits across train/val/test are detailed in the Appendix. All houses are fully navigable, allowing an agent to traverse through each room without any interaction. In terms of scale, \mbox{\sc{ProcTHOR}}\xspace-10K is one of the largest sets of interactive home environments for Embodied AI -- as a comparison, AI2-iTHOR~\cite{kolve2017ai2} includes 120 scenes, RoboTHOR~\cite{Deitke2020RoboTHORAO} has 89 scenes, iGibson~\cite{Shen2020iGibsonAS} has 15 scenes, Habitat Matterport 3D~\cite{Ramakrishnan2021HabitatMatterport3D} has 1,000 static (non-interactive) scenes, and Habitat 2.0~\cite{szot2021habitat} has 105 scene layouts. Scaling beyond 10K houses is straightforward and inexpensive. This set of 10K houses was generated in 1 hour on a local workstation with 4 NVIDIA RTX A5000 GPUs. Fig.~\ref{fig:10k} shows examples of ego-centric and top-down views of houses present in \mbox{\sc{ProcTHOR}}\xspace{}-10K.
\noindent \textbf{Scene statistics.} Houses in \mbox{\sc{ProcTHOR}}\xspace-10K are generated using 16 different room specifications. An example room spec is: \emph{A house with 1 bedroom connected to 1 bathroom, 1 kitchen, and 1 living room} and is visualized in Fig.~\ref{fig:genOverview}. Houses in this dataset have as few as 1 room and as many as 10.
Fig.~\ref{fig:dists} shows the distribution of areas (middle) and the number of rooms (right) of these generated houses. Our use of room specifications enables us to change the distribution of the size and complexity of houses fairly easily. \mbox{\sc{ProcTHOR}}\xspace-10K encompasses a wider spectrum of scenes than AI2-iTHOR~\cite{kolve2017ai2} and \textsc{RoboTHOR}~\cite{Deitke2020RoboTHORAO} (biased towards room-sized scenes) and Gibson \cite{xia2018gibson} and HM3D \cite{Ramakrishnan2021HabitatMatterport3D} (biased towards large houses).
Rooms in each of these houses contain objects from 95 different categories including common household objects such as fridges, countertops, beds, toilets, and house plants, and structure objects such as doorways and windows. Fig.~\ref{fig:dists} (left) shows the distribution of the number of objects per room per house, which shows that houses in \mbox{\sc{ProcTHOR}}\xspace-10K are well populated. They also contain objects sampled via 18 different Semantic Asset groups. Examples of Semantic asset groups (SAG) are a \emph{Dining Table with 4 Chairs} or \emph{Bed with 2 Pillows}. Given our large asset library and SAGs, we can create 19.3 million combinations of group instantiations.
\begin{table}
\centering
\small
\begin{tabular}{l cc c cc c cc}
\toprule
& \multicolumn{2}{c}{Navigation FPS} && \multicolumn{2}{c}{Isolated Interaction FPS} && \multicolumn{2}{c}{Environment Query FPS} \\
\cmidrule{2-3}\cmidrule{5-6}\cmidrule{8-9}
Compute & Small & Large && Small & Large && Small & Large \\
\midrule
8 GPUs & 8,599{\scriptsize$\pm$359} & 3,208{\scriptsize$\pm$127} && 6,488{\scriptsize$\pm$250} & 2,861{\scriptsize$\pm$107} && 480,205{\scriptsize$\pm$19,684} & 433,587{\scriptsize$\pm$18,729} \\
1 GPU & 1,427{\scriptsize$\pm$74} & 6,280{\scriptsize$\pm$40} && 1,265{\scriptsize$\pm$71} & 597{\scriptsize$\pm$37} && 160,622{\scriptsize$\pm$2,846} & 157,567{\scriptsize$\pm$2,689}\\
1 Process & 240{\scriptsize$\pm$69} & 115{\scriptsize$\pm$19} && 180{\scriptsize$\pm$42} & 93{\scriptsize$\pm$15} &&
14,825{\scriptsize$\pm$199} & 14,916{\scriptsize$\pm$186}\\
\bottomrule
\end{tabular}%
\vspace{0.05in}
\caption{\textbf{Rendering speed.} Benchmarking FPS for navigation (\emph{e.g.}\xspace moving/rotating), interaction (\emph{e.g.}\xspace pushing an object), and querying the environment for data (\emph{e.g.}\xspace checking the dimensions of the agent). We report FPS for Small and Large houses. See Appendix for details.}
\label{tab:fps}
\vspace{-0.2in}
\end{table}
\noindent \textbf{Rendering speed.} A crucial requirement for large-scale training is high rendering speed since the training algorithms require millions of iterations to converge. Table~\ref{tab:fps} shows these statistics. Experiments were run on a server with 8 NVIDIA Quadro RTX 8000 GPUs. For the 1 GPU experiments, we use 15 processes and for the 8 GPU experiments, we use 120 processes, evenly distributed across the GPUs. \mbox{\sc{ProcTHOR}}\xspace provides framerates comparable to iTHOR and RoboTHOR environments in spite of having larger houses (See Appendix for details), rendering it fast enough for training large models for hundreds of millions of steps in a reasonable amount of time.
\section{Experiments}
\label{sec:experiments}
\noindent \textbf{Tasks.}
We now present results for models pre-trained on \mbox{\sc{ProcTHOR}}\xspace{}-10K on several navigation and manipulation benchmarks to demonstrate the benefits of large-scale training. We consider ObjectNav (navigation towards a specific object category) in \mbox{\sc{ProcTHOR}}\xspace{}, \mbox{\sc{ArchitecTHOR}}\xspace{}, RoboTHOR~\cite{Deitke2020RoboTHORAO}, HM3D~\cite{Ramakrishnan2021HabitatMatterport3D}, and AI2-iTHOR~\cite{kolve2017ai2}. We also consider two manipulation-based tasks: ArmPointNav~\cite{manipulathor} and 1-phase Room Rearrangement~\cite{weihs2021visual}. In ArmPointNav, the agent moves an object using a robotic arm from a source location to a destination location specified in the 3D coordinate frame. In Room Rearrangement, the goal is to move objects or change their state to reach a target scene state.
\noindent \textbf{Models.}
Our models for all tasks consist of a CNN to encode visual information and a GRU to capture temporal information. We deliberately use a simple architecture across all tasks to show the benefits of large-scale training. Our ObjectNav and Rearrangement models use the CLIP-based architectures of \cite{khandelwal2021simple}. Our ArmPointNav model uses a simpler visual encoder with 3 convolutional layers; we found this more effective than the CLIP encoder. All models are trained with the AllenAct~\cite{weihs2020allenact} framework, see the Appendix for training details.
\noindent \textbf{Results.}
\label{sec:results}
We present results in two settings: zero-shot and after fine-tuning on the training scenes provided by the downstream benchmark. Zero-shot experiments show us how well models trained on \mbox{\sc{ProcTHOR}}\xspace generalize to new environments, whereas fine-tuning experiments tell us if representations learned from \mbox{\sc{ProcTHOR}}\xspace can serve as a good initialization for quick tuning. For all experiments, we use only RGB images (no depth and other modalities is used).
Zero-shot is particularly challenging since other environments have different appearance statistics, layouts, and object distributions compared to \mbox{\sc{ProcTHOR}}\xspace{}. \mbox{\sc{ArchitecTHOR}}\xspace{} and AI2-iTHOR~\cite{kolve2017ai2} are high-fidelity artist-designed scenes with high-quality shadows and lighting. HM3D is constructed from 3D scans of houses which can differ quite a bit from synthetic environments. RoboTHOR~\cite{Deitke2020RoboTHORAO} houses use wall panels and floors with very specific textures.
\noindent \textbf{\emph{Zero-shot transfer results.}} Models trained only on \mbox{\sc{ProcTHOR}}\xspace and evaluated zero-shot outperform previous SoTA models on 3 benchmarks (refer to \emph{zero-shot} rows of Table~\ref{tab:allresults}). These are very strong results since the models generalize to not only unseen objects and scenes, but also different appearance and layout statistics.
\noindent \textbf{\emph{Fine-tuning results.}} Further fine-tuning of the model using each benchmark's training data, achieves state-of-the-art results on all benchmarks (refer to \emph{fine-tune} rows of Table~\ref{tab:allresults}). Notably, our model is ranked first on three public leaderboards as of 10am PT, June 14th 2022: Habitat 2022 ObjectNav challenge, AI2-THOR Rearrangement 2022 challenge, and RoboTHOR ObjectNav challenge. It should be noted that our model achieves these results using a very simple architecture and only RGB images. Other techniques typically use more complex architectures that include mapping or visual odometry modules and use additional perception sensors such as depth images.
\noindent \textbf{Scale ablation.} To evaluate the effect of scale we train the models on 10, 100, 1,000, and 10,000 houses. For this experiment, we do not use any material augmentations. As shown in Table~\ref{tab:ablation}, the performance improves as we use more houses for training, demonstrating the benefits of large-scale data for Embodied AI tasks.
\input{tables/all_tasks_results}
\input{tables/scale_ablation_results}
\section{Conclusion}
\label{sec:conclusion}
We propose \mbox{\sc{ProcTHOR}}\xspace{}, a framework to procedurally generate \emph{arbitrarily large} sets of interactive, physics-enabled houses for Embodied AI research.
We pre-train simple models on 10,000 generated houses and show state-of-the-art results across 6 embodied navigation and manipulation benchmarks with strong 0-shot results, even outperforming prior state-of-the-art on 3 of these benchmarks.
\section*{Appendix}
\startcontents[sections]
\printcontents[sections]{l}{1}{\setcounter{tocdepth}{3}}
}
\newpage
\newpage
\section{ProcTHOR Assets}
\label{sec:procthorObjects}
\vspace{-0.15in}
\begin{figure}[htbp]
\centering
\hfill
\begin{subfigure}[b]{0.57\textwidth}
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Fridge_1-front.png}
\caption*{\textsc{Fridge\_1}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Fridge_10-front.png}
\caption*{\textsc{Fridge\_10}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Fridge_11-front.png}
\caption*{\textsc{Fridge\_11}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Fridge_12-front.png}
\caption*{\textsc{Fridge\_12}}
\end{subfigure}
\\[0.1in]
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Fridge_13-front.png}
\caption*{\textsc{Fridge\_13}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Fridge_14-front.png}
\caption*{\textsc{Fridge\_14}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Fridge_15-front.png}
\caption*{\textsc{Fridge\_15}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Fridge_16-front.png}
\caption*{\textsc{Fridge\_16}}
\end{subfigure}
\\[0.22in]
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Sofa_201_2-front.png}
\caption*{\textsc{Sofa\_201\_2}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Sofa_203_1-front.png}
\caption*{\textsc{Sofa\_203\_1}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Sofa_204_1-front.png}
\caption*{\textsc{Sofa\_204\_1}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Sofa_205_1-front.png}
\caption*{\textsc{Sofa\_205\_1}}
\end{subfigure}
\\[0.1in]
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Sofa_207_3-front.png}
\caption*{\textsc{Sofa\_207\_3}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Sofa_214_2-front.png}
\caption*{\textsc{Sofa\_214\_2}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Sofa_218_1-front.png}
\caption*{\textsc{Sofa\_218\_1}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Sofa_227_1-front.png}
\caption*{\textsc{Sofa\_227\_1}}
\end{subfigure}
\\[0.22in]
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Chair_002_1-front.png}
\caption*{\textsc{Chair\_002\_1}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Chair_007_1-front.png}
\caption*{\textsc{Chair\_007\_1}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Chair_201_1-front.png}
\caption*{\textsc{Chair\_201\_1}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Chair_203_1-front.png}
\caption*{\textsc{Chair\_203\_1}}
\end{subfigure}
\\[0.15in]
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Chair_204_1-front.png}
\caption*{\textsc{Chair\_204\_1}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Chair_205_1-front.png}
\caption*{\textsc{Chair\_205\_1}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Chair_210_1-front.png}
\caption*{\textsc{Chair\_210\_1}}
\end{subfigure}
\hfill
\begin{subfigure}{0.2\textwidth}
\centering
\includegraphics[width=\textwidth, cfbox=black!30]{figures/assets/Chair_215_1-front.png}
\caption*{\textsc{Chair\_215\_1}}
\end{subfigure}
\caption{Examples of assets in the asset database. The forward-facing direction for each asset is consistent across all assets within its type, which allows us to do things like not spawn fridges facing the wall.}
\end{subfigure}
\hfill\;
\begin{subfigure}[b]{0.37\textwidth}
\centering
\includegraphics[width=\textwidth]{figures/assetTypes2.pdf}
\caption{The number of unique 3D modeled assets for each of the 108 asset types. There are 1,633 unique assets in total.}
\end{subfigure}
\caption{Examples and statistics of assets in the asset database.}
\end{figure}
\begin{minipage}{\textwidth}
\section{House Generation}
\label{sec:houseGeneration}
This section gives more details about the process we developed to procedurally sample houses.
\subsection{Examples}
\end{minipage}
\newpage
\subsubsection{3-Room Houses}
\begin{figure}[H]
\centering
\vspace{0.015in}
\makebox[\textwidth][c]{
\includegraphics[width=1.07\textwidth]{figures/full-kitchen-living-bedroom-room2.jpg}
}
\vspace{0.025in}
\caption{Examples of 3-room houses generated in \mbox{\sc{ProcTHOR}}\xspace-10K.}
\end{figure}
\newpage
\subsubsection{4-Room Houses}
\begin{figure}[H]
\centering
\vspace{0.015in}
\makebox[\textwidth][c]{
\includegraphics[width=1.07\textwidth]{figures/room-specs/full-4-room2.jpg}
}
\vspace{0.025in}
\caption{Examples of 4-room houses generated in \mbox{\sc{ProcTHOR}}\xspace-10K.}
\end{figure}
\newpage
\subsubsection{5-Room Houses}
\begin{figure}[H]
\centering
\vspace{0.015in}
\makebox[\textwidth][c]{
\includegraphics[width=1.07\textwidth]{figures/room-specs/full-5-room.jpg}
}
\vspace{0.025in}
\caption{Examples of 5-room houses generated in \mbox{\sc{ProcTHOR}}\xspace-10K.}
\end{figure}
\newpage
\subsubsection{6-Room Houses}
\begin{figure}[H]
\centering
\vspace{0.015in}
\makebox[\textwidth][c]{
\includegraphics[width=1.07\textwidth]{figures/room-specs/6-room-2.jpg}
}
\vspace{0.025in}
\caption{Examples of 6-room houses generated in \mbox{\sc{ProcTHOR}}\xspace-10K.}
\end{figure}
\newpage
\subsubsection{7+ Room Houses}
\begin{figure}[H]
\centering
\vspace{0.015in}
\makebox[\textwidth][c]{
\includegraphics[width=1.07\textwidth]{figures/full-large-2.jpg}
}
\vspace{0.025in}
\caption{Examples of 7+ room houses generated in \mbox{\sc{ProcTHOR}}\xspace-10K.}
\end{figure}
\newpage
\subsection{Room Specs}
\begin{figure}
\centering
\begin{subfigure}[b]{0.32\textwidth}
\centering
\includegraphics[width=\textwidth]{figures/spec1.pdf}
\caption{4-Room House}
\label{fig:roomSpecExsA}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.32\textwidth}
\centering
\includegraphics[width=\textwidth]{figures/spec2.pdf}
\caption{5-Room House}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.32\textwidth}
\centering
\includegraphics[width=\textwidth]{figures/spec3.pdf}
\caption{7-Room House}
\end{subfigure}
\caption{Examples of room spec hierarchies used to sample differently sized houses.}
\label{fig:roomSpecExs}
\end{figure}
Room specs provide the ability to specify the rooms that appear in a house, the relative size of each room, and how the rooms are connected with doors. Their idea was first proposed in \cite{marson2010automatic}. A room spec is manually specified with a tree data structure.
Figure \ref{fig:roomSpecExsA} shows a simplified example of a room spec with four rooms: bedroom, bathroom, kitchen, and living room. In this room spec, there are two subtrees, comprising $\mathcal Z_{bb} = \{$\text{bedroom}, \text{bathroom}$\}$ and $\mathcal Z_{klv} = \{$\text{kitchen}, \text{living room}$\}$. At each level of the tree, there is a constraint that there must be a direct path connecting every child node of a parent. Thus, in our example, there will be a path between the bedroom and the bathroom, a path between the kitchen and the living room, and another path connecting $\mathcal Z_{bb}$ to $\mathcal Z_{klv}$. We can also specify which room types we would prefer not to have a path between it and the parent. For example, we typically do not want the bathroom to have 2 doors, such as between it and the bedroom and between it and a room in $\mathcal Z_{klv}$.
Each tree node, below the root of the tree, is also assigned a growth weight, which approximates the relative size of the node compared to all other nodes that share the same parent. For instance, we might assign both $\mathcal Z_{bb}$ and $\mathcal Z_{klv}$ a growth rate of $1$, to be roughly the same size. But, if we want the bedroom to take up roughly $60\%$ of the $\mathcal Z_{bb}$'s area, then we might assign the bedroom a growth rate of $3$ and the bathroom a growth rate of $2$.
Room specs allow us to flexibly choose the distribution of houses we sample, allowing us to specify massive mansions, studio apartments, and anything in-between. Moreover, just a few room specs can go a long way. To generate our houses, we use 16 room specs, which each uses between 1 to 10 rooms. To generate the houses dataset, we assign a sampling weight to each of our room specs, and then use weighted sampling to sample a room spec for each house.
\subsection{Sampling Floor Plans}
\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figures/boundaries.pdf}
\caption{An example of the interior boundary cut algorithm. The images show a top-down view of the house's floor plan. First, we sample an interior boundary rectangle $(x_s, z_s)$, which is shown on the left. Then, we make $n_c$ rectangular cuts to the corners of the rectangle to make the interior boundary of the house a more complex polygon. In this case, we make $n_c=3$ cuts to form the final interior boundary, which is shown on the right.}
\label{fig:interior}
\end{figure}
The size and shape of the house are sampled to form the interior boundaries. Room specs specify the distribution over the dimensions of the house. Figure \ref{fig:interior} visualizes the process of sampling an interior boundary, where we first sample the size of the boundary and then make cuts to the corners to add randomness. The sampling starts off by choosing the initial upper bound of the top-down $x$ and $z$ size of the house, in meters, respectively denoted as $x_s$ and $z_s$. Each dimension is an integer. In most room specs, each dimension is independently sampled from the discrete uniform distribution $x_s, z_s \sim U(\max(\ell_{\min}, \mu_a\sqrt{n_r} - \nicefrac{\mu_a}{2}), \mu_a \sqrt{n_r} + \nicefrac{\mu_a}{2})$, inclusive. However, individual room specs can override the $x_s$ and $z_s$ sampling distributions. Here, $n_r$ represents the number of rooms in the house, $\ell_{\min}$ is set to $2$ and represents the minimum size of $x_s$ and $z_s$, and $\mu_a$ is set to $3$ and represents the average size of $x_s$ and $z_s$ per room.
\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figures/cuts-2.pdf}
\caption{The probability distribution over the number of cuts, $n_c$, made to the rectangular boundary ($x_s$, $z_s$) with respect to the number of rooms in the house, $n_r$. Notice that when there are more rooms in the house, the number of cuts in the distribution increases.}
\label{fig:ncuts}
\end{figure}
Once we have the rectangular boundary $(x_s, z_s)$, we then make several \textit{cuts} to the outside of the rooms such that the interior boundaries can take on the shape of more complex polygons. The number of cuts, $n_c$, is sampled from the distribution $n_c\sim \lfloor 10\cdot \text{Beta}(\alpha_c, \beta_c) + \nicefrac{1}{2}\rfloor$, where $\alpha_c=\nicefrac{n_r}{2}$ and $\beta_c = 6$. Figure \ref{fig:ncuts} shows the distribution that is formed with respect to the number of rooms in the house, $n_r$. When there are more rooms, the probability distribution over the number of cuts increases. Since the range of the beta distribution is $(0, 1)$, the upper bound on the number of cuts is exactly 10.
The size of each cut is a rectangle, in meters, denoted by $(c_x$, $c_z)$. Both $c_x$ and $c_z$ are sampled from integer distributions. We sample from $c_x\sim U(1, \max(2, \min(x_s - 1, \lfloor a_{\max} / 2\rfloor) - 1)$, inclusive, where $a_{\max}$ is set to $6$ representing the maximum cut area. We then sample $c_z\sim U(1, a_{\max} - c_x)$. The position of where the cut happens is anchored to one of the 4 corners of the interior boundary, where the exact corner is independently and uniformly sampled each time.
Since the size of each cut is an integer, and the rectangular boundary sizes are also integers, we can efficiently represent the interior boundary with a $(x_s, z_s)$ boolean matrix. Here, we could have $1$s representing where the inside of the interior boundary and $0$s representing the outside of the interior house boundary.
\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figures/gen-spec.pdf}
\caption{An example of the recursive floor plan generation algorithm, given an interior boundary and the room spec in Figure~\ref{fig:roomSpecExsA}. Here, we first divide the room into a ``bedroom \& bathroom'' and a ``kitchen \& living room'' zone. Then, within the ``bedroom \& bathroom'' zone we place both the bedroom and bathroom, and within the ``kitchen \& living Room'' zone, we place both the kitchen and living room.}
\label{fig:recFP}
\end{figure}
Given a room spec and an interior boundary, we use the algorithm proposed in \cite{lopes2010constrained} to divide the interior boundary into rooms. The algorithm recursively subdivides the interior boundary for each subtree in the room spec. Figure \ref{fig:recFP} shows an example using Figure~\ref{fig:roomSpecExsA}'s room spec. The algorithm first divides the interior boundary into two zones, the ``bedroom \& bathroom'' zone and the ``kitchen \& living room'' zone. The ``bedroom \& bathroom'' zone then subdivides into two rooms, the bedroom and bathroom. Similarly, the ``kitchen \& living room'' zone is also subdivided into two rooms, the kitchen and living room. The growth weight is used to approximate the size of each subdivision. By recursively subdividing the zones of each subtree, we satisfy the constraint that we can traverse between child nodes of the same parent in the room spec.
Finally, we scale the entire floor plan by $s\sim U(1.6, 2.2)$. Scaling the interior boundary to be larger provides more room for the agent to be able to navigate within the houses. Using a range of values also provides more variability on the size of the houses. We set the upper bound to 2.2 based on the empirical quality of the houses, where values above that often left too much empty space.
\subsection{Connecting Rooms}
\begin{figure}[htbp]
\centering
\begin{subfigure}{0.32\textwidth}
\includegraphics[width=\textwidth]{figures/doorway.jpg}
\caption{Doorway Connection}
\end{subfigure}
\begin{subfigure}{0.32\textwidth}
\includegraphics[width=\textwidth]{figures/doorframe.jpg}
\caption{Door Frame Connection}
\end{subfigure}
\begin{subfigure}{0.32\textwidth}
\includegraphics[width=\textwidth]{figures/open-room.jpg}
\caption{Open Room Connection}
\end{subfigure}
\caption{An example of the 3 ways to connect different rooms, using either a doorway, door frame, or open room connection.}
\label{fig:door-connections}
\end{figure}
Figure \ref{fig:door-connections} shows the 3 types of ways adjacent rooms may be connected. Specifically, rooms may be connected using 3 different types of connections: doorways, door frames, or open room connections. We determine which rooms should have doors between them based on the constraints in the room spec. Amongst adjacent rooms that may have doors between them, subject to the constraints in the room spec, we randomly sample which rooms have doors. We also impose the constraint that neighboring rooms in the room spec may have at most 1 room connected to it.
To choose the type of connection, we consider the rooms we are connecting. Specifically, we only allow open room connections and door frame connections between kitchen and living room room types. We impose this constraint because it would be unrealistic for a room like a bathroom to be fully visible from another room. For connecting room types that do support open room connections or door frames, we annotate the probability of sampling a doorway, door frame, and open room connection. Between a kitchen and living room the probability is 0.375 for sampling both an open room connection and a door frame connection, and 0.25 for sampling a doorway connection.
If a doorway or door frame is sampled, we filter to use a valid asset that is smaller than the wall connecting the rooms. For our generation, the minimum wall size is always greater than a single door size, but occasionally the filter might remove double doors from valid doors that can be sampled as they would be too big. The placement of the door is then uniformly sampled from anywhere along the wall. For doorways, the open direction is uniformly sampled. Finally, if the open state from any 2 doorways collides, we also use rejection sampling to potentially change the open direction and modify the placement of doorways.
Each house also has a permanently closed exterior door connecting to the outside. We prioritize placing this door in kitchen and living room room types, as it is unnatural to have to go through a bathroom or bedroom to go outside. However, in the case where the room spec does not include a kitchen or living room (\textit{e.g.} if the room is a standalone bathroom), we randomly place a door to the outside in one of the remaining rooms.
\subsection{Structure Materials}
\textbf{Wall materials.} To choose the materials that make up the walls, we consider 2 families of wall materials: solid colors and texture-based materials. Our solid color materials consist of 40 unique colors of popular paint colors found in houses. We constrain ourselves to only using popular paint colors, so we do not randomize the walls to unrealistic colors such as bright green or yellow. For the texture-based materials, we annotate 122 different AI2-THOR materials to be suitable as wall materials. These include materials for brick textures, drywall textures, and tiling textures, amongst others.
Each wall in a room shares the same materials. For each room, we sample it if its materials are a solid color with $w_{\textit{solid}} \sim \text{Bernoulli}(0.5)$. It is sometimes the case in real life that all rooms in a house share the same material (\textit{e.g.} every room in an apartment is painted with white walls). We therefore also have a parameter $w_{\textit{same}} \sim \text{Bernoulli}(0.35)$ that specifies if all rooms in the house will have the same material.
\textbf{Ceiling material.} The entire ceiling of the house is always assigned to a single wall material. If $w_{\textit{same}}$, then the ceiling material is also set to the wall material. Otherwise, it is independently sampled with the same wall material sampling process.
\textbf{Floor materials.} We annotate 55 materials in AI2-THOR as floor materials. Most commonly, these materials are wood materials. For each room, we independently sample its floor material from the set of annotated floor materials. However, similar to wall materials, we independently sample $f_{\textit{same}} \sim \text{Bernoulli}(0.15)$ that specifies if all rooms in the house will have the same material.
\subsection{Ceiling Height}
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{figures/ceiling-distribution-function.pdf}
\caption{The distribution of the ceiling height of each house, in meters.}
\label{fig:ceilingHeight}
\end{figure}
The ceiling height for the house, in meters, is sampled from $c_h\sim h_{\min} + (h_{\max} - h_{\min})\cdot \text{Beta}(\alpha_h, \beta_h)$, where we set $h_{\min}=2.5$, $h_{\max}=7$, $\alpha_h=1.25$, and $\beta_h=5.5$. Figure \ref{fig:ceilingHeight} shows the ceiling height distribution that is formed. All rooms in the house have the same ceiling height.
The minimum and mean values were chosen based on the typical height of an American apartment, while $\beta_h$ allows some of the train houses to have much larger ceilings.
\subsection{Lighting}
\textbf{Lighting Placement.} Each procedural house places two types of lights: a directional light and point lights. The directional light is analogous to the sun in the scene, where only 1 is placed in each scene. Light from point lights are analogous to the light emitted from lightbulbs. We place a point light in each room near the ceiling, centered at the centroid of the room's floor polygon. Using the centroid ensures that the light is always placed inside of the room, even for L-shaped rooms. Additionally, desk lamp and floor lamp objects have a point light associated with them.
\begin{figure}[htbp]
\centering
\begin{subfigure}{0.325\textwidth}
\includegraphics[width=\textwidth]{figures/skyboxes/midday-small.jpg}
\caption{Midday Skybox}
\end{subfigure}
\begin{subfigure}{0.325\textwidth}
\includegraphics[width=\textwidth]{figures/skyboxes/golden-hour-small.jpg}
\caption{Golden Hour Skybox}
\end{subfigure}
\begin{subfigure}{0.325\textwidth}
\includegraphics[width=\textwidth]{figures/skyboxes/blue-hour-small.jpg}
\caption{Blue Hour Skybox}
\end{subfigure}
\caption{Examples different skyboxes in a scene. Notice how the colors of the images differ and how the content outside of the window changes with the skybox.}
\label{fig:skyboxes}
\end{figure}
\textbf{Effects by the time of day}. Skyboxes may appear at 3 different times of day: midday, golden hour, and blue hour. The time of day determines the intensity, hue, and direction of the ambient outdoor lighting. For each time of day, there exist multiple \textit{skyboxes}, which dictate the lighting of the environment. Figure \ref{fig:skyboxes} shows examples of how the time of day visually affects the scene. At this time, there are 16 midday skyboxes, 5 golden hour skyboxes, and 1 blue hour skybox, based on full 360-degree photos taken in Seattle and San Francisco.
\subsection{Object Placement}
\label{sec:op}
In this section, we discuss how objects are placed realistically in the house. We hypothesize reasonable object placement is necessary in order to train efficient agents. For instance, if a toilet could appear anywhere in the house, the agent would have a much harder search problem, leading to longer episodes, than if the toilet was always in the bathroom. Moreover, we do not want objects to appear in unnatural positions, such as a fridge facing the wall, as it would make it unnatural, and even unusable, for interaction.
Finally, we do not always want objects to spawn independently. For instance, we might want a table to be surrounded by chairs. We achieve dependant sampling by developing SAGs, which are described in the section that follows.
\subsubsection{Assets}
\label{sec:assets}
The ProcTHOR asset database consists of 1,633 interactive household assets across 108 object types (see Appendix~\ref{sec:procthorObjects} for more details). The majority of assets come from AI2-THOR. Windows, doors, and counter tops are built into the exterior of rooms in AI2-THOR, which prevents us from spawning them in as standalone assets. Thus, we have also hand-built 21 windows, 20 doors, and 33 counter tops.
\textbf{Asset Annotations.} Our assets include several annotations that help us place them realistically in a house. Figure~\ref{fig:assetAnnotations} shows an example of the asset annotations used to place an arm chair. For an individual asset, we annotate its object type, computationally obtain its 3D bounding box, and partition assets of object types into training, validation, and testing splits. Then, we annotate how each object type might be spawned into the house. Annotating the 108 object types, as opposed to annotating the 1,633 individual assets, allows us to scale up the number of unique assets dramatically. Moreover, it does not require any new annotation to add an asset that can be grouped with an existing object type.
\begin{figure}[htbp]
\centering
\includegraphics[width=1\textwidth]{figures/asset-annotations.pdf}
\caption{An example of the asset annotations used to place an arm chair asset. This particular instance is annotated with its object type, bounding box, and split. Annotations about how it is placed in the house are done at an object type level, applying to all instances of that type.}
\label{fig:assetAnnotations}
\end{figure}
If instances of an object type cannot be placed independently on the floor, the rest of its annotations are not considered. For instance, we do not allow television object types to be placed alone on the floor, rather they are often placed on top of a television stand or mounted on the wall, which is discussed later in this section. Similarly, we also annotate small objects, like a fork, pen, and mug to not be placed independently on the floor. However, typical large object types, such as counter top, arm chair, or fridge object types can be placed independently on the floor.
Among the remaining object types, we annotate where and in which rooms the object type may appear. Each object type has a room weight, $r_w\in \{0, 1, 2, 3\}$, corresponding to how likely it is to appear in each room type. For each room type, a $0$ indicates the object should never appear (e.g., a fridge in a bathroom); a $1$ indicates the object may appear, but is unlikely; a $2$ indicates that the object appears quite often; and a $3$ indicates that the object nearly always appears (e.g., a bed in a bedroom). To determine where the object is placed, we annotate whether it may appear on the edge, in the corner, or in the middle of a room. For example, we annotate that a fridge can be placed on the edge or in the corner of the room, but not in the middle. We also annotate whether there can be multiple instances of an object type in a single room. Here, we annotate that multiple toilet object types cannot be in the same room, for instance.
\noindent\textbf{Asset Splits.} If an object type has over 5 unique assets, then those assets are partitioned into train, validation, and testing splits. Specifically, approximately $\nicefrac{2}{3}$ of the assets are assigned to the train split, and approximately $\nicefrac{1}{6}$ of the assets are assigned to each of the validation and testing splits. For object types that have 5 or fewer unique assets, they may appear in any split. In general, the more visual diversity an object type has, the more instances of that object type exist. For instance, there are many chair objects, but there are much fewer CD, toilet, and fork objects. Appendix~\ref{sec:procthorObjects} shows the precise count of each object type.
\subsubsection{Semantic Asset Groups (SAGs)}
\begin{figure}[htbp]
\centering
\begin{minipage}{0.58\linewidth}
\includegraphics[width=1\linewidth]{figures/asset-group-3.pdf}
\subcaption{An interface for viewing SAGs showing child asset anchoring and rotational randomness.}
\label{sub:anchor}
\end{minipage}
\qquad\quad
\begin{minipage}{0.22\linewidth}
\includegraphics[width=1\linewidth]{figures/hierarchy-sampler.pdf}
\subcaption{Hierarchy}
\vspace{0.05in}
\centering
\includegraphics[width=0.70\linewidth]{figures/annotation2.pdf}
\vspace{-0.03in}
\subcaption{Annotation}
\end{minipage}
\caption{An example of a semantic asset group (SAG), where two chair samplers are parented to a dining table sampler. Both chairs are anchored to the top middle of the table.}
\label{fig:semGroupExamples}
\end{figure}
A \textit{Semantic Asset Group} (SAG) provides a flexible and diverse way to encode which objects may appear near each other. The power of SAGs comes in their ability to support randomized asset and rotational sampling. SAGs can be created and exported in seconds with our user-friendly drag-and-drop web interface.
Figure~\ref{fig:semGroupExamples} shows an example of how we might construct a SAG that has two chairs pushed into the side of a dining table. The SAG includes two chair samplers and a dining table sampler. Asset samplers contain a set of unique 3D modeled asset instances that may be sampled. When the SAG is instantiated, each asset sampler randomly chooses one of its instances. Asset samplers can also be linked, where multiple samplers sample the same asset instance each time. Here, linking may allow for multiple instances of the same chair to be placed at a dining table, instead of independently sampling a different chair for each sampler.
The ability to randomly sample assets to place in a SAG is incredibly expressive. For instance, consider a SAG with samplers for a TV stand, television, sofa, and arm chair. If each of these samplers can sample from just 30 different 3D modeled asset instances, then there are over $800$k unique combinations of instances that can make be sampled from that SAG.
Asset samplers define how assets are positioned relative to one another. SAGs are constructed by looking at instances of asset samplers from their top-down orthographic images, such as the one shown in Figure \ref{sub:anchor}. Here, both of the chair samplers are parented to the dining table sampler. Each child asset sampler is anchored to its parent asset sampler vertically in $\mathcal V = \{\textsc{Top}, \textsc{Center}, \textsc{Bottom}\}$ and horizontally in $\mathcal H = \{\textsc{Left}, \textsc{Center}, \textsc{Right}\}$. Each child asset sampler's pivot position can similarly be set vertically in $\mathcal V$ and horizontally in $\mathcal H$. For instance, in Figure \ref{sub:anchor}, both chair samplers are anchored to the parent vertically on \textsc{Top} and horizontally in the \textsc{Center}. But, the chair sampler on the left's pivot position is vertically in the \textsc{Center} and horizontally on the \textsc{Right}, whereas the chair sampler on the right's pivot position is vertically in the \textsc{Center} and horizontally on the \textsc{Left}. Figure \ref{fig:plant} shows more examples of how a plant or floor lamp sampler may be positioned around an arm chair sampler. Each child asset sampler can then have an $(x, y)$ offset, which is the distance from the parent sampler's anchor point to the child sampler's pivot position.
\begin{figure}[ht!]
\vspace{-0.05in}
\centering
\begin{subfigure}[b]{0.24\textwidth}
\captionsetup{justification=centering}
\centering
\includegraphics[width=0.9\textwidth]{figures/a1.pdf}
\caption{\\ \vspace{0.05in} \scriptsize \textsc{Center Right} Anchor \\ \textsc{Center Left} Pivot}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.24\textwidth}
\centering
\captionsetup{justification=centering}
\includegraphics[width=\textwidth]{figures/a2.pdf}
\vspace{0in}
\caption{\\ \vspace{0.05in} \scriptsize \textsc{Center Right} Anchor\\\textsc{Bottom Left} Pivot}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.24\textwidth}
\centering
\captionsetup{justification=centering}
\includegraphics[width=0.8\textwidth]{figures/a3.pdf}
\caption{\\ \vspace{0.05in} \scriptsize \mbox{\textsc{Bottom Center} Anchor}\\\textsc{Center Center} Pivot}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.24\textwidth}
\centering
\captionsetup{justification=centering}
\includegraphics[width=0.6\textwidth]{figures/a4.pdf}
\caption{\\ \vspace{0.05in} \scriptsize \mbox{\textsc{Bottom Center} Anchor}\\\textsc{Top Center} Pivot}
\end{subfigure}
\caption{
Instantiations of a SAG that places a plant or floor lamp sampler $\mathcal S_{c}$ around a parented arm chair sampler $\mathcal S_{p}$ with anchor and pivot position annotations. Notice that the placement from $\mathcal S_c$ reacts to the size of the asset sampled from $\mathcal S_{p}$. None of the examples have any offset.
}
\label{fig:plant}
\vspace{-0.05in}
\end{figure}
The motivation for the relative positioning of asset samplers is to prevent the meshes from clipping into each other. For instance, with the same SAG in Figure \ref{sub:anchor}, consider what would happen if the dining table sampler samples a table that is double the size of the current table. Instead of the chairs being stuck in a fixed global position, and effectively colliding with the new dining table, the chairs will reactively move back, and be re-positioned to remain slightly tucked under the larger table. Moreover, consider that the size of instances that are sampled from an asset sampler are often quite different. For instance, one table might be square-ish, while another is elongated. If we only used a \textsc{Center Center} pivot and an offset, one would not be able to reliably place asset samplers, containing differently sized objects, directly beside each other without it resulting in clipping.
\begin{figure}
\centering
\vspace{-1in}
\begin{subfigure}[b]{0.49\textwidth}
\centering
\includegraphics[width=0.925\textwidth]{figures/rejected-sag.png}
\vspace{-0.20in}
\caption{\includegraphics[width=0.085in]{figures/failure.pdf} Rejected}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.49\textwidth}
\centering
\includegraphics[width=0.75\textwidth]{figures/accepted-sag.png}
\vspace{-0.15in}
\caption{\includegraphics[width=0.115in]{figures/success.pdf} Accepted}
\end{subfigure}
\caption{Rejection sampling is used to make sure objects placed in SAGs do not collide. \emph{Left:} the chair collides with the dining table, and hence it is rejected; \emph{Right:} none of the objects in the instantiated SAG collide with each other, so the SAG is accepted as valid.}
\label{fig:rej}
\end{figure}
While setting anchoring and pivot positions solves many mesh clipping issues, some cases may still arise. Figure \ref{fig:rej} shows an example, where if our dining table sampler samples a short dining table, it may clip into certain chairs. Such issues are rare in practice, but object clipping would lead to less realistic and interactive houses. To solve the clipping issue, we use rejection sampling to resample the assets of a SAG until none of the 3D meshes of the sampled assets are clipping.
In \mbox{\sc{ProcTHOR}}\xspace{}-10K, we construct 18 SAGs, which can be instantiated with over 20 million unique combinations of assets. These include semantic asset groups for chairs around tables, pillows on top of beds, sofas and arm chairs looking at a television on top of a TV stand, faucets on top of sinks, and a desk with a chair, amongst others.
\subsubsection{Floor Object Placement}
\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figures/placement.pdf}
\caption{Diagram detailing how floor objects are placed in a room. First, we rectangularize the top-down view of the room's open floor plan by drawing horizontal and vertical dividers from each corner point. Then, we construct all possible rectangles that are formed within the dividers. We then sample one of those rectangles and place the object within that rectangle. The sampled object's top-down bounding box (with margin) is shown in blue. The bounding box is then subtracted from the open floor plan before repeating the process again.}
\label{fig:lpo}
\end{figure}
We start object placement by first placing objects on the floor of the house. Objects are independently placed on a room-by-room basis, where we may first place objects in the bedroom and then place objects in the bathroom, without either affecting each other.
For each room, we filter the objects down into only using objects that have a room weight $r_w > 0$ in the given room type, and that have the annotation that they can be placed on the floor. Here, for instance, a chair object may have the annotation that it can be placed on the floor, but a knife object may not.
At this stage, we simplify rooms to just look at the top-down 2D bounding box that makes up the room in the floor plan. We also simplify objects to just look at its top-down 2D bounding box, of size $(o_w, o_h)$. These simplifications make it easier to determine if an object will fit in the room, specifically in a particular rectangle.
Figure \ref{fig:lpo} illustrates the iterative process of placing objects in the scene. First, the polygon forming the area left to place an object is partitioned into rectangles. The rectangles come from drawing a horizontal and vertical grid line at all corner points of the open polygon. Here, we can easily obtain the largest rectangle remaining in the open room polygon. We sample $r_\ell\sim \text{Bernoulli}(0.8)$ to determine if the next object to be placed should be placed inside of the largest rectangle. Otherwise, we randomly choose amongst all possible rectangles, weighted by the area of each rectangle.
Once we have the rectangle $(r_w, r_h)$ where the object should be placed in, we filter our objects to only those that would fit, both semantically and physically, in the rectangle. Semantically, we consider 3 scenarios: the rectangle being on the corner, edge, or middle of the room's polygon.
If any of the rectangle's corners is in a corner of the room, then we will place an object in that corner of the room. If multiple of the rectangle's corners are in a corner of the room, then we uniformly sample a corner amongst one of those corners.
Now, we will filter down objects and asset groups to only consider:
\begin{enumerate}[leftmargin=0.25in]
\item Those that are annotated specifying that they can be placed in the corner of the room. For example, we might annotate a fridge to be placed in the corner of the room, but we might not annotate a SAG consisting of a dining table to be placed in the corner of the room.
\item The annotated split of the asset instance matches the current split of the generated house. See Appendix~\ref{sec:assets} which talks about asset splits to create train/val/test homes.
\item The top-down bounding box of the object (with margin) must fit within the chosen rectangle. For a corner object, Figure \ref{fig:cornerRots} shows the 2 valid rotations that this object may take on. Specifically, the back of the object may be against either wall. Then, we filter down remaining objects to only use those where the object's bounding box fits within the rectangle's bounding box; that is, $(o_h + w_{\textit{pad}}\leq r_w \text{ and } o_w + w_{\textit{pad}} \leq r_h) \text{ or } (o_h + w_{\textit{pad}} \leq r_h \text{ and } o_w + w_{\textit{pad}} \leq r_w)$. If both conditions are valid, we uniformly choose one of the rotations of the object's bounding box.
We add margin around objects to make sure it is always possible to navigate around them. Objects to be placed in the middle of the room have $m_{\textit{pad}}=0.35$ meters of margin on each side. Objects on the edge or corner of the room have $w_{\textit{pad}} = 0.5$ meters of margin only in front of the object, which enables objects to be placed directly beside it.
\end{enumerate}
\begin{figure}[htbp]
\centering
\begin{subfigure}{0.19\textwidth}
\centering
\vspace{1.055in}
\includegraphics[width=\linewidth]{figures/placement/edge-rotation.jpg}
\caption{Edge Rotations}
\label{fig:edgeR}
\end{subfigure}
\qquad\qquad
\begin{subfigure}{0.19\textwidth}
\centering
\includegraphics[width=\linewidth]{figures/placement/corner-placement.jpg}\\
\includegraphics[width=\linewidth]{figures/placement/corner-placement-2.jpg}
\caption{Corner Rotations}
\label{fig:cornerRots}
\end{subfigure}
\qquad\qquad
\begin{subfigure}{0.39\textwidth}
\centering
\includegraphics[width=0.48\linewidth]{figures/placement/mid-1.jpg}
\includegraphics[width=0.48\linewidth]{figures/placement/mid-2.jpg}
\includegraphics[width=0.48\linewidth]{figures/placement/mid-3.jpg}
\includegraphics[width=0.48\linewidth]{figures/placement/mid-4.jpg}
\caption{Middle Rotations}
\label{fig:midR}
\end{subfigure}
\caption{Valid rotations of objects when placed on the edge, corner, and middle of the room. Objects placed on the edge or corner of the room always have their backs to the wall. Objects in the middle of the scene can be rotated in any direction. By constraining rotations of objects, we ensure an object on the edge of the room, such as a fridge or drawer, can still be opened.}
\label{fig:objRotations}
\end{figure}
We sample an object or asset group that satisfies all of the previous conditions. If there are no objects or asset groups that satisfy all conditions, we continue to the next iteration and remove the selected rectangle from consideration. We slightly prioritize placing asset groups over standalone assets when possible. Once we have chosen an object or asset group, the bounding box with margin is then anchored to the corner of the rectangle, and hence to the corner of the room. We then subtract the object's bounding box, with margin, from the open polygon representing the space remaining in the room before doing the same process again.
If the rectangle is along the edge, we sample $r_{\textit{edge}} \sim \text{Bernoulli}(0.7)$ to determine if we should try to place an object on the edge of the rectangle, or if we should try and place it in the middle. If the rectangle is not along the edge or on the corner of the room, then we will always try to place an object in the middle of it. We use a similar filtering process, as the one described with edge rectangles, to filter down objects to those that only fit within the bounds of the rectangle. However, as depicted in Figure~\ref{fig:edgeR} and Figure~\ref{fig:midR}, edge objects can only have their backs to the wall, and middle objects can be rotated in any 90-degree rotation.
The iterative process of sampling a rectangle from the open polygon of the room, placing an object in that rectangle, and subtracting the bounding box formed by the object in the rectangle, continues on for $r_{i}$, where $r_i$ is sampled from
\begin{equation}
r_i\sim \begin{cases}
1 & p=\nicefrac{1}{200}\\
4 & p=\nicefrac{2}{200}\\
5 & p=\nicefrac{4}{200}\\
6 & p=\nicefrac{20}{200}\\
7 & p=\nicefrac{173}{200}
\end{cases}.
\end{equation}
Sampling $r_i$ allows us to infrequently have rooms in the house where there are very few objects, which is sometimes the case in real-world homes. It should also be noted that there can be more than $r_i$ objects on the floor of the scene if some objects in the scene are in SAGs.
By iteratively choosing the largest, or near largest, rectangle in the room's open polygon, placing an object in it, and subtracting the object's bounding box with margin from the open room polygon, we enable great coverage across the entirety of the room, and hence the entirety of the house.
\subsubsection{Wall Object Placement}
\begin{figure}
\centering
\begin{subfigure}{0.325\textwidth}
\includegraphics[width=\textwidth]{figures/wall-objects/wall-window.jpg}
\caption{Window}
\end{subfigure}
\begin{subfigure}{0.325\textwidth}
\includegraphics[width=\textwidth]{figures/wall-objects/wall-painting.jpg}
\caption{Painting}
\end{subfigure}
\begin{subfigure}{0.325\textwidth}
\includegraphics[width=\textwidth]{figures/wall-objects/wall-tv.jpg}
\caption{Television}
\end{subfigure}
\caption{Examples of objects placed on the wall of a house.}
\label{fig:wall-objects}
\end{figure}
After placing objects on floors, we then place objects on walls. We currently place window, painting, and television objects on the walls. Figure \ref{fig:wall-objects} shows some examples. Window and television objects may appear in kitchen, living room, and bedroom room types. Paintings may appear in any room type.
\textbf{Windows.} Window objects are the first objects we place on the walls of the house. We only consider placing a window on walls that are connected to the outside of the house, such that we do not place a window between two indoor rooms. For each kitchen, living room, and bedroom in the house, we sample
\begin{equation}
n_w\sim \begin{cases}
0 & p=0.125\\
1 & p=0.375\\
2 & p=0.5
\end{cases}
\end{equation}
maximum window objects to be placed.
For each wall in a given room, we look at the segment formed by each edge connecting 2 adjacent corners. If there is a floor object placed along that edge (or corner) of the wall, we subtract it from the segment. Here, the segment may break into different segments, where each segment is treated just like the original one. If the length of any segment is smaller than the minimum window size in the split, we remove the segment. We then use a uniform sample over the remaining segments, weighted by their lengths, to determine where to place the window. If no segments are longer than the smallest window, we move on to the next room in the house. A window smaller than the length of the segment is then uniformly placed somewhere along the sampled segment. The window is vertically centered along the wall between the floor and $w_{\max}=\min(3, c_h)$. All segments along the wall where the window was placed are removed from future sampling calls, and we continue this process $n_w$ times.
\textbf{Paintings.} Painting objects are placed on the walls after window objects. They may be placed in any room. The maximum number of painting objects that are attempted to be placed in each room is sampled from
\begin{equation}
n_p\sim\begin{cases}
0 & p=0.05\\
1 & p=0.1\\
2 & p=0.5\\
3 & p=0.25\\
4 & p=0.1
\end{cases}.
\end{equation}
The placement of painting objects is similar to the placement of window objects. However, multiple painting objects may be placed along the same wall, so instead of removing the entire wall segment after an object is placed on it, we subtract the width of the painting from the segment. Moreover, we also allow painting objects to be placed above edge floor objects if the height of the edge object is less than 1.15 meters. Here, this allows for a painting to be above an object like a counter top, but not behind a taller object like a fridge.
The vertical position of each painting is sampled at $o_y\sim w_{\min} + (w_{\max} - w_{\min})\cdot \text{Beta}(12, 12)$, where $w_{\min}$ is the maximum height of a floor object along the wall line. Here, we allow a painting to be placed above an object along the wall of the room, such as placing it above a counter top. Sampling from $\text{Beta}(12, 12)$ allows for some randomness in the sampling process while still having a large density near the center.
\textbf{Televisions.} Television wall objects may only be placed in living room, kitchen, and bedroom room types. Only 1 wall television may be placed in each room. From our annotations, television objects cannot be placed standalone on the floor. However, a television is often placed in a SAG, on top of an object like a TV stand. So as to not place too many television objects in the same room, we only filter by rooms that do not have a television object already in them. Amongst the remaining rooms, if the room type is a living room, we sample $\text{Bernoulli}(0.8)$ if we should try placing a wall television in the room. For kitchen and bedroom room types, we sample from $\text{Bernoulli}(0.25)$ and $\text{Bernoulli}(0.4)$, respectively. We only consider television objects that could be mounted to a wall (\textit{i.e.} they do not have a base that is sticking out of the object). Television wall objects sample from the same vertical position distribution as painting objects, and follow the same placement on the walls as painting objects.
\subsubsection{Surface Object Placement}
\label{sec:SurfOP}
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{figures/bias-dist-2.pdf}
\caption{The house bias distribution $b_{\textit{house}}$ that offsets the probability of attempting to spawn an object in a receptacle.}
\label{fig:house-bias}
\end{figure}
After placing objects on the floor and wall of the house, we focus on placing objects on the surface of the floor objects just placed. For example, we may place objects like a coffee machine, plate, or knife on of a receptacle like a counter top.
For each receptacle object, we approximate the probability that each object type appears on its surface. We use the hand-modeled AI2-iTHOR or RoboTHOR rooms to obtain these approximations. Here, we compute the total number of times each object type is on the receptacle type and divide it by the total number of times the receptacle type appears across the scenes.
For each receptacle placed on the floor, we look at the probability of each object type $p_{\textit{spawn}}$ that it has been placed on that receptacle. We then iterate over the object types that may be on the receptacle. For each object type, we try spawning it on the receptacle if $\text{Bernoulli}(p_{\textit{spawn}} + b_{\textit{house}} + b_{\textit{receptacle}} + b_{\textit{object}})$, where
\begin{itemize}[leftmargin=0.25in]
\item $b_{\textit{house}}$ denotes the additional bias of how likely objects are to be spawned on receptacles in this particular house. Each house samples
\begin{equation}
b_{\textit{house}}\sim (b_{\textit{house-max}} - b_{\textit{house-min}}) \cdot \text{Beta}(3.5, 1.9) + b_{\textit{house-min}},
\end{equation}
where $b_{\textit{house-min}} = - 0.3$ and $b_{\textit{house-max}}=0.1$. Figure \ref{fig:house-bias} shows the distribution that $b_{\textit{house}}$ forms. Using a house bias allows for some houses to be much cleaner or dirtier than others, whereas cleaner houses would have more objects put away that are not on receptacles.
\item $b_{\textit{receptacle}}$ denotes the additional bias of how likely an object is to be spawned on a receptacle. The default receptacle bias is $0.2$, which is only overwritten by shelving unit ($0.4$ bias), counter top ($0.2$ bias), arm chair ($0$ bias), and chair ($0$ bias). Receptacle biases were manually set based on the empirical quality of the houses.
\item $b_{\textit{object}}$ denotes the additional bias of how likely a particular object is to spawn in the scene. By default, $b_{\textit{object}}$ is set to $0$, and overwritten by house plant ($0.25$ bias), basketball ($0.2$ bias), spray bottle ($0.2$ bias), pot ($0.1$ bias), pan ($0.1$ bias), bowl ($0.05$ bias), and baseball bat ($0.1$ bias). Object biases were also manually set based on the empirical quality of the houses to ensure more target objects appear in each of the procedurally generated houses.
\end{itemize}
Note that $p_{\textit{spawn}} + b_{\textit{house}} + b_{\textit{receptacle}} + b_{\textit{object}}$ may be greater than 1, in which case we will always try to spawn the object on the receptacle, or less than 0, where we will never try to spawn the object on the receptacle.
To attempt to spawn an object of a given type on a receptacle, we will sample an instance of that object type and randomly try $n_{\textit{pa}}=5$ poses of the object to try and fit the object instance on the receptacle. If the object instance fits and does not collide with another object, we keep it there. Otherwise, we try another pose of the object on the receptacle until we reach $n_{\textit{pa}}$ attempted poses. If none of the attempted poses work, we continue on to the next object type that may be on the receptacle.
If the first object of a given type is placed successfully on a receptacle, we attempt to place $n_{\textit{or}}\sim\min(s_{\max}, \text{Geom}(p_{\textit{spawn}}) - 1) - 1$ more objects of that type given type on the receptacle. Here, $s_{\max}$ is set to $3$, representing the maximum number of objects of a type that may be on a receptacle. We ignore the biases to not have too many objects of a given type on the same receptacle.
\subsection{Material and Color Randomization}
\begin{figure}
\centering
\begin{subfigure}{\textwidth}
\centering
\includegraphics[width=0.24\textwidth]{figures/color-randomization/default-vase.jpg}
\includegraphics[width=0.24\textwidth]{figures/color-randomization/vase-1.jpg}
\includegraphics[width=0.24\textwidth]{figures/color-randomization/vase-2.jpg}
\includegraphics[width=0.24\textwidth]{figures/color-randomization/vase-3.jpg}
\caption{Examples of color randomization for a vase object. The original color is shown on the left. Notice that the vase still looks realistic with many possible colors.\\[-0.05in]}
\label{fig:colorRand}
\end{subfigure}
\begin{subfigure}{\textwidth}
\centering
\includegraphics[width=0.24\textwidth]{figures/procthor-material-randomization/om.jpg}
\includegraphics[width=0.24\textwidth]{figures/procthor-material-randomization/o1.jpg}
\includegraphics[width=0.24\textwidth]{figures/procthor-material-randomization/o2.jpg}
\includegraphics[width=0.24\textwidth]{figures/procthor-material-randomization/o3.jpg}
\caption{Examples of material randomization in ProcTHOR. Notice that only the objects randomize in materials, where the walls, floor, and ceiling remain the same.}
\label{fig:materialRand}
\end{subfigure}
\caption{Examples of color randomization and material randomization in ProcTHOR.}
\end{figure}
Several object types may have their color randomized to a randomly sampled RGB value. Specifically, for each vase, statue, or bottle in the scene, we independently sample from $r_c\sim \text{Bernoulli}(0.8)$ to determine if we should randomize the object's color. These objects were chosen because they all still looked natural as any solid color. Figure \ref{fig:colorRand} shows some examples of randomizing the color of a vase.
For each training episode, we sample from $r_m\sim \text{Bernoulli}(0.8)$ to determine if we should randomize the default object materials in the scene. Wall, ceiling, and floor materials are left untouched to preserve $w_{\textit{solid}}$ and $w_{\textit{same}}$ sampling parameters. Materials are only randomized within semantically similar classes, which ensures objects still look and behave like the class they represent. For instance, an apple will not swap materials with an orange. Figure \ref{fig:materialRand} shows some examples of randomizing the materials in the scene.
\subsection{Object States}
\begin{figure}[htbp]
\centering
\begin{subfigure}{\textwidth}
\centering
\includegraphics[width=0.32\textwidth]{figures/open1.jpg}
\includegraphics[width=0.32\textwidth]{figures/open2.jpg}
\includegraphics[width=0.32\textwidth]{figures/open3.jpg}
\caption{Openness state randomness example with a laptop.}
\label{fig:openness}
\end{subfigure}
\\[0.05in]
\begin{subfigure}{\textwidth}
\centering
\includegraphics[width=0.32\textwidth]{figures/dirty.jpg}
\includegraphics[width=0.32\textwidth]{figures/clean.jpg}
\caption{Clean state randomness example with a bed.}
\label{fig:clean}
\end{subfigure}
\\[0.05in]
\begin{subfigure}{\textwidth}
\centering
\includegraphics[width=0.32\textwidth]{figures/off.jpg}
\includegraphics[width=0.32\textwidth]{figures/on.jpg}
\caption{On or off state randomness with a floor lamp.}
\label{fig:toggle}
\end{subfigure}
\\[0.05in]
\caption{Examples of object state randomness.}
\label{fig:stateRand}
\end{figure}
We randomize object states to expose the agent to more diverse objects during training. For instance, instead of always having an open laptop or a clean bed, we randomize the openness of each laptop and if each bed is clean or dirty. Figure \ref{fig:stateRand} shows some examples. Our current set of state randomizations include:
\begin{itemize}[leftmargin=0.25in]
\item \textbf{Toggling objects.} Floor lamp and desk lamp object types have their state toggled on or off.
\item \textbf{Cleaning or dirtying objects.} Bed object types may appear as either clean or dirty.
\item \textbf{Opening or closing objects.} Box and laptop object types may
\end{itemize}
toggling objects on or off (for floor lamp and desk lamp object types), setting objects to clean or dirty (for bed object types), and openness randomizations (for box and laptop object types).
\subsection{Validator}
Once a house is generated, we use a validator to make sure that the agent can successfully navigate to each room in the house, without modifying the scene through interaction (\emph{e.g.}\xspace moving an object out of the way). Specifically, we first make sure the agent can teleport to a location inside the house. Then, from that position, we perform a BFS over neighboring positions on a $0.25\times0.25$ meter grid to obtain all reachable positions from the agent's current position. The validator checks to make sure that every room in the house has at least 5 reachable positions on the grid. If the validator fails, we resample a new house using the same room spec, so as to not change the distribution of room specs that we sample from.
\subsection{Limitations and Future Work}
ProcTHOR-10K only uses 1-floor houses. We plan to support multi-floor houses in ProcTHOR-v2.0. This will allow us to capture a wider range of houses and provide better fine-tuning results. Additionally, we plan to scale up our asset databases by leveraging many open-source 3D asset databases, such as ABO~\cite{collins2021abo}, PartNet~\cite{Mo_2019_CVPR}, ShapeNet~\cite{chang2015shapenet}, Google Scanned Objects~\cite{downs2022google}, and CO3D~\cite{reizenstein2021common}, among others.
\section{\mbox{\sc{ProcTHOR}}\xspace{} Datasheet}
\label{sec:datasheet}
\begin{longtable}{p{0.35\linewidth} |p{0.6\linewidth} }
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Motivation}\vspace{0.10in}}\\
\toprule
For what purpose was the dataset created? & The dataset was created to enable the training of simulated embodied agents in substantially more diverse environments.\\[0.15in]
\midrule
Who created and funded the dataset? &
This work was created and funded by the PRIOR team at Allen Institute for AI. See the contributions section for specific details.\\
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Composition}\vspace{0.10in}}\\
\toprule
What do the instances that comprise the dataset represent? & Each house is specified as a JSON file, which specifies how to populate a 3D Unity scene in AI2-THOR.
\\[0.15in]
\midrule
How many instances are there in total (of each type, if appropriate)? & There are 10K houses released in the dataset, along with the code to sample substantially more. Section~\ref{sec:analysis} shows the distribution of houses in \mbox{\sc{ProcTHOR}}\xspace{}-10K. \\[0.15in]
\midrule
Does the dataset contain all possible instances or is it a sample (not necessarily random) of instances from a larger set? & We make 10K houses available, but more houses can easily be sampled with the procedural generation scripts.\\[0.15in]
\midrule
What data does each instance consist of? & Each house is specified as a JSON file, which precisely describes how our AI2-THOR build should create the house. The procedurally generated JSON files are typically several thousand lines long.\\[0.15in]
\midrule
Is there a label or target associated with each instance? & No.\\[0.15in]
\midrule
Is any information missing from individual instances? & No.\\[0.15in]
\midrule
Are relationships between individual instances made explicit (e.g., users' movie ratings, social network links)? & Each house is generated independently, meaning there are no relationships between the houses.\\[0.15in]
\midrule
Are there recommended data splits? & Yes. See Appendix~\ref{sec:assets}.\\[0.15in]
\midrule
Are there any errors, sources of noise, or redundancies in the dataset? & No.\\[0.15in]
\midrule
Is the dataset self-contained, or does it link to or otherwise rely on external resources (e.g., websites, tweets, other datasets)? & The dataset is self-contained.\\[0.15in]
\midrule
Does the dataset contain data that might be considered confidential? & No.\\[0.15in]
\midrule
Does the dataset contain data that, if viewed directly, might be offensive, insulting, threatening, or might otherwise cause anxiety? & No.\\
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Collection Process}\vspace{0.10in}}\\
\toprule
How was the data associated with each instance acquired? & Each house was procedurally generated. See Appendix~\ref{sec:procthorObjects}.\\[0.15in]
\midrule
If the dataset is a sample from a larger set, what was the sampling strategy? & The dataset consists of 1 million houses sampled from the procedural generation scripts.\\[0.15in]
\midrule
Who was involved in the data collection process? & The authors were the only people involved in constructing the dataset.\\[0.15in]
\midrule
Over what timeframe was the data collected? & Data was collected between the end of 2021 and the beginning of 2022.\\[0.15in]
\midrule
Were any ethical review processes conducted? & No.\\
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Preprocessing/Cleaning/Labeling}\vspace{0.10in}}\\
\toprule
Was any preprocessing/cleaning/labeling of the data done? & Section~\ref{sec:op} describes the labeling that was done to make the assets spawn in realistic places.\newline
We have also gone through every asset in the asset database to make sure the pivots for each asset are facing a consistent direction.\\[0.15in]
\midrule
Was the ``raw'' data saved in addition to the preprocessed/cleaned/labeled data? & There is no raw data associated with the house JSON files.\\[0.15in]
\midrule
Is the software that was used to preprocess/clean/label the data available? & The code to generate the houses is made available.\\
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Uses}\vspace{0.10in}}\\
\toprule
Has the dataset been used for any tasks already? & Yes. See Section~\ref{sec:experiments} of the paper.\\[0.15in]
\midrule
What (other) tasks could the dataset be used for? & The houses can be used in a wide variety of interactive tasks in embodied AI and computer vision.\newline
Any task that can be performed in AI2-THOR can be performed in ProcTHOR. For instance, in embodied AI, the houses may be used for navigation \cite{khandelwal2021simple, perez2021robot, wortsman2019learning, zhu2017target, wijmans2019dd, yitzhak2022clip, luo2022stubborn, Zheng2022TowardsOp}, multi-agent interaction \cite{jain2020cordial, jain2019two, team2021open}, rearrangement and interaction \cite{weihs2021visual, gadre2022continuous, gan2021threedworld, Chitnis2021LearningNe, Srivastava2021BEHAVIORBF}, manipulation \cite{manipulathor, ni2021towards, ehsani2022object, Xia2021ReLMoGenIM}, Sim2Real transfer \cite{Deitke2020RoboTHORAO, kadian2020sim2real, kumar2021rma}, embodied vision-and-language \cite{shridhar2020alfred, padmakumar2021teach, huang2022language, krantz2020beyond, gordon2018iqa, karamcheti2020learning}, audio-visual navigation \cite{chen2020soundspaces, gan2020look, chen2021savi}, and virtual reality interaction \cite{wu2021communicative, murnane2021simulator, higgins2022head}, among others.\newline
In the broader field of computer vision, the dataset may be used to study object detection \cite{kotar2022interactron}; NeRFs \cite{mildenhall2020nerf, tancik2022block, greff2022kubric, li20223d}; segmentation, depth, and optimal flow estimation \cite{Feng2021DeepMO, greff2022kubric}; generative modeling \cite{kim2020learning, koh2021pathdreamer, koh2022simple}; occlusion reasoning \cite{ehsani2018segan}; and pose estimation \cite{Charco2021CameraPE}, among others.\newline
Our framework for loading in procedurally generated houses from a JSON spec also enables the study of scene clutter generation, building more realistic procedurally generated homes, and the development of synthetically generated spaces to train embodied agents in factories \cite{narang2022factory}, offices, grocery stores \cite{mata2022standardsim}, and full procedurally generated cities.\\[0.15in]
\midrule
Is there anything about the composition of the dataset or the way it was collected and preprocessed/cleaned/labeled that might impact future uses? & No.\\[0.15in]
\midrule
Are there tasks for which the dataset should not be used? & Our dataset may be used for both commercial and non-commercial purposes.\\
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Distribution}\vspace{0.10in}}\\
\toprule
Will the dataset be distributed to third parties outside of the entity on behalf of which the dataset was created? & Yes. We plan to make the entirety of the work open-source, including the code used to generate and load houses, the initial static dataset of 1 million procedurally generated house JSON files, and the asset and material databases.\\[0.15in]
\midrule
How will the dataset be distributed? & The static house JSON files will be distributed with a custom Python package.\newline
The code, asset, and material databases will be distributed on GitHub.\\[0.15in]
\midrule
Will the dataset be distributed under a copyright or other intellectual property (IP) license, and/or under applicable terms of use (ToU)? & The house dataset, 3D asset database, and generation code will be released under the Apache 2.0 license. \\[0.15in]
\midrule
Have any third parties imposed IP-based or other restrictions on the data associated with the instances? & No.\\[0.15in]
\midrule
Do any export controls or other regulatory restrictions apply to the dataset or to individual instances? & No.\\
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Maintenance}\vspace{0.10in}}\\
\toprule
Who will be supporting/hosting/maintaining the dataset? & The authors will be providing support, hosting, and maintaining the dataset.\\[0.15in]
\midrule
How can the owner/curator/manager of the dataset be contacted? & For inquiries, email <mattd@allenai.org>.\\[0.15in]
\midrule
Is there an erratum? & We will use GitHub issues to track issues with the dataset.\\[0.15in]
\midrule
Will the dataset be updated? & We expect to continue adding support for new features to continue to make procedurally generated houses even more diverse and realistic. We also intend to support new tasks in the future.\\[0.15in]
\midrule
If the dataset relates to people, are there applicable limits on the retention of the data associated with the instances (e.g., were the individuals in question told that their data would be retained for a fixed period of time and then deleted)? & The dataset does not relate to people. \\[0.15in]
\midrule
Will older versions of the dataset continue to be supported/hosted/maintained? & Yes. Revision history will be available for older versions of the dataset.\\[0.15in]
\midrule
If others want to extend/augment/build on/contribute to the dataset, is there a mechanism for them to do so? & Yes. The work will be open-sourced and we intend to provide support to help others use and build upon the dataset.\\[0.15in]
\bottomrule
\caption{A datasheet \cite{Gebru2021DatasheetsFD} for \mbox{\sc{ProcTHOR}}\xspace{} and \mbox{\sc{ProcTHOR}}\xspace{}-10K.}
\end{longtable}
\newpage
\section{\mbox{\sc{ArchitecTHOR}}\xspace}
\begin{figure}[htbp]
\vspace{-0.1in}
\centering
\includegraphics[width=\textwidth]{figures/architecthor-2.jpg}
\caption{Top-down images of the 5 custom-built interactive validation houses in \mbox{\sc{ArchitecTHOR}}\xspace{}. The goal of these houses is to evaluate interactive agents in more realistic and larger home environments.}
\label{fig:elienv}
\end{figure}
\pagebreak
\subsection{Datasheet}
\label{sec:eli-datasheet}
\begin{longtable}{p{0.35\linewidth} |p{0.6\linewidth} }
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Motivation}\vspace{0.10in}}\\
\toprule
For what purpose was the dataset created? & \mbox{\sc{ArchitecTHOR}}\xspace{} was created to enable the evaluation of embodied agents in large, realistic, and interactive household environments.\\[0.15in]
\midrule
Who created and funded the dataset? &
This work was created and funded by the PRIOR team at Allen Institute for AI. See the contributions section for specific details.\\
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Composition}\vspace{0.10in}}\\
\toprule
What do the instances that comprise the dataset represent? & Instances of the dataset comprise interactive 3D houses that were built in Unity and can be used with our custom build of the AI2-THOR API.
\\[0.15in]
\midrule
How many instances are there in total (of each type, if appropriate)? & There are 10 total houses, comprising 5 validation houses and 5 testing houses.\\[0.15in]
\midrule
Does the dataset contain all possible instances or is it a sample (not necessarily random) of instances from a larger set? & The dataset is self-contained.\\[0.15in]
\midrule
What data does each instance consist of? & Each instance of a house is a Unity scene, which includes data such as the placement of objects, lighting, and texturing.\\[0.15in]
\midrule
Is there a label or target associated with each instance? & No.\\[0.15in]
\midrule
Is any information missing from individual instances? & No.\\[0.15in]
\midrule
Are relationships between individual instances made explicit (e.g., users' movie ratings, social network links)? & Each house was independently created.\\[0.15in]
\midrule
Are there recommended data splits? & Yes. The houses themselves are partitioned as 5 validation houses and 5 testing houses. The assets placed in the house follow the same train/val/test splits used in \mbox{\sc{ProcTHOR}}\xspace{}-10K.\\[0.15in]
\midrule
Are there any errors, sources of noise, or redundancies in the dataset? & No.\\[0.15in]
\midrule
Is the dataset self-contained, or does it link to or otherwise rely on external resources (e.g., websites, tweets, other datasets)? & The dataset is self-contained.\\[0.15in]
\midrule
Does the dataset contain data that might be considered confidential? & No.\\[0.15in]
\midrule
Does the dataset contain data that, if viewed directly, might be offensive, insulting, threatening, or might otherwise cause anxiety? & No.\\
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Collection Process}\vspace{0.10in}}\\
\toprule
How was the data associated with each instance acquired? & Each house was professionally hand-modeled by 3D artists. Most objects placed in the hosues come from the \mbox{\sc{ProcTHOR}}\xspace{} asset database. However, countertops, showers, and many cabinets were custom built.\\[0.15in]
\midrule
If the dataset is a sample from a larger set, what was the sampling strategy? & The dataset consists of 1 million houses sampled from the procedural generation scripts.\\[0.15in]
\midrule
Over what timeframe was the data collected? & The houses were built towards the beginning of 2022.\\[0.15in]
\midrule
Were any ethical review processes conducted? & No.\\
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Preprocessing/Cleaning/Labeling}\vspace{0.10in}}\\
\toprule
Was any preprocessing/cleaning/labeling of the data done? & No.\\[0.15in]
\midrule
Was the ``raw'' data saved in addition to the preprocessed/cleaned/labeled data? & There is no raw data associated with the \mbox{\sc{ArchitecTHOR}}\xspace{} houses.\\[0.15in]
\midrule
Is the software that was used to preprocess/clean/label the data available? & Yes. We will open-source the \mbox{\sc{ArchitecTHOR}}\xspace{} houses and they can be opened and viewed in Unity.\\
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Uses}\vspace{0.10in}}\\
\toprule
Has the dataset been used for any tasks already? & Yes. Please see Section~\ref{sec:experiments} of the paper.\\[0.15in]
\midrule
What (other) tasks could the dataset be used for? & The tasks can be used for any type of navigation and interaction tasks in embodied AI. The houses are built into our build of AI2-THOR, meaning \mbox{\sc{ArchitecTHOR}}\xspace{} can work with any task that can be performed in AI2-THOR.\newline
We especially think \mbox{\sc{ArchitecTHOR}}\xspace{} will be useful as an evaluation suite for evaluating different sets of \mbox{\sc{ProcTHOR}}\xspace{} tasks and evaluating agents trained on different sets of procedurally generated houses.\\[0.15in]
\midrule
Is there anything about the composition of the dataset or the way it was collected and preprocessed/cleaned/labeled that might impact future uses? & No.\\[0.15in]
\midrule
Are there tasks for which the dataset should not be used? & Our dataset may be used for both commercial and non-commercial purposes.\\
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Distribution}\vspace{0.10in}}\\
\toprule
Will the dataset be distributed to third parties outside of the entity on behalf of which the dataset was created? & Yes. All houses in \mbox{\sc{ArchitecTHOR}}\xspace{} will be released to the open-source community and available through our build of the AI2-THOR Python API.\\[0.15in]
\midrule
How will the dataset be distributed? & The houses will be distributed on GitHub and available to open as Unity scenes.\\[0.15in]
\midrule
Will the dataset be distributed under a copyright or other intellectual property (IP) license, and/or under applicable terms of use (ToU)? & \mbox{\sc{ArchitecTHOR}}\xspace{} will be released under the Apache 2.0 license.\\[0.15in]
\midrule
Have any third parties imposed IP-based or other restrictions on the data associated with the instances? & No.\\[0.15in]
\midrule
Do any export controls or other regulatory restrictions apply to the dataset or to individual instances? & No.\\
\bottomrule
\multicolumn{2}{c}{\rule{0in}{0.2in}\textbf{Maintenance}\vspace{0.10in}}\\
\toprule
Who will be supporting/hosting/maintaining the dataset? & The authors will be providing support, hosting, and maintaining the dataset.\\[0.15in]
\midrule
How can the owner/curator/manager of the dataset be contacted? & \textit{Omitted for anonymous review.}\\[0.15in]
\midrule
Is there an erratum? & We will use GitHub issues to track issues with the dataset once it is published.\\[0.15in]
\midrule
Will the dataset be updated? & \mbox{\sc{ArchitecTHOR}}\xspace{} is currently in maintenance mode and we do not expect it to update much from its current state. However, we plan to actively support future AI2-THOR functionalities in \mbox{\sc{ArchitecTHOR}}\xspace, such as support for new robots, more advanced interaction capabilities, and bug fixes.\\[0.15in]
\midrule
If the dataset relates to people, are there applicable limits on the retention of the data associated with the instances (e.g., were the individuals in question told that their data would be retained for a fixed period of time and then deleted)? & The dataset does not relate to people. \\[0.15in]
\midrule
Will older versions of the dataset continue to be supported/hosted/maintained? & Yes. Revision history will be available in the GitHub repository.\\[0.15in]
\midrule
If others want to extend/augment/build on/contribute to the dataset, is there a mechanism for them to do so? & Yes. The work will be open-sourced and we intend to provide support to help others use and build upon the dataset.\\[0.15in]
\bottomrule
\caption{A datasheet \cite{Gebru2021DatasheetsFD} for the artist-designed \mbox{\sc{ArchitecTHOR}}\xspace{} houses.}
\end{longtable}
\subsection{Analysis}
\mbox{\sc{ArchitecTHOR}}\xspace{} consists of 10 remarkably high-quality large interactive 3D houses. Figure \ref{fig:elienv} shows top-down images of the 5 validation houses. Figure \ref{fig:eliExamples} shows some examples of images taken inside of 2 kitchens and a bedroom from \mbox{\sc{ArchitecTHOR}}\xspace{} validation.
\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figures/design-3.jpg}
\caption{Examples of images inside of 2 hand-modeled kitchens and 1 hand-modeled bathroom from \mbox{\sc{ArchitecTHOR}}\xspace{} validation.}
\label{fig:eliExamples}
\end{figure}
\mbox{\sc{ArchitecTHOR}}\xspace{} was built to be much larger than AI2-iTHOR and RoboTHOR. Figure \ref{fig:archNav} shows the size comparisons between comparable hand-built scene datasets in AI2-iTHOR and RoboTHOR, measured in navigable area. Notice that the navigable area in \mbox{\sc{ArchitecTHOR}}\xspace{} is substantially larger than in those. The figure also shows the navigable areas in \mbox{\sc{ProcTHOR}}\xspace{}-10K span the spectrum of navigable areas between AI2-iTHOR, RoboTHOR, and \mbox{\sc{ArchitecTHOR}}\xspace{}.
\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figures/navigable-area.pdf}
\caption{Box plots of the navigable areas for \mbox{\sc{ArchitecTHOR}}\xspace{} compared to AI2-iTHOR, RoboTHOR, and \mbox{\sc{ProcTHOR}}\xspace{}-10K. Validation scenes were used to calculate the data for \mbox{\sc{ArchitecTHOR}}\xspace{}, and training scenes were used to calculate the data for AI2-iTHOR, RoboTHOR, and \mbox{\sc{ProcTHOR}}\xspace{}-10K.}
\label{fig:archNav}
\end{figure}
In total, the creation of the 10 houses in \mbox{\sc{ArchitecTHOR}}\xspace{} took approximately 320 hours of cumulative work by professional 3D artists. Figure \ref{fig:eliTime} shows the time breakdown of which parts of the process took the longest. In particular, the creation of custom assets for the kitchen, such as modeling each of the countertops and cabinets, took the longest amount of time, followed by modeling the 3D structure of house.
\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figures/time-breakdown.pdf}
\caption{Cumulative time breakdown of the development of \mbox{\sc{ArchitecTHOR}}\xspace{} across 3D artists.}
\label{fig:eliTime}
\end{figure}
\pagebreak
\newpage
\section{Input Modalities}
\begin{figure}[hb]
\vspace{-0.1in}
\centering
\begin{subfigure}{0.405\textwidth}
\centering
\includegraphics[width=\textwidth]{figures/rgb.jpg}
\caption{RGB}
\end{subfigure}
\begin{subfigure}{0.405\textwidth}
\centering
\includegraphics[width=\textwidth]{figures/depth.jpg}
\caption{Depth}
\end{subfigure}\\[0.05in]
\begin{subfigure}{0.405\textwidth}
\centering
\includegraphics[width=\textwidth]{figures/instance-segmentation.jpg}
\caption{Instance Segmentation}
\end{subfigure}
\begin{subfigure}{0.405\textwidth}
\centering
\includegraphics[width=\textwidth]{figures/class-segmentation.jpg}
\caption{Semantic Segmentation}
\end{subfigure}\\[0.05in]
\begin{subfigure}{0.405\textwidth}
\centering
\includegraphics[width=\textwidth]{figures/bounding-box.jpg}
\caption{Bounding Box Annotations}
\end{subfigure}
\begin{subfigure}{0.405\textwidth}
\centering
\includegraphics[width=\textwidth]{figures/normals.jpg}
\caption{Surface Normals}
\end{subfigure}\\[0.00in]
\caption{Examples of image-based modalities available in ProcTHOR include RGB, depth, instance segmentation, semantic segmentation, bounding box annotations, and surface normals. More image modalities can be added by modifying the Unity backend.}
\label{fig:modalities}
\end{figure}
\newpage
\section{Experiment details}
This section discusses the training details used for our experiments. We discuss baselines, \mbox{\sc{ProcTHOR}}\xspace{} pre-training, and environment-specific fine-tuning details for the tasks of ObjectNav, ArmPointNav, and rearrangement.
\subsection{ObjectNav experiments}
For ObjectNav experiments, agents are given a target object type (\emph{e.g.}\xspace a bed) and are tasked with finding a path in the environment that navigates to that target object type. The task setup matches what is commonly used in embodied AI \cite{Deitke2020RoboTHORAO, batra2020objectnav, khandelwal2021simple, Ramrakhya2022HabitatWebLE}, although we only utilize forward-facing egocentric RGB images at each time step. All ObjectNav experiments are trained with a simulated LoCoBot (Low Cost Robot) agent \cite{locobot}. The task and training details are described below.
\paragraph{Evaluation.}
Following \cite{Anderson2018OnEO}, an ObjectNav task is considered successful if all of the following conditions are met:
\begin{enumerate}[leftmargin=0.25in]
\item The agent terminates the episode by issuing the \textsc{Done} action.
\item The target object type is within a distance of 1 meter from the agent's camera.
\item The object is visible in the final frame from the agent's camera. For instance, if (1) and (2) are satisfied, and the agent is looking in the direction of the object, but the target object is occluded behind a wall, then the task is unsuccessful. Similarly, if the target object type is located in the opposite direction of where the agent is looking, then the task will be unsuccessful.
\end{enumerate}
We also use SPL to evaluate the efficiency of the agent's trajectory to the target object. SPL is defined and discussed in \cite{Anderson2018OnEO, batra2020objectnav}. A house may have multiple instances of objects for a given type that the agent can successfully reach. For instance, a house may have multiple bedrooms, where each bedroom includes a bed. Here, if the agent navigates to any of the beds, the episode is successful. To calculate SPL in these scenarios, the shortest path length for the task is the minimum shortest path length from the starting position of the agent to any of the reachable target objects of the given type, regardless of which instance the agent navigates towards.
\paragraph{Actions.}
For each of the trained models, we use a discrete action space consisting of 6 actions, which is shown in Table \ref{tab:ONActions}. Following common practice \cite{Deitke2020RoboTHORAO, kadian2020sim2real}, we use stochastic actuation to better simulate noise in the real world.
\begin{table}[htbp]
\centering
\begin{tabular}{ p{0.2\textwidth} p{0.7\textwidth} }
\toprule
\textbf{Action}\qquad\qquad\qquad & \textbf{Description}\\
\midrule
\textsc{MoveAhead} & Attempts to move the agent forward by $\delta_m\sim\mathcal N(\mu=0.25, \sigma=0.01)$ meters from its current facing direction. If moving the agent forward by $\delta_m$ meters results in a collision in the scene (\emph{e.g.}\xspace there is a wall directly in-front of the agent within $\delta_m$ meters), the action fails and the agent's position remains unchanged. \\~\\
\textsc{RotateRight}\newline\textsc{RotateLeft} & Rotates the agent rightwards or leftwards from its current forward facing direction by $\delta_r\sim\mathcal N(\mu=30, \sigma=0.5)$ degrees.\\~\\
\textsc{LookUp}\newline\textsc{LookDown} & Tilts the agent's camera up or down by 30 degrees.\\~\\
\textsc{Done} & A signal from the agent to terminate the episode and evaluate the trajectory from its current state. Discussed in \cite{Anderson2018OnEO}.\\
\toprule\\[-0.05in]
\end{tabular}
\caption{The action space for ObjectNav experiments.}
\label{tab:ONActions}
\end{table}
\paragraph{Model.} We use the relatively simple EmbCLIP~\cite{khandelwal2021simple} training setup for training all ObjectNav experiments. Table~\ref{tab:onhps} shows the hyperparameters used during training, which are adapted from~\cite{khandelwal2021simple}. Except for the ``ProcTHOR+Large'' model trained for HM3D (described below), we otherwise use the same model architecture across ObjectNav experiments. Namely, at each time step, the agent receives a $3\times 224\times224$ egocentric RGB image from its camera. The image is processed with a frozen RN50 CLIP-ResNet visual encoder \cite{Radford2021LearningTV} to produce a $2048\times 7\times7$ visual embedding, $\mathbf V_t$. The embedding is compressed through a 2-layer CNN (going from $2048$ to $128$ to $32$ channels) with $1\times1$ convolutions \cite{szegedy2015going} to obtain a $32\times 7\times 7$ tensor, $\mathbf V^\prime_t$.
The target object type is represented as an integer in $\{0, 1, \ldots, T\}$, where $T$ is the number of target object types used during training. We use an embedding of $t$ to obtain a 32-dimensional vector. The vector is resized to be a $32\times1\times1$ tensor. The tensor is then expanded to be of size $32\times7\times7$, to form our goal target object type embedding $\mathbf G_t$, where the $32\times1\times1$ tensor is copied $7\times7$ times.
We concatenate $\mathbf V^\prime_t$ and $\mathbf G_t$ to form a $64\times7\times7$ tensor, which is compressed with a 2-layer CNN to form a $32\times7\times7$ tensor, $\mathbf Z_t$. The tensor $\mathbf Z$ is flattened to form a 1568 dimensional vector, $\mathbf z_t$. Following \cite{ni2021towards}, we use an embedding of the previous action, represented as an integer in $\{0, 1, \ldots, 5\}$, to obtain a 6 dimensional vector $\mathbf a_{t-1}$. We concatenate $\mathbf z_t$ and $\mathbf a_{t-1}$ to form a 1574 dimensional vector $\mathbf x_t$. The vector $\mathbf x_t$ is passed through a 1-layer GRU \cite{cho2014learning, chung2014empirical} with a hidden belief state $\mathbf b_{t-1}$, of size 512, to obtain $\mathbf b_t$.
Using an actor-critic formulation, the 512-dimensional belief state $\mathbf b_t$ is passed through a 1-linear layer, representing the \textit{actor}, to get a 6-dimensional vector, where each entry represents an action. The 6-dimensional vector is passed through a softmax function to obtain the agent's policy $\pi$ (\emph{i.e.}\xspace the probability distribution over the action space). We sample from $\pi$ to choose the next action. We also pass the belief state $\mathbf b_t$ through a separate 1-linear layer, representing the \textit{critic} to obtain the scalar $v$, estimating the value of the current state.
The ``ProcTHOR+Large'' is similar to the above except we: (1) use the larger RN50x16 CLIP-ResNet model, (2) use a 1024-dimensional hidden belief state in our GRU, and (3) input images to the model at a $512{\times}384$ resolution.
\begin{table}[htbp]
\centering
\begin{tabular}{ l l }
\toprule
\textbf{Hyperparameter}\qquad\qquad\qquad & \textbf{Value}\\
\midrule
Discount factor ($\gamma$) & 0.99 \\
GAE parameter ($\lambda$) & 0.95 \\
Value loss coefficient & 0.5 \\
Entropy loss coefficient & 0.01 \\
Clip parameter ($\epsilon$) & 0.1 \\
Rollout timesteps & 20\\
Rollouts per minibatch & 1\\
Learning rate & 3e-4\\
Optimizer & Adam \cite{kingma2014adam} \\
Gradient clip norm & 0.5 \\
\toprule\\[-0.05in]
\end{tabular}
\caption{Training hyperparameters for ObjectNav experiments.}
\label{tab:onhps}
\end{table}
\paragraph{Training.} Each agent is trained using DD-PPO~\cite{schulman2017proximal, wijmans2019dd}, using a clip parameter $\epsilon=0.1$, an entropy loss coefficient of 0.01, and a value loss coefficient of 0.5. Agents are trained to maximize the cumulative discounted rewards $\sum_{t=0}^H\gamma^t\cdot r_t$, where we set the discount factor $\gamma$ to $0.99$ and the episode's horizon $H$ to 500 steps. We also employ GAE~\cite{schulman2015high} parameterized by $\lambda=0.95$.
\paragraph{Reward.} The reward function follows that of \cite{khandelwal2021simple}. Specifically, at each time step, it is calculated as $r_t = \max(0, \min\Delta_{0:t-1} - \Delta_{t}) + s_t - \rho$, where:
\begin{itemize}[leftmargin=0.25in]
\item $\min\Delta_{0:t-1}$ is the minimum L2 distance from the agent to any of the reachable instances of the target object type that the agent has observed over steps $\{0,1,\ldots,t-1\}$.
\item $\Delta_t$ is the current L2 distance from the agent to the nearest reachable instance of the target object type.
\item $s_t$ is the reward for successfully completing the episode. If the agent takes the \textsc{Done} action and the episode is deemed successful, then $s_t$ is $10$. Otherwise, it is $0$.
\item $\rho$ is the step penalty that encourages the agent to finish the episode quickly. It is set to $0.01$.
\end{itemize}
\paragraph{ProcTHOR pre-training.} We pre-train our ObjectNav agents on the full set of 10k training houses in \mbox{\sc{ProcTHOR}}\xspace{}-10K.\footnote{When training the ``ProcTHOR+Large'' model used in the HM3D challenge, we use a modified set of 10K houses, see below for details.} We pre-train with all $T=16$ target object types, which are shown in Table~\ref{tab:targetObjectTypes}. The agent is trained for 423 million steps, although by 200 million steps, the agent has reached 90\% of its peak performance. We used multi-node training to train on 3 AWS g4dn.12xlarge machines, which takes approximately 5 days to complete.
\newcommand\y{\includegraphics[width=0.135in]{figures/success.pdf}}
\newcommand\n{\includegraphics[width=0.097in]{figures/failure.pdf}}
\begin{table}[htbp]
\centering
\begin{tabular}{lcccc}
\toprule
Object Type & RoboTHOR & HM3D-Semantics & AI2-iTHOR & \mbox{\sc{ArchitecTHOR}}\xspace{}\\
\midrule
Alarm Clock & \y & \n &\y &\y \\[0.035in]
Apple & \y & \n & \y & \y\\[0.035in]
Baseball Bat & \y & \n & \y& \y \\[0.035in]
Basketball & \y & \n & \y& \y \\[0.035in]
Bed & \n & \y & \y& \y \\[0.035in]
Bowl & \y & \n & \y& \y \\[0.035in]
Chair & \n & \y & \y& \y \\[0.035in]
Garbage Can & \y & \n & \y& \y \\[0.035in]
House Plant & \y & \y & \y& \y \\[0.035in]
Laptop & \y & \n & \y& \y \\[0.035in]
Mug & \y & \n & \y& \y \\[0.035in]
Sofa & \n & \y & \y& \y \\[0.035in]
Spray Bottle & \y & \n & \y& \y \\[0.035in]
Television & \y & \y & \y& \y \\[0.035in]
Toilet & \n & \y & \y& \y \\[0.035in]
Vase & \y& \n & \y& \y \\
\toprule\\[-0.05in]
\end{tabular}
\caption{The target objects that are used for each ObjectNav task.}
\label{tab:targetObjectTypes}
\end{table}
\emph{Sampling target object types.} To sample the target object type for a given episode, we restrict ourselves to only sampling target object types that have a possibility of leading to a successful episode. For instance, even if there is an object like an apple in the scene, it might be located in the fridge, and so if it was used as a target object, the agent would never succeed because the object would never appear visible in the frame (without any manipulation actions). Therefore, we impose a constraint that the target object must be visible without any form of manipulation.
For each house, we use an approximation to determine the set of target object instances that the agent can successfully reach, without any manipulation. Specifically, we start by teleporting the agent into the house, and then perform a BFS over a $0.25\times 0.25$ meter grid to obtain the reachable positions in the scene. A position is considered reachable if teleporting to it would not cause any collisions with any other objects, and the agent is successfully placed on the floor. Then, for each candidate instance of every target object type, we look at the nearest 6 reachable agent positions $\langle x^{(a)}, z^{(a)}\rangle$ to the candidate object instance's center position. For each reachable agent position, we perform a raycast from the agent's camera height $y^{(a)}$ to up to 6 random \textit{visibility points} on the object $\langle x^{(o)}, y^{(o)}, z^{(o)}\rangle$. Each object is annotated with visibility points, which are used as a fast approximation to determine if an object is visible with just using a few raycasts, instead of using full segmentation masks. If any of the raycasts from the agent's reachable position to the object's visibility point do not have any collisions with other objects (\emph{e.g.}\xspace the raycast does not collide with the outside of the fridge), and the L2 distance between $\langle x^{(o)}, y^{(o)}, z^{(o)}\rangle$ and $\langle x^{(a)}, y^{(a)}, z^{(a)}\rangle$ is less than 1 meter, then the object instance is considered successfully reachable by the agent.
To choose a target object type, we use an $\epsilon$-greedy sampling method. Specifically, with a probability of $\epsilon=0.2$, we randomly sample a target object type that has at least 1 reachable object instance in a given house. With a probability of $1-\epsilon$, the target object type is the target object type that has been most infrequently sampled in the training process. Since some objects appear much more frequently than others (\emph{e.g.}\xspace beds appear in many more houses than baseball bats), sampling based on the least commonly sampled target object types allows us to maintain a more uniform distribution of sampled target object types.
\paragraph{RoboTHOR.} RoboTHOR is evaluated in both a 0-shot and fine-tuned setting. For 0-shot, we take the pre-trained model on \mbox{\sc{ProcTHOR}}\xspace{}-10K and run it on the RoboTHOR evaluation tasks. For fine-tuning, we reduce $T$ to the 12 RoboTHOR target object types, shown in Table~\ref{tab:targetObjectTypes} and train on the 60 provided training scenes. We fine-tune for 29 million steps, before validation performance starts to go down, on a machine with 8 NVIDIA Quadro RTX 8000 GPUs. Fine-tuning took about 7 hours to complete.
\paragraph{HM3D-Semantics.} We evaluate on HM3D-Semantics in both a 0-shot and fine-tuned setting using the ``ProcTHOR'' and ``ProcTHOR+Large'' architectures described above, these two architectures have slightly different pretraining strategies.
\noindent \emph{``ProcTHOR'' model.} For 0-shot, we take the pre-trained model on \mbox{\sc{ProcTHOR}}\xspace{}-10K, and run it on the HM3D-Semantics evaluation tasks. For fine-tuning, we reduce $T$ to the 6 target object types used in HM3D-Semantics (see Table~\ref{tab:targetObjectTypes}) and train on the 80 provided training houses. We use an early checkpoint from \mbox{\sc{ProcTHOR}}\xspace{} pre-training, specifically from after 220 million steps. We performed fine-tuning on a machine with 8 NVIDIA RTX A6000 GPUs for approximately 220M steps, which took about 43 hours to complete.
\noindent \emph{``ProcTHOR+Large'' model.} We pre-train this model using \mbox{\sc{ProcTHOR}}\xspace{}\textsc{Large}-10K a variant of \mbox{\sc{ProcTHOR}}\xspace{}-10K with houses sampled to better align to the distribution of houses in HM3D. In particular, \mbox{\sc{ProcTHOR}}\xspace{}\textsc{Large}-10K contains 10K procedurally generated houses each of which contains between 4 and 10 rooms (houses in \mbox{\sc{ProcTHOR}}\xspace{}\textsc{Large}-10K thus tend to be much larger than houses in \mbox{\sc{ProcTHOR}}\xspace{}-10K). Moreover, during pretraining we only train our agent to navigate to the 6 object categories used in HM3D-Semantics. Fine-tuning is done identically as above. We use an early checkpoint from \mbox{\sc{ProcTHOR}}\xspace{} pre-training, specifically from after 125 million steps. We performed fine-tuning on a machine with 8 NVIDIA RTX A6000 GPUs for approximately 185M steps taking 85 hours to complete.
\paragraph{AI2-iTHOR.} Similar to RoboTHOR and HM3D-Semantics, we use AI2-iTHOR for both 0-shot and fine-tuning. For 0-shot, we take the pre-trained model on \mbox{\sc{ProcTHOR}}\xspace{}-10K, and run it on the AI2-iTHOR evaluation tasks. Since the AI2-iTHOR evaluation tasks use the full set of target objects used during \mbox{\sc{ProcTHOR}}\xspace{} pre-training, we do not need to update $T$. For fine-tuning, we use a machine with 8 TITAN V GPUs. We fine-tune for approximately 2 million steps before validation performance starts to go down, which takes about 1.5 hours to complete.
\paragraph{ArchitecTHOR.} Since \mbox{\sc{ArchitecTHOR}}\xspace{} does not include any training scenes, we only use it for evaluation of the \mbox{\sc{ProcTHOR}}\xspace{} pre-trained model. As shown in Table~\ref{tab:targetObjectTypes}, \mbox{\sc{ArchitecTHOR}}\xspace{} evaluation uses the full-set of target object types that are used during \mbox{\sc{ProcTHOR}}\xspace{} pre-training.
\subsection{ArmPointNav experiments}
In ArmPointNav, we followed the same architecture as \cite{manipulathor}. The task is to move a target object from a starting location to a goal location using the relative location of the target in the agent's coordinate frame. The visual input is encoded using 3 convolutional layers followed by a linear layer to obtain a $512$ feature vector. The 3D relative coordinates, specifying the targets, are embedded using three linear layers to a $512$ embedding which combined with the visual encoding is input to the GRU. The agent is allowed to take up to 200 steps or the episode will automatically fail.
\begin{table}[htbp]
\centering
\begin{tabular}{ l l }
\toprule
\textbf{Hyperparameter}\qquad\qquad\qquad & \textbf{Value}\\
\midrule
Learning rate & 3e-4\\
Gradient steps & 128\\
Discount factor ($\gamma$) & 0.99 \\
GAE parameter ($\lambda$) & 0.95 \\
Gradient clip norm & 0.5 \\
Rotation Degrees & 45\\
Step penalty & -0.01\\
Number of RNN Layers & 1\\
Rollouts per minibatch & 1\\
Optimizer & Adam \cite{kingma2014adam} \\
\toprule\\[-0.05in]
\end{tabular}
\caption{Training hyperparameters for ArmPointNav experiments.}
\label{tab:apnHp}
\end{table}
\paragraph{ProcTHOR pre-training.} We pre-train our model on a subset of 7000 houses, on 58 object categories. For each episode, we move the agent to a random location, randomly choose an object in the room that is pickupable, and randomly select a target location. We train our model for 100M frames, running on 4 AWS g4dn.12xlarge machines. Running on a total of 16 GPUs and 192 CPU cores took 3 days of training. Table \ref{tab:apnHp} shows the hyperparameters used for pre-training.
\paragraph{AI2-iTHOR evaluation.} We evaluate our model on 20 test rooms of AI2-THOR (5 kitchens, 5 living rooms, 5 bedrooms, 5 bathrooms), on a subset of 28 object categories for a total of 528 tasks. We attempted to perform fine-tuning on AI2-iTHOR, but none of the fine-tuning models performed better than the zero-shot model trained with \mbox{\sc{ProcTHOR}}\xspace{} pre-training.
\subsection{Rearrangement experiments}
Following \cite{weihs2021visual,khandelwal2021simple}, we use imitation learning (IL) to train all models for the 1-phase modality of the task. We divide the full training of the final model into two stages: pre-training in \mbox{\sc{ProcTHOR}}\xspace{} and fine-tuning in AI2-iTHOR.
\begin{table}[htbp]
\centering
\begin{tabular}{ l l }
\toprule
\textbf{Hyperparameter}\qquad\qquad\qquad & \textbf{Value}\\
\midrule
Rollout timesteps & 64\\
Batch size & 7,680 \\
Learning rate & $7.4\cdot10^{-4}$\\
Optimizer & Adam \cite{kingma2014adam} \\
Gradient clip norm & 0.5 \\
BC$^{\text{tf}=1}$ steps & 200,000 \\
DAgger steps & 2,000,000 \\
\toprule\\[-0.05in]
\end{tabular}
\caption{ProcTHOR pre-training hyperparameters for Rearrange experiments.}
\label{tab:rearHp}
\end{table}
\paragraph{ProcTHOR pre-training.} We pre-train our model on a subset of 2,500 one and two-room \mbox{\sc{ProcTHOR}}\xspace{}-10K houses where a number of 1 to 5 objects are shuffled from their target poses in each episode, including two shuffle modalities: different openness degree (at most one object in an episode) and a different location (up to five objects in an episode). For each house, 20 episodes are sampled such that all shuffled objects are in the same room where the agent is initially spawned. We train with $2\cdot10^{5}$ steps of teacher forcing and 2 million steps of dataset aggregation \cite{Ross2011ARO}, followed by about 180 million steps of behavior cloning. We use a small set of 200 episodes sampled from 20 validation houses unseen during training to select a checkpoint to evaluate every 5 million steps.
Running on 6 AWS g4dn.12xlarge (totaling 24 GPUs and 288 virtual CPU cores), pre-training with 240 parallel simulations took 4 days. Table~\ref{tab:rearHp} shows the hyperparameters used during pre-training.
\paragraph{AI2-iTHOR fine-tuning.} We use the training dataset provided by \cite{roomr-challenge} (4,000 episodes over 80 single-room scenes), and a small subset of 200 episodes from the also provided full validation set to perform model selection. We fine-tune for 3 million steps with 64-step long rollouts, 6 additional million steps with 96-step long rollouts, and another 6 million steps with 128-step long rollouts.
Running on 8 Titan X GPUs and 56 virtual CPU cores, fine-tuning with 40 parallel simulations took 16 hours.
\section{Performance Benchmark}
To calculate the FPS performance benchmark shown in the Analysis section, we partitioned houses into small houses (1-3 room houses) and large houses (7-10 room houses). For the navigation benchmark, we perform move and rotate actions. For the interaction benchmark, we performing a pushing object action. For querying the environment for data, we obtain a piece of metadata from the environment that is not commonly provided at each time step (\emph{e.g.}\xspace checking the dimensions of the agent). At each time step, we render a single $3\times224\times224$ RGB image from the agent's egocentric perspective. Experiments were conducted on a server with 8 NVIDIA Quadro RTX 8000 GPUs. We employ 15 processes for the single GPU tests and 120 processes for the 8 GPU tests, evenly divided across the GPUs. Table~\ref{tab:baseFps} shows the comparisons to AI2-iTHOR and RoboTHOR.
\begin{table}
\centering
\small
\resizebox{\textwidth}{!}{%
\begin{tabular}{l cc c cc c cc}
\toprule
& \multicolumn{2}{c}{Navigation FPS} && \multicolumn{2}{c}{Isolated Interaction FPS} && \multicolumn{2}{c}{Environment Query FPS} \\
\cmidrule{2-3}\cmidrule{5-6}\cmidrule{8-9}
Compute & AI2-iTHOR & RoboTHOR && AI2-iTHOR & RoboTHOR && AI2-iTHOR & RoboTHOR \\
\midrule
8 GPUs & 5,779{\scriptsize$\pm$189} & 9,195{\scriptsize$\pm$294} && 5,411{\scriptsize$\pm$190} & 6,331{\scriptsize$\pm$137} && 463,446{\scriptsize$\pm$18,577} & 412,550{\scriptsize$\pm$21,806} \\
1 GPU & 1,316{\scriptsize$\pm$19} & 1,648{\scriptsize$\pm$11} && 1,451{\scriptsize$\pm$72} & 1,539{\scriptsize$\pm$5} && 169,092{\scriptsize$\pm$4,232} & 163,660{\scriptsize$\pm$3,336}\\
1 Process & 180{\scriptsize$\pm$9} & 340{\scriptsize$\pm$26} && 141{\scriptsize$\pm$2} & 217{\scriptsize$\pm$1} &&
15,584{\scriptsize$\pm$156} & 15,578{\scriptsize$\pm$164}\\
\cmidrule{2-3}\cmidrule{5-6}\cmidrule{8-9}
& \mbox{\sc{ProcTHOR}}\xspace{}-S & \mbox{\sc{ProcTHOR}}\xspace{}-L && \mbox{\sc{ProcTHOR}}\xspace{}-S & \mbox{\sc{ProcTHOR}}\xspace{}-L && \mbox{\sc{ProcTHOR}}\xspace{}-S & \mbox{\sc{ProcTHOR}}\xspace{}-L \\
\cmidrule{2-3}\cmidrule{5-6}\cmidrule{8-9}
8 GPUs & 8,599{\scriptsize$\pm$359} & 3,208{\scriptsize$\pm$127} && 6,488{\scriptsize$\pm$250} & 2,861{\scriptsize$\pm$107} && 480,205{\scriptsize$\pm$19,684} & 433,587{\scriptsize$\pm$18,729} \\
1 GPU & 1,427{\scriptsize$\pm$74} & 6,280{\scriptsize$\pm$40} && 1,265{\scriptsize$\pm$71} & 597{\scriptsize$\pm$37} && 160,622{\scriptsize$\pm$2,846} & 157,567{\scriptsize$\pm$2,689}\\
1 Process & 240{\scriptsize$\pm$69} & 115{\scriptsize$\pm$19} && 180{\scriptsize$\pm$42} & 93{\scriptsize$\pm$15} &&
14,825{\scriptsize$\pm$199} & 14,916{\scriptsize$\pm$186}\\
\bottomrule
\end{tabular}%
}
\vspace{0.05in}
\caption{Comparing performance benchmarks in \mbox{\sc{ProcTHOR}}\xspace{} to baselines in AI2-iTHOR and RoboTHOR. FPS for navigation, interaction, and querying the environment for data. \mbox{\sc{ProcTHOR}}\xspace{}-S and \mbox{\sc{ProcTHOR}}\xspace{}-L denotes small and large \mbox{\sc{ProcTHOR}}\xspace{} houses, respectively.}
\label{tab:baseFps}
\vspace{-0.2in}
\end{table}
\section{Broader Impact}
This work focuses on increasing the generalization abilities of robotic agents on various tasks. We specifically focus on robots that operate in household environments. More capable robotic agents can help improve the lives of many by assisting with cooking, cleaning, and providing social interaction. Furthermore, robots can provide a wide range of health benefits. For example, they could give domestic assistance to individuals with physical and mental disabilities and the elderly. They could provide social and emotional support to children, adolescents, and adults, such as delivering personalized educational content, reducing loneliness, and counseling in times of crisis. We can also use home-assisted robots to monitor and provide feedback on people's physical activity, sleep, and diet.
However, the adoption of home-assisted robots could have several undesirable social consequences. One is that home-assisted social robots may lead individuals to become more dependant on robots for companionship and care, leading to increased social isolation and loneliness. Another concern is that they may exacerbate existing inequities, as those who can afford to buy and maintain robots will have access to care and assistance that those who cannot will not. Furthermore, because robots would have access to sensitive information about people's daily lives, they could threaten privacy and security. Finally, robots have the potential to be exploited for malicious intent, such as for mass surveillance or being used for autonomous warfare. As a community, we need to work to reduce the risks of social robots while maximizing the benefits for the common good.
| {
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{"url":"https:\/\/ham.stackexchange.com\/questions\/5547\/what-is-the-difference-between-channel-frequency-band-in-rf","text":"# What is the difference between channel & frequency & band in RF?\n\nI am reading about wireless networks basics. I found three terms I cannot find exact definition for: channel, frequency band, frequency.\n\nCan anyone give exact definitions for them?\n\n## 5 Answers\n\nIf you don't know what a frequency is, you need to read up on waves-in-general and radio waves. But the other two terms can be defined in terms of frequency; frequencies are the \u201cnatural\u201d thing and everything else are things people invented on top of that.\n\nA frequency band, or band, is a range of frequencies with a specific least frequency and greatest frequency. Generally bands are used to describe some relevant range:\n\n\u2022 A radio is capable of operating within some band of frequencies; outside that band its performance will not meet specification or it will be incapable of tuning there.\n\u2022 The legal limits on transmissions are defined in terms of many bands; when people say \"the 2.4 GHz band\" they mean the ISM band that extends from 2.400 GHz to 2.500 GHz, which is purely a legal definition and has no technical significance other than that devices may be internally restricted to operate in those bounds.\n\u2022 When a signal is actually transmitted, we can talk about the band of that signal, that is, the range of frequencies which have significant\/useful signal power on them. This usage is where the terms \"in-band\" and \"out-of-band\" come from. (The bandwidth of a signal is the size of the band, the lowest frequency subtracted from the highest frequency.)\n\nChannel has two different meanings:\n\n\u2022 Usage of a band can be channelized, which means that the radios which transmit on it do not pick frequencies arbitrarily but stick to a certain step size (e.g. 10 KHz for CB radio, so frequencies like 27.105, 27.115, 27.125 MHz). This makes it easier for a receiver to match a transmitter, and allows more efficient use overall as there are no wasted narrow gaps between signals. If you want to see a spectacular example of precise channelization, take a look at broadcast FM radio: stations with added HD Radio digital signals transmit right up to the limits of their channel.\n\n\u2022 In communications theory, the channel is the medium that carries the signal. This is a different kind of word than the others because it's an abstraction that is not about frequency, but it is like the above in that to look at an RF channel you ignore everything outside of the frequency range that defines the channel. Within that range, you care about the effects on the signal \u2014 loss, noise, multipath, fading, etc. \u2014 and those effects are frequency-dependent on a larger scale and possibly even within the channel.\n\nA channel is a generally accepted stopping point - somewhere that we know other people or devices will be listening. For example, in the United States, amateurs get access to 5 distinct channels on the 5 MHz band. Or your WiFi router uses several channels, but most of those channels overlap.\n\nA frequency band is a range of frequencies. They're usually referred to by the wavelength (e.g. 40 meters is the band from 7000 KHz to 7300 KHz).\n\nA frequency is the reference point for tuning your transceiver. Depending on how you're communicating, you'll be using far more than that single frequency, but when people mention a frequency, that's what they're referring to - where you should set your transceiver.\n\n\u2022 3.5 MHz band or 5 MHz band? Nov 29, 2015 at 21:09\n\u2022 D'OH! I'll fix that. Nov 30, 2015 at 14:14\n\nFor regulatory purposes, a frequency is usually used to refer to a carrier frequency, which has a specific meaning related to the mode of transmission (for example, in an SSB transmitter the carrier frequency is in theory never actually transmitted, but in a morse code CW transmitter it is the only frequency ever transmitted).\n\nA frequency band is a range of frequencies with a lower and upper limit. If the regulations state that you must only transmit signals within a specified band, then you must make sure that your transmitted signals never go outside that range of frequencies - again, very easy to determine when transmitting CW, not so easy with SSB, AM or FM (requires knowledge of the bandwidth of the transmitted signal on each side of the carrier).\n\nA 'channel' is an agreed-upon set of specific frequencies with additional information included in the agreement. For example, in the amateur 2m and 70cm bands, a portion of the band is 'channelised' and set aside for repeaters. These repeaters use specific spot frequencies for both their inputs and outputs, and have certain other requirements regarding mode (FM), deviation (for example, max. 3kHz) and other requirements for CTCSS tones and the like.\n\nEven though this is an amateur \"ham\" radio forum, the OP's question seems to be about how these terms are used for wireless networks or maybe also in the field of telecommunication system engineering.\n\nA channel has a more defined meaning in telecommunications and generally implied the use of specific modulation\/demodulation schemes (e.g. FSK, PSK, etc.) and also specific management of control parameters and channel performance. This is all done to ensure quality communications.\n\nWhole books in telecommunications engineering are written about channels and how to use them effectively for digital (usually) communications. Topics such as phase distortion, attenuation distortion, level control, channel capacity, equalization are all topics associated with channels in telecommunications engineering.\n\nAlternatively, in ham radio, the use of the term channel is rare and about the only times I have heard it mention by someone it is referring to the US Citizens Band channels.\n\n\u2022 A bit of non-US perspective: Here in Europe, it's not uncommon to use channels for FM and digital voice. There are specified, named, 10 kHz channels for HF FM use, which can be either simplex or repeater channels, there are 12.5 kHz VHF channels, again simplex and repeater with their names and so on. Nov 29, 2015 at 21:13\n\u2022 And, the 60 meter band (US) is channelized but I have never operated on the 60 meter band. In fact, I have disabled switching to it with the band up\/down buttons on my K3. Nov 30, 2015 at 1:32\n\nFrequency $$f$$ is the number of cycles that an RF electromagnetic wave undergoes per second.\n\nFrequency band, sometimes denoted by $$B$$, is simply a range of frequencies (e.g. the band from 1-2 MHz).\n\n\u2022 It may, however, refer to a standard band of frequencies established in some government regulation.\n\u2022 Ham radio bands are usually referred to in terms of their wavelength rather than frequency. Wavelength refers to the distance traveled by an electromagnetic wave in 1 cycle. The wavelength of a band is given by the dividing the speed of light ($$c$$ = 299,792,458 m\/s) by the average frequency within the band, perhaps rounded to some nearest decimal place. (For example, the U.S. 40 meter ham radio band is from 7.0 to 7.3 MHz. Dividing $$c$$ by the average frequency $$f$$ = 7.15 MHz yields 41.9 m, which rounding to the nearest 10 is 40 m)\n\nChannel can be understood as \"mini-band\" within a band. For example, the CB radio band in the U.S. occupies 26.96 MHz to 27.41 MHz, with 40 distinct channels, allocated according to this chart by the FCC. Equipment manufactured for the CB service must provide discrete channels only according to the regulation. Wireless telephone services have similar channel allocations (though a cell phone user won't notice). Ham radio has no such channel restrictions.\n\n\u2022 You might add to your fine answer by saying that channels are meant to be just wide enough for one signal, and that the intent is to organize the frequencies used to minimize interference by eliminating overlapping signals. Please feel to plagiarize from this comment all you like ;) Feb 23 at 17:42","date":"2022-05-21 10:10:51","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 5, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6387939453125, \"perplexity\": 1022.4825906672706}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-21\/segments\/1652662539049.32\/warc\/CC-MAIN-20220521080921-20220521110921-00015.warc.gz\"}"} | null | null |
{"url":"https:\/\/codereview.stackexchange.com\/questions\/114959\/java-string-iterations","text":"Java String iterations\n\nI am working with some Java code. Basically I have a wrapper class that holds a string and implements some of the many useful python string methods in Java. My goal here is to implement the Python method .ljust and my hope is to be as efficient as possible. Currently, I am using a while loop which I imagine is terrible inefficient especially because it includes a +=. What's more, I am not sure which of the following alternatives is more efficient\n\nString news = \"\";\nnews = this.toString();\nint length = news.length();\nwhile (length < size) {\nnews += \" \";\nlength++;\n}\nreturn new PythonString(news);\n\n\nIn the above case, news.length() is only called once, but now there is an extra int and a new instruction length++.\n\nThe other option would be\n\nString news = \"\";\nnews = this.toString();\nwhile (news.length() < size) {\nnews += \" \";\n}\nreturn new PythonString(news);\n\n\nIn this case, news.length() is called every time.\n\nI am interested in perspectives on which of these alternatives is most efficient as well as any other optimizations you could provide for this method, which is meant to pad a string with size spaces to the right so that all following characters line up at the same column.\n\n\u2022 you should actually measure the differences. There are several options to do this, as explained in the answers. \u2013\u00a0eis Dec 24 '15 at 11:29\n\nI am interested in perspectives on which of these alternatives is most efficient\n\nUsing StringBuilder in the loop instead of += will likely be far faster than either of your current approaches, especially as size - length gets big. I'm not sure how much more space it would take.\n\n\u2022 Space-wise, likely normally less as you won't need to constantly reallocate. \u2013\u00a0Veedrac Dec 25 '15 at 10:27\n\nThe String class can do this already, see answer here: https:\/\/stackoverflow.com\/a\/391978\/4217399. You can always look at the source of the String class to check how it's done, should be fairly optimized there, as it's a part of the JDK. It's actually offloaded to the java.util.Formatter class.\n\n\u2022 I thought I looked through the documentation, that is why i implemented these, but thanks for the info \u2013\u00a0Tom Dec 24 '15 at 16:13\n\nWhat your code seems to be doing is to add spaces at the end of a string to make it at least size long.\n\nYou could write it in a way that better expresses your intent:\n\nString news = this.toString(); \/\/no need to allocate an empty string first\nint padding = size - news.length();\n\n\n\nAnd have a utility method that does the appending:\n\nprivate static String appendSpaces(String s, int n) {\nif (n <= 0) return s;\n\nchar[] spaces = new char[n];\nArrays.fill(spaces, ' ');\nreturn s.concat(new String(spaces));\n}\n\n\nThis will also be more efficient than your approach of concatenating the spaces one by one.\n\n\u2022 This. No need to reinvent the wheel when all the cogs are already there! \u2013\u00a0Boris the Spider Dec 24 '15 at 12:55","date":"2021-08-06 02:30:49","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.317504346370697, \"perplexity\": 1263.314829266436}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-31\/segments\/1627046152112.54\/warc\/CC-MAIN-20210806020121-20210806050121-00353.warc.gz\"}"} | null | null |
{"url":"https:\/\/en.wikipedia.org\/wiki\/Schwinger_limit","text":"# Schwinger limit\n\nA Feynman diagram (box diagram) for photon\u2013photon scattering; one photon scatters from the transient vacuum charge fluctuations of the other.\n\nIn quantum electrodynamics (QED), the Schwinger limit is a scale above which the electromagnetic field is expected to become nonlinear. The limit was first derived in one of QED's earliest theoretical successes by Fritz Sauter in 1931[1] and discussed further by Werner Heisenberg and his student Hans Heinrich Euler.[2] The limit, however, is commonly named in the literature[3] for Julian Schwinger, who derived the leading nonlinear corrections to the fields and calculated the rate of electron\u2013positron pair production in a strong electric field.[4] The limit is typically reported as a maximum electric field or magnetic field before nonlinearity for the vacuum of\n\n${\\displaystyle E_{\\text{c}}={\\frac {m_{\\text{e}}^{2}c^{3}}{q_{\\text{e}}\\hbar }}\\simeq 1.32\\times 10^{18}\\,\\mathrm {V} \/\\mathrm {m} }$\n${\\displaystyle B_{\\text{c}}={\\frac {m_{\\text{e}}^{2}c^{2}}{q_{\\text{e}}\\hbar }}\\simeq 4.41\\times 10^{9}\\,\\mathrm {T} ,}$\n\nwhere me is the mass of the electron, c is the speed of light in vacuum, qe is the elementary charge, and \u0127 is the reduced Planck constant. These are enormous field strengths. Such an electric field is capable of accelerating a proton from rest to the maximum energy attained by protons at the Large Hadron Collider in only approximately 5 micrometers. The magnetic field is associated with birefringence of the vacuum and is exceeded on magnetars.\n\nIn a vacuum, the classical Maxwell's equations are perfectly linear differential equations. This implies \u2013 by the superposition principle \u2013 that the sum of any two solutions to Maxwell's equations is another solution to Maxwell's equations. For example, two intersecting beams of light should simply add together their electric fields and pass right through each other. Thus Maxwell's equations predict the impossibility of any but trivial elastic photon\u2013photon scattering. In QED, however, non-elastic photon\u2013photon scattering becomes possible when the combined energy is large enough to create virtual electron\u2013positron pairs spontaneously, illustrated by the Feynman diagram in the adjacent figure.\n\nA single plane wave is insufficient to cause nonlinear effects, even in QED.[4] The basic reason for this is that a single plane wave of a given energy may always be viewed in a different reference frame, where it has less energy (the same is the case for a single photon). A single wave or photon does not have a center of momentum frame where its energy must be at minimal value. However, two waves or two photons not traveling in the same direction always have a minimum combined energy in their center of momentum frame, and it is this energy and the electric field strengths associated with it, which determine particle\u2013antiparticle creation, and associated scattering phenomena.\n\nPhoton\u2013photon scattering and other effects of nonlinear optics in vacuum is an active area of experimental research, with current or planned technology beginning to approach the Schwinger limit.[5] It has already been observed through inelastic channels in SLAC Experiment 144.[6][7] However, the direct effects in elastic scattering have not been observed. As of 2012, the best constraint on the elastic photon\u2013photon scattering cross section belonged to PVLAS, which reported an upper limit far above the level predicted by the Standard Model.[8]\n\nProposals were made to measure elastic light-by-light scattering using the strong electromagnetic fields of the hadrons collided at the LHC.[9] In 2019, the ATLAS experiment at the LHC announced the first definitive observation of photon\u2013photon scattering, observed in lead ion collisions that produced fields as large as 1025\u00a0V\/m, well in excess of the Schwinger limit.[10] Observation of a cross section larger or smaller than that predicted by the Standard Model could signify new physics such as axions, the search of which is the primary goal of PVLAS and several similar experiments. ATLAS observed more events than expected, potentially evidence that the cross section is larger than predicted by the Standard Model, but the excess is not yet statistically significant.[11]\n\nThe planned, funded ELI\u2013Ultra High Field Facility, which will study light at the intensity frontier, is likely to remain well below the Schwinger limit[12] although it may still be possible to observe some nonlinear optical effects.[13] Such an experiment, in which ultra-intense light causes pair production, has been described in the popular media as creating a \"hernia\" in spacetime.[14]\n\n## References\n\n1. ^ F. Sauter (1931), \"\u00dcber das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs\", Zeitschrift f\u00fcr Physik (82 ed.): 742\u2013764, doi:10.1007\/BF01339461, S2CID\u00a0122120733\n2. ^ W. Heisenberg and H. Euler (1936), \"Folgerungen aus der Diracschen Theorie des Positrons\", Zeitschrift f\u00fcr Physik (98 ed.), 98 (11\u201312): 714\u2013732, doi:10.1007\/BF01343663, S2CID\u00a0120354480CS1 maint: uses authors parameter (link) English translation\n3. ^ M. Buchanan (2006), \"Thesis: Past the Schwinger limit\", Nature Physics (2 ed.): 721, doi:10.1038\/nphys448, S2CID\u00a0119831515\n4. ^ a b J. Schwinger (1951), \"On Gauge Invariance and Vacuum Polarization\", Phys. Rev. (82 ed.), 82 (5): 664\u2013679, doi:10.1103\/PhysRev.82.664\n5. ^ Stepan S. Bulanov, Timur Zh. Esirkepov, Alexander G. R. Thomas, James K. Koga, and Sergei V. Bulanov (2010), \"On the Schwinger limit attainability with extreme power lasers\", Phys. Rev. Lett. (105 ed.), 105 (22): 220407, arXiv:1007.4306, doi:10.1103\/PhysRevLett.105.220407, PMID\u00a021231373, S2CID\u00a036857911CS1 maint: uses authors parameter (link)\n6. ^ C. C. Bula, K. T. McDonald, E. J. Prebys, C. Bamber, S. Boege, T. Kotseroglou, A. C. Melissinos, D. D. Meyerhofer, W. Ragg, D. L. Burke, R. C. Field, G. Horton-Smith, A. C. Odian, J. E. Spencer, D. Walz, S. C. Berridge, W. M. Bugg, K. Shmakov, and A. W. Weidemann (1996), \"Observation of Nonlinear Effects in Compton Scattering\", Phys. Rev. Lett. (76 ed.), 76 (17): 3116\u20133119, doi:10.1103\/PhysRevLett.76.3116, PMID\u00a010060879CS1 maint: uses authors parameter (link)\n7. ^ C. Bamber, S. J. Boege, T. Koffas, T. Kotseroglou, A. C. Melissinos, D. D. Meyerhofer, D. A. Reis, W. Ragg, C. Bula, K. T. McDonald, E. J. Prebys, D. L. Burke, R. C. Field, G. Horton-Smith, J. E. Spencer, D. Walz, S. C. Berridge, W. M. Bugg, K. Shmakov, and A. W. Weidemann (1999), \"Studies of nonlinear QED in collisions of 46.6\u00a0GeV electrons with intense laser pulses\", Phys. Rev. D (60 ed.), 60 (9), doi:10.1103\/PhysRevD.60.092004CS1 maint: uses authors parameter (link)\n8. ^ G. Zavattini et al., \"Measuring the magnetic birefringence of vacuum: the PVLAS experiment\", Accepted for publication in the Proceedings of the QFEXT11 Benasque Conference, [1]\n9. ^ D. d'Enterria, G. G. da Silveira (2013), \"Observing Light-by-Light Scattering at the Large Hadron Collider\", Phys. Rev. Lett. (111 ed.), 111 (8): 080405, arXiv:1305.7142, doi:10.1103\/PhysRevLett.111.080405, PMID\u00a024010419, S2CID\u00a043797550CS1 maint: uses authors parameter (link)\n10. ^ ATLAS Collaboration, \"ATLAS observes light scattering off light\", [2], (2019)\n11. ^ The ATLAS Collaboration, \"Observation of light-by-light scattering in ultraperipheral Pb+Pb collisions with the ATLAS detector\", [3], (2019)\n12. ^ T. Heinzl, \"Strong-Field QED and High Power Lasers\", Plenary talk QFEXT11 Benasque Conference, [4][5]\n13. ^ G. Yu. Kryuchkyan and K. Z. Hatsagortsyan (2011), \"Bragg Scattering of Light in Vacuum Structured by Strong Periodic Fields\", Phys. Rev. Lett. (107 ed.), 107 (5): 053604, arXiv:1102.4013, doi:10.1103\/PhysRevLett.107.053604, PMID\u00a021867070, S2CID\u00a025991919CS1 maint: uses authors parameter (link)\n14. ^ I. O'Neill (2011). \"A Laser to Give the Universe a Hernia?\". Discovery News. Archived from the original on November 3, 2011.","date":"2020-09-20 02:36:48","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 2, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8254802823066711, \"perplexity\": 3416.1787610030956}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-40\/segments\/1600400193087.0\/warc\/CC-MAIN-20200920000137-20200920030137-00740.warc.gz\"}"} | null | null |
Legit Reviews Reviews XFX Radeon R9 290 Double Dissipation Video Card Review
XFX Radeon R9 290 Double Dissipation Video Card Review
Posted by Nathan Kirsch | Wed, Apr 02, 2014 - 10:53 AM
Jump To: Page 1: XFX Throws Some DDs Up On the Radeon R9 290 Page 2: XFX Radeon R9 290 Double Dissipation Retail Box and Bundle Page 3: Test System Page 4: Batman: Arkham Origins Page 5: Battlefield 4 Page 6: Crysis 3 Page 7: Far Cry 3 Page 8: Metro Last Light Page 9: Thief Page 10: 3DMark 2013 Page 11: Temperature & Noise Testing Page 12: VRM Temperature Concerns Page 13: Power Consumption Page 14: XFX DD Radeon R9 290 GPU Overclocking Page 15: Final Thoughts and Conclusions
XFX Throws Some DDs Up On the Radeon R9 290
The AMD Radeon R9 290X graphics card came out in October 2013 and gets a ton of attention due to the fact that it is the flagship single-GPU card by AMD. The AMD Radeon R9 290 came out a month later and doesn't get much attention since it isn't the flagship card. The funny thing is both share the same Hawaii GPU, albeit the Radeon R9 290 GPU has had 256 stream processors (9% fewer) and 16 texture units (9% fewer) fused off along with a 53MHz lower core clock (5% decrease). If you are okay with owning something other than the flagship card, the AMD Radeon R9 290 might be the right card for you.
Today we will be reviewing the XFX Double Dissipation Radeon R9 290 4GB graphics card that is sold under part number R9290AEDFD for $439.99 shipped with a Limited Lifetime Warranty if you register within 30 days of purchase. It is powered by a single 28nm AMD Hawaii GPU that has 2,560 stream processors running at 947MHz and the 4GB of GDDR5 memory on a 512-bit wide bus that is clocked at 1250MHz (5000MHz effective). These clock speeds are fairly standard for a Radeon R9 290 from any brand, so we wouldn't consider this a factory overclocked card. If you were looking for a factory overclocked card there is the XFX Black Edition DD R9 290 that is listed under part number R9290AEDBD for $504.99 shipped. That Black Edition series card is factory overclocked up to 980MHz and for that you'll be paying an extra $65. Paying an extra $65 to get the same card with a 33MHz higher core clock is far from a deal though, so the best bang for the buck is clearly the standard Double D card that we are looking at here today.
The XFX DD R9 290 4GB has two 90mm cooling fans (actual fan blade measurement is ~85mm) that each have 9-blades on them. XFX claims that the Double Dissipation GPU cooler with Ghost2 thermal cooling should offer improved cooling and reduced noise versus the AMD Radeon R9 290 reference card. XFX is uses seven 6mm copper heatpipes on this card that measures 11.125″ in length. The black PCB measures 10.5-inches, but the GPU cooler extends past the end of the card by more than half an inch. This is a fairly long card, so be sure to measure your case before ordering! The XFX logo on the right side of the card has white LED's behind it that are always on when the system is running. It looks great if you have a window as the inside of your case glows, but there is no way to easily turn them off.
Looking down at the top of the card you can see the two sets of cooling fins with seven copper heatpipes running between them to help dissipate heat from the GPU. The black fan shroud oh the GPU cooler looks sharp with the chrome accent piece that wraps both sections of the housing. If you like black and silver, you should really like the look of this card!
The XFX DD R9 290 supports up to six displays off a single card. All of the video outputs are full sized and you have DisplayPort 1.2 with Multi-Stream Transport, HDMI 1.4b and a pair of Dual-Link DVI outputs. The DVI outputs support screen resolutions up to 2560×1600 and the DP and HDMI ports support screen resolutions up to 4096×2160.
The XFX Radeon R9 290 Double Dissipation video card has one 8-pin PCIe and one 6-pin PCIe power connector located along the top edge of the card that are both needed for proper operation. XFX suggests using a 750W or greater power supply for proper single card operation.Note that the backplate and GPU cooler extend well beyond the PCB.
XFX kept the BIOS selector switch on the card, but there is just not BIOS on the card that has the maximum fan speed set to 45%. There is no Uber and Quiet mode on this Radeon R9 290 card. It should be noted that the card does ship with two BIOS's on it, but both are identical. This switch is still useful though as if a BIOS every gets corrupted you can just switch over to the other one. There are also no CrossFire interconnects on this card as they are no longer needed to run CrossFire. If you get a second, third of fourth card you can just enable CrossFire in AMD's Catalyst Control Center and go about your day.
Here is a quick look at the back of the card. There is no backplate or memory ICs located on the back, so the only thing really worth pointing out is the serial number sticker.
Let's take a look at the retail box or accessory bundle before we move along to benchmarking!
Questions or Comments? View this thread in our forums!
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Copyright © 2002-2021 LegitReviews.com -- All Rights Reserved. | {
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'use strict';
const {
userPut,
userDelete
} = require('./../controllers/userController');
const {
locationGet,
locationPost,
locationPut,
locationPutName,
locationDelete
} = require('./../controllers/locationController');
const {
roomGet,
roomPost,
roomPut,
roomDelete
} = require('./../controllers/roomController');
const {
reservationGet,
reservationPost,
reservationPut,
reservationDelete
} = require('./../controllers/reservationController');
const routeConfig = (router) => {
// user routes
router.put('/user/:userId', userPut);
router.delete('/user/:userId', userDelete);
// location routes
router.get('/location/:id', locationGet);
router.post('/location/:userID', locationPost);
router.put('/location/:locationID/:userID', locationPut);
router.put('/location/:locationID', locationPutName);
router.delete('/location/:locationID', locationDelete);
// room routes
router.get('/room/:locationID', roomGet);
router.post('/room/:locationID', roomPost);
router.put('/room/:roomID', roomPut);
router.delete('/room/:roomID', roomDelete);
// reservation routes
router.get('/reservation', reservationGet);
router.post('/reservation', reservationPost);
router.put('/reservation/:reservationID', reservationPut);
router.delete('/reservation/:reservationID', reservationDelete);
};
module.exports = routeConfig; | {
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Q: Extract number from a line with awk/sed I have this string:
Stream #0:0: Video: vp6f, yuv420p, 852x478, 1638 kb/s, 25 tbr, 1k tbn, 1k tbc
and I would like to extract 25 from it.
I use:
sed -r 's/.+([0-9]{2} tbr).+/\1/'
and it returns what I need.
Anyway, if instead I encounter a string like
Stream #0:0(eng): Video: mpeg4 (Simple Profile) (mp4v / 0x7634706D), yuv420p, 1920x1080 [SAR 1:1 DAR 16:9], 11981 kb/s, 29.97 fps, 29.97 tbr, 30k tbn, 30k tbc
It won't return what I need anymore.
I tried different alternate ways so the value for tbr is returned in both cases but couldn't find the right expression.
A: Your current sed command would work well if you tweak the regex a bit:
sed -r 's/.+ (\S+) tbr,.+/\1/'
A: Here is one approach with awk:
$ awk '/tbr/{print $1}' RS=, file
25
29.97
Explanation:
By default awk treats each line as a record, By setting RS to , we set the record separator to a comma. The script looks at each record and prints the first field of any record that matches tbr.
A GNU grep approach that uses positive lookahead:
$ grep -Po '[0-9.]+(?= tbr)' file
25
29.97
| {
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package org.pescuma.buildhealth.cli.commands.add.staticanalysis.console;
import io.airlift.airline.Command;
import org.pescuma.buildhealth.cli.BaseBuildHealthFilesCliCommand;
import org.pescuma.buildhealth.extractor.staticanalysis.console.CodeAnalysisConsoleExtractor;
@Command(name = "code-analysis-console", description = "Add warnings from CodeAnalysis output files")
public class CodeAnalysisConsoleExtractorCommand extends BaseBuildHealthFilesCliCommand {
@Override
public void execute() {
buildHealth.extract(new CodeAnalysisConsoleExtractor(getFiles()));
}
}
| {
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{"url":"https:\/\/www.physicsforums.com\/threads\/calculus-3-vector-projections.465429\/","text":"# Calculus 3 - Vector Projections\n\n## Homework Statement\n\nIn three dimensions, consider the vector V = a1i + a2j +a3k. Determine the projections of V onto the x, y, z axis.\n\n## Homework Equations\n\nThese are formulas from my textbook related to projection:\n\nAll underscores mean subscript.\n\nProj_A B = (B * A\/|A|) A\/|A| = ((B * A)\/(A * A)) A\n\nB*A = a_1b_1 + a_2b_2 + a_3b_3\n\nNote: The asterisk * in the equation above is the 'dot' used in vector dot products.\n\nPS. Sorry for not using the latex coding to make the equations look nicer. I've used this before and I know how to use the codes but when I submit them the images are broken.\n\n## The Attempt at a Solution\n\nI don't think I'm even close but here's what I did:\n\n(B*A \/ A*A) A = (a_1 \/ 1) j = a_1i\n\nThat's for the x axis. The projection answers for the other axes I get a_2j and a_3k respectively.\n\nLast edited:\n\ntiny-tim\nHomework Helper\nwelcome to pf!\n\nhi calcphys92! welcome to pf!\nProj_A B = (B * A\/|A|) A\/|A| = ((B * A)\/(A * A)) A\n\n(B*A \/ A*A) A = (a_1 \/ 1) j = a_1i\n\nThat's for the x axis. The projection answers for the other axes I get a_2j and a_3k respectively.\n\nyes\n\nbut that definition is a bit complicated, and difficult to remember\n\nit's much easier to say that to find the projection on A, use eA, the unit vector in the A direction \u2026\n\nthen ProjAB = (B.eA)eA\n\nThanks for the confirmation and advice. Also can you explain to me what the answer actually means? I'm asked \"How do you interpret the results?\" But I don't exactly know what vector projections actually are. Thanks in advance\n\ntiny-tim","date":"2021-05-05 22:57:34","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8078709840774536, \"perplexity\": 1906.1141215218117}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-21\/segments\/1620243988696.23\/warc\/CC-MAIN-20210505203909-20210505233909-00064.warc.gz\"}"} | null | null |
Torver railway station served the village of Torver, in Lancashire, England (now in Cumbria). It was on the branch line to Coniston.
History
Authorised by Parliament in August 1857 the line to Coniston was opened by the Coniston Railway less than two years later on 18 June 1859. The station was used for the shipment of slate and stone from the local quarries as well as by passengers.
The station was host to a LMS camping coach from 1934 to 1939.
British Railways closed the station and the branch to passengers on 6 October 1958 and completely on 3 April 1962. The station building remains and has been converted into holiday accommodation.
References
Sources
Gallery
External links
The station on an Edwardian 25" OS map National Library of Scotland
Torver on a navigable 1946 O. S. map NPE maps
The station Rail Map Online
The station and line with mileages Railway Codes
Former Coniston Railway stations
Disused railway stations in Cumbria
Railway stations in Great Britain opened in 1859
Railway stations in Great Britain closed in 1958
1859 establishments in England | {
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Хамза Шахбаз (; ) — пакистанский государственный и политический деятель. Действующий главный министр Пенджаба с 30 апреля 2022 года, его присягу принял спикер Национальной ассамблеи Пакистана Раджа Первез Ашраф. С августа 2018 года являлся членом Ассамблеи провинции Пенджаб, а до этого был членом Национальной ассамблеи Пакистана с июня 2008 года по май 2018 года.
Ранний период и личная жизнь
Родился 6 сентября 1974 года в семье Шехбаза Шарифа. Является бизнесменом и известен как «Король домашней птицы Пенджаба». Руководил семейным бизнесом, когда его семья находилась в изгнании.
У него предположительно три жены, одна из которых — Аиша Ахад Малик, которая утверждала, что вышла замуж за него в 2010 году. Однако, Хамза отрицал свой брак с Аишей. В 2012 году женился на Рабии Хамзе.
В 2014 году издание Dawn сообщило, что Хамза Шахбаз богаче своего отца, имея чистые активы на сумму 250,46 млн рупий. В отчете отмечается, что активы Хамзы увеличились с 583 191 рупий, заявленных в 2008 году, до 211 080 295 рупий в 2011 году.
В 2018 году указал данные двух своих жен в документах о выдвижении кандидатуры на выборах: Мехруниссу Хамзу и Рабиа Хамзу.
По состоянию на 2018 год объявленная стоимость активов Хамзы Шахбаза составляла 411 миллионов рупий.
Обвинения в коррупции
Был арестован 11 июня 2019 года Национальным бюро отчетности по обвинению в коррупции. Арест был осуществлен на основании предполагаемого отмывания денег и удержания активов сверх средств.
В ходе другого расследования Федеральное агентство расследований выявило 28 счетов, через которые, как сообщается, осуществлялось отмывание денег в размере рупий. Через семнадцать тысяч кредитных операций было проведено 16,3 млрд рупий. Федеральное агентство расследований утверждало, что для совершения этих транзакций использовались одиннадцать низкооплачиваемых сотрудников компании Шарифа. Хамзе Шахбазу и его отцу должны были быть предъявлены обвинения 10 февраля 2022 года. Однако, вынесение обвинительного заключения было отложено 18 февраля 2022 года Специальным центральным судом Лахора.
В деле о сахарном скандале Федеральное агентство расследований утверждало, что отмывание денег в размере 25 миллиардов рупий было сделано сотрудниками Ramzan и AI-Arabia Sugar Mills с использованием поддельных аккаунтов. Однако, Хамза Шахбаз отверг эти утверждения и назвал это коммерческой сделкой. Затем освобожден под залог до ареста за мошенничество с сахаром 28 января 2022 года, впоследствии был освобожден под залог 24 февраля 2022 года Высоким судом Лахора.
Примечания
Главные министры Пенджаба | {
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When my friend Jessie and I met she was looking for a Family Photographer in Hawkes Bay. And there I was! We spoke about doing some family photos for about a year after this. Either one of us was always busy that in the end we even gave up for about six months. I think the universe made it that way because then things changed.
Jessie and I see each other every Friday. I eventually shared with her on one of these Fridays this new idea I had about capturing the everyday. I'm talking messy hair, mismatched socks and knobbly, muddy knees. Because I believe where there are muddy knees there are sparkling eyes.
Taking photos of what really happens in your home on a usual day. I want to showcase the family unit. The dynamics between siblings, the love shared between mum and dad, and the ways in which everyone comes together. No posing, no retrying an action to get the perfect shot. Just real, raw, honest images about the beautiful and simple intricacies of everyday life. There is so much beauty in our every day, so much beauty that we will never remember if it goes uncaptured.
To me, this is such a special project. My family is one of my biggest passions, which is why I am certain that we need to lock in the moments we deem as small in the everyday family life. The small moments that actually equate to the big ones! Basically just real life everyday tasks you do as a family that you are not going to do forever. So that in twenty years time you can look back and smile (heck, even laugh out loud) at all the bits you overlooked.
I believe we need to document the stories of your life right now because kids are kids for such a short time (even when it feels like it will never end).
Eventually, Jessie and I found the time on a sunny Hawkes Bay Winter afternoon last year, the photos were everything I had hoped they would be. I don't think I could have done a better job of convincing the Wallace's that this was the best way to do a family photo session.
The best bit was they got all the edited images simply given on a USB. For me, this is crucial because I know if it was my family, I would want the full story. Telling you that I will only give you 20 images of the hundreds I took feels like robbery. So I always, always throw in all the goods!
You can check out more from this gorgeous family here. | {
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\section{Introduction}
With dialog speech technology increasingly entering the mainstream of our every day lives (Siri, Cortana, Alexa, \dots), there is a
growing interest in dialog systems that are not only utilitarian (to answer questions or carry out tasks), but also to entertain and
to be social. Humanoid robots, interactive toys, virtual assistants and even virtual psychiatrists and pets attempt to add an
emotional and social dimension to human interaction that may go beyond improving the user experience of existing dialog systems,
and thus require increasingly skillful and adept social interaction.
Social dialogs are, however, much less well understood than goal directed ones. They do not aim for a particular outcome
other than the more indirect goals of growing a mutual understanding, empathizing, bonding and entertaining between humans.
In the present paper, we are proposing a neural network based system to generate a social response. Our first attempt in this
regard aims to predict a suitable social response, when human speakers take "the floor" and are sharing thoughts and experiences.
The so-called "backchannel" (BC) involves short phrases ("uh-huh", "hum", "yeah", "right", etc.) whose role is to signal to another
speaker that one is listening and paying attention. Further extensions also empathize, confirm, approve or disapprove.
In conversational speech, BCs complement turn taking where more rapid questions and responses are exchanged. Despite
its simple function, however, the BC is surprisingly complex: It must be chosen properly, timed correctly and placed at appropriate
intervals. It also responds to content, emotion and discourse state.
In this paper, we describe a neural network approach to learning the production of proper BC cues. We will focus on
short phrasal BC cues during longer stretches of conversational speech, where another speaker has taken the floor.
Appropriate prediction of backchanneling is learned from human conversation and includes acoustic and linguistic features.
In our work, we use recurrent neural networks to learn the choice and placement of appropriate BC cues from
conversational data (Switchboard).
Special attention is given to producing "causal" backchanneling, i.e., so that the generation of a BC can be produced in
real-time systems with information of the past.
This paper is organized as follows: In the next Section, we provide an overview of related work. In Section \ref{sec:extraction}, we describe our approach in detail, followed by an overview of the experimental setup in Section \ref{experiments}. The results of the experiments are presented in Section \ref{results}. This paper concludes with an outlook to future work in Section \ref{sec:outlook}.
\section{Related Work}
\label{sec:rel_work}
Different approaches towards BC prediction have been proposed in the past.
They are based on different types of predictors and use a wide variety of input modalities.
These modalities include acoustic features like pause and pitch, but also visual cues like head movement.
In addition to these direct features, additional information sources like language models or part of speech tagging exist.
Many approaches are rule based.
\cite{eemcs18627} proposed a method that uses acoustic features.
The authors state that the most important acoustic phenomena for BC prediction occur right before a BC.
As features, they used pause information, as well as pitch (falling or rising slope).
They conducted their experiments on a Dutch corpus and report that the most important feature in their work is the duration of the pause.
\cite{ward2000prosodic} proposed a similar approach triggering BCs at low pitch and pause regions in English and Japanese.
But building a rule based system might prove difficult as these rules have to be manually created, which is a time-consuming and difficult to generalize.
Other works included data-driven methods in which a classifier is trained and the output of this classifier is then post-processed.
\cite{Morency2010} proposes an approach that incorporates sequential probabilistic models like Hidden Markov Models or Conditional Random Fields.
They used a set of features including eye gaze and several features derived from the audio signal, e.g., downslopes in pitch or certain types of volume changes.
In another approach, predicting different types of BC was attempted \cite{kawahara2016prediction}.
Detecting BCs in real-time was also proposed \cite{schroder2012building} in the past.
There exists another category of systems that make use of artificial neural networks (ANNs).
Being a data-driven method, NNs do not require handwritten rules.
They have shown to be a versatile tool with the ability to learn relevant features automatically.
A first approach towards detecting speech acts (including BCs) was proposed by Ries \cite{ries1999hmm}.
He used an NN in combination with an HMM.
Stolcke also proposed NN based methods for modelling dialogue acts \cite{stolcke1998dialog,stolcke2000dialogue}.
In the past, we also proposed an NN based approach \cite{mueller} that was mainly data-driven, requiring only minimal post-processing of the network outputs.
In this first approach, we used a very basic ANN based setup, which we now refined.
The objective evaluation of systems for BC prediction is difficult because BC behaviour is very speaker-dependent and subjective.
As an objective measurement, the use of the F1-Score has been established.
\cite{kok2012survey} provides a comparison of different approaches for evaluation.
In addition to objective measures, user studies are also a possibility to evaluate BC systems, like we did in the past \cite{mueller}.
A general study about the occurrence of BCs with respect to their role in facilitating attentive listening also exists \cite{kawahara2015toward}.
\section{Backchannel Prediction}
\label{sec:extraction}
\subsection{BC Utterance Selection}
\label{sec:extractio:subsec:bc-utterance-selection}
There are different kinds of phrasal BCs, they can be non-committal, positive, negative, questioning, et cetera.
To simplify the problem of predicting BCs, we only try to predict the trigger
times for any type of BC, ignoring the distinction between different kinds of responses.
\subsection{Feature Selection}\label{feature-selection}
A neural network is able to learn advantageous feature representations on its own.
Hence, feeding the absolute pitch and power (signal energy) values for a given time context enables the network
to automatically extract the relevant information such as pitch slopes and pause triggers, as used in related research \cite{Morency2010}.
In addition to pitch and power, we also evaluated using other acoustic features such as the fundamental frequency variation (FFV) \cite{laskowski2008fundamental} and the Mel-frequency cepstral coefficients (MFCCs).
Finally, we tried adding an encoding of the speakers' word history before the listener backchannel using word2vec \cite{mikolov_efficient_2013} to assess whether our setup benefits from multimodal input features.
\subsection{Training and Neural Network Design}\label{training}
We assumed to have two separate, but synchronized audio channels and corresponding transcripts: One for the speaker and one for the listener. We needed to decide which areas of audio to use to train the network.
As we wanted to predict the BCs in an online fashion without using future information, we needed to train the network to detect segments of audio from the speaker track that would potentially cause a
BC in the listener track.
We chose the beginning of the BC utterance as an
anchor and used a fixed context before that as the positive prediction area.
We also needed to choose negative examples, so
the network would not be biased to always predict a BC.
We did this by selecting the range a few seconds before each BC, because in that area
the listener explicitly decided not to give a backchannel response yet. This resulted in a fully balanced training dataset.
We initially used a feed forward network architecture.
The input layer consists of all the chosen features over the previously selected fixed time context.
The output layer has two softmax neurons representing the "categories" [BC, non-BC]. We used back-propagation to train the network on the outputs [1, 0] for BC and [0, 1] for non-BC prediction areas. We only need to consider one of these outputs because the softmax function guarantees that they add up to one. We evaluated multiple different combinations of network depths and neuron counts. An example of the architecture with two hidden layers can be seen in \autoref{fig:nn}.
\tikzstyle{layer}=[draw=black,fill=black!30]
\tikzstyle{layerlid}=[draw=black,fill=green!30]
\tikzstyle{dots}=[draw=black,fill=black]
\begin{figure}[htbp]
\tikzset{>=latex}
\centering
\begin{tikzpicture}[scale=0.7]
\def 2 {2}
\def 1.5 {1.5}
\fill[layer] (0,-1.75) -- (0.5,-1.75) coordinate(l1br) -- (0.5,1.75) coordinate(l1tr) -- (0,1.75) -- (0,-1.75);
\fill[layer] (3,-2) coordinate(l2bl) -- (3.5,-2) coordinate(l2br) -- (3.5,2) coordinate(l2tr) -- (3,2) coordinate(l2tl) -- (3,-2);
\fill[layer] (6,-1.5) coordinate(l3bl) -- (6.5,-1.5) coordinate(l3br) -- (6.5,1.5) coordinate(l3tr) -- (6,1.5) coordinate(l3tl) -- (6,-1.5);
\fill[layer] (9,-0.5) coordinate(o1b) -- (9.5,-0.5) -- (9.5,0.5) --
(9,0.5) coordinate(o1t) -- (9,-0.5);
\draw[draw=black] (0.25,1.5) circle (0.15) node {\tiny A};
\draw[draw=black] (0.25,1) circle (0.15) node {\tiny B};
\draw[draw=black] (0.25,0.5) circle (0.15) node {\tiny A};
\draw[draw=black] (0.25,0) circle (0.15) node {\tiny B};
\draw[draw=black] (0.25,-1) circle (0.15) node {\tiny A};
\draw[draw=black] (0.25,-1.5) circle (0.15) node {\tiny B};
\node[left,text width=2cm] at (1,2.5) {input features with context};
\draw (-0.25,1.7) -- (-0.5,1.7) -- (-0.5,0.8) -- (-0.25,0.8) (-0.25,0.7) -- (-0.5,0.7) -- (-0.5,-0.2) -- (-0.25,-0.2) (-0.25,-0.8) -- (-0.5,-0.8) -- (-0.5,-1.7) -- (-0.25,-1.7);
\draw (-1,-0.25) circle (0.01) ++(0,-0.25) circle (0.01) ++(0,-0.25) circle (0.01);
\node[left] at (-0.5,1.25) {-1500ms};
\node[left] at (-0.5,0.25) {-1490ms};
\node[left] at (-0.5,-1.25) {-10ms};
\draw[draw=black] (-2,-3) circle (0.15) node {\tiny A} +(0.2,0) node [right](power) {Feature 1 (e.g. power)};
\draw[draw=black] (-2,-3.5) circle (0.15) node {\tiny B} +(0.2,0) node[right](pitch) {Feature 2 (e.g. pitch)};
\fill (9.25,0.25) circle (0.15);
\draw (9.25,-0.25) circle (0.15);
\fill (9.25,-3) circle (0.15) +(0.2,0) node[right](power) {BC};
\draw (9.25,-3.5) circle (0.15) +(0.2,0) node[right](pitch) {non-BC};
\draw[->] (l1br) -- (l2tl);
\draw[->] (l1tr) -- (l2bl);
\draw[->] (l2tr) -- (l3bl);
\draw[->] (l2br) -- (l3tl);
\draw[->] (l3tr) -- (o1b);
\draw[->] (l3br) -- (o1t);
\draw[<->] (l2bl) +(-0.5,-0.5) -- ++(4,-0.5);
\node[below](hL) at (4.75,-3.5) {hidden layers};
\end{tikzpicture}
\caption{Example for a neural network architecture for BC prediction.\label{fig:nn}}
\end{figure}
The placement of future BCs is dependent on the timing of previous BCs.
The probability of a BC increases with longer periods without any listener feedback. To accommodate for this, we want the network to also take its previous internal state or outputs into account. We do this by modifying the above architecture to use Long-short term memory (LSTM) layers instead of feed forward layers.
\section{Experimental Setup}
\label{experiments}
\subsection{Dataset}\label{dataset}
We used the Switchboard dataset \cite{swb}, which consists of 2,438 English
telephone conversations of five to ten minutes, 260 hours in total. Pairs of participants from across the United States were encouraged to talk about a specific topic chosen randomly from 70 possibilities. Conversation partners and topics were selected so two people would only talk once with each other, and every person would only discuss a specific topic once.
These telephone conversations are annotated with transcriptions and word alignments \cite{swbalign} with a total of 390k utterances or 3.3 million words. We split the dataset randomly into 2,000 conversations for training, 200 for validation and 238 for evaluation.
We used annotations from the Switchboard Dialog Act Corpus (SwDA) \cite{swda} to
decide which utterances to classify as BCs. The SwDA contains
categorical annotations for the utterances of about half of the data of the
Switchboard corpus.
\subsection{Extraction}\label{extraction-1}
We chose to use the top 150 most common unique utterances marked as BCs
from the SwDA. Because the SwDA is incomplete, we had to identify
utterances as BCs just by their text. We manually included some additional utterances that were missing from the SwDA
transcriptions but present in the original transcriptions, by going
through the most common utterances and manually selecting those that
seemed relevant, such as `um-hum yeah' and `absolutely'.
The most common BCs in the data set are "yeah", "um-hum", "uh-huh" and "right", adding up to 68\% of all extracted BC phrases.
To select which utterances should be categorized as BCs and
used for training, we first filtered noise and other markers such as laughter from the
transcriptions. Some utterances such as ``uh'' can be both BCs and speech disfluencies, so we only chose those that have either silence or another
BC before them. With this method a total of 15.7\% of utterances or 2.21\% of words were labelled as BCs.
We used the Janus Recognition Toolkit \cite{janus} for parts of the feature extraction (power, pitch tracking, FFV, MFCC). Features were extracted for \SI{32}{ms} frame windows with a frame shift of \SI{10}{ms}, resulting in 100 samples per feature dimension per second. Because most of the data does not change much every 10\,ms, we also test different context strides by only extracting every n-th frame. As an example, 800\,ms of context with a stride of 2 corresponds to 40 data frames.
For word2vec, we chose to also emit one frame every 10\,ms for consistency, containing the encoding of the last non-silent word that ended before or at the time of the frame.
\subsection{Training}\label{training-1}
We used Theano \cite{theano} with Lasagne \cite{lasagne} for rapid prototyping and testing of different parameters.\footnote{Our code for extraction, training, postprocessing and evaluation will be available at \mbox{\url{https://github.com/phiresky/backchannel-prediction}}. The repository also contains a script to reproduce all of the results of this paper.}
To evaluate different hyperparameters, we trained multiple network configurations with various context lengths (500ms to 2000ms), context strides (1 to 4 frames), network depths (one to four hidden layers), layer sizes (15 to 125 neurons), activation functions (tanh and relu), optimization methods (SGD, Adadelta and Adam \cite{adam}), weight initialization methods (constant zero and Glorot \cite{glorot}), and layer types (feed forward and LSTM).
The LSTM networks we tested were prone to overfitting quickly. We tried two methods of regularization to overcome this. The first was Dropout training, where we randomly dropped a specific portion of neuron outputs in each layer for each training batch \cite{dropout}. We evaluated dropout layer combinations from 0 to 50\% while increasing layer sizes proportionately, but this did not improve the results. The second was adding L2-Regularization with a constant factor of 0.0001. This greatly reduced overfitting and slightly improved the results.
\subsection{Postprocessing}\label{postprocessing}
We interpret the output value of the neural networks as the probability of a BC occurring at a given time. As the output is very noisy, we first apply a low-pass filter. To ensure our prediction does not use any future information, we use a Gaussian filter which is asymmetrically cut off at some multiple $c$ of the standard deviation $\sigma$ for the side that would range into the future, and offset it so the last frame is at $\pm\SI{0}{ms}$ from the prediction target time. This means the latency of our prediction increases by $c\cdot\sigma\,ms$. If we choose $c=0$, we cut off the complete right half of the bell curve, keeping the latency at 0 at the cost of accuracy of the filter.
After the low-pass filter, we select every area for which the value exceeds a given threshold. We trigger either at the beginning of each of these areas or at their first local maximum, depending on the largest acceptable latency. This varies depending on the chosen allowed margin of error as defined in \autoref{eval-1}.
An example of this postprocessing process can be seen in \autoref{fig:postproc}.
\begin{figure}
\centering
\includegraphics[width=\textwidth]{img/1.pdf}
\caption{Postprocessing example}
\label{fig:postproc}
\end{figure}
We determined the optimal postprocessing hyperparameters for each network configuration and allowed margin of error automatically using Bayesian optimization \cite{bayes} with the validation F1-Score as the utility function. For a margin of error of [0\,ms, +1000\,ms], the resulting standard deviation $\sigma$ ranged from \SIrange{200}{350}{ms}, and the filter cut-off ranged from $0.9\sigma\text{ to }1.4\sigma$. With this margin of error, the prediction can happen with a delay of up to one second after the ground truth. When choosing a margin of error that only allows a smaller delay such as [-200\,ms, +200\,ms], the selected standard deviation ranged from \SIrange{150}{250}{ms}, and the filter cut-off ranged from $0.0\sigma\text{ to }1.0\sigma$, causing the predicted trigger to happen earlier.
\subsection{Evaluation}\label{eval-1}
The training data contains two-sided conversations. Because the output of our predictor is only relevant for segments with just one person talking, we run our evaluation on monologuing segments.
We define a monologuing segment as the maximum possible time range in which one person is continuously \emph{talking} and the other person is continuously \emph{not talking} for at least five seconds. A person is continuously talking \emph{iff} they are only emitting utterances that are not silence or BCs. We only consider segments of a minimum length of five seconds to exclude sections of alternating conversation. This way we get segments where one participant is talking, and the other is producing backchannels without taking the turn.
We define a prediction time as correct if it is within a given margin of error of the onset of a correct BC utterance. We did most of the testing of our predictions with an error margin of [0\,ms, +1000\,ms], but also provide results for other margins used in related research.
For comparison, we also evaluated a random predictor as a baseline. This predictor knows the correct count of BCs for a audio file and returns a uniformly distributed set of trigger times.
\section{Results}\label{results}
We use "$70 : 35$" to denote a network layer configuration of \(\text{input} \rightarrow 70\text{ neurons} \rightarrow 35\text{ neurons} \rightarrow \text{output}\).
We tested different context widths. A context width of $n\,\si{ms}$ means we use the range $[-n\,\si{ms},\allowbreak 0\,\si{ms}]$ from the beginning of the backchannel utterance. The results improved when increasing the context width from our initial value of 500\,ms. Performance peaked with a context of about 1500\,ms, as can be seen in Table \ref{varycontext}, longer contexts tended to cause the predictor to trigger too late.
We tested using only every n-th frame of input data. Even though we initially did this for performance reasons, we noticed that training on every single frame has worse performance than skipping every second frame due to overfitting. Taking every fourth frame seems to miss too much information, so performance peaks at a context stride of 2, as seen in Table \ref{varystrides}.
We tested different combinations of features, with using solely power in a first approach.
But adding prosodic features gives great improvements. Using FFV as the only prosodic feature performs worse than FFV together with the absolute pitch value. Adding MFCCs does not seem to improve performance in a meaningful way, when also using pitch, see Table \ref{varyfeatures} for more details. Note that using \emph{only} word2vec performs reasonably well, because with our method it indirectly encodes the time since the last utterance, similar to the power feature.
Table \ref{varylstm} shows a comparison between feed forward and LSTM networks. The parameter count is the number of connection weights the network learns during training. Note that LSTMs have higher performance, even with similar parameter counts.
We compared different layer sizes for our LSTM networks, as shown in Table \ref{varylayers}. A network depth of two hidden layers worked best, but the results are adequate with a single hidden layer or three hidden layers.
In \autoref{fig:final}, our final results are given for the completely independent evaluation data set. We compared the results from \cite{mueller} with our system. \cite{mueller} used the same dataset, but focused on offline predictions, meaning their network had future information available, and they evaluated their performance on the whole corpus including segments with silence and with alternating conversation. We adjusted our baseline and evaluation system to match their setup by removing the monologuing constraint described in \autoref{eval-1} and changing the margin of error to [-200\,ms, +200\,ms]. As can be seen in Table \ref{fig:mueller}, our predictor performs better.
All other related research used different languages, datasets or evaluation methods, rendering a direct comparison difficult because of slightly different tasks.
Table \ref{fig:ourbest} shows the results with our presented evaluation method. We provide scores for different margins of error used in other research. Subjectively, missing a BC trigger may be more acceptable than a false positive, so we also provide a result with balanced precision and recall. Note that a later margin center with the same margin width has higher performance because it allows more latency in the predictions, which means we can choose better postprocessing parameters as described in \autoref{postprocessing}.
\section{Conclusion and Future Work}
\label{sec:outlook}
We have presented a new approach to predict BCs using neural networks.
With refined methods for network training as well as different network architectures, we could improve the F1-Score in contrast to our previous experiments.
In addition to evaluating different hyperparameter configurations, we also experimented with LSTM networks, which lead to improved results.
Our best system achieved an F1-Score of 0.388.
We used linguistic features via word2vec only in a very basic way, assuming the availability of an instant speech recognizer by using the reference transcripts.
As low-latency speech recognition is possible \cite{niehues2016dynamic}, one of the next steps would be to combine both systems.
Further work is needed to evaluate other methods for adding word vectors to the input features and to analyze problems with our approach.
We only tested feed forward neural networks and LSTMs, other architectures like time-delay neural networks \cite{waibel1989phoneme}, also called convolutional neural networks, may also give interesting results.
Our approach of choosing the training areas may not be optimal because the delay between the last utterance of the speaker and the backchannel can vary significantly. One possible solution would be to align the training area by the last speaker utterance instead of the backchannel start.
Because backchannels are a largely subjective phenomenon, a user study would be helpful to subjectively evaluate the performance of our predictor and to compare it with human performance in our chosen evaluation method. Another method would be to find consensus for backchannel triggers by combining the predictions of multiple human subjects for a single speaker channel as described by Huang et al. (2010) as "parasocial consensus sampling" \cite{huang2010learning}.
\begin{table}
\caption{Results on the Validation Set. All results use the following setup if not otherwise stated: LSTM, configuration: $(70 : 35)$; input features: power, pitch, ffv; context width: 1500\,ms; context frame stride: 2; margin of error: 0\,ms to +1000\,ms. Precision, recall, and F1-Score are given for the validation data set.}\label{fig:survey}
\centering
\subfloat[Results with various context lengths. Performance peaks at 1500\,ms.]{
\begin{tabular}{cccc}
\hline\noalign{\smallskip}
Context & Precision & Recall & F1-Score \\
\noalign{\smallskip}\svhline\noalign{\smallskip}
500\,ms & 0.219 & 0.466 & 0.298 \\
1000\,ms & 0.280 & 0.497 & 0.358 \\
1500\,ms & 0.305 & 0.488 & \bf{0.375} \\
2000\,ms & 0.275 & 0.577 & 0.373 \\
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\label{varycontext}
}
\qquad
\subfloat[Results with various context frame strides.]{
\begin{tabular}{cccc}
\hline\noalign{\smallskip}
Stride & Precision & Recall & F1-Score \\
\noalign{\smallskip}\svhline\noalign{\smallskip}
1 & 0.290 & 0.490 & 0.364 \\
2 & 0.305 & 0.488 & \bf{0.375} \\
4 & 0.285 & 0.498 & 0.363 \\
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\label{varystrides}
}
\centering
\subfloat[Results with various input features, separated into only acoustic features and acoustic plus linguistic features.]{
\begin{tabular}{lccc}
\hline\noalign{\smallskip}
Features & Precision & Recall & F1-Score \\
\noalign{\smallskip}\svhline\noalign{\smallskip}
power & 0.244 & 0.516 & 0.331 \\
power, pitch & 0.307 & 0.435 & 0.360 \\
power, pitch, mfcc & 0.278 & 0.514 & 0.360 \\
power, ffv & 0.259 & 0.513 & 0.344 \\
power, ffv, mfcc & 0.279 & 0.515 & 0.362 \\
power, pitch, ffv & 0.305 & 0.488 & \bf{0.375} \\
\noalign{\smallskip}\hline\noalign{\smallskip}
word2vec$_{dim=30}$ & 0.244 & 0.478 & 0.323 \\
power, pitch, word2vec$_{dim=30}$ & 0.318 & 0.486 & 0.385 \\
power, pitch, ffv, word2vec$_{dim=15}$ & 0.321 & 0.475 & 0.383 \\
power, pitch, ffv, word2vec$_{dim=30}$ & 0.322 & 0.497 & \bf{0.390} \\
power, pitch, ffv, word2vec$_{dim=50}$ & 0.304 & 0.527 & 0.385 \\
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\label{varyfeatures}
}
\subfloat[Feed forward vs LSTM. LSTM outperforms feed forward architectures.]{
\begin{tabular}{ccccc}
\hline\noalign{\smallskip}
Layers & Parameter count & Precision & Recall & F1-Score \\
\noalign{\smallskip}\svhline\noalign{\smallskip}
FF ($56 : 28$) & 40k & 0.230 & 0.549 & 0.325 \\
FF ($70 : 35$) & 50k & 0.251 & 0.468 & 0.327 \\
FF ($100 : 50$) & 72k & 0.242 & 0.490 & 0.324 \\
LSTM ($70 : 35$) & 38k & 0.305 & 0.488 & \bf{0.375} \\
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\label{varylstm}
}
\subfloat[Comparison of different network configurations. Two LSTM layers give the best results.]{
\begin{tabular}{cccc}
\hline\noalign{\smallskip}
Layer sizes & Precision & Recall & F1-Score \\
\noalign{\smallskip}\svhline\noalign{\smallskip}
$100$ & 0.280 & 0.542 & 0.369 \\
$50 : 20$ & 0.291 & 0.506 & 0.370 \\
$70 : 35$ & 0.305 & 0.488 & \bf{0.375} \\
$100 : 50$ & 0.303 & 0.473 & 0.369 \\
$70 : 50 : 35$ & 0.278 & 0.541 & 0.367 \\
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\label{varylayers}
}
\end{table}
\newcommand{\csubfloat}[2][]{%
\makebox[0pt]{\subfloat[#1]{#2}}%
}
\captionsetup[subfigure]{width=\textwidth}
\begin{table}
\centering
\caption{Final best results on the evaluation set (chosen by validation set)}\label{fig:final}
\csubfloat[Comparison with previous research. \cite{mueller} did their evaluation without the constraints defined in \autoref{eval-1}, so we adjusted our baseline and evaluation to match their setup.]{
\begin{tabular}{lccc}
\hline\noalign{\smallskip}
Predictor & Precision & Recall & F1-Score \\
\noalign{\smallskip}\svhline\noalign{\smallskip}
Baseline (random) & 0.042 & 0.042 & 0.042 \\
Müller et al. (offline) \cite{mueller} & -- & -- & 0.109 \\
Our results (offline, context of \SIrange{-750}{750}{ms}) & 0.114 & 0.300 & \bf{0.165} \\
Our results (online, context of \SIrange{-1500}{0}{ms}) & 0.100 & 0.318 & 0.153 \\
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\label{fig:mueller}
}
\csubfloat[Results with our evaluation method with various margins of error used in other research \cite{survey}. Performance improves with a wider margin width and with a later margin center.]{
\begin{tabular}{clccc}
\hline\noalign{\smallskip}
Margin of Error & Constraint & Precision & Recall & F1-Score \\
\noalign{\smallskip}\svhline\noalign{\smallskip}
\SIrange{-200}{+200}{ms} && 0.172 & 0.377 & 0.237 \\
\SIrange{-100}{+500}{ms} && 0.239 & 0.406 & 0.301 \\
\SIrange{-500}{+500}{ms} && 0.247 & 0.536 & 0.339 \\
\hline\noalign{\smallskip}
\SIrange{0}{+1000}{ms} & Baseline (random, correct BC count) & 0.111 & 0.052 & 0.071 \\
& Baseline (random, 8x correct BC count) & 0.079 & 0.323 & 0.127 \\
& Balanced Precision and Recall & 0.342 & 0.339 & 0.341 \\
& Best F1-Score (only acoustic features) & 0.294 & 0.488 & 0.367 \\
& Best F1-Score (acoustic and linguistic features) & 0.312 & 0.511 & \bf{0.388} \\
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
\label{fig:ourbest}
}
\end{table}
\begin{acknowledgement}
This work has been conducted in the SecondHands project
which has received funding from the European Union's
Horizon 2020 Research and Innovation programme (call:H2020-
ICT-2014-1, RIA) under grant agreement No 643950.
\end{acknowledgement}
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\sidecaption[t]
\includegraphics[scale=.65]{figure}
\caption{If the width of the figure is less than 7.8 cm use the \texttt{sidecapion} command to flush the caption on the left side of the page. If the figure is positioned at the top of the page, align the sidecaption with the top of the figure -- to achieve this you simply need to use the optional argument \texttt{[t]} with the \texttt{sidecaption} command}
\label{fig:2}
\end{figure}
\runinhead{Run-in Heading Boldface Version} Use the \LaTeX\ automatism for all your cross-references and citations as has already been described in Sect.~\ref{sec:2}.
\subruninhead{Run-in Heading Italic Version} Use the \LaTeX\ automatism for all your cross-refer\-ences and citations as has already been described in Sect.~\ref{sec:2}\index{paragraph}.
\begin{table}
\caption{Please write your table caption here}
\label{tab:1}
\begin{tabular}{p{2cm}p{2.4cm}p{2cm}p{4.9cm}}
\hline\noalign{\smallskip}
Classes & Subclass & Length & Action Mechanism \\
\noalign{\smallskip}\svhline\noalign{\smallskip}
Translation & mRNA$^a$ & 22 (19--25) & Translation repression, mRNA cleavage\\
Translation & mRNA cleavage & 21 & mRNA cleavage\\
Translation & mRNA & 21--22 & mRNA cleavage\\
Translation & mRNA & 24--26 & Histone and DNA Modification\\
\noalign{\smallskip}\hline\noalign{\smallskip}
\end{tabular}
$^a$ Table foot note (with superscript)
\end{table}
\section{Section Heading}
\label{sec:3}
Instead of simply listing headings of different levels we recommend to
let every heading be followed by at least a short passage of text.
Further on please use the \LaTeX\ automatism for all your
cross-references and citations as has already been described in
Sect.~\ref{sec:2}.
Please note that the first line of text that follows a heading is not indented, whereas the first lines of all subsequent paragraphs are.
If you want to list definitions or the like we recommend to use the Springer-enhanced \verb|description| environment -- it will automatically render Springer's preferred layout.
\begin{description}[Type 1]
\item[Type 1]{That addresses central themes pertainng to migration, health, and disease. In Sect.~\ref{sec:1}, Wilson discusses the role of human migration in infectious disease distributions and patterns.}
\item[Type 2]{That addresses central themes pertainng to migration, health, and disease. In Sect.~\ref{subsec:2}, Wilson discusses the role of human migration in infectious disease distributions and patterns.}
\end{description}
\subsection{Subsection Heading} %
In order to avoid simply listing headings of different levels we recommend to let every heading be followed by at least a short passage of text. Use the \LaTeX\ automatism for all your cross-references and citations citations as has already been described in Sect.~\ref{sec:2}.
Please note that the first line of text that follows a heading is not indented, whereas the first lines of all subsequent paragraphs are.
\begin{svgraybox}
If you want to emphasize complete paragraphs of texts we recommend to use the newly defined Springer class option \verb|graybox| and the newly defined environment \verb|svgraybox|. This will produce a 15 percent screened box 'behind' your text.
If you want to emphasize complete paragraphs of texts we recommend to use the newly defined Springer class option and environment \verb|svgraybox|. This will produce a 15 percent screened box 'behind' your text.
\end{svgraybox}
\subsubsection{Subsubsection Heading}
Instead of simply listing headings of different levels we recommend to
let every heading be followed by at least a short passage of text.
Further on please use the \LaTeX\ automatism for all your
cross-references and citations as has already been described in
Sect.~\ref{sec:2}.
Please note that the first line of text that follows a heading is not indented, whereas the first lines of all subsequent paragraphs are.
\begin{theorem}
Theorem text goes here.
\end{theorem}
\begin{definition}
Definition text goes here.
\end{definition}
\begin{proof}
Proof text goes here.
\qed
\end{proof}
\paragraph{Paragraph Heading} %
Instead of simply listing headings of different levels we recommend to
let every heading be followed by at least a short passage of text.
Further on please use the \LaTeX\ automatism for all your
cross-references and citations as has already been described in
Sect.~\ref{sec:2}.
Note that the first line of text that follows a heading is not indented, whereas the first lines of all subsequent paragraphs are.
\begin{theorem}
Theorem text goes here.
\end{theorem}
\begin{definition}
Definition text goes here.
\end{definition}
\begin{proof}
\smartqed
Proof text goes here.
\qed
\end{proof}
\begin{acknowledgement}
If you want to include acknowledgments of assistance and the like at the end of an individual chapter please use the \verb|acknowledgement| environment -- it will automatically render Springer's preferred layout.
\end{acknowledgement}
\section*{Appendix}
\addcontentsline{toc}{section}{Appendix}
When placed at the end of a chapter or contribution (as opposed to at the end of the book), the numbering of tables, figures, and equations in the appendix section continues on from that in the main text. Hence please \textit{do not} use the \verb|appendix| command when writing an appendix at the end of your chapter or contribution. If there is only one the appendix is designated ``Appendix'', or ``Appendix 1'', or ``Appendix 2'', etc. if there is more than one.
\begin{equation}
a \times b = c
\end{equation}
\input{referenc}
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,205 |
Казими́ра Дану́те Пру́нскене (; 26 лютого 1943) — литовська економістка й політична діячка, перший прем'єр-міністр Литви після відновлення незалежності (17 березня 1990 — 10 січня 1991).
Біографія
Казимира Прунскене народилась в окупованому Німеччиною під час другої світової війни селі Васюлішкес Швянченіського району Литовської РСР 26 лютого 1943 року. 1949 року пішла навчатись до Калтаненської школи, яку закінчила 1956, наступні 4 роки провчилась у середній школі Вільнюса. 1960 року вступила до Вільнюського університету на факультет економіки промисловості. 1965 року здобула диплом про вищу освіту.
Наукова кар'єра
У 1970—1971 роках навчалась в аспірантурі Вільнюського університету, захистила кандидатську дисертацію та здобула науковий ступінь кандидата економічних наук. У 1965—1986 роках працювала викладачем, від 1978 року — доцентом на факультеті економіки промисловості Вільнюського університету. У 1981—1988 роках перебувала в наукових відрядженнях в університетах Угорщини та Німеччини (ФРН). 1986 року захистила докторську дисертацію. У 1986—1988 роках обіймала посаду заступника директора з науки Інституту економіки сільського господарства. У 1988—1989 роках ректор Інституту підвищення кваліфікації керівних працівників і фахівців народного господарства.
Політична кар'єра
1988 року стала однією з головних розробників концепції економічної самостійності Литовської РСР й однією з засновників литовського Руху за перебудову — Саюдіс (входила до його ініціативної групи та Ради сейму). У 1989—1990 роках була заступником голови Ради міністрів Литовської РСР. 1989 року обрана народним депутатом СРСР від Шауляйського виборчого округу, брала участь у роботі Верховної ради СРСР і З'їзду народних депутатів СРСР.
У лютому 1990 року Казимиру Прунскене обрали депутаткою Верховної Ради Литовської РСР, яка вже 11 березня того ж року проголосила відновлення незалежності Литви та перейменувалась згодом на Відновлювальний Сейм. Прунскене стала прем'єр-міністром першого незалежного литовського уряду 17 березня 1990 року. Її зустрічі 1990 року з лідерами західних країн: США (Джордж Буш), Великої Британії (Маргарет Тетчер), Франції (Франсуа Міттеран), Німеччини (Гельмут Коль) принесли їй широку популярність як «Бурштиновій леді» (за аналогією із «Залізною леді» Маргарет Тетчер) і змусили Михайла Горбачова почати перемовини з литовським урядом. Звинувачення в безуспішних перемовинах з керівництвом Радянського Союзу на тлі економічної блокади, зростання цін, невдоволення населення — усе це змусило її уряд піти у відставку незадовго до подій 13 січня 1991 року. Після виходу у відставку активно опонувала курсу литовських правих, очолюваних головою Верховної Ради Вітаутасом Ландсберґісом. В результаті її звинуватили у зв'язках з КДБ. Згодом вона неодноразово спростовувала ті наклепи через суд.
Казимира Прунскене — одна із засновниць 1995 року Жіночої партії Литви (), яку очолювала від 25 лютого 1995 до 1998 року. 1998 року очолила оновлену партію Нова демократія/Жіноча партія (). 2000 року очолила оновлену партію Нової демократії (). Обиралася членкинею Сейму від Жіночої партії Литви 1996, а 2000 року переобралась від Партії нової демократії.
2001 року очолила Союз партій селян і нової демократії ().
У другому турі дострокових президентських виборів, що відбувся 27 червня 2004 року, виборола 47,8 % голосів виборців, поступившись Валдасу Адамкусу. Після виборів до лав Сейму в листопаді 2004 року під час розподілу місць в уряді між коаліцією Соціал-демократичної партії, Нового союзу, Партії праці та Союзу партій селян отримала портфель міністра сільського господарства.
Брала участь у президентських виборах 2009 року, за результатами яких посіла п'яте місце, здобувши 3,86 % голосів виборців; перемогу виборола Даля Грибаускайте.
5 грудня 2009 року а на з'їзді Литовського народного союзу Казимиру Прунскене обрали його головою.
Громадська кар'єра
Казимира Прунскене є однією із засновниць Балтійської жіночої баскетбольної ліги () яку очолювала понад 15 років, від лютого 2013 року — почесний президент.
Очолює громадську організацію, що сприяє економічному обміну між Литвою і Україною — «УкраЛит».
Подальше життя
26 лютого 2012 року перенесла інсульт. Він порушив ліву півкулю мозку, Прунскене розбив параліч (не володіє лівою рукою і тому потребує постійної допомоги близьких). Вона зазнала двох операцій з відновлення кісток черепа, які вилучили через набряк головного мозку. Після проведеної операції Прунскене впадала в кому. Відновну реабілітацію проходила в Московському науковому центрі неврології. Після реабілітації у Москві, у перших числах квітня 2013 року повернулася до Литви, проживає в садибі сина у селі Жвірблішкес Швянченіського району.
Родина
Була одружена (розлучена), в шлюбі народила сина й двох доньок:
Вайдотас Прунскус — діяч Союзу партій селян і нової демократії, член ради самоврядування Швянченіського району;
Раса Вайткене.
Нагороди та звання
Почесний громадянин Швянченіського району.
Орден Великого князя Литовського Гедиміна II ступеня.
Великий хрест ордена «За заслуги перед Федеративною Республікою Німеччина».
Орден Дружби II ступеня — 14 грудня 2015 року.
Праці
Казимира Прунскене є авторкою низки праць на економічну та політичну тематику:
Gintarinės ledi išpažintis. Vilnius: Politika, 1991.
Leben für Litauen. Frankfurt/Main, Berlin, Ullstein, 1992
Užkulisiai. Vilnius: Politika, 1992.
Iššūkis drakonui. Kaunas: Europa,1992.
Išsivadavimo kaina. Vilnius: Politika, 1993.
Laisvėjimo ir permainų metai. Vilnius: Viltis, 1995.
Markt Baltikum: Geshäfts- und Investionsratgeber für die Praxis. Freiburg, Berlin: Rudolf Haufe Verlag, 1995.
Apie dabartį ir ateitį. Vilnius, 2002.
Lietuvos moterys. Vilnius: Lietuvos Europos institutas, 2002.
Примітки
Посилання
Казимира Прунскене на сайті ru.delfi.lt
Уродженці Швянченіса
Економісти Литви XX століття
Політики Литви XX століття
Прем'єр-міністри Литви
Литовські жінки-політики
Економісти Литви XXI століття
Політики Литви XXI століття
Прихильники Балто-Чорноморського союзу | {
"redpajama_set_name": "RedPajamaWikipedia"
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{"url":"https:\/\/www.mersenneforum.org\/showthread.php?s=208b22670c625935d228c2694954eeb3&t=23042&page=44","text":"mersenneforum.org mtsieve\n Register FAQ Search Today's Posts Mark Forums Read\n\n 2020-12-02, 00:08 #474 rogue \u00a0 \u00a0 \"Mark\" Apr 2003 Between here and the 5\u00b71,249 Posts That shouldn't be hard to do.\n 2020-12-02, 08:51 #475 Happy5214 \u00a0 \u00a0 \"Alexander\" Nov 2008 The Alamo City 7608 Posts Also, don't report a fatal error when running the programs with the \"--help\" switch. It's unnecessarily scary.\n2020-12-02, 13:33 \u00a0 #476\nrogue\n\n\"Mark\"\nApr 2003\nBetween here and the\n\n11000011001012 Posts\n\nQuote:\n Originally Posted by Happy5214 Also, don't report a fatal error when running the programs with the \"--help\" switch. It's unnecessarily scary.\nI've gone back and forth on that. Technically the programs allow you to sieve even if you used -h, but I could probably make an exception in this case.\n\n2020-12-02, 13:57 \u00a0 #477\nhenryzz\nJust call me Henry\n\n\"David\"\nSep 2007\nCambridge (GMT\/BST)\n\n10110101110102 Posts\n\nQuote:\n Originally Posted by rogue I've gone back and forth on that. Technically the programs allow you to sieve even if you used -h, but I could probably make an exception in this case.\nMost programs only display help with -h\n\n2020-12-02, 21:14 \u00a0 #478\nrogue\n\n\"Mark\"\nApr 2003\nBetween here and the\n\n141458 Posts\n\nQuote:\n Originally Posted by henryzz Most programs only display help with -h\nChanging the behavior for -h is easy, but after looking at the code I can say that factor validation of files input with -I is going to take more time.\n\nLast fiddled with by rogue on 2020-12-02 at 21:14\n\n 2020-12-11, 17:31 #479 YaoPlaysMC \u00a0 Nov 2020 2\u00b75 Posts Can you make a program for sieving Generalized Unique primes of the form Phi(3, -k^b)?\n2020-12-11, 20:08 \u00a0 #480\nrogue\n\n\"Mark\"\nApr 2003\nBetween here and the\n\n5\u00d71,249 Posts\n\nQuote:\n Originally Posted by YaoPlaysMC Can you make a program for sieving Generalized Unique primes of the form Phi(3, -k^b)?\nI suggest that you start with the Prime Pages and search for \"Generalized Unique\" to see if any of those primes were found with the help of sieving software that you can use.\n\nI'm not saying that I don't want to do this. I just don't want to cover ground done by someone else, unless I believe that I can write something either more accessible to the average use or much faster than what's available.\n\n 2021-01-05, 20:14 #481 YaoPlaysMC \u00a0 Nov 2020 2\u00b75 Posts Can you make a program to sieve generalized Gaussian Mersenne primes of the form ((b^n-1)^2+1)\/2? Side note: These numbers are considered to be half-GFN because they are of the form (k^2+1)\/2\n2021-01-05, 21:59 \u00a0 #482\nrogue\n\n\"Mark\"\nApr 2003\nBetween here and the\n\n5\u00d71,249 Posts\n\nQuote:\n Originally Posted by YaoPlaysMC Can you make a program to sieve generalized Gaussian Mersenne primes of the form ((b^n-1)^2+1)\/2? Side note: These numbers are considered to be half-GFN because they are of the form (k^2+1)\/2\nPossibly. Is there an efficient way to sieve them?\n\n 2021-01-06, 15:10 #483 rogue \u00a0 \u00a0 \"Mark\" Apr 2003 Between here and the 5\u00b71,249 Posts I have posted 2.1.3 over at sourceforge. Here are the changes: Code: framework: Improve determination of \"largest prime\" tested for per minute stats by ignoring workers that haven't done any work. dmdsieve: version 1.3 Added working factor validation logic with -I. Modify factor validation logic to only verify the first 5 factors for each small prime. If there is a problem it will reveal itself immediately. This improves the speed when starting a new sieve. gnfdsieve, gfndsievecl: version 1.9 Added working factor validation logic with -I. Modify factor validation logic to only verify the first 5 factors for each small prime. If there is a problem it will reveal itself immediately. This improves the speed when starting a new sieve. Allow the GPU to start sieving at (kMax-kMin)\/2 instead of kMax. Switched to Montgomery mulitplication in the GPU. Changed GPU code to handle \"too many factors\" similar to other GPU sievers in the framework as opposed to crashing if not enough GPU memory. GPU code is about 9x faster than CPU code, but GPU code is only of value if one needs to sieve more deeply than (kMax-kMin)\/2, which is somwhere over n=1000. mfsieve: version 1.9 Used vectorized Montgomery logic to get a 1% to 5% speed boost. srsieve2: version 1.3.1 Modify factor validation logic to only verify the first 5 factors for each small prime. If there is a problem it will reveal itself immediately. This improves the speed when starting a new sieve.\n 2021-01-10, 02:27 #484 MisterBitcoin \u00a0 \u00a0 \"Nuri, the dragon :P\" Jul 2016 Good old Germany 32\u00b789 Posts Code: p=24662984657, 428.2K p\/sec, 2771 factors found at 13.13 sec per factor, 98.6% done. ETC 2021-01-10 03:06 Sieve completed at p=25000000013. Processor time: 9358.14 sec. (15.48 sieving) (3.87 cores) I wonder how he took 15,48 for sieving. Maybe its just an error, i used srsieve v 1.1 with the -W 4 flag. This is the first time sieving goes above 1 for me :D","date":"2021-03-02 10:40:23","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.32319575548171997, \"perplexity\": 4850.607439467136}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-10\/segments\/1614178363809.24\/warc\/CC-MAIN-20210302095427-20210302125427-00607.warc.gz\"}"} | null | null |
using System;
using System.Collections.Generic;
using System.Linq;
using System.Web;
using System.Web.UI;
using System.Web.UI.WebControls;
using ProjectData;
using Approve.Common;
using ProjectBLL;
using System.Data;
using Approve.RuleCenter;
using System.Text;
using System.Collections;
using System.Web.UI.HtmlControls;
public partial class JNCLEnt_mangeInfo_equipment : System.Web.UI.Page
{
RCenter rc = new RCenter(); Share sh = new Share();
protected void Page_Load(object sender, EventArgs e)
{
if (!Page.IsPostBack)
{
hfYWBM.Value = YWBM;
ShowInfo();
EnabledControl();
}
}
private void ShowInfo()
{
string sql = "select * from YW_JN_AppEquipment where YWBM='" + YWBM + "' and type='0' order by ftime desc ";
this.Pager1.className = "dbCenter";
this.Pager1.sql = sql;
this.Pager1.pagecount = 20;
this.Pager1.controltopage = "DG_List";
this.Pager1.controltype = "DataGrid";
this.Pager1.dataBind();
}
protected void btnDel_Click(object sender, EventArgs e)
{
pageTool tool = new pageTool(this.Page);
SortedList sl = new SortedList();
sl.Add("YW_JN_AppEquipment", "FID");
tool.DelInfoFromGrid(this.DG_List, sl, "dbCenter");
ShowInfo();
}
protected void btnQuery_Click(object sender, EventArgs e)
{
ShowInfo();
}
protected void DG_List_ItemDataBound(object sender, DataGridItemEventArgs e)
{
if (e.Item.ItemIndex > -1)
{
string FID = EConvert.ToString(DataBinder.Eval(e.Item.DataItem, "FID"));
string SBMC = EConvert.ToString(DataBinder.Eval(e.Item.DataItem, "SBMC"));
e.Item.Cells[1].Text = (e.Item.ItemIndex + 1 + this.Pager1.pagecount * (this.Pager1.curpage - 1)).ToString();
e.Item.Cells[2].Text = "<a href=\"javascript:showAddWindow('editEquipment.aspx?FID=" + FID + "&YWBM=" + YWBM + "',800,400);\" >" + SBMC + "</a>";
}
}
private void EnabledControl()
{
if (Audit == "1" || FIsApprove == "1") //审核页面跳转
{
foreach (Control control in this.form1.Controls)
{
WebHelper.SetControlEnabled(control);
}
}
}
private string YWBM
{
get
{
return Request.QueryString["YWBM"];
}
}
private string FIsApprove
{
get
{
string value = Session["FIsApprove"] == null ? "" : Session["FIsApprove"].ToString();
if (string.IsNullOrEmpty(value))
return "0";
return value;
}
}
private string Audit
{
get
{
return Request.QueryString["audit"];
}
}
} | {
"redpajama_set_name": "RedPajamaGithub"
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Q: Cannot see the desktop panels and desktop shortcut software control panels When booting up Ubuntu 14.04.4 by virtualbox, there are no desktop panels and the shortcut application program with no select items panel doesn't appear, as shown in the image.
How can I fix these two problems?
| {
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12 Best Solar Companies in El Reno, OK (Jan 2023 Review)
and have selected the top 12 in El Reno based on:
HOME > SOLAR > SOLAR COMPANIES > OKLAHOMA > EL RENO
Best solar companies in El Reno
Hoping to obtain energy freedom in El Reno? Installing solar panels can be a rewarding course of action since there are a lot of perks when you go solar. Because of El Reno's very high level of sunshine on average, it's long been on the leading edge of solar energy.
Here, we'll give you a list of some of the top solar companies in El Reno to make your decision much easier. To get an idea of what it could cost to put solar panels on your roof, you can click the button below to be connected to a certified installer near you.
EcoWatch Rankings for Solar Companies in El Reno
My Roof Solar
Website: http://myroofsolarus.com/
Address: 810 W Robinson St, Norman, OK 73069
Starry Solar System
Address: Oklahoma City, OK, OK OK
Sola Solutions
Website: http://www.solasolutionsokc.com/
Address: 2402 N Moore Ave, Moore, OK 73160
Shine Solar LLC
Licensing and credentials transparency
Website: http://www.shinesolar.com/
Address: 4495 SW 119th St, Oklahoma City, OK 73173
Master Solar LLC
Website: https://usasolarpower.com/
Advanced Power Inc.
Website: http://www.solarpumps.com/
Address: 1520 Eagle Rd, Weatherford, OK 73096
Green Wind & Solar
Assists with maximizing rebate
Website: http://www.greenwindandsolar.com/index.html
Address: 3700 Akerman Dr, Norman, OK 73026
SoLiv Solar
Website: https://solivsolar.com/contact
Address: 341 NW 2nd St, Lawton, OK 73507
Green Energy Solutions L.L.C.
Website: https://green-energy-solutions-3.ueniweb.com/
Address: 528 N Louisa Ave A, Shawnee, OK 74801
The Cost and Benefits of Solar in El Reno
For a lot of homeowners, the decision to invest in a solar energy system boils down to the cost. Some important things that influence how much it will cost and how much you could save include:
How much energy your home consumes: Households that use plenty of power each month may need more solar panels and, consequently, more upfront cost, but will also enjoy more savings over time.
Your income and budget: This shapes what model of solar panels you can get.
How much sunlight your roof gets: If your rooftop gets limited direct sunlight, your solar panels won't be able to make as much energy, which will leave you with lower savings on electric bills than a house with a roof that gets plenty of sunlight.
Incentives: Something that can reduce the cost of your solar project is the solar investment tax credit (ITC), which is a tax credit that lets you deduct from your taxes a percentage of the project cost. You can also save a decent amount of money on your energy bills, which can result in an average of $18,000 of savings over 20 years.
Even though a solar panel system costs a decent chunk of money upfront, it can save you thousands of dollars over time. The question of how much, though, depends on several factors, like the amount of daily direct sunlight available and your current power bills.
Adopting a renewable source of energy can greatly impact both the environment and your bills. To see how much, use the calculator below. You can also view our solar panel cost guide for El Reno, OK.
Solar Incentives in El Reno
If you're planning on making the switch to solar power, a variety of government incentives and subsidies can drastically reduce the installation costs and expedite the return on your investment. Everyone can take advantage of the federal Solar Investment Tax Credit (ITC), which lets you claim 30% of how much your solar project cost when you file taxes, reducing the amount of taxes you owe that year. Additionally, there may be some state and city incentives you can benefit from too. Our article on solar incentives has more in-depth information on the incentives you can take advantage of in El Reno.
Environmental Impact of Switching to Solar in El Reno
Replacing nonrenewable energy with solar power is a great way to do your part for a more sustainable future. A question many might be asking themselves is how much can they really help the environment by switching to solar power anyway? In a city like El Reno where energy use is particularly high, switching to solar energy is a fantastic idea for households who want to do their part for the environment. In El Reno, the average person can reduce their carbon footprint by 100 pounds a year once they go solar. For homeowners who care about the environment, the upfront cost of solar is a small price to pay for the offset carbon emissions.
EcoWatch's El Reno, OK Solar Company Rankings FAQs
Which solar panel installer is the best in El Reno?
The highest-rated local solar company in El Reno is My Roof Solar, with a rating of 5.00 stars.
What is the negative environmental impact of solar panels?
Solar panels can be harmful for the environment when manufacturers use toxic chemicals in the manufacturing process. Chemicals can make solar panels difficult to dispose of safely once they've reached the end of their lifespan. Solar panel manufacturing requires a lot of energy as well. The energy payback period is about 1 to 4 years.
How long does it take to see a return on your investment after buying solar panels?
The average payback period for solar panel installation is about 9.6 years, but the exact period is influenced by the cost of electricity where you are, incentives and net metering programs.
How much solar panel capacity do I need for my house?
Solar panel capacity is rated based on how much power they produce under standard testing conditions. Since each panel can generally produce about 250 to 400 watts per hour, the average home will need 20 to 35 panels.
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Northlake, TX | {
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Nikhil Upreti Biography
Nikhil Upreti is a Nepalese actor. His first film was Pinjada, released in 2000, in which he jumped off a seven storied building of Manipal Hospital.
Nikhil Upreti (निखिल उप्रेती) is a Nepalese actor. His first film was Pinjada, released in 2000, in which he jumped off a seven storied building of Manipal Hospital.
He has worked in more than 110 films, won Best Actor in National Films Award for Hami Tin Bhai. He was awarded with Rastriya Nagarik Swarna Samman in 2006. Nikhil Upreti is well known for doing his own stunts. Some of his movies are Pinjada, Nikhil Dai, Hami Tin Bhai, Dhadkan, Bhairav and Lootera.
After years in Mumbai (home of Bollywood), he was scheduled to direct and act in a Hindi movie called Commitment. He made a comeback to Nepalese Film Industry with 'Bhairav' in 2015, which was a commercial hit.
Nikhil Upreti was interested in sports like football (soccer) and Karate in his childhood days. When he got a black belt in Karate, he moved to Mumbai to worked in different movies as an assistant fight director and a stunt boy. Apart from working in movies he was also studying acting in which he got a Diploma in acting from Roshan Taneja's studio, Mumbai. He likes to mention his work experience as an assistant fight director in ABCL company of Amitabh Bachhan.
Born: August 10, 1980 (age 36), Sarlahi District
Spouse: Sanchita Luitel (m. 2009), Kopila Upreti (m. 2002–2009)
Children: Sahisha Upreti, Kashal Upreti
Parents: Bhoj Kumari Upreti, Govinda Upreti
Other names: Nikhil, niks
Nepali Celebrity Biography, Famous Nepali Celebrities Biography: Nikhil Upreti Biography
https://3.bp.blogspot.com/-55f-OILwfNY/WIdkwvZLDdI/AAAAAAAAAl4/pskfHnl34kUANYhZJ3TOnmt-atYyZ9lCQCK4B/s640/Nikhil%2BUpreti.jpg
https://3.bp.blogspot.com/-55f-OILwfNY/WIdkwvZLDdI/AAAAAAAAAl4/pskfHnl34kUANYhZJ3TOnmt-atYyZ9lCQCK4B/s72-c/Nikhil%2BUpreti.jpg
https://biography.lumbinimedia.com/2017/01/nikhil-upreti-biography.html | {
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Out of home advertising: Kawasaki, Cardo and Kymco.
At EICMA 2016 planning for Kawasaki, Cardo e Kymco.
Wheels, billboards at the mezzanine level (strategic point for visitors coming by the subway), billboards on columns and tripods in Corso Italia. Once again, we take the visitor through his way to the halls. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,910 |
{"url":"https:\/\/andrescaicedo.wordpress.com\/2014\/08\/20\/414514-advanced-analysis-analysis-i-syllabus\/","text":"## 414\/514 Advanced Analysis (Analysis I) \u2013\u00a0Syllabus\n\nInstructor: Andr\u00e9s E. Caicedo\nFall 2014\n\nTime: MWF 10:30-11:45 am.\nPlace: Mathematics building, Room 139.\n\nContact Information\n\n\u2022 Office: 239-A Mathematics building.\n\u2022 Phone number: (208)-426-1116. (Not very efficient.)\n\u2022 Office Hours: W 12:00-1:15 pm. (Or by appointment.)\n\u2022 Email: caicedo@math.boisestate.edu\n\nText\nWe will use three textbooks and complement with papers and handouts for topics not covered there.\n\n\u2022 MR1886084 (2003e:00005).\nPugh, Charles Chapman\nReal mathematical analysis.\nUndergraduate Texts in Mathematics. Springer-Verlag, New York, 2002. xii+437 pp.\nISBN: 0-387-95297-7.\n\u2022 MR0655599 (83j:26001).\nvan Rooij, A. C. M.; Schikhof, W. H.\nA second course on real functions.\nCambridge University Press, Cambridge-New York, 1982. xiii+200 pp.\nISBN: 0-521-23944-3; 0-521-28361-2.\n\u2022 MR1996162. See also MR0169961 (30 #204).\nGelbaum, Bernard R.; Olmsted, John M. H.\nCounterexamples in analysis.\nCorrected reprint of the second (1965) edition. Dover Publications, Inc., Mineola, NY, 2003. xxiv+195 pp.\nISBN: 0-486-42875-3.\n\nThe book by van Rooij and Schikhof will be our primary reference, supplemented naturally by the Counterexamples book.\u00a0 The book assumes some knowledge beyond what is covered in our undergraduate course Math 314: Foundations of Analysis, and does not cover the theory in dimension $n>1$; for these topics, we will follow Pugh\u2019s text.\n\nContents\nMath 414\/514 covers Analysis on Euclidean spaces (${\\mathbb R}^n$) with emphasis on the theory in dimension one. The approach is theoretical, as opposed to the more computational approach of calculus, and a certain degree of mathematical maturity is required. The course is cross-listed, and accordingly the level will be aimed at beginning graduate students.\n\nFrom the Course Description on the Department\u2019s site:\n\nIntroduction to fundamental elements of analysis on Euclidean spaces including the basic differential and integral calculus. Topics include: infinite series, sequences and series of function, uniform convergence, theory of integration, implicit function theorem and applications.\n\nHere is a short list of topics we expect to cover. This list may change based on students\u2019 interest:\n\n1. Set theoretic preliminaries.\n\u2022 Cantor\u2019s approach to infinite cardinalities. Countable vs. uncountable sets. Sets of size continuum. The Bernstein-Cantor-Schr\u00f6der theorem.\n\u2022 The axiom of choice. Zorn\u2019s lemma. Countable and dependent choice.\n\u2022 Transfinite recursion. The first uncountable ordinal $\\omega_1$.\n2. Axiomatization and construction of the set of reals.\n\u2022 The least upper bound property; uniqueness of $\\mathbb R$ up to isomorphism.\n\u2022 Dedekind cuts, and complete orders.\n\u2022 Metric spaces, and Cauchy completions. Banach contraction mapping theorem.\n3. Topology on $\\mathbb R$.\n\u2022 Open and closed sets. Compact sets and Cantor sets. Baire space.\n\u2022 Borel sets. Analytic sets.\n\u2022 Notions of smallness.\n\u2022 Meagerness and the Baire category theorem. The Baire-Cantor stationary principle.\n\u2022 Sets of Jordan content zero and of measure zero.\n\u2022 Introduction to the theory of strong measure zero sets.\n4. Continuity.\n\u2022 Sets of discontinuity of functions.\n\u2022 Monotonicity. Functions of bounded variation.\n5. Differentiability.\n\u2022 The problem of characterizing derivatives. Baire class one functions. The intermediate value property. Sets of continuity of derivatives.\n\u2022 The mean value theorem. L\u2019H\u00f4pital\u2019s rule.\n\u2022 The dynamics of Newton\u2019s method.\n\u2022 The Baire hierarchy of functions.\n\u2022 Continuous nowhere differentiable functions.\n6. Power series.\n\u2022 Real analytic functions. Taylor series.\n\u2022 $C^\\infty$ functions. Zahorsky\u2019s characterization of the sets of points where a $C^\\infty$ function fails to be analytic.\n7. Integration.\n\u2022 Riemann integration. Lebesgue\u2019s characterization of Riemann integrability.\n\u2022 Weierstra\u00df approximation theorem.\n\u2022 Lebesgue integration. The fundamental theorem of calculus.\n\u2022 The Henstock-Kurzweil integral. Denjoy\u2019s approach to reconstructing primitives.\n8. Introduction to multivariable calculus.\n\u2022 (Frechet) derivatives.\n\u2022 The inverse and implicit function theorems.\n\nBased on homework. No late homework is allowed. Collaboration is encouraged, although students must turn in their own version of the solutions, and give credit to books\/websites\/\u2026 that were consulted and people with whom the problems where discussed.\n\nThere will be no exams. However, an important component of being proficient in mathematics is a certain amount of mental agility in recalling notions and basic arguments. I plan to assess these by requesting oral presentations of solutions to some of the homework problems throughout the term. If I find the students lacking here, it will be necessary to have an exam or two. The final exam is currently scheduled for Wednesday, December 17, 2014, 12:00-2:00 pm.\n\nAdditional information will be posted in this blog, and students are encouraged to use the comments feature. Please use full names, which will simplify my life filtering spam out.\n\nOn occasion, I post links to supplementary material on Google+ and Twitter.","date":"2017-02-20 03:53:42","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 7, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7633621692657471, \"perplexity\": 3069.0934379101677}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-09\/segments\/1487501170404.1\/warc\/CC-MAIN-20170219104610-00485-ip-10-171-10-108.ec2.internal.warc.gz\"}"} | null | null |
\section{Introduction}
The BaBar measurements of the rates of $B^-$ and ${\bar B}^0$ semileptonic decays into $D^{(*)}$ and a $\tau$ lepton seem to indicate a significant deviation from the standard model (SM) expectation.
The experimental results concern the $B\to D^{(*)} \tau {\bar \nu}_\tau $ decay widths normalized to the widths of the corresponding modes having a light $\ell=e,\,\mu$ lepton in the final state \cite{Lees:2012xj}:
\begin{eqnarray}
{\cal R}^-(D)=\frac{{\cal B}(B^- \to D^0 \tau^- \,{\bar \nu}_\tau)}{{\cal B}(B^- \to D^0 \ell^- \,{\bar \nu}_\ell)}=0.429 \pm 0.082 \pm 0.052 \,\,\, , &\hskip 0.1 cm &
{\cal R}^-(D^*)=\frac{{\cal B}(B^- \to D^{*0} \tau^- \,{\bar \nu}_\tau)}{{\cal B}(B^- \to D^{*0} \ell^- \, {\bar \nu}_\ell)}=0.322 \pm 0.032 \pm 0.022\,\, , \nonumber \\
{\cal R}^0(D)=\frac{{\cal B}({\bar B}^0 \to D^+ \tau^- \, {\bar \nu}_\tau)}{{\cal B}({\bar B}^0 \to D^+ \ell^- \, {\bar \nu}_\ell)}=0.469 \pm 0.084 \pm 0.053 \,\,\, , & \hskip 0.1 cm &
{\cal R}^0(D^*)=\frac{{\cal B}({\bar B}^0 \to D^{*+} \tau^- \, {\bar \nu}_\tau)}{{\cal B}({\bar B}^0 \to D^{*+} \ell^- \, {\bar \nu}_\ell)}=0.355 \pm 0.039 \pm 0.021 \,\,\nonumber \\ \label{data}
\end{eqnarray}
(the first and second error are the statistic and systematic uncertainty, respectively). The measurements have been estimated to deviate at the global level of 3.4$\sigma$ with respect to SM predictions \cite{Lees:2012xj,Fajfer:2012vx}.
Therefore, there is the possibility that semileptonic processes involving heavy quarks and the $\tau$ lepton are unveiling the effects of particles with large couplings to the heavier fermions, as it is natural for charged scalars which could contribute to the tree-level $b \to c \ell \bar \nu$ transitions
\cite{Fajfer:2012vx,Fajfer:2012jt,Becirevic:2012jf,Datta:2012qk,Celis:2012dk,Crivellin:2012ye,Choudhury:2012hn,Tanaka:2012nw}.
Before the observation of these possible hints of new physics (NP) in semileptonic $b \to c$ decays, the first experimental analyses of the purely leptonic $B^- \to \tau^- {\bar \nu}_\tau$ mode also reported an excess of events. In SM
the ${\cal B}(B^- \to \tau^- {\bar \nu}_\tau)$ branching fraction is given by
\begin{equation}
{\cal B}(B^- \to \tau^- {\bar \nu}_\tau)={G_F^2 m_B m_\tau^2 \over 8 \pi} \left(1- {m_\tau^2 \over m_B^2}\right)^2f_B^2 \, |V_{ub}|^2\, \tau_{B^-} \,\,, \label{brBtaunutau}
\end{equation}
neglecting a tiny electromagnetic radiative correction.
Using the lattice QCD average for the $B$ decay constant $f_B=(190.6 \pm 4.7)$ MeV quoted in \cite{Laiho:2009eu}, and varying the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{ub}|$ in the range determined from inclusive and exclusive $B$ decays: $|V_{ub}|=0.0035 \pm 0.0005$, the prediction follows: ${\cal B}(B^- \to \tau^- {\bar \nu}_\tau)=(0.79 \pm 0.23)\times 10^{-4}$, in agreement with the outcome of CKM matrix fits \cite{Bona:2009cj,Lenz:2010gu}. This value is smaller by about a factor of 2 than the experimental results
reported in \cite{Ikado:2006un,Hara:2010dk,Aubert:2007xj,Aubert:2009wt} and compiled in \cite{Rosner:2012np}: ${\cal B}(B^- \to \tau^- {\bar \nu}_\tau)=(1.68 \pm 0.31)\times 10^{-4}$. However, new Belle \cite{Adachi:2012mm} and BaBar \cite{Lees:2012ju} measurements, obtained using the hadronic tagging method,
\begin{eqnarray}
{\cal B}(B^- \to \tau^- {\bar \nu}_\tau)&=& \left(0.72^{+0.27}_{-0.25}\pm 0.11\right) \times 10^{-4} \,\,\,\,\, {\rm (Belle)} \nonumber \\
{\cal B}(B^- \to \tau^- {\bar \nu}_\tau)&=& \left(1.83^{+0.53}_{-0.49} \pm 0.24 \right) \times 10^{-4} \,\,\,\,\, {\rm (BaBar)}
\end{eqnarray}
are more consistent with SM, and draw the average ${\cal B}(B^- \to \tau^- {\bar \nu}_\tau)$ to a smaller value: ${\cal B}(B^- \to \tau^- {\bar \nu}_\tau)=(1.12 \pm 0.22)\times 10^{-4}$, after the combination with the semileptonic tagging method results, see fig.\ref{fig:Bleptonic}.
\begin{figure}[!h]
\centering
\includegraphics[width = 0.35\textwidth]{Btaunu.pdf}
\caption{Experimental results for ${\cal B}(B^- \to \tau^- {\bar \nu}_\tau)$ \cite{Aubert:2009wt,Hara:2010dk,Adachi:2012mm,Lees:2012ju} together with the SM expectation corresponding to $|V_{ub}|=0.0035 \pm 0.0005$ (vertical band).}\label{fig:Bleptonic}
\end{figure}
The different trend of the measurements involving $\tau$ in $B$ leptonic and semileptonic decay modes poses two questions. The first one concerns the level of accuracy of the SM predictions for the ratios in (\ref{data}). The second one is which kind of new physics effects, if any, could modify the ratios (\ref{data}) without affecting the purely leptonic mode. Indeed,
several analyses devoted to try to explain the anomalies in $B\to D^{(*)} \tau {\bar \nu}_\tau $ within new physics scenarios have considered as possible candidates models with new scalars having couplings to leptons proportional to the lepton mass, to guarantee the enhancement of the $\tau$ modes. This is the case of models with two Higgs doublets (2HDM), the best known example being the minimal supersymmetric standard model in which two Higgs doublets are required to give mass to down-type quarks and charged leptons in one case, and up-type quarks in the other. In this framework, the ratios (\ref{data}) depend on the mass of the charged Higgs $H^\pm$ and the ratio $\beta$ of the two Higgs doublet VEVs, and no choice of such parameters allows to simultaneously reproduce the experimental data on ${\cal R}(D)$ and ${\cal R}(D^*)$ \cite{Lees:2012xj}. Variants of the 2HDM \cite{Crivellin:2012ye,Celis:2012dk}, together with other models providing explicit flavour violation \cite{Fajfer:2012jt}, might explain the measurements (\ref{data}); however, an enhancement of the purely leptonic $B$ decay rate is generally implied.
In this paper we reconsider both the above mentioned issues. We reanalyse the SM prediction for $B \to D^{(*)} \ell {\bar \nu}_\ell$, specifying the main sources of uncertainties and possible improvements. Our results confirm that the most significant deviation is for ${\cal R}(D^*)$.
Then, we scrutinize the effects of possible NP contributions in the effective weak Hamiltonian having a structure able to affect the ratios (\ref{data}) but leaving the pure $B$ leptonic modes unchanged. In particular, we focus on a NP operator
constructed from tensor quark and lepton currents. Such a kind of operators have been also investigated in \cite{Becirevic:2012jf} and \cite{Tanaka:2012nw}, but we devote the main attention to differential distributions, namely the lepton forward-backward differential asymmetries, in which the sensitivity to the new Dirac structure is maximal, as emphasized in \cite{Datta:2012qk} for different operators. Although there are scenarios in which tensor operators are generated,
in our analysis we do not rely on explicit models: our purpose is to identify physical observables having a mild sensitivity to hadronic uncertainties, which therefore can be used to unveil effects easier to interpret.
It is only worth mentioning that these operators emerge,
for example, in models with new coloured bosons carrying both lepton and baryon quantum number (referred to as leptoquarks, LQ): SU(5)$_{GUT}$ \cite{Georgi:1974sy}, Pati-Salam SU(4) \cite{Pati:1974yy}, composite \cite{Schrempp:1984nj}, superstrings \cite{Hewett:1988xc} and technicolor models \cite{Dimopoulos:1979es}. In the most general formulation of these
models scalar operators may also occur. Leptoquarks couple to quarks and leptons and, from limits on flavour changing neutral currents, preferably to those within the same SM generation. Searches for leptoquarks decaying to 2$\tau$ and 2$b$ jets, performed by the CMS Collaboration at the CERN LHC, bound (preliminarly) the mass of a possible scalar leptoquark to $M(LQ)>525$ GeV, and to $M(LQ)>760$ GeV for a vector leptoquark \cite{cms}; other bounds can be found in \cite{leptoquarks}.
In our analysis of semileptonic $B$ decays, we first consider $D$ and $D^*$ mesons in the final state, and then turn to the interesting case of final states with excited positive parity charmed mesons.
\section{Exclusive $b \to c \ell {\bar \nu}_\ell$ Decays}
We consider the $b \to c \ell {\bar \nu}_\ell$ effective hamiltonian comprising the SM term and an additional operator \cite{Becirevic:2012jf,Tanaka:2012nw}:
\begin{equation}
H_{eff}=H_{eff}^{SM}+H_{eff}^{NP} = {G_F \over \sqrt{2}}V_{cb} \left[ {\bar c} \gamma_\mu (1-\gamma_5) b \, {\bar \ell} \gamma^\mu (1-\gamma_5) {\bar \nu}_\ell + \epsilon_T^\ell \, {\bar c} \sigma_{\mu \nu} (1-\gamma_5) b \, {\bar \ell} \sigma^{\mu \nu} (1-\gamma_5) {\bar \nu}_\ell \right] \,\,\, . \label{heff}
\end{equation}
$G_F$ is the Fermi constant and $V_{cb}$ the CKM matrix element. $\epsilon_T^\ell$ is the relative complex coupling of the new tensor term with respect to the SM one. It is assumed that the main coupling is to the heaviest lepton, hence we set $\epsilon_T^\ell=0$ for $\ell=e,\mu$ and $\epsilon_T\equiv \epsilon_T^\tau$. This coupling can be bound experimentally, so that the effects of the new operator can be scrutinized
in physical observables which, in general, are expressed as a SM, a new physics and an interference contribution.
For example, the differential $B(p) \to M_c(p^\prime) \ell(p_1) {\bar \nu}_\ell(p_2)$ decay rate, with $M_c$ a charmed meson, reads:
\begin{equation}
{d \Gamma \over dq^2}(B \to M_c \ell \bar \nu_\ell)=C(q^2) \left[ {d \tilde \Gamma \over dq^2}(B \to M_c \ell \bar \nu_\ell)\Big|_{SM}+{d \tilde \Gamma \over dq^2}(B \to M_c \ell \bar \nu_\ell)\Big|_{NP}+{d \tilde \Gamma \over dq^2}(B \to M_c \ell \bar \nu_\ell)\Big|_{INT} \right]\,, \label{dgammadq2-generic}
\end{equation}
with $q=p-p^\prime$ and $C(q^2)$ defined as
\begin{equation}
C(q^2)={G_F^2 |V_{cb}|^2 \lambda^{1/2}(m_B^2,m_{M_c}^2,q^2) \over 192 \pi^3 m_B^3}
\left(1 -{m_\ell^2 \over q^2 } \right)^2 \,\,\, ; \label{C-factor}
\end{equation}
$\lambda(x,y,z)=x^2+y^2+z^2-2(xy+xz+yz)$ is the triangular function.
To compute the three terms in (\ref{dgammadq2-generic}) we need the relevant hadronic matrix elements.
\subsection{$B \to D \ell {\bar \nu}_\ell$ }
The hadronic matrix elements in $B \to D \ell {\bar \nu}_\ell$ can be parametrized in a standard way,
\begin{eqnarray}
<D(p^\prime)|{\bar c} \gamma_\mu b| B(p)>&=&F_1(q^2)(p+p^\prime)_\mu+{m_B^2-m_D^2 \over q^2} \left[F_0(q^2)-F_1(q^2)\right] q_\mu \,\,\, , \label{V-A-D} \\
<D(p^\prime)|{\bar c} \sigma_{\mu \nu}(1-\gamma_5) b| B(p)>&=&{F_T(q^2) \over m_B+m_D} \, \epsilon_{\mu \nu \alpha \beta} p^{\prime \alpha} p^\beta+i\,{G_T(q^2) \over m_B+m_D} \, (p_\mu p^\prime_\nu-p_\nu p^\prime_\mu)\,, \label{T-D}
\end{eqnarray}
(with $F_T=G_T$ from the relation $\sigma_{\mu \nu} \gamma_5=\frac{i}{2}\epsilon_{\mu \nu \alpha \beta}\,\sigma^{\alpha \beta}$),
so that the three terms in (\ref{dgammadq2-generic}) read:
\begin{eqnarray}
{d \tilde \Gamma \over dq^2}(B \to D \ell \bar \nu_\ell)\Big|_{SM} &=&
\lambda (m_B^2,m_{D}^2,q^2)\left(1+{m_\ell^2 \over 2 q^2} \right) \left[F_1(q^2)\right]^2+m_B^4 \left(1-{m_D^2 \over m_B^2} \right)^2{3 m_\ell^2 \over 2 q^2} \left[F_0(q^2)\right]^2 \,, \label{D-SM}
\\
{d \tilde \Gamma \over dq^2}(B \to D \ell \bar \nu_\ell)\Big|_{NP} &=&{|\epsilon_T|^2 \over 2} {q^2 \over (m_B+m_D)^2}\, \lambda (m_B^2,m_{D}^2,q^2) \left(1+2{m_\ell^2 \over q^2} \right) \, \left[F_T(q^2)+G_T(q^2)\right]^2 \label{D-NP} \,, \\
{d \tilde \Gamma \over dq^2}(B \to D \ell \bar \nu_\ell)\Big|_{INT}& =&-3 Re[\epsilon_T]{ m_\ell \over m_B + m_D}\, \lambda (m_B^2,m_{D}^2,q^2) \, F_1(q^2)\, \left[F_T(q^2)+G_T(q^2)\right] \label{D-INT}\,.
\end{eqnarray}
In the infinite heavy quark mass limit, formalized by the heavy quark effective theory (HQET), the form factors in (\ref{V-A-D}-\ref{T-D}) can all be related to the Isgur-Wise function $\xi$ \cite{Isgur:1989ed}. The result is known \cite{hqet,hqet1}:
expressing $F_1(q^2)$ and $F_0(q^2)$ in terms of two other form factors $h_+(w)$ and $h_-(w)$:
\begin{eqnarray}
F_1(q^2)&=& \frac{1}{ 2 \sqrt{m_B m_D}} \left[(m_B+m_D) h_+(w) - (m_B-m_D)h_-(w)\right] \\
\frac{m_B^2 -m_D^2}{q^2}\left[F_0(q^2)-F_1(q^2)\right]&=& \frac{1}{ 2 \sqrt{m_B m_D}} \left[(m_B+m_D) h_-(w) - (m_B-m_D)h_+(w) \right]\,\,,
\end{eqnarray}
and defining the meson momenta in terms of four-velocities, $p=m_B v$ and $p^\prime=m_D v^\prime$, with $w=v \cdot v^\prime$ and $q^2 = m_B^2+m_D^2-2m_B m_D w$,
at the leading order in the heavy quark and $\alpha_s$ expansion one has
\begin{equation}
h_+(w)=\xi(w) \,\,\,\, , \hskip 1 cm h_-(w)=0 \,\,\, , \label{hpiu-meno-xi}
\end{equation}
with $\xi(w)$ the Isgur-Wise function.
Also the form factors in (\ref{T-D}) are related to $\xi(w)$ at the same order expansion:
\begin{equation}
F_T(q^2)=G_T(q^2)={m_B+m_D \over \sqrt{m_B m_{D}}} \,\xi(w) \,\,\, . \label{FT-GT-xi}
\end{equation}
At the next-to-leading order, corrections must be taken into account, which at first are needed for the
study of the decay in SM. We elaborate a determination of the functions $h_+$, $h_-$ and $\xi $ based on a combination of experimental and theoretical information. The experimental input comes from the
BaBar analysis of $B \to D \mu {\bar \nu}_\mu$ \cite{Aubert:2009ac}, the differential rate of which, neglecting the lepton mass, reads:
\begin{equation}
{d \Gamma \over dw}( B \to D \ell \bar \nu_\ell)={G_F^2 |V_{cb}|^2 \over 48 \pi^3 } m_B^5 r^3(1+r)^2 (w^2-1)^{3/2} [F_D(w)]^2 \,\,\, ,
\end{equation}
with
\begin{equation}
F_D(w)= \left[ h_+(w)-{1-r \over 1+r} h_-(w) \right] \end{equation}
and $\displaystyle r=\frac{m_D}{m_B}$. Using the parametrization \cite{Caprini:1997mu}
\begin{equation}
F_D(w)=F_D(1) \Big\{ 1-8 \rho_1^2 z+(51 \rho_1^2-10)z^2-(252\rho_1^2-84)z^3 \Big\} \,\,\, \label{FD}
\end{equation}
in terms of the variable
\begin{equation}
z={ \sqrt{w+1}-\sqrt{2} \over \sqrt{w+1}+\sqrt{2}} \,\,\, , \label{zeta}
\end{equation}
from the fit of the product $G^{BaBar}(w)=F_D(w)|V_{cb}|$ the BaBar Collaboration provides the parameters $G^{BaBar}(1)=F_D(1)|V_{cb}|$ and $\rho_1^2$.
The outcome of the fit is slightly different for $B^-$ or ${\bar B}^0$ modes; we consider for definiteness the ${\bar B}^0$ case \cite{Aubert:2009ac}
\footnote{The average between the charged and neutral $B$ decay modes is quoted as $G^{BaBar}(1)=(42.3 \pm 1.9 \pm 1.4) \, 10^{-3}$ , $ \rho_1^2=1.20 \pm 0.09 \pm 0.04$.},
\begin{equation}
G^{BaBar}(1)=(44.9 \pm 3.2 \pm 1.6) \, 10^{-3}\,\,\, , \hskip 1cm \rho_1^2=1.29 \pm 0.14 \pm 0.05\,\,.
\end{equation}
This result can be translated into a determination of $\xi(w)$, expressing the form factors $h_\pm(w)$ in terms of the Isgur-Wise function and including the $\alpha_s$ and $1/m_{b,c}$ corrections worked out by M. Neubert in \cite{hqet} and by I. Caprini et al., in \cite{Caprini:1997mu}:
\begin{eqnarray}
h_+(w)&=&\left[C_1 +{w+1 \over 2} (C_2+C_3) +(\epsilon_b+\epsilon_c) L_1 \right] \xi(w)={\tilde h}_+(w) \, \xi(w) \label{hpiu} \\
h_-(w)&=&\left[{w+1 \over 2} (C_2-C_3) +(\epsilon_c -\epsilon_b) L_4 \right] \xi(w)={\tilde h}_-(w) \, \xi(w) \label{hmeno}
\end{eqnarray}
with $\epsilon_b=\displaystyle{1 \over 2 m_b}$, $\epsilon_c=\displaystyle{1 \over 2 m_c}$.
The coefficients $C_{1,2,3}$ and $L_i$ are collected in appendix \ref{app:coefficients}. $C_i$ account for the perturbative corrections, $L_i$ for the heavy quark mass corrections and depend on the hadronic parameter $\bar \Lambda$, the difference between the heavy meson ($B,\,D$) and the heavy quark ($b,\,c$) mass in the heavy quark limit.
We use $m_b=4.8$ GeV and $m_c=1.4$ GeV and a conservative value ${\bar \Lambda}=0.5 \pm 0.2$ GeV \cite{hqet}, so that the uncertainty in ${\bar \Lambda}$ encompasses the error on
${\bar \Lambda}/m_b$ and ${\bar \Lambda}/m_c$.
The Isgur-Wise function $\xi(w)$ resulting from
\begin{equation}
|V_{cb}| \, \xi(w)=\frac{G^{BaBar}(w)}{\left[ \tilde h_+(w)-{1-r \over 1+r} \, \tilde h_-(w) \right]} \,\,
\label{xi}
\end{equation}
is depicted in fig.\ref{fig:xi} (left panel).
\begin{figure}[!t]
\centering
\includegraphics[width = 0.4\textwidth]{csiBabar.pdf}\hspace*{0.5cm}
\includegraphics[width = 0.4\textwidth]{csiBelle.pdf}
\caption{Isgur-Wise function $\xi(w)$ (times $|V_{cb}|\times 10^2$) obtained using the BaBar data on ${\bar B}^0 \to D^+ \ell^- \bar \nu_\ell$ (left) and the Belle data on ${\bar B}^0 \to D^{*+} \ell^- \bar \nu_\ell$ (right) . The width of the curves is due to the errors in the parameters fitted in the two cases and to the uncertainty on ${\bar \Lambda}$ and $\alpha_s$ in the determination of the form factor.}\label{fig:xi}
\end{figure}
The form factors needed for analysis of the mode with $\tau$ can be separately derived using again Eqs.(\ref{hpiu},\ref{hmeno}):
\begin{eqnarray}
|V_{cb}| \, h_+(w)&=& \frac{1}{1- {1-r \over 1+r} \, A(w)} \,\, G^{BaBar}(w) \\
|V_{cb}| \, h_-(w)&=& \frac{A(w)}{1- {1-r \over 1+r} \, A(w)} \,\, G^{BaBar}(w)
\end{eqnarray}
with $A=\tilde h_-/\tilde h_+$. For the matrix elements of the tensor operator, we use $\xi(w)$ also in (\ref{FT-GT-xi}). In the standard model, the results for the semileptonic
${\bar B}^0 \to D^+$ branching fractions can be quoted as
\begin{eqnarray}
{\cal B}({\bar B}^0 \to D^+ \ell^- {\bar \nu}_\ell)\Big|_{SM} &=& (2.15 \pm 0.45) \times 10^{-2} \\
{\cal B}({\bar B}^0 \to D^+ \tau^- {\bar \nu}_\tau)\Big|_{SM} &=& (0.70 \pm 0.12) \times 10^{-2}
\end{eqnarray}
and, taking the correlation between the predictions for $\ell$ and $\tau$ into account,
\begin{equation}
{\cal R}^0(D)\Big|_{SM}=\frac{{\cal B}({\bar B}^0 \to D^+ \tau^- {\bar \nu}_\tau)}{{\cal B}({\bar B}^0 \to D^+ \ell^- {\bar \nu}_\ell) }\Big|_{SM}=0.324 \pm 0.022 \,\,\, . \label{R0res}
\end{equation}
The SM prediction for ${\cal R}^0(D)$ deviates from the measurement (\ref{data}) (with statistic and systematic uncertainties combined in quadrature) by about 1.5$\sigma$ .
The deviation is smaller in the charged ${\cal R}^-(D)$ case.
The stability of (\ref{R0res}) against changes of the input information on form factors is noticeable: sensitivity to $1/m_Q$ corrections can be estimated varying $\bar \Lambda$, and this modifies the central value
at a few per mille level. Sensitivity to the radiative corrections can be assessed changing the scale in $\alpha_s$ as indicated in appendix \ref{app:coefficients}, and also these corrections are not effective. Since the value at zero recoil $G^{BaBar}(1)$ cancels out in the ratio,
the main uncertainty in (\ref{R0res}) comes from the error on the parameter $\rho_1^2$ experimentally determined. The value of ${\cal R}^0(D)$ coincides with the one obtained using the form factors $F_1$ and $F_0$ from lattice QCD with finite quark masses \cite{Becirevic:2012jf}.
\subsection{$B \to D^* \ell {\bar \nu}_\ell$}
While the results for ${\cal R}^0(D)$ and ${\cal R}^-(D)$ do not display a statistically significant deviation from the SM expectation, the case of ${\cal R}^0(D^*)$, ${\cal R}^-(D^*)$ is quite different.
The standard parameterization of the $B \to D^*$ matrix element in terms of form factors is
\begin{eqnarray}
<D^*(p^\prime,\epsilon)|{\bar c} \gamma_\mu(1-\gamma_5) b| {\bar B}(p)>&=&- {2 V(q^2) \over m_B+m_{D^*}} i \epsilon_{\mu \nu \alpha \beta} \epsilon^{*\nu} p^\alpha p^{\prime \beta} -\Bigg\{ (m_B+m_{D^*}) \left[ \epsilon^*_\mu -{(\epsilon^* \cdot q) \over q^2} q_\mu \right] A_1(q^2) \nonumber\\
&&- {(\epsilon^* \cdot q) \over m_B+m_{D^*}} \left[ (p+p^\prime)_\mu -{m_B^2-m_{D^*}^2 \over q^2} q_\mu \right] A_2(q^2)
+ (\epsilon^* \cdot q){2 m_{D^*} \over q^2} q_\mu A_0(q^2) \Bigg\} \nonumber \\ \label{FF-D*-mio}
\end{eqnarray}
(with the condition $\displaystyle A_0(0)= \frac{m_B + m_{D^*}}{2 m_{D^*}} A_1(0) - \frac{m_B - m_{D^*}}{2 m_{D^*}} A_2(0)$) and
\begin{eqnarray}
<D^*(p^\prime,\epsilon)|{\bar c} \sigma_{\mu \nu}(1-\gamma_5) b| {\bar B}(p)>&=&T_0(q^2) {\epsilon^* \cdot q \over (m_B+ m_{D^*})^2} \epsilon_{\mu \nu \alpha \beta} p^\alpha p^{\prime \beta}+
T_1(q^2) \epsilon_{\mu \nu \alpha \beta} p^\alpha \epsilon^{*\beta}+T_2(q^2) \epsilon_{\mu \nu \alpha \beta} p^{\prime \alpha} \epsilon^{*\beta}\nonumber \\
&+&i \, \Big[ T_3(q^2) (\epsilon^*_\mu p_\nu -\epsilon^*_\nu p_\mu)+T_4(q^2) (\epsilon^*_\mu p^\prime_\nu -\epsilon^*_\nu p^\prime_\mu) \nonumber \\
&+&T_5(q^2) {\epsilon^* \cdot q \over (m_B+ m_{D^*})^2}(p_\mu p^\prime_\nu -p_\nu p^\prime_\mu)\Big] \,\,, \label{mat-tensor-Dstar}
\end{eqnarray}
with $\epsilon$ the $D^*$ polarization vector.
We choose the helicity basis for $D^*$
\begin{equation}
\epsilon^\mu_L = {1 \over m_{D^*}} \left( |\vec p^\prime|, 0,0, E^\prime \right) \,\,\,\, , \hspace*{0.5cm}
\epsilon^\mu_\pm={1 \over \sqrt{2}} \left(0,1, \mp i, 0 \right)\,\,\,\, , \label{pol-vec}
\end{equation}
with $E^\prime$ and $\vec p^\prime$
the $D^*$ energy and three-momentum in the $B$ rest frame ($E^\prime=\sqrt{m_{D^*}^2+|\vec p^\prime|^2}$ and $\displaystyle |\vec p^\prime|=\lambda (m_B^2,m_{D^*}^2,q^2)/2 m_B$).
The conditions $\epsilon^\mu_a \cdot p^\prime=0$ and $\epsilon^\mu_a \cdot \epsilon_{\mu,b}=-\delta_{ab}$, with $a,b=L,\pm$, are fulfilled.
The differential decay rates for the longitudinal and the transverse $D^*$ polarization in terms of form factors are obtained from
\begin{eqnarray}
{d \tilde \Gamma_L \over dq^2}(B \to D^* \ell \bar \nu_\ell)\Big|_{SM} &=&
\frac{1}{4m_{D^*}^2}\Bigg\{6\lambda(m_B^2,m_{D^*}^2,q^2) m_{D^*}^2 \frac{m_\ell^2}{q^2}[A_0(q^2)]^2 \nonumber \\
&&+\left(1+\frac{m_\ell^2}{2q^2} \right) \left[(m_B+m_{D^*})(m_B^2-m_{D^*}^2-q^2)A_1(q^2)-\frac{\lambda(m_B^2,m_{D^*}^2,q^2)}{m_B+m_{D^*}}A_2(q^2) \right]^2 \Bigg\} \,\, ,
\label{DstarSML} \\
{d \tilde \Gamma_L \over dq^2}(B \to D^* \ell \bar \nu_\ell)\Big|_{NP} & = &|\epsilon_T|^2 \frac{q^2}{8}\left(1+\frac{2m_\ell^2}{q^2} \right) \Big[\frac{\lambda(m_B^2,m_{D^*}^2,q^2)}{m_{D^*}(m_B+m_{D^*})^2}{\tilde T}_0(q^2)+2\frac{m_B^2+m_{D^*}^2-q^2}{m_{D^*}}{\tilde T}_1(q^2)+4m_{D^*}{\tilde T}_2(q^2) \Big]^2, \nonumber \\
\label{DstarNPL} \\
{d \tilde \Gamma_L \over dq^2}(B \to D^* \ell \bar \nu_\ell)\Big|_{INT} &=&-Re(\epsilon_T)\frac{3m_\ell}{4(m_B+m_{D^*})}\Big[(m_B+m_{D^*})^2(m_B^2-m_{D^*}^2-q^2)A_1(q^2)-\lambda(m_B^2,m_{D^*}^2,q^2)A_2(q^2) \Big] \nonumber\\
&&\left[\frac{\lambda(m_B^2,m_{D^*}^2,q^2)}{m_{D^*}^2(m_B+m_{D^*})^2}{\tilde T}_0(q^2)+\frac{2(m_B^2+m_{D^*}^2-q^2)}{m_{D^*}^2}{\tilde T}_1(q^2)+4{\tilde T}_2(q^2) \right] \,\, , \label{DstarINTL}
\end{eqnarray}
\begin{eqnarray}
{d \tilde \Gamma_\pm \over dq^2}(B \to D^* \ell \bar \nu_\ell)\Big|_{SM} &=& q^2\left(1+\frac{m_\ell^2}{2q^2} \right) \Bigg\{(m_B+m_{D^*})^2[A_1(q^2)]^2+\frac{\lambda(m_B^2,m_{D^*}^2,q^2)}{(m_B+m_{D^*})^2}[V(q^2)]^2\Bigg\} \,\, ,\label{DstarSMpm} \\
{d \tilde \Gamma_\pm \over dq^2}(B \to D^* \ell \bar \nu_\ell)\Big|_{NP} &=&|\epsilon_T|^2 \left(1+\frac{2m_\ell^2}{q^2} \right)
\Bigg\{\lambda(m_B^2,m_{D^*}^2,q^2)[{\tilde T}_1(q^2)+{\tilde T}_2(q^2)]^2 \nonumber \\
&&+2q^2\left[m_B^2[{\tilde T}_1(q^2)]^2+m_{D^*}^2[{\tilde T}_2(q^2)]^2+(m_B^2+m_{D^*}^2-q^2){\tilde T}_1(q^2){\tilde T}_2(q^2)\right]\Bigg\} \,\, ,
\label{DstarNPpm} \\
{d \tilde \Gamma_\pm \over dq^2}(B \to D^* \ell \bar \nu_\ell)\Big|_{INT} &=&-Re(\epsilon_T)3m_\ell\Bigg\{2q^2(m_B+m_{D^*})A_1(q^2){\tilde T}_1(q^2)
\nonumber \\
&&+\left[(m_B+m_{D^*})(m_B^2-m_{D^*}^2-q^2)A_1(q^2)-
\frac{\lambda(m_B^2,m_{D^*}^2,q^2)}{(m_B+m_{D^*})}V(q^2) \right][{\tilde T}_1(q^2)+{\tilde T}_2(q^2)]\Bigg\} \,\,,\nonumber \\ \label{DstarINTpm}
\end{eqnarray}
to be multiplied by the factor $C(q^2)$ in (\ref{C-factor}).
We have used the combinations
\begin{eqnarray}
{\tilde T}_0(q^2)&=&T_0(q^2)-T_5(q^2) \nonumber \\
{\tilde T}_1(q^2)&=&T_1(q^2)+T_3(q^2) \\
{\tilde T}_2(q^2)&=&T_2(q^2)+T_4(q^2) \,\,. \nonumber
\end{eqnarray}
At the leading order in the heavy quark expansion, the form factors in (\ref{FF-D*-mio}) and (\ref{mat-tensor-Dstar}) are related to the Isgur-Wise function, while other contributions appear at the next-to-leading order. Analogously to the decay to $D$, one expresses $V$ and $A_i$ in terms of form factors $h_V$ and $h_{A_i}$,
\begin{eqnarray}
V(q^2)&=& {m_B+m_{D^*} \over 2 \sqrt{m_B m_{D^*}}} h_V(w) \,\,\, \nonumber \\
A_1(q^2) &=& \sqrt{m_B m_{D^*}}{w+1 \over m_B+m_{D^*}} h_{A_1}(w) \,\,\, \nonumber \\
A_2(q^2) &=& { m_B+m_{D^*} \over 2 \sqrt{m_B m_{D^*}}} \left[h_{A_3}(w)+{m_{D^*} \over m_B} h_{A_2}(w)\right] \,\,\, \nonumber \\
A_0(q^2) &=& { 1 \over 2 \sqrt{m_B m_{D^*}}} \Big[ m_B (w+1) h_{A_1}(w) -(m_B-m_{D^*} w)h_{A_2}(w)-(m_Bw-m_{D^*})h_{A_3}(w) \Big] \,\,\,
\end{eqnarray}
with $q^2=m_B^2+m_{D^*}^2-2 m_B m_{D^*} w$.
Including $\alpha_s$ and $\displaystyle{\frac{1}{m_{b}}}$ and $\displaystyle{\frac{1}{m_{c}}}$ corrections, the relations have been worked out \cite{hqet,Caprini:1997mu}:
\begin{eqnarray}
h_V(w) &=& \left[ C_1 +\epsilon_c (L_2 -L_5) +\epsilon_b (L_1 -L_4) \right] \, \xi(w) \label{hv}\\
h_{A_1}(w) &=& \left[ C_1^5 +\epsilon_c \left(L_2-{w-1 \over w+1}L_5 \right) +\epsilon_b \left(L_1 -{w-1 \over w+1}L_4 \right) \right] \, \xi(w)\label{ha1} \\
h_{A_2}(w) &=& \left[ C_2^5 +\epsilon_c (L_3+L_6) \right] \, \xi(w) \label{ha2}\\
h_{A_3}(w) &=& \left[ C_1^5+C_3^5 +\epsilon_c (L_2 -L_3 -L_5+L_6) + \epsilon_b (L_1 -L_4) \right] \, \xi(w) \,\,\, . \label{ha3}
\end{eqnarray}
The expressions of $C_i$, which incorporate the radiative corrections, and $L_i$ are collected in appendix \ref{app:coefficients}: the $L_i$ terms account for the ${\cal O}(1/m_Q)$ corrections in the heavy quark expansion, and are determined from
QCD sum rule analyses of the subleading form factors \cite{hqet}.
On the other hand, the relations of the form factors $T_i$ in (\ref{mat-tensor-Dstar}) to $\xi(w)$ in the heavy quark limit are:
\begin{eqnarray}
T_0(q^2)&=&T_5(q^2)=0 \nonumber \\
T_1(q^2)&=&T_3(q^2)=\sqrt{m_{D^*} \over m_B} \xi(w) \\
T_2(q^2)&=&T_4(q^2)=\sqrt{ m_B\over m_{D^*} } \xi(w) \,\,\,\ ; \nonumber
\end{eqnarray}
we use these expressions in the analysis of the tensor operator.
Let us focus on the SM.
Due to the heavy quark spin symmetry a unique form factor describes both $B \to D$ and $B \to D^*$ transitions, so that we could use the Isgur-Wise function found in the previous section. To partially take into account the different experimental systematics, we choose to use the determination of $\xi$ obtained by Belle Collaboration from the analysis of ${\bar B}^0 \to D^{*+} \mu {\bar \nu}_\mu$ \cite{Dungel:2010uk}, for which the
differential decay rate, neglecting the lepton mass, is
\begin{equation}
{d \Gamma \over dw}(B \to D^* \ell \bar \nu_\ell)= {G_F^2 |V_{cb}|^2 \over 48 \pi^3} (m_B-m_{D^*})^2 m_{D^*}^3 {\cal G}(w) {\cal F}^2(w) \,\,\, ,
\end{equation}
with
\begin{eqnarray}
{\cal G}(w) {\cal F}^2(w) &=& h_{A_1}^2(w) \sqrt{w^2-1} \, (w+1)^2 \nonumber \\
&& \left\{2\left[{1-2wr^*+r^{*2} \over (1-r^*)^2} \right] \left[1+R_1(w)^2 {w-1 \over w+1} \right]+\left[1+(1-R_2(w)){w-1 \over 1-r^*} \right]^2 \right\} \,\,\, . \label{eq:G}
\end{eqnarray}
In (\ref{eq:G}) $r^*=\displaystyle{m_{D^*} \over m_B}$, and ${\cal G}$, $R_1$ and $R_2$ are given by
\begin{eqnarray}
{\cal G}(w)&=& \sqrt{w^2-1} (w+1)^2 \left[1+4{w \over w+1}{1-2wr^*+r^{*2} \over (1-r^*)^2}\right] \,\,\, , \nonumber \\
R_1(w)&=& (R^{*})^2 {w+1 \over 2}{V(w) \over A_1(w)}\,\,\, , \label{R1}\\
R_2(w)&=& (R^{*})^2 {w+1 \over 2}{A_2(w) \over A_1(w)} \,\,\, , \nonumber
\end{eqnarray}
with $R^*=2 \displaystyle{\sqrt{m_B m_{D^*}} \over m_B+m_{D^*}}$.
The three unwnown functions in (\ref{eq:G},\ref{R1}) have been determined by Belle
adopting the parametrization \cite{Caprini:1997mu}
\begin{eqnarray}
h_{A_1}(w)&=&h_{A_1}(1) [\, 1-8 \rho^2 z+(53 \rho^2 -15)z^2-(231\rho^2-91)z^3] \label{ha1-belle} \\
R_1(w)&=&R_1(1)-0.12 \, (w-1)+0.05 \, (w-1)^2 \label{R1-belle} \\
R_2(w)&=&R_1(1)+0.11 \, (w-1)-0.06 \, (w-1)^2 \label{R2-belle}
\end{eqnarray}
(with $z$ defined in (\ref{zeta})). The fit of the parameters in (\ref{ha1-belle}-\ref{R2-belle}) is quoted as
\cite{Dungel:2010uk}
\begin{eqnarray}
{\cal F}(1)|V_{cb}|&=&(34.6 \pm 0.2 \pm 1.0) \times 10^{-3} \,\, \nonumber \\
\rho^2 &=& 1.214 \pm 0.034 \pm 0.009 \,\, \nonumber \\
R_1(1)&=& 1.401 \pm 0.034 \pm 0.018 \,\, \label{belle-par} \\
R_2(1) &=& 0.864 \pm 0.024 \pm 0.008 \,\, . \nonumber
\end{eqnarray}
From these expressions one can reconstruct $\xi(w)$,
\begin{equation}
h_{A_1}(w)={\tilde h}_{A_1}(w) \, \xi(w)
\end{equation}
with ${\tilde h}_{A_1}$ defined through Eq.(\ref{ha1}).
The fit provides us with the determination depicted in fig.\ref{fig:xi} (right panel). Through Eqs.(\ref{hv},\ref{ha2},\ref{ha3}) the form factors $h_V$, $h_{A_2}$ and $h_{A_3}$ can be reconstructed including the NLO
$1/m_Q$ and $\alpha_s$ corrections, and also ${\cal B}({\bar B}^0 \to D^{*+} \tau^- \bar \nu_\ell)$ can be computed. The results are:
\begin{eqnarray}
{\cal B}({\bar B}^0 \to D^{*+} \ell^- \bar \nu_\ell)\Big|_{SM} &=& (4.62 \pm 0.33 )\times 10^{-2} \nonumber\\
{\cal B}({\bar B}^0 \to D^{*+} \tau^- \bar \nu_\tau)\Big|_{SM} &=& (1.16 \pm 0.08 )\times 10^{-2} \,\, \label{brsSM} \end{eqnarray}
and, taking the correlation between the predictions for the $\ell$ and $\tau$ mode into account,
\begin{equation}
{\cal R}^0(D^*)\Big|_{SM}=\frac{{\cal B}({\bar B}^0 \to D^{*+} \tau^- {\bar \nu}_\tau)}{{\cal B}({\bar B}^0 \to D^{*+} \ell^- {\bar \nu}_\ell) }\Big|_{SM}=0.250 \pm 0.003 \,\,\, .\label{eq:RD*SM}
\end{equation}
The result (\ref{eq:RD*SM}) deviates from the measurement in (\ref{data}) (with statistic and systematic errors combined in quadrature) by 2.3$\sigma$.
It coincides with the one in \cite{Fajfer:2012vx,Celis:2012dk,Tanaka:2012nw},
due to the stability of the ratio ${\cal R}^0(D^*)$ against changes of the input parameters:
varying the central value of $\bar \Lambda$ and of the quark masses by 30$\%$ produces less than $1\%$ variation in the result. The radiative corrections, changing the scale in $\alpha_s$ as
mentioned in appendix \ref{app:coefficients}, do not produce an appreciable variation of the result.
On the other hand, in the individual branching fractions there is a mild sensitivity to $\bar \Lambda$: setting this parameter to zero (i.e. ignoring $1/m_Q$ corrections) the branching fractions in (\ref{brsSM}) are reduced by about $5\%$. In the charged case, there is a deviation of 1.8$\sigma$ between the SM prediction for ${\cal R}(D^*)$ and the measurement in (\ref{data}).
\section{Effects of the tensor operator on ${\cal R}(D^{(*)})$ and other observables}
If the tensions in ${\cal R}(D)$ and ${\cal R}(D^*)$
are due to NP effects, it is interesting to investigate the new operator in the effective Hamiltonian (\ref{heff}) which affects the observables in $B \to D^{(*)} \tau \nu_\tau$ transitions, focusing on the signatures with minimal dependence on hadronic quantities. As done in \cite{Fajfer:2012vx,Fajfer:2012jt,Becirevic:2012jf,Datta:2012qk,Celis:2012dk,Crivellin:2012ye,Tanaka:2012nw},
${\cal R}(D)$ and ${\cal R}(D^*)$ data allow to constrain the values of the new effective dimensionless coupling. In our case $\epsilon_T$ is bounded as shown in fig.\ref{fig:oases}.
Using the parameterization
\begin{equation}
\epsilon_T=|a_T| e^{i \theta}+\epsilon_{T0} \,\,\, ,
\end{equation}
the tightest bound to $\epsilon_{T0}$ and $|a_T|$ is obtained from the measurement of ${\cal R}(D^*)$, while the combination of ${\cal R}(D)$ and ${\cal R}(D^*)$ data fixes the range of the phase $\theta$. We select the overlap of the two regions determined by ${\cal R}(D)$ and ${\cal R}(D^*)$ both at $1 \sigma$. In this overlap region, the function
$\chi^2(\epsilon_T)=\left( \frac{{\cal R}(D,\epsilon)-{\cal R}(D)^{exp}}{\Delta{\cal R}(D)^{exp}}\right)^2+\left( \frac{{\cal R}(D^*,\epsilon)-{\cal R}(D^*)^{exp}}{\Delta{\cal R}(D^*)^{exp}}\right)^2$ has values running between $1.51$ and $1.75$.
This permitted range of $\epsilon_T$ is represented as
\begin{eqnarray}
Re[\epsilon_{T0}]&=&0.17 \,\,\,\,\, ,\,\, Im[\epsilon_{T0}]=0 \,\,\, , \nonumber \\
|a_T| &\in& [0.24,\,0.27] \label{ranges-for-epsilonT}\\
\theta &\in&[2.6,\,3.7]\, {\rm rad} \,\, \nonumber
\end{eqnarray}
and is also depicted in fig.\ref{fig:oases}.
\begin{figure}[!b]
\centering
\includegraphics[width = 0.35\textwidth]{PlotSovrapposti1.pdf} \hspace*{0.5cm}
\includegraphics[width = 0.35\textwidth]{chisqr.pdf}
\caption{(left) Regions in the $(Re(\epsilon_T),Im(\epsilon_T))$ plane determined from the experimental data (to $1$ and $2 \sigma$) on ${\cal R}(D)$ (large rings) and ${\cal R}(D^*)$ (small rings). (right) Region corresponding to values of $\chi^2$ between the minimum (indicated by the star), $1.55$ (yellow, light) and $1.65$ (orange, gray) and $1.75$ (brown, dark).}\label{fig:oases}
\end{figure}
Varying the effective coupling in this region we can analyze the impact of the new operator on various differential distributions.
We start with the longitudinal and transverse $D^*$ polarization distributions in $ B \to D^* \tau {\bar \nu}_\tau$.
\begin{figure}[!b]
\centering
\includegraphics[width = 0.4\textwidth]{Larghezze_DstarLNP.pdf}\hspace*{0.2cm}
\includegraphics[width = 0.4\textwidth]{Larghezze_DstarTNP.pdf}\\
\caption{
Differential branching ratios with polarized $D^*$: $\displaystyle{\frac{d {\cal B}(B \to D^* \tau {\bar \nu}_\tau)_{L}}{dq^2}}$ (left) and $\displaystyle{\frac{d {\cal�B} (B \to D^* \tau {\bar \nu}_\tau)_T}{dq^2}}$ (right). The lower (blue) bands
are the SM prediction, the upper (orange) bands include NP effects. In SM, the uncertainties on the parameters of the Isgur-Wise function in Eq.(\ref{belle-par}), together with the errors on $\overline{\Lambda}$ and $\alpha_s$ are included. In the case of the NP curves, the uncertainty on $\epsilon_T$ is also considered.}
\label{fig:dBrTL}
\end{figure}
We consider the decay to a $D^*$ with definite helicity, with differential decay width $\displaystyle{\frac{d \Gamma_{L,\pm}}{dq^2}}$ for the three cases $L, \pm$. We define $\displaystyle{\frac{d \Gamma_T}{dq^2}=\frac{d \Gamma_+}{dq^2}+\frac{d \Gamma_-}{dq^2}}$\,, and show
in fig.\ref{fig:dBrTL} the differential branching fractions. The uncertainty in the distributions reflects the uncertainty on the parameters of the Belle Isgur-Wise function, on $\bar \Lambda$ and, in the case of NP, on $\epsilon_T$. While the shape of the distributions are slightly modified from SM to NP, the maxima increase, a consequence of the increase of the branching fractions.
The differential decay width distributions for $D$ and $D^*$ (summed over the $D^*$ polarizations) have been measured by BaBar
\cite{Lees:2013uzd}, and can be compared to the SM and the NP scenario predictions. Once normalized to the total number of events, not only the SM distributions are compatible with data, as remarked in \cite{Lees:2013uzd}, but also the distributions in the considered NP scenario agree with measurements, as one can argue considering fig.\ref{fig:newspectrum}. This confirms that the shape of such distributions does not allow at present to select between these possibilities, and other observables should be analyzed for a more efficient discrimination.
%
\begin{figure}[!b]
\centering
\includegraphics[width = 0.4\textwidth]{Babar2013NP.pdf}\hspace*{0.2cm}
\includegraphics[width = 0.4\textwidth]{Babar2013NPstar.pdf}\\
\caption{
$\displaystyle{\frac{d \Gamma(B \to D \tau {\bar \nu}_\tau)}{dq^2}}$ (left) and $\displaystyle{\frac{d \Gamma(B \to D^* \tau {\bar \nu}_\tau)}{dq^2}}$ (right) distributions in the NP scenario (for the central value of $\epsilon_T$, shaded histograms) compared to BaBar data (points) \cite{Lees:2013uzd}; the distributions are normalized to the total number of events.}
\label{fig:newspectrum}
\end{figure}
\begin{figure}[!h]
\centering
\includegraphics[width = 0.4\textwidth]{R_L_Dstar.pdf}\hspace*{0.4cm}
\includegraphics[width = 0.4\textwidth]{R_T_Dstar.pdf}
\caption{$D^*$ polarization ratios $R_L^{D^*}(q^2)$ (left) and $R_T^{D^*}(q^2)$ (right) defined in (\ref{RLT}). Notations are the same as in fig.\ref{fig:dBrTL}.}\label{fig:RL}
\end{figure}
\begin{figure}[!b]
\centering
\includegraphics[width = 0.4\textwidth]{FL_Overlap.pdf}\hspace*{0.4cm}
\includegraphics[width = 0.4\textwidth]{FT_Overlap.pdf}
\caption{ Polarization fractions $F_L(q^2)$ (left) and $F_T(q^2)$ (right) for $B \to D^* \tau {\bar \nu}_\tau$ defined in (\ref{FLT}). Notations are the same as in fig.\ref{fig:dBrTL}.}\label{fig:ft}
\end{figure}
Other observables are the longitudinal and transverse $D^*$ polarization distributions in $B \to D^* \tau {\bar \nu}_\tau$ normalized to $B \to D^* \ell {\bar \nu}_\ell$. They are defined as
\begin{equation}
R_ {L,T}^{D^*}(q^2)=\frac{d \Gamma_{L,T}(B \to D^* \tau {\bar \nu}_\tau)/dq^2}{d \Gamma_{L,T}(B \to D^* \ell {\bar \nu}_\ell)/dq^2} \,\,\, . \label{RLT}
\end{equation}
The SM predictions are shown in fig. \ref{fig:RL} together with the modifications induced by the tensor operator. At large $q^2$ the observables are enhanced by $30-50$ $\%$, a noticeable effect.
Furthermore, at odds with scenarios in which
only $R_L$ is affected by new physics \cite{Celis:2012dk}, in the case of the tensor operator both the longitudinal and the transverse $R_L$ and $R_T$ distributions are modified.
The longitudinal and transverse polarization fractions of the $D^*$ meson
\begin{equation}
F_{L,T}(q^2)=\frac{d \Gamma_{L,T}(B \to D^* \tau {\bar \nu}_\tau)}{dq^2} \times \left(\frac{d \Gamma(B \to D^* \tau {\bar \nu}_\tau)}{dq^2}\right)^{-1} \label{FLT}
\end{equation}
are shown in fig.\ref{fig:ft}.
Both the SM and NP predictions are affected by a small error, since in the heavy quark limit the observables in (\ref{FLT}) are free of hadronic uncertainties, due to the cancellation of the form factor $\xi(w)$ in the ratio. The residual uncertainty reflects that on $\bar \Lambda$ which controls the $1/m_Q$ corrections. The uncertainty on $\bar \Lambda$ also enters in the curves obtained in the NP scenario in combination with $\epsilon_T$.
In SM, $F_L(q^2)$ ranges between 0.75 at low $q^2$ and about 0.35 at high squared momentum transfer; in NP in the allowed region of $\epsilon_T$, $F_L(q^2)$ is between 0.35 and about 0.65 at low $q^2$, while this observable converges to the SM value at high $q^2$.
The SM predicts a dominant longitudinal polarization at small $q^2$, in NP the longitudinal and transverse polarizations have similar fractions up to $q^2=6$ GeV$^2$.
An important observable is the forward-backward ${\cal A}_{FB}(q^2)$ asymmetry in $ B \to D \tau {\bar \nu}_\tau$ and $ B \to D^* \tau {\bar \nu}_\tau$, defined as
\begin{equation}
{\cal A}_{FB}(q^2)= \frac{\int_0^1 \,d \cos \theta_\ell \,\frac{d \Gamma}{dq^2 d \cos \theta_\ell} -\int_{-1}^0 \,d \cos \theta_\ell \, \frac{d \Gamma}{dq^2 d \cos \theta_\ell}}{\frac{d \Gamma}{dq^2}} \,\,\, ,
\label{eq:AFB}
\end{equation}
where $\theta_\ell$ is the angle between the direction of the charged lepton and the $D^{(*)}$ meson in the lepton pair rest frame.
We use the notation
\begin{equation}
{\cal A}_{FB}(q^2)= \frac{1}{\frac{d \Gamma}{dq^2}}\frac{3C(q^2)}{16}\left\{ \tilde{\cal A}_{FB}^{SM}(q^2)+\tilde{\cal A}_{FB}^{NP}(q^2)+\tilde{\cal A}_{FB}^{INT}(q^2) \right\} \,\,\, ,
\end{equation}
with $C(q^2)$ defined in (\ref{C-factor}) and the three terms in the parentheses given for $D$ and $D^*$:
\begin{itemize}
\item $D$
\begin{eqnarray}
\tilde{\cal A}_{FB}^{SM}(q^2)&=& 8F_0(q^2)F_1(q^2)(m_B^2-m_D^2)\frac{m_\ell^2}{q^2}\left(1 -\frac{m_\ell^2}{q^2}\right)\lambda^{1/2}(m_B^2,m^2,q^2)
\nonumber
\\
\tilde{\cal A}_{FB}^{NP}(q^2)&=&0 \nonumber \\
\tilde{\cal A}_{FB}^{INT}(q^2)&=& - 8 Re(\epsilon_T) F_0(q^2)[F_T(q^2)+G_T(q^2)] (m_B-m_D)m_\ell \left(1 -\frac{m_\ell^2}{q^2}\right)\lambda^{1/2}(m_B^2,m^2,q^2)
\end{eqnarray}
\item $D^*$
\begin{eqnarray}
\tilde{\cal A}_{FB}^{SM}(q^2)&=&\frac{4}{m_{D^*}(m_B+m_{D^*})q^2}\left(1 -\frac{m_\ell^2}{q^2}\right) \lambda^{1/2}(m_B^2,m_{D^*}^2,q^2) \nonumber \\
&&\Big\{m_\ell^2 A_0(q^2) \left[ A_1(q^2)(m_B+m_{D^*})^2(m_B^2-m_{D^*}^2-q^2)-\lambda(m_B^2,m_{D^*}^2,q^2)A_2(q^2) \right] \nonumber \\
&&-4m_{D^*}(m_B+m_{D^*})q^4A_1(q^2)V(q^2) \Big\}
\end{eqnarray}
\begin{eqnarray}
\tilde{\cal A}_{FB}^{NP}(q^2)&=& 16 |\epsilon_T|^2 \frac{m_\ell^2}{q^2}\left(1 -\frac{m_\ell^2}{q^2}\right) \lambda^{1/2}(m_B^2,m_{D^*}^2,q^2)({\tilde T}_1(q^2)+{\tilde T}_2(q^2))\nonumber \\
&&\left[(m_B^2-m_{D^*}^2)({\tilde T}_1(q^2)+{\tilde T}_2(q^2))+q^2({\tilde T}_1(q^2)-{\tilde T}_2(q^2)) \right]
\end{eqnarray}
\begin{eqnarray}
\tilde{\cal A}_{FB}^{INT}(q^2)&=& -4 Re(\epsilon_T) m_\ell \left(1 -\frac{m_\ell^2}{q^2}\right) \lambda^{1/2}(m_B^2,m_{D^*}^2,q^2) \Big\{ 4(m_B+m_{D^*}) A_1(q^2) ({\tilde T}_1(q^2)+{\tilde T}_2(q^2)) \nonumber \\
&+&A_0(q^2) \left[\frac{\lambda(m_B^2,m_{D^*}^2,q^2)}{m_{D^*}(m_B+m_{D^*})^2}{\tilde T}_0(q^2)+2\frac{m_B^2+m_{D^*}^2-q^2}{m_{D^*}}{\tilde T}_1(q^2)+4m_{D^*}{\tilde T}_2(q^2) \right] \nonumber \\
&-&\frac{V(q^2)}{m_B+m_{D^*}}\left[q^2( {\tilde T}_1(q^2)-{\tilde T}_2(q^2))+(m_B^2-m_{D^*}^2)({\tilde T}_1(q^2)+{\tilde T}_2(q^2)) \right]\Big\} \,\,\, .
\end{eqnarray}
\end{itemize}
In fig.\ref{fig:afb} we plot ${\cal A}_{FB}(q^2)$ for $B \to D \tau {\bar \nu}_\tau$ and $B \to D^* \tau {\bar \nu}_\tau$.
The SM prediction is affected by almost no theoretical uncertainty, because of a nearly complete cancellation of the hadronic parameters in the ratio.
In the case of NP, we have taken into account also the uncertainty on $\theta$ and $|a_T|$.
The SM curve lies in both cases below the NP distribution for all values of $q^2$. The most interesting deviation concerns the $D^*$ mode: the SM predicts a zero for ${\cal A}_{FB}$ at $q^2\simeq 6.15$ GeV$^2$, in the NP case the zero is shifted towards larger values $q^2 \in[8.1, 9.3]$ GeV$^2$.
\begin{figure}[!b]
\centering
\includegraphics[width = 0.4\textwidth]{AFB_D.pdf}\hspace*{0.5cm}
\includegraphics[width = 0.4\textwidth]{AFB_Dstar.pdf}
\caption{ Forward-backward asymmetry ${\cal A}_{FB}(q^2)$ for $B \to D \tau {\bar \nu}_\tau$ (left) and $B \to D^* \tau {\bar \nu}_\tau$ (right). The lower (blue) curves are the SM predictions, the upper (orange) bands the NP expectations.
Uncertainty on $\overline{\Lambda}$ has been included and, in the case of NP, also on the parameters $|a_T|$ and $\theta$. }\label{fig:afb}
\end{figure}
Even though the experimental determination of the zero of the forward-backward asymmetry is challenging, this observable effectively discriminates SM from the NP model.
The integrated asymmetries, obtained integrating separately the numerator and the denominator in (\ref{eq:AFB}), are collected in Table \ref{tab:afb}: for $D^*$, in the NP scenario the integrated asymmetry has opposite sign with respect to SM.
\begin{table*}[!tb]
\centering
\begin{tabular}{|c | c |c |c|c|c| c| }\hline
& ${\bar B}^0 \to D^+ \tau {\bar \nu}_\tau$ & ${\bar B}^0 \to D^{*+} \tau {\bar \nu}_\tau$ & ${\bar B}^0 \to D_0^{*+} \tau {\bar \nu}_\tau$ & ${\bar B}^0 \to D_1^{\prime +} \tau {\bar \nu}_\tau$ & ${\bar B}^0 \to D_1^+ \tau {\bar \nu}_\tau$ & ${\bar B}^0 \to D_2^{*+} \tau {\bar \nu}_\tau$ \\ \hline
${\cal A}_{FB}^{SM}$ & $0.357 \pm 0.002$ & $-0.040\pm 0.003$&$0.315$&$0.026$ & $ 0.24$ & $0.07$\\ \hline
${\cal A}_{FB}$ & $0.40 \pm 0.005$ & $0.048 \pm 0.013$ &$0.30\pm0.005$&$0.08\pm0.01$& $0.21 \pm 0.003$ & $0.14 \pm 0.01$\\ \hline
\end{tabular}
\caption{ Integrated forward-backward asymmetry for the considered decay modes.
The first line reports the SM results, in the second line the effect of the tensor operator is included. }\label{tab:afb}
\end{table*}
\section{Tensor operator in $B \to D^{**} \ell {\bar \nu}_\ell$ decays}
The new operator in the effective hamiltonian (\ref{heff}) affects other exclusive decay modes that are worth investigating. Of peculiar interest are the semileptonic $B$ and $B_s$ transitions into excited
charmed mesons. The lightest multiplet of such hadrons, corresponding to the quark model $p$-wave ($\ell=1$) mesons and generically denoted $D_{(s)}^{**}$, comprises four positive parity states which, in the heavy quark limit, fill two doublets labeled by the (conserved) angular momentum ${\vec s}_\ell={\vec s}_q+{\vec \ell}$ (${\vec s}_q$ is spin of the light antiquark), hence
$s_\ell=1/2$ or $s_\ell=3/2$.
The two mesons belonging to the first doublet, $(D^*_{(s)0},\,D_{(s)1}^\prime)$, have spin-parity $J^P=(0^+,1^+)$; the mesons in the second doublet have $J^P=(1^+,2^+)$ and are named $(D_{(s)1},\,D_{(s)2}^*)$. All the members of the doublets, with and without strangeness, have been observed, and the two $s_\ell^P=1/2^+$ states without strangeness are found to be broad, as expected \cite{Colangelo:2012xi}.
In the heavy quark limit also the semileptonic $B$ transitions to mesons belonging to the same charmed doublet can be described in terms of a single form factor. $B$ decays to $(D^*_0,\,D_1^\prime)$ are governed by a universal function denoted as $\tau_{1/2}(w)$, $B$ decays to $(D_1,\,D_2^*)$ by the $\tau_{3/2}(w)$ form factor (the matrix elements are collected in appendix \ref{app:me}).
There are several determinations of the $\tau_i(w)$ parametrized in terms of the zero-recoil value $\tau_i(1)$ (contrary to the Isgur-Wise function, $\tau_i(w)$ are not normalized to unity at $w=1$), of the slope $\rho_i^2$ and of the curvature $c_i$. In the ratios of branching fractions and asymmetries the zero-recoil value does not play any role, and this reduces the main dependence of the observables on the hadronic parameters. The present experimental situation needs to be settled, since the semileptonic $B$ decay rates into $(D^*_0,\,D_1^\prime)$ exceed the predictions obtained using computed $\tau_i(1)$; the origin of the discrepancy is still unknown, and could be related to the broad widths of the final charmed mesons, which determine a difficulty in the exclusive reconstruction, and to a possible pollution from other (e.g. radial) excited states. Semileptonic $B_s$ decays to $s_\ell^P=1/2^+$ $c \bar s$ mesons could clarify the issue, due to the narrow width of the strange charmed resonances
\cite{Becirevic:2012te}. On the other hand, the tensor operator produces precise correlations among various observables, therefore its effects could be distinguished from others.
For definiteness, we use a QCD sum rule
determination of $\tau_{3/2}(w)$ at leading order in $\alpha_s$ \cite{Colangelo:1992kc,Colangelo:1998sf}, and of $\tau_{1/2}(w)$ at ${\cal O}(\alpha_s)$ \cite{Colangelo:1998ga}:
\begin{eqnarray}
\tau_{3/2}(w)&=&\tau_{3/2}(1) \left[1-\rho^2_{3/2}(w-1) \right] \label{tau32}
\\
\tau_{1/2}(w)&=&\tau_{1/2}(1) \left[1-\rho^2_{1/2}(w-1) +c_{1/2}(w-1)^2 \right] \label{tau12}
\end{eqnarray}
with
\begin{eqnarray}
\tau_{3/2}(1)&=& 0.28 \hskip 2. cm \rho^2_{3/2}=0.9 \label{32parameters}
\\
\tau_{1/2}(1)&=& 0.35 \pm 0.08 \hskip 1 cm \rho^2_{1/2}=2.5 \pm 1.0 \hskip 1 cm c_{1/2}=3 \pm 3 \,\,.\label{12parameters}
\end{eqnarray}
The differential decay rates for $B \to D^{**} \ell {\bar \nu}_\ell$ can be written as in (\ref{dgammadq2-generic}), see appendix \ref{app:me}.
The ratios
\begin{equation}
{\cal R}(D^{*}_0)=\frac{{\cal B}(B \to D^{*}_0 \tau \,{\bar \nu}_\tau)}{{\cal B}(B \to D^{*}_0 \ell \,{\bar \nu}_\ell)}
\label{rdstarstar}
\end{equation}
and the analogous ${\cal R}(D^\prime_1)$, ${\cal R}(D_1)$ and ${\cal R}(D^*_2)$ depend on the effective coupling $\epsilon_T$. This also happens in $B_s \to D^{**}_s \ell {\bar \nu}_\ell$ transitions, in the $SU(3)_F$ symmetry limit for the form factors.
In fig.\ref{fig:r12-r32} for each meson doublet we show the correlation between the ratios (\ref{rdstarstar}) for $B$ and $B_s$, together with
the SM predictions $({\cal R}(D^{*}_{0}),{\cal R}(D^\prime_{1}))=(0.077,0.100)$, $({\cal R}(D^{*}_{s0}),{\cal R}(D^\prime_{s1}))=(0.107,0.112)$, $({\cal R}(D_{1}),{\cal R}(D^*_{2})=(0.065,0.059)$ and $({\cal R}(D_{s1}),{\cal R}(D^*_{s2})=(0.060,0.055)$.
The tensor operator produces a sizeable increase in the ratios $\cal R$, which is correlated for the two members in each doublet.
The hadronic uncertainty is mild: using the $\tau_i$ functions in \cite{Morenas:1997nk}, the results remain almost unchanged in the case of the $s_\ell=3/2$ doublet, while for $s_\ell=1/2$ they are smaller by about $25\%$ in SM and in the NP case. The same effect is found using the form factors obtained by lattice QCD \cite{Blossier:2009vy}.
\begin{figure}[!h]
\centering
\includegraphics[width = 0.35\textwidth]{D0starsVSD1ps_Overlap.pdf}\hspace*{0.5cm}
\includegraphics[width = 0.35\textwidth]{D1sVSD2starsp_Overlap.pdf}
\caption{(left) Correlations between the ratios ${\cal R}(D^{*}_{(s)0})$ and ${\cal R}(D^\prime_{(s)1})$ for mesons belonging to the $(D^*_{(s)0},\,D_{(s)1}^\prime)$ doublet without (orange, dark) and with strangeness (green, light). (right) Correlation between ${\cal R}(D_{(s)1})$ and ${\cal R}(D^*_{(s)2})$ for mesons in the $(D_{(s)1},\,D_{(s)2}^*)$ doublet. The dots (triangles) correspond to the SM results for mesons without (with) strangeness.
}\label{fig:r12-r32}
\end{figure}
The differential forward-backward asymmetries in the case of the four positive parity charmed mesons are collected in fig.\ref{fig:afbD**}, and the integrated ones in Table \ref{tab:afb}.
\begin{figure}[!h]
\centering
\includegraphics[width = 0.4\textwidth]{AFB_D0star.pdf}\hspace*{0.5cm}
\includegraphics[width = 0.4\textwidth]{AFB_D1p.pdf}\\\vspace*{0.2cm}
\includegraphics[width = 0.4\textwidth]{AFB_D1.pdf}\hspace*{0.5cm}
\includegraphics[width = 0.4\textwidth]{AFB_D2star.pdf}
\caption{Forward-backward asymmetry ${\cal A}_{FB}$ for the decays $B \to D_0^* \tau {\bar \nu}_\tau$ (top, left), $B \to D^\prime_1 \tau {\bar \nu}_\tau$ (top, right),
$B \to D_1 \tau {\bar \nu}_\tau$ (bottom, left) and $B \to D^*_2 \tau {\bar \nu}_\tau$ bottom, (right) as function of $q^2$. The solid (blue) curves are the SM predictions, the dotted (orange) bands the NP expectations. }\label{fig:afbD**}
\end{figure}
While in $B \to (D^*_0, D_1) \tau {\bar \nu}_\tau$ the forward-backward asymmetry does not discriminate between SN and NP, in the modes with $D_1^\prime$ and
$D_2^*$ it is a sensitive observable: The inclusion of the tensor operator produces an enhancement of ${\cal A}_{FB}$ with respect to SM for all values of $q^2$. Moreover, in SM there is a zero
which, in the case of $B \to D^\prime_1 \tau {\bar \nu}_\tau$ moves towards larger values of $q^2$, and disappears in $B \to D^*_2 \tau {\bar \nu}_\tau$ once NP is included.
We close this section remarking that, while the tensor operator in (\ref{heff}) does not affect the purely leptonic $B_c \to \tau^- {\bar \nu}_\tau$ mode, it can have an impact on the transitions $B_c \to (\eta_c, J/\psi) \tau^- {\bar \nu}_\tau$ and
$\Lambda_b \to \Lambda_c \tau^- {\bar \nu}_\tau$; therefore, sets of other observables can be identified and investigated, with precise correlated deviations from the SM predictions.
\section{Conclusions}
The detailed experimental information provided us on flavour physics shows an astonishing consistency with the SM predictions. The very few tensions identify possible paths to new physics searches.
The BaBar anomalous enhancement of the ratios $\displaystyle R(D^{(*)})=\frac{{\cal B}(B \to D^{(*)} \tau {\bar \nu}_\tau)}{{\cal B}(B \to D^{(*)} \mu {\bar \nu}_\mu)}$ with respect to SM is one of these few cases. The analyses of $R(D^{(*)})$ in specific models also evidentiate the enhancement the purely leptonic $B \to \tau {\bar \nu}_\tau$ rate, for which data are better compatible with SM. A mechanism enhancing the semileptonic modes $B \to D^{(*)} \tau {\bar \nu}_\tau$ with respect to $B \to D^{(*)} \mu {\bar \nu}_\mu$, leaving $B \to \tau {\bar \nu}_\tau$ unaffected, can be based on a
tensor operator in the effective hamiltonian. We have bound the relative weight $\epsilon_T$ of this operator and studied the impact on several observables, the most sensitive one being
the forward-backward asymmetry in $ B \to D^* \tau {\bar \nu}_\tau$ with a shift in the position of its zero.
If the anomaly in $B \to D^{(*)} \tau {\bar \nu}_\tau$ is due to this NP effect, analogous deviations should be found in B to excited $D$ transitions. The ratios $R$ for these mesons are enhanced with respect to SM, and the forward-backward asymmetry is a sensitive observable in the channels involving $D_1^\prime$ and $D_2^*$.
These signatures in exclusive semileptonic $b \to c \,\tau {\bar \nu}_\tau$ modes make the understanding of the role of the new contribution to the effective weak hamiltonian feasible, a step towards possibly disclosing new interactions through flavour physics measurements.
\section*{Acknowledgement}
This work is supported in part by the Italian MIUR Prin 2009.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,859 |
\section{Introduction}
The control and manipulation of mesoscopic mechanical resonators by radiation pressure has fueled enormous interest in the use of optomechanical systems for applications to sensing, transduction and optomechanical information processing, as well as for foundational tests of quantum mechanics in the macroscopic domain \cite{OM_review}. While cavity optomechanics has seen remarkable advances in recent years, the preparation of mesoscopic mechanical resonators in the quantum regime remains a significant challenge. In particular, the requirements for ground state cooling include the ability to isolate the resonator from environmental sources of dissipation as well as the realization of a cavity optomechanical system in the `resolved-sideband' regime \cite{OM_cooling}. Both these requirements become particularly challenging for optomechanical systems characterized by low frequency ($<$ 1 MHz) mechanical resonators. Thus, for optomechanical systems operating in the optical domain, ground state cooling has, to date, only been demonstrated by the use of high frequency mechanical resonators and cryogenic cooling to reduce the thermal coupling to the environment \cite{Cleland,Teufel, Painter}. On the other hand, low frequency resonators are particularly compelling for a variety of sensing applications due to the long coherence times and large zero-point motion, and methods to cool such resonators to the quantum regime will enable a variety of technical applications as well as fundamental studies.
A promising avenue to circumvent the limitations inherent to optomechanical cooling is the use of an auxiliary quantum system that can enhance the effective optomechanical response of the resonator. Several proposals involving such hybrid schemes \cite{hybrid2014} and other approaches~\cite{PKU} have been advanced to improve the performance of cavity cooling. Coupling a cold atomic ensemble to the mechanical resonator is of particular interest due to the precise control, wide tunability and strong optical interactions exhibited by atomic systems \cite{atom_cavity,treutlein-genes,bowen,genes}.
\begin{figure}[b]
\begin{center}
\includegraphics[width=\columnwidth]{CARLfigure1.pdf}
\caption{(Colors online). Hybrid optomechanical setup with atoms. The cavities containing an atomic ensemble and an optomechanical element are coupled by an optical field that interacts with both the systems. }
\label{fig:AtomOM}
\end{center}
\end{figure}
This article investigates the hybrid optical interaction between a cavity optomechanical system and an ensemble of ultracold atoms. We consider the situation where the mechanical resonator and the ultracold gas are embedded within distinct optical cavities that interact via a common `coupling' laser (see Fig. 1). In addition to alleviating technical constraints, this modular approach also represents a powerful method to combine the coherence, sensitivity and tunability of the atoms with the robustness and scalability of the optomechanical device.
As discussed below, the atomic gas is described as a three-level $\Lambda$ system whose optical response to the coupling light field can be modified by a strong `control' field. Such $\Lambda$ configurations in atomic ensembles exhibit narrow resonances due to the competition between dissipation and dispersion. We consider specifically two well-known and complementary approaches towards that goal, Electromagnetically Induced Transparency (EIT) \cite{EIT_review} and Recoil Induced Resonances (RIR)~\cite{Grynberg1992, Grynberg1994, Moore1998, Vengalattore2005, Hafezi2008}. In either case, and for experimentally demonstrated values of the quality factor and of the $Q \times f$ product for the mechanical resonator \cite{Chakram2014} and the cavity optomechanical system, we find a broad and robust range of parameters for which the mechanical resonator can be cooled to its quantum ground state from room temperature.
In EIT, quantum interference between different excitation pathways to the same atomic level induces a narrow transparency window for the propagation of a weak resonant field that can be controlled via an external `control' laser. The effect may be tuned by separating two lower-lying states via e.g. Zeeman splitting by means of an additional magnetic field. Intracavity EIT has already been proposed for cooling and entanglement in an optomechanical setup \cite{Genes2009,Genes2011}. Here, we explore a new regime in separate cavities and we obtain the surprising result of a very effective blue-sideband cooling.
In contrast, RIR is generated when the exchange of energy between the control and the coupling lasers is resonant with the transition between different atomic momentum states. This nonlinear effect can be tuned by changing the frequencies of the lasers or the intensity of the control field. In particular, long-lived momentum coherences, narrow resonance features and large gain in the coupling beam amplitude have been demonstrated \cite{Hafezi2008}. We show that this spectrally narrow gain feature enhances the asymmetry between the optical sidebands at the mechanical frequency, which in turn leads to efficient cooling.
This paper is organized as follows. In Section II we present the complete Hamiltonian for the system, comprising the optical, mechanical and atomic parts, as well as the coupling between the different cavities. We expand on the atomic Hamiltonian in Section III, reviewing the theory for the atomic response and discussing the atomic susceptibilities for EIT and RIR. Section IV is devoted to the analysis of the optomechanical dynamics, with emphasis on two possible configurations: cascade and feedback coupling between the cavities. Finally, we draw some conclusions and we discuss the perspectives of this work in Section V.
\section{Model Hamiltonian}
We consider two coupled cavities, one containing an atomic ensemble and another including a mechanical resonator. We will refer to them as the atomic cavity and the optomechanical cavity, respectively. The two cavities are optically coupled to obtain an effective interaction between the atomic ensemble and the mechanical element. A possible realization of the system is sketched in Fig. \ref{fig:AtomOM}. The full Hamiltonian describing this setup is
\begin{equation}
H=H_{\rm ca}+H_{\rm atom}+H_{\rm cm}+H_{OM}+H_{AM}+H_{\rm loss},
\label{eq:totalH}
\end{equation}
where $ H_{\rm ca}, H_{\rm cm} $ describe the optical fields in the two cavities, $H_{AM}$ represents the coupling between the two cavities, $H_{OM}$ contains the optomechanical interaction, $H_{\rm atom}$ accounts for the atomic dynamics that will be discussed in detail in the following Section, and $H_{\rm loss}$ denotes the various (atomic, optical and mechanical) loss mechanisms.
The cavities have the decay rates $\kappa_\mathrm{ci}={\rm FSR}_i/\mathcal{F}_\mathrm{ci}$, where ${\rm FSR}_i =2 \pi c/2L_\mathrm{ci}$ is the free spectral range, $L_\mathrm{ci}$ being the length of the cavity and $\mathcal{F}_\mathrm{ci}$ the cavity finesse. Here the subscripts $i \in \{a,m\}$ denote the atomic and optomechanical cavity, respectively. We assume throughout that $\mathcal{F}_\mathrm{ca}\ll\mathcal{F}_\mathrm{cm}$. The dynamics in the atomic cavity is described by $H_{\rm atom} + H_{\rm ca}$, with
\begin{equation}
H_{\rm ca}=\hbar\omega_\mathrm{ca} \hat{a}^\dagger \hat{a} +i\hbar(\eta_a \hat{a}^\dagger-\eta_a^*\hat{a}),
\label{eq:HoptA}
\end{equation}
where $\hat{a}$ denotes the annihilation operator for the cavity mode, which acts as the coupling field. The cavity is driven by $\eta_a=\sqrt{P_{\rm in,a} \kappa_\mathrm{l,ca}/\hbar\omega_\mathrm{ca}}$, with $P_{\rm in,a}$ the power of the input coupling beam and $\omega_\mathrm{ca}$ the cavity resonance frequency and $\kappa_\mathrm{l,ca}$ indicates the coupling through the left (input) mirror of the atomic cavity. Its value depends on the type of cavity we are considering \cite{kappa}.
Similarly the Hamiltonian for the optomechanical cavity can be written as $H_{\rm cm}+H_{OM}$ where
\begin{equation}
H_{\rm cm}=\hbar\omega_\mathrm{cm} \hat{c}^\dagger \hat{c} +i\hbar(\eta_c \hat{c}^\dagger-\eta_c^*\hat{c}),
\end{equation}
and $\hat{c}$ is the annihilation operator for the cavity mode with frequency $\omega_\mathrm{cm}$, $\eta_c=\sqrt{P_{\rm in,c} \kappa_\mathrm{l,cm}/\hbar\omega_\mathrm{cm}}$, $P_{\rm in,c}$ being the input power. The optomechanical interaction is
\begin{equation}
H_{OM}=\hbar\omega_m \hat{b}^\dagger \hat{b}+\hbar g_0 \hat{c}^\dagger \hat{c}(\hat{b}+\hat{b}^\dagger),
\end{equation}
where $\hat{b}$ annihilates phonons of the relevant mechanical oscillator mode, with frequency $\omega_m$, and $g_0$ is the single photon optomechanical coupling. Finally, we describe the coupling between the cavities by the Hamiltonian
\begin{equation}
H_{AM} = \hbar J (\hat{a}^{\dagger}\hat{c} + \hat{c}^{\dagger}\hat{a}),
\end{equation}
where $J$ is a the phenomenological constant. The technical details leading to its specific value depend on the specifics of the experimental setup, in particular the mode matching of the coupling field between the two cavities. Neglecting all coupling losses and assuming perfect mode matching, we set $J=\sqrt{\kappa_\mathrm{l,ca}\kappa_\mathrm{l,cm}}$~\cite{GardinerZollerbook}.
\section{Optical response of atomic $\Lambda$ schemes}
In this section we introduce two specific atomic $\Lambda$ configurations. The intent is to exploit their {\it narrow} and {\it tunable} spectral features to resolve the mechanical degree of freedom. The level diagrams are given in \fig{EITschemes}(A,C). In both cases, we assume that the atomic ensemble is confined in an optical cavity, as shown in \fig{EITschemes}B. A strong (classical) control laser with frequency $\omega_1$ and a weak coupling laser with frequency $\omega_2$ interact with a chosen atomic transition of frequency $\omega_0$. To study the optical response of the atomic ensembles we consider an isolated atomic cavity with Hamiltonian
\begin{equation}
H=H_{\rm ca}+H_{\rm atom}+H'_{\rm loss},
\end{equation}
where $H'_{\rm loss}$ accounts for all relevant (atomic and optical) loss mechanisms.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=\columnwidth]{CARLfigure2.pdf}
\caption{(Colors online). Atomic level scheme for EIT (A) and RIR (C). Generic setup for an atomic ensemble in a single mode cavity (B). }
\label{fig:EITschemes}
\end{center}
\end{figure}
\subsection{Electromagnetically Induced Transparency}
In this scheme, sketched in \fig{EITschemes}A, we take advantage of the internal energy level structure of the atoms, in particular the splitting in Zeeman sublevels of a hyperfine manifold, where the energy difference between the states can be tuned via an external magnetic field $B_{\rm ext}$. The two levels $|g\rangle$ and $|m\rangle$ are Zeeman sublevels of the ground state manifold with energy difference $\Delta_m \mu_B g_F B_{\rm ext}$, where $\mu_B$ is the Bohr magneton, $g_F$ is the Land{\' e} factor and $\Delta_m$ is the difference in the magnetic quantum number.
The state $|e\rangle$ is instead chosen from an excited manifold.
We assume a tightly trapped atomic sample, such that recoil effects are negligible. Furthermore, to ensure stable steady-state conditions we assume that the atomic ensemble is simultaneously cooled by Raman sideband cooling, so as to repopulate the ground state with high fidelity \cite{Patil2014} even in the presence of the coupling laser.
\begin{figure*}[ht]
\begin{center}
\includegraphics[width = \textwidth]{chiv2}
\caption{(Colors online). Atomic susceptibility for EIT. We consider a sample of atomic $^{87}$Rb in the $|F=1\rangle$ ground state manifold with $\Delta_a = 500\gamma_e$ and $N = 10^{8}$. The control amplitude is $\Omega = 4 \gamma_e$ (red dot-dashed line) and $\Omega = 6 \gamma_e$ (blue dashed line). For the single atom Rabi frequency of the coupling field we assume $\mathcal{E}_a = 2\pi \times 100$ kHz, while the mechanical frequency used only as normalization is $\omega_m = 2\pi \times 300$ kHz.}
\label{fig:Zchi}
\end{center}
\end{figure*}
In terms of the atomic operators $\hat{\sigma}_{ab} = \ket{a}\bra{b}$ the atomic Hamiltonian is
\begin{equation}
H_{\rm atom} = H_0 + H_\mathrm{af},
\end{equation}
where $H_0 = \sum_{a = \{g,e,m\}} \hbar \omega_a \hat{\sigma}_{aa}$ describes the non-interacting internal level structure and the second term contains the interaction of the atomic levels with the control and coupling fields,
\begin{eqnarray}
H_\mathrm{af} &=& \hbar \Omega \left[e^{i\omega_1t}\hat{\sigma}_{me} + e^{-i\omega_1t}\hat{\sigma}_{em} \right] \nonumber \\
&+&\hbar\mathcal{E}_a\left[\hat{a}^\dagger e^{i\omega_2t} \hat{\sigma}_{ge} + \hat{a} e^{-i\omega_2t}\hat{\sigma}_{eg}\right].
\end{eqnarray}
Here $\Omega$ is the Rabi frequency for the (classical) control field and $\mathcal{E}_a$ is the real single atom Rabi frequency for the intra-cavity field, $\hat{a}$. We adopt the interaction picture for the atomic levels and work in a rotating frame at the coupling frequency $\omega_2$. Assuming that the light and the atomic system correlation functions factorize, the equations of motion for the expectation values of the atom-light system in the cavity are then
\begin{align}
&\langle\dot{\hat{a}}\rangle = \left(i \Delta_\mathrm{ca} - \frac{\kappa_\mathrm{ca}}{2}\right)\langle\hat{a}\rangle +\eta_a - i \mathcal{E}_a\langle \hat{\sigma}_{ge}\rangle e^{i \Delta_a t}, \\
&\langle\dot{\hat{\sigma}}_{ge}\rangle = i \mathcal{E}_a\langle \hat{a}\rangle(\langle\hat{\sigma}_{ee}\rangle -\langle \hat{\sigma}_{gg}\rangle) e^{-i \Delta_a t} - i \Omega\langle \hat{\sigma}_{gm}\rangle e^{-i \Delta_c t}\nonumber\\
&\qquad\quad - \frac{\gamma_e}{2}\langle \hat{\sigma}_{ge}\rangle, \\
&\langle\dot{\hat{\sigma}}_{gm}\rangle = i \mathcal{E}_a\langle \hat{a}\rangle\langle \hat{\sigma}_{em}\rangle e^{-i \Delta_a t} - i \Omega\langle \hat{\sigma}_{ge}\rangle e^{i \Delta_c t} - \frac{\gamma_m}{2}\langle \hat{\sigma}_{gm}\rangle, \\
&\langle\dot{\hat{\sigma}}_{em}\rangle = i \mathcal{E}_a\langle \hat{a}^{\dagger}\rangle\langle \hat{\sigma}_{gm}\rangle e^{i \Delta_a t} + i \Omega (\langle\hat{\sigma}_{mm}\rangle - \langle\hat{\sigma}_{ee}\rangle) e^{-i \Delta_c t}\nonumber\\
&\qquad\quad - \frac{\gamma_e}{2} \langle\hat{\sigma}_{em}\rangle.
\end{align}
The terms $\gamma_l$, $l = \{e,m\}$ lead to decay of coherence due to atomic dephasing mechanisms, mainly spontaneous emission from the excited or metastable levels $\ket{e}$, $\ket{m}$. We have also introduced the detunings $\Delta_\mathrm{ca}=\omega_2-\omega_\mathrm{ca}$, $\Delta_a=\omega_2-\omega_{eg}$ and $\Delta_c=\omega_1-\omega_{em}$. For $\Delta_{a}$ and $\Delta_{c}$ much larger than the width of the excited state, the atoms are populating only the lower two states, such that $\langle\hat{\sigma}_{ee}\rangle = 0$ and the total number of atoms is $N = N_g + N_m$ with $\langle\hat{\sigma}_{gg}\rangle = N_g$ and $\langle\hat{\sigma}_{mm}\rangle = N_m$. To find the atomic susceptibility we consider the steady state of the atomic coherences in their respective rest frames and neglect higher order terms in the atom-field coupling $\mathcal{E}_a$
\begin{align}
\langle\hat{\sigma}_{em}\rangle =\,& \frac{\Omega N_m}{\Delta_c - i \gamma_e/2}, \\
\langle\hat{\sigma}_{gm}\rangle =\,& \left[ \Omega \langle\hat{\sigma}_{ge}\rangle - \mathcal{E}_a \langle\hat{a}\rangle \langle\hat{\sigma}_{em}\rangle \right] \frac{1}{\delta - i \gamma_m/2}, \\
\langle\hat{\sigma}_{ge}\rangle =\,& \frac{i \chi_{\rm EIT} \langle\hat{a}\rangle}{-i\mathcal{E}_a}, \\
\chi_{\rm EIT} = \,&\mathcal{E}_a^2 \left(N_g - \frac{\Omega^2 N_m}{(\Delta_c - i \gamma_e/2)(\delta+ i \gamma_m/2)}\right) \nonumber \\
&\times \left(\Delta_a + i\frac{\gamma_e}{2} - \frac{\Omega^2}{\delta + i \gamma_m/2}\right)^{-1}. \label{eq:chiZ}
\end{align}
Here we have introduced the two-photon detuning $\delta = \Delta_a - \Delta_c$. The first term in the atomic susceptibility \eq{chiZ}, dependent on $N_g$, is the usual EIT susceptibility with zero population in the metastable state. In the following we consider that situation and choose $N_g = N$. The equation of motion for the expectation value of the intracavity field becomes then
\begin{equation}
\frac{d \langle\hat{a}\rangle}{dt} = \left(i \Delta_\mathrm{ca} -\frac{ \kappa_\mathrm{ca}}{2}\right) \langle\hat{a}\rangle + \eta_a + i \chi_{\rm EIT} \langle\hat{a}\rangle,
\label{eq:fieldEOMz}
\end{equation}
and the steady state for the cavity field is
\begin{equation}
\langle\hat{a}\rangle = \frac{\eta_a}{-i \Delta_\mathrm{ca} + \kappa_\mathrm{ca}/2 - i \chi_{\rm EIT}},
\label{eq:ssfieldZ}
\end{equation}
which clearly shows the modification of the cavity response by the the atomic system in the form of a modified detuning $\Delta_\mathrm{af} = \Delta_\mathrm{ca} + \mathrm{Re}[\chi_{\rm EIT}]$ and decay rate $\kappa_\mathrm{af} = \kappa_\mathrm{ca} + \mathrm{Im}[\chi_{\rm EIT}]$ with
\begin{widetext}
\begin{eqnarray}
\mathrm{Re}[\chi_{\rm EIT}] &=& - \mathcal{E}_a^2 N \left[\Delta_a \left(\delta^2 + \frac{\gamma_m^2}{4}\right) - \Omega^2 \delta \right] \left[\left(\Delta_a^2 + \frac{\gamma_e^2}{4}\right)\left(\delta^2 + \frac{\gamma_m^2}{4}\right) + \Omega^4 - 2\Omega^2 \left(\Delta_a\delta - \frac{\gamma_e\gamma_m}{4} \right) \right]^{-1}, \\
\mathrm{Im}[\chi_{\rm EIT}] &=& \mathcal{E}_a^2 N \left[\frac{\gamma_e}{2} \left(\delta^2 + \frac{\gamma_m^2}{4}\right) + \Omega^2 \frac{\gamma_m}{2}\right]\left[\left(\Delta_a^2 + \frac{\gamma_e^2}{4}\right)\left(\delta^2 + \frac{\gamma_m^2}{4}\right) + \Omega^4 - 2\Omega^2 \left(\Delta_a\delta - \frac{\gamma_e\gamma_m}{4} \right) \right]^{-1}.
\end{eqnarray}
\end{widetext}
Figure \ref{fig:Zchi} shows the imaginary and real parts of the EIT susceptibility as a function of the two-photon detuning. It displays are two main features: an \emph{atomic resonance}, due to the metastable state $|m\rangle$ dressed by the strong control field; and the \emph{EIT} or \emph{two-photon resonance}, due to the Raman coherence established between $|g\rangle$ and $|m\rangle$. The latter is located at $\delta = 0$ and it is characterized by a vanishing dispersion, while the former is dominated by atomic absorption and its position is set by the dynamical Stark shift, $\delta = \Omega^2/\Delta_a$. The strength of the absorption is directly proportional to the total number of atoms and inversely proportional to the single-photon detuning, since the coupling is mediated by the excited state, and its linewidth may by tuned by changing the amplitude $\Omega$.
Figure \ref{fig:alpha} shows the corresponding intracavity field amplitude as a function of the detuning from the \emph{cavity resonance}. Note the drastic reduction in the effective cavity line width as a result of the interaction with the atoms. The origin of this narrowing is the interplay between atomic absorption and dispersion. There is a strong suppression corresponding to the atomic resonance, where the light is almost completely absorbed by the atomic cloud. The atomic dispersion corresponding to the real part of the susceptibility has a smaller peak value than its imaginary counterpart, but its baseline tends to a constant value away from the resonance and it affects the cavity response. Note that the position of the cavity resonance is not shifted as compared to the bare case since the atomic dispersion vanishes at the two-photon resonance, a well-known property of EIT. The absorption at cavity resonance determines the small difference between the bare cavity response and the atomic case.
The effective linewidth of the cavity is also influenced by the separation between the atomic and EIT resonances: this can be controlled via the intensity of the control field $\Omega$, as shown in \fig{alpha}, or via the single-photon detuning $\Delta_a$.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width = \columnwidth]{alpha_cav2}
\caption{(Colors online). Normalized intracavity electric field of the atomic cavity. The cavity has a decay rate $\kappa_{ca} = 2\pi \times 70$~MHz and it is resonant with the two-photon resonance of EIT, $\delta = \Delta_{ca}$. We consider an atomic ensemble in EIT configuration with $N = 10^8$ atoms and control amplitude: $\Omega = 4 \gamma_e$ (red dot-dashed line), $\Omega = 6 \gamma_e$ (blue dashed line). The black solid line represents the cavity response without atoms.}
\label{fig:alpha}
\end{center}
\end{figure}
\subsection{Recoil Induced Resonances}
We turn next to an atomic $\Lambda$ system that relies on the motional states of the ultracold gas. In particular, we evaluate the optical response of the gas in the vicinity of a recoil-induced resonance wherein the motion of the atoms under the influence of optical fields can mediate the conversion of atomic kinetic energy into radiation. We consider an atomic cloud of $N$ atoms confined in a cylindrically symmetric trap with the axial confinement significantly weaker than the radial confinement. This one-dimensional geometry enhances atomic recoil effects along the weakly confined axis. Along this axis, the atoms are illuminated by a strong control laser with frequency $\omega_1$ and wave vector $k_1$, and a weak counter-propagating coupling laser with frequency $\omega_2$ and wave vector $k_2$. The relevant energy levels are sketched in Fig. \ref{fig:EITschemes}C. The energy difference between the two lower lying states can be changed by detuning one of the lasers.
In the absence of collisions but accounting for photon recoil, the Hamiltonian describing the interaction of the atomic ensemble with the light fields is $H=\sum_k H_k$, with
\begin{eqnarray}\nonumber
H_k&=&\frac{\hbar^2k^2}{2m_a}\hat{c}_g^\dagger(k)\hat{c}_g(k)+\left(\frac{\hbar^2k^2}{2m_a}+\hbar\omega_0\right)\hat{c}_e^\dagger(k)\hat{c}_e(k)\\ \nonumber
&+&\hbar\Omega\left[i e^{i\omega_1t}\hat{c}_g^\dagger(k-k_1)\hat{c}_e(k) + \mathrm{h.c.} \right] \\
&+&\hbar\left[i \mathcal{E}_a\hat{a}^\dagger e^{i\omega_2t}\hat{c}_g^\dagger(k-k_2)\hat{c}_e(k) + \mathrm{h.c.}\right]
\label{eq:aHamiltonian}
\end{eqnarray}
Here $\hat{c}_{g}(k)$ and $\hat{c}_{e}(k)$ are the annihilation operator of a ground and excited state atom with momentum $\hbar k$, respectively. They follow standard bosonic commutation relations, $\left[\hat{c}_i(k),\hat{c}_j^\dagger(k')\right]=\delta_{kk'}\delta_{ij}$. As before the Rabi frequency for the control field is $\Omega$ and $\mathcal{E}_a$ is the single atom Rabi frequency for the intracavity field, $\hat{a}$.
The expectation value for the intracavity field is governed by the equation of motion
\begin{equation}\label{eq:fieldeom1}
\langle\dot{\hat{a}}\rangle=-\left(i\omega_\mathrm{ca}+ \frac{\kappa_\mathrm{ca}}{2}\right)\langle\hat{a}\rangle+\mathcal{E}_a e^{i\omega_2 t}\sum_k\langle \hat{c}_g^\dagger(k-k_2)\hat{c}_e(k)\rangle+\eta_a,
\end{equation}
where we have added cavity dissipation and drive in the familiar fashion.
We introduce the single-photon detuning $\Delta_a=\omega_0-\omega_1$, and the two-photon detuning, $\delta=\omega_2-\omega_1$ and, as in the case for EIT, assume a large single-photon detuning such that $(\delta,\Omega) \ll \Delta_a$. In this limit, we can adiabatically eliminate the excited state and evaluate the equations of motion for the ground state populations and momentum state coherences of the atomic gas \cite{Hafezi2008}. Details of this calculation are outlined in Appendix A.
We define the momentum-dependent population in the ground state, $\Pi_p$, and the ground state coherences between adjacent momentum classes, $\zeta_{p \pm 1}$, as
\begin{widetext}
\begin{eqnarray}
\Pi_p&=&\rho_{gg}(k,k) =\langle \hat{c}_g^\dagger(k)\hat{c}_g(k)\rangle= N_g,\nonumber \\
\zeta_{p+1}&=&\rho_{gg}(k+2k_0,k)e^{-i\delta t}=\rho_{gg}(p+1,p)e^{-i\delta t}=\langle \hat{c}_g^\dagger(k)\hat{c}_g(k+2k_0)\rangle e^{-i\delta t},\nonumber \\
\zeta_{p-1}&=&\rho_{gg}(k-2k_0,k)e^{i\delta t}=\rho_{gg}(p-1,p)e^{i\delta t}=\langle \hat{c}_g^\dagger(k)\hat{c}_g(k-2k_0)\rangle e^{i\delta t},
\end{eqnarray}
Assuming an initial ground state population momentum distribution $\Pi_{\rm th}$ that is in thermal equilibrium at temperature $T_a$, we can write the coupled system of equations for the atomic populations and coherences as
\begin{eqnarray}
\frac{d}{dt}\Pi_p&=&i\beta\mathcal{E}_a\langle\hat{a}\rangle\left(\zeta_{p+1}-\zeta_{p-1}\right)+i\beta \mathcal{E}_a \langle\hat{a}^{\dagger}\rangle\left(\zeta_{p-1}-\zeta_{p+1}^*\right) -\gamma_{\rm pop}\Pi_p+\gamma_{\rm pop}\Pi_{{\rm th},p}\ \label{eq:gseom1}\\
\frac{d}{dt}\zeta_{p+1}&=&-\left(4i\omega_r(2p+1)+i\delta+\gamma_{\rm coh}\right)\zeta_{p+1} -i\beta \mathcal{E}_a \langle\hat{a}^{\dagger}\rangle(\Pi_{p+1}-\Pi_{p}),\\
\frac{d}{dt}\zeta_{p-1}&=&\left(4i\omega_r(2p-1)+i\delta-\gamma_{\rm coh}\right)\zeta_{p-1} -i\beta \mathcal{E}_a\langle\hat{a}\rangle(\Pi_{p-1}-\Pi_{p}),
\end{eqnarray}
\end{widetext}
where
\begin{equation}
\omega_r=\hbar k^2/2m_a
\end{equation}
is the atomic recoil frequency, $2k_0=k_1-k_2$, the dimensionless momentum $p=\hbar k/(2\hbar k_0)$, and we have introduced the normalized control strength $ \beta=\Omega/\Delta_a$.
The last two terms in the equation for the population are due to the fluctuation-dissipation theorem.
\begin{figure*}[hbt]
\begin{center}
\includegraphics[width=\textwidth]{chiRIR}
\caption{ (Color online) Real and imaginary parts of the atomic susceptibility for a thermal ensemble of atoms at [$T_a=21 \mu$K, $\Omega= 1.8 \gamma_e$] (red dot-dashed line), [$T_a= 21\mu$K, $\Omega = 2.6 \gamma_e$] (blue dashed line). Here $N = 10^8$ atoms, $\Delta_a=-15 \gamma_{e}$, $\omega_r=2 \pi \times 3.77$~kHz, $\gamma_{e}=2\pi \times 6.07 $~MHz, $\gamma_{\rm coh}=2 \pi \times 10$~kHz, and $\mathcal{E}_a= 2 \pi \times 500$~kHz. }
\label{fig:RIRchi}
\end{center}
\end{figure*}
Assuming that the atomic populations remain in thermal equilibrium and that the coherences reach steady state over the time scale of the evolution of the electric fields, the equation of motion for the mean intracavity field becomes
\begin{equation}
\frac{d \langle\hat{a}\rangle}{dt}=\left(i\Delta_\mathrm{ca}-\frac{\kappa_\mathrm{ca}}{2}\right)\langle\hat{a}\rangle+\eta_a+i\chi_{\rm RIR} \langle\hat{a}\rangle,
\label{eq:fieldEOMr}
\end{equation}
where $\Delta_\mathrm{ca}=\omega_2-\omega_\mathrm{ca}$ is the detuning of the cavity from the coupling frequency. This is essentially the same as for EIT, except that the susceptibility is now $\chi_{\rm RIR}$. For a strong control beam that does not suffer any significant depletion, we can solve for the steady state of the intra-cavity field to get
\begin{equation}
\langle\hat{a}\rangle = \frac{\eta_a}{-i \Delta_\mathrm{ca} + \kappa_\mathrm{ca}/2 - i \chi_{\rm RIR}}.
\label{eq:ssfieldRIR}
\end{equation}
with
\begin{widetext}
\begin{eqnarray}\nonumber
{\rm Re}[\chi_{\rm RIR}]&=& \frac{\mathcal{E}_a ^2N}{\Delta_a}+ (\beta \mathcal{E}_a)^2N\left\{ \sum_p\frac{\Pi_{{\rm th},p}(\delta+4\omega_r(2p+1))}{(\gamma_{\rm coh}^2+(\delta+4\omega_r(2p+1))^2)}-\frac{\Pi_{{\rm th},p}(\delta+4\omega_r(2p-1))}{(\gamma_{\rm coh}^2+(\delta+4\omega_r(2p-1))^2)}\right\},\\
{\rm Im}[\chi_{\rm RIR}]&=&- (\beta \mathcal{E}_a)^2N\gamma_{\rm coh}\left\{\sum_p\frac{\Pi_{{\rm th},p}}{(\gamma_{\rm coh}^2+(\delta+4\omega_r(2p+1))^2)}-\frac{\Pi_{{\rm th},p}}{(\gamma_{\rm coh}^2+(\delta+4\omega_r(2p-1))^2)}\right\}.
\label{eq:chi}
\end{eqnarray}
\end{widetext}
Figure \ref{fig:RIRchi} shows ${\rm Im}[\chi_{\rm RIR}]$ and ${\rm Re}[\chi_{\rm RIR}]$ as functions of the two-photon detuning for a thermal ensemble of ultracold atoms. The atomic susceptibility depends on the number of atoms $N$, the Rabi frequency $\Omega$, the single-photon detuning $\Delta_a$ and the temperature of the ensemble $T_a$. The decoherence rate $\gamma_{\rm coh}$ depends both on off-resonant light scattering as well as atomic collisions. For a laser cooled atomic gas, decoherence rates as low as 1 ms$^{-1}$ have been demonstrated \cite{Hafezi2008}. This is more than two orders of magnitude smaller than the typical mechanical resonance frequency $\omega_m$ that we consider in this work.
As with EIT, the RIR results in modifications to the atomic susceptibility with the detuning changing to $ \Delta_\mathrm{af}=\Delta_\mathrm{ca}+ {\rm Re}[\chi_{\rm RIR}]$ and the decay rate changing to $ \kappa_\mathrm{af}=\kappa_\mathrm{ca}/2+ {\rm Im}[\chi_{\rm RIR}]$. As will become apparent in Section IV, the effect of recoil resonances on the coupling field is formally analogous to the optomechanical effects inside a cavity with a moving mirror, with the difference that instead of having a single frequency as is the case in single-mode optomechanics, we now have a distribution of frequencies associated with the center-of-mass momentum distribution of the atoms. The presence of a negative susceptibility $\rm Im[\chi_{RIR}]$ for negative detunings $\delta$ is indicative of gain in the atomic medium, leading to an exponential build up of the coupling laser in the linear, small signal regime.
Figure \ref{fig:RIRprobe} shows the normalized cavity field amplitude as a function of the cavity detuning $\Delta_{ca}$ for the parameters of Fig.~\ref{fig:RIRchi}. The field amplitude is strongly suppressed for small positive detunings. Also, for various combinations of scaled control fields $\beta$ and temperature $T_a$, there is a dramatic build-up of intensity for a narrow range of frequencies at negative detuning. Within this window, the atomic gas mediates the coherent transfer of energy from the control field to the coupling field, leading to gain in the latter. The gain feature can be tuned in frequency by varying the control detuning, intensity and the temperature of the atomic ensemble.
Importantly we note that while the linearized theory would predict an exponential growth of the coupling field with increasing atom number, the actual gain is limited in practice by depletion of the control field. Such saturation effects are not accounted for in the present description. Our specific examples of experimental parameters have been chosen so as to safely stay away from such limiting effects.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=\columnwidth]{ProbeRIR}
\caption{(Color online). Normalized steady state coupling field after the atomic medium for the parameters of Fig.~\ref{fig:RIRchi}.
The atomic ensemble is in free space which corresponds to a decay rate $\kappa_{ca} = c/L_a = 2\pi \times 600$ GHz, and with $\Delta_\mathrm{ca}=0$.
We show the result for [$T_a=21 \mu$K, $\Omega= 1.8 \gamma_e$] (red dot-dashed line), [$T_a= 21\mu$K, $\Omega = 2.6 \gamma_e$] (blue dashed line) and without atomic medium (black solid line).}
\label{fig:RIRprobe}
\end{center}
\end{figure}
Summarizing this section, both the EIT and RIR schemes lead to frequency dependent atomic susceptibilities with spectrally narrow features as shown in Fig.~\ref{fig:Zchi} and \fig{RIRchi}. In the EIT scheme, the two-photon resonance corresponds to a narrow window of vanishing absorption and dispersion that leaves the coupling field unchanged. In the case of RIR, the atoms act as a gain medium, converting control photons to coupling field photons via atomic recoil, leading to an enhancement of the latter within a narrow range of frequencies as shown in Fig. \ref{fig:RIRprobe}. Both effects can be used to enhance optomechanical cooling. In the EIT scheme, this results from a reduction of the effective linewidth of the cavity down to the range of the transparency window of the atomic medium while in the RIR scheme, the atomic gas acts as a gain medium enhancing the coupling field around the anti-Stokes sideband.
\section{Hybrid atom-optomechanics}
We are now in a position to investigate the effect of the atomic ensemble on the cooling properties of the hybrid optomechanical setups of section II. From the Hamiltonian~(\ref{eq:totalH}) the equations of motion for the optomechanical cavity field $\hat{c}$ and the mechanical mode $\hat{b}$ are
\begin{eqnarray}
\dot{\hat{c}}&=&-\left(i\omega_\mathrm{cm}+\frac{\kappa_\mathrm{cm}}{2}\right)\hat{c}+\eta_c-iJ\hat{a}-ig_0\hat{c}(\hat{b}+\hat{b}^\dagger),\\
\dot{\hat{b}}&=&-\left(i\omega_{m}+\frac{\gamma_{m}}{2}\right)\hat{b}-ig_0\hat{c}^\dagger\hat{c},
\end{eqnarray}
where we have introduced the mechanical damping rate $\gamma_m = \omega_m/Q$, with $Q$ the quality factor of the mechanics. We assume $\kappa_\mathrm{ca} \gg \kappa_\mathrm{cm}$ which implies that, over the time-scale of the dynamics of the optomechanical system, the atomic cavity follows adiabatically the dynamics of the mechanical resonator.
We consider in the following the two specific scenarios of feedback and cascade couplings illustrated in Fig.~\ref{fig:coupling}. In the former case, light is pumped (from the left) into the optomechanical cavity, and then coupled (from the right) into the atomic cavity. In the latter configuration, the driving field first propagates through the atomic medium and is then injected into the optomechanical resonator.
\begin{figure}[h]
\begin{center}
\includegraphics[width=\columnwidth]{CouplingSetup.pdf}
\caption{(Colors online). Schematic of the two atom mediated optomechanical coupling schemes. In setup A, the atomic cavity provides a feedback system for the optomechanical cavity. In setup B, the external drive is filtered through the atomic medium before being injected into the optomechanical cavity.}
\label{fig:coupling}
\end{center}
\end{figure}
\subsection{Feedback coupling}
Consider first the feedback scheme of Fig.~\ref{fig:coupling}A. The output of the optomechanical cavity drives the atomic cavity, so that the cavity field driving term $\eta_a$ in Eqs.~(\ref{eq:ssfieldZ}) and (\ref{eq:ssfieldRIR}) is now $-iJ\hat{c}$. The assumption that the atomic cavity follows adiabatically the evolution of the optomechanical cavity field allows to replace $\langle \hat{a} \rangle$ by
\begin{equation}
\langle\hat{a}\rangle = \frac{iJ\langle\hat{c}\rangle}{i (\Delta_\mathrm{ca} +\chi)- \kappa_\mathrm{ca}/2},
\end{equation}
where we dropped the subscript for the atomic susceptibility for notational convenience. In a frame rotating at the drive frequency $\omega_2$, the equation of motion for $\langle \hat{c} \rangle $ then simplifies to
\begin{eqnarray}
\langle \dot{\hat c}\rangle &=&i\left(\Delta_\mathrm{cm}-\frac{\kappa_{\rm cm}}{2}- g_0\langle\hat{b}+\hat{b}^\dagger\rangle\right)\langle\hat{c}\rangle -iJ\langle \hat a \rangle +\eta_c\nonumber \\
&=&i\left(\Delta_\mathrm{cm}- g_0\langle\hat{b}+\hat{b}^\dagger\rangle\right)\langle\hat{c}\rangle \nonumber\\
&+&\left(-\frac{\kappa_\mathrm{cm}}{2}+\frac{J^2}{i (\Delta_\mathrm{ca} +\chi)-\kappa_\mathrm{ca}/2}\right)\langle\hat{c}\rangle+\eta_c,
\end{eqnarray}
where $\Delta_\mathrm{cm} = \omega_2 - \omega_\mathrm{cm}$.
It is clear from this expression that the linewidth $\kappa_{cm}$ of the optomechanical cavity is modified by the field in the atomic cavity: this is exactly the effect of the feedback coupling.
\begin{figure*}[ht]
\begin{center}
\includegraphics[width =\textwidth]{EITcooling_gs}\\
\includegraphics[width =\textwidth]{EITcooling_bs}
\caption{(Color online). Cooling characteristics of the hybrid atomic EIT optomechanical system with feedback coupling for $\omega_m = 2\pi\times 300$~kHz, $Q = 5 \times 10^7$, $T_{\rm bath} = 300$~K, $P_{\rm in} = 200$~nW, $g_0=2 \pi \times 200$~Hz, $\kappa_{\rm ca} = 2\pi \times 70$~MHz, $N=10^8$ atoms, $\Omega = 6\gamma_e$, and $\Delta_a = 500 \gamma_e$. Plots (a) and (d) show the mean optomechanical cavity field $\langle \hat c \rangle$, plots (b) and (e) the optical damping $\Gamma_{\rm opt}$ and plots (c) and (f) the minimum number of phonons as a function of $\tilde{\Delta}_{cm}/\omega_m$ near the resolved sideband regime, $\kappa_{\rm cm} = 2\pi \times 240$~kHz $ < \omega_m$ (a,b,c), and in the Doppler regime, $\kappa_{\rm cm} = 2\pi \times 3.6$~MHz $ > \omega_m$(d,e,f). The red dashed lines represent the hybrid case and the black solid lines represent the case without coupling to the atomic cavity ($J = 0$) for comparison.}
\label{fig:hybrid_EIT}
\end{center}
\end{figure*}
We now introduce the normalized displacement operator $\hat{x}=\hat{b}+\hat{b}^\dagger$, and we decompose the operators $\hat{c}=\langle \hat c \rangle+\delta\hat{c}$ and $\hat{x}=\langle \hat x \rangle+\delta\hat{x}$, into a classical average value corresponding to the steady state, and small fluctuations around it. Linearizing the equations of motion we arrive at
\begin{equation}
\langle \hat c \rangle=\eta_c\left(-i\tilde{\Delta}_\mathrm{cm}-\frac{J^2}{i (\Delta_\mathrm{ca} +\chi)-\kappa_\mathrm{ca}/2}+\frac{\kappa_\mathrm{cm}}{2}\right)^{-1},
\label{eq:barc}
\end{equation}
where $\tilde{\Delta}_\mathrm{cm}=\Delta_\mathrm{cm}-g_0\langle \hat x \rangle$.
The fluctuations in the cavity field are governed by the equation of motion
\begin{equation}
\delta \dot{\hat{c}}=\left(i\tilde{\Delta}_\mathrm{cm}+\frac{J^2}{i (\Delta_\mathrm{ca} +\chi)-\kappa_\mathrm{ca}/2}-\frac{\kappa_\mathrm{cm}}{2}\right)\delta\hat{c}-ig \delta\hat{x}.
\end{equation}
where we have introduced the linearized coupling constant $g = g_0\langle \hat c \rangle$, which can be taken to be real without loss of generality.
This equation can be solved easily in the Fourier domain to get
\begin{align}\nonumber
&\delta \hat c[\omega]=-ig\delta \hat x[\omega] \times \\
&\left(-i(\tilde{\Delta}_\mathrm{cm}+\omega)-\frac{J^2}{i (\Delta_\mathrm{ca}+\omega +\chi[\omega])-\kappa_\mathrm{ca}/2}+\frac{\kappa_\mathrm{cm}}{2}\right)^{-1},
\end{align}
and $\delta \hat c^\dagger[\omega]=(\delta \hat c[-\omega])^\dagger$. The dynamical radiation pressure force at the mechanical frequency is given by $\delta \hat F_{\rm RP}[\omega_m]=-\hbar G (\delta \hat c[\omega_m]+\delta \hat c^\dagger[\omega_m])$, where $G = g/x_{\rm zpt}$ and $x_{\rm zpt} = \sqrt{\hbar/(2m\omega_m)}$ is the zero point motion of the mechanical oscillator. This gives
\begin{equation}
\delta \hat F_{\rm RP}[\omega_m]=i\hbar \frac{g^2}{x_{\rm zpt}} \delta \hat x[\omega_m]\left(\frac{1}{A^{(+)}-i\omega_m}-\frac{1}{A^{(-)*}-i\omega_m}\right),
\end{equation}
where
\begin{equation}
A^{(\pm)}=-i\tilde{\Delta}_\mathrm{cm}-\frac{J^2}{i (\Delta_\mathrm{ca} \pm \omega +\chi^{(\pm)})-\kappa_\mathrm{ca}/2}+\frac{\kappa_\mathrm{cm}}{2},
\end{equation}
and $\chi^{(\pm)}$ is the susceptibility evaluated at $\omega_2\pm\omega_m$. The real and imaginary parts of $\langle \delta \hat F_{\rm RP} \rangle$ change the spring constant and damping rate of the mechanical oscillator via dynamical back-action~\cite{OM_review,OM_cooling}, with
\begin{align}
&\Gamma_{\rm opt}=2 g^2 {\rm Re}\left[\frac{1}{A^{(+)}-i\omega_m}-\frac{1}{A^{(-)*}-i\omega_m}\right],\\
&k_{\rm opt}=2 m \omega_m g^2 {\rm Im}\left[\frac{1}{A^{(+)}-i\omega_m}-\frac{1}{A^{(-)*}-i\omega_m}\right].
\end{align}
We recognize the familiar two components deriving from the Stokes (red-) and anti-Stokes (blue-) sidebands. In particular, the optical damping rate can be written as
\begin{equation}
\Gamma_{\rm opt}=\Gamma_{\rm anti-Stokes}-\Gamma_{\rm Stokes}.
\label{eq:gammaopt}
\end{equation}
Solving for the steady state minimum occupation number for the mechanical mode coupled to a thermal bath, we obtain
\begin{equation}
n_{\min}=\frac{\Gamma_{\rm Stokes}+\gamma_m n_{\rm bath}}{\Gamma_{\rm opt}+\gamma_m}.
\label{eq:nmin}
\end{equation}
Here, $n_{\rm bath} = k_B T_{\rm bath}/\hbar \omega_m \gg 1$,with $T_{\rm bath}$ the temperature of the thermal bath of the oscillator.
If we assume $\omega_m = 2\pi \times 300$ kHz with $Q = 5 \times 10^7$ at room temperature \cite{Chakram2014}, we can estimate the minimum optical damping needed to reach ground state cooling as $\Gamma_{\rm opt} > 2\pi \times 125$~kHz.
\begin{figure}[htb]
\begin{center}
\includegraphics[width =\columnwidth]{EITcooling_color}
\caption{(Color online). Maximum optical damping rate for the hybrid atomic EIT optomechanical system with feedback couplingumber $N$. Here $\omega_m = 2\pi\times 300$~kHz with a quality factor $Q = 5 \times 10^7$ and temperature $T_{\rm bath} = 300$~K, $P = 200$~nW, $g_0=2 \pi \times 200$~Hz, $\kappa_{\rm ca} = 2\pi \times 70$~MHz, $\Delta_a = 500 \gamma_e$, and $\kappa_{\rm cm} = 2\pi \times 240$~kHz. The area enclosed by the black line corresponds to $\Gamma_{\rm opt} > 2\pi \times 125$~kHz and hence to ground state cooling, $n_{\rm min} < 1$, for these parameters. }
\label{fig:EIT_color}
\end{center}
\end{figure}
Figure \ref{fig:hybrid_EIT}
summarizes important cooling features of the EIT based hybrid optomechanical system and compares them to the purely optomechanical cooling ($J=0$) situation. The upper plots (a,b,c) are for an intermediate situation close to the resolved side band regime of optomechanics, with $\kappa_{\rm cm} \approx \omega_m$, and the lower series of plots (d,e,f) for the so-called Doppler regime $\kappa_{\rm cm} \gg \omega_m$.
Remarkably, we find in the intermediate regime a configuration that leads to ground state cooling from room temperature, as clearly shown in Fig.~\ref{fig:hybrid_EIT}(c). Introducing the hybrid system improvement factor
\begin{equation}
\label{eq:improvf}
\xi = n_{\rm min}^{\rm cm}/n_{\rm min}^{\rm cm + \rm ca},
\end{equation}
we have $\xi \approx 2$ for this situation, a value necessary to obtain $n_{\rm min} < 1$ in that case. We observe also that the best cooling is obtained for $-\omega_m < \tilde{\Delta}_{\rm cm} < 0$ on the red side of the resonance, but slightly shifted compared to the familiar resolved side band condition $\tilde{\Delta}_{\rm cm} = -\omega_m$.
Figure \ref{fig:hybrid_EIT}(f) shows that in the Doppler regime the improvement factor increases to $\xi \approx 3$, even though the system is cooled to a mean phonon number still far removed from the ground state. Interestingly, though, the strongest cooling feature is now on the blue-side of the resonance, corresponding to $\tilde{\Delta}_{\rm cm} = \omega_m$.
We can gain some degree of intuitive understanding of these results by considering the intracavity fields of Eq.~\eq{barc}, see~\fig{hybrid_EIT}(a,d). As is well known \cite{OM_cooling} the optical damping finds its origin in the difference between the two mechanically generated sidebands, located at $\tilde{\Delta}_{\rm cm} = \omega_2 \pm \omega_m$, whose shape is determined by the intracavity field. Without feedback each sideband has a single peak. Their difference is always positive on the red-side of the resonance, corresponding to cooling. Instead, in the hybrid configuration there is a dip in the field at resonance. The situation is less clear-cut in the presence of feedback, and a more detailed quantitative analysis is required in general to understand the detailed features of cooling, in particular whether it occurs on the red or blue-detuned side of the resonance. First, we note that at the atomic resonance the light entering into the feedback cavity is completely absorbed, thus providing no coupling back to the optomechanical cavity. Second, for situations where the atomic cavity field is small, the field in the optomechanical cavity remains closer to the uncoupled $(J = 0)$ case. Finally, at the cavity resonances $\tilde{\Delta}_{\rm cm} = \Delta_{\rm ca} = 0$, where the atomic susceptibility vanishes, the feedback field simply contributes an additional term $2J^2/\kappa_\mathrm{\rm ca}$ to the optomechanical cavity linewidth. This induces a dip in the field that is absent without feedback, see dotted red lines in \fig{hybrid_EIT}a and \fig{hybrid_EIT}d. Away from these limiting situations both the spectral properties and amplitude of the feedback field depend on the linewidth established by the combined effects of $\Omega$ and $N$. In the extreme Doppler regime $\kappa_{\rm cm} \gg \omega_m$, the widths of the sidebands are much broader than their separation, see \fig{hybrid_EIT}d. This results in a situation opposite to the familiar resolved side band regime, with cooling on the blue-side and heating on the red-side, see \fig{hybrid_EIT}(e). When reducing $\kappa_{\rm cm}$ and moving towards the resolved sideband regime, the two peaks in the field start to be be resolved, and this enhances cooling on the red side of the cavity resonance as emerges from \fig{hybrid_EIT}(b).
Figure \ref{fig:EIT_color} shows the dependence of the optical damping on the control Rabi frequency $\Omega$ and atom number $N$ for the case leading to ground state cooling from room temperature. Importantly, the parameter region that results in such cooling is large, an indication of the robustness of the hybrid system approach with respect to parameter fluctuations.
Finally, \fig{EIT_improvement} plots the improvement factor $\xi$ for a large range of optomechanical cavity decay rates. Deep in the Doppler regime the atomic ensemble provides an improvement of almost two orders of magnitude over conventional cooling. This factor decreases as one approaches the resolved side-band regime, but interestingly, the border between the two regimes is characterized by a feature that allows for ground state cooling as highlighted in the inset. We remark that the advantage of working in an intermediate regime between the resolved side band and Doppler regime has also recently been pointed out in Ref.~\cite{PKU} in a different context.
\begin{figure}[h]
\begin{center}
\includegraphics[width = 1\columnwidth]{EIT_improvement}
\caption{Improvement factor $\xi$ when varying the cavity damping rate from the Doppler (right) towards the resolved-sideband (left) regime. The inset shows the area where ground state cooling may be achieved (arrow). Here $\omega_m = 2\pi\times 300$~kHz, $Q = 5 \times 10^7$, $T_{\rm bath} = 300$~K, $P = 200$~nW, $g_0=2 \pi \times 200$~Hz, $\kappa_{ca} = 2\pi \times 70$~MHz, $N=10^8$ atoms, $\Omega = 6\gamma_e$and $\Delta_a = 500 \gamma_e$.}
\label{fig:EIT_improvement}
\end{center}
\end{figure}
\subsection{Cascade coupling}
\begin{figure*}
\begin{center}
\includegraphics[width=\textwidth]{RIRcooling_gs}\\
\includegraphics[width=\textwidth]{RIRcooling_bs}
\caption{(Color online). Features of the hybrid optomechanical cooling via RIR. Here $\omega_m = 2\pi\times 300$~kHz, $Q = 5 \times 10^7$, $T_{\rm bath} = 300$~K. $P = 1$~nW, and $g_0=2 \pi \times 200$~Hz. A $0.5$~mm atomic ensemble of $10^8$ atoms is illuminated with a control field of strength $\Omega = 2.6\gamma_e$ and $\Delta_a = -15 \gamma_e$. We show the intensity in the optomechanical cavity, the optical damping $\Gamma_{opt}$ and the minimum number of phonons for $\kappa_{cm} = 2\pi \times 240$~kHz (a,b,c) and $\kappa_{cm} = 2\pi \times 3.6$~MHz (d,e,f), respectively. Black solid lines: no cavity coupling, $J = 0$. Red dashed lines: hybrid case.}
\end{center}
\label{fig:OMeffects}
\end{figure*}
One can envison a similar enhancement of optomechanical cooling using the motional states of the atomic gas via a recoil-induced resonance. In order to take advantage of the spectrally narrow gain feature associated with the RIR, we turn to a configuration where the amplified output from the atomic medium directly drives the optomechanical cavity. Furthermore, in order to ensure gain within a single frequency window, we assume that the atomic medium is trapped in free space instead of within a cavity (see Fig.~\ref{fig:coupling} B).
To account explicitly for the effects of photon recoil is is useful to introduce the new bosonic annihiltion operations $\hat{a}\rightarrow\hat{a}_p=(1/\sqrt{2})\hat{a}e^{ikz}$, where the factor of $1/\sqrt{2}$ accounts for quantization of the field in terms of running waves modes \ and $e^{ikz}$ is the phase of the propagating field along the $z$ axis. The coupling field Hamiltonian Eq.\ref{eq:HoptA} becomes then
\begin{equation}
H'_{\rm optA}=\hbar \omega_2 \hat{a}_p^\dagger \hat{a}_p+i\hbar (\eta_a\hat{a}_p^\dagger-\eta_a^* \hat{a}_p),
\end{equation}
and the coupling between the two field modes
\begin{equation}
H'_{AM}=\hbar J(\hat{a}_p^\dagger \hat{c}+\hat{a}_p\hat{c}^\dagger),
\end{equation}
where $J=\sqrt{\kappa_{a} \kappa_\mathrm{cm}/2}$ and $\kappa_a = c/L_a$ is the free-space decay rate of an atomic cloud of length $L_a$. A large decay rate implies that the expectation value of the coupling field comes to a steady state over a very short time period. Thus,
\begin{equation}
\langle \hat{a}_p\rangle \rightarrow \langle \hat{a}_p\rangle =\frac{\eta_a}{-i\chi+\kappa_a/2}.
\end{equation}
Inserting this form in the equation of motion for $\langle \hat{c} \rangle$, and in a frame rotating at $\omega_2$ gives
\begin{equation}
\langle \dot{\hat{c}}\rangle =\left(i\tilde{\Delta}_\mathrm{cm}-\frac{\kappa_\mathrm{cm}}{2}\right)\langle \hat{c}\rangle +(\eta_c-iJ\langle \hat{a}_p\rangle).
\end{equation}
We now have an additional drive term that has a frequency dependence due to the susceptibility of the atomic cloud. As a result, the steady state and fluctuations of the optomechanical cavity field are given by
\begin{align}
&\langle \hat c \rangle=(\eta_c-iJ\langle \hat{a}_p\rangle)\left(-i\tilde{\Delta}_\mathrm{cm}+\frac{\kappa_\mathrm{cm}}{2}\right)^{-1},\\
&\langle \delta c[\omega]\rangle =-ig_0\langle \hat c \rangle\langle \delta x[\omega]\rangle \left(-i(\tilde{\Delta}_\mathrm{cm}+\omega)+\frac{\kappa_\mathrm{cm}}{2}\right)^{-1}.
\end{align}
The dynamical radiation pressure force at the mechanical frequency thus becomes
\begin{align}\nonumber
&\langle \delta \hat F_{RP}[\omega_m]\rangle =i\hbar (g^2/x_{\rm zpt}) \langle \delta \hat x[\omega_m] \rangle \times\\
&\left(\frac{1}{-i(\tilde{\Delta}_\mathrm{cm}+\omega_m)+\kappa_\mathrm{cm}/2}-\frac{1}{i(\tilde{\Delta}_\mathrm{cm}-\omega_m)+\kappa_\mathrm{cm}/2}\right),
\end{align}
where $g=g_0|\langle \hat c \rangle|^2$, and the intra-cavity field evaluated at $\omega=\omega_2+ \omega_m$. The optically mediated cooling rate and spring constant become
\begin{eqnarray}\nonumber
\Gamma_{\rm opt}&=& 2 g_0^2|\langle \hat c \rangle|^2\, {\rm Re}\left[\frac{1}{-i\tilde{\Delta}_\mathrm{cm}^++\kappa_\mathrm{cm}/2}
-\frac{1}{i\tilde{\Delta}_\mathrm{cm}^-+\kappa_\mathrm{cm}/2}\right],\\ \nonumber
k_{\rm opt}&=& 2 m \omega_m\,g_0^2 |\langle \hat c \rangle|^2\nonumber \\
&&{\rm Im}\left[\frac{1}{-i\tilde{\Delta}_\mathrm{cm}^++\kappa_\mathrm{cm}/2}
-\frac{1}{i\tilde{\Delta}_\mathrm{cm}^-+\kappa_\mathrm{cm}/2}\right],
\end{eqnarray}
where $\tilde{\Delta}_\mathrm{cm}^{\pm}=\tilde{\Delta}_\mathrm{cm}\pm\omega$.
Figure 11
shows the intracavity intensity, optomechanical cooling rates, and minimum steady state occupation number of the mechanical mode with and without the atomic medium. In these results, the parameters for the atomic ensemble and the coupling field are chosen so as to realize a gain feature around the mechanical resonance frequency $\omega_m$. The optomechanical cavity parameters and the mechanical oscillator parameters are the same as for the EIT case, except for a lower input power of 1 nW to avoid parametric instabilities. As can be seen, the coupling to the atomic medium results in a dramatic enhancement to the cooling rate for $\tilde{\Delta}_{\rm cm} \approx - \omega_m$. It corresponds to a decrease in the phonon number of the mechanical resonator by over two orders of magnitude.
\begin{figure}[h]
\begin{center}
\includegraphics[width =\columnwidth]{RIRimprov}
\caption{Improvement factor for RIR-based hybrid optomechanical cooling with varying cavity damping rate. Here, $\omega_m = 2 \pi \times 300$~kHz, $Q = 5 \times 10^7$, $T_{bath} = 300$~K and $P = 1$~nW. The atomic parameters for the RIR are the same as in Fig. 11. }
\label{fig:RIRimprov}
\end{center}
\end{figure}
The enhancement to optomechanical cooling due to the RIR can be quantified in terms of the dimensionless parameter $\xi$ of Eq.~(\ref{eq:improvf}), see Fig.~\ref{fig:RIRimprov}. It reveals substantial optomechanical cooling due to the atomic medium over a wide region extending well into the Doppler regime of the optomechanical cavity. (Note that for very large $\kappa_{\rm cm}$, the optomechanical cavity becomes too lossy for an appreciable intensity to build up within the cavity, leading to a decreased influence of the atomic medium.)
\subsection{Comparison of the two coupling schemes}
While distinct physical mechanisms are at the origin of these results both the EIT-feedback coupling and the RIR-cascade coupling contribute to a substantial improvement of the mechanical cooling in the Doppler regime.
In the case of EIT, the creation of a narrow window of field suppression around cavity resonance allows to eliminate the unwanted sideband thus improving cooling. This explains why cooling occurs on the blue side of the cavity resonance, in contrast to the more familiar resolved sideband regime situation. In the case of cascade coupling, the intrinsic asymmetry in the two sidebands is strongly enhanced as a result of interaction of the single-mode coupling field with the atomic medium, resulting in cooling on the red side of the cavity resonance.
A comparison of the improvement factors for the EIT and the RIR scheme, see Figs. 10 and 12, indicates that the latter yields the most dramatic improvement in optomechanical cooling. However, this comes at the expense of diminished tunability due to the sensitive dependence of the RIR process on trap parameters and the temperature of the atomic ensemble.
\section{Conclusion}
In summary we have investigated two hybrid quantum systems consisting of a cavity optomechanical system optically coupled to an ultracold atomic gas. We demonstrated theoretically how the dispersive and gain optical properties of the atomic gases are exploited to modify the optomechanical response of the mechanical resonator, resulting in significantly enhanced cooling of the resonator, even for an optomechanical system that is nominally in the unresolved sideband regime. We considered both the interaction of the optomechanical system with the spin degree of freedom of the atomic gas through a EIT feature as well as an interaction with its motional degree of freedom through a recoil induced resonance (RIR). In either case we found broad and robust parameter regimes wherein the mechanical resonator can be cooled to the ground state from room temperature. In the case of EIT, the improvement in optomechanical cooling is due to the narrow transparency window at the two-photon resonance that enhances the spectral asymmetry between the Stokes and anti-Stokes sidebands induced by mechanical motion. In the case of the RIR, optical gain enhances the anti-Stokes sideband leading to enhanced cooling. These results pave the way towards ground state optical cooling of low frequency mechanical resonators.
The concrete examples considered here illustrate in relatively simple situations realizable with existing technology the considerable advantages provided by the exquisite optical control of ultracold atomic gases for the quantum control and manipulation of a mesoscopic mechanical resonators. They also hint at powerful schemes that can be conceived to dynamically tune the optical response of cavity optomechanical systems for various sensing, transduction and state transfer protocols. These aspects of hybrid systems with ultracold atoms will be considered in some detail in future work.
\section{Acknowledgements}
We thank S. Steinke, Y. S. Patil, S. Chakram and S. Yelin for useful discussions. This work was supported by the DARPA QuASAR and ORCHID programs through grants from AFOSR and ARO, the U.S. Army Research Office, the US NSF, the Cornell Center for Materials Research with funding from the NSF MRSEC program (DMR-1120296) and the NSF INSPIRE program. M. V. acknowledges support from the Alfred P. Sloan Foundation. F. B. dedicates this work to his wife Elizabeth and his son Paolo.
| {
"redpajama_set_name": "RedPajamaArXiv"
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James Whitbourn has conducted choirs and ensembles since he was a teenager. Early in his professional life, he became one of the regular conductors of the BBC's professional choir that broadcasts the Daily Service live to an audience of millions every day. He went on to form his own professional choir The Choir, specializing in music for film and television, with whom he recorded the Gramophone Award-nominated DVD of the music of his British compatriot John Tavener, Choral Ikons. The Choir has since broadcast on numerous programmes for the BBC.
For nine years, he was the Musical Director of the Sevenoaks-based Chantry Choir, for whom he wrote the Son of God Mass and Glory to Thee O Lord. During those years, the choir was known for its adventurous and innovative programming.
He has conducted the BBC Philharmonic Orchestra for many broadcasts and recordings, including several of his own scores for film and television. He has also conducted the orchestra on several recordings for radio and television. Other orchestras he has conducted include the Academy of St Martin in the Fields and numerous session ensembles for media recordings.
Whitbourn has been a guest conductor of many choirs and ensembles, including the BBC Singers, the Westminster Williamson Voices, the Kent Youth Choir, Kent Youth Singers, the Royal Liverpool Philharmonic Chorus, Rochester Cathedral Choir, Liverpool Cathedral Choir and the Bernadi Chamber Orchestra. He has directed numerous rehearsals and workshops for ensembles while working with them on his own scores, including the Band of the Blues and Royals, for whom he composed the Christmas Suite.
Whitbourn is co-Director of the Westminster Choir College Choral Institute at Oxford whose home is at his present college, St Stephen's House, Oxford. | {
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Raymond Scott, Avant-Garde Creator of Classic Cartoon Music
BY Jay Serafino
Wikimedia // Public Domain
If you've ever parked yourself in front of the TV to watch Looney Tunes, The Ren & Stimpy Show, or countless other cartoons, the music of Raymond Scott should be instantly recognizable, even if you've never heard of the man himself. The musical mind behind countless Wile E. Coyote chase scenes (unwittingly) gave cartoons their signature sound, but his real passion was invention—especially when it came to the burgeoning world of electronic music.
Scott was born Harry Warnow in Brooklyn, New York in 1908, and was said to be composing his own music by 1924 in the "audio laboratory" he built as a kid. After graduating from New York's Institute of Musical Art in 1931 (now known as Juilliard), he got a job as a pianist for the CBS Radio orchestra, which was conducted by his brother, Mark. To avoid charges of nepotism, he changed his name to Raymond Scott (which he picked from a Manhattan phone book) and began his career in earnest, establishing a studio, Universal Recording Company, Inc., and a music publishing company, Circle Music, Inc. in 1935.
In 1936, Scott formed the Raymond Scott Quintette (which actually had six members, including the father of film composer John Williams) and his unique musical voice began to appear. Scott's style was a wholly different take on the music of the time—the manic energy and violent rhythms perfectly suited his weariness with modern swing and jazz, and his pieces regularly featured bizarre titles such as "Square Dance for Eight Egyptian Mummies," "Dinner Music for a Pack of Hungry Cannibals," and "Harlem Hillbilly."
Scott's deconstruction of modern swing music made him something of an eccentric curiosity, but when Warner Bros. bought the rights to his music publishing company in 1942 and began pairing it with their Looney Tunes shorts, he forever became a part of pop culture:
Even though Scott never actually wrote music for these cartoons (and may never have even seen them), the pairing was a natural one. Warner's music director Carl Stalling thought so, too, because he used Scott's tunes in about 120 Looney Tunes shorts over the next 20 years, with the most popular piece being Scott's "Powerhouse."
The deal with Warner Bros. (along with numerous commercial jingles) gave Scott the flexibility to work toward his ultimate goal: invention. In the years after the Warner Bros. purchase, he renewed his focus in the nascent field of electronic music, receiving patents on a number of different instruments, including a sound-effects machine named the Karloff, an early electronic keyboard known as the Clavivox, and his now-legendary attempt at artificial intelligence, the Electronium.
Despite his wild sound, Scott was known for his expectation of perfection from his musicians during practice and a disdain for improvisation. This machine-like attitude toward his musicians helped him make strides in the electronic revolution, as he built an armory of instruments that were less about emotion and more about precision.
Scott spent more than 20 years working on the Electronium, which was conceived as an "Instantaneous Composing Performance Machine" that would compose music while performing it—dubbed by some as "Beethoven in a box." As advanced as this machine was at the time, Scott's vision of music's future ultimately entered the realm of the metaphysical:
"Perhaps within the next hundred years, science will perfect a process of thought transference from composer to listener. The composer will sit alone on the concert stage and merely 'think' his idealized conception of his music. Instead of recordings of actual music sound, recordings will carry the brainwaves of the composer directly to the mind of the listener."
Scott's later career was marked with all manner of electronic experimentation, including a strange yet pioneering album of synthesized lullabies recorded in 1963 called Soothing Sounds for Baby—a three-volume forerunner to the minimalist movement, composed with his Electronium. His array of unique instruments, musical trinkets, and an inimitable sound led to a number of collaborations with a young Jim Henson, who brought Scott on board in the mid-1960s to provide the music for some of the creator's early—very non-Muppet-y—films:
However, as Scott's inventions and experiments became more and more idiosyncratic, his music began to move away from profitability. No longer writing music for commercials or mainstream projects, his later work very rarely saw the light of day, as he spent most of his time tinkering away on the Electronium and other projects—living as a recluse, according to some accounts. Scott reportedly sunk close to a million dollars into the development of the Electronium, but despite the investment—and interest from Motown, where he worked as Director of Electronic Music Research and Development in the '70s—it never became the commercial wonder he imagined, nor was it ever actually completed.
When speaking about Scott's unconventional mind, electronic music icon (and one of Scott's occasional collaborators) Bob Moog said:
"He had so much imagination, and so much intuition—this funny intuition that some people have—that he could sort of fish around and get something to work, and do exactly what he wanted it to do. Obviously not everybody could do this. It took a huge amount of money, and a huge amount of imagination. And an impressive amount of craziness too!"
Scott died in 1994, but since then his music has seen something of a rediscovery, at least in certain corners of the industry. To this day, you can still hear "Powerhouse" and other pieces in your favorite cartoons, and Scott's legacy as a trailblazing figure of electronic music is taking shape as a new generation has come along to add a modern flair to his work. Though people might not have been able to wrap their minds around his inventions and eccentricities at the time, his vision of the future of electronic music no longer sounds so far-fetched.
music Music History Retrobituaries | {
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Evers unveils plan to address state's farm crisis, nonpartisan redistricting during State of the State address
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FIU's Borregales helped beat Miami, now joins Hurricanes
by AP News
in AP News, National
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By TIM REYNOLDS
CORAL GABLES, Fla. (AP) — Jose Borregales finally was wanted by the Miami Hurricanes. Beating them was all it took.
The former FIU kicker — who played a huge role in the Panthers' stunning upset win over the Hurricanes in November — announced in a tweet Sunday that he's enrolling at Miami as a graduate transfer. He'll be on campus Monday, when the Hurricanes will be able to officially confirm his arrival.
"UM has always been my dream school and still is," Borregales said in a telephone interview. "I was raised here in Miami. I watched them play growing up. It was pretty much a straightforward decision on where I was going."
Hundreds of players transfer each year, but Borregales' story stands out for many reasons.
Borregales made it known in his high school days that he wanted to play at Miami; the Hurricanes ignored him, so he committed to FIU in 2015 and has "had a chip on my shoulder ever since," he said. His brother, Andres Borregales, is committed to Miami and is scheduled to be part of the school's 2021 recruiting class.
And then FIU 30, Miami 24 happened.
Borregales kicked three field goals — from 29, 50 and 53 yards — in FIU's win over the Hurricanes at Marlins Park in November. That's not all he did that night: After one of his kicks, he put his hands together in an upside-down "U" shape, a favorite sign of disrespect by Miami opponents, and he was accused by some of making a throat-slashing gesture after a late FIU score helped put the game away.
"Let me explain this," said Borregales, who freely acknowledges how emotional that game was and how badly he wanted to beat the Hurricanes. "My hand wasn't on my neck. It was in front of my face mask. I was doing the slide, just spread my arms out like saying that was game, that the game was over. I did it pretty quick and it looked like I was doing the throat slash, but I really wasn't."
Miami doesn't seem to have any hard feelings.
When Borregales announced that he was entering the transfer portal, plenty of schools reached out to gauge his interest. Miami slid into his direct messages; Hurricanes assistant coach and special teams coordinator Jonathan Patke simply sent him an emoji of two eyeballs to get the conversation started.
The message from Miami was clear: We see you, Jose.
Besides, kicker was a major position of need for Miami. The Hurricanes used three kickers this season, lost at least three games in large part because of kicking miscues and missed eight field goals from 40 yards or closer. Borregales, meanwhile, shook off a slow start to make 19 of his final 23 field-goal tries.
So when the Hurricanes asked, Borregales didn't need long to make up his mind. He leaves FIU with a bachelor's degree in recreation and sports management; at Miami, he'll pursue a master's degree in liberal studies.
"I went to FIU wanting to get all these records and be the best kicker that ever came out of FIU," Borregales said. "And I did that in three years. That was something I didn't think would happen, but it did. I didn't have anything left to play for so I decided to transfer."
With that, the dreams he had five or six years ago of wearing The U — not flipping it upside down — are about to become reality.
Borregales came to the U.S. from his family's native Venezuela when he was 6, started playing football by accident when he was 9 (he liked the helmets he saw some kids wearing at a park, so his mother signed him up without knowing what football really was), was mocked by friends for abandoning soccer for the game and wasn't even really that good at kicking until his sophomore year of high school.
And now he's with the Hurricanes.
"Leaving FIU was one of the hardest decisions I ever made," Borregales said. "Once you get comfortable with something or someplace, you tend not to get away from it because you don't know what the future holds. But that was a risk I'm willing to take."
Defying police, Iranians protest over plane shootdown
FIU's Borregales helped beat Miami, now joins Hurricanes
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{"url":"https:\/\/www.physicsforums.com\/threads\/the-earth-takes-exactly-24-hours-for-one-full-rotation-calculate.616470\/","text":"The earth takes exactly 24 hours for one full rotation calculate\n\n1. Jun 25, 2012\n\nsazzy\n\nthe speed of rotation of a point on the equator\n\nthe title is the only information I have been given to work out this questions and it relates to a2 phyics uniform circular motion and the answer is 465ms-1 I just cannot get it I know the eqautor must have something to do with it PLEASE HELP\n\nFull calculations shown please!\n\nthe textbook gives equations speed = 2pi*r\/T but I am not given radius and using the radius does not give the correct answer anyway\n\nthe closest I got was 471 ms-1 using pi\/24*3600 and I just used pi because I am assuming because it asks along the equ I should use 180 degrees\n\n2. Jun 25, 2012\n\ngbaby370\n\nIf you're getting 471, it could just be a matter of how you're rounding some of the variables like pi or the radius of the Earth.\n\nI used the exact same equation using the pi option on my calculator and for r, I used 6.378x10^6 and I got 463.82m\/s.\n\nHope this helps!\n\n3. Jun 25, 2012\n\nD H\n\nStaff Emeritus\nThe Earth takes 24 hours to make a full rotation with respect to the Sun. The Earth is also orbiting the Sun. This means it takes a bit less than 24 hours for that Earth to make a full rotation with respect to the stars. Another way to look at it is that the Earth rotates a bit more than 360 degrees in 24 hours. This extra little bit of rotation is what gives that answer of 465.1 m\/s as opposed to the 463.8 m\/s that gbaby370 obtained.\n\n4. Jun 25, 2012\n\nSammyS\n\nStaff Emeritus\nHello sazzy. Welcome to PF.\n\nLook up the radius of Earth.\n\nUsing that, you can find circumference of Earth, which is the distance that a point on the equator travels in one day.\n\nThe number of seconds in one day is 24*3600.\n\nIf you want to divide some number by 24*3600, you should put (24*3600) in parentheses.\n\nWhen you computed \u03c0\/24*3600, that was equivalent to 3600*\u03c0\/24 . It's just a coincidence that this gave a result that's close to the correct answer.","date":"2018-03-18 01:18:43","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8092502951622009, \"perplexity\": 602.0169716272663}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-13\/segments\/1521257645405.20\/warc\/CC-MAIN-20180317233618-20180318013618-00097.warc.gz\"}"} | null | null |
Юрий Архипович Буйняков (1930—2005) — специалист по гироскопическим приборам и устройствам.
После окончания Ленинградского института точной механики и оптики в 1953 году Юрий Архипович работает контрольным мастером на приборостроительном предприятии в городе Саратове, а с 1953 по 1960 годы — инженером, начальником лаборатории на аналогичном предприятии в Серпухове Московской области.
С 1960 года работал в Миасском электромеханическом НИИ. Прошел путь от начальника лаборатории до начальника отдела, заместителя главного инженера, директора — главного конструктора НИИ (1962—1977), генерального директора — главного конструктора объединения (1977—1983, 1990—1995). В 1983 году Ю. А. Буйняков работал заместителем начальника отдела предприятия «Звезда» в Осташкове Калининской области. С 1995 года на пенсии.
Под руководством Ю. А. Буйнякова прошло становления предприятия как уникальной научно-исследовательской и производственной базы на Урале, созданы гироскопические приборы для систем управления ракетно-космических комплексов различного назначения, включая «Энергию-Буран». Он автор 57 изобретений, внедренных в разработки предприятия. Внес большой вклад в социально-экономическое развитие Миасса. При нем в северной части города (Машгородок) построено 74 жилых дома, две средние школы, восемь дошкольных учреждений, медсанчасть-92, Миасский электромеханический техникум, СГПТУ-89, пионерлагерь «Солнечный» на озере Тургояк.
Умер 30 мая 2005 года, похоронен на Тургоякском кладбище.
Награды, премии, почётные звания
Лауреат Ленинской премии (1966 г.)
Кавалер ордена Ленина (1975 г.)
Кавалер ордена Трудового Красного Знамени (1971 г.)
Лауреат Государственной премии СССР (1981 г.)
Почетный гражданин города Миасса (2003 г.)
Источники
https://www.names52.ru/tpost/b8p3eet0i1-buinyakov-yurii-arhipovich
Примечания
Инженеры СССР
Выпускники Санкт-Петербургского университета информационных технологий, механики и оптики | {
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Q: How do I represent URNs (Uniform Resource Names) in .NET so that Equals works as expected RFC2141 mentions:
*Examples of lexical equivalence
The following URN comparisons highlight the lexical equivalence
definitions:
1- URN:foo:a123,456
2- urn:foo:a123,456
3- urn:FOO:a123,456
4- urn:foo:A123,456
5- urn:foo:a123%2C456
6- URN:FOO:a123%2c456
URNs 1, 2, and 3 are all lexically equivalent.
The subsequent RFC8141 preserves that equivalence:
2.1. Namespace Identifier (NID)
NIDs are case insensitive (e.g., "ISBN" and "isbn" are equivalent).
The closest representation for a URN that I could easily find in the .NET framework is the URI class. However, it does not seem to fully respect the RFC definition of equivalence:
[TestMethod]
public void TestEquivalentUrnsAreBroken()
{
Assert.AreEqual(
new Uri("URN:foo:a123,456"),
new Uri("urn:foo:a123,456"));
Assert.AreEqual(
new Uri("urn:foo:a123,456"),
new Uri("urn:FOO:a123,456"));
}
In the code example above the first assert works as expected, whereas the second assert fails.
Is there any reasonable way to get the URI class to respect the equivalence definition? Is there any other class I should be using instead?
Please note that I have found the URN class, but the documentation mentions that it should not be used directly.
A: The Uri class does not support a specific parser for the urn: scheme out of the box. Maybe understandably so, because even if the comparison rules for the NID specify that it is case-insensitive, the rules for comparing two NSS would depend on rules as defined by the particular namespace, per RFC 8141.
For a quick and dirty approach, you could try using the Uri.Compare() method. It will return zero for cases where both URI are equivalent, and non-zero otherwise.
var u1 = new Uri("URN:foo:a123,456");
var u2 = new Uri("urn:foo:a123,456");
var u3 = new Uri("urn:FOO:a123,456");
var u4 = new Uri("urn:nope:a123,456");
Console.WriteLine(Uri.Compare(u1, u2, UriComponents.AbsoluteUri, UriFormat.SafeUnescaped, StringComparison.OrdinalIgnoreCase)); // 0
Console.WriteLine(Uri.Compare(u1, u3, UriComponents.AbsoluteUri, UriFormat.SafeUnescaped, StringComparison.OrdinalIgnoreCase)); // 0
Console.WriteLine(Uri.Compare(u2, u3, UriComponents.AbsoluteUri, UriFormat.SafeUnescaped, StringComparison.OrdinalIgnoreCase)); // 0
Console.WriteLine(Uri.Compare(u3, u4, UriComponents.AbsoluteUri, UriFormat.SafeUnescaped, StringComparison.OrdinalIgnoreCase)); // -8
For a more adventurous approach, you can do something along the lines of the following. This would require careful thinking to implement correctly. This code is not meant to be used as-is, but rather as a starting point.
using System;
using System.Text.RegularExpressions;
public class Program
{
public static void Main()
{
var u1 = new Urn("URN:foo:a123,456");
var u2 = new Urn("urn:foo:a123,456");
var u3 = new Urn("urn:foo:a123,456");
var u4 = new Urn("urn:FOO:a123,456");
var u5 = new Urn("urn:not-this-one:a123,456");
Console.WriteLine(u1 == u2); // True
Console.WriteLine(u3 == u4); // True
Console.WriteLine(u4 == u5); // False
}
public class Urn : Uri
{
public const string UrnScheme = "urn";
private const RegexOptions UrnRegexOptions = RegexOptions.Singleline | RegexOptions.CultureInvariant;
private static Regex UrnRegex = new Regex("^urn:(?<NID>[a-z|A-Z][a-z|A-Z|-]{0,30}[a-z|A-Z]):(?<NSS>.*)$", UrnRegexOptions);
public string NID { get; }
public string NSS { get; }
public Urn(string s) : base(s, UriKind.Absolute)
{
if (this.Scheme != UrnScheme) throw new FormatException($"URN scheme must be '{UrnScheme}'.");
var match = UrnRegex.Match(this.AbsoluteUri);
if (!match.Success) throw new FormatException("URN's NID is invalid.");
NID = match.Groups["NID"].Value;
NSS = match.Groups["NSS"].Value;
}
public override bool Equals(object other)
{
if (ReferenceEquals(other, this)) return true;
return
other is Urn u &&
string.Equals(NID, u.NID, StringComparison.InvariantCultureIgnoreCase) &&
string.Equals(NSS, u.NSS, StringComparison.Ordinal);
}
public override int GetHashCode() => base.GetHashCode();
public static bool operator == (Urn u1, Urn u2)
{
if (ReferenceEquals(u1, u2)) return true;
if (ReferenceEquals(u1, null) || ReferenceEquals(u2, null)) return false;
return u1.Equals(u2);
}
public static bool operator != (Urn u1, Urn u2)
{
if (ReferenceEquals(u1, u2)) return false;
if (ReferenceEquals(u1, null) || ReferenceEquals(u2, null)) return true;
return !u1.Equals(u2);
}
}
}
| {
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Saint-Mamet-la-Salvetat je naselje in občina v osrednjem francoskem departmaju Cantal regije Auvergne. Leta 1999 je naselje imelo 1.321 prebivalcev.
Geografija
Kraj se nahaja v pokrajini Auvergne 18 km jugozahodno od središča Aurillaca.
Uprava
Saint-Mamet-la-Salvetat je sedež istoimenskega kantona, v katerega so poleg njegove vključene še občine Cayrols, Marcolès, Omps, Parlan, Pers, Roannes-Saint-Mary, Roumégoux, Saint-Saury, La Ségalassière, Vitrac in Le Rouget s 5.499 prebivalci.
Kanton Saint-Mamet-la-Salvetat je sestavni del okrožja Aurillac.
Zunanje povezave
Uradna stran
Naselja departmaja Cantal | {
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Dental implants are now considered the all-rounder solution for anyone having missing, damaged or loose teeth. It has now become so famous because of the benefits it bestows on the person. We have listed a few of them below.
Dentures and bridges are the short term and temporary solutions that need replacement in every 5 to 7 years. But dental implants are permanent and needs less maintenance.
You don't want your teeth to slip around in the middle of a conversation or a meal. But this is not the case with the dental implants at all. Bid farewell to all the shifting and clicking. When you install dental implants they integrate and fuse naturally with your jawbone and stay put.
When the issue of missing teeth is left unaddressed, it can cause the surrounding jawbone some damage. Dental implants fix this issue by supporting the healthy bone and promotes further bone growth.
Dental implants look and feel natural.
Smiling denotes happiness and confidence. But it all goes astray when you have teeth that look different from one another. Dental implants look so natural that it is nearly impossible to distinguish between the implants and the normal teeth. So smile all the way with confidence and utmost confidence.
At implants dentaires St-Onge, we dedicate our valuable time and effort to the patients by keeping in mind that lives never slow down because of a few dental issues. We deliver the same day dental implant processes which entail both the extraction as well as the placement of the dental implant. There are many options to choose from besides the dental implants like dentures and bridges, but dental implants are the hands down the best solution. Just pay one visit to our clinic, and we promise you to give your confidence and happiness back to you.
If you have been procrastinating the dental implant procedure, we recommend you to get treated as soon as possible so as to address the issues and prevent them to not get worse as the time goes by. If you want to read similar insights, or explore the range of services we deliver, visit our website. So, what are you waiting for? Book an appointment with us today! | {
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Q: BackboneJS collection.reset() vs collection.fetch() I have read and read the docs on these two methods, but for the life of me cannot work out why you might use one over the other?
Could someone just give me a basic code situation where one would be application and the other wouldn't.
A: We're assuming here that you've read the documentation, else it'l be a little confusing here.
If you look at documentation of fetch and reset, what it says is, suppose you have specified the url property of the collection - which might be pointing to some server code, and should return a json array of models, and you want the collection to be filled with the models being returned, you will use fetch.
For example you have the following json being returned from the server on the collection url:
[{
id : 1,
name : "a"
}, {
id : 2,
name : "b"
}, {
id : 3,
name : "c"
}]
Which will create 3 models in your collection after successful fetch. If you hunt for the code of collection fetch here you will see that fetch will get the response and internally will call either reset or add based on options specified.
So, coming back to discussion, reset assumes that we already have json of models, which we want to be stored in collection, we will pass it as a parameter to it. In your life, ever if you want to update the collection and you already have the models on client side, then you don't need to use fetch, reset will do your job.
Hence, if you want to the same json to be filled in the collection with the help of reset you can do something like this:
var _self = this;
$.getJSON("url", function(response) {
_self.reset(response); // assuming response returns the same json as above
});
Well, this is not a practice to be followed, for this scenario fetch is better, its just used for example.
Another example of reset is on the documentation page.
Hope it gives a little bit of idea and makes your life better :)
A: reset sets the collection with an array of models that you specify:
collection.reset( [ { name: "model1" }, { name: "model2" } ] );
fetch retrieves the collection data from the server, using the URL you've specified for the collection.
collection.fetch( { url: someUrl, success: function(collection) {
// collection has values from someUrl
} } );
Here's a Fiddle illustrating the difference.
A: reset() is used for replacing collection with new array. For example:
@collection.reset(@full_collection.models)
would load @full_collections models, however
@collection.reset()
would return empty collection.
And fetch() function returns default collection of model
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,131 |
Over the past year, the deadly bacterial infection known of Leptospirosis or "Lepto" has been on the rise. This disease can affect all mammal species (including humans) and veterinarians have seen an increase in the number of cases over the past several years, and spiking over the past few months. With early intervention of a sick pet, survival rates rarely go above 75%. Given the seriousness of illness, it's important to know the facts of this deadly and highly contagious disease. As a professional in this field, I'm passionate about preventing what we can, where and when we can, and there is, frankly, a lot of bad information out there right now.
Leptospirosis has a worldwide distribution, including much of the United States and particularly in the northeast where temperatures may be between 80-90 F or areas where there is reliable rainfall. Direct contact with an infected animal's bodily fluids, or indirect contact from urine – such as contaminated water or soil – can increase your pet's risk. The bacteria can live for long periods of time in contaminated water and soil and has the ability to penetrate intact or broken skin and mucus membranes. Within 7-10 days, the bacteria spreads systemically to the kidneys, liver, spleen, central nervous system, eyes and genital tract. This can cause jaundice (yellowing of the skin and whites of the eyes) as a result of liver damage, and excessive drinking and urination from acute damage to the kidneys. Clinical signs are highly variable and can mimic many other conditions – lethargy, anorexia, vomiting, frequent urination – and many dogs have no overt clinical signs at all, making this a particularly dangerous and deadly disease.
Since Leptospirosis is not a "core" vaccination like "Distemper" (DHPP) and "Rabies", many pet owners may opt out of getting their pet vaccinated if they feel they are not at risk, or more often, if they don't feel like their pet is the "outdoorsy" type. This is a common misconception with urban living that should be reevaluated by pet owners. In Boston alone, the number of leptospirosis positive dogs has increased substantially over the past few years. This is in part due to the fact that we – like anywhere, still have rodents in our old homes and buildings and any interaction with rodents, animal urine, streams, ponds and puddles can put our pets at risk.
Currently, there is a perception of increased severe adverse reactions with the leptospirosis vaccines, and I've personally seen several breeders in the area discourage or even make owners sign contracts against vaccination for leptospirosis. On facebook and Google there are countless "this vaccine will kill your dog" campaigns from seemingly reputable and well-funded websites. And while I don't know where these come from, I can confidently say I have no conflicts of interest, nor receive any payment or endorsements from any of the vaccine manufacturers when I say that this vaccine can save lives. Further, one large study showed that these vaccines were no more likely to cause adverse reactions than any other vaccine (Spiri, et al., 2017).
So what should you do? Keep an open and honest relationship with your veterinarian – many build the lepto portion into the Distemper vaccine for either the same cost or slightly more. If you want your pet protected but have concerns about safety, ask your vet if your pet could stay a few hours after receiving their vaccine for monitoring… I'm sure they'll say yes!
Dr. Evans found his passion for working with animals at a young age. After growing up in West Des Moines, Iowa he moved to Colorado where he earned a Biology Degree before transferring to Cornell College where he earned a Bachelor's of Special Studies in Biology with a focus in Animal Sciences. He attended St. George's University and was then clinically trained at the Ohio State University. He's spent years in private practice working on the North Shore of Massachusetts and now is the Medical Director at Boston Animal Hospital in Boston's South End. He has a special interest in soft tissue surgery and dentistry and works with numerous dog and cat rescues around the state. When not helping animals, Dr. Evans can be found paddle boarding, kayaking or hanging out with his fiancée, Abby, and his rescue animals – a Pit Bull named Ollie and his two rescue cats, Charlie and Jackson. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,748 |
<sqx-title message="Event Consumers"></sqx-title>
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<button class="btn btn-link" (click)="reset(eventConsumer)" *ngIf="!eventConsumer.isResetting" title="Reset Event Consumer">
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<button class="btn btn-link" (click)="start(eventConsumer)" *ngIf="eventConsumer.isStopped" title="Start Event Consumer">
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<button class="btn btn-link" (click)="stop(eventConsumer)" *ngIf="!eventConsumer.isStopped" title="Stop Event Consumer">
<i class="icon icon-pause"></i>
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</sqx-modal-dialog> | {
"redpajama_set_name": "RedPajamaGithub"
} | 7,262 |
Q: INSERT varchar from a UTF-8 text file into MSSQL table I am inserting a text file into the database with my following query:
DECLARE @json NVARCHAR(MAX)
SELECT @json = BulkColumn
FROM OPENROWSET(BULK 'c:\mydata.db', SINGLE_CLOB) AS [Insert]
INSERT INTO [neDB].[dbo].[tbl_api] (
number
,DESC
,inf
)
SELECT number
,DESC
,inf
FROM OPENJSON(CONCAT (
'['
,REPLACE(@json, CONCAT (
'}'
,CHAR(10)
,'{'
), '},{')
,']'
)) WITH (
number VARCHAR(200) '$.number'
,DESC VARCHAR(50) '$.desc'
,inf VARCHAR(150) '$.inf'
)
The file "mydata.db" is UTF-8 which contains ü,ä,ö, etc. which will be stored as "ü", "ö" ... in the table.
If I convert the file to ANSI, all looks fine, but I don't want to convert the file all the time. Is there a way to design the query to insert UTF-8 directly?
A: Try adding the parameter
CODEPAGE = '65001'
to the OPENROWSET call, which is the codepage for UTF-8 (docs).
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,808 |
\section{Introduction}
\label{intro}
Effective and practical classification of network traffic is crucial to many network management and security tasks. Categorization of network traffic yields valuable information on a network's activity, and timely classification enables this information to be quickly acted upon to ensure a secure and efficient network. Anomaly detection, quality of service monitoring, intrusion or attack detection, and resource allocation planning are all difficult network management tasks where traffic classification plays a critical role in solving \cite{sdn-attacks}.
With the pervasive and diverse usage of the internet and online devices, large volumes of traffic from many different applications are constantly hosted on networks. Robust and flexible traffic classification is a difficult task due to the wide variety of traffic and dynamic nature of source applications. Traffic classification techniques have changed greatly over time, in reaction to changes in networking as a field.
Early and simple methods of traffic classification use port numbers to identify the traffic sources \cite{port-1, port-2, port-3}.
However as more applications used undisclosed, protocol-based, or configurable ports, port numbers became too unpredictable to be a reliable source of classification \cite{moore-towards, 2006-survey, clustering-erman}.
In response to port-based classification becoming less effective, research turned to classification methods that use data packet inspection to find application or protocol signatures, i.e. patterns or data specific to the source application or protocol \cite{moore-towards, construction-of-app-sigs, p2p-app-sigs, blinc}. These methods require the ability to inspect packet payloads, so they are unable to classify encrypted traffic. Additionally, they are computationally expensive and require up-to-date application or protocol signatures to match traffic with \cite{intrustion-detection}. These issues present considerable limitations to inspection-based classification.
Most current approaches to traffic classification use machine learning algorithms and statistical properties of traffic flows to categorize traffic. A flow is usually defined by all packets with the same 5-tuple: source/destination IP, source/destination port, protocol. The statistical properties of flows, e.g., Inter-arrival time, Total Bytes, Average Packet Size, are referred to as features. Using statistical features of networking activity for classification avoids using port numbers or packet payloads, thereby remedying the limitations of the previously mentioned port and payload based methods. Machine learning techniques rely on the fact that different applications have differing networking behavior and patterns. These differences are represented in features, then discovered and used to discern flows' classes by a machine learning model.
In this paper, we focus on traffic in the Science DMZ \cite{science-dmz}, where we have a predominance of ``elephant flows" vs. ``mice flows"\cite{LAN200646}. We present a machine learning technique that uses the statistics of subflows, i.e. some subset of packets from a flow, to classify traffic with a measure of certainty.
We classify traffic using probabilistic learning with likelihood estimation and adjustable certainty levels. This approach allows our method to classify traffic at higher or lower confidence levels, based on network preferences.
This approach also allows network administrators to configure and use our classification so that it performs best on the most important traffic in their network.
Our method can operate in three different classification scenarios: (1) classification performed with strict certainty thresholds resulting in known, unknown, and uncertain classification decisions; (2) classification with majority likelihood, eliminating any uncertain classification decisions; (3) incremental classification, where the classifier gathers information subflow by subflow, enabling the classifier to reach a classification decision as soon as possible. These different classification options along with the adjustable classification certainty level allows our technique to be easily customized to best fit a network's needs.
We classify traffic into known and unknown classes. The known class consists of traffic from some group of applications approved for network usage, and the unknown class consists of traffic from any applications not in the known group. These class definitions fit well into real-world networks like the Science DMZ, and take advantage of the fact that networks with specific intended application usage usually allow applications with similar functions and behaviors. The broad definition of the unknown class allows it to include a huge array of diverse application traffic, so the variation between unknown traffic and known traffic is bound to be greater than the variation within the known traffic class. The known class will generally contain applications with similar functions and traffic, but the unknown class will include a huge variety of applications that have different behaviors from the known traffic. Our method successfully finds and utilizes these differences for classification via machine learning.
This class scheme is also flexible since the known class can be defined with any set of applications, allowing network administrators to define a custom known class for their network with applications that are allowed for usage on their network.
Thus, our technique is easily configured to fit a variety of network needs and is widely applicable to many real-world networks.
This work makes these main contributions:
\begin{trivlist}
\item $\bullet$ We present a probabilistic machine learning method that classifies traffic with a measure of certainty. We describe how the certainty of classification decisions can be easily configured to yield different results.
\item $\bullet$ We show that our method can be applied in 3 different classification scenarios, each prioritizing a different classification goal.
\item $\bullet$ We demonstrate how our method and all of its configurations can be used to effectively classify traffic in the Science DMZ \cite{science-dmz} network setting.
\end{trivlist}
\section{Background and Related Work}
Traffic classification techniques using machine learning comprise two main components: the representation of network traffic and the machine learning algorithm. Additionally, many different classification schemes have been used. From the vast existing research, we present a brief overview of work relevant to ours.
\subsection{Existing Work on Network Traffic Representation}
Many different representations and statistical features of flows have been explored in previous work. Statistics on packet size, arrival times, and packet types have resulted in high classification accuracy when used with a wide variety of machine learning methods \cite{dl-survey, 2006-survey, internet-traffic-classification-demystified, blinc}. These features can be calculated over all the packets in an entire flow or on some series of packets sampled from the flow \cite{dl-survey, 2006-survey, subflow-1, subflow-2}. Research also exists on feature selection techniques which are used to reduce the number of features needed for classification and to find optimal features that result in the best classification performance \cite{internet-traffic-classification-demystified, feature-select-2012}. In these works, packet size statistics and discrete feature values were found to enable classification accuracy of 93\% and above for multiple machine learning algorithms \cite{internet-traffic-classification-demystified}.
Calculating features over an entire flow is not ideal for timely classification, prompting more practical methods that classify sequences of packets in a flow. Using features on only the first few packets of flows was found to yield reasonable classification results \cite{dl-survey, internet-traffic-classification-demystified}.
Earlier work also found that using a sequence of packets, or subflows, of as few as 25 packets can result in classification precision and recall of above 95\% \cite{subflow-1}.
This subflow work was expanded upon by \cite{subflow-2}, finding that classification performance is not affected by the position of the subflow within the overall flow or the direction of the packets.
In \cite{subflow-1, subflow-2, rnn-cnn} the length of the subflow (value of $N$) results in a trade off between classification performance and processing requirements. They found that higher values of $N$ lead to better classification, but require more processing time and memory \cite{subflow-1, subflow-2, subglow-3}.
\subsection{Existing Work on Machine Learning Algorithms for Network Traffic Classification}
Many different machine learning algorithms have been used for traffic classification. Early work used traditional supervised learning methods that classify traffic into pre-defined classes, such as decision trees and Bayesian analysis techniques~\cite{2006-survey, bayesian, subflow-1, comparison}. These methods have been shown to perform classification at accuracy above 95\% on various sets of applications \cite{2006-survey, bayesian}. Unsupervised and semi-supervised learning methods, where traffic is grouped based on similarity rather than explicitly classified into a class, have also been explored in \cite{clustering-erman, semi-supervised, minetrac, robust, offline-semi, intrustion-detection, data-stream}. Clustering unlabelled or partially labelled traffic resulted in classification accuracy of 90-93\% \cite{clustering-erman, semi-supervised}.
Recent methods have used deep learning, with supervised classification performed by convolutional neural networks and recurrent neural networks \cite{dl-survey, rnn-cnn}. Some other neural network methods have used unsupervised learning to learn traffic representations as well as how to imitate traffic, using auto-encoders and generative adversarial neural networks \cite{dl-survey}. Various architectures of neural nets used for classification have achieved high accuracy of up to 96\% \cite{rnn-cnn}.
\subsection{Network Traffic Classification Schemes}
Most of this existing work classifies traffic by mapping it to an application, application type, or protocol. A few classify traffic into known and unknown classes by discerning a specific, known application or group of applications from other traffic \cite{subflow-1, subflow-2, Baker}. Our work uses this latter scheme of known and unknown classification as it is less explored, more flexible, and widely applicable. In one setting, known traffic could be defined as a broad set of non-malicious activities for a well-protected, general usage network. But in another setting it might be a small set of specifically approved applications on a network designed for specialized uses only, like the Science DMZ. The flexibility of this known vs. unknown classification brings additional challenges, as our classification method must be robust enough to perform well on many different sets of known applications.
In addition to addressing the more challenging task of classifying traffic into flexible known and unknown classes, we consider classification in the Science DMZ network setting which has not been previously explored.
A Science DMZ is a subnetwork, usually part of a university network, that is configured and designed to optimize the usage of high-performance scientific computing applications \cite{science-dmz}. This network definition fits well with our known vs. unknown classification, as a Science DMZ is intended to host traffic from specific scientific computing applications and no other traffic. Our traffic dataset is sourced from the University of Utah's Science DMZ, which allows us to evaluate our method on realistic high-performance computing traffic. Our approach performs classification at or near 100\% accuracy on representative Science DMZ traffic. In addition, we evaluated our classification performance on a more challenging traffic dataset to show that our method generalizes well.
\section{Traffic Representation Methodology}
A series of network traffic statistics (e.g., Total Bytes, Standard Deviation of Packet Size, Largest Packet Size) forms a feature vector representation of network traffic; this feature vector representation is necessary in order to use machine learning algorithms to classify network traffic. In this section we discuss how we represent network traffic flows in our machine learning approach.
\subsection{Use of Sub-flows}
Network traffic flows are composed of packets with the same 5-tuple: source/destination IP, source/destination port, and protocol. No existing work uses statistical properties of individual packets to classify flows, as single packets do not provide enough information for effective classification. A notable amount of existing work uses statistics on all packets in a flow to classify flows \cite{2006-survey, clustering-erman, semi-supervised, Baker}. However, using all packets in a flow for classification requires the flow to finish before it can be classified. Therefore, techniques that analyze all packets fail to stop flows of unapproved network activity from completing, making them less viable for real-world networks. Using all packets for classification also incurs high memory and computational costs, since flows can be long and data-intensive, especially in the large science dataset transfers seen in the Science DMZ.
Because of the aforementioned issues with using single or all packets in a flow, our classification method uses subflows: some subset of $N$ packets taken from any point in a flow. The use of subflows was first introduced in \cite{subflow-1}.
We use $N$-packet subflows to represent our traffic, where $N=\{25, 100, 1000\}$. These values of $N$ were discussed, experimented upon extensively, and found to be sufficient subflow lengths in \cite{subflow-1, subflow-2, subglow-3}, with the larger values of $N$ leading to better classification performance but requiring more processing time and memory. Our statistical features are calculated over each $N$-packet subflow and all of our flows are split into $N$-packet subflows for classification.
Using subflows gives our classification approach the additional advantage of being able to gather multiple data points per flow. Each subflow gives our classifier some statistical data on the overall flow, so it can use each subflow to increase or decrease certainty in a classification decision for the overall flow. Thus, our classification approach can gain valuable classification progress for each encountered subflow, and can make a decision on an overall flow when a certainty threshold is reached.
\subsection{Statistical Features of Traffic}
Selecting useful statistical features calculated over a series of packets to represent network traffic is crucial to effective machine learning.
Table 1 on page 71 of \cite{2006-survey} breaks down various network traffic statistics and groups them according to previously used machine learning approaches. We considered a broad set of statistics used in previous work that were found to achieve the best network traffic classification performance \cite{Baker, internet-traffic-classification-demystified, bayesian, blinc, clustering-erman}.
To narrow down which features to use, we graphed the cumulative density function (CDF) of feature value distributions for our known and unknown traffic datasets to ensure that the features we use capture notable differences between known and unknown traffic.
Fig. \ref{fig:feature-CDFs} shows example CDFs for various feature values.
\begin{figure}
\includegraphics[width=\linewidth]{feature-cdfs.PNG}
\caption{Feature Value CDFs for 100-Packet Subflows}
\label{fig:feature-CDFs}
\end{figure}
From our CDF analysis, we found that 14 of the following features effectively showed differences between known and unknown traffic: Total Bytes, Largest Packet Size, Smallest Packet Size, Number of TCP ACKs, Minimum Advertised Receive Window, Maximum Advertised Receive Window, Standard Deviation of Packet Size, Average Packet Size, Average Packet Inter-Arrival Time, Standard Deviation of Packet Inter-arrival Time, Maximum Packet Inter-arrival Time, Minimum Packet Inter-arrival Time, Average Packet Throughput (packets per second), Average Byte Throughput (bytes per second).
Out of these 14 features, an even smaller subset of only 8 features were used in previous work that classified subflows to achieve high accuracies \cite{subflow-1, subflow-2}. Using a smaller number of features is favorable due to lower computational and memory costs; so we ran experiments using both sets of 14 and 8 features, to investigate whether or not using 14 features would yield performance gains that outweighed the higher computational cost. We found that using 14 features did not notably improve classification performance, so we used the following 8 features to represent our traffic: Maximum, Minimum, Mean, and Standard Deviation of Packet Inter-arrival Time and Packet Size. We calculate these 8 statistical features over all packets in each subflow; so each subflow is represented by an 8 element data point where each element is a feature value and is subsequently processed by our machine learning method as an 8-dimensional vector.
\section{Machine Learning Methodology}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{jouranl-overview.PNG}
\caption{Machine Learning Approach and Applications (with corresponding paper sections)}
\vspace{-0.1in}
\label{method-flow}
\end{figure}
In this section we discuss the formulation and components of our machine learning approach as well as the different ways our classification method may be applied.
Fig. \ref{method-flow} shows our methodology's components, pipeline, and multiple usage options.
\subsection{Classification of Individual Subflows}
Our machine learning approach classifies subflows, then utilizes the classification of individual subflows of a flow to classify the entire flow. We performed experiments comparing the subflow classification performance of Naive Bayes, Gradient Boosted Decision Tree (GBDT), Singular Vector Machine (SVM), and K-Nearest Neighbors (KNN) models, as these classifiers have been found to achieve high accuracies on traffic classification tasks in previous work \cite{bayesian, Baker, subflow-1, 2006-survey, comparison}. Gradient-boosted decision trees are known to be more powerful and robust than single decision trees \cite{GBDT}. For the SVM model, we use the one-class variant which has performed well on anomaly detection for networking traffic in previous work \cite{svm}. For our KNN experiments, we used $K=3$.
\begin{table}
\vspace{0.2in}
\caption{Science DMZ Dataset Accuracies}
\begin{tabularx}{\linewidth} {
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X|}
\hline
\textbf{Classifier}: & \textbf{25-Packet-Subflows} & \textbf{100-Packet-Subflows} & \textbf{1000-Packet-Subflows} \\
\hline
Naive Bayes & 98.4 & 97.6 & 99.1 \\
\hline
Gradient-Boosted Decision Tree & 100 & 100 & 100 \\
\hline
One Class SVM & 28.2 & 36.7 & 81.4 \\
\hline
KNN & 100 & 100 & 100 \\
\hline
\end{tabularx}
\label{science-dmz-indv}
\vspace{0.1in}
\caption{General Dataset Accuracies}
\begin{tabularx}{\linewidth} {
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X|}
\hline
\textbf{Classifier}: & \textbf{25-Packet-Subflows} & \textbf{100-Packet-Subflows} & \textbf{1000-Packet-Subflows} \\
\hline
Naive Bayes & 83.4 & 84.96 & 77.6 \\
\hline
Gradient-Boosted Decision Tree & 99.6 & 99.8 & 99.8 \\
\hline
One Class SVM & 67.9 & 68.6 & 68.5 \\
\hline
KNN & 98.3 & 98.7 & 98.4 \\
\hline
\end{tabularx}
\label{general-indv}
\end{table}
Tables \ref{science-dmz-indv} and \ref{general-indv} show accuracies of all models for all subflow lengths, evaluated on test sets from both of our datasets; these test sets are held out from the data used to train these models. All datasets and splits are described in more detail in Section 5.
Our results show that the GBDTs and KNN models perform very well on subflow classification, achieving accuracies above 98\%. Our ultimate goal is to classify entire flows rather than just individual subflows, so these high subflow classification accuracies serve as an important building block for our overall solution.
Performing classification using KNN requires the calculation of distances between each data point to its $K$ nearest neighbors, which is much more computationally expensive than classification using the GBDT algorithm. Computational cost is especially important for practical network traffic classification approaches, as real-world flows can be large and real-time security actions based on classification decisions are ideal. Because the GBDT had the highest accuracies and is more computationally efficient than KNN, we use a GBDT model in the remainder of our machine learning framework.
\subsection{Establishing Flow Class Likelihoods From Individual Subflow Classification}
Our goal is to classify entire flows while only seeing subflows. The general idea is that each encountered subflow gives our classifier some statistical data on the overall flow; so the classifier can use each subflow to increase or decrease certainty in a classification decision for the overall flow.
We achieve this by assigning each subflow classification known and unknown flow class likelihoods. These flow class likelihoods can be thought of as estimated probabilities that a subflow belongs to an overall flow that is known or unknown, based on the subflow's label, or what the subflow is classified as.
So we define and assign known and unknown flow class likelihoods to the known and unknown labels of subflows.
In the set of training subflows $S$, each has a true label (known or unknown) and is given a predicted label (known or unknown). On subflows outside of the training set, we only observe the predicted labels, so we can use the ratio of true labels to estimate the likelihood of the class on new data.
Divide $S$ into $4$ sets:
\begin{itemize}
\item $S_k^k$ are from the known class and predicted as known,
\item $S_u^k$ are from the known class and predicted as unknown,
\item $S^u_k$ are from the unknown class and predicted as known, and
\item $S^u_u$ are from the unknown class and predicted as unknown.
\end{itemize}
We define flow class likelihoods in the following manner. Given a subflow is predicted as known, the sample likelihood it is actually known is:
$p_{k,k} = |S_k^k|/|S_k^k \cup S^k_u|$.
Similarly, the likelihood it is actually unknown is:
$p_{k,u} = |S_u^k|/|S_k^k \cup S^k_u|$.
For subflows predicted as unknown, we write the sample likelihood it is known as $p_{u,k} = |S_k^u|/|S_k^u \cup S^u_u|$ and the likelihood that it is unknown as $p_{u,u} = |S_u^u|/|S_k^u \cup S^u_u|$.
With these class likelihoods associated with subflow labels, our machine learning approach can build up the likelihoods that a flow is known or unknown each time a subflow is encountered. In the next section, we explain in detail how these flow class likelihoods are utilized to classify flows.
\subsection{Classification Via Likelihood Estimation and Certainty Threshold}
We perform classification of a flow by combining the class likelihoods of a sequence of subflows belonging to that flow, using the class joint likelihoods of the subflows.
To create the class joint likelihoods over multiple subflows, we assume independence and take the product of all subflow likelihoods of the same class. These class joint likelihoods can be used as estimated probabilities that the sequence of subflows is of the corresponding class. The flow likelihoods can also be used to form a likelihood ratio, which we use as a measure of certainty for classification. The likelihood ratio is a fraction of the class likelihoods, indicating how much larger one class likelihood is than the other. For example, if the known class likelihood is 0.95 and the unknown class likelihood is 0.05 then the likelihood ratio is $\frac{0.95}{0.05}$. This indicates that under our model, we are 95\% certain that the flow is known, as the marginal probability that the flow is known, given all the subflows the classifier has seen, is $0.95$. However, likelihoods of the numerator and denominator may not sum to $1$, and in general the joint ones will not. But if the ratio is still $19$, e.g., $\frac{0.019}{0.001}$, then the confidence is still $95\%$.
In particular, using our classifier, and these statistics, each subflow $s_j$ has a likelihood it is known $p_K(s_j)$ and a likelihood it is unknown $p_U(s_j)$. These are defined based on the label:
\[
p_U(s_j) = \begin{cases} p_{u,u} & \text{ if } s_j \text{ labeled unknown } \\
p_{k,u} & \text{ if } s_j \text{ labeled known } \end{cases}
\]
and
\[
p_K(s_j) = \begin{cases} p_{k,k} & \text{ if } s_j \text{ labeled known } \\
p_{u,k} & \text{ if } s_j \text{ labeled unknown. } \end{cases}
\]
We estimate the likelihood that a series of observed subflows $s_1, s_2, \ldots, s_m$ are known as:
\[
\hat L_K = p_{K}(s_1) \cdot p_{K}(s_2) \cdot \ldots \cdot p_{K}(s_m)
\]
and we use the same likelihood estimation for unknown $\hat L_U$ with the unknown likelihoods $p_U(s_j)$.
We define the likelihood ration as:
\[
\frac{\hat L_K}{\hat L_U} = \frac{p_{K}(s_1) \cdot p_{K}(s_2) \cdot \ldots \cdot p_K(s_m)}{p_{U}(s_1) \cdot p_{U}(s_2) \cdot \ldots \cdot p_U(s_m)}.
\]
By using a certainty threshold for classification, we can easily enforce the likelihood required for a flow to be classified.
We enforce that $m \geq 15$, otherwise, because our subflow classifier has such high accuracy, it will always reach a $>95\%$ threshold after a single subflow.
The use of different certainty thresholds for each class is also possible, which may be useful if the certainty of classification should be different between known and unknown traffic. For example, if a network is using our classification to block unknown traffic and wants to avoid disrupting allowed traffic, our technique would be applied with a very high certainty threshold for unknown classifications to ensure blocked traffic is classified as unknown with high confidence. The ease of adjusting classification certainty allows the certainty to be used as a parameter for classification. Different certainties can yield different classification accuracies depending on the underlying known and unknown traffic, and certainty can be a cross-validated hyperparameter that optimizes classification performance.
This likelihood estimation classification method can be applied in 3 different scenarios that we describe below and evaluate in our experiments:
\subsubsection{Strict Certainty Classification}
In this classification scenario, flows are classified as known, unknown, or uncertain. If the known or unknown likelihood ratio reaches the desired certainty level, then the flow is classified as known or unknown. However, it is possible that neither likelihood ratio reaches the certainty level, so the flow is considered uncertain as its subflows do not yield a likelihood of high enough certainty for either class. Uncertain flows are indicative of traffic that is not similar enough to either class for a confident classification.
This designation of uncertain flows may be useful as a means of filtering and monitoring traffic, enabling uncertain flows to be found and tracked. Uncertain flows may be used for further analysis with a more specific method of classification or inspected as the potential source of network issues. The amount of traffic classified as uncertain is configurable with the certainty level, as higher certainties result in more uncertain decisions.
\subsubsection{Majority Likelihood Classification}
For this classification scenario, if neither of the class likelihood ratios have reached the certainty level after all available subflows are seen, then the flow is classified as the class with the larger likelihood. This scenario results in no uncertain flow classifications since all uncertain flows are classified by their majority likelihood. This approach allows some flows to be classified with less certainty than the given certainty level, but generally increases accuracy in our experiments and is a viable option if uncertain flows are not desired.
\subsubsection{Incremental Classification}
In this classification scenario, the class likelihood ratios are updated with each encountered subflow's likelihoods, and classification occurs immediately once either class likelihood ratio reaches the given certainty level. Incremental classification takes full advantage of our usage of subflows, utilizing each sequence of packets in a flow to gain information on the flow and classify it after seeing the least amount of subflows possible. A classification decision is made as soon as possible, so this scenario prioritizes classification speed. In our Results section, we show that this scenario results in very fast classification after encountering a small fraction of subflows with excellent unknown detection capabilities.
Note that incremental classification can use strict certainty or majority likelihood classification when making its classification decisions.
\section{Experiments And Results}
\subsection{Dataset}
To demonstrate and evaluate our classification method, we use the Science DMZ network. A Science DMZ is a security zone of a university campus network that is configured and designed to optimize the transfer of large scientific datasets \cite{science-dmz}. Researchers use the Science DMZ to transfer their datasets at high bandwith around the world, so a Science DMZ has performance-optimized security measures or other policy differences to enable faster data transfers. This networking environment fits well with our known vs. unknown classification, as a Science DMZ hosts traffic of specific scientific research applications and little other traffic.
\begin{figure}[
\centering
\includegraphics[width=\linewidth]{science-dmz-anaon.png}
\caption{Data Collection Point in the University of Utah Science DMZ Sub-network}
\vspace{-0.05in}
\label{science-dmz}
\end{figure}
\begin{table}[]
\caption{Dataset Statistics}
\begin{tabularx}{\linewidth} {
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X |}
\hline
& Globus & FDT & rclone & Mirror & WIDE \\
\hline
Bytes (GB) & 51.6 & 129 & 82.1 & 42.6 & 30.48 \\
\hline
Flows & 185 & 72 & 12,292 & 2,239 & $1.112e6$ \\
\hline
\end{tabularx}
\vspace{-0.15in}
\label{data-table}
\end{table}
Fig. \ref{science-dmz} shows the location of our traffic capture tap in the University of Utah's Science DMZ, and Table \ref{data-table} shows size statistics of our dataset.
Note that we have different numbers of known and unknown flows, so our experimental accuracies are calculated separately for each label. All of our traffic is TCP and uses IPv4. We randomly select 80\% of our data for training and the rest for evaluation and ensured that the flows in the train and evaluation sets are mutually exclusive.
The specifics and application breakdowns of our known and unknown datasets are below.
\subsubsection{Known Datasets}
Our known traffic is from 3 widely used large file transfer applications: Globus \cite{globus-1, globus-2}, FDT \cite{fdt}, and rclone \cite{rclone}.
We consulted domain experts and system administrators
at the Center for High Performance Computing at the University of Utah
to ensure that these 3 applications are commonly used by science researchers on the Science DMZ. The Globus captures were of ongoing file transfers between Globus endpoints at a university and various other universities in the United States. The FDT traffic was generated by moving DNA sequencing datasets from
the Hunstman Cancer Institute to and from Data Transfer Nodes \cite{esnet-dtn} in the Science DMZ. The rclone traffic was generated by transferring ESnet test datasets \cite{esnet-test-data} to and from Google Drive. We verified with domain experts that our usage of FDT and rclone to generate traffic was consistent with their common usage in science research workflows, to ensure that our data is representative of real FDT and rclone traffic.
\subsubsection{Unknown Datasets}
For our unknown traffic, we use the Mirror and WIDE datasets. The Mirror dataset consists of random captures from a mirror server on the
University of Utah's Science DMZ subnetwork that hosts repositories and other downloadable content. The WIDE dataset consists of captures, performed on the same dates as the Mirror captures, from the WIDE Traffic Archive \cite{WIDE}. The WIDE captures are from the main internet exchange link and internet service provider transit link of the WIDE organization \cite{WIDE}.
\hfill
For all of our classification experiments, we train and evaluate our models using 2 different datasets. The known dataset always consists of the Globus, FDT, and rclone datasets but we use 2 different unknown class definitions: Science DMZ and General. The Science DMZ unknown class consists of only the Mirror traffic dataset, which was captured from
the University of Utah's Science DMZ subnetwork but does not contain known application traffic. This approach allows us to simulate traffic classification in a realistic Science DMZ setting.
The General unknown class consists of both the Mirror and WIDE datasets, resulting in a much broader, more diverse unknown traffic class since WIDE's traffic is not from the same network and contains many more flows. Using this more varied unknown traffic allows us to evaluate how well our classification method generalizes when classifying more challenging, varied traffic.
\subsection{Strict Certainty Classification Results}
\begin{table}
\caption{Science DMZ Dataset - Strict Certainty and Majority Likelihood Accuracies}
\begin{tabularx}{\linewidth} {
| p{2cm}
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X|}
\hline
\textbf{Percentages of Subflows} & \textbf{25\%} & \textbf{50\%} & \textbf{75\%} & \textbf{100\%} \\
\hline
\multicolumn{5}{|c|}{Known Accuracies:} \\
\hline
25-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
100-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
1000-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
\multicolumn{5}{|c|}{Unknown Accuracies:} \\
\hline
25-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
100-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
1000-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
\end{tabularx}
\label{table:mirror-strict}
\end{table}
To evaluate Strict Certainty classification, we perform our likelihood estimation classification and require a flow's class likelihood ratio to reach the given certainty threshold to be classified as known or unknown. Flows with class likelihood ratios that do not surpass the certainty threshold are considered uncertain.
In our experiments, we perform classification using 25\%, 50\%, 75\%, and 100\% of subflows in each of the test set flows in order to evaluate classification performance when varying amounts of packets in flows are seen. Note that 100\% of subflows does not necessarily mean that all packets of the flow (from handshake to termination) are used, just that all captured packets of the flow are used. We use real-world datasets so, where it would be very limiting to only use completely captured flows for our experimental data. We require at least 15 subflows in a flow portion to perform classification. We also perform classification on features calculated over subflows of different packet lengths, using 25, 100, and 1000 packet subflows.
We use these different combinations of percentage-defined subflow subsets and differing lengths of subflows to thoroughly evaluate classification in many situations where different portions of flows are seen.
\subsubsection{Science DMZ Dataset}
Table \ref{table:mirror-strict} shows classification accuracies on the Science DMZ dataset, when using a strict certainty threshold of 95\%.
Our accuracies are extremely high across all subflow sizes and subflow percentage subsets, with all experimental settings reaching 100\% accuracy. These results show that the unknown traffic is very different from the known application traffic and our method can successfully find and utilize these differences for classification. No flows were classified as uncertain across all experiments, even when requiring a high certainty threshold of 95\%.
\subsubsection{General Dataset}
Fig. \ref{table:strict-general} shows classification accuracies on the General dataset, using the same strict certainty threshold of 95\%.
Our accuracies are extremely high across all subflow sizes and subflow percentage subsets, with a minimum accuracy of 97.5\% and most experiments reaching 100\% accuracy.
These accuracies are slightly lower than the Science DMZ accuracies, which is expected since the General dataset contains unknown traffic that is more varied and similar to the known traffic, resulting in a more challenging classification task.
For both known and unknown classificatoin, the 25-packet subflows had the poorest accuracies.
This indicates that our classification method performs better when subflows contain more packets, which makes sense as this means there's more networking traffic available for classification to be based on.
Only one experimental setting resulted in any flows that were unable to reach the 95\% certainty threshold necessary for classification, and thus considered uncertain. When performing classification on 50\% of 25-packets subflows, approximately 0.1\% of flows were considered uncertain.
\begin{table}
\caption{General Dataset - Strict Certainty Accuracies}
\begin{tabularx}{\linewidth} {
| p{2cm}
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X|}
\hline
\textbf{Percentages of Subflows} & \textbf{25\%} & \textbf{50\%} & \textbf{75\%} & \textbf{100\%} \\
\hline
\multicolumn{5}{|c|}{Known Accuracies:} \\
\hline
25-Packet Subflows & 97.5 & 97.5 & 97.5 & 97.5 \\
\hline
100-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
1000-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
\multicolumn{5}{|c|}{Unknown Accuracies:} \\
\hline
25-Packet Subflows & 100 & 99.8 & 99.8 & 99.8 \\
\hline
100-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
1000-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
\end{tabularx}
\label{table:strict-general}
\end{table}
Across both datasets, a very small amount of flows were considered uncertain even when a small percentage of subflows are seen.
This shows that even if a high certainty for classification is enforced and not all packets in a flow are seen, our method can classify a majority of flows.
\subsection{Majority Likelihood Classification Results}
To evaluate Majority Likelihood classification, we perform our likelihood estimation classification to classify a flow as known or unknown if that flow's corresponding class likelihood ratio reaches the given certainty threshold. If after all available subflows are seen and the flow has no class likelihood ratio that has reached the certainty threshold, then the flow is classified as whichever class has the larger, or majority, likelihood estimate.
We use the same percentage-defined subflow subsets and differing lengths of subflows as the Strict Certainty Classification experiments (25\%, 50\%, 75\%, and 100\% of a flow's subflows each with 25, 100, and 1000 packet subflows).
\subsubsection{Science DMZ Dataset}
For this dataset, all flows had class likelihood ratios that reached the 95\% certainty threshold across all percentages and sizes of subflows; so, no flows were considered uncertain and none needed to be classified using the majority class likelihood. This means that there are no differences in accuracy between Strict Certainty and Majority Likelihood classification for all experiments on the Science DMZ dataset, and Table \ref{table:mirror-strict} shows the unknown and known flow classification accuracies for Majority Likelihood classification.
\subsubsection{General Dataset}
\begin{table}
\caption{General Dataset - Majority Certainty Accuracies}
\begin{tabularx}{\linewidth}
{
| p{2cm}
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X
| >{\centering\arraybackslash}X|
}
\hline
\textbf{Percentages of Subflows} & \textbf{25\%} & \textbf{50\%} & \textbf{75\%} & \textbf{100\%} \\
\hline
\multicolumn{5}{|c|}{Known Accuracies:} \\
\hline
25-Packet Subflows & 97.5 & 97.5 & 97.5 & 97.5 \\
\hline
100-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
1000-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
\multicolumn{5}{|c|}{Unknown Accuracies:} \\
\hline
25-Packet Subflows & 100 & 99.9 & 99.8 & 99.8 \\
\hline
100-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
1000-Packet Subflows & 100 & 100 & 100 & 100 \\
\hline
\end{tabularx}
\label{table:general-maj}
\end{table}
Fig. \ref{table:general-maj} shows classification accuracies on the General dataset when using a certainty threshold of 95\%. Both the known and unknown accuracies do not notably differ from the Strict Certainty classification accuracies, as there were very few uncertain flows with class likelihood ratios that did not reach the 95\% threshold.
Using Strict Certainty classification, only the experimental setting using 50\% of 25-packet subflows resulted in uncertain flows; so only this experimental setting has a difference between the Strict Certainty and Majority Certainty classification accuracies.
It can be seen from the 0.1\% increase in accuracy from Strict Certainty classification that the 0.1\% of flows that were considered uncertain using Strict Certainty classification were classified correctly using Majority Certainty classification. This indicates that classification by the larger class likelihood is an effective way to classify traffic that is not similar enough to either class for a classification at the certainty required by the given threshold.
\subsection{Incremental Classification Results}
To evaluate Incremental classification, we update a flow's class likelihoods and check if the given certainty threshold is reached for every encountered subflow. Classification of the flow occurs immediately once a class likelihood reaches the certainty threshold, and subflows are encountered in chronological order of packet arrival; so flows are classified as soon as possible.
Thus, these experiments allow us to evaluate how well our classification performs when reaching a classification decision in the fastest manner possible. We use both Strict Certainty and Majority Likelihood classification with this Incremental classification scheme, where Strict Certainty will allow for uncertain flows and Majority Likelihood will classify all flows as known or unknown even if no certain decision is reached after all subflows are seen. We evaluate on all lengths of 25, 100, and 1000 packet subflows.
\subsubsection{Science DMZ Dataset}
\begin{figure}
\centering
\begin{subfigure}{.90\linewidth}
\centering
\includegraphics[width=\linewidth]{mirror-strict-incremental.png}
\caption{Strict Certainty Classification}
\end{subfigure}
\begin{subfigure}{.90\linewidth}
\centering
\includegraphics[width=\linewidth]{mirror-maj-incremental.png}
\caption{Majority Likelihood Classification}
\end{subfigure}
\caption{Science DMZ Dataset: Incremental Classification}
\vspace{-0.1in}
\label{fig:mirror-incremental}
\end{figure}
Fig. \ref{fig:mirror-incremental} shows classification accuracies on the Science DMZ dataset when using Incremental classification with both Strict Certainty and Majority Certainty classifications and a 95\% certainty threshold.
With Incremental classification, there are flows with class likelihood ratios that did not reach the certainty threshold, so the accuracies of Strict Certainty and Majority Likelihood classification notably differ.
Known accuracies of Strict Certainty classification are high across all subflow sizes, with a minimum accuracy of $95.5$\%. The average percentage of subflows needed to make a classification decision are overall very low: 1\% for 25-packet subflows, 5.4\% for 100-packet subflows, and 1.7\% for 1000-packet subflows. This shows that our method can classify known traffic very quickly with high accuracy, after seeing a very small percentage of packets or subflows. With Majority Likelihood classification, all known accuracies reach 100\%. This indicates that the small percentage of flows incorrectly classified by Strict Certainty classification were classified as uncertain and were correctly classified using Majority Likelihood classification.
Unknown accuracies of Strict Certainty classification for 25 and 100 packet subflows are around 98\%, but drop to 42.9\% for 1000-packet subflows. This accuracy drop is due to the 1000-packet subflow flows having considerably less subflows available for classification compared to the 25 and 100 packet subflow flows, since 1000-packet subflows require 10 times more packets per subflow than 100-packet subflows. This smaller number of subflows available for classification resulted in many flows being classified as uncertain, dropping the accuracy. With Majority Likelihood, all unknown accuracies reach 100. This indicates that classifying uncertain flows that did not reach the required certainty threshold by their majority class likelihood is an effective approach.
These results show that classifying traffic using majority likelihood is a viable and simple option that enables improved classification accuracy and the elimination of uncertain flows.
\subsubsection{General Dataset}
\begin{figure}
\centering
\begin{subfigure}{.90\linewidth}
\centering
\includegraphics[width=\linewidth]{general-strict-incremental.png}
\caption{Strict Certainty Classification}
\end{subfigure}
\begin{subfigure}{.90\linewidth}
\centering
\includegraphics[width=\linewidth]{general-maj-incremental.png}
\caption{Majority Likelihood Classification}
\end{subfigure}
\caption{General Dataset: Incremental Classification}
\vspace{-0.1in}
\label{fig:general-incremental}
\end{figure}
Fig. \ref{fig:general-incremental} shows classification accuracies on the General dataset from Incremental classification with both Strict Certainty and Majority Likelihood classifications and a 95\% certainty threshold.
Known accuracies of Strict Certainty classification are high across all subflow sizes, with a minimum accuracy of $95.12$\%. The average percentage of subflows needed to make a classification decision for all subflow sizes were in the 1-5\% range, very low and similar to the percentages on the Science DMZ dataset. This shows that even on a more difficult dataset, our method is very effective at classifying known traffic as quickly as possible. Majority Likelihood classification either improves known accuracies to 100\% or does not change accuracy.
Unknown accuracies from Strict Certainty classification are low but this is remedied by using Majority Likelihood classification, where accuracies reach a minimum of 99.85\%. This indicates that the low Strict Certainty classification accuracies are due to a considerable portion of flows being incorrectly classified as uncertain, but with Majority Likelihood classification these flows can be correctly classified.
These results further support the viability of Majority Likelihood classification as a method to improve classification performance, especially when there are many uncertain flows from Strict Certainty classification.
The average percentage of subflows needed to make a classification decision is 41\% for 25-packet subflows, 43.2\% for 100-packet subflows, and 53\% for 1000-packet subflows; so overall a classification decision was made before half of available subflows were seen.
Across both datasets, Incremental classification has better performance on known traffic than unknown traffic.
A classification can be made quickly after seeing less than half of subflows for both traffic classes, reinforcing our conclusions from Strict Certainty and Majority Likelihood that our method can classify a flow correctly after seeing a small portion of the flows' packets. Classifications of known traffic were made especially quickly, after seeing only 1-5\% of subflows, at accuracies above 95\%. This indicates our method can correctly classify known flows very quickly with minimal computation, as it only needs to process a tiny percentage of packets before making a classification. For unknown traffic, incremental classification using a strict certainty threshold of 95\% yields many uncertain flows. When Majority Likelihood classification is used, unknown flows that were considered uncertain with Strict Certainty classification can be correctly classified.
\section{Conclusion and Future Work}
In this paper, we introduced a machine learning method that uses statistics on sequences of packets, called subflows, to classify networking traffic as known or unknown with a measure of certainty.
Our technique uses a gradient-boosted decision tree-based subflow classifier to assign class likelihoods to subflows, then uses joint likelihood estimations over multiple subflows to classify entire flows at a customizable certainty threshold.
This method of classification allows traffic to be classified at an easily configurable certainty threshold and in three different ways. If used with Strict Certainty thresholds, flows are only classified as known or unknown if they can be classified at the given certainty level, and our method can find uncertain flows that are not similar enough to either class. If used with Majority Likelihood, all flows are classified as known or unknown by allowing some flows to be classified with whichever class likelihood estimate is higher rather than strictly requiring the certainty level. If used in an Incremental classification manner, each subflow updates the flow's class likelihood estimate and classification of a flow occurs after seeing the fewest number of subflows possible.
We evaluated our technique on traffic from the Science DMZ subnetwork domain \cite{science-dmz}, as it naturally fits our class scheme and has not been used as a traffic classification setting before. We also evaluate on a more general, challenging dataset to ensure that our method can generalize well.
Our results show that our classification performs very well in the Science DMZ setting, able to reach 100\% accuracy for all classification options. On the general dataset, we maintained high accuracy on known traffic classification, reaching up to 100\%, though unknown classification accuracies dropped in the Strict Certainty classification scenario.
Our method was shown to perform well even when only seeing a small percentage of flows, reaching accuracies up to 100 on both datasets when only a fourth of available subflows in a flow are used for classification. With Strict Certainty classification, very few flows are considered uncertain even when requiring 95\% certainty and seeing partial flows. The use of Majority Likelihood classification was shown to correctly classify flows deemed uncertain in Strict Certainty classification, improving classification performance. The Incremental classification approach reached classification decisions very quickly after seeing small amounts of subflows and maintained high accuracies on known flows across both datasets.
Our experiments show that in a real-world Science DMZ, our method is effective at classifying known and unknown traffic very quickly. With Incremental classification, accuracies above 95\% were reached after encountering as little as 1\% of subflows. Our Strict Certainty and Majority Likelihood results indicate that for all subflow sizes there's no drop in performance between the different percentages of subflows used for classification. This indicates our method can classify a flow well without needing to see a certain percentage of the flow's packets. Strict Certainty is able to correctly classify flows that reach the given certainty threshold and identify uncertain flows.
If uncertain flows are not desired in a network setting, then Majority Likelihood classification can be used effectively; as it had extremely high accuracy across all experiments, even when used with Incremental classification. Incremental classification with Majority Likelihood has high performance and can classify known flows after seeing a tiny amount of subflows, meaning classification requires minimal time and computation.
Out of all the classification scenarios, Incremental classification accuracies dropped the most between the Science DMZ and General dataset results, so further work could be done to achieve more generalizable Incremental classification performance.
In Incremental classification unknown accuracies are also generally lower than known accuracies, especially on the more difficult dataset.
Maintaining high performance on unknown traffic classification is an expected challenge, as we define unknown traffic as any traffic that is not from the known applications, so unknown traffic can have huge variety. The most challenging datasets and network settings would have unknown traffic that has similar function and behavior as known traffic. Future work applying our approach to more challenging datasets could explore more sophisticated subflow classifiers, different formulations of class likelihoods of subflow classifications, or the use of regularization on class likelihoods to maintain high accuracies.
\hfill
\hfill
\hfill
\section*{Declarations}
\subsection*{Funding}
This work was funded by NSF Awards ACI-1642158 and IIS-1816149.
\subsection*{Conflicts of Interest}
None
\subsection*{Availability of Data and Material}
The datasets used are available here: \url{https://hive.utah.edu/concern/datasets/nk322d36m?locale=en}
\subsection*{Code availability}
The experimentation code is available here: \url{https://anonymous.4open.science/r/d6b2b12b-dfd4-4d45-98d9-d404caf02797/}
\subsection*{Informed Consent Statement}
Not applicable
\subsection*{Author Contribution}
Jiahui Chen is first author and implemented all experimentation as well as completed the majority of the writing. All the other authors supervised this work equally.
\bibliographystyle{spbasic}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,337 |
import { remoteConfigApiOrigin } from "../api";
import { Client } from "../apiv2";
import { RemoteConfigTemplate } from "./interfaces";
const apiClient = new Client({
urlPrefix: remoteConfigApiOrigin,
apiVersion: "v1",
});
const TIMEOUT = 30000;
/**
* Rolls back to a specific version of the Remote Config template
* @param projectId Remote Config Template Project Id
* @param versionNumber Remote Config Template version number to roll back to
* @return Returns a promise of a Remote Config Template using the RemoteConfigTemplate interface
*/
export async function rollbackTemplate(
projectId: string,
versionNumber?: number
): Promise<RemoteConfigTemplate> {
const params = new URLSearchParams();
params.set("versionNumber", `${versionNumber}`);
const res = await apiClient.request<void, RemoteConfigTemplate>({
method: "POST",
path: `/projects/${projectId}/remoteConfig:rollback`,
queryParams: params,
timeout: TIMEOUT,
});
return res.body;
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 789 |
AnimeNews
Jujutsu Kaisen HBO Max Debut Set for December
By Jenni Lada November 27, 2020
On December 4, 2020, Jujutsu Kaisen HBO Max streaming will begin. Warner Media announced the anime would become part of the streaming service as part of the established Crunchyroll collection. The anime series is currently running in Japan, with eight episodes available on Crunchyroll. The original Japanese voice acting and English dubs are available.
Jujutsu Kaisen follows Yuji Itadori who's part of his high school's occult club. This probably wasn't the best idea, because the group unleashed something evil through the Double-Faced Specter's finger. Yuji eats the finger to save his friends, unwittingly becoming one with the Curse. To keep from being immediately killed by sorcerers, he's joins the Tokyo Metropolitan Technical High School of Sorcery. The first season of the show will consist of 24 episodes.
In addition to the anime being available in English, people can read the manga too. Viz Media picked it up. While there are 14 volumes so far in Japan, as of November 2020, the English translation's seventh volume will release on December 1, 2020. There are no video game adaptations of the series available just yet.
As for the Crunchyroll Collection itself, there are generally over 20 shows available on HBO Max. None of these shows are exclusive to that service, as they are all animes already available on Crunchyroll. Some of the notable shows on the service right now include Berserk, Blue Exorcist, Bungo Stray Dogs, Death Note, Food Wars: Shokugeko no Soma, Fullmetal Alchemist: Brotherhood, Hunter x Hunter, Inuyasha, Kill la Kill, Konosuba: God's Blessing on This Wonderful World, Mob Psycho 100, The promised Neverland, Puella Magi Madoka Magica, and Re:Zero Starting Life in Another World.
The Jujutsu Kaisen HBO Max debut is set for December 4, 2020. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 311 |
package org.apache.gobblin.runtime;
import java.io.IOException;
import java.util.Map;
import java.util.Properties;
import java.util.Queue;
import java.util.concurrent.BlockingQueue;
import java.util.concurrent.Callable;
import java.util.concurrent.ExecutionException;
import java.util.concurrent.ExecutorService;
import java.util.concurrent.Executors;
import java.util.concurrent.Future;
import java.util.concurrent.TimeUnit;
import org.apache.gobblin.util.JobLauncherUtils;
import org.apache.hadoop.conf.Configuration;
import org.apache.hadoop.fs.FileSystem;
import org.apache.hadoop.fs.Path;
import static org.mockito.Mockito.mock;
import static org.mockito.Mockito.when;
import org.slf4j.Logger;
import org.testng.Assert;
import org.testng.annotations.Test;
import com.google.common.base.Joiner;
import com.google.common.base.Predicate;
import com.google.common.collect.Lists;
import com.google.common.collect.Maps;
import com.google.common.collect.Queues;
import com.google.common.io.Files;
import org.apache.gobblin.commit.DeliverySemantics;
import org.apache.gobblin.configuration.ConfigurationKeys;
import org.apache.gobblin.util.Either;
import org.apache.gobblin.util.Id;
import javax.annotation.Nullable;
import lombok.extern.slf4j.Slf4j;
@Slf4j
public class JobContextTest {
@Test
public void testNonParallelCommit()
throws Exception {
Properties jobProps = new Properties();
jobProps.setProperty(ConfigurationKeys.JOB_NAME_KEY, "test");
jobProps.setProperty(ConfigurationKeys.JOB_ID_KEY, "job_id_12345");
jobProps.setProperty(ConfigurationKeys.METRICS_ENABLED_KEY, "false");
Map<String, JobState.DatasetState> datasetStateMap = Maps.newHashMap();
for (int i = 0; i < 2; i++) {
datasetStateMap.put(Integer.toString(i), new JobState.DatasetState());
}
final BlockingQueue<ControllableCallable<Void>> callables = Queues.newLinkedBlockingQueue();
final JobContext jobContext =
new ControllableCommitJobContext(jobProps, log, datasetStateMap, new Predicate<String>() {
@Override
public boolean apply(@Nullable String input) {
return true;
}
}, callables);
ExecutorService executorService = Executors.newSingleThreadExecutor();
Future future = executorService.submit(new Runnable() {
@Override
public void run() {
try {
jobContext.commit();
} catch (IOException ioe) {
throw new RuntimeException(ioe);
}
}
});
// Not parallelized, should only one commit running
ControllableCallable<Void> callable = callables.poll(1, TimeUnit.SECONDS);
Assert.assertNotNull(callable);
Assert.assertNull(callables.poll(200, TimeUnit.MILLISECONDS));
// unblock first commit, should see a second commit
callable.unblock();
callable = callables.poll(1, TimeUnit.SECONDS);
Assert.assertNotNull(callable);
Assert.assertNull(callables.poll(200, TimeUnit.MILLISECONDS));
Assert.assertFalse(future.isDone());
// unblock second commit, commit should complete
callable.unblock();
future.get(1, TimeUnit.SECONDS);
Assert.assertEquals(jobContext.getJobState().getState(), JobState.RunningState.COMMITTED);
}
@Test
public void testParallelCommit()
throws Exception {
Properties jobProps = new Properties();
jobProps.setProperty(ConfigurationKeys.JOB_NAME_KEY, "test");
jobProps.setProperty(ConfigurationKeys.JOB_ID_KEY, "job_id_12345");
jobProps.setProperty(ConfigurationKeys.METRICS_ENABLED_KEY, "false");
jobProps.setProperty(ConfigurationKeys.PARALLELIZE_DATASET_COMMIT, "true");
Map<String, JobState.DatasetState> datasetStateMap = Maps.newHashMap();
for (int i = 0; i < 5; i++) {
datasetStateMap.put(Integer.toString(i), new JobState.DatasetState());
}
final BlockingQueue<ControllableCallable<Void>> callables = Queues.newLinkedBlockingQueue();
final JobContext jobContext =
new ControllableCommitJobContext(jobProps, log, datasetStateMap, new Predicate<String>() {
@Override
public boolean apply(@Nullable String input) {
return true;
}
}, callables);
ExecutorService executorService = Executors.newSingleThreadExecutor();
Future future = executorService.submit(new Runnable() {
@Override
public void run() {
try {
jobContext.commit();
} catch (IOException ioe) {
throw new RuntimeException(ioe);
}
}
});
// Parallelized, should be able to get all 5 commits running
Queue<ControllableCallable<Void>> drainedCallables = Lists.newLinkedList();
Assert.assertEquals(Queues.drain(callables, drainedCallables, 5, 1, TimeUnit.SECONDS), 5);
Assert.assertFalse(future.isDone());
// unblock all commits
for (ControllableCallable<Void> callable : drainedCallables) {
callable.unblock();
}
// check that future is done
future.get(1, TimeUnit.SECONDS);
// check that no more commits were added
Assert.assertTrue(callables.isEmpty());
Assert.assertEquals(jobContext.getJobState().getState(), JobState.RunningState.COMMITTED);
}
@Test
public void testSingleExceptionSemantics()
throws Exception {
Properties jobProps = new Properties();
jobProps.setProperty(ConfigurationKeys.JOB_NAME_KEY, "test");
jobProps.setProperty(ConfigurationKeys.JOB_ID_KEY, "job_id_12345");
jobProps.setProperty(ConfigurationKeys.METRICS_ENABLED_KEY, "false");
Map<String, JobState.DatasetState> datasetStateMap = Maps.newHashMap();
for (int i = 0; i < 3; i++) {
datasetStateMap.put(Integer.toString(i), new JobState.DatasetState());
}
final BlockingQueue<ControllableCallable<Void>> callables = Queues.newLinkedBlockingQueue();
// There are three datasets, "0", "1", and "2", middle one will fail
final JobContext jobContext =
new ControllableCommitJobContext(jobProps, log, datasetStateMap, new Predicate<String>() {
@Override
public boolean apply(@Nullable String input) {
return !input.equals("1");
}
}, callables);
ExecutorService executorService = Executors.newSingleThreadExecutor();
Future future = executorService.submit(new Runnable() {
@Override
public void run() {
try {
jobContext.commit();
} catch (IOException ioe) {
throw new RuntimeException(ioe);
}
}
});
// All three commits should be run (even though second one fails)
callables.poll(1, TimeUnit.SECONDS).unblock();
callables.poll(1, TimeUnit.SECONDS).unblock();
callables.poll(1, TimeUnit.SECONDS).unblock();
try {
// check future is done
future.get(1, TimeUnit.SECONDS);
Assert.fail();
} catch (ExecutionException ee) {
// future should fail
}
// job failed
Assert.assertEquals(jobContext.getJobState().getState(), JobState.RunningState.FAILED);
}
@Test
public void testCleanUpOldJobData() throws Exception {
String rootPath = Files.createTempDir().getAbsolutePath();
final String JOB_PREFIX = Id.Job.PREFIX;
final String JOB_NAME1 = "GobblinKafka";
final String JOB_NAME2 = "GobblinBrooklin";
final long timestamp1 = 1505774129247L;
final long timestamp2 = 1505774129248L;
final Joiner JOINER = Joiner.on(Id.SEPARATOR).skipNulls();
Object[] oldJob1 = new Object[]{JOB_PREFIX, JOB_NAME1, timestamp1};
Object[] oldJob2 = new Object[]{JOB_PREFIX, JOB_NAME2, timestamp1};
Object[] currentJob = new Object[]{JOB_PREFIX, JOB_NAME1, timestamp2};
Path currentJobPath = new Path(JobContext.getJobDir(rootPath, JOB_NAME1), JOINER.join(currentJob));
Path oldJobPath1 = new Path(JobContext.getJobDir(rootPath, JOB_NAME1), JOINER.join(oldJob1));
Path oldJobPath2 = new Path(JobContext.getJobDir(rootPath, JOB_NAME2), JOINER.join(oldJob2));
Path stagingPath = new Path(currentJobPath, "task-staging");
Path outputPath = new Path(currentJobPath, "task-output");
FileSystem fs = FileSystem.getLocal(new Configuration());
fs.mkdirs(currentJobPath);
fs.mkdirs(oldJobPath1);
fs.mkdirs(oldJobPath2);
log.info("Created : {} {} {}", currentJobPath, oldJobPath1, oldJobPath2);
gobblin.runtime.JobState jobState = new gobblin.runtime.JobState();
jobState.setProp(ConfigurationKeys.WRITER_STAGING_DIR, stagingPath.toString());
jobState.setProp(ConfigurationKeys.WRITER_OUTPUT_DIR, outputPath.toString());
JobContext jobContext = mock(JobContext.class);
when(jobContext.getStagingDirProvided()).thenReturn(false);
when(jobContext.getOutputDirProvided()).thenReturn(false);
when(jobContext.getJobId()).thenReturn(currentJobPath.getName().toString());
JobLauncherUtils.cleanUpOldJobData(jobState, log, jobContext.getStagingDirProvided(), jobContext.getOutputDirProvided());
Assert.assertFalse(fs.exists(oldJobPath1));
Assert.assertTrue(fs.exists(oldJobPath2));
Assert.assertFalse(fs.exists(currentJobPath));
}
/**
* A {@link Callable} that blocks until a different thread calls {@link #unblock()}.
*/
private class ControllableCallable<T> implements Callable<T> {
private final BlockingQueue<Boolean> queue;
private final Either<T, Exception> toReturn;
private final String name;
public ControllableCallable(Either<T, Exception> toReturn, String name) {
this.queue = Queues.newArrayBlockingQueue(1);
this.queue.add(true);
this.toReturn = toReturn;
this.name = name;
}
public void unblock() {
if (!this.queue.isEmpty()) {
this.queue.poll();
}
}
@Override
public T call()
throws Exception {
this.queue.put(false);
if (this.toReturn instanceof Either.Left) {
return ((Either.Left<T, Exception>) this.toReturn).getLeft();
} else {
throw ((Either.Right<T, Exception>) this.toReturn).getRight();
}
}
}
private class ControllableCommitJobContext extends DummyJobContext {
private final Predicate<String> successPredicate;
private final Queue<ControllableCallable<Void>> callablesQueue;
public ControllableCommitJobContext(Properties jobProps, Logger logger,
Map<String, JobState.DatasetState> datasetStateMap, Predicate<String> successPredicate,
Queue<ControllableCallable<Void>> callablesQueue)
throws Exception {
super(jobProps, logger, datasetStateMap);
this.successPredicate = successPredicate;
this.callablesQueue = callablesQueue;
}
@Override
protected Callable<Void> createSafeDatasetCommit(boolean shouldCommitDataInJob, boolean isJobCancelled,
DeliverySemantics deliverySemantics, String datasetUrn, JobState.DatasetState datasetState,
boolean isMultithreaded, JobContext jobContext) {
ControllableCallable<Void> callable;
if (this.successPredicate.apply(datasetUrn)) {
callable = new ControllableCallable<>(Either.<Void, Exception>left(null), datasetUrn);
} else {
callable = new ControllableCallable<>(Either.<Void, Exception>right(new RuntimeException("Fail!")), datasetUrn);
}
this.callablesQueue.add(callable);
return callable;
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,060 |
{"url":"http:\/\/mathhelpforum.com\/differential-geometry\/185692-bolzano-weierstrass-bounded-functions.html","text":"## Bolzano\u2013Weierstrass for bounded functions\n\nNeed help understanding this proof please\n\nTheorem\nIf $[f_n]$ is a pointwise bounded sequence of complex functions on a countable set $E$, then $[f_n]$ has a subsequence $[f_{n_k}]$ such that $[f_{n_k}(x)]$ converges $\\forall{x\\in{E}}$\n\nProof\nLet $[x_i], i=1,2,3...$, be the points of $E$, arranged in a sequence. Since $[f_n(x_1)]$ is bounded, $\\exists$ a subsequence, which we shall denote by $[f_{1,k}]$ such that $[f_{1,k}(x_1)]$ converges as $k\\rightarrow\\infty$\n\nLet us now consider sequences $S_1,S_2,S_3,...$, which we represent by the array\n\n$S_1$: $f_{1,1}$ $f_{1,2}$ $f_{1,3}$ $f_{1,4}$ ....\n$S_2$: $f_{2,1}$ $f_{2,2}$ $f_{2,3}$ $f_{2,4}$ ....\n$S_3$: $f_{3,1}$ $f_{3,2}$ $f_{3,3}$ $f_{3,4}$ ....\n.................................\n\nand which have the following properties:\n(a) $S_n$ is a subsequence of $S_{n-1}$ for $n=2,3,4,...$\n\n(b) $[f_{n,k}(x_n)]$ converges, as $k\\rightarrow\\infty$ (the boundedness of $[f_n(x_n)]$ makes it possible to choose $S_n$ in this way)\n\n(c) The order in which the functions appear is the same in each sequence; i.e, if one function precedes another in $S_1$, they are in the same relation in every $S_n$, until one or the other is deleted. Hence, when going from one row in the above array to the next below, functions may move to the left but never to the right.\n\nWe now go down the diagonal of the array; i.e, we consider the sequence\n\n$S$: $f_{1,1}$ $f_{2,2}$ $f_{3,3}$ $f_{4,4}$\n\nBy (c), the sequence $S$ (except possibly its first $n-1$ terms) is a subsequence of $S_n$, for $n=1,2,3,..$ Hece (b) implies that $[f_{n,n}(x_i)]$ converges,, as $n\\rightarrow\\infty$, $\\forall{x_i}\\in{E}$\n\nQED\n\nQuestions\n1) For $S_m$: $f_{m,1}$ $f_{m,2}$ $f_{m,3}$ $f_{m,4}$ ....\nAre the terms of this sequence, S_m, the terms of the sequence $[f_{m,k}]$, the convergent subsequence of the sequence $[f_n(x_m)]$?\n\nIf question 1 is true\n\n2) Regards to property (a), is this a property intrinsic to an array of sequences constructed in this manner; i.e an array of sequences made of the terms of $[f_{n,k}]$, or must the array be specially constructed to have this property?\nIf so, how do I guarantee this can always be done?\n\n3) Would't property (a) imply $f_{n,j}=f_{n-1,p}$ for all $j=1,2,3...$ and some $p\\in{\\mathbb{N}}$?","date":"2014-07-31 18:09:06","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 61, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9175599813461304, \"perplexity\": 254.29937278427758}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-23\/segments\/1406510273513.48\/warc\/CC-MAIN-20140728011753-00282-ip-10-146-231-18.ec2.internal.warc.gz\"}"} | null | null |
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"redpajama_set_name": "RedPajamaC4"
} | 4,448 |
Home Academy Awards Collection Rules, 1978 (51st) Academy Awards
Rules, 1978 (51st) Academy Awards
SPECIAL RULES FOR THE MUSIC AWARDS
General Music Rules
l. For an achievement to be considered for possible nomination in
one of the three Music Awards categories, an Official Submission Form,
obtained from the Academy, must be submitted by the creator(s) of that
achievement who must personally (by phone, letter or cable) request this
form. Any member of the Music Branch may recommend a work by anyone
other than himself for submission. If such recommendation is made,
the creator will be so notified and informed that he must request the
Official Submission Form from the Academy if he wishes to submit the
work. The creator need not be an Academy member. The work submitted
must appear in an eligible feature film and must be submitted not
later than thirty days after the qualifying Los Angeles release opening
(see Paragraph 1 of Rule One). Works from films which begin their
qualifying Los Angeles run after November 10 must be submitted not
later than December 11, after which no submissions will be accepted (i.e.,
the signed Official Submission Form must be in the Academy Office not
later than December 11, even though the film is released between December
11 and December 31). However, the Executive Committee reserves
to itself the right, but not the obligation, to submit a candidate after said
thirty-day period and after December 11 but no later than December 12.
2. All Submission Forms submitted by the creator ( s) must be accompanied
by a copy of the music cue sheet. In the category of Best
Original Song Score and Its Adaptation, lead sheets or "piano parts" for
all the songs must accompany the submission. In the Best Adaptation
Score category, a complete musical bibliography of the material adapted
(e.g., sheet music, records, other germane material, and/or a detailed list
of standard source material) must accompany the submission. In the Best
Original Song category, a lead sheet or "piano part" must accompany
each song submitted.
3. To Qualify:
( a) The work submitted must be specifically created for the eligible
(b) The work must be submitted on the Official Submission Form
which will require the creator ( s) to certify that, in his/their
view, the work is an outstanding achievement worthy of consideration
for nomination for an Academy Award. It must be
related to the total theatrical entity and must serve the
dramatic, emotional or atmospheric mood. The measure of
its qualification shall be the degree of its effectiveness,
craftsmanship and importance in relation to the dramatic
whole.
(c) The work submitted must have been recorded for use in the
sound track of the eligible film prior to any other recording
with the following specific exceptions:
( 1) Temporary track for demonstration or production
( 2) Artist rehearsal.
( 3) Score audition.
( 4) Any legitimate technical need of the production.
Title Rules, 1978 (51st) Academy Awards
Description 29 pages.
Award Year 1978 51st Academy Awards
Full text Fifteen SPECIAL RULES FOR THE MUSIC AWARDS General Music Rules l. For an achievement to be considered for possible nomination in one of the three Music Awards categories, an Official Submission Form, obtained from the Academy, must be submitted by the creator(s) of that achievement who must personally (by phone, letter or cable) request this form. Any member of the Music Branch may recommend a work by anyone other than himself for submission. If such recommendation is made, the creator will be so notified and informed that he must request the Official Submission Form from the Academy if he wishes to submit the work. The creator need not be an Academy member. The work submitted must appear in an eligible feature film and must be submitted not later than thirty days after the qualifying Los Angeles release opening (see Paragraph 1 of Rule One). Works from films which begin their qualifying Los Angeles run after November 10 must be submitted not later than December 11, after which no submissions will be accepted (i.e., the signed Official Submission Form must be in the Academy Office not later than December 11, even though the film is released between December 11 and December 31). However, the Executive Committee reserves to itself the right, but not the obligation, to submit a candidate after said thirty-day period and after December 11 but no later than December 12. 2. All Submission Forms submitted by the creator ( s) must be accompanied by a copy of the music cue sheet. In the category of Best Original Song Score and Its Adaptation, lead sheets or "piano parts" for all the songs must accompany the submission. In the Best Adaptation Score category, a complete musical bibliography of the material adapted (e.g., sheet music, records, other germane material, and/or a detailed list of standard source material) must accompany the submission. In the Best Original Song category, a lead sheet or "piano part" must accompany each song submitted. 3. To Qualify: ( a) The work submitted must be specifically created for the eligible film. (b) The work must be submitted on the Official Submission Form which will require the creator ( s) to certify that, in his/their view, the work is an outstanding achievement worthy of consideration for nomination for an Academy Award. It must be related to the total theatrical entity and must serve the dramatic, emotional or atmospheric mood. The measure of its qualification shall be the degree of its effectiveness, craftsmanship and importance in relation to the dramatic whole. (c) The work submitted must have been recorded for use in the sound track of the eligible film prior to any other recording with the following specific exceptions: Page 14 ( 1) Temporary track for demonstration or production purposes. ( 2) Artist rehearsal. ( 3) Score audition. ( 4) Any legitimate technical need of the production.
Page 28-29 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,730 |
Q: Updating observableArray in a computedObservable creates a circular reference? I have created a View Model object for use with KnockoutJS.
It has a property called 'Years' which is an observable array...
viewModel.Years = ko.observableArray([]);
I then have a computed observable, in which I want to update the contents of the array...
viewModel.FuturePrediction = ko.computed(function () {
viewModel.Years.removeAll();
// etc...
});
The problem I'm having is that this appears to create an infinite loop. I'm guessing that Knockout is detecting that I'm accessing the 'Years' property and creating a dependency between it and the 'FuturePrediction' property.
As soon as I attempt to modify the contents of the array, the computed function gets triggered again. The problem is that all I'm doing is updating the 'Years' array, not reading it - and therefore there isn't actually a dependency.
Any ideas what I can do to resolve this?
A: In KO 2.1, computed observables cannot trigger themselves, so you would be in better shape with 2.1.
Calling the array manipulation methods do read and set the array, so it would create a dependency. You could do viewModel.Years([]); as long as you are not depending on the original underlying array for anything (have references to it elsewhere).
I am not sure about your full scenario, but an option would be to build up your "new" array and then finally set the result as the value of Years rather than clearing it first.
Like:
viewModel.FuturePrediction = ko.computed(function () {
var result = [];
//add things to result
viewModel.Years(result);
});
Again, I am not sure about your exact scenario, but if the end goal is to create a new array based on some criteria, then you could have FuturePrediction be the array and return it as the result of the computed observable. Just not sure about your situation exactly.
| {
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} | 108 |
{"url":"http:\/\/mathematica.stackexchange.com\/tags\/error-tracking\/hot","text":"# Tag Info\n\n16\n\nWhile I agree that the debugging tools could have been better developed by now, let me just throw in a few notes and links. Function chaining (f[g[h[...]]]): I'd argue that this is a good thing. Why: Functions return expressions, which are immutable. You don't introduce as much state (or at all), as in imperative languages. This makes it easier to debug ...\n\n15\n\nWhile I wait for better answers from some very knowledgable people in the matter on the site, I'll write what I'm thinking... I think that most of your problems are due to lack of practice with functional thinking rather than lack of debugability itself. I think one that on the contrary, one of the advantages of programming functionally is that the state ...\n\n15\n\nTwo of the most common error messages that users encounter when working with parts of lists are Part::partd and Part::partw (look up Message for the error message syntax). Both of these are because the user is trying to access an invalid part of the expression (the \"object\" referred to in the error message), but there's a subtle difference between the two: ...\n\n14\n\nQuantityForm (and some other formatting functions) issues messages at typesetting instead of evaluation, and Trace is generating output that is in an unevaluated state, which QuantityForm isn't expecting. Here's a couple of similar examples: Trace[Block[{form = \"LongForm\"}, QuantityForm[Quantity[1, \"Meters\"], form]]] Trace[Block[{digits = 3}, ...\n\n10\n\nThe function Shuffle is not defined. If you define it (say, replace it with RandomSample) it works. Apparently, Rotate in the latter part of the code is being applied to the output of a function that uses edgeNoise which, in turn, (because Shuffle is undefined) is producing the error message you are seeing. To replicate what is happening in a simple setting ...\n\n6\n\nFollowing R.M's suggestion, and shamelessly lifting code from the Wizard\u2019s fine answer there, you can use Stack[] and get the following: SetAttributes[withTaggedMsg, HoldAll] withTaggedMsg[] := Function[, InternalInheritedBlock[{MessagePacket}, Unprotect[MessagePacket]; MessagePacket[name__, BoxData[obj_, form_]] \/; ! TrueQ[$tagMsg] := ... 5 Here's another, reliable way: messages = {} clearMessages[] := messages = {} collectMessages[m_] := AppendTo[messages, m] InternalAddHandler[\"Message\", collectMessages] Then do clearMessages[] 1\/0; 0\/0; messages InternalRemoveHandler[\"Message\", collectMessages] Reference and details: How to abort on any message generated? 5 What you look for is the function Check which will give you the possibility to implement what you ask for in several variants, the most simple probably be this: success=Check[Import[\"test1.txt\", \"Table\"];True, False] See the documentation of Check for more details... 4 I would do this: DefFn[f_[args___], body_] := lhs : f[args] := WithStackFrame[lhs, body]; Then make WithStackFrame HoldFirst and do de-structuring there. For example: SetAttributes[WithStackFrame, HoldFirst] WithStackFrame[f_[args___], expr_] := Print[{f, {args}}]; If for some reason this were unacceptable I would do: DefFn[f_[args___], body_] := ... 4 You need a parser for the argument patterns. I wrote a simplistic one for this answer. I will reproduce it here to keep things self-contained: splitHeldSequence[Hold[seq___], f_: Hold] := List @@ Map[f, Hold[seq]]; getFunArguments[Verbatim[HoldPattern][Verbatim[Condition][f_[args___], test_]]] := getFunArguments[HoldPattern[f[args]]]; ... 4 Simply you could use$MessagePrePrint to get the \"fillers\" and $MessageList as you did to get the message name they belong to:$MessagePrePrint = Sow; Reap[ Module[{}, 1\/0; 0^0]; $MessageList ] {{Power::infy,Power::indet},{{1\/0,0^0}}} For complete control you could go low-level and intercept MessagePacket as I did for: Prepend Information to Warning ... 3 You could always capture the information directly, myMessageList = {}; InternalInheritedBlock[{Message,$InMsg = False}, Unprotect[Message]; Message[msg_, vars___] \/; ! $InMsg := Block[{$InMsg = True}, AppendTo[myMessageList, {msg, vars}]; Message[msg, vars] ]; (* code to run *) Module[{}, 1\/0; 0^0] ]; myMessageList (* ...\n\n2\n\nYou can use Messages[foo] to get the text of any message. With that, we can proceed as follows to extract the text of the messages that were last generated: Module[{}, 1\/0;0^0]; msg = \\$MessageList; (* last errors *) With[{messages = ReleaseHold@ DeleteDuplicates[# \/. HoldPattern@MessageName[s_, _] :> Messages@s] &}, # \/. messages@#] ...\n\nOnly top voted, non community-wiki answers of a minimum length are eligible","date":"2013-05-21 21:34:41","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.544571042060852, \"perplexity\": 3691.999196358511}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2013-20\/segments\/1368700626424\/warc\/CC-MAIN-20130516103706-00008-ip-10-60-113-184.ec2.internal.warc.gz\"}"} | null | null |
{"url":"https:\/\/stats.stackexchange.com\/questions\/433224\/number-of-causal-assumptions-in-an-overview-by-pearl\/437699","text":"# Number of Causal Assumptions in an Overview by Pearl\n\nIn the paper Causal Inference in Statistics: an Overview by Pearl, in page 11 (106 if you go by the Journal's indexing), a graphical model is presented in figure 2(a). The text reads (picture below):\n\nThe chain model of Fig. 2(a), for example, encodes seven causal assumptions, each corresponding to a missing arrow or a missing double-arrow between a pair of variables.\n\nHow did the author conclude there are seven missing arrows?\n\nNone of the below causal arrows appear in Fig. 2(a). I am assuming time flows from top left to bottom right (i.e. so that $$Y \\to X$$ cannot be a causal assumption because causes must precede effects.).\n\n1. $$U_{Z} \\to U_{X}$$\n2. $$U_{Z} \\to U_{Y}$$\n3. $$U_{Z} \\to X$$\n4. $$U_{Z} \\to Y$$\n5. $$U_{X} \\to U_{Y}$$\n6. $$U_{X} \\to Y$$\n7. $$Z \\to Y$$\n\nThis means that the causal world in Fig. 2(a) assumes there are none of the above seven direct causal effects. By contrast, each of the arrows actually appearing in the graph (e.g., $$U_{Z} \\to Z$$, etc.) are assumptions of direct causal effects.\n\nEDIT: Based on correspondence with Judea Pearl. [Judea's quote is edited for the grammar\/typos common in a brief email exchange.]\n\nI had in mind the following\n\n$$U_{Z} \\longleftrightarrow U_{X}$$\n\n$$U_{Z} \\longleftrightarrow U_{Y}$$\n\n$$U_{X} \\longleftrightarrow U_{Y}$$\n\n$$Z \\to Y$$\n\n$$X \\to Z$$\n\n$$Y \\to Z$$\n\n$$Y \\to X$$\n\nThe missing arrows you listed e.g., $$U_{X} \\to Y$$ are implied by the above, because $$U_{Y}$$ is defined as everything that affects $$Y$$ when $$X$$ is held constant.\n\n\u2022 Why don't we count $Y \\to X$? Is the time assumption not worthy like other causal assumptions?And why don't we count $Z \\to U_Y$? \u2013\u00a0Yair Daon Oct 26 '19 at 18:45\n\u2022 @YairDaon $Z \\to U_{Y}$ is a good question... gonna mull, and may edit my off the cuff answer. However $Y \\to X$ is forbidden as an assumption given the temporality of the variables: time causes cannot follow effects (see the parenthetical). \u2013\u00a0Alexis Oct 28 '19 at 2:18\n\u2022 Since the $U$ are unobserved causes of a variable, $Z \\rightarrow U_Y$ is not distinguishable from $Z \\rightarrow Y$. A relation like $Z \\rightarrow Y$ always masks that there are many other variables along that path through which the effect runs. $Z \\rightarrow Y$ means \"Z affects the value of Y by means other than affecting $X$ in this model. \u2013\u00a0CloseToC Oct 28 '19 at 8:56\n\u2022 @Alexis: My reading of the comments was that it's not clear what the 7 assumptions exactly are, in particular why $Z \\rightarrow U_Y$ which would be an 8th isn't counted. I believe it is because it would amount to doubly counting $Z \\rightarrow Y$ for the reason I mentioned. Have you thought of a different explanation? \u2013\u00a0CloseToC Oct 30 '19 at 9:44\n\u2022 @CloseToC Judea Pearl clarified the assumptions and I have edited my answer to incorporate. \u2013\u00a0Alexis Oct 31 '19 at 3:51\n\nAn exchange of comments with @Alexis (and their correspondence with Pearl himself) cleared things up for me. I can summarize as follows:\n\n1. For the exogenous variables $$U_X, U_Y, U_Z$$ we only allow\/count double arrows (just... because?). For these variables we have three missing (double) arrows, which are $$U_X \\leftrightarrow U_Y, U_Z \\leftrightarrow U_Y$$ and $$U_X \\leftrightarrow U_Z$$.\n\n2. For the endogenous variables $$X,Y,Z$$, we count only directed arrows (again, just because) and we have four missing such arrows, which are $$X\\to Z, Y\\to Z, Y \\to X$$ and $$Z\\to Y$$.\n\n3. We do not count arrows such as $$U_X \\to Z$$ since $$U_Z$$ is defined as everything that affects $$Z$$ outside of the other endogenous variables ($$X,Y$$, in this case), so no other influence is allowed, specifically not $$U_X$$.\n\nThis count gives us seven missing arrows total, as the text suggests.","date":"2020-01-17 12:50:19","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 31, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7967646718025208, \"perplexity\": 994.5500938235266}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-05\/segments\/1579250589560.16\/warc\/CC-MAIN-20200117123339-20200117151339-00269.warc.gz\"}"} | null | null |
George and Walter John Bearman
Walter & George Bearman - Taken by John Readman 27 Oct 2003
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St Thomas of Canterbury Church
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BEARMAN George, Engine Room Artificer 4th Class M/17677, Royal Navy. HMS 'Pembroke'. Born Theddlethorpe, Lincs 1892 and died 15th March 1916. Son of (the late) George and Mary Bearman of Mumby, Lincs. Brother of Walter John Bearman. Commemorated HUTTOFT (ST MARGARET) CHURCHYARD. / Mumby St Thomas A naval funeral took place here [Huttoft] on Tuesday, the remains of George Bearman, who had responded to his country's call, but had succumbed to disease, being brought from Gillingham for interment. Four coastguardsmen, under Chief Divisional Officer Fletcher. Were the bearers. A full military escort was provided by the Northern Cyclists Company, and the gun carriage was drawn by eight horses. The coffin was covered by the Union Jack, surmounted with lovely spring flowers. The Rev, A. G. Malster, vicar of Manby, conducted the service in the church, and after the committal prayers the military fired the salute, and the "Last Post" was sounded. The greatest sympathy is felt for the widow and family, especially as the father lost his life in the Wells disaster and another son in the sinking of the Good Hope. The two surviving sons, clad in khaki-one direct from the war zone-took part in the obsequies. L&NLA 23rd March 1916 In loving and sorrowful memory of George Bearman, who died at the Royal Naval Hospital, Gillingham, March 15th, 1916, aged 24 years; also, his brother Walter John, lost on the H.M.S. Good Hope, Nov. 1st. 1914, aged 20 years L&NLA. 17TH March 1917 [Obits] BEARMAN Walter John, Stoker 2nd Class K/21160, Royal Navy. HMS 'Good Hope'. Born Theddlethorpe, Lincs 1894 and died 1st November 1914. Son of (the late) George and Mary Bearman of Mumby, Lincs. Brother of George Bearman. Commemorated PORTSMOUTH NAVAL MEMORIAL. 5. / Mumby St Thomas http://www.worldwar1.co.uk/coronel.html
THE GREAT WAR 1914 – 1918 / PRAY FOR THE SOULS OF / WALTER JOHN BEARMAN / H.M.S. GOOD HOPE / DIED NOVEMBER 11TH 1914 / AGED 20 YEARS / GEORGE BEARMAN / H.M.S. PEMBROKE / DIED MARCH 18TH, 1916 / AGED 24 YEARS. / MAY THEY REST IN PEACE
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{"url":"http:\/\/opentradingsystem.com\/quantNotes\/Orthogonality_across_scales_.html","text":"I. Basic math.\n II. Pricing and Hedging.\n III. Explicit techniques.\n IV. Data Analysis.\n V. Implementation tools.\n VI. Basic Math II.\n VII. Implementation tools II.\n 1 Calculational Linear Algebra.\n 2 Wavelet Analysis.\n A. Elementary definitions of wavelet analysis.\n B. Haar functions.\n C. Multiresolution analysis.\n D. Orthonormal wavelet bases.\n E. Discrete wavelet transform.\n F. Construction of MRA from scaling filter or auxiliary function.\n G. Consequences and conditions for vanishing moments of wavelets.\n H. Existence of smooth compactly supported wavelets. Daubechies polynomials.\n I. Semi-orthogonal wavelet bases.\n a. Biorthogonal bases.\n b. Riesz bases.\n c. Generalized multiresolution analysis.\n d. Dual generalized multiresolution analysis.\n e. Dual wavelets.\n f. Orthogonality across scales.\n g. Biorthogonal QMF conditions.\n h. Vanishing moments for biorthogonal wavelets.\n i. Compactly supported smooth biorthogonal wavelets.\n j. Spline functions.\n k. Calculation of spline biorthogonal wavelets.\n l. Symmetric biorthogonal wavelets.\n J. Construction of (G)MRA and wavelets on an interval.\n 3 Finite element method.\n 4 Construction of approximation spaces.\n 5 Time discretization.\n 6 Variational inequalities.\n VIII. Bibliography\n Notation. Index. Contents.\n\n## Orthogonality across scales.\n\nn this section we present a procedure for construction of dual wavelets with orthogonality across scales. The disadvantage of this construction is non-compactness of support for one of the wavelets . In the section ( Compactly supported smooth biorthogonal wavelets section ) we present a pair with compact support but without orthogonality across scales (property (d) below).\n\nProposition\n\n(Existence of wavelets with orthogonality across scales) Let be a GMRA with a compactly supported scaling function . There exists a scaling function : and the associated dual GMRA is equipped with the following properties.\n\n(a) .\n\n(b) , when .\n\nWe use notation , the closure is in .\n\n(c) , , .\n\n(d)\n\n(e) such that\n\nProof\n\nof existence of GMRA and (a).\n\nAccording to the proposition ( Property of transport 2 ), the function has the form for some numbers and finite . By the proposition ( Frame property 1 ) and definition ( Generalized multiresolution analysis )-5, is separated from 0. Therefore the function is in . It also has period 1. Therefore, we write for some .\n\nWe introduce according to the relationship By the proposition ( Existence of biorthogonal basis 1 ) we have biorthogonality of and . In addition hence is a Riesz basis on by the proposition ( Frame property 2 ).\n\nWe take inverse Fourier transform of : thus Therefore The inverse inclusion is a consequence of biorthogonality of and . Indeed, suppose there is an such that . We have for some numbers . Because of biorthogonality, Let Since we must have Let are numbers such that We have We obtained a contradiction. Hence, and by the formula ( Property of scale and transport 2 ) and definition ( Generalized multiresolution analysis )-4 we have\n\nProof\n\nof (b),(c),(d). We define and the same way we did in the definition ( Dual wavelets ). We get biorthogonality of and by the proposition ( Dual wavelets properties )-f. We also have ( Dual wavelets properties )-a,d,e: and (a) of the present proposition: From and we get and Then, by the formula ( Property of scale and transport 2 ), and by Then, by the formula ( Property of scale and transport 2 ), Thus (b) and (c). The (d) follows because, by proposition ( Dual wavelets properties )-f, and are bases in .\n\nProof\n\nof (e). For every we have where For each we have by the proposition ( Dual wavelets properties )-c and formula ( Property of scale and transport 2 ) we sum the above in and combine with and to obtain (e).\n\n Notation. Index. Contents.","date":"2018-11-21 06:25:05","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9234053492546082, \"perplexity\": 1984.1212112986816}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-47\/segments\/1542039747215.81\/warc\/CC-MAIN-20181121052254-20181121074254-00415.warc.gz\"}"} | null | null |
\section{Introduction}\label{sec:introduction}
Every wall confined flow is subject to wall shear stress, affecting the efficiency of many industrial systems such as pumps, turbines, heat exchangers or any application implying fluid circulation. Despite the considerable efforts in developing new methods over the years, measurement of wall shear stress remains a challenge, especially when both time and space resolution are required. Among the many available methods, the floating element is interesting due to the probe size and considerably large bandwidth \citep[sometimes up to 4\,kHz, see][]{padmanabhan1997}. However, spatial resolution of the floating element is generally limited by the overall electronic components surrounding the probe and those sensors can rarely measure at the same time the shear stress direction. The hot-film anemometer has also been widely used to assess wall shear rate in unsteady flows. On paper, hot-film frequency response stays flat up to a few kHz \citep{wietrzak1994wall}, but this value is largely weakened considering heat conduction through the wall, which also introduces a bias error. Regardless of the many adaptations developed over the last few decades (among other things: reduction of the substrate thermal conductivity, creation of a vacuum cavity below the sensor), this problem persists and accurate measurements under unsteady conditions are still an issue \citep{sheplak2004mems}. Natural convection caused by heat transfer to the fluid, known as the induced buoyancy, can also locally alter the flow conditions. \citet{he2011wall} attributed the large dispersions in their calibration data to this phenomenon, observing discrepancies as high as 10\,\% (turbulent pipe flow with $\Rey<18\,000$). Although flow direction can be assessed by arranging two or more hot-film sensors with different orientations, the poor probe sensitivity in the transverse direction limits its uses to small angles; such sensor configuration is usually reserved for detecting shear reversal rather than its direction \citep{bruun1995hot}.
The electrodiffusion (ED) method measures the electrolysis reaction rate between an electrode flush-mounted to a wall and a redox couple contained in the flow. The method is in many ways similar to the hot-film anemometry, where the local \textit{mass} transfer is measured instead of the heat transfer; the theory behind the two techniques overlaps in several aspects. Still, one major asset of the ED is the lack of heat loss to the wall, especially profitable in low convection flows. In their review of the wall shear stress produced by an impinging jet, \citet{phares2000wall} indeed concluded that the ED method provided `the most accurate data close to the stagnation point', as the ones from hot-film probes suffered from strong discrepancies. While the cutoff frequency associated with ED probes is rather low, adequate post-processing can correct the attenuation and phase shift of the sensor response in highly unsteady flows. In particular, by considering that the reaction at the probe interface is governed by the convection--diffusion equation, one can take advantage of the so-called \textit{inverse problem} to deal with the probe inertia. With this approach, the input wall shear rate is iteratively adjusted by solving the \textit{direct problem} (i.e. the convection--diffusion equation) until the numerical data converge to the experimental ones. According to \citet{rehimi2006inverse}, such method allows to accurately correct the probe response in high amplitude unsteady flows, including the case of shear reversal. The authors have demonstrated that this method outmatches every other post-treatments in two-dimensional flows. Considering its success, we propose an enhancement of the method adapted to three-dimensional flows able to capture the wall shear rate magnitude along with its direction in any unsteady flow when using a three-segment probe. The method is validated numerically for flows subjected to periodic and stochastic variations of the wall shear rate.
\begin{figure*}
\centering
\includegraphics[scale=0.95]{fig1.pdf}
\caption{Principle of the electrodiffusion (ED) method. (a) Under constant voltage, a time varying current $I(t)$ flows throw the loop cathode-solution-anode, generating concentration gradients at the electrodes surface from $C_0$ in the bulk to a concentration $c=0$ at the probe--solution interface. (b) Typical probes, viewed from above. From left to right: single, double (sandwich) and three-segment probes.}
\label{fig:1}
\end{figure*}
\subsection{Basic principles of the electrodiffusion method}
The ED method relies on the mass transfer between a redox couple ($O$--$R$) contained in a solution and two electrodes flush mounted to a wall (Fig.~\ref{fig:1}). The reaction is initiated by imposing a constant voltage between the anode and the cathode, where a concentration gradient gradually builds up at the electrodes--solution interface. The current $I$ flowing through the electrodes and electrolyte is then a function of the solution supply and is directly related to the wall shear rate $s$ under steady conditions. When streamwise convection is dominant, the relation $s\propto I^3$ typically holds over a certain voltage range, namely when the \textit{limiting current} condition is achieved \citep{hanr1996meas}; the electrode process then occurs at the maximal rate possible and the concentration at the probe surface is essentially null ($c_{y=0}=0$). Under this electrolysis process, mass transfer is manifested by an exchange of electrical charges between the $O$--$R$ species. While this transfer is normally assured by three methods (migration, diffusion and convection), a non-reactive or background electrolyte is usually added in excess to the solution so as to limit migration effects. The divergence of the resulting Nernst--Planck equation, which dictates the mass transfer at an electrode, results in the general convection--diffusion equation in absence of migration:
\begin{equation}
\pd{c}{t} + \vec{u}\cdot\nabla c = D\nabla^2 c,
\label{eq:CD}
\end{equation}
with $D$ the diffusion coefficient. The relation between \eqref{eq:CD} and measures of $I(t)$ can also be derived from the Nernst--Planck equation. Under the assumption of a Nernst diffusion layer\footnote{At the electrode surface, a stagnant layer of thickness $\delta_c$ is assumed; in other words, convection is neglected in this area, resulting in a frozen diffusion layer \citep{bard2001electrochemical}.}, only the diffusion term remains and the flux or reaction rate $J$ at the probe can be written as
\begin{equation}
J_{y=0} = \frac{I}{nFA} = -\frac{1}{A}\iint_{A}D\left.\pd{c}{y}\right|_{y=0}dA,
\label{eq:fluxJ}
\end{equation}
with $n$, $F$, $A$ the number of electron(s) involved in the reaction, the Faraday number and the probe area, respectively. The reaction is then said to be diffusion-controlled.
The fundamental principle behind the ED method is that the reaction occurs very close to the wall owing to the thinness of the concentration boundary layer (also called \textit{diffusion layer}) compared to the hydrodynamic one, so as to assume a linear velocity profile in the vicinity of the probe, $\vec{u}=\vec{s}y$, with $\vec{s}$ the two-dimensional wall shear rate. This is expected when the Schmidt number $\Sc=\nu/D$ is large\footnote{A typical value encountered is $\Sc\sim1000$.}, where $\nu$ is the kinematic viscosity. While two electrodes are needed for the process to occur, only the half-reaction arising at the working electrode will be of interest. The cathode is generally chosen as the working electrode, which will be referred to as the probe throughout the rest of the paper.
\subsection{Common post-treatment methods}
Various methods have been developed over the years to relate the measured current $I$ from an ED probe to the wall shear rate $s$ using assumptions on the flow or electrochemical conditions to model the process. When one only seeks a time averaged value, the L\'{e}v\^{e}que\xspace solution can be used, obtained from the analytical solution of the two-dimensional steady state convection--diffusion equation with linear velocity profile. The current can then be related to $s=\lVert\vec{s}\rVert$ through \eqref{eq:fluxJ}, where
\begin{equation}
I = k_\text{q} s^{1/3},
\label{eq:Ilev}
\end{equation}
with $k_\text{q}=0.80755nFAC_0l^{-1/3}D^{2/3}$ \citep{reiss1963expe} and $l$ is the rectangular probe size (cf. Fig.~\ref{fig:1}b). Equation \eqref{eq:Ilev} is also known as the \textit{quasi-steady method} and its validity is limited to slow time varying processes as the probe inertia is felt even at very low frequencies. The potential of ED probes to study wall turbulence first drove authors to develop models that would improve its frequency response, most of them based on the linearised turbulent fluctuations equation (among others: \cite{mitc1966stud,fort1971freq,mao1985use}). In particular, the ED probe transfer function derived by \citet{desl1990freq} can accurately correct this capacitive effect over a broad frequency range; its usage is however limited to small fluctuations on the wall shear rate as a result of the linear theory approximation. The most popular post-treatment for large amplitude unsteady flows is the one developed by \citet{sobolik1987simultaneous}, which was also derived a few years later in the work of \citet{wang1993approximate}. Commonly referred to as the \textit{Sobol\'ik\xspace method}, it basically corrects the quasi-steady wall shear rate $s_{\text{q}}$ using its time derivative, namely
\begin{equation}
s_{\text{sob}} = s_{\text{q}} + \frac{2}{3}\chis_{\text{q}}^{-2/3}\d{s_{\text{q}}}{t},
\end{equation}
with $\chi=0.80755^{-2}\pi^{-1}l^{2/3}D^{-1/3}$. Sobol\'ik\xspace method is simple and very efficient to correct for the probe inertia, but it fails when dealing with flow reversal. Techniques have been developed to tackle this issue (in particular, the works of \citet{pedley1976heat} and \citet{menendez1985use}), but none of them can match the efficiency of the inverse method to evaluate the magnitude of the wall shear stress in high amplitude unsteady flows. When one also seeks the flow direction, either double or three-segment probes can be used (see Fig.~\ref{fig:1}b), while for the former sensitivity to transverse flow is poor and the use of the so-called `sandwich' probe (as first developed by \citet{son1969velo}) is thus normally limited to flow reversal detection in low-frequency oscillating flows. Turbulent fluctuations in the transverse direction were also extensively investigated by modeling the two-segment probe response \citep[see][]{sirk1970limi, tour1978beha, desl2004near}, but the linear theory again involved limits such usage to low-amplitude perturbations and none have demonstrated the ability to measure the instantaneous two components of the wall shear rate. The three-segment sensor was first developed to fill this gap \citep{wein1987theory}. In steady or low-frequency flows, the probe can successfully detect local flow direction $\alpha$ with precision often better than $10\,^\circ$ with an appropriate calibration \citep{sobolik1990three}, but actually fails when unsteadiness is dominant due to the probe inertia (see Section~\ref{sec:valinv}). No direct method can currently correct the capacitive effect on each individual segment, thus explaining the three-segment sensor deficiency for instantaneous measurements. The inverse method was previously used with a sandwich probe by \citet{mao1992measurement}. The authors showed that shear reversal in a turbulent pipe flow is well captured by the method when using such a probe; however, no complementary measures were available to evaluate the actual precision of the method. Axial diffusion was also neglected in their model, hypothesis that is questionable near shear reversal phases and was blamed by the authors and others \cite{labraga2002wall} to cause discontinuities.
In this work, the inverse method is revisited. Taking advantage of the three-segment probe, both magnitude and direction of the wall shear stress can be assessed in high amplitude unsteady flows. This is possible by considering a second unknown in the inverse problem, which is the wall shear direction $\alpha$. In the following section, the direct problem will first be introduced, followed by a description of the inverse problem and algorithm. In Section~\ref{sec:numres}, simulated data are used to validate the inverse process in flows of growing complexity, including the case of a three-dimensional turbulent flow. Different probe geometries are also considered to investigate the impacts of the gap size and possible imperfections.
\section{Statement of the problems}
\subsection{Direct problem \label{sec:dirprob}}
\begin{figure*}
\centering
\includegraphics{fig2}
\caption{(a) Geometry and (b) boundary conditions used for the direct and the inverse problems. An overall diameter $D=50d$ and height $H=10d$ ensured that boundary conditions would not interfere with the probe reaction, even in cases of flow reversal. The inlet/outlet switches between Dirichlet ($C=1$) and Neumann ($\partial C/\partial n=0$) conditions depending on the flow direction $\alpha$. (c) Discretized null-gap three-segment probe (mesh G0 in Section \ref{sec:probdis}). Usage of small triangles near the probe edges are twofold: they help to manage the local strong concentration gradients, but they also serve for numerical stabilization of the problem without the need for a stabilization scheme. (d) Cut view in the $x-z$ plane of a typical mesh used. The three-segment probe is surrounded by the smallest elements.}
\label{fig:2}
\end{figure*}
The three-dimensional convection--diffusion equation with a parallel linear velocity profile $\vec{u}=\vec{s}y$ is considered. In the presence of periodic flow fluctuations characterized by a frequency $f$, the dimensionless form of \eqref{eq:CD} can be written as
\begin{multline}
\Sr\pd{C}{\tau} +SY\left(\sin\alpha\pd{C}{X} + \cos\alpha\pd{C}{Z}\right) = \\ \Pen^{-2/3}\left( \pdd{C}{X} + \pdd{C}{Z}\right) + \pdd{C}{Y},
\label{eq:cdadim3D}
\end{multline}
using the following dimensionless variables
\begin{gather}
\begin{array}{c}
X = \dfrac{x}{d}, \qquad Z = \dfrac{z}{d}, \qquad Y = \dfrac{y}{\delta}, \qquad \tau = tf, \\ \vspace{-5pt}\\
\Pen = \dfrac{\ol{s}d^2}{D}, \qquad \Sr = \dfrac{fd^{2/3}}{\ol{s}^{2/3}D^{1/3}}, \qquad S = \dfrac{s}{\ol{s}}, \qquad C = \dfrac{c}{C_0},
\end{array}
\label{eq:adim}
\end{gather}
where $\Sr$, $\Pen$ will be respectively referred to the Strouhal and P\'eclet numbers, while $\delta=d^{-1}\Pen^{1/3}$ is the diffusion layer thickness under Nernstian approximation and $\ol{(\sim)}$ refers to a time averaged quantity over one period. The direct problem consists of solving \eqref{eq:cdadim3D} for given $S$ and $\alpha$ using the domain and boundary conditions synthesized in Figs.~\ref{fig:2}(a,b). A mix Dirichlet--Neumann condition (referred to as `inlet/outlet') is applied on the boundary $X^2+Z^2 = D^2/4$, which imposes $\partial C/\partial n=0$ when $\vec{u}\cdot\vec{n}>0$ (outflow) and $C=1$ otherwise. The dimensionless flux at the probe surface can be represented by the Sherwood number, defined as
\begin{equation}
\Sh = \frac{Jd}{C_0D}
\label{eq:Shdef}
\end{equation}
which becomes, using \eqref{eq:fluxJ} and \eqref{eq:adim} for the segment $m\in\{0,1,2\}$ of a three-segment probe,
\begin{equation}
\Sh_m=\frac{\Pen^{1/3}}{A}\iint_{A_m}\left.\pd{C}{Y}\right|_{Y=0}dA
\label{eq:Shseg}
\end{equation}
with $A_m$ the area of the discretized segment $m$. Often, one is more interested in the more convenient modified Sherwood number, simply defined as $\Sh^*=\Sh\Pen^{-1/3}$. The problem is solved using the open-source finite element equation solver \texttt{FreeFem++} \citep{MR3043640} with the use of P1 and P2 tetrahedral elements. Considering the discontinuity of the boundary conditions at the probe edges, anisotropic triangles were opted to discretize the probe surface (see Fig.~\ref{fig:2}c) which greatly reduced the computational cost and helped to stabilize the problem. In fact, solution of the convection--diffusion equation is subject to spurious oscillations at high $\Pen$. Using elements of small size thus eliminates the need for classical upwinding techniques such as SUPG methods; those inevitably add diffusion contributions in the vicinity of the probe, which here is undesirable considering that diffusion is the actual reaction to measure. The form of \eqref{eq:cdadim3D}, being stretched in the $y$ direction, also allowed the use of anisotropic tetrahedral elements. Such effect is observed in Fig.~\ref{fig:2}(d). Metrics associated with the concentration field surrounding the probe were used to evaluate the anisotropy parameters and construct the meshes, thanks again to \texttt{FreeFem++}. The time derivative was discretized using a backward differentiation formula (BDF) scheme of first and second orders.
\subsection{Inverse problem \label{sec:invpro}}
The time evolution of the \textit{true} (indicated with the subscript `exp') wall shear rate magnitude $S_{\text{exp}}(\tau)$ and direction $\alpha_{\text{exp}}(\tau)$ are to be found, with $\Sh^*_{\text{exp}}(\tau)$ the only known information from, say, three-segment probe mass transfer measurements. For convenience, let $M_{m,i}=\Sh^*_{\text{exp},m,i}$ be the $\Sh^*$ measured by segment $m$ at time step $i$. The inverse method iteratively solves \eqref{eq:cdadim3D} by correcting the input values $S_i$ and $\alpha_i$ from time step $i$ to $T$ until a certain tolerance \texttt{tol} is reached. Then, one can expect the numerical conditions to represent the experimental ones well and so $S_i=S_{\text{exp},i}$, $\alpha_i=\alpha_{\text{exp},i}$. One of the most important aspects in a multidimensional inverse problem is the choice of the correction to be applied, which will affect both the convergence speed and stability of the algorithm, but also the smoothness and accuracy of the solution. For the case being, three $M_m$ measures are known at each time step and two variables are to be found. Hence, instead of using a classic Newton method, a Gauss--Newton algorithm is proposed. Let's consider the residual $r_m=M_m-\Sh^*_m$ at time step $i$ and the vector of unknowns $\vec{p}=[S,\alpha]$. Gauss--Newton algorithm will minimize the function $f=\sum r_m^2$ by using the following correction on vector $\vec{p}$:
\begin{equation}
\vec{p}^{(j+1)} = \vec{p}^{(j)} - (\mat{J}'\mat{J})^{-1}\mat{J}'\vec{r}^{(j)}
\label{eq:GN}
\end{equation}
with
\begin{equation}
\mat{J}=
\begin{bmatrix} \vspace{.3em}
\dpd{r_0}{S} & \dpd{r_0}{\alpha} \\ \vspace{.3em}
\dpd{r_1}{S} & \dpd{r_1}{\alpha} \\
\dpd{r_2}{S} & \dpd{r_2}{\alpha}
\end{bmatrix}
=
-
\begin{bmatrix} \vspace{.3em}
\dpd{\Sh^*_0}{S} & \dpd{\Sh^*_0}{\alpha} \\ \vspace{.3em}
\dpd{\Sh^*_1}{S} & \dpd{\Sh^*_1}{\alpha} \\
\dpd{\Sh^*_2}{S} & \dpd{\Sh^*_2}{\alpha}
\end{bmatrix}
\label{eq:jac}
\end{equation}
the jacobian matrix for iteration $j$. $\mat{J}$ can be interpreted as the sensitivity matrix, that is the sensitivity of the segment Sherwood number $\Sh^*_m$ to a variation of the parameter $p_n$, $n\in\{0,1\}$. One usually wants the magnitude of coefficients $J_{mn}$ to be as large as possible to increase accuracy in the estimates and reduce the effect of measurement errors. Hence, some smoothing methods exist to modify the matrix $\mat{J}$ when dealing with noisy experimental data so as to maximize the product $\mat{J'}\mat{J}$ \citep{ozisik2000inverse} or sometimes to remove singular values that make $\mat{J}$ ill-conditioned, using for instance SVD or other filtering methods \citep{shen2002solu,beck2016inve}. Nevertheless, such treatments were not needed and are not employed in the present paper.
The traditional method to evaluate the sensitivity coefficients $J_{mn}$ in the one-dimensional inverse problem (i.e. when only the wall shear rate magnitude $S$ is sought) is with the finite difference approximation \citep[see for example][]{rehimi2006inverse}
\begin{equation}
\pd{\Sh^*}{S} = \frac{\Sh^*(S+\epsilon S) - \Sh^*(S-\epsilon S)}{2\epsilon S},
\end{equation}
with $\Sh^*(S+\epsilon S)$ the Sherwood number under a wall shear rate $(1+\epsilon)S$, with $\epsilon\sim1\e{-5}$. Considering the present two-dimensional problem with $N=2$ unknowns, this process would require to solve \eqref{eq:cdadim3D} $2N$ additional times. A procedure also encountered in inverse problems is the use of sensitivity equations derived from the direct problem \citep{ozisik2000inverse}, obtained here by differentiating \eqref{eq:cdadim3D} with respect to $S$ and $\alpha$, namely
\begin{subequations}
\begin{multline}
\Sr\pd{C_1}{\tau} + SY\left(\sin\alpha\pd{C_1}{X} + \cos\alpha\pd{C_1}{Z}\right) = \Pen^{-2/3}\left( \pd{C_1}{X} + \pd{C_1}{Z}\right) \\
+ \pd{C_1}{Y} - Y\left(\sin\alpha\pd{C}{X} + \cos\alpha\pd{C}{z}\right)
\label{eq:C1}
\end{multline}
an
\begin{multline}
\Sr\pd{C_2}{\tau} + SY\left(\sin\alpha\pd{C_2}{X} + \cos\alpha\pd{C_2}{Z}\right) = \Pen^{-2/3}\left( \pd{C_2}{X} + \pd{C_2}{Z}\right) \\
+ \pd{C_2}{Y} - SY\left(\cos\alpha\pd{C}{X} - \sin\alpha\pd{C}{z}\right),
\label{eq:C2}
\end{multline}
\label{eq:C1C2}
\end{subequations}
with $C_1=\partial C/\partial S$ and $C_2=\partial C/\partial \alpha$. The sensitivity coefficients of \eqref{eq:jac} are accordingly derived by differentiating \eqref{eq:Shseg} and thus
\begin{equation}
J_{mn} = \frac{1}{A}\iint_{A_m}\left.\pd{C_{n+1}}{Y}\right|_{Y=0}dA.
\end{equation}
Such a procedure is in many ways more appealing than the finite difference one considering that the computation of $N$ additional equations is required instead of $2N$ and no parameter $\epsilon$ needs to be defined. The major benefit still arises from the fact that \eqref{eq:C1} and \eqref{eq:C2} are actually the same equation as \eqref{eq:cdadim3D} added with a known source term, given that $C$ was already solved for. Hence, no matrix reconstruction is needed by the finite element solver when solving \eqref{eq:C1C2}, reducing computation time of each sensitivity equation by a factor $\sim10$.
\begin{figure*}
\centering
\includegraphics{fig3.pdf}
\caption[Validation of the direct problem]{Validation of the direct problem. In (a), solution of the stationary case for increasing values of $\Pen$ with $S=1$ indicates that discrepancies with L\'{e}v\^{e}que\xspace solution \eqref{eq:Shlev} is below 1.3\,\% (0.5\,\% using P2 tetrahedral elements) for $\Pen>5\e{6}$. (b) The directional characteristics (marks, where symbols refer to distinct segments) of the three-segment probe shown in Fig.~\ref{fig:2}(c) are compared to the modeled ones
(solid lines, see \cite{wein1987theory}). Also shown is the variation of the total Sherwood number $\Sh^*_\text{tot}=\sum\Sh^*_m$ over a complete rotation of the probe (dashed--dotted line), which is below $0.1\%$ of the mean value.}
\label{fig:3}
\end{figure*}
The following iterative procedure is then proposed, given the starting guesses $\vec{p}^{(0)}$ from, for instance, the quasi-steady solutions. For each time step $i<T$,
\begin{enumerate}[(i)]
\item solve the direct problem (cf. Section~\ref{sec:dirprob}) for time $\tau_i$ using $S=p_0^{j}$ and $\alpha=p_1^{j}$ and compute $f$;
\item if $f<\texttt{tol}$, return to (i) for time $\tau_{i+1}$; otherwise
\item solve the sensitivity equations \eqref{eq:C1C2} and compute $\mat{J}$.
\item evaluate the new guesses $\vec{p}^{(j+1)}$ with \eqref{eq:GN} and return to (i) for iteration $j+1$.
\end{enumerate}
Note that for stabilization purposes, it is preferred to solve the first time step in steady condition ($\Sr=0$). Convergence speed is also very sensitive to the initial guesses, especially for $\alpha$, and the quasi-steady estimates are often not the best choices at high $\Sr$ number. For the one-dimensional inverse problem, \citet{rehimi2006inverse} suggest supposing that $S(\tau)=a\tau^2+b\tau+c$ on a short time interval and estimate the coefficients using the Levenberg--Marquardt method to ensure the start-up stability. For the present case, a line search method is coupled to the Gauss--Newton algorithm to ensure boundness of the process. When such approach is not sufficient (for instance, in some high-frequency cases), the safer but costlier conjugated gradient method is used instead of \eqref{eq:GN} to evaluate the corrections on $\vec{p}$. Most numerical methods and algorithms were implemented using procedures found in \cite{press2007numerical}. Moreover, a zero gradient verification is often preferred for the convergence criterion of step (ii), especially for high-frequency cases where the sensitivity coefficients are damped. As the main steps of the inverse process are very similar to the one-dimensional case, the reader is referred to other exhaustive sources for more details \citep[see][]{mao1991analysis,maquin99,ozisik2000inverse,rehimi2006inverse}. However, note that compared to most previous methods, a few iterations (denoted with superscript $(j)$) per time step are performed. Overall, this ensures better convergence properties.
\section{Results and discussion\label{sec:numres}}
Validation of the direct problem is first performed by analyzing the stationary case, i.e. equation \eqref{eq:cdadim3D} with $\Sr=0$. Considering a perfectly circular three-segment probe with negligible gaps (see Fig.~\ref{fig:2}c) and equivalent length $l_\text{eq}=0.81356d$ \citep{hanr1996meas}, the non-dimensional variant of the L\'{e}v\^{e}que\xspace solution \eqref{eq:Ilev} is formulated as
\begin{equation}
\Sh^*_\text{q}=k^*S^{1/3},
\label{eq:Shlev}
\end{equation}
with $k^*=0.86505$, which value is expected when the tangential and transverse diffusion terms in \eqref{eq:cdadim3D} are negligible, that is for high P\'eclet numbers. As observed in Fig.~\ref{fig:3}, discrepancies with \eqref{eq:Shlev} is negligible when $\Pen\gtrsim1\e6$. To assess the direction $\alpha$ using a three-segment probe, its directional characteristics are required, obtained when performing the so-called directional calibration (as modeled by \citet{wein1987theory}). Under a steady flow, the probe signal is recorded while being gradually rotated; then, each segment relative signal $\Sh^*_m/\Sh^*_\text{tot}$ can be represented with a Fourier series expansion in $\alpha$ to deal with the probe geometry and imperfections. Such calibration was performed numerically to validate the directional characteristics of the discretized three-segment probe. Only small deviations are observed in Fig.~\ref{fig:3}(b) with the modeled characteristics of the perfect sensor \citep{wein1987theory}.
\subsection{Validation of the inverse problem \label{sec:valinv}}
The use of the null-gap three-segment probe only being theoretical, a sensor with small gaps (see Fig.~\ref{fig:9}a) is used in the following section. Nevertheless, the use of the null-gap geometry in the previous section was necessary for validation purposes, considering that the L\'{e}v\^{e}que\xspace solution is not valid with an imperfect disk. Note that the mesh generation procedure was the same for all geometries.
Validation of the inverse algorithm was accomplished by first simulating data using the direct problem for various flow parameters and then applying the inverse procedure of Section~\ref{sec:invpro}. Test cases are here based on the periodic fluctuation of both $S$ and $\alpha$, as per the following equations:
\begin{subequations}
\begin{align}
S(\tau) &= 1 + \beta_S\sin(2\pi\tau), \label{eq:SalphaA}\\
\alpha(\tau) &= \alpha_0 + \beta_\alpha\sin(2\pi\tau + \phi).
\end{align}
\label{eq:Salpha}
\end{subequations}
\begin{table}[h!]
\centering
\caption{Parameters used in the simulations, as per equations \eqref{eq:Salpha}. }
\begin{tabular*}{0.4\textwidth}{@{\extracolsep{\fill}} cccccc}
\toprule
Case & $\Sr$ & $\beta_S$ & $\beta_\alpha$ & $\alpha_0$ & $\phi$ \\
\midrule
0 & 1.5 & 0.5 & 0 & $\pi/3$ & 0 \\
1 & 0.1 & 1.5 & 0 & $\pi/3$ & 0 \\
2 & 1.5 & 1.5 & 0 & $\pi/3$ & 0 \\
3 & 1.5 & 0.5 & $\pi/4$ & $\pi/2$ & $\pi/6$ \\
4 & 2 & 0.9 & $2\pi/3$ & $\pi/2$ & $\pi/6$ \\
5 & 0.5 & 0.5 & $\pi/4$ & $\pi/2$ & $\pi/6$ \\
\bottomrule
\end{tabular*}
\label{tab:parnum}
\end{table}
\begin{figure}[h!]
\centering
\includegraphics{fig4}
\caption[Inverse results 1]{Results of the inverse algorithm for constant direction $\alpha$, moderate amplitude and high-frequency fluctuation on $S$ (case 0, see Table~\ref{tab:parnum}). (a) After less than one period, $S$ and $\alpha$ converge on the true values (indicated by the dashed lines). Slower convergence for $\alpha$ could be explained by the lesser sensitivity of the back segment; convergence of both $\alpha$ and $\Sh^*_0$ appear in fact to be linked as observed in (b).}
\label{fig:4}
\end{figure}
Simulations parameters are detailed in Table~\ref{tab:parnum}. For all cases, a P\'eclet number $\Pen~\to~\infty$ was used to offer the best comparison with other post-treatment methods since all are based on the L\'{e}v\^{e}que\xspace solution. P1 (linear) tetrahedral elements instead of P2 were employed for the tests. This does not affect the results as the same mesh and element type are used in both direct and inverse problems. Main drawback concerns the sensitivity equations, resulting in a less sensitive process and may thus imply one or two additional iterations for convergence; still, this greatly reduces computational costs ($\sim 10$ times faster). Note that the same frequency was used for $S(\tau)$ and $\alpha(\tau)$ in \eqref{eq:Salpha} to simplify the first step validation. This, however, does not limit the proposed algorithm as it will be exposed in Section \ref{sec:nonPer}.
\begin{figure*}[h!]
\centering
\includegraphics{fig5}
\caption[Inverse results 2]{Comparison of different post-treatment methods in two flows involving shear reversal. (a) In the low-frequency case 1 (see Table~\ref{tab:parnum}), the combined information of $S_{\text{sob}}$ and $\alpha_{\text{q}}$ still gives a decent approximation of the true wall shear rate, although the reversal period is out of phase; (b) at larger $\Sr$ (case 2), no valuable information can be retrieved from $S_{\text{sob}}$ in the reversal period, while the quasi-steady method $\alpha_{\text{q}}$ does not detect at all the shear reversal. In both cases, the inverse method shows almost perfect results. Only the last period of the inverse process is shown; two or more periods are sometimes needed for a suitable convergence depending on cases and initial guesses. Note that only the magnitude of $S$ is shown for visualization; when $S$ becomes negative (in cases with $\beta_S>1$), a $180\deg$ offset is added to $\alpha$.}
\label{fig:5}
\end{figure*}
The inverse method efficiency and convergence speed can first be appreciated in Fig.~\ref{fig:4} for the constant direction, moderate shear fluctuation amplitude and high-frequency case 0, where only a few time steps are needed to converge on both the imposed values of $S$ and $\alpha$. Note that only part of the time steps used in the simulations are shown in all figures. In Fig.~\ref{fig:4}(b), one can notice that more time steps are needed for $\Sh^*_0$ to properly converge; being in the wake of the other two segments, the sensitivity coefficients related to this segment are lower. While this affects both sensitivity on $S$ and $\alpha$, the latter is more apparent considering the constant direction.
Since all post-treatment methods give good results for low $\Sr$ without shear reversal, the following examples are limited to flows exhibiting either high $\Sr$, shear reversal, periodic fluctuation of $\alpha$ ($\beta_\alpha\neq0$) or a combination of the former, namely situations where both quasi-steady and Sobol\'ik\xspace solutions fail. Also note that for the remainder of the paper, only results from the last period of periodic processes are shown, after which no further convergence improvements were observed. Cases 1 and 2 (Fig.~\ref{fig:5}) involve shear reversal in low- and high-frequency ranges, respectively. Although Sobol\'ik\xspace method theory is limited for flows with constant direction, the combine information of $S_{\text{sob}}$ and $\alpha_{\text{q}}$ actually suggests the presence of shear reversal, yet suffering from an appreciable phase lag as observed in Fig.~\ref{fig:5}(a). At higher $\Sr$ however, the quasi-steady method cannot detect at all the reversal period and no valuable information is neither obtained from $S_{\text{sob}}$ under such conditions (Fig.~\ref{fig:5}b). One can notice that $S_{\text{inv}}$ and $\alpha_{\text{inv}}$ converge almost perfectly on the imposed fluctuations in both cases.
\begin{figure}
\centering
\includegraphics{fig6}
\caption[Sensitivites]{$\Sh^*_m$ (dashed lines) and absolute values of the $S$ sensitivity coefficients $J_{m0}$ (solid lines) for (a) case 1 and (b) case 2. Refer to Fig.~\ref{fig:5} for segments numbering. $J_{10}$ is not shown in (a) for visualization purposes.}
\label{fig:6}
\end{figure}
\begin{figure*}
\centering
\includegraphics{fig7}
\caption[Inverse results 3]{Large amplitude, high-frequency fluctuations on both magnitude $S$ and direction $\alpha$ of the imposed wall shear rate, for (a) case 3 and (b) case 4 (see Table~\ref{tab:parnum}). Dashed lines indicate the true constraints.}
\label{fig:7}
\end{figure*}
Evolutions of $\Sh^*_m(\tau)$ and $J_{m0}(\tau)$, the $S$ sensitivity coefficients, are plotted in Fig.~\ref{fig:6}. A rule of thumb is that the larger the $\Sh^*_m$, the higher this segment sensitivity will be, at least for quasi-steady processes. This is indeed observed for case 1 (Fig.~\ref{fig:6}a): as the shear reverses, the signal on the back segment $\Sh^*_0$ becomes the largest and so does its sensitivity magnitude $|J_{00}|$, which was essentially null for $\tau\lesssim1.6$. In the high-frequency case however (Fig.~\ref{fig:6}b), the duration of the shear reversal is too short considering the inertia of the process; the lagged sensitivity $|J_{00}|$ only slightly increases and $\Sh^*_0$ always stays with the lowest signal. Note that a similar trend is expected for the $\alpha$ sensitivity coefficients $J_{10}$ and $J_{12}$ (not shown here). Also notice the large drop of sensitivity between the two cases of Fig.~\ref{fig:6} (close to a factor $\sim10$), affecting the inverse process on both its stability and convergence speed as more iterations and time steps are needed for $\Sh^*_m$ to converge on $M_m$. As a matter of fact, the more stable conjugated-gradient algorithm is required to procure the results shown for case 2; otherwise, oscillations like those observed on $\alpha$ after shear reversal (Fig.~\ref{fig:5}b) are more frequent and intense. The inverse method is also flawless when involving large amplitude fluctuations on both $S$ and $\alpha$ at high-frequency, as observed in Fig.~\ref{fig:7} for cases 3 and 4. Here again, quasi-steady and Sobol\'ik\xspace methods exhibit strong departure from the imposed shear rate. Note that for the constant direction cases 1 and 2, the use of the three-segment probe is not essential as the problem becomes one-dimensional; the traditional sandwich probe (see Fig.~\ref{fig:1}b) is more convenient for treating shear reversal cases. Results shown although demonstrate that the proposed inverse method can deal with a very steep variation of the unknown variables such as the $\alpha(\tau)$ step-like signals in cases 1 and 2.
\begin{figure}
\centering
\includegraphics{fig8}
\caption[$\beta_\alpha$ effect on $\ol{\Sh}$]{Variation of $\zeta=\ol{\Sh^*}/\Sh^*_\text{std}$ with $\Sr$ for a constant amplitude (a) $\beta_S=0.5$ and (b) $\beta_\alpha=\pi/4$. Values are $\beta_\alpha=\{\pi/12,\,\pi/6,\,\pi/4,\,\pi/2,\,2\pi/3\}$ and $\beta_S=\{0.5,\,0.7,\,0.9\}$ in (a) and (b), respectively. $\zeta$ is calculated using the time averaged $\Sh^*$ over one period of the solicitation.}
\label{fig:8}
\end{figure}
\begin{figure*}[t]
\centering
\includegraphics[scale=0.95]{fig9}
\caption[Gap effect]{Different geometries used to discretize the three-segment probe. (a) Smallest gap with a size equivalent to $g/4$; (b) largest gap, with the size $g$ close to the real probe G3; (c) discretization of the real probe geometry, which was shaped using a contour detection algorithm on (d), the optical microscope photograph of a real three-segment probe. All meshes were constructed so the total area of the three segments would respect $A=\pi/4$, that is the area of the equivalent null-gap probe G0 (Fig.~\ref{fig:2}b) with $d=1$.}
\label{fig:9}
\end{figure*}
\begin{figure*}[h!]
\centering
\includegraphics{fig10}
\caption[Gap effet on inverse results]{Effect of the probe geometry on the inverse method results for (a) case 5, (b) case 2 with $\alpha_0=\pi/2$ and (c) case 4, here with $\Pen=1\e{5}$. In all cases, results using G2 are better than with the null-gap geometry G0, yet offering a decent estimate of the true wall shear rate (illustrated with dashed lines). Phase lag and amplitude attenuation are nonetheless apparent, especially in the shear reversal period of case 2, justified in particular by the form of the filled segment $\Sh$ number (bottom figures). Using geometry G2 with large gaps, the convergence is considerably better. Note that the same effect occurs on the other segments, yet at a lesser extent. Results using G1 (not shown here) are very similar to those with G0.}
\label{fig:10}
\end{figure*}
It is interesting to note that in both cases 3 and 4 the time average $\ol{S_{\text{q}}}$ is shifted from the expected unitary value ($\ol{S_{\text{q}}}\neq1$). Recalling $\eqref{eq:Shlev}$, $S_{\text{q}}$ is calculated from the total Sherwood number $\Sh^*_\text{tot}=\sum\Sh^*_m$. As a result of the probe imperfections, the value of $k^*$ for mesh G1 (cf. Fig.~\ref{fig:9}a) differs from the theoretical null-gap geometry and is obtained by solving the stationary direct problem with $S=1$ and $\Pen\to\infty$, where in such case $k^*=\Sh^*_\text{tot}$. Although Fig.~\ref{fig:3}(b) exposes a slight variation of $\Sh^*_\text{tot}$ with $\alpha$ for a constant shear rate, this variation is not sufficient to explain the shift of $\ol{S_{\text{q}}}$ as seen in Fig.~\ref{fig:7}. The offset actually arises considering that the ratio
\begin{equation}
\zeta=\ol{\Sh^*}/\Sh^*_\text{std}<1
\label{eq:zeta}
\end{equation}
for the unsteady case, with $\Sh^*_\text{std}$ the steady Sherwood number measured under corresponding conditions (i.e. same $\Pen$ and $\alpha_0$, $\Sr=0$). Fig.~\ref{fig:8} exposes this effect for a constant $\beta_S$ value in (a). At low $\Sr$, $\zeta$ is only slightly affected by variation of $\beta_\alpha$ whereas it largely depends on $\beta_S$ as observed in (b); values at $\Sr\to0$ actually tend to the one-dimensional case ($\beta_\alpha=0$) and are indeed fairly close to the ones obtained by \citet{kaip1983unst} for the one-dimensional shear rate case. For increasing values of $\beta_\alpha$ however, the $\zeta$ evolutions with $\Sr$ considerably differ since they do not converge to a value $\zeta=1$ at high $\Sr$\footnote{Tested up to $\Sr=50$ for the case $\beta_S=0.5$, $\beta_\alpha=\pi/4$, where $\zeta=0.957$.} as observed by \citeauthor{kaip1983unst}: the ratio decreases for larger $\beta_\alpha$ and smaller $\beta_S$. With $\zeta\neq1$, the steady calibration parameter $k^*$ then leads to an erroneous mean wall shear rate $\ol{S_{\text{q}}}$, altering both $S_{\text{q}}(\tau)$ and $S_{\text{sob}}(\tau)$ as shown in Fig.~\ref{fig:7}. Note that while those results stand for the geometry of Fig.~\ref{fig:9}(a), the trends are similar for the null-gap geometry. $\zeta$ also varies only slightly with $\alpha_0$.
\subsection{Influence of the probe discretization \label{sec:probdis}}
When treating experimental data from a real three-segment sensor, one could use the actual geometry of the probe in the mesh construction in order to procure simulations as faithful as possible. Yet, taking into account the surface imperfections brings additional computational costs, both in the time committed to mesh generation and in the simulations themselves as more elements may be needed for a proper discretization. Respect of the gaps dimension in the simulated geometry might actually be the most important element in the process. To verify that statement, the two meshes of Figs.~\ref{fig:9}(b,c) were generated, namely G2 and G3. The geometry of the former consists in a perfect three-segment probe with regular gaps of dimension $g$ close to that of a real sensor; the latter is the real geometry itself, retrieved from a contour detection on an optical microscope photograph of the sensor (Fig.~\ref{fig:9}d). To simulate experimental conditions, mesh G3 was therefore used in the manner of Section~\ref{sec:valinv} to generate $M_m$ data using the direct problem for three different cases. Both meshes G0\footnote{As the inverse method results for meshes G0 (see Fig.~\ref{fig:2}c) and G1 are very similar, the latter are not presented. Also note that if one would use mesh G3 in the inverse problem, nearly perfect results are expected as the same mesh would be used in both direct and inverse problems.} and G2 were then used separately in the inverse problem to obtain the corrected time evolutions of $S$ and $\alpha$ corresponding to the simulated $M_m$. To account for the differences in $k^*$ exposed in Section~\ref{sec:valinv} for the different meshes, a scaling factor of the form $k^*_{\text{G}i}/k^*_\text{G3}$, $i\in\{0,2\}$, was applied on the $M_m$ data. Using this procedure, the impact of the geometry is inspected.
\begin{figure*}[th!]
\centering
\includegraphics[]{fig11}
\caption{Two-component wall shear rate extracted from a DNS database of a turbulent Poiseuille flow at $\Rey=1\e{4}$ (colored curves). Results of the inverse method for the high $\Pen$ case are illustrated with thin black lines for both $S$ and $\alpha$. A close-up of the dashed rectangle region is presented in Figs.~\ref{fig:12} and \ref{fig:13}. Values for the dimensionless time $\tau=t^*\ol{s^*}\Pen^{-1/3}$ on the top and bottom abscissae concern the low and high $\Pen$ cases, respectively.}
\label{fig:11}
\end{figure*}
Results for cases 5, 2 and 4 (here with $\alpha_0=0$ and $\Pen=1\e{5}$, see Table~\ref{tab:parnum}) are shown in Fig.~\ref{fig:10}. In all three examples, the mesh with realistic gaps G2 provides a better representation of $S$ and $\alpha$, in particular for case 2 near the shear reversal. As the proposed inverse method is based on minimizing the residuals $r_m$ (see Section~\ref{sec:invpro}) of all three segments, a compromise is unavoidable when the time evolution of the experimental data $M_m$ is complex like the one of case 2, characterized by two adjacent inflection points as seen in the lower Fig.~\ref{fig:10}(b). The absence of gaps in G0 cannot allow such evolution for the back segment Sherwood number and the best fit obtained is largely distorted. The convergence is somewhat better for the two other segments (not shown here), hence providing decent results for $S$ and $\alpha$. The major drawback is the phase lag and damping especially observable in the shear reversal period. With appropriate gaps, $\Sh^*_m(\tau)$ using G2 is remarkably more accurate, providing very good results for both $S$ and $\alpha$ even in the intense flow conditions of case 4 (Fig.~\ref{fig:10}c). The use of G0 here brings additional stabilization issues, manifested by sharp oscillations on $S$ and $\alpha$. Thus, for a real three-segment geometry without excessive imperfections like the one of Fig.~\ref{fig:9}(d), a perfect geometry with appropriate gaps would be an adequate trade-off between meshing complexity and inverse method results, although a mesh modeled on the actual geometry like G3 is always preferred when achievable. Still, Fig.~\ref{fig:10}(a) also illustrates that discrepancies using the null-gap geometry G0 could still be acceptable for many applications involving a two-dimensional oscillating shear rate.
\subsection{Non-periodic flow \label{sec:nonPer}}
\begin{figure*}[t]
\centering
\begin{minipage}{.48\textwidth}
\centering
\includegraphics[]{fig12}
\caption{Results in the close-up region of Fig.~\ref{fig:11} for $\Pen=1.2\e{7}$. See Fig.~\ref{fig:7} for legend. Dashed lines indicate the true constraints.}
\label{fig:12}
\end{minipage}%
\begin{minipage}{.04\textwidth}
\hfill
\end{minipage}%
\begin{minipage}{.48\textwidth}
\centering
\includegraphics[]{fig13}
\caption{Results in the close-up region of Fig.~\ref{fig:11} for $\Pen=1.2\e{5}$. See Fig.~\ref{fig:7} for legend. Dashed lines indicate the true constraints.}
\label{fig:13}
\end{minipage}
\end{figure*}
While previous test cases were limited to periodic flows, the proposed inverse method can deal with stochastic variations of the wall shear rate magnitude and direction as those observed in turbulent flows. Hence, a direct numerical simulation (DNS) was performed\footnote{The finite difference solver \texttt{Incompact3d} \citep{incompact3d-0} was used for the DNS.} to generate a velocity database for the three-dimensional turbulent channel flow. The time evolution of the two-component wall shear rate was extracted at an arbitrary wall position (see Fig.~\ref{fig:11}) and then used to solve the direct problem and generate $M_m$ data for this turbulent flow.
Instead of using a Strouhal number in the convection--diffusion and sensitivity equations, the dimensionless time in \eqref{eq:adim} is replaced with
\begin{equation}
\tau = t\ol{s}\Pen^{-1/3}
\label{eq:tauInst}
\end{equation}
or, using the dimensionless DNS variables (here represented with starred coefficients),
\begin{equation}
\tau = t^*\ol{s^*}\Pen^{-1/3}.
\label{eq:tauInst0}
\end{equation}
With such a parameter, a unitary coefficient then replaces the Strouhal number in front of the time derivative of equations \eqref{eq:cdadim3D} and \eqref{eq:C1C2} (equivalent to $\Sr=1$). $s^*$ was evaluated using finite difference approximation in the viscous sub-layer where a linear velocity profile was observed. Averaging was performed over the entire period shown in Fig.~\ref{fig:11} to evaluate $\ol{s^*}$. One can notice from \eqref{eq:tauInst0} that a higher $\Pen$ will decrease the resulting time step $\Delta\tau$ for the ED analysis, thus creating a more intense case for the inverse method considering its convergence properties are lessened with smaller time steps \citep{ozisik2000inverse}. Two values for the P\'eclet number were tested, namely $\Pen=1.2\e{7}$ and $\Pen=1.2\e{5}$, which respectively correspond to mean wall shear rates of \SI{36000}{\per\second} and \SI{360}{\per\second} provided that the typical values $d=0.5\,$mm and $D=7.5\e{-4}$\,$\si{\milli\meter\squared\per\second}$ are used \citep{sobolik1998calibration}. The Reynolds number $\Rey=Uh/\nu$ used in the DNS was $\Rey=1\e{4}$, with $U$, $h$ the average cross-sectional velocity and the channel height, respectively.
To simulate experimental ED conditions, a procedure similar to that of Section~\ref{sec:probdis} was adopted. The $M_m$ data were first generated using mesh G3 while G2 was used to solve the inverse problem. One could see this additional complexity as the inevitable geometrical discordance between a real probe and the discretized one, considering for instance inactive areas on the sensor. Overall results for the high $\Pen$ case are presented in Fig.~\ref{fig:11} (where the inverse problem was started at $\tau=0.45$) while Figs.~\ref{fig:12} and \ref{fig:13} show a close-up view on the results for $\Pen=1.2\e{7}$ and $\Pen=1.2\e{5}$, respectively. As per \eqref{eq:tauInst0}, the corresponding dimensionless time is $\Pen$ dependent; thus, the same DNS data is here characterized by two time evolutions (top and bottom abscissae in Fig.~\ref{fig:11}). A very good agreement is observed with the imposed wall shear rate for both $S$ and $\alpha$ in the two cases. The unstable character of the inverse method is well illustrated in Fig.~\ref{fig:11} by the large oscillations in the first tenth time steps, where boundness is ensured using a line search method; otherwise, the process would likely diverge. Time step size is also critical, where larger steps tend to stabilize the process and damp the oscillations. Only one out of four time steps from the simulated turbulent data was indeed used, which could explain the small discrepancies with the imposed solicitations. Note that the distinct meshes used in the data generation and inverse problem also inevitably introduces a certain degree of error, which most likely cannot be accounted for. This may also explain why in Fig.~\ref{fig:12}(c) an offset is observed between the lower $\Sh^*_m$ curve and its relative $M_m$. It is interesting to note the smooth and damped evolution of each segment signal $M_m$ in Fig.~\ref{fig:12}(c) for such unsteady flow, being a consequence of the severe inertia of the diffusion layer which, without usage of the inverse method, could hardly be accounted for. Such damping on the $M_m$ signals also justifies why the inverse method is so sensitive to noise; the use of filtering techniques thus appears to be essential when dealing with real experimental data. Besides, one can notice from Fig.~\ref{fig:12} that the straightforward Sobol\'ik\xspace correction still procures acceptable results for $S(\tau)$, while the quasi-steady method is highly damped. At lower $\Pen$, one can notice from the $M_m$ curves in Fig.~\ref{fig:13}(c) that the probe is far more responsive to the imposed fluctuations; a slightly better agreement is also observed on the inverse results (Fig.~\ref{fig:13}a,b), although this effect is more apparent for the quasi-steady and, to a lesser extent, Sobol\'ik\xspace methods. The reduced $\Pen$ also makes the inverse process less sensitive to noise and start-up instabilities.
\section{Concluding remarks}
An inverse problem algorithm coupled with the three-dimensional convection--diffusion equation is proposed in order to assess both magnitude and direction of the wall shear rate using electrodiffusion probes in high amplitude unsteady flows. The method was first validated and tested in flows of increasing complexity using simulated data. Results demonstrate that the inverse process not only surpasses all other post-treatment methods, but is the only valid one when dealing with shear reversal, periodically varying wall shear rate direction and turbulent flows, especially regarding the instantaneous shear direction. Numerical discretization of a real three-segment probe was also inspected. When the actual probe geometry is not accessible or easily discretized, a perfectly circular geometry with realistic interstices is suggested, which should offer satisfying results in most applications. Experimental work should be performed to complete the validation process and for further improvements of the two-dimensional inverse problem.
\section*{Acknowledgements}
The authors would like to acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Fonds de recherche du Qu\'ebec - Nature et technologies (FRQNT). A most grateful thanks to Prof. V. Sobol\'ik, LaSIE Universit\'e de La Rochelle, for valuable advice and teaching of the electrodiffusion method and to Prof. A. Garon, Polytechnique Montreal, for the many recommendations regarding the finite element method.
\section*{References}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,501 |
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"redpajama_set_name": "RedPajamaC4"
} | 8,946 |
Євге́н Петро́вич Веденьков ( — ) — геоботанік, активний діяч у галузі охорони природи, понад 25 років пропрацював у заповіднику «Асканія-Нова».
Життєпис
Євген Петрович Веденьков народився 16 березня 1927 року в с. Криуліно Красноуфимського району Свердловської області в селянській родині. Його батька — Єлохіна П. О. — в 1933 р. разом з родиною заслали до Омської обл., де батьки незабаром померли від тифу, а діти потрапили до дитячих будинків, звідки їх зуміла забрати в 1936 р. на батьківщину бабуся — Веденькова М. Т.
У 1942 р. Євгена мобілізували до Красноуфимського залізничного училища і після дострокового випуску він працював спочатку кочегаром, а потім помічником машиніста. Після закінчення війни продовжив освіту в Красноуфимському сільськогосподарському технікумі, а потім з відзнакою закінчив плодоовочевий факультет Ленінградського сільськогосподарського інституту (1948—1953). При рідному інституті закінчив аспірантуру і успішно захистив в 1956 р. дисертацію — «Досвід будівництва та використання парників на технічному обігріві в господарствах Московської та Ленінградської областей», опублікував близько десятка робіт, присвячених впливу інтенсивності світла в початкові фази розвитку томатів. У вересні 1956 р. побажав працювати на цілині і півтора року пропрацював на Північно-Казахстанській дослідній станції. У 1958 р. пройшов за конкурсом у Білоцерківський сільськогосподарський інститут на кафедру селекції та насінництва. Наступного року перейшов на роботу в щойно організований Акмолинський, пізніше Целиноградський сільськогосподарський інститут на аналогічну кафедру. У 1964 р. здобув вчене звання доцента.
У серпні 1965 р. Євген Петрович за конкурсом зайняв посаду старшого наукового співробітника заповідного степу в УНІІЖ степових районів «Асканія-Нова». Тут він самостійно студіює основи геоботаніки, вивчає місцеву флору і результати своїх досліджень оприлюднить згодом у 70 публікаціях. Йому довелося займатися залужением перелогів і старих доріг, охороною степу від овечого випасу і невпорядкованого сінокосіння, браконьєрами, єгерської службою. Постійною помічницею Євгена Петровича у всіх трудах була його дружина Олександра Георгіївна. Особливо багато ним зроблено для організації геоботанічного картографічного моніторингу заповідного степу і відновлення залежів. Спільно з ботаніком В. Г. Водоп'яновою він реінвентаризував флору вищих рослин природного ядра заповідника. Протягом 1965—1987 рр. Євген Петрович займав різні посади в інституті тваринництва — від старшого наукового співробітника до завідувача відділом цілинного степу і був беззмінним науковим керівником з природоохоронної тематики. Навесні 1987 р. по віком пішов на пенсію. У 1995—1998 рр. запрошений як старший науковий співробітник на роботу в Біосферний заповідник «Асканія -Нова», де здійснив картування рослинності залежів і заповідної ділянки «Старий».
Нагороди
Медаль «За освоєння цілинних земель» (1962),
Почесна Грамота Президії ВР УРСР (1979),
знак «Відмінник охорони природи УРСР» (1981),
орден «За заслуги» III ступеня (1998).
Публікації
Про нього
Евгений Петрович Веденьков (Некролог)
Примітки
Посилання
Електронічна книжниця
Уродженці Свердловської області
Українські екологи
Українські ботаніки
Кандидати сільськогосподарських наук України
Відмінники охорони природи України | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,233 |
Q: button that works with either click or pressing enter I have only been able to get a button to work by creating 2 seperate events:
$('#loginSubmit').click (function ()
{
var userName = $('#userName').val();
var password = $('#password').val();
event.preventDefault();
$.ajax({
type: "POST",
url: "auth.php",
data:"userName="+userName+"&password="+password,
success: function(result)
{
//$('#mainBody').html(result);
window.location.replace('chooseGroup.php');
}
})
});
$('input').keypress(function(event)
{
if (event.which == 13) {
var userName = $('#userName').val();
var password = $('#password').val();
event.preventDefault();
$.ajax({
type: "POST",
url: "auth.php",
data: "userName="+userName+"&password="+password,
success: function(result)
{
//$('#mainBody').html(result);
window.location.replace('chooseGroup.php');
}
})
}
})
});
html:
<div class='Lrow'><input type='button' id='loginSubmit' value='Login'></div>
i know there is probably a better way. Id love to hear it. In any event, in the keypress function "event" is undefined if i use mozilla browser. this works fine in chrome. Any thoughts?
A: Put the common code into a function.
var mySubmitFunction (event) {
//the code
}
$('#loginSubmit').on("click", mySubmitFunction );
$('input').keypress(function(event){
if (event.which == 13) {
mySubmitFunction(event);
}
});
BUT there is a better way without listening to clicks/enter key. The better way is to let the form do what it wants.
Forms will submit on enter when you write it correctly. You just to add a submit button and an onsubmit event. You cancelling the submission there and make your Ajax call. Set the button type to submit and it should work. Bonus is if JS is disabled, form still submits to the server.
$("#YourForm").on("submit", function(event){ /* code here */ });
A: Put your code in a function Eg: ajaxSubmit() then use jquery on to call your function
function ajaxSubmit(){
var userName = $('#userName').val();
var password = $('#password').val();
event.preventDefault();
$.ajax({
type: "POST",
url: "auth.php",
data: "userName="+userName+"&password="+password,
success: function(result){
//$('#mainBody').html(result);
window.location.replace('chooseGroup.php');
}
});
}
$('#loginSubmit').on("click", ajaxSubmit );
$('#loginSubmit').on("click", function(event){
if (event.which == 13) {
ajaxSubmit(event);
}
});
A: On method takes one or more params as event name as the following:
$('#loginSubmit').on("click keypress", function(event){
if (event.type == "keypress" ) {
if(event.which == 13)
{
put your code here or call function
}
}
else//click event
{
put your code here or call function
}
});
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,466 |
The "Acidobacteriia" is a class of Acidobacteriota.
Phylogeny
The currently accepted taxonomy is based on the List of Prokaryotic names with Standing in Nomenclature and National Center for Biotechnology Information. Numbered orders do not yet have any cultured representatives.
See also
List of bacterial orders
List of bacteria genera
References
Bacteria classes
Acidobacteriota | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,127 |
namespace ants
{
extern int
ExtractRegionFromImageByMask(std::vector<std::string>, // equivalent to argv of command line parameters to main()
std::ostream * out_stream // [optional] output stream to write
);
} // namespace ants
#endif // EXTRACTREGIONFROMIMAGEBYMASK_H
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,094 |
whiteswan wrote: I love Strictly as well Mrs64....but Mr Swan sits there with me and suffers whilst I watch it Who's your tip for the Strictly title this year?
Isn't there a local pub he could walk to.
Worth he effort and risk I'd say.
My mum and other halfs mum love Strictly too, certainly an age and gender division thing. Fortunately my other half can't stand that sort of thing, I don't have to suffer.
gessa wrote: Isn't there a local pub he could walk to.
He's a good bloke, a good Rioja is a very nice compensate.
Enjoying the new Barr Brothers offering.
Someone else mentioned kng krule, not on here but can't remember where.
Will have to give it a listen.
Could have been you then.
After almost dying of terminal embarrassment I eventually got the album a few weeks back, and this week I actually plucked up the courage to play it in the car (obviously on a low volume and only whilst Mrs H wasn't in there).
Oh......... You want to know the album? | {
"redpajama_set_name": "RedPajamaC4"
} | 8,222 |
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org.quartz.utils.counter.sampled</FONT>
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Interface SampledRateCounter</H2>
<DL>
<DT><B>All Superinterfaces:</B> <DD><A HREF="../../../../../org/quartz/utils/counter/Counter.html" title="interface in org.quartz.utils.counter">Counter</A>, <A HREF="../../../../../org/quartz/utils/counter/sampled/SampledCounter.html" title="interface in org.quartz.utils.counter.sampled">SampledCounter</A></DD>
</DL>
<DL>
<DT><B>All Known Implementing Classes:</B> <DD><A HREF="../../../../../org/quartz/utils/counter/sampled/SampledRateCounterImpl.html" title="class in org.quartz.utils.counter.sampled">SampledRateCounterImpl</A></DD>
</DL>
<HR>
<DL>
<DT><PRE>public interface <B>SampledRateCounter</B><DT>extends <A HREF="../../../../../org/quartz/utils/counter/sampled/SampledCounter.html" title="interface in org.quartz.utils.counter.sampled">SampledCounter</A></DL>
</PRE>
<P>
Interface of a sampled rate counter -- a counter that keeps sampled values of
rates
<P>
<P>
<DL>
<DT><B>Since:</B></DT>
<DD>1.8</DD>
<DT><B>Author:</B></DT>
<DD><a href="mailto:asanoujam@terracottatech.com">Abhishek Sanoujam</a></DD>
</DL>
<HR>
<P>
<!-- ========== METHOD SUMMARY =========== -->
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/quartz/utils/counter/sampled/SampledRateCounter.html#decrement(long, long)">decrement</A></B>(long numerator,
long denominator)</CODE>
<BR>
Decrements the numerator and denominator by the passed values</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/quartz/utils/counter/sampled/SampledRateCounter.html#increment(long, long)">increment</A></B>(long numerator,
long denominator)</CODE>
<BR>
Increments the numerator and denominator by the passed values</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/quartz/utils/counter/sampled/SampledRateCounter.html#setDenominatorValue(long)">setDenominatorValue</A></B>(long newValue)</CODE>
<BR>
Sets the value of the denominator to the passed value</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/quartz/utils/counter/sampled/SampledRateCounter.html#setNumeratorValue(long)">setNumeratorValue</A></B>(long newValue)</CODE>
<BR>
Sets the value of the numerator to the passed value</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE> void</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/quartz/utils/counter/sampled/SampledRateCounter.html#setValue(long, long)">setValue</A></B>(long numerator,
long denominator)</CODE>
<BR>
Sets the values of the numerator and denominator to the passed values</TD>
</TR>
</TABLE>
<A NAME="methods_inherited_from_class_org.quartz.utils.counter.sampled.SampledCounter"><!-- --></A>
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<TH ALIGN="left"><B>Methods inherited from interface org.quartz.utils.counter.sampled.<A HREF="../../../../../org/quartz/utils/counter/sampled/SampledCounter.html" title="interface in org.quartz.utils.counter.sampled">SampledCounter</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../org/quartz/utils/counter/sampled/SampledCounter.html#getAllSampleValues()">getAllSampleValues</A>, <A HREF="../../../../../org/quartz/utils/counter/sampled/SampledCounter.html#getAndReset()">getAndReset</A>, <A HREF="../../../../../org/quartz/utils/counter/sampled/SampledCounter.html#getMostRecentSample()">getMostRecentSample</A>, <A HREF="../../../../../org/quartz/utils/counter/sampled/SampledCounter.html#shutdown()">shutdown</A></CODE></TD>
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</TABLE>
<A NAME="methods_inherited_from_class_org.quartz.utils.counter.Counter"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from interface org.quartz.utils.counter.<A HREF="../../../../../org/quartz/utils/counter/Counter.html" title="interface in org.quartz.utils.counter">Counter</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="../../../../../org/quartz/utils/counter/Counter.html#decrement()">decrement</A>, <A HREF="../../../../../org/quartz/utils/counter/Counter.html#decrement(long)">decrement</A>, <A HREF="../../../../../org/quartz/utils/counter/Counter.html#getAndSet(long)">getAndSet</A>, <A HREF="../../../../../org/quartz/utils/counter/Counter.html#getValue()">getValue</A>, <A HREF="../../../../../org/quartz/utils/counter/Counter.html#increment()">increment</A>, <A HREF="../../../../../org/quartz/utils/counter/Counter.html#increment(long)">increment</A>, <A HREF="../../../../../org/quartz/utils/counter/Counter.html#setValue(long)">setValue</A></CODE></TD>
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<A NAME="increment(long, long)"><!-- --></A><H3>
increment</H3>
<PRE>
void <B>increment</B>(long numerator,
long denominator)</PRE>
<DL>
<DD>Increments the numerator and denominator by the passed values
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>numerator</CODE> - <DD><CODE>denominator</CODE> - </DL>
</DD>
</DL>
<HR>
<A NAME="decrement(long, long)"><!-- --></A><H3>
decrement</H3>
<PRE>
void <B>decrement</B>(long numerator,
long denominator)</PRE>
<DL>
<DD>Decrements the numerator and denominator by the passed values
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>numerator</CODE> - <DD><CODE>denominator</CODE> - </DL>
</DD>
</DL>
<HR>
<A NAME="setValue(long, long)"><!-- --></A><H3>
setValue</H3>
<PRE>
void <B>setValue</B>(long numerator,
long denominator)</PRE>
<DL>
<DD>Sets the values of the numerator and denominator to the passed values
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>numerator</CODE> - <DD><CODE>denominator</CODE> - </DL>
</DD>
</DL>
<HR>
<A NAME="setNumeratorValue(long)"><!-- --></A><H3>
setNumeratorValue</H3>
<PRE>
void <B>setNumeratorValue</B>(long newValue)</PRE>
<DL>
<DD>Sets the value of the numerator to the passed value
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>newValue</CODE> - </DL>
</DD>
</DL>
<HR>
<A NAME="setDenominatorValue(long)"><!-- --></A><H3>
setDenominatorValue</H3>
<PRE>
void <B>setDenominatorValue</B>(long newValue)</PRE>
<DL>
<DD>Sets the value of the denominator to the passed value
<P>
<DD><DL>
</DL>
</DD>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>newValue</CODE> - </DL>
</DD>
</DL>
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| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,948 |
title: "Välkommen!"
tags: etusivu rub11.2
---
Tervetuloa aloittamaan ruotsin opiskelua lukiossa! Ruotsin opiskelu meillä painottuu suulliseen kommunikaatioon ja keskitymmekin opettelemaan kieltä elämää varten. Muista että suurin työ tehdään oppituntien aikana, olethan siis korvat höröllä ja aktiivisesti mukana. Näin helpotat huomattavasti työtaakkaasi kotona :)
Mukavia oppitunteja ykköskurssilaisille toivottaa,
Riikka | {
"redpajama_set_name": "RedPajamaGithub"
} | 7,642 |
Cruise Ports Northeast Asia
A Guide to Perfect Days on Shore
# Contents
## Plan Your Trip
### Welcome to Northeast Asia
### Northeast Asia's Top 16
### Need to Know
### Hot Spots for...
### Month by Month
### Get Inspired
### Essential Northeast Asia
### Choose Your Cruise
### Sustainable Cruising
### Family Time Ashore
## On The Road
### Tokyo
#### Tokyo National Museum
#### Sensō-ji
#### Shopping in Harajuku
#### Meiji-jingū
#### Sights
#### Courses
#### Shopping
#### Eating
#### Drinking
#### Entertainment
### Mt Fuji
### Yokohama
#### Chinatown
#### Yokohama Port Heritage Walk
#### Sights
#### Activities
#### Tours
#### Eating
#### Drinking
### Nagoya
#### Ōsu Temple & Shopping District
#### Sights
#### Shopping
#### Eating
### Kyoto
#### Fushimi Inari-Taisha
#### Kyoto's Geisha Culture
#### Kinkaku-ji
#### Sights
#### Activities
#### Shopping
#### Eating
#### Drinking
#### Entertainment
### Nara
### Osaka
#### Eating Out in Osaka
#### Osaka-jō
#### Sights
#### Activities
#### Shopping
#### Eating
#### Drinking
### Kōbe
#### Kitano-chō
#### Sights
#### Shopping
#### Eating
#### Drinking
### Kōchi
#### Kōchi-jō
#### Godaisan
#### Sights
#### Eating
#### Drinking
### Hiroshima
#### Peace Memorial Park
#### Sights & Activities
#### Shopping
#### Eating
### Nagasaki
#### Nagasaki Atomic Bomb Museum
#### Sights
#### Tours
#### Shopping
#### Eating
### Kanazawa
#### Kenroku-en
#### Kanazawa Castle Park
#### Sights
#### Tours
#### Shopping
#### Eating & Drinking
### Hokkaidō
#### Hokkaidō Food & Beer Culture
#### Kushiro-shitsugen National Park
#### Otaru
#### Sapporo
#### Hakodate
#### Kushiro
### Okinawa-hontō
#### Tsuboya Pottery Street
#### WWII Memorial Sites
#### Naha
### Keelung & Taipei
#### Chiang Kai-shek Memorial Hall
#### Taipei
#### Jiufen & Jinguashi
### Shànghăi
#### Exploring the Bund
#### Yùyuán Gardens & Bazaar
#### The French Concession
#### Sights
#### Shopping
#### Eating
#### Drinking
### Jeju Island
#### Sanbang-san
#### Sights
#### Tours
#### Eating & Drinking
### Busan
#### Beomeo-sa
#### Sights & Activities
#### Shopping
#### Eating & Drinking
## In Focus
### Northeast Asia Today
### History
### Arts & Architecture
### Food & Drink
### The People of Northeast Asia
## Survival Guide
### Directory A–Z
#### Directory A–Z
#### Accessible Travel
#### Climate
#### Discount Cards
#### Health
#### Insurance
#### Internet Access
#### Language
#### LGBT+ Travellers
#### Money
#### Opening Hours
#### Safe Travel
#### Telephone
#### Time
#### Toilets
#### Tourist Information
#### Visas
#### Transport
#### Getting There & Away
#### Getting Around
#### Language
### Behind the Scenes
### Our Writers
## Welcome to Northeast Asia
Modern metropolises and ancient capitals fringe the coastlines of Northeast Asia. Volcanic mountain peaks, glittering ski fi elds and semi tropical islands, blended with world-class eating, irresistible shopping and a fascinating cultural heritage, await those cruising between the region's historic port cities.
Ship in port, Shànghăi | BLACKSTATION/GETTY IMAGES ©
Each stop along your voyage tells a different chapter of the region's story. Some of these historic cities bear few traces of what came before, while others offer windows to the past amid the modernity. It's there in the Ming-dynasty Yùyuán Gardens, the graceful temples and tea ceremonies of Kyoto, and the haunting reminders of unimaginable loss in Okinawa-hontō and Hiroshima.
For generations, the ports of Northeast Asia have been the site of international exchange, meeting points for goods, cultures and people. There's an intoxicating buzz to the region's urban centres, with their vibrant street life, glowing streetscapes, 24-hour drinking-and-dining scenes, and architectural wonders that redefine what buildings – and cities – should look like. Not only Tokyo and Shanghai, but rising stars Taipei and Busan, too.
Beyond the cities lie scenic stars of the natural world: the dramatic volcanic island of Jeju-do, steaming onsen amid powdery winter snow in Hokkaidō, and iconic Mt Fuji among them.
Wherever you go, you're never far from a great meal. Restaurants often specialise in just one dish, and most towns have their own signature preparations and ingredients. From the splendour of a Kyoto geisha dance to the spare beauty of a Zen rock garden to the glamour of a sky-high cocktail bar, Northeast Asia tells a spellbinding tale.
# Plan Your Trip
Northeast Asia's Top 16
## 1Tokyo
**_Planet earth's unrivalled 24/7 megalopolis_**
Tokyo is one of the world's reigning cities of superlatives – the dining, drinking and shopping are all top class. It's a city always in flux, which is one of its enduring charms, forever sending up breathtaking new structures and dreaming up new culinary delights. It truly has something for everyone, whether your ideal afternoon is spent in an art museum or racing through the streets of Akihabara in a go-kart.
Sakarin Sawasdinaka/SHUTTERSTOCK ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 2Shànghǎi
**_China's neon-lit beacon of change and modernity_**
Its sights set squarely on the not-too-distant future, Shànghǎi offers a taste of all the superlatives China can dare to dream up, from the world's highest observation deck to its fastest commercially operating train. Start with the Bund, Shànghǎi's iconic riverfront area, then head to the French Concession, where the Paris of the East turns on its European charms to maximum effect.
The Bund | Nikada/GETTY IMAGES ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 3Busan
**_Mountains, beaches, street food and a cosmopolitan vibe_**
South Korea's second-largest metropolis, Busan is one of the country's most enjoyable cities. Its top attraction is the atmospheric, waterside Jagalchi Fish Market, where you can buy and eat the freshest of seafood. Also don't miss walking the tranquil path to Beomeo-Sa temple, strolling the lanes of Gamcheon Culture Village, sampling the local dessert _sulbing_ and knocking back shots of _soju_.
Jagalchi Fish Market | MASOVAIDA MORGAN/LONELY PLANET ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 4Kyoto
**_National treasures, historic temples and modern-day geisha_**
There are said to be more than 1000 Buddhist temples in Kyoto. The city is a showroom for centuries of Japanese religious architecture, which produced both the glittering Kinkaku-ji (Golden Temple) and the stark Zen garden at Ryōan-ji. But don't equate religiosity with temperance here: Kyoto is also the city where geisha entertained in lantern-lit teahouses (and still do).
Kiyomizu-dera | BENNY MARTY/ALAMY STOCK PHOTO ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 5Taipei
**_A multitude of influences make up one unique city_**
Surrounded by forested hills, within Taipei's city limits are world-class museums, historic temples and never-ending opportunities for snacking and shopping. Temples and markets dating back centuries coexist with Taipei's flashy modernity. Plus you'll find culinary influences from every corner of China, some of the best Japanese food outside Japan, Asia's best coffee and a night-market scene loaded with unique local snacks.
Chiang Kai-shek Memorial Hall | BLACK SALMON/SHUTTERSTOCK ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 6Osaka
**_The friendly metropolis of food and fun_**
Osaka is a city that packs more colour than most; its acres of concrete are cloaked in dazzling neon billboards. The best way to get under its skin is by chowing down on local cuisine and enjoying a drink at an _izakaya_ (pub restaurant) alongside locals. The city's unofficial slogan is _kuidaore_ ('eat until you drop'), and it seems that everyone is always out for a good meal and a good time. It's the perfect stop for your urban Japan fix.
Dōtombori | THANYA JONES/SHUTTERSTOCK ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 7Hokkaidō
**_Pristine nature and outdoor adventures galore_**
Hokkaidō, Japan's northernmost island, is an untamed landscape of mountains that is pockmarked with crystal-blue caldera lakes and sulphur-rich hot springs. This is 'big mountain and snow' country, where skiers carve snow drifts reaching several metres in depth. In the green season, hikers and cyclists are drawn to the island's wide open spaces and dramatic topography. This is a place of seasonal thrills galore: don't miss out.
Hakodate | SEAN PAVONE/SHUTTERSTOCK ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 8Hiroshima
**_Heartbreaking history with a message of hope_**
It's not until you visit the Peace Memorial Museum that the true extent of human tragedy wrought by the atomic bomb in 1945 becomes vividly clear. A visit here is a sobering history lesson and the park around the museum offers opportunities for reflection. But the city's here spirit of determination – and its food – will ensure that you'll have good memories to take with you when you leave.
Atomic Bomb Dome | NICEPIX/SHUTTERSTOCK ©
Hiroshima-jō | GRANT M HENDERSON/SHUTTERSTOCK ©
Peace Memorial Park | ITZAVU/SHUTTERSTOCK ©; ARCHITECT: KENZō TANGE
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 9Okinawa-hontō
**_Spectacular beaches, intriguing history and 'island time'_**
Originally settled by the Ryūkyū people, Okinawa-hontō offers a totally different experience from the rest of Japan. War memorials are clustered in the south of the island, while the bustling capital Naha offers the chance to sip fresh juice from the market, fill up on island delicacies, and gain insight into Okinawa's rich cultural heritage.
Tsuboya Pottery Street | VASSAMON ANANSUKKASEM/SHUTTERSTOCK ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 10Kanazawa
**_Feudal-era capital on the Sea of Japan coast_**
In its heyday, Kanazawa rivalled Kyoto as a centre for the arts. This artisan tradition is today evident in a number of shops and galleries. Kanazawa also has one of Japan's top gardens, Kenroku-en, an excellent art museum and a food culture that draws heavily from the seafood pulled from the ocean. Kanazawa has long flown under the radar, though that's changing. Go now, before everyone else catches on.
Kenroku-en | ANDREAS H/SHUTTERSTOCK ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 11Jeju Island
**_Where volcanic scenery accompanies leisurely hikes_**
A volcanic landmass with spectacular craters and lava tubes, Jeju-do holds unique charms amid beautiful, accessible surroundings. The frequently dramatic landscape is best seen on foot – spending a day following all or part of a trail is a wonderful way to soak up Jeju's unique charms and beautiful surroundings. Jeju's separately developed island culture is revealed in its distinct cuisine and customs.
Seongsan Ilchul-bong | CJ NATTANAI/SHUTTERSTOCK ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 12Nagasaki
**_WWII tragedy and a colourful trading history_**
History weighs heavily on Nagasaki, the second Japanese city destroyed by an atomic bomb. But as Japan's only truly open port during the 200-year period of isolation in the 17th to 19th centuries, Nagasaki has a cosmopolitan legacy that lives on today in its food and architecture. As paradoxical as it may seem, Nagasaki is vibrant and charming, and it begs to be explored far beyond the bomb museums, monuments and memorials.
Dejima Wharf | SANGA PARK/SHUTTERSTOCK ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 13Yokohama
**_Sophisticated portside city_**
Japan's second-largest city and part of the Greater Tokyo Metropolitan Area along with Tokyo and Kawasaki, Yokohama is often overshadowed by the nation's capital. Come to sample craft beer, contemporary art and jazz tunes. The rejuvenated port area, fringed by amusement parks, museums and historic and contemporary architecture, generously repays a day's exploring.
Yokohama Cosmoworld | PATARA/SHUTTERSTOCK ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 14Nagoya
**_Underestimated and underappreciated – a hidden gem_**
Although its GDP tops that of many small countries, Nagoya struggles to shake its reputation among Japanese (many of whom have never visited) as the nation's most boring metropolis. But those who visit discover a friendly city with fabulous shopping, food and parks. Hit Japan's first Legoland, explore the absorbing train and Toyota museums, and paint your own Noritake china keepsake.
Ōsu area | FBDESIGNCENTER/SHUTTERSTOCK ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 15Kōbe
**_Historic naval gateway to Japan_**
Sandwiched between the sea and the mountains, in 1859 Kōbe became one of just five ports in Japan open to international trade. The legacy of this period lives on in modern Kōbe, a hub of international maritime travel and commerce to this day. Famous for its namesake top-grade beef, the city also boasts waterfalls, shopping, gardens, historic houses and fabulous views.
Kōbe port | F11PHOTO/SHUTTERSTOCK ©
NORTHEAST ASIA'S TOP 16 PLAN YOUR TRIP
## 16Kōchi
**_A laid-back yet lively city_**
Home to one of Japan's most famous and best-preserved castles, Kōchi has a deserved reputation as a city that enjoys a good time. This smart, friendly and compact city is small (for a Japanese city), making its many interesting sights super accessible. It's home to an impressive pilgrimage temple, beautiful botanical gardens, a paper museum with occasional workshops, and a terrific Sunday market.
Kōchi-jō | MASAOTAIRA/GETTY IMAGES ©
# Plan Your Trip
Need to Know
Currencies
China: yuán (元; ¥); Japan: yen (¥); South Korea: Korean won (₩); Taiwan: New Taiwanese dollar (NT$)
Languages
China: Mandarin, Cantonese; Japan: Japanese; South Korea: Korean; Taiwan: Mandarin, Taiwanese
Visas
Visas on arrival in Japan, South Korea and Taiwan for most nationalities for stays of up to 90 days. Not needed for 72 hours or less in Shànghǎi.
Money
Credit cards are widely accepted in midrange and top-end restaurants and shops, though less so in Shànghǎi. ATMs are common, but not all accept foreign cards.
Mobile Phones
Different networks operate across the region. Prepaid SIM cards for unlocked smartphones are available at electronics stores.
Time
Japan and South Korea are nine hours ahead of GMT/UTC; China and Taiwan are eight hours ahead.
### When to Go
### High Season _(Apr–Aug)_
oGolden Week (early May) and O-Bon (mid-August) in Japan: sights are packed and prices are sky-high.
oApril brings cherry blossoms and crowds of admirers.
oTemperatures and humidity soar July through August – prepare for summer downpours.
### Shoulder _(Mar, Sep & Oct)_
oIn the north this is the optimal season, with fresh weather and clear skies.
oIn autumn (roughly September through October) you can experience nature in all its russet shades.
### Low Season _(Nov–Feb)_
oCrowds dwindle. Bitterly cold in Hokkaidō, cool and dry in the south.
oMany businesses close over the New Year period (end of December to early January).
### Costs for a Day in Port
#### Budget: Less than ¥5000
oBowl of noodles: ¥750
oPublic-transport pass: ¥600
oTemple or museum entry: ¥500
#### Midrange: ¥5000–10,000
oLunch for two at a midrange eatery: ¥6000
oGourmet coffee: ¥700
oHalf-day organised tour: ¥5000
#### Top End: More than ¥10,000
oLunch for two at a top-end restaurant: from ¥15,000
oTaxi between city sights: ¥2500
oPrivate, customised tours: from ¥10,000
### Useful Websites
**Lonely Planet** (www.lonelyplanet.com) Destination information, hotel bookings, traveller forum and more.
**Japan National Tourism Organization** (www.jnto.go.jp) Official tourist site with planning tools and events calendar.
**Cruise Critic** (www.cruisecritic.com) Cruise forum, reviews and info on cruise deals.
**Cruise Line** (www.cruiseline.com) Ship reviews, deals and a cruise forum.
### What to Pack
Wear slip-on shoes, as you'll be taking your shoes off a lot; during sandal season many locals will carry socks to slip into to avoid walking barefoot. You also may find yourself sitting on the floor, so dress comfortably for that. Neat, smart casual wear will fit right in; pack more formal attire for top-end bars and restaurants. Winters can be bitterly cold, especially in the north, and summers hot and humid. Dressing in layers is ideal.
An umbrella won't go astray in winter or summer, nor a good hat and sunscreen in summer.
### Wi-Fi Access
oWi-fi is often available in port, on buses and trains, and at major tourist sites, train stations, cafes and restaurants.
oSouth Korea has a particularly fast and widespread connection.
oService in Japan and Taipei can be spotty and slow. Service in China is particularly frustrating. The Chinese authorities maintain strong controls on internet access; the list is constantly changing but sites and apps such as Facebook, Google-owned sites (YouTube, Google Maps, Gmail, Google Drive), WhatsApp and many international media outlets have been blocked in the past, so plan ahead.
oWi-fi is generally unsecured, so take care what kind of information you enter if you're using a wireless connection.
### Arriving in Northeast Asia
**Kōbe** Regular high-speed ferries connect Kansai International Airport (near Osaka) and Kōbe airport (adult/child ¥1850/930, 30 minutes). From here it's a short trip on the Portliner monorail to Kōbe Port Terminal.
**Shànghǎi** There's no direct public transport from Pǔdōng or Hóngqiáo airports to the cruise terminals. A private transfer company or taxi are your best bets. Times and prices vary, up to about ¥200 and a little over an hour to get from Pǔdōng airport to Shànghǎi Port International Cruise Terminal. A fun option is to take the maglev (www.smtdc.com) warp-speed train into the city centre, and a taxi or metro from there to your port.
**Yokohama** Regular JR Narita Express trains (adult/child ¥4290/2145, 80 minutes) run direct from Narita airport to Yokohama station. From here take the subway to Nihon-ōdōri station, from where it's a short walk to port. Friendly Airport Limousine (www.limousinebus.co.jp; adult/child ¥3600/1800) runs to Yokohama's waterfront.
For more, see Getting Around A
# Plan Your Trip
Hot Spots for...
## Regional Cuisine
Eating is one of the great pleasures of visiting Northeast Asia. Discover just how varied the cuisine is, from region to region and season to season.
OPERATION SHOOTING/SHUTTERSTOCK ©
Kyoto
Japan's ancient imperial capital is the birthplace of _kaiseki_ (haute cuisine) and the tea ceremony.
Roan Kikunoi
An experimental and creative approach to _kaiseki_.
Osaka
Colourful Osaka is Japan's capital of street food: fierce competition turns humble dishes to high art.
Wanaka Honten
Top for _tako-yaki_ (octopus dumplings, pictured above).
Taiwan
Taiwan is synonymous with night markets: sweet, savoury and fresh, the food is an explosion of flavours.
Miaokou Night Market
Step into one of Taiwan's best night markets.
## Art & Architecture
The region's sublime artistic tradition transcends gallery walls, embodying its past and present.
TRAVELLIGHT/SHUTTERSTOCK ©; ARCHITECT: XING TONGHE
Tokyo
Art museums, theatres and the creations of Japan's modern-day architects.
Tokyo National Museum
The world's largest collection of Japanese art.
Shànghǎi
Shànghǎi: few cities in the world evoke so much history and mystique in name alone.
Shanghai Museum
Explores Chinese history through art.
Osaka
An urban sprawl that lacks Tokyo's grace but offers unexpected delights amid the chaos.
Abeno Harukas
Japan's tallest building opened in 2014.
## Outdoor Activities
Northeast Asia is a year-round destination for walkers keen for relaxed strolls or serious peaks. In winter, a day of skiing is a top option.
TORJRTRX/SHUTTERSTOCK ©
Fuji Five Lakes
Iconic Mt Fuji is the main draw, but the pretty lake district offers gentler hikes through the foothills, too.
Mt Fuji
Watch sunrise from Japan's highest summit.
Hokkaidō
Japan's northernmost island has become a playground for outdoor enthusiasts.
Kushiro-shitsugen
An important habitat for the red-crowned crane.
Jeju Island
Amazing volcanic scenery accompanies leisurely hikes, topped off with spectacular views.
Sanbanggul-sa
Take in the sea views from this cave temple.
## Historic Sites
See the sights where the region's history – the samurai warrior, the wandering ascetic and the rice-paddy farmer – is brought to life.
KHONG KATESORN/SHUTTERSTOCK ©
Nara
The nation's first capital hosts Buddhist art, architecture and historical relics from the 8th century.
Tōdai-ji
Home of Nara's Daibutsu statue.
Hiroshima
This city has numerous monuments commemorating the day that changed history for Japan and the world.
Peace Memorial Museum
Evocative account of the bomb's aftermath.
Okinawa-hontō
Today it feels like a tropical paradise, but this island saw tremendous carnage in WWII.
Okinawa Prefectural Peace Memorial Museum
Details the US invasion.
# Plan Your Trip
Month by Month
## January
January is wet and cool in Taipei and Okinawa, and icy cold up in Hokkaidō. In Japan, many businesses close for the whole first week of the new year, and transport is busy.
## February
### z Yuki Matsuri
Two million visitors head to Sapporo's annual snow festival (www.snowfes.com) in early February. Highlights include an international snow-sculpture contest, ice slides and mazes for kids.
### z Lunar New Year
Families gather in China, South Korea and Taiwan to greet the New Year together, feasting on traditional food and giving gifts. Expect parades, fireworks and lots of colour. Many businesses take a holiday in the days following.
### z Lantern Festival
Music, street performers, light shows and floating lanterns fill this week-long event held at the end of the Lunar New Year in Taipei Expo Park. See www.taipeitravel.net/en for details.
## March
Spring begins in fits and starts. The Japanese have a saying: _sankan-shion_ – three days cold, four days warm.
## April
Warmer weather and blossoming trees make April a favoured month, but places such as Kyoto and Jeju-do can be crowded.
### z Cherry-Blossom Viewing
When the cherry blossoms burst into bloom, the Japanese hold rollicking _hanami_ (blossom-viewing) parties. The blossoms are fickle and hard to time: on average, they hit their peak in Tokyo and Kyoto between 25 March and 7 April. In Taiwan they appear a little earlier – mid to late February.
Cherry blossoms, Tokyo | BYJENG/SHUTTERSTOCK ©
## May
May is lovely: it's warm and sunny in most places. On 1 May, the whole of China gears up for a hard-earned three-day holiday.
### z Sanja Matsuri
The grandest Tokyo festival of all, this three-day event, held over the third weekend of May, attracts around 1.5 million spectators to Asakusa, for a rowdy parade of _mikoshi_ (portable shrines) carried by men and women in traditional dress.
### z Buddha's Birthday
Brings a kaleidoscope of light and colour, as rows of paper lanterns are strung down main thoroughfares and in temple courtyards across South Korea.
## June
Through June and July the summer heat picks up and rains set in.
### z Hyakumangoku Matsuri
In early June, Kanazawa's biggest festival celebrates the city's 16th-century glory days with period-costume parades, cultural performances and more.
Gion Matsuri, Kyoto | TAKAYUKI OHAMA/SHUTTERSTOCK ©
o Best Festivals
Cherry-Blossom Viewing April
Gion Matsuri July
Lunar New Year February
Yuki Matsuri February
Dream Parade October
## July
### z Gion Matsuri
Japan's most vaunted festival is held on 17 and 24 July in Kyoto, when huge, elaborate floats are paraded through the streets. Three evenings prior, locals stroll through street markets dressed in beautiful _yukata_ (light cotton kimonos).
### 2 Peiron Dragon-Boat Races
In late July, dragon-boat races are held in the harbour of Nagasaki, a tradition introduced from China in the 17th century.
### 6 Sapporo Summer Matsuri
The big names plus microbrewers set up outdoor beer gardens in Ōdōri-kōen from mid-July to mid-August. A whole month (www.sapporo-natsu.com) of beer drinking in the sun!
### z Minato Matsuri
Held around 'Ocean Day' (the third Monday in July), this street festival in Nagoya Port features a parade, dancing, fireworks and a water-logging contest dating back to the Edo period.
## August
Hot, humid summer hits a peak – watch out for rainstorms. In Japan, three days in mid-August are set aside to honour the dead; public transport is hectic and shops may close.
### z Hakodate Port Festival
In early August, thousands of locals gather to perform traditional dances in the streets, including Hakodate's signature squid dance.
### z Peace Memorial Ceremony
On 6 August, a memorial service is held in Hiroshima for victims of the WWII atomic bombing of the city. Thousands of paper lanterns are floated down the river.
### 3 World Cosplay Summit
Some 30 countries compete in early August (or late July) in Nagoya (www.worldcosplaysummit.jp) to see who has the best _cosplayers_ (manga and anime fans who dress up as their fave characters).
## September
Days are still warm, hot even, though less humid – though the odd typhoon rolls through this time of year.
### z Kishiwada Danjiri Matsuri
Osaka's wildest festival, held over the third weekend in September, is a kind of running of the bulls except with _danjiri_ (floats), many weighing more than 3000kg.
## October
Autumn is a great time to visit; outdoors you'll enjoy a palate of rustic colours.
### 3 Busan International Film Festival
South Korea's top international film festival (www.biff.kr), held in the architecturally stunning Busan Cinema Center, attracts stars from across Asia and beyond.
### z Ryūkyū-no-Saiten
Brings together more than a dozen festivals and special events celebrating Okinawan culture for three days at the end of the month.
### z Dream Parade
Dream Parade is Taipei's Mardi Gras. Not to be missed if you can help it!
### 6 Yokohama Oktoberfest
For two weeks in early October much beer drinking goes down during this event held in Yokohama's historic harbour district.
## November
### 3 China Shanghai International Arts Festival
A month-long program (www.artsbird.com) of cultural events in October and November, which includes the Shanghai Art Fair, a program of international music, dance, opera and acrobatics, and exhibitions of the Shanghai Biennale (www.shanghaibiennale.org).
## December
December is cold across most of the region, although Taipei and Okinawa remain fairly mild.
### z Luminarie
Kōbe streets are lined with illuminated arches every year for this event (<http://kobe-luminarie.jp>) in early December, in memory of the victims of the 1995 Great Hanshin Earthquake.
# Plan Your Trip
Get Inspired
### Read
**Shōgun** (James Clavell; 1975) An historic tale based on the true story of a Brit who visited Japan in 1600.
**Kyoto: A Cultural History** (John Dougill; 2006) Touches on everything from courtly verse to Zen Buddhism to modern film.
**Norwegian Wood** (Murakami Haruki; 1987) Coming-of-age story set in 1960s Tokyo, by Japan's most popular living writer.
**Shanghai: The Rise and Fall of a Decadent City 1842–1949** (Stella Dong; 2000) Rip-roaring profile of Shànghǎi's good-old, bad-old days.
Arashiyama Bamboo Grove, Kyoto | LKUNL/SHUTTERSTOCK ©
### Watch
**Spirited Away** (Miyazaki Hayao; 2001) Academy Award–winning animated feature, said to be inspired by Jiufen, near Taipei.
**Eat Drink Man Woman** (Ang Lee; 1994) A must-see for those interested in Taiwanese culture.
**Train to Busan** (Yeon Sang-ho; 2016) Just when you thought it was good to go 1st class: rail-roading apocalyptic zombie horror.
**Your Name** (Shinkai Makoto; 2016) Popular anime where a city boy and country girl swap places.
**Shanghai Triad** (Zhang Yimou; 1995) Stylish take on Shànghǎi's 1930s gangster scene.
### Listen
**Shimanchu nu Takara** (Begin) Love song to Okinawa with _eisa_ (Okinawan folk-style) chanting.
**Hanamizuki** (Hitoto Yō) Tender ode to love and loss and a perennial karaoke favourite.
**Tokyo, Mon Amour** (Pizzicato Five) Moody lounge track from the '90s Shibuya indie scene.
**Love Yourself: Tear** (BTS) The first-ever K-Pop album to take the number-one spot on the Billboard 200.
**13 Classic Shanghai Pop Rock Songs** (Top Floor Circus) This legendary outfit sang in Shanghainese and played anything from folk to punk.
# Plan Your Trip
Essential Northeast Asia
### Activities
Many ports offer easy access to short walks; in Sapporo you can even zip up to the snowfields. Follow up with a massage, a spa or an onsen (hot-spring bath). Many believe the waters to have curative properties; at the very least, you will sleep very, very well after a soak.
Amusement parks are another regional highlight, from big international names (Disney and Lego), to homegrown ones.
### Shopping
Tokyo is the fashion trendsetter for all of Japan; Osaka has a street-smart style of its own. Kyoto is the place to pick up traditional goods, such as anything tea related. Around the country are pottery towns (Naha is a highlight) and others famous for local crafts.
Shànghǎi shoppers buy up big-time. Whether you're after boutique threads, handmade ceramics or a period poster from the Mao era, Shànghǎi is an A to Z of shopping.
In South Korea, make-up and beauty products are particularly hot items. More unique mementos include pottery, tea, _soju_ (local vodka), K-Pop branded food, Korean sweets and _hanbok_ (traditional clothing).
Nishiki Market, Kyoto | BEATRICE SIRINUNTANANON/GETTY IMAGES ©
### Eating
As visitors to Northeast Asia quickly discover, people here are absolutely obsessed with food. Every region has its own proud specialities and traditions, and, unsurprisingly, sublime seafood is common across the ports. Seasonal cuisine is also a key feature, with each season bringing signature ingredients and dishes.
Lavish restaurants featuring Michelin stars, celebrity chefs and degustation menus abound, but just as satisfying are hole-in-the-wall dumpling joints (a Shànghǎi classic) and bustling markets (Taipei's are renowned). In Japan, look to food courts in department stores and train stations for easy options. Few sights lack an on-site cafe, kiosk or street stalls selling tasty snacks.
### Drinking
Tea is a fundamental part of life in Northeast Asia. In Japan, _o-cha_ (tea) means green tea and broadly speaking there are two kinds: _ryokucha_ (steeped with leaves) and _matcha_ , which is made by whisking dried and milled leaves with water until a cappuccino level of frothiness is achieved. Green tea is also popular in South Korea. Prized high-mountain oolong, found in Shànghǎi and Taipei, makes a great gift for the folks back home. A newer tradition is bubble tea – a mixture of tea, milk, flavouring, sugar and giant black tapioca balls.
Coffee culture has taken off and you won't have trouble finding a good coffee shop. For something harder, look for _nihonshū_ (sake) and whisky in Japan, cocktails in Shànghǎi, _soju_ in Korea and craft beers everywhere you go.
### Entertainment
Many ships are greeted on arrival by dancers in gorgeous, traditional dress, a fantastic introduction to local traditions.
Sumo, steeped in ancient ritual, is Japan's national sport. Tournaments take place in January, May and September in Tokyo and in March in Osaka. A geisha performance in Kyoto is also worth seeking out. Cinema is booming in Busan; if you can't catch a movie while in port, check out the city on screen in _Black Panther_ (2018) or _Train to Busan_ (2016).
Yosakoi Yume Matsuri, Nagoya | HENRY WESTHEIM PHOTOGRAPHY/ALAMY STOCK PHOTO ©
o Best Markets
Tsukiji, Tokyo
Nishiki, Kyoto
Daichi Makishi Kōsetsu Ichiba, Okinawa
Jagalchi Fish Market, Busan
Miaokou Night Market, Taipei
Hakodate Morning Market, Hokkaidō
# Plan Your Trip
Choose Your Cruise
_Matching your expectations, budget and travel style to the right cruise is the most important decision of the trip, so it pays to think carefully about what's important to you. There's a very wide range of trips, from floating cities with thousands of passengers to smaller, more intimate ships._
Osaka | STOCKPHOTO MANIA/SHUTTERSTOCK ©
### Narrow it Down
So many options! So many decisions! Things to consider:
**Budget** Check the small print about what's included in the price before you commit. Unless you're on a luxury cruise, you'll likely be paying extra for alcoholic beverages, shore excursions, wi-fi and tips. Then there's the spa, casino, gift shop and other money sinks to look out for.
**Style** A mass-market, upscale or specialist cruise? Do you prefer numerous formal evenings or would you rather keep things casual? What are your special interests?
**Itinerary** Where do you want to go and what ports of call appeal? Do you like the idea of days spent just at sea?
**Size** The megaships are geared for various budgets, so the important decision is how many people you want to sail with. On large ships, you can have 5000 potential new friends and the greatest range of shipboard diversions. Small ships, while sometimes exclusive and luxurious, are not always so, and usually lack the flashier amenities (such as climbing walls). They are, however, able to stop at smaller ports that can't cater for the larger vessels, and disembarking can be considerably quicker.
**Demographics** Different cruise lines, and even ships within cruise lines, tend to appeal to different groups. Although cruisers in general are often slightly older, some ships have quite a party reputation; others are known for their art auctions and old-timey music in the lounges.
### Cabin Types
Some modern ships offer only exterior cabins with balcony, but typically you'll have a choice. It's worth looking at a map of the ship before you choose, as you may want to prioritise being near the pool, the bar, the lifts or a play area.
Interior cabins are generally compact, with little or no natural light, though some have interior windows. They are the cheapest category and will suit those who plan to spend most of their time in public areas.
Sea-view cabins offer a porthole or window but no exterior access. They are typically as compact as interior rooms or more so.
Balcony cabins give you some access to the outside. Balconies are often quite small but will have space for a couple of chairs and small table at least. This is generally the first category in which spending significant time in your room is appealing.
Suites are a significant upgrade in size and usually separate the sleeping and sitting areas.
Some ships have a few single cabins, but these get snapped up fast. Solo travellers will usually have to pay a hefty single supplement at best, or pay the full rate for a double cabin at worst.
Hiroshima Bay | KATHRYNHATASHITALEE/GETTY IMAGES ©
o Best Online Resources
**Cruise Critic** (www.cruisecritic.com)
**Cruise Line** (www.cruiseline.com)
**Cruise Mates** (www.cruisemates.com)
**Cruise Reviews** (www.cruisereviews.com)
### Bigger Ships
It's not so much about the destination as it is about the panoply of amenities on board. These aren't mere cruises – they're floating cities stocked with every entertainment option under the sun. The competition in this category is fierce. Some options:
**Celebrity** (www.celebritycruises.com) Family-friendly, upscale and laid-back cruises on large 2000-plus-passenger ships.
**Costa Cruises** (www.costacruises.com) Costa is aimed at European travellers: bigger spas, smaller cabins and better coffee. Ships are huge.
**Dream Cruise Line** (www.dreamcruiseline.com) Asia-based cruise company with large, luxurious ships.
**Holland America** (www.hollandamerica.com) Offers a traditional cruising experience, generally to older passengers.
**MSC Cruises** (www.msccruises.com) Italian-inflected cruising on large, luxurious ships.
**Norwegian Cruise Line** (NCL; www.ncl.com) Offers 'freestyle cruising' on large ships; dress codes are relaxed and dining options are more flexible than on many other lines.
**Princess** (www.princess.com) Has large ships that offer a slightly older crowd a range of pampering activities while aboard.
**Royal Caribbean** (www.royalcaribbean.com) Has a huge fleet of megaships, aimed right at the middle of the market, with lots of activities for kids. Despite the name, it offers voyages to Asia as well.
**Star Cruises** (www.starcruises.com) Large ships sailing purely Asian itineraries; plenty of on-board entertainment.
Cruise ship in port, Shànghǎi | HELLORF ZCOOL/SHUTTERSTOCK ©
### Luxury & Smaller Vessels
These luxury lines promise a palpable uptick in service across the board. From small 100-person ships with sails to large 1000-person cruisers that feel more like floating five-star hotels, opulence and exclusivity are the major draws. Expect sweet suites and perks on board. Some luxury lines include the following:
**Azamara Club Cruises** (www.azamaraclubcruises.com) Specialises in destination immersion – longer calls and more overnights allow passengers more time to soak up the local atmosphere and to experience the nightlife.
**Crystal Cruises** (www.crystalcruises.com) Offers excellent service without stuffiness or dated formality. Also promotes social responsibility, encouraging passengers to participate in volunteering excursions on some trips.
**Cunard Line** (www.cunard.com) Operating since the 19th century, the atmosphere on these ships is sophisticated. Attracts an older crowd.
**Ponant** (www.ponant.com) This French operator runs intimate trips with a social atmosphere.
**Seabourn Cruise Line** (www.seabourn.com) Competing in the ultra-luxury market, Seabourn's ships can dock in smaller ports. But you'll remember the on-board experience as much as the destinations.
**Silversea Cruises** (www.silversea.com) Expect formal service – couples in their forties and older dress for dinner.
**Viking Cruises** (www.vikingcruises.com) A fairly new operator that is growing rapidly. The cruises are designed for travellers with an interest in geography, culture and history.
### Theme Cruises
Gardens, WWII, music, crafting, food, bridge... What these have in common is that they're all themes for cruises.
Cruise lines sell group space to promoters of theme cruises, but typically no theme is enough to fill an entire ship. Rather, a critical mass of people will occupy a block of cabins and have activities day and night just for them, including lectures, autograph sessions, costume balls and performances.
No theme or interest is too obscure or improbable. To find one, jump online and search your phrase with 'cruise'.
Ship send off, Yokohama | SETSUKON/GETTY IMAGES ©
### LGBT+ Cruises
One of the largest segments of special-interest cruises are those aimed at lesbian, bisexual, gay and transgender people. So popular are these cruises that often an entire ship will be devoted to catering for LGBT+ passengers. The following sites can help you find a cruise:
**All Gay Cruises** (www.cruisingwithpride.com)
**Atlantis Events** (www.atlantisevents.com)
**Happy Gay Travel** (www.happygaytravel.com)
# Plan Your Trip
Sustainable Cruising
_From air and water pollution to the swamping of popular destinations by hordes of tourists, travelling on cruise ships isn't without significant impacts – choose your cruise line carefully._
Yamashita-kōen, Yokohama | ASIA/ALAMY STOCK PHOTO ©
### Environmental Issues
Although all travel comes with an environmental cost, by their very size, cruise ships have an outsized effect. Among the main issues:
**Air pollution** According to UK-based Climate Care, a carbon-offsetting company, cruise ships emit more carbon per passenger than airplanes – nearly twice as much – and that's not factoring in the flights that most passengers take to get to their point of departure. Most ships burn low-grade bunker fuel, which contains more sulphur and particulates than higher-quality fuel.
**Water pollution** Cruise ships generate enormous amounts of sewage, solid waste and grey water, which often just gets dumped directly (or with minimal treatment) into the sea. Some countries are beginning to introduce legislation to curb this behaviour, but unfortunately legislation is lacking when it comes to international waters.
**Cultural impact** Although cruise lines generate money for their ports of call, thousands of people arriving at once can change the character of a town and may seem overwhelming to locals and noncruising travellers.
### What You Can Do
The cruise industry notes that it complies with international regulations, and adapts to stricter regional laws as required. As consumer pressure grows, more ships are being equipped with new waste-water treatment facilities, LED lighting and solar panels. Some operators are also upping their game when it comes to recycling and waste management.
If you're planning a cruise, it's worth doing some research. Email the cruise lines and ask them about their environmental policies: waste-water treatment, recycling initiatives and whether they use alternative energy sources. Knowing that customers care about these matters has an impact on cruise-ship operations.
There are also organisations that review the environmental records of cruise lines and ships. These include the following:
**Friends of the Earth** (www.foe.org/projects/cruise-ships) Letter grades given to cruise lines and ships for environmental and human health impacts.
**World Travel Awards** (www.worldtravelawards.com) Annual awards for the 'World's Leading Green Cruise Line'.
#### On the Ship
oAsk about recycling facilities on the ship and use them.
oConserve water and energy.
oDon't use sinks and toilets as rubbish bins – only flush away what you must.
oNever throw rubbish from the ship into the sea.
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Cruising into port, Shànghǎi | Igor Grochev/SHUTTERSTOCK ©
o Most Sustainable Companies
According to Friends of the Earth, two of the most sustainable large cruise-ship companies running cruises in Asia are Holland America and Norwegian Cruise Line.
#### In Port
**Skip bottled water** Apart from in Shànghǎi, the water in Northeast Asia is generally safe to drink, so pack a reusable water bottle.
**Ride the bus, train or tram** Most cities in the region have excellent public-transport networks. Also take the opportunity to explore cities on foot.
**Hire a bike** Some ports have easily accessible rental or share bikes.
**Say no to plastic** Bring your own reusable bags to carry anything you buy. Avoid plastic straws.
**Make a positive impact** Support independently owned businesses and look for opportunities to interact with locals.
# Plan Your Trip
Family Time Ashore
_Safe, lively and full of mod cons, Northeast Asia is a great place to travel with kids. Pop culture, neon streetscapes and big-name amusement parks are easy wins; street markets, interactive museums and endless snack options sweeten the deal._
Skiers at Sapporo Teine, Hokkaidō | TASCH/SHUTTERSTOCK ©
### Practicalities
oBe sure to bring any necessary medicines from home (prescription or over the counter), as pharmacies may not stock them.
oA small fork and spoon can be handy, as not all restaurants have these on hand.
oBaby food, nappies and milk powder are widely available in supermarkets.
oFew restaurants have baby chairs.
oConvenience stores stock sandwiches and other familiar foods – and the quality and range on offer is often eye-opening.
oLonely Planet's book _Travel with Children_ prepares you for the joys and pitfalls of travelling with little ones.
### Attitudes to Children
Children are adored and welcomed throughout the region, and people will go out of their way to help you if needed. In Shànghǎi and South Korea, children may find themselves the centre of attention and curiosity, which can be a great way to meet some locals, and can also be a little overwhelming. In Taipei and Japan, you may find local children are expected to be a bit quieter than you're used to back home.
Crowded trains and streets do make prams a challenge, and may be overwhelming for little ones; if possible avoid riding trains and subways during peak commuting hours in the larger cities (7am to 9am and 5pm to 7pm).
Breastfeeding is generally not done in public, though some mothers do (find a quiet corner and use a shawl).
### Top Stops for Kids
Shanghai Natural History Museum, Shànghǎi Kids will love this new-look museum, with its dinosaur fossils, taxidermied animals, live reptiles and butterfly house.
Universal Studios Japan, Osaka The Japanese version of the American theme park.
SCMAGLEV & Railway Park, Nagoya See an actual maglev (the world's fastest train) and test-ride a _shinkansen_ simulator.
Miniatures Museum of Taiwan, Taipei Dozens of tiny creations, with so many details to discover, intrigue and delight.
Sapporo Teine, Sapporo Quality, family-friendly snowfields, just minutes from Sapporo. Ski or just throw snowballs.
Cup Noodles Museum, Yokohama Make-your-own cup noodles. Who can resist?
Tokyo Disney Resort, Tokyo Visit the only-in-Japan Disney Sea park (along with classic Disney attractions).
Shànghǎi Disneyland, Shànghǎi Set to suck in Chinese tots and young kids nationwide, this is mainland China's first Disney Resort. Expect epic queues.
Shanghai Natural History Museum | AKKHARAT JARUSILAWONG/SHUTTERSTOCK ©
o Best Bites for Kids
**Dumplings** Shànghǎi
**Bubble tea** Taipei
**Okonomiyaki** Osaka and Hiroshima
**Castella sponge cake** Nagasaki
**Ramen** Sapporo
# TOKYO
#### Tokyo National Museum
#### Sensō-ji
#### Shopping in Harajuku
#### Meiji-jingū
#### Sights
#### Courses
#### Shopping
#### Eating
#### Drinking
#### Entertainment
#
Tokyo at a Glance
Tokyo (東京) is a city forever reaching into the future, resulting in sci-fi streetscapes of crackling neon and soaring towers. Yet it is also steeped in history, and you can find traces of the shogun's capital on the kabuki stage or under the cherry blossoms in Ueno. There are excellent museums here, along with everything else you could ask of Japan: historic temples and shrines, fascinating contemporary architecture and, yes, even hot springs. To get to know the city, enjoy it as the locals do: by splurging on sushi in Ginza, scouting new looks in Harajuku or raising a glass in Shinjuku.
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Tokyo skyline | ANEK.SOOWANNAPHOOM/SHUTTERSTOCK ©
CLOCKWISE FROM TOP LEFT: TOOYKRUB/SHUTTERSTOCK ©; BEIBAOKE/SHUTTERSTOCK ©; MOSAYMAY/SHUTTERSTOCK ©; KORKUSUNG/SHUTTERSTOCK ©; COWARDLION/SHUTTERSTOCK ©; PIGPROX/SHUTTERSTOCK ©, HACHIKO THE DOG SCULPTOR: TAKESHI ANDO
With a Day in Port
Begin your day at the Tokyo National Museum, before making the short journey east to Sensō-ji. Visit Meiji-jingū and then explore Harajuku, where you can experience a traditional tea ceremony at Sakurai Japanese Tea Experience.
Best Places for...
**Sushi** Kyūbey
**Soba** Honmura-An
**Souvenirs** Japan Traditional Crafts Aoyama Square
**Kaiseki** Kikunoi
**Tea** Chashitsu Kaboku
**Onsen** Spa LaQua
Getting from the Port
oMost cruise ships dock at Harumi Wharf. The Harumi-Futo bus stop is right at the port. Kachidoki Station on the Toei Oedo subway line is five minutes by bus or taxi or a 20-minute walk away.
oLarge ships dock at Oi Wharf, which is a five-minute walk to Yashio 2-chome bus stop. Shuttle buses run to Shinagawa JR train station.
oSome larger ships dock at Ōsanbashi Pier in Yokohama.
oAt the time of research Tokyo International Cruise Terminal Pier was under construction and due to be completed in time for the 2020 Olympics.
Fast Facts
**Tourist information** The Tokyo Metropolitan Government Building Tourist Information Center has English-language information and publications.
**Transport** Tokyo's public transport system is the envy of the world. Of most use to travellers is the train and subway system, which is easy to navigate thanks to English signage.
**Wi-fi** The city has an increasing number of free hotspots. Look for the sticker that says 'Japan Wi-Fi'.
Sensō-ji | SEAN HSU/SHUTTERSTOCK ©
TOP EXPERIENCE
# Tokyo National Museum
If you visit only one museum, make it this one. Established in 1872, this collection of Japanese art covers ancient pottery, Buddhist sculpture, samurai swords, colourful ukiyo-e (woodblock prints), gorgeous kimonos and more.
Great For...
h v b
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For a couple of weeks in spring and autumn, the back garden, home to five vintage teahouses, opens to the public.
Explore Ashore
From Harumi Wharf take a bus to Yūrakuchō station then a train to Ueno; it'll take about 45 minutes. From Oi Wharf take a bus to Shinagawa JR train station to connect to a train running to Ueno; allow an hour to get from the port to the museum.
8Need to Know
東京国立博物館, Tokyo Kokuritsu Hakubutsukan; MAP; %03-3822-1111; www.tnm.jp; 13-9 Ueno-kōen, Taitō-ku; adult/child ¥620/free; h9.30am-5pm Tue-Thu, to 9pm Fri & Sat, to 6pm Sun; dJR lines to Ueno, Ueno-kōen exit
Honkan (Japanese Gallery) | MAURO_REPOSSINI/GETTY IMAGES ©
### Honkan (Japanese Gallery)
The museum is divided into several buildings, the most important of which is the Honkan (Japanese Gallery), which houses the collection of Japanese art. Visitors with only an hour or two should hone in on the galleries here. The building itself is in the Imperial Style of the 1930s, with art deco flourishes throughout. Allow two hours to take in the highlights, a half-day to do the Honkan in depth or a whole day to take in everything else as well.
### Gallery of Hōryū-ji Treasures
Next on the priority list is the enchanting Gallery of Hōryū-ji Treasures, which displays masks, scrolls and gilt Buddhas from Hōryū-ji (in Nara Prefecture, dating from 607) in a spare, elegant, box-shaped contemporary building (1999) by Taniguchi Yoshio. Nearby, to the west of the main gate, is the **Kuro-mon** (Black Gate), transported from the Edo-era mansion of a feudal lord. On weekends it opens for visitors to pass through.
Buddha statue | LEO DAPHNE/ALAMY STOCK PHOTO ©
### Tōyōkan & Heiseikan
Visitors with more time can explore the three-storied Tōyōkan (Gallery of Asian Art), with its collection of Buddhist sculptures from around Asia and delicate Chinese ceramics. The Heiseikan, accessed via a passage on the 1st floor of the Honkan, houses the Japanese Archaeological Gallery, full of pottery, talismans and articles of daily life from Japan's palaeolithic and neolithic periods. Temporary exhibitions (which cost extra) are held on the 2nd floor of the Heiseikan; these can be fantastic, but sometimes lack the English signage found throughout the rest of the museum.
### Kuroda Memorial Hall
Kuroda Seiki (1866–1924) is considered the father of modern Western-style painting in Japan. The Kuroda Memorial Hall (map Google map; 黒田記念室; %03-5777-8600; www.tobunken.go.jp/kuroda/index_e.html; 13-9 Ueno-kōen, Taitō-ku; h9.30am-5pm Tue-Sun; dJR lines to Ueno, Ueno-kōen exit) F, an annexe to the Tokyo National Museum, has some of his works, including key pieces such as _Maiko Girl_ and _Wisdom, Impression and Sentiment_ , a striking triptych of three nude women on canvases coated with ground gold.
TOP EXPERIENCE
# Sensō-ji
According to legend, in AD 628, two fishermen brothers pulled out a golden image of Kannon (the bodhisattva of compassion) from the nearby Sumida-gawa. Sensō-ji, the capital's oldest temple, was built to enshrine it.
Great For...
vaA
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Sensō-ji is home to many traditional festivals: ask for a list at a Tourist Information Center.
Explore Ashore
From Oi Wharf take a bus to Shinagawa station, a train running to Ueno and then the Ginza line subway to Asakusa, which will take just over an hour. From Harumi Wharf take a bus to Ginza station, then a Ginza line subway to Asakusa; it'll take 50 minutes.
8Need to Know
浅草寺; MAP; %03-3842-0181; www.senso-ji.jp; 2-3-1 Asakusa, Taitō-ku; admission free; h24hr; bGinza line to Asakusa, exit 1
5Take a Break
Dandelion Chocolate (map Google map; %03-5833-7270; <http://dandelionchocolate.jp>; 4-14-6 Kuramae, Taitō-ku; h10am-8pm; W; bAsakusa line to Kuramae, exit A3) specialises in bean-to-bar, small-batch chocolate, made on the premises, but also has delicious drink and food offerings that are impossible to resist.
RUDY BALASKO/SHUTTERSTOCK ©
### Kaminari-mon
The temple precinct begins at the majestic Kaminari-mon (雷門), which means Thunder Gate. An enormous _chōchin_ (lantern), which weighs 670kg, hangs from the centre. On either side are a pair of ferocious protective deities: Fūjin, the god of wind, on the right; and Raijin, the god of thunder, on the left. Kaminari-mon has burnt down countless times over the centuries; the current gate dates to 1970.
### Nakamise-dōri Shopping Street
Beyond Kaminari-mon is the bustling shopping street, Nakamise-dōri. With its lines of souvenir stands it is very touristy, though that's nothing new: Sensō-ji has been Tokyo's top tourist sight for centuries, since travel was restricted to religious pilgrimages during the feudal era. In addition to the usual T-shirts, you can find Edo-style crafts and oddities (such as wigs done up in traditional hairstyles). There are also numerous snack vendors serving up crunchy _sembei_ (rice crackers) and _age-manju_ (deep-fried _anko_ – bean-paste – buns).
Five-Storey Pagoda | MANUEL ASCANIO/SHUTTERSTOCK ©
### Hōzō-mon
At the end of Nakamise-dōri is Hōzō-mon (宝蔵門), another gate with fierce guardians. On its rear are a pair of 2500kg, 4.5m-tall _waraji_ (straw sandals) crafted for Sensō-ji by some 800 villagers in northern Yamagata Prefecture.
These are meant to symbolise the Buddha's power, and it's believed that evil spirits will be scared off by the giant footwear.
### Hondō
In front of the grand Hondō (Main Hall), with its dramatic sloping roof, is a large cauldron with smoking incense. The smoke is said to bestow health and you'll see people wafting it over their bodies. The current Hondō was constructed in 1958, replacing the one destroyed in WWII air raids. The style is similar to the previous one, though the roof tiles are now made of titanium.
The **Kannon image** (a tiny 6cm) is cloistered away from view deep inside the Hondō (and admittedly may not exist at all). Nonetheless, a steady stream of worshippers visits the temple to cast coins, pray and bow in a gesture of respect. Do feel free to join in.
Off the courtyard stands a 53m-high Five-Storey Pagoda (map Google map; 五重塔), a 1973 reconstruction of a pagoda built by Tokugawa Iemitsu. The current structure, renovated in 2017, is the second-highest pagoda in Japan.
### Omikuji
Don't miss getting your fortune told by an _omikuji_ (paper fortune). Drop ¥100 into the slots by the wooden drawers at either side of the approach to the Hondō, grab a silver canister and shake it. Extract a stick and note its number (in kanji). Replace the stick, find the matching drawer and withdraw a paper fortune (there's English on the back). If you pull out 大凶 ( _dai-kyō,_ great curse), never fear. Just tie the paper on the nearby rack, ask the gods for better luck, and try again!
### Asakusa-jinja
On the east side of the temple complex is Asakusa-jinja (map Google map; 浅草神社; %03-3844-1575; www.asakusajinja.jp; 2-3-1 Asakusa, Taitō-ku; h9am-4.30pm; bGinza line to Asakusa, exit 1), built in honour of the brothers who discovered the Kannon statue that inspired the construction of Sensō-ji. (Historically, Japan's two religions, Buddhism and Shintō, were intertwined and it was not uncommon for temples to include shrines and vice versa.) This section of Sensō-ji survived WWII and Asakusa-jinja's current structure dates from 1649. Painted a deep shade of red, it is a rare example of early Edo architecture.
Next to the shrine is the temple complex's eastern gate, Niten-mon (map Google map; 二天門; 2-3-1 Asakusa, Taitō-ku; bGinza line to Asakusa, exit 1), which has stood since 1618. Though it appears minor today, this gate was the point of entry for visitors arriving in Asakusa via boat – the main form of transport during the Edo period.
### What's Nearby?
The Edo-Tokyo Museum (map Google map; 江戸東京博物館; %03-3626-9974; www.edo-tokyo-museum.or.jp; 1-4-1 Yokoami, Sumida-ku; adult/child ¥600/free; h9.30am-5.30pm, to 7.30pm Sat, closed Mon; dJR Sōbu line to Ryōgoku, west exit) documents the city's transformation from tidal flatlands to feudal capital to modern metropolis via detailed scale re-creations of townscapes, villas and tenement homes, plus artefacts such as _ukiyo-e_ and old maps. Reopened in March 2018 after a renovation, the museum also has interactive displays, multilingual touch-screen panels and audio guides. Still, the best way to tour the museum is with one of the gracious English-speaking volunteer guides, who can really bring the history to life.
The woodblock artist Hokusai Katsushika (1760–1849) was born and died close to the location of the Sumida Hokusai Museum (map Google map; すみだ北斎美術館; %03-5777-8600; <http://hokusai-museum.jp>; 2-7-2 Kamezawa, Sumida-ku; adult/child/student & senior ¥400/free/300; h9.30am-5.30pm Tue-Sun; bOedo line to Ryōgoku, exit A4), which opened in 2016 in a striking aluminium-clad building designed by Pritzker Prize–winning architect Sejima Kazuyo. The small permanent exhibition gives an overview of his life and work, mostly through replicas.
Tokyo Skytree (map Google map; 東京スカイツリー; %0570-55-0102; www.tokyo-skytree.jp; 1-1-2 Oshiage, Sumida-ku; 350m/450m observation decks ¥2060/3090; h8am-10pm; bHanzōmon line to Oshiage, Tokyo Sky Tree exit) opened in May 2012 as the world's tallest 'free-standing tower' at 634m. Its silvery exterior of steel mesh morphs from a triangle at the base to a circle at 300m. There are two observation decks, at 350m and 450m. You can see more of the city during daylight hours – at peak visibility you can see up to 100km away, all the way to Mt Fuji – but it is at night that Tokyo appears truly beautiful.
oDid You Know?
Tokyo Skytree employs an ancient construction technique used in pagodas: an independent _shimbashira_ column that acts as a counterweight when the tower sways, cutting vibrations by 50%.
Edo-Tokyo Museum | COWARDLION/SHUTTERSTOCK ©
TOP EXPERIENCE
# Shopping in Harajuku
Harajuku is the gathering point for Tokyo's eccentric fashion tribes: teens who hang out on Takeshita-dōri, polished divas who strut up and down Omote-sandō, and trendsetters and peacocks who haunt the side streets.
Great For...
zsr
yDon't Miss
The narrow streets on either side of Omote-sandō, known as Ura-Hara ('back' Harajuku).
Explore Ashore
From Harumi Wharf take a bus to Hibiya station, then the Chiyoda line to Meiji-jingūmae subway station. From Oi Wharf take a bus to Shinagawa station, then take the JR Yamanote line to Harajuku. Both routes take 45 to 50 minutes.
8Need to Know
Trends move fast in Harajuku. To keep up, follow @TokyoFashion on Instagram.
PIUS LEE/SHUTTERSTOCK ©
### Takeshita-dōri
Takeshita-dōri (map Google map; 竹下通り; Jingūmae, Shibuya-ku; dJR Yamanote line to Harajuku, Takeshita exit) is Tokyo's famously outré fashion bazaar and a pilgrimage site for teens from all over Japan. Here trendy duds sit alongside the trappings of decades of fashion subcultures (plaid and safety pins for the punks; colourful tutus for the decora; Victorian dresses for the Gothic Lolitas).
### Laforet
Laforet (map Google map; ラフォーレ; www.laforet.ne.jp; 1-11-6 Jingūmae, Shibuya-ku; h11am-9pm; dJR Yamanote line to Harajuku, Omote-sandō exit) has been a beacon of cutting-edge Harajuku style for decades and lots of quirky, cult-favourite brands still cut their teeth here (you'll find some examples at the ground-floor boutique, Wall).
### KiddyLand
Multistorey toy emporium KiddyLand (map Google map; キデイランド; %03-3409-3431; www.kiddyland.co.jp; 6-1-9 Jingūmae, Shibuya-ku; h11am-9pm Mon-Fri, 10.30am-9pm Sat & Sun; dJR Yamanote line to Harajuku, Omote-sandō exit) is packed to the rafters with character goods, including all your Studio Ghibli, Sanrio and Disney faves. It's not just for kids either; you'll spot plenty of adults on a nostalgia trip down the Hello Kitty aisle.
PHOTOGRAPHER253/SHUTTERSTOCK ©
### Cat Street
Had enough of crowded Harajuku? Exit, stage right, for Cat Street (map Google map; キャットストリート; dJR Yamanote line to Harajuku, Omote-sandō exit), a windy road closed to cars and lined with a mishmash of boutiques and more room to move.
### House @Mikiri Hassin
Hidden deep in Ura-Hara (Harajuku's backstreet area), thisshop (ハウス@ミキリハッシン; MAP; %03-3486-7673; <http://house.mikirihassin.co.jp>; 5-42-1 Jingūmae, Shibuya-ku; hnoon-9pm Thu-Tue; bGinza line to Omote-sandō, exit A1) stocks an ever-changing selection of experimental Japanese fashion brands. Contrary to what the cool merch might suggest, the sales clerks are polite and friendly – grateful, perhaps, that you made the effort to find the place. Look for 'ハウス' spelled vertically in neon.
### 6% Doki Doki
Tucked away on an Ura-Hara backstreet in a bubblegum-pink building, 6% Doki Doki (map Google map; ロクパーセントドキドキ; www.dokidoki6.com; 2nd fl, 4-28-16 Jingūmae, Shibuya-ku; hnoon-8pm; dJR Yamanote line to Harajuku, Omote-sandō exit) sells acid-bright accessories that are part raver, part schoolgirl and, according to the shop's name, 'six percent exciting'. It's 100% Harajuku.
TOP EXPERIENCE
# Meiji-jingū
Tokyo's largest and most famous Shintō shrine feels a world away from the city. The grounds are vast, enveloping the classic wooden shrine buildings and a landscaped garden in a thick coat of green.
Great For...
hAg
yDon't Miss
Meiji-jingū Gyoen when the irises bloom in June.
Explore Ashore
From Harumi Wharf take a bus to Hibiya station, then the Chiyoda line to Meiji-jingūmae subway station (use exit 2). From Oi Wharf take a bus to Shinagawa station, then take the JR Yamanote line to Harajuku (take the Omote-sandō exit). Both routes take 45 to 50 minutes.
8Need to Know
明治神宮; MAP; www.meijijingu.or.jp; 1-1 Yoyogi Kamizono-chō, Shibuya-ku; admission free; hdawn-dusk; dJR Yamanote line to Harajuku, Omote-sandō exit
COWARDLION/SHUTTERSTOCK ©
### History
Meiji-jingū is dedicated to the Emperor Meiji and Empress Shōken, whose reign (1868–1912) coincided with Japan's transformation from isolationist, feudal state to modern nation.
### The Gates
Several wooden _torii_ (gates) mark the entrance to Meiji-jingū. The largest, created from a 1500-year-old Taiwanese cypress, stands 12m high. It's the custom to bow upon passing through a _torii,_ which marks the boundary between the mundane world and the sacred one.
### The Font
Before approaching the main shrine, visitors purify themselves by pouring water over their hands at the _temizuya_ (font). Dip the ladle in the water and first rinse your left hand then your right. Pour some water into your left hand and rinse your mouth, then rinse your left hand again. Make sure none of this water gets back into the font!
Ladles at the font | VACANCYLIZM/SHUTTERSTOCK ©
### Main Shrine
Constructed in 1920 and destroyed in WWII air raids, the shrine was rebuilt in 1958; however, unlike so many of Japan's postwar reconstructions, Meiji-jingū has an authentic old-world feel. The main shrine is made of cypress from the Kiso region of Nagano. To make an offering, toss a ¥5 coin in the box, bow twice, clap your hands twice and then bow again. To the right, you'll see kiosks selling _ema_ (wooden plaques on which prayers are written) and _omamori_ (charms).
### Meiji-jingū Gyoen
The shrine itself occupies only a small fraction of the sprawling forested grounds, which contain some 120,000 trees collected from all over Japan. Along the path towards the main shrine is the entrance to Meiji-jingū Gyoen (map Google map; 明治神宮御苑, Inner Garden; ¥500; h9am-4.30pm, to 4pm Nov-Feb), a landscaped garden. It once belonged to a feudal estate; however, when the grounds passed into imperial hands, the emperor himself designed the iris garden to please the empress.
Ginza & Marunouchi
1Sights
1Hama-rikyū Onshi-teienC5
2Imperial PalaceB2
3IntermediathequeD2
4Tokyo TowerA6
5Tsukiji MarketD4
7Shopping
6ItōyaD3
7Okuno BuildingD3
5Eating
8KyūbeyC4
9Tempura KondōC3
10Tofuya-UkaiA6
6Drinking & Nightlife
11Chashitsu KabokuC3
12Nakajima no OchayaC6
1Sights
### 1 Ginza & Marunouchi
Tsukiji MarketMarket
(map Google map; 場外市場, Jōgai Shijō; MAP; www.tsukiji.or.jp; 6-chōme Tsukiji, Chūō-ku; hmostly 5am-2pm; bHibiya line to Tsukiji, exit 1) Tokyo's main wholesale market may have moved to Toyosu (豊洲市場, Toyosu Shijō; www.shijou.metro.tokyo.jp; 6-chōme Toyosu, Kōtō-ku; h5am-5pm Mon-Sat, closed some Wed; dYurikamome line to Shijō-mae)
but there are many reasons to visit its old home. The tightly packed rows of vendors (which once formed the Outer Market) hawk market and culinary-related goods, such as dried fish, seaweed, kitchen knives, rubber boots and crockery. It's also a fantastic place to eat, with great street food and a huge concentration of small restaurants and cafes, most specialising in seafood.
Imperial PalacePalace
(map Google map; 皇居, Kōkyo; MAP; %03-5223-8071; <http://sankan.kunaicho.go.jp>; 1 Chiyoda, Chiyoda-ku; htours usually 10am & 1.30pm Tue-Sat; bChiyoda line to Ōtemachi, exits C13b & C10) F
The Imperial Palace occupies the site of the original Edo-jō, the Tokugawa shogunate's castle. In its heyday this was the largest fortress in the world, though little remains today apart from the moat and stone walls. Most of the 3.4-sq-km complex is off limits, as this is the emperor's home, but join one of the free tours organised by the Imperial Household Agency to see a small part of the inner compound.
IntermediathequeMuseum
(map Google map; インターメディアテク; %03-5777-8600; www.intermediatheque.jp; 2nd & 3rd fl, JP Tower, 2-7-2 Marunouchi, Chiyoda-ku; h11am-6pm, to 8pm Fri & Sat, usually closed Sun & Mon; dJR Yamanote line to Tokyo, Marunouchi exit) F
Dedicated to interdisciplinary experimentation, Intermediatheque cherry-picks from the vast collection of the University of Tokyo (Tōdai) to craft a fascinating, contemporary museum experience. Go from viewing the best ornithological taxidermy collection in Japan to a giant pop art print or the beautifully encased skeleton of a dinosaur. A handsome Tōdai lecture hall is reconstituted as a forum for events, including playing 1920s jazz recordings on a gramophone or old movie screenings.
teamLab Borderless
Art collective teamLab has created 60 artworks for this new museum ( %03-6406-3949; <https://borderless.teamlab.art>; 1-3-8 Aomi, Kōtō-ku; adult/child ¥3200/1000; h10am-7pm Mon-Thu & Sun, to 9pm Fri & Sat, closed 2nd & 4th Tue; c; dYurikamome line to Aomi) that tests the border between art and the viewer, and many of them are interactive. Not sure how? That's the point – go up to the artworks, move and touch them (or just stand still) and see how they react. There is no suggested route; teamLab Borderless is all about exploration. Buy tickets in advance online.
Interactive exhibit | TEAMLAB BORDERLESS, ODAIBA, TOKYO ©
Hama-rikyū Onshi-teienGardens
(map Google map; 浜離宮恩賜庭園, Detached Palace Garden; MAP; %03-3541-0200; www.tokyo-park.or.jp/teien; 1-1 Hama-rikyū-teien, Chūō-ku; adult/child ¥300/free; h9am-5pm; bŌedo line to Shiodome, exit A1)
This beautiful garden, one of Tokyo's finest, is all that remains of a shogunate palace that was also an outer fort for Edo Castle. The main features are a large duck pond with an island that's home to a functioning tea pavilion, Nakajima no Ochaya (map Google map; 中島の御茶屋; tea ¥510 or ¥720; h9am-4.30pm), as well as three other teahouses and wonderfully manicured trees (black pine, Japanese apricot, hydrangeas etc), some hundreds of years old.
### 1 Roppongi & Akasaka
National Art Center TokyoMuseum
(map Google map; 国立新美術館; %03-5777-8600; www.nact.jp; 7-22-1 Roppongi, Minato-ku; admission varies; h10am-6pm Wed, Thu, Sun & Mon, to 8pm Fri & Sat; bChiyoda line to Nogizaka, exit 6)
Designed by Kurokawa Kishō, this architectural beauty has no permanent collection, but boasts the country's largest exhibition space for visiting shows, which have included Renoir and Modigliani. A visit here is recommended to admire the building's awesome undulating glass facade, its cafes atop giant inverted cones and the great gift shop, Souvenir from Tokyo (map Google map; スーベニアフロムトーキョー; %03-6812 9933; www.souvenirfromtokyo.jp; h10am-6pm Sat-Mon, Wed & Thu, to 8pm Fri) in the basement.
21_21 Design SightMuseum
(map Google map; 21_21デザインサイト; %03-3475-2121; www.2121designsight.jp; Tokyo Midtown, 9-7-6 Akasaka, Minato-ku; adult/child ¥1100/free; h11am-7pm Wed-Mon; bŌedo line to Roppongi, exit 8)
An exhibition and discussion space dedicated to all forms of design, the 21_21 Design Sight is a beacon for local art enthusiasts, whether they be designers or onlookers. The striking concrete and glass building, bursting out of the ground at sharp angles, was designed by Pritzker Prize–winning architect Andō Tadao.
Ghibli Museum, Mitaka
Master animator Miyazaki Hayao's Studio Ghibli (pronounced 'jiburi') is responsible for some of the best-loved films in Japan – and the world. Miyazaki designed the Ghibli Museum, Mitaka (ジブリ美術館; www.ghibli-museum.jp; 1-1-83 Shimo-Renjaku, Mitaka-shi; adult ¥1000, child ¥100-700; h10am-6pm Wed-Mon; dJR Chūō-Sōbu line to Mitaka, south exit) and the end result is faithful to the dreamy, vaguely steampunk atmosphere that makes his animations so enticing.
Looking like it was plucked from the pages of a fairy tale, the museum houses a whimsical workshop filled with books and artworks that inspired Miyazaki, oodles of original sketches and models, vintage animation tech and, of course, a hundreds-strong cast of your favourite characters and critters.
A highlight is a giant, plush replica of the cat bus from the classic _My Neighbor Totoro_ (1988) that kids can climb on. There's also a small theatre where original animated shorts – only seen here! – are screened (you'll get a ticket when you enter). The film changes monthly to keep fans coming back.
Museum tickets are like gold and go quick, especially during holiday periods. With luck, there'll be a date and time-slot that suits your plans: changes aren't possible and you can't just show up. Order up to four months in advance from select travel agencies, or up to a month ahead using Lawson Ticket; see the museum website for info.
COWARDLION/SHUTTERSTOCK ©
Roppongi, Harajuku & Shibuya
1Sights
121_21 Design SightF2
2Cat StreetB2
3Meiji-jingūA1
4Meiji-jingū GyoenA1
5National Art Center TokyoE3
6Nezu MuseumD3
7Omote-sandōC3
8Shibuya CrossingB4
9Takeshita-dōriB2
10Ukiyo-e Ōta Memorial Museum of ArtB2
11Yoyogi-kōenA2
7Shopping
126% Doki DokiB2
13House @Mikiri HassinB3
14Japan Traditional Crafts Aoyama SquareE1
15KiddyLandB2
16LaforetB2
Souvenir from Tokyo(see 5)
17Tokyu HandsA3
5Eating
18Honmura-AnF3
19KikunoiF2
6Drinking & Nightlife
20Sakurai Japanese Tea ExperienceC3
21Two Dogs TaproomF3
### 1 Shibuya & Harajuku
Shibuya CrossingStreet
(map Google map; 渋谷スクランブル交差点, Shibuya Scramble; MAP; dJR Yamanote line to Shibuya, Hachikō exit)
Rumoured to be the busiest intersection in the world (and definitely in Japan), Shibuya Crossing is like a giant beating heart, sending people in all directions with every pulsing light change. Nowhere else says 'Welcome to Tokyo' better than this. Hundreds of people – and at peak times upwards of 3000 people – cross at a time, coming from all directions at once, dodging each other with a practised, nonchalant agility.
Yoyogi-kōenPark
(map Google map; 代々木公園; www.yoyogipark.info; Yoyogi-kamizono-chō, Shibuya-ku; dJR Yamanote line to Harajuku, Omote-sandō exit)
If it's a sunny and warm weekend afternoon, you can count on there being a crowd lazing around the large grassy expanse that is Yoyogi-kōen. You'll usually find revellers and noisemakers of all stripes, from hula-hoopers to African drum circles to retro greasers dancing around a boom box. It's an excellent place for a picnic and probably the only place in the city where you can reasonably toss a Frisbee without fear of hitting someone.
Ukiyo-e Ōta Memorial Museum of ArtMuseum
(map Google map; 浮世絵太田記念美術館; %03-3403-0880; www.ukiyoe-ota-muse.jp; 1-10-10 Jingūmae, Shibuya-ku; adult ¥700-1000, child free; h10.30am-5.30pm Tue-Sun; dJR Yamanote line to Harajuku, Omote-sandō exit)
This small museum (where you swap your shoes for slippers) is the best place in Tokyo to see _ukiyo-e_. Each month it presents a seasonal, thematic exhibition (with English curation notes), drawing from the truly impressive collection of Ōta Seizo, the former head of the Toho Life Insurance Company. Most exhibitions include a few works by masters such as Hokusai and Hiroshige. The museum closes the last few days of the month (between exhibitions).
Nezu MuseumMuseum
(map Google map; 根津美術館; %03-3400-2536; www.nezu-muse.or.jp; 6-5-1 Minami-Aoyama, Minato-ku; adult/child ¥1100/free, special exhibitions extra ¥200; h10am-5pm Tue-Sun; bGinza line to Omote-sandō, exit A5)
Nezu Museum offers a striking blend of old and new: a renowned collection of Japanese, Chinese and Korean antiquities in a gallery space designed by contemporary architect Kuma Kengo. Select items from the extensive collection are displayed in seasonal exhibitions. The English explanations are usually pretty good. Behind the galleries is a woodsy strolling garden laced with stone paths and studded with teahouses and sculptures.
Omote-sandōStreet
(map Google map; 表参道; bGinza line to Omote-sandō, exits A3 & B4, dJR Yamanote line to Harajuku, Omote-sandō exit)
This broad, tree-lined boulevard is lined with boutiques from the top European fashion houses. More interesting are the buildings themselves, designed by some of the biggest names in Japanese architecture. There's no better (or more convenient) place to gain an overview of Japan's current sense of design. Highlights include the Dior boutique by SANAA (Nishizawa Ryue and Sejima Kazuyo) and the Tod's boutique by Itō Toyō.
### 1 Shinjuku
Tokyo Metropolitan Government BuildingObservatory
(東京都庁, Tokyo Tochō; www.metro.tokyo.jp/english/offices; 2-8-1 Nishi-Shinjuku, Shinjuku-ku; hobservatories 9.30am-11pm; bŌedo line to Tochōmae, exit A4) F
Tokyo's city hall – a landmark building designed by Tange Kenzō – has observatories atop both the south and north towers of Building 1 (the views are virtually the same). On a clear day (morning is best), you may catch a glimpse of Mt Fuji beyond the urban sprawl to the west. Direct-access elevators are on the ground floor.
Golden GaiArea
(ゴールデン街; <http://goldengai.jp>; 1-1 Kabukichō, Shinjuku-ku; dJR Yamanote line to Shinjuku, east exit)
Golden Gai – a Shinjuku institution for over half a century – is a collection of tiny bars, often literally no bigger than a closet and seating maybe a dozen. Each is as unique and eccentric as the 'master' or 'mama' who runs it. In a sense, Golden Gai, which has a strong visual appeal, with its low-slung wooden buildings, is their work of art. It's more than just a place to drink.
CCourses
WanariyaTraditional Craft
(map Google map; 和なり屋; %03-5603-9169; www.wanariya.jp; 1-8-10 Senzoku, Taitō-ku; indigo dyeing/weaving from ¥1920/1980; h10am-7pm irregular holidays; bHibiya line to Iriya, exit 1)
A young and friendly team runs this indigo-dyeing and traditional _hataori_ (hand-loom-weaving) workshop. In under an hour you can learn to dye a T-shirt or a tote bag or weave a pair of coasters. It's a fantastic opportunity to make your own souvenirs. Book at least three days in advance.
Kitchen Kujo TokyoCooking
(map Google map; %03-5832-9452; www.kujo.tokyo; 1-2-10 Yanaka, Taitō-ku; classes ¥6000-12,000; hclasses 10.30am or 1.30pm, bar 6-10.30pm Mon-Sat; bChiyoda line to Nezu, exit 2)
The Kobayashi family and their translator and ramen chef Jun offer an interesting variety of cooking and culture classes at this handy studio devoted to cooking with organic products. Learn how to make tofu, miso, vegan ramen and curry rice with guest instructor Curryman (who dresses in a wacky costume). Also available are calligraphy, tea-ceremony and yoga classes.
7Shopping
Ginza, home to high-end department stores and boutiques, has long been Tokyo's premier shopping district, though Harajuku – popular with younger shoppers – puts up a good fight for the title. Shibuya is another trendy district, while Asakusa is good for traditional crafts.
Japan Traditional Crafts Aoyama SquareArts & Crafts
(map Google map; 伝統工芸 青山スクエア; %03-5785-1301; www.kougeihin.jp; 8-1-22 Akasaka, Minato-ku; h11am-7pm; bGinza line to Aoyama-itchōme, exit 4)
Supported by the Japanese Ministry of Economy, Trade and Industry, this is as much a showroom as a shop, exhibiting a broad range of traditional crafts from around Japan, including lacquerwork boxes, woodwork, cut glass, textiles and pottery. There are some exquisite heirloom pieces here, but also beautiful items at reasonable prices.
Spa LaQua
One of Tokyo's few true onsen, this chic spa complex (スパ ラクーア; %03-5800-9999; www.laqua.jp; 5th-9th fl, Tokyo Dome City, 1-1-1 Kasuga, Bunkyō-ku; weekday/weekend ¥2850/3174; h11am-9am; bMarunouchi line to Kōrakuen, exit 2), renovated in 2017, relies on natural hot-spring water from 1700m below ground. There are indoor and outdoor baths, saunas and a bunch of add-on options, such as _akasuri_ (Korean-style whole-body exfoliation). It's a fascinating introduction to Japanese health and beauty rituals.
An extra ¥865 gives you access to the Healing Baden area, with even more varieties of saunas and a lounge area styled like a Balinese resort. Here, men and women can hang out together (everyone gets a pair of rental pyjamas). There are lounging areas too, with reclining chairs.
NED SNOWMAN/SHUTTERSTOCK ©
ItōyaArts & Crafts
(map Google map; 伊東屋; %03-3561-8311; www.ito-ya.co.jp; 2-7-15 Ginza, Chūō-ku; h10.30am-8pm Mon-Sat, to 7pm Sun; bGinza line to Ginza, exit A13)
Explore the nine floors (plus several more in the nearby annex) of stationery at this famed, century-old Ginza establishment. There are everyday items (such as notebooks and greeting cards) and luxuries (fountain pens and Italian leather agendas). You'll also find _washi_ (handmade paper), _tenugui_ (beautifully hand-dyed thin cotton towels) and _furoshiki_ (wrapping cloths).
Okuno BuildingArts & Crafts
(map Google map; 奥野ビル; 1-9-8 Ginza, Chūō-ku; hmost galleries noon-7pm; bYūrakuchō line to Ginza-itchōme, exit 10)
This 1932 apartment block (cutting edge for its time) is a retro time capsule, its seven floors packed with some 40 tiny boutiques and gallery spaces. Climbing up and down the Escher-like staircases, or using the antique elevator, you'll come across mini-exhibitions that change weekly.
Tokyu HandsDepartment Store
(map Google map; 東急ハンズ; <http://shibuya.tokyu-hands.co.jp>; 12-18 Udagawa-chō, Shibuya-ku; h10am-9pm; dJR Yamanote line to Shibuya, Hachikō exit)
This DIY and _zakka_ (miscellaneous things) store has eight fascinating floors of everything you didn't know you needed – reflexology slippers, bee-venom face masks and cartoon-character-shaped rice-ball moulds, for example. Most stuff is inexpensive, making it perfect for souvenir- and gift-hunting. Warning: you could lose hours in here.
Beams JapanFashion & Accessories
(ビームス·ジャパン; www.beams.co.jp; 3-32-6 Shinjuku, Shinjuku-ku; h11am-8pm; dJR Yamanote line to Shinjuku, east exit)
Beams, a national chain of trendsetting boutiques, is a Japanese cultural institution and this multistorey Shinjuku branch has a particular audience in mind: you, the traveller. It's full of the latest Japanese streetwear labels, traditional fashions with cool modern twists, artisan crafts, pop art and more – all contenders for that perfect only-in-Tokyo souvenir. Set your budget before you enter.
Marugoto NipponFood & Drinks
(map Google map; まるごとにっぽん; %03-3845-0510; www.marugotonippon.com; 2-6-7 Asakusa, Taitō-ku; h10am-8pm; bGinza line to Tawaramachi, exit 3)
Think of this as a minimall, showcasing the best of Japan's speciality food and drink (ground floor) and arts and crafts (2nd floor). The 3rd floor showcases the products and attractions of different Japanese regions on a regularly changing basis.
5Eating
Honmura-AnSoba¥
(map Google map; 本むら庵; %03-5772-6657; www.honmuraantokyo.com; 7-14-18 Roppongi, Minato-ku; noodles from ¥900, set meals lunch/dinner ¥1600/7400; hnoon-2.30pm & 5.30-10pm Tue-Sun, closed 1st & 3rd Tue of month; W; bHibiya line to Roppongi, exit 4)
This fabled soba shop, once located in Manhattan, now serves its handmade buckwheat noodles at this rustically contemporary noodle shop on a Roppongi side street. The noodles' delicate flavour is best appreciated when served on a bamboo mat, with tempura or with dainty slices of _kamo_ (duck).
InnsyouteiJapanese¥
(map Google map; 韻松亭; %03-3821-8126; www.innsyoutei.jp; 4-59 Ueno-kōen, Taitō-ku; lunch/dinner from ¥1680/5500; hrestaurant 11am-3pm & 5-9.30pm, tearoom 3-5pm; dJR lines to Ueno, Ueno-kōen exit)
In a gorgeous wooden building dating to 1875, Innsyoutei (pronounced 'inshotei' and meaning 'rhyme of the pine cottage') has long been a favourite spot for fancy _kaiseki_ -style meals while visiting Ueno-kōen (map Google map; 上野公園; www.ueno-bunka.jp). Without a booking (essential for dinner) you'll have a long wait but it's worth it. Lunchtime _bentō_ (boxed meals) offer beautifully presented morsels and are great value.
HanteiJapanese¥¥
(map Google map; はん亭; %03-3287-9000; www.hantei.co.jp; 2-12-15 Nezu, Bunkyō-ku; lunch/dinner from ¥3200/3000; hnoon-3pm & 5-10pm Tue-Sun; bChiyoda line to Nezu, exit 2)
Housed in a beautifully maintained, century-old traditional wooden building, Hantei is a local landmark. Delectable skewers of seasonal _kushiage_ (fried meat, fish and vegetables) are served with small, refreshing side dishes. Lunch includes eight or 12 sticks and dinner starts with six, after which you can order additional rounds (three/six skewers ¥800/1600).
Fun for Young & Old
In need of amusement-park thrills? The latest virtual-reality gaming? Brownie points with the kids?
Tokyo Joypolis (東京ジョイポリス; <http://tokyo-joypolis.com>; 3rd-5th fl, DECKS Tokyo Beach, 1-6-1 Daiba, Minato-ku; adult/child ¥800/500, all-rides passport ¥4300/3300, passport after 5pm ¥3300/2300; h10am-10pm; dYurikamome line to Odaiba Kaihin-kōen, north exit) is an indoor amusement park stacked with virtual-reality attractions and thrill rides.
Sky Circus (スカイサーカス; %03-3989-3457; www.skycircus.jp; Sunshine 60, 3-1-1 Higashi-Ikebukuro, Toshima-ku; observatory ticket adult/child ¥1200/600, attractions extra; h10am-10pm; dJR Yamanote line to Ikebukuro, east exit) is a giddying exploration of VR-tech to send you bouncing, flying and zooming around the 'future' city.
**Tokyo Disney Resort** (東京ディズニーリゾート; %domestic calls 0570-00-8632, from overseas +81-45-330-5211; www.tokyodisneyresort.jp; 1-1 Maihama, Urayasu-shi, Chiba-ken; 1-day ticket for 1 park adult/child ¥7400/4800, after 6pm ¥4200; hvaries by season; dJR Keiyō line to Maihama, south exit) was one of the first Disney parks outside the US, and is still a great day or weekend out.
Tokyo Joypolis | TK KURIKAWA/SHUTTERSTOCK ©
Kappō YoshibaJapanese¥¥
(map Google map; 割烹吉葉; %03-3623-4480; www.kapou-yoshiba.jp; 2-14-5 Yokoami, Sumida-ku; dishes ¥650-7800; h11.30am-2pm & 5-10pm Mon-Sat; bŌedo line to Ryōgoku, exit 1)
The former Miyagino sumo stable is the location for this one-of-a-kind restaurant that has preserved the _dōyō_ (practice ring) as its centrepiece. Playing up to its sumo roots, you can order the protein-packed stew _chanko-nabe_ (for two people from ¥5200), but Yoshiba's real strength is its sushi, freshly prepared in jumbo portions.
KikunoiKaiseki¥¥¥
(map Google map; 菊乃井; %03-3568-6055; www.kikunoi.jp; 6-13-8 Akasaka, Minato-ku; lunch/dinner course from ¥11,900/16,000; hnoon-12.30pm Tue-Sat, 5-7.30pm Mon-Sat; bChiyoda line to Akasaka, exit 7)
Exquisitely prepared seasonal dishes are as beautiful as they are delicious at this Tokyo outpost of one of Kyoto's most acclaimed _kaiseki_ (Japanese haute cuisine) restaurants. Kikunoi's third-generation chef, Murata Yoshihiro, has written a book on _kaiseki_ (translated into English) that the staff helpfully use to explain the dishes you are served.
Tofuya-UkaiKaiseki¥¥¥
(map Google map; とうふ屋うかい; %03-3436-1028; www.ukai.co.jp/english/shiba; 4-4-13 Shiba-kōen, Minato-ku; set meals lunch/dinner from ¥5940/10,800; h11.45am-3pm & 5-7.30pm Mon-Fri, 11am-7.30pm Sat & Sun; v; bŌedo line to Akabanebashi, exit 8)
One of Tokyo's most gracious restaurants is located in a former sake brewery (moved from northern Japan), with an exquisite traditional garden in the shadow of Tokyo Tower (東京タワー). Seasonal preparations of tofu and accompanying dishes are served in the refined _kaiseki_ style. Make reservations well in advance. Vegetarians should advise staff when they book, and last orders for weekday lunch is 3pm, for dinner 7.30pm.
KyūbeySushi¥¥¥
(map Google map; 久兵衛; %03-3571-6523; www.kyubey.jp; 8-7-6 Ginza, Chūō-ku; set meals lunch/dinner from ¥4400/11,000; h11.30am-2pm & 5-10pm Mon-Sat; bGinza line to Shimbashi, exit 3)
Since 1935, Kyūbey's quality and presentation have won it a moneyed and celebrity clientele. Despite the cachet, this is a relaxed restaurant. The friendly owner, Imada-san, speaks excellent English as do some of his team of talented chefs, who will make and serve your sushi, piece by piece. The ¥8000 lunchtime _omakase_ (chef's choice) is great value.
Tempura KondōTempura¥¥¥
(map Google map; てんぷら近藤; %03-5568-0923; 9th fl, Sakaguchi Bldg, 5-5-13 Ginza, Chūō-ku; lunch/dinner course from ¥6500/11,000; hnoon-3pm & 5-10pm Mon-Sat; bGinza line to Ginza, exit B5)
Nobody in Tokyo does tempura vegetables like chef Kondō Fumio. The carrots are julienned to a fine floss, the corn is pert and juicy, and the sweet potato is comfort food at its finest. Courses include seafood, too. Lunch at noon or 1.30pm; last dinner booking at 8pm. Reserve ahead.
Ueno & Asakusa
1Sights
1Asakusa-jinjaE1
2Edo-Tokyo MuseumD4
3Five-Storey PagodaD2
4Hōzō-monE2
5Kaminari-monD2
6Kuroda Memorial HallB1
7Niten-monE2
8Sensō-jiE2
9Sumida Hokusai MuseumE4
10Tokyo National MuseumB1
11Tokyo SkytreeF2
12Ueno-kōenB1
2Activities, Courses & Tours
13Kitchen Kujo TokyoA1
14WanariyaD1
7Shopping
15Marugoto NipponD2
5Eating
16HanteiA1
17InnsyouteiB2
18Kappō YoshibaD3
6Drinking & Nightlife
19Dandelion ChocolateD3
3Entertainment
20Ryōgoku KokugikanD4
6Drinking
Sakurai Japanese Tea ExperienceTeahouse
(map Google map; 櫻井焙茶研究所; %03-6451-1539; www.sakurai-tea.jp; 5th fl, Spiral Bldg, 5-6-23 Minami-Aoyama, Minato-ku; tea from ¥1400, course from ¥4800; h11am-11pm; bGinza line to Omote-sandō, exit B1)
Tea master (and former bartender) Sakurai Shinya's contemporary take on the tea ceremony is a must for anyone hoping to be better acquainted with Japan's signature brew. The course includes several varieties – you might be surprised how different tea can taste – paired with small bites, including some beautiful traditional sweets. Reservations recommended.
Purchase loose tea and beautiful teapots and cups at the attached shop (open until 8pm)
Chashitsu KabokuTeahouse
(map Google map; 茶室 嘉木; %03-6212-0202; www.ippodo-tea.co.jp; 3-1-1 Marunouchi, Chiyoda-ku; tea set ¥1080-2600; h11am-7pm; dJR Yamanote line to Yurakuchō, Tokyo International Forum exit)
Run by famed Kyoto tea producer Ippōdō – which celebrated 300 years of business in 2017 – this teahouse is a fantastic place to experience the myriad pleasures of _ocha_ (green tea). It's also one of the few places that serves _koicha_ (thick tea), which is even thicker than ordinary _matcha_ (powdered green tea). Sets are accompanied by a pretty, seasonal _wagashi_.
Toyama BarBar
(トヤマバー; %03-6262-2723; www.toyamakan.jp; 1-2-6 Nihombashi-muromachi, Chūō-ku; h11am-9pm; bGinza line to Mitsukoshimae, exit B5)
This slick counter bar offers a selection of sakes from 17 different Toyama breweries. A set of three 30mL cups costs a bargain ¥700 (90mL cups from ¥700 each). English tasting notes are available. It's part of the Nihonbashi Toyama-kan (日本橋とやま館), which promotes goods produced in Japan's northern Toyama Prefecture. Pick up a bottle of anything you like at the attached shop.
Two Dogs TaproomCraft Beer
(map Google map; %03-5413-0333; www.twodogs-tokyo.com; 3-15-24 Roppongi, Minato-ku; h11.30am-2.30pm Mon-Fri, 5-11pm Sun & Mon, until midnight Tue & Wed, until 2am Thu-Sat; bHibiya line to Roppongi, exit 3)
There are 24 taps devoted to Japanese and international craft beers, including its own Roppongi Pale Ale, at this convivial pub just off the main Roppongi drag. Work your way through a few jars to wash down the tasty and decent-sized pizzas.
3Entertainment
Ryōgoku KokugikanSpectator Sport
(map Google map; 両国国技館, Ryōgoku Sumo Stadium; MAP; %03-3623-5111; www.sumo.or.jp; 1-3-28 Yokoami, Sumida-ku; tickets ¥3800-11,700; dJR Sōbu line to Ryōgoku, west exit)
If you're in town when a tournament is on, don't miss the chance to catch the big boys of Japanese wrestling in action at the country's largest sumo stadium. The key spectacle is at around 3.45pm, when the _makuuchi_ (top division) wrestlers in elaborately decorated aprons parade into the ring. Tickets can be bought online one month before the tournament opens.
8INFORMATION
DANGERS & ANNOYANCES
The biggest threat to travellers in Tokyo is the city's general aura of safety; keep up the same level of caution and common sense that you would back home.
oDrink-spiking continues to be a problem in Roppongi (resulting in robbery, extortion and, in extreme cases, physical assault). This is most often the case when touts are involved; never follow a tout into a bar, anywhere.
oMen are likely to be solicited in Roppongi and neighbourhoods that are considered red-light districts, including Kabukichō (in Shinjuku) and Dōgenzaka (in Shibuya). Women – particularly solo women – are likely to be harassed in these districts.
TOURIST INFORMATION
**Tokyo Metropolitan Government BuildingTourist Information Center** ( %03-5321-3077; info@tokyo-tourism.jp; 1st fl, 2-8-1 Nishi-Shinjuku, Shinjuku-ku; h9.30am-6.30pm; bŌedo line to Tochōmae, exit A4) Has English-language information and publications. There are additional branches in **Keisei Ueno Station** (MAP; %03-3836-3471; 1-60 Ueno-kōen, Taitō-ku; h9.30am-6.30pm; W; dJR & Keisei lines to Ueno, Ikenohata exit) and on the 3rd floor of the **Shinjuku Bus Terminal** ( %03-6274-8192; 5-24-55 Sendagaya, Shibuya-ku; h6.30am-11pm; dJR Yamanote line to Shinjuku, new south exit).
8GETTING AROUND
TRAIN & SUBWAY
Tokyo's extensive rail network includes JR lines, a subway system and private commuter lines that depart in every direction for the suburbs, like spokes on a wheel. Journeys that require transfers between lines run by different operators cost more than journeys that use only one operator's lines. Major transit hubs include Tokyo, Shinagawa, Shibuya, Shinjuku, Ikebukuro and Ueno Stations. Trains arrive and depart precisely on time and are generally clean and pleasant, though they get uncomfortably crowded during rush hours.
Tokyo has 13 subway lines, nine of which are operated by **Tokyo Metro** (www.tokyometro.jp) and four by **Toei** (www.kotsu.metro.tokyo.jp). The lines are colour-coded, making navigation fairly simple. Unfortunately a transfer ticket is required to change between the two; a Pasmo or Suica card makes this process seamless, but either way a journey involving more than one operator comes out costing slightly more. Rides on Tokyo Metro cost ¥170 to ¥240 (¥90 to ¥120 for children) and on Toei ¥180 to ¥320 (¥90 to ¥160 for children), depending on how far you travel.
KEY ROUTES
**Ginza subway line** Shibuya to Asakusa, via Ginza and Ueno. Colour-coded orange.
**Hibiya subway line** Naka-Meguro to Ebisu, Roppongi, Ginza, Akihabara and Ueno. Colour-coded grey.
**JR Yamanote line** Loop line stopping at many sightseeing destinations, such as Shibuya, Harajuku, Shinjuku, Tokyo and Ueno. Colour-coded light green.
**JR Chūō line** Express between Tokyo Station and Shinjuku, and onwards to points west. Colour-coded reddish-orange.
**JR Sōbu line** Runs across the city centre connecting Shinjuku with Iidabashi, Ryōgoku and Akihabara. Colour-coded yellow.
**Yurikamome line** Elevated train running from Shimbashi to points around Tokyo Bay.
TAXI
Taxis only make economic sense for short distances or groups of four.
oFares start at ¥410 for the first 1km, then rise by ¥80 for every 237m you travel or for every 90 seconds spent in traffic.
oThere's a surcharge of 20% between 10pm and 5am.
oDrivers rarely speak English, though most taxis have navigation systems. Have your destination written down in Japanese, or better yet, a business card with an address.
oTaxis take credit cards and IC passes.
TOP EXPERIENCE
# Mt Fuji
Of all Japan's iconic images, Mt Fuji (富士山; 3776m) is the real deal. Admiration for the mountain appears in Japan's earliest recorded literature, dating from the 8th century.
Great For...
gAc
yDon't Miss
The famous mountain view from Motosu-ko.
Explore Ashore
Cruise ships dock in Shimizu, 90km southwest of Kawaguchi-ko. The quickest and easiest way to get there (or to other great mountain-view locations) is by taxi, which takes about 1¾ hours.
8Need to Know
Most visitors head straight for Mt Fuji as soon as they step off the ship so as to make the most of their time. If you have any extra time in port it's worthwhile exploring beautiful Shimizu.
Mt Fuji views from Kawaguchi-ko | IAMDOCTOREGG/SHUTTERSTOCK ©
Japan's highest and most famous peak is the big draw of the Fuji Five Lakes (富士五湖) region, but even without climbing Fuji-san, it's still worth coming here to enjoy the great outdoors around the volcano's northern foothills, and to admire the mountain photogenically reflected in the lakes. Culture buffs can also delve into the fascinating history of Mt Fuji worship at several sites.
Yamanaka-ko is the easternmost lake, followed by Kawaguchi-ko, Sai-ko, Shōji-ko and Motosu-ko.
### Fuji-Spotting
Mt Fuji has many different personalities depending on the season. Winter and spring months are your best bet for seeing it in all its clichéd glory; although even during these times the snowcapped peak may be visible only in the morning before it retreats behind its cloud curtain. Its elusiveness, however, is part of the appeal, making sightings all the more special. Here are some of our top spots for viewing, both in the immediate and greater areas:
**Kawaguchi-ko** On the north side of the lake, where Fuji looms large over its shimmering reflection.
**Motosu-ko** The famous view depicted on the ¥1000 bill can be seen from the northwest side of the lake.
**Hakone** The mountain soars in the background of Ashino-ko and the red _torii_ (shrine gate) rising from the water.
**Izu Peninsula** Journey along the west coast to catch glimpses of Fuji and the ocean, bathed in glorious sunsets.
**Panorama-dai** The end of this hiking trail (パノラマ台) rewards you with a magnificent front-on view of the mountain.
**Kōyō-dai** Mt Fuji can be seen from this lookout (adult/child ¥200/150), particularly stunning in the autumn colours.
Ashino-ko | AFLO CO., LTD/ALAMY STOCK PHOTO ©
### Sightseeing Bus
The **Fuji Lakes Sightseeing Bus** (adult/child ¥1500/750) has three looping routes that start and finish at Kawaguchi-ko Station, with numbered stops for all the sightseeing spots around the western lakes. It's a hop-on, hop-off service with buses every 15 to 30 minutes (seasonal). Pick up the excellent map and timetable from Kawaguchi-ko Station, where patient English-speaking staff can answer all sightseeing bus-related queries.
The red line follows Kawaguchi-ko's northern shore and western area, the green line goes around Sai-ko and Aokigahara, and the blue line travels around Shōji-ko to the eastern end of Motosu-ko.
# YOKOHAMA
#### Chinatown
#### Walking Tour: Yokohama Port Heritage
#### Sights
#### Activities
#### Tours
#### Eating
#### Drinking
#
Yokohama at a Glance
Just a 30-minute train ride south of central Tokyo, Yokohama (横浜) has an appealing flavour and history all its own. Locals are likely to cite the uncrowded, walkable streets or neighbourhood atmosphere as the main draw, but for visitors its appeal lies in the breezy bay front, creative arts scene, multiple microbreweries, jazz clubs and great international dining.
Minato Mirai | OKIMO/SHUTTERSTOCK ©
With a Day in Port
Start your day seeing an exhibition at Yokohama Museum of Art, then stop in at the Cup Noodles Museum on the way to Chinatown. Explore some of the area's 600 shops before ending the day at NYK Hikawa Maru.
Best Places for...
**Okonomiyaki** Colombus Okonomiyaki
**Tea** Bashamichi Jyuban-Kan
**Beer** Kirin Beer Yokohama Factory
**Travel with children** Yokohama Cosmoworld
Getting from the Port
Ships visiting Yokohama dock at **Ōsanbashi International Passenger Terminal** (大さん橋国際客船ターミナル; www.osanbashi.jp; 1-1-4 Kaigan-dōri, Naka-ku). It's an easy walk to many highlights and Nihon-ōdōri station is nearby.
At the time of research two new cruise ports were about to open: Daikoko Cruise Terminal (northeast of Ōsanbashi) and Shinko Cruise Terminal (west of Ōsanbashi).
Fast Facts
**Tourist information** See www.yokohamajapan.com and www.yokohamaseasider.com.
**Transport** Trains are the most convenient way to get around, but there is an extensive bus network.
TOP EXPERIENCE
# Chinatown
Yokohama's frenetic Chinatown packs some 600 speciality shops and restaurants within a space of several blocks, marked by 10 elaborately painted gates. It's very touristy, but fun to visit for a meal or stroll.
Great For...
khr
yDon't Miss
The delicious food in the area.
Explore Ashore
While Motomachi-Chūkagai station is nearby, it's only a 15-minute walk from Ōsanbashi pier.
8Need to Know
The most convenient subway for the area is Motomachi-Chūkagai, with an information center just a few blocks away.
DKOJICH/SHUTTERSTOCK ©
### Kantei-byō
Chinatown's heart is Kantei-byō (map Google map; 関帝廟; 140 Yamashita-chō; h9am-7pm; bMotomachi-Chūkagai) F, an elaborately decorated shrine dedicated to Guan Yu, an adopted deity of business. This incarnation (the fourth) was built in 1990.
Yamashita-kōen | DIGIPUB/GETTY IMAGES ©
### Masan-no-mise Ryūsen
The walls at cheerful little canteen Masan-no-mise Ryūsen (map Google map; 馬さんの店龍仙; %045-651-0758; www.ma-fam.com; 218-5 Yamashita-chō, Naka-ku; dishes from ¥700; h7am-2am; dIshikawachō) are literally wallpapered with appetizing photos of the stir-fries, dumplings, noodle soups and salads on offer. It has two other branches in Chinatown.
### Manchinrō Honten
The palatial Cantonese restaurant Manchinrō Honten (map Google map; 萬珍樓本店; %045-681-4004; www.manchinro.com; 153 Yamashita-chō, Naka-ku; lunch/dinner set menus from ¥2800/6000; h11am-10pm; dMotomachi-Chūkagai) is one of Chinatown's oldest (1892) and most respected. It serves a great selection of dim sum from 11am to 4pm, all in opulent surrounds, though it's a rather more formal affair for dinner. Book ahead on weekends.
### What's Nearby?
**Yamashita-kōen** (山下公園周辺; 279 Yamashitachō; dMotomachi-Chūkagai) is an elegant bayside park that is ideal for strolling and ship-spotting. Moored at the eastern end is the 1930s passenger liner _Hikawa Mar_ u.
At the Yokohama Archives of History (map Google map; 横浜開港資料館; %045-201-2100; www.kaikou.city.yokohama.jp; 3 Nihon-ōdōri, Naka-ku; adult/child ¥200/100; h9.30am-5pm Tue-Sun; bNihon-ōdōri), displays in English chronicle the saga of Japan's opening up at the Yokohama port following the arrival of Commodore Matthew Perry and his persuasively well-armed steamships. It's located inside the former British consulate.
Yokohama
1Sights
1Cup Noodles MuseumC2
2Hara Model Railway MuseumA1
3Kanagawa Prefectural Museum of Cultural HistoryB2
4Kantei-byōC3
5Nippon Maru Sailing ShipB2
6NYK Hikawa MaruD3
7Yamashita-kōenC3
8Yokohama Archives of HistoryC3
9Yokohama Museum of ArtB2
10Yokohama Port MuseumB2
2Activities, Courses & Tours
11Yokohama CosmoworldB2
7Shopping
12Akarenga SōkōC2
5Eating
13AraiyaB2
14BillsC2
15Charcoal Grill GreenB2
16Colombus OkonomiyakiC3
17Manchinrō HontenC3
18Masan-no-mise RyūsenC3
6Drinking & Nightlife
19Antenna AmericaB3
20Bashamichi Jyuban-KanB3
21Zō-no-hana TerraceC2
1Sights
Yokohama Museum of ArtGallery
(map Google map; 横浜美術館; %045-221-0300; www.yaf.or.jp/yma; 3-4-1 Minato Mirai, Nishi-ku; adult/child ¥500/free; h10am-6pm, closed Thu; bMinato Mirai)
The focus of the Yokohama Triennale (2020, 2023), this museum hosts exhibitions that swing between safe-bet shows with European headliners to more daring contemporary Japanese and up-and-coming Southeast Asian artists. There are also permanent works, including by Picasso, Miró and Dalí, in the catalogue.
Cup Noodles MuseumMuseum
(map Google map; %045-345-0918; www.cupnoodles-museum.jp; 2-3-4 Shinkō, Naka-ku; adult/child ¥500/free; h10am-6pm, closed Tue; c; bBashamichi)
Dedicated to the 1956 invention of instant ramen by Momofuku Ando (the 'cup' came in 1971), this impressively slick attraction has a host of wacky exhibits that drive home the message to go against the grain, be creative and 'Never give up!'. The highlight is the chance to design your own Cup Noodle (additional ¥300) to take away.
NYK Hikawa MaruMuseum
(map Google map; 氷川丸; www.nyk.com; Yamashita-kōen, Naka-ku; adult/child ¥300/100; h10am-5pm Tue-Sun; bMotomachi-Chūkagai)
Moored at the eastern end of Yamashita-kōen, this 1930s luxury liner has stories to tell from its days conveying well-heeled Japanese passengers to Seattle, and later as a hospital ship in WWII. Inside you can see cabins (one of the staterooms was used by Charlie Chaplin), lounges, the engine room and bridge.
Shin-Yokohama Rāmen MuseumMuseum
(新横浜ラーメン博物館; %045-471-0503; www.raumen.co.jp; 2-14-21 Shin-Yokohama, Kohoku-ku; adult/child ¥310/100, dishes around ¥900; h11am-10pm Mon-Sat, from 10.30am Sun; dShin-Yokohama)
Nine ramen restaurants from around Japan were hand-picked to sell their wares in this theme-park-style replica of a 1958 _shitamachi_ (downtown district) that's lit to feel like perpetual, festive night-time. It's a short walk from Shin-Yokohama station – ask for directions at the station's information centre.
Nippon Maru Sailing ShipMuseum
(map Google map; 日本丸; ship & museum adult/child ¥600/300; h10am-5pm Tue-Sun; dSakuragichō)
This magnificent, four-masted barque (built in 1930 as a training ship for naval cadets) sits in a wet dock adjacent to the Yokohama Port Museum (map Google map; 横浜みなと博物館; %045-221-0280; www.nippon-maru.or.jp; 2-1-1 Minato Mirai, Nishi-ku; museum adult/child ¥400/200; h10am-5pm Tue-Sun), and is fascinating to board and explore. Tickets also include entry to the museum building.
Hara Model Railway MuseumMuseum
(map Google map; 原鉄道模型博物館; www.hara-mrm.com; 2nd fl, Yokohama Mitsui Bldg, 1-1-2 Takashima, Nishi-ku; adult/child ¥1000/500; h10am-5pm Wed-Mon; dShin-takashima)
Hara Nobutaro (1919–2014) was Japan's pre-eminent trainspotter, taking the pastime to a delightfully surprising level of obsessiveness as this superb personal collection of model trains and other railway-associated memorabilia shows.
Kanagawa Prefectural Museum of Cultural HistoryMuseum
(map Google map; 神奈川県立歴史博物館; <http://ch.kanagawa-museum.jp/english>; 5-60 Minaminaka-dori, Naka-ku; adult/child ¥300/100; h9.30am-4.30pm Tue-Sun; bBashamichi)
Housed in the grand former Yokohama Specie Bank building (c1904) is this rather scholarly history museum charting the course of Kanagawa Prefecture from neolithic times through to the opening up of the city's port.
2Activities
Kawasaki WarehouseAmusement Park
(アミューズメントパーク ウェアハウス川崎店, Anata no Warehouse; 3-7 Nisshin-cho, Kawasaki; h9am-11.45pm, from 7am Sat & Sun; dKawasaki) F
If you check out just one video-game arcade in Japan, make it this cyber-punk styled 'warehouse' designed to resemble Kowloon Walled City. Step through the smoking, hissing entranceway and up the escalators to find arcade machines galore, as well as crane games, slots, and even pool and table tennis. The arcade is 500m southwest of Kawasaki station. Adults only.
Yokohama CosmoworldAmusement Park
(map Google map; 横浜コスモワールド; www.cosmoworld.jp; 2-8-1 Shinkō, Naka-ku; admission free, rides ¥100-800; h11am-9pm Mon-Wed & Fri, to 10pm Sat & Sun; bMinato Mirai)
Perfect for children, this compact amusement park is home to one of the world's tallest Ferris wheels, the 112.5m Cosmo Clock 21 (tickets ¥800).
Minato Mirai 21
Over the last three decades Yokohama's former shipping docks have been transformed into this planned city of tomorrow ('Minato Mirai' means 'port future'). There are plenty of recreation areas, including the old Akarenga Sōkō (map Google map; 横浜赤レンガ倉庫; www.yokohama-akarenga.jp; 1-1 Shinkō, Naka-ku; h11am-8pm; bBashamichi) red-brick warehouses, transformed into a shopping, dining and events space; and a series of breezy **promenades** connecting the area's main attractions.
_Nippon Maru_ ship | PICTURE CELLS/SHUTTERSTOCK ©
TTours
Kirin Beer Yokohama FactoryTours
(キリンビール 横浜工場; %045-503-8250; 1-17-1 Namamugi, Tsurumi-ku; h10am-5pm Tue-Sun; dNamamugi) F
Even teetotallers will be charmed by this hi-tech romp through one of the major breweries for Kirin beer. The free tour (in Japanese, but with translation cards) takes an hour to explain the stages of beer production with the help of touch screens and 3D goggles, finishing with a tasting of three beers. Reserve in advance (English spoken).
5Eating
Feast on culinary variety in cosmopolitan Yokohama: Texas-style barbecue joints, Cantonese dim sum, and the full smorgasbord of Japanese fare including local takes on ramen and sukiyaki.
Colombus OkonomiyakiOkonomiyaki¥
(map Google map; お好み焼きころんぶす; %045-633-2748; 1-3-7 Matsukage-chō, Naka-ku; mains ¥890-1120; h11.30am-3pm & 5-10pm Mon-Thu, 11.30am-3pm & 5-11pm Fri, 11.30am-11pm Sat, 3-10pm Sun; dIshikawachō)
Friendly staff grill up a wide range of _okonomiyaki_ (savoury pancakes) at your table, with prawn, squid, pork or veg (the English menu has some cute manga to help). It's a two-minute walk from the Ishikawachō Station. Turn right from the north exit, left at the first traffic lights and Colombus is 40m on your right.
Charcoal Grill GreenGrill¥¥
(map Google map; チャコールグリル グリーン 馬車道; %045-263-8976; www.greenyokohama.com; 6-79 Benten-dōri, Naka-ku; mains from ¥1380; h11.30am-2pm & 5pm-midnight; bBashamichi)
Char is the star at this hip grill restaurant and bar that serves pink-centred steaks and smoky chicken to go with craft beers on tap and a decent wine list. The lunch specials are a great deal.
BillsInternational¥¥
(map Google map; ビルズ; %045-650-1266; www.bills-jp.net; Akarenga Sōkō Bldg 2, 1-1-2 Shinkō, Naka-ku; mains ¥1420-2200; h9am-11pm Mon-Fri, from 8am Sat & Sun; v; bBashamichi)
Popular for brunch, the zesty fusion food here comes from the cookbooks of Australian celebrity chef Bill Granger. Try his signature ricotta hotcakes, the berry pancakes, or go for the 'full Aussie' breakfast blowout. There are a couple of vegan options on the breakfast and dinner menus.
AraiyaJapanese¥¥¥
(map Google map; 荒井屋; %045-226-5003; www.araiya.co.jp; 4-23 Kaigan-dōri, Naka-ku; set lunch/dinner from ¥1540/2970; h11am-2.30pm & 5-10pm; bBashamichi)
Yokohama has its own version of the beef hotpot dish sukiyaki, called _gyū-nabe_. This elegant restaurant, established in 1895, is the place to sample it.
6Drinking
Antenna AmericaCraft Beer
(map Google map; アンテナアメリカ; %45-315-5228; www.antenna-america.com; 5th fl, 5-4-6 Yoshida-machi, Naka-ku; h3-11pm Mon-Fri, from 11am Sat & Sun; dKannai)
Sup imported cans of American craft beer for just ¥500 at this showroom-turned-bar attached to a beer distribution company. Staff know their hops and the selection is impressive; the decor less so. A tiny kitchen turns out respectable fish tacos.
Bashamichi Jyuban-KanCafe
(map Google map; 馬車道十番館; %045-651-2621; www.yokohama-jyubankan.co.jp; 5-67 Tokiwa-chō, Naka-ku; h10am-10pm; bBashamichi)
Soak up the old Yokohama vibes at this former trading company building turned cafe-bar and French restaurant. You can join the well-to-do regulars for tea and pastries at dainty tables, or seek out the clubby little bar up the wooden staircase past old photographs of the port area.
Zō-no-hana TerraceCafe
(map Google map; 象の鼻テラス; %045-661-0602; www.zounohana.com; 1 Kaigan-dōri, Naka-ku; dishes ¥750; h10am-6pm; c; bNihon-ōdōri)
There's a literal elephant in the room at this bright bayside cafe space (elephant is _zō_ in Japanese), a welcome promenade pit stop for bottled beer, coffee, ice cream and light snacks.
8INFORMATION
The following all have an English speaker.
**Chinatown 80Information Center** (横浜中華街インフォメーションセンター; %045-681-6022; 80 Yamashita-chō; h10am-8pm Sun-Thu, to 9pm Fri & Sat; dMotomachi-Chūkagai) A few blocks from Motomachi-Chūkagai Station.
**Sakuragichō Station Tourist Information** ( %045-211-0111; h9am-6pm; dSakuragichō) Outside the south exit of Sakuragichō Station.
**Yokohama Convention & Visitors Bureau** ( %045-221-2111; www.yokohamajapan.com; 1st fl, Sangyō-Bōeki Center, 2 Yamashita-chō, Naka-ku; h9am-5pm Mon-Fri; dNihon-ōdōri) A 10-minute walk from Nihon-ōdōri Station.
**Yokohama Station Tourist Information Center** ( %045-441-7300; h9am-7pm) It's in the east–west corridor at Yokohama Station.
Yokohama's History
Up until the mid-19th century, Yokohama was an unassuming fishing village. Things started to change rapidly, however, in 1853, when the American fleet under Commodore Matthew Perry arrived off the coast to persuade Japan to open to foreign trade.
From 1858, when it was designated an international port, through to the early 20th century, Yokohama served as a gateway for foreign influence and ideas. Among the city's firsts in Japan: a daily newspaper, gas lamps and a train terminus (connected to Shimbashi in Tokyo).
The Great Kantō Earthquake of 1923 destroyed much of the city, but the rubble was used to reclaim more land, including Yamashita-kōen. The city was devastated yet again in WWII air raids. Despite all this, central Yokohama retains some rather fine early 20th-century buildings.
8GETTING AROUND
BUS
Although trains are more convenient, Yokohama has an extensive bus network. The cute, red-coloured Akai-kutsu ('red shoe') bus loops every 20 minutes from 10am to around 7pm through the major tourist spots (adult/child ¥220/110 per ride).
SUBWAY & TRAIN
The Yokohama City blue line _(shiei chikatetsu)_ connects Yokohama with Shin-Yokohama (¥240, 11 minutes), Sakuragichō (¥210, four minutes) and Kannai (¥210, six minutes). JR trains connect Yokohama with Shin-Yokohama (¥170, 14 minutes), Sakuragichō (¥140, four minutes) and Kannai (¥140, five minutes).
# NAGOYA
#### Ōsu Temple & Shopping District
#### Sights
#### Shopping
#### Eating
#
Nagoya at a Glance
Affable Nagoya (名古屋), birthplace of Toyota and pachinko (a pinball-style game), is a manufacturing powerhouse. But its manufacturing roots don't mean that Nagoya is a city of factories: well-maintained parks and green spaces prevail in the inner wards. Nagoya has cosmopolitan aspects, including some fantastic museums, significant temples and excellent shopping, and Nagoyans are vivacious and unpretentious.
Nagoya skyline | F11PHOTO/SHUTTERSTOCK ©
With a Day in Port
Explore the streets surrounding Ōsu Kannon for a sampler of Nagoya's culture, shopping and cuisine. Swap ships for trains at SCMAGLEV & Railway Park or cars at Toyota Commemorative Museum of Industry & Technology, and imagine life as a shogun at reconstructed Nagoya-jō.
Best Places for...
**Local cuisine** Misen
**Shopping** Komehyō
**Souvenir crafting** Noritake Garden
**A restorative drink** Smash Head
Getting from the Port
Both Garden and Kinjo Piers have nearby train stations, making city access straightforward. Allow about half an hour from either pier to Nagoya Station.
To get from Garden Pier to Kinjo Pier, home of Legoland and the SCMAGLEV & Railway Park, you can make a bus and subway trip to Kinjofuto Station, or stick to the water with Nagoya Cruise (<http://cruise-nagoya.jp>).
Fast Facts
**Money** Look for Japan Post ATMs at Garden Pier and Nagoya Station.
**Tourist information** There's a small information kiosk at Garden Pier.
**Wi-fi** Free wi-fi is available at all subway stations, at Jetty mall (Garden Pier), Makers Pier centre (Kinjo Pier) and at the port building at Garden Pier.
TOP EXPERIENCE
# Ōsu Temple & Shopping District
The area between Ōsu Kannon and Kamimaezu Stations, crammed with retailers, eateries and street vendors, has a delightfully young and alternative vibe. Patient shoppers can be rewarded with funky vintage threads and offbeat souvenirs. Take a break with a visit to Ōsu Kannon temple.
Great For...
hzc
yDon't Miss
Ōsu Kannon hosts a colourful antique market on the 18th and 28th of each month.
Explore Ashore
Travel to Ōsu Kannon from Garden Pier takes about half an hour on the subway; take the Meiko line to Kanayama, then change to the Meijo line for Kamimaezu. It takes another 20 minutes or so from Kinjo Pier.
8Need to Know
For cheap eats, head to the shopfronts of the Ōsu Shopping Arcade, where street vendors hawk everything from kebabs to crêpes and pizza.
Ōsu Kannon | DAVID QUIXLEY/SHUTTERSTOCK ©
### Exploring the Neighbourhood
From Kamimaezu Station, take exit 9 and walk north two blocks. Turn left on to Banshoji street (万松寺通), a covered shopping arcade that becomes Ōsu Kannon street and continues on to Ōsu Kannon temple. The streets either side are alive with activity. Along Akamon-dōri, Banshō-ji-dōri and Niomon-dōri are hundreds of funky vintage boutiques and discount clothing retailers. East of Ōsu, Otsu-dōri has a proliferation of manga (Japanese comic) shops.
### Ōsu Kannon
The much-visited, workaday Ōsu Kannon (map Google map; 大須観音; %052-231-6525; www.osu-kannon.jp; 2-21-47 Osu, Naka-ku; h24hr; bŌsu Kannon, exit 2) temple traces its roots back to 1333. Devoted to the Buddha of Compassion, the temple was moved to its present location in 1610, although the current buildings date from 1970. The library inside holds the oldest known handwritten copy of the _Kojiki_ – the ancient mythological history of Japan.
### Drink Break
Through the passageway to the left of the main Ōsu Kannon temple building you'll find the motorcycle- and Vespa-repair shop-pub Smash Head (map Google map; スマッシュヘッド; %052-201-2790; <http://smashhead.main.jp>; 2-21-90 Ōsu; h11.30am-9pm Wed-Sun, to 3.30pm Mon; bŌsu Kannon, exit 2). Guinness and Corona are the beers of choice, the patrons are cool and the bacon cheeseburgers cost ¥1100.
### Komehyō
Just a couple of hundred metres west of the temple, enjoy the genius of Komehyō (map Google map; コメ兵; %052-242-0088; www.en.komehyo.co.jp; 2-20-25 Ōsu; h10.30am-7.30pm Thu-Tue; bŌsu Kannon, exit 2), Japan's largest discounter of secondhand, well...everything. Housed over seven floors in the main building, clothes, jewellery and accessories are of excellent quality and are sold at reasonable prices. With patience, you can find some real bargains, especially at 'yen=g' on the 7th floor, where clothing is sold by weight.
### Local Lunch Specials
Yabaton Honten (map Google map; 矢場とん本店; %052-252-8810; <http://english.yabaton.com>; 3-6-18 Ōsu; dishes from ¥1200; h11am-9pm; bYaba-chō, exit 4) has been the place to try Nagoya's famed _miso-katsu_ (a type of _tonkatsu_ – deep-fried pork cutlet) since 1947. Signature dishes include _waraji-tonkatsu_ (schnitzel-style flattened, breaded pork) and _teppan-tonkatsu_ (breaded pork cutlet with miso on a sizzling plate of cabbage). Look for the massive pig over the door, just south of the overpass. It's next to McDonald's.
Nagoya
1Sights
1Nagoya TV TowerD2
Noritake Craft Centre & Museum(see 2)
2Noritake GardenA1
Noritake Garden Gallery(see 2)
3Ōsu KannonC3
7Shopping
4KintetsuA2
5KomehyōC3
6Loft Department StoreC3
5Eating
7ChomoranmenD2
8Din Tai FungA2
9Love Pacific CafeC3
10MisenC3
11Suzunami HontenD2
12Yabaton HontenC3
6Drinking & Nightlife
Smash Head(see 3)
1Sights
SCMAGLEV & Railway ParkMuseum
(JR リニア・鉄道館, JR Rinia Tetsudō-kan; %050-3772-3910; <http://museum.jr-central.co.jp>; 3-2-2 Kinjo-futo, Minato-ku; adult/child ¥1000/200, shinkansen-driving simulator ¥500; h10am-5.30pm Wed-Mon; p; dJR Aonami line to Kinjofuto)
Trainspotters will be in heaven at this fantastic hands-on museum. Featuring an actual maglev (the world's fastest train – 581km/h), _shinkansen_ (bullet trains), historical rolling stock and rail simulators, the massive museum offers a fascinating insight into Japanese postwar history through the development of a railroad like no other. The 'hangar' is a short walk from Kinjo Pier, on the Taiko-dōri side of JR Nagoya Station.
The _shinkansen-_ driving-simulator tickets are assigned on a lottery basis. You must apply to the lottery on the day you wish to drive the simulator, and wait for the results.
Toyota Commemorative Museum of Industry & TechnologyMuseum
(トヨタテクノミュージアム産業技術記念館, Toyota Techno-museum Zangyō Gijutsu Kinenkan; %052-551-6115; www.tcmit.org; 4-1-35 Noritake-shinmachi; adult/child ¥500/200; h9.30am-4.30pm Tue-Sun; dMeitetsu Nagoya line to Sako)
The world's largest car manufacturer had humble beginnings in the weaving industry. This museum occupies the site of Toyota's original weaving plant. Car enthusiasts will find things textile heavy before warming to the 7900-sq-metre automotive and robotics pavilion. Science-minded folk will enjoy the countless hands-on exhibits. Displays are bilingual and there's an English-language audio tour available.
Don't confuse this museum with the Toyota Exhibition Hall (トヨタ会館, Toyota Kaikan; %museum 0565-29-3345, tours 0565-29-3355; www.toyota.co.jp/en/about_toyota/facility/toyota_kaikan; 1 Toyota-chō; h9.30am-5pm Mon-Sat, tours 11am; dAichi Kanjō line to Mikawa Toyota) F and factory tours – the hall is about two hours out of town; tours need to be booked at least two weeks in advance.
Toyota Commemorative Museum of Industry & Technology | PICNOTE/SHUTTERSTOCK ©
Nagoya-jōCastle
(名古屋城; %052-231-1700; www.nagoyajo.city.nagoya.jp; 1-1 Honmaru; adult/child ¥500/free; h9am-4.30pm; bShiyakusho, exit 7)
The original structure, built between 1610 and 1614 by Tokugawa Ieyasu for his ninth son, was levelled in WWII. Today's castle is a concrete replica (with elevator) completed in 1959. Renovations are ongoing. On the roof, look for the 3m-long gilded _shachi-hoko_ (legendary creatures possessing a tiger's head and a carp's body). Inside, find treasures, an armour collection and the histories of the Oda, Toyotomi and Tokugawa families. Free English tours run every day at 1pm from the castle's east gate.
The beautiful year-round garden, **Ninomaru-en** (二の丸園) has a number of pretty teahouses.
Port of Nagoya Public AquariumAquarium
(名古屋港水族館, Nagoya-ko Suizoku-kan; %052-654-7080; www.nagoyaaqua.com/english; 1-3 Minato-machi, Minato-ku; adult/child/student ¥2000/500/1000; h9.30am-5.30pm Tue-Sun; bNagoya-ko)
Among Nagoya's most well-known attractions, this port-side aquarium features one of the largest outdoor tanks in the world, and the permanently moored **Fuji Icebreaker** ship, now an **Antarctic Museum**. The dolphin shows may concern some visitors: there's increasing evidence to suggest that it's harmful and stressful to keep cetaceans (Nagoya's aquarium has both dolphins and orcas) in captivity.
Noritake GardenGardens
(map Google map; ノリタケの森, Noritake no Mori; %052-561-7290; www.noritake.co.jp/eng; 3-1-36 Noritake-shinmachi; h10am-6pm; bKamejima)
Pottery fans will enjoy a stroll around Noritake Garden, the 1904 factory grounds of one of Japan's best-known porcelain makers, featuring remnants of early kilns and the pleasant Noritake Gallery (ノリタケの森ギャラリー; %052-562-9811; www.noritake.co.jp/eng/mori/look/gallery; 3-1-36 Noritake-shinmachi; h10am-6pm; bKamejima) F. Glaze your own porcelain dish (from ¥1800 plus shipping) in the Craft Centre & Museum (ノリタケクラフトセンター; %052-561-7114; www.noritake.co.jp/eng/mori/look/museum; 3-1-36 Noritake-shinmachi; adult/child ¥500/free; h10am-5pm; bKamejima), which demonstrates the production process. The 'Box Outlet Shop', ironically, has unboxed wares at discounted prices. English signs throughout.
Legoland
Nagoya is home to Japan's only **Legoland** (<https://www.legoland.jp/en/>) theme park. It's handily located a short walk away from Kinjo Pier (about 1km). Allow about 45 minutes for the bus and subway trip from Garden Pier, or try for a boat trip with Nagoya Cruise (<http://cruise-nagoya.jp>). The park features seven different themed areas, rides, shows and (naturally) many, many pieces of Lego.
Garden Pier is home to its own small theme park, **Sea Train Land** (<http://www.senyo.co.jp/seatrainland/attraction.html>).
BLANSCAPE/SHUTTERSTOCK ©
7Shopping
Nagoya's manufacturing roots make it a great place to shop. Look for **Jetty** shopping mall at Garden Pier and **Makers Pier** (<http://www.makerspier.com/en>) at Kinjo. The areas of Meieki and Sakae are home to gargantuan malls and department stores, good for clothing, crafts and food, and the streets around Ōsu Kannon are filled with retail opportunities.
KintetsuDepartment Store
(map Google map; 近鉄; %052-582-3411; 1-2-2 Meieki; h10am-7pm; dKintetsu Nagoya)
The Nagoya HQ of this Osaka-based railway and department-store chain.
Loft Department StoreDepartment Store
(map Google map; ロフト; %052-219-3000; 3-18-1 Sakae, Nadya Park; h10am-8pm; bYaba-chō, exit 5 or 6)
One of Japan's coolest department stores has a definite design bent. You can't miss the yellow-and-black livery.
5Eating
Nagoya is a fantastic place to experience Japan's passion for food, with many local specialities.
MisenTaiwanese¥
(map Google map; 味仙; %052-238-7357; www.misen.ne.jp; 3-6-3 Ōsu, Naka-ku; dishes ¥480-1500; h11.30am-2pm & 5pm-1am Sun-Thu, to 2am Fri & Sat; a v; bYaba-chō, exit 4)
Folks line up for opening time at this jolly place, where the _Taiwan rāmen_ (台湾ラーメン; a spicy concoction of ground meat, chilli, garlic and green onion, served over noodles in broth) induces rapture. It may be Taiwanese, but locals will tell you: 'this is real Nagoya food'.
Love Pacific CafeVegan¥
(map Google map; ラブ・パシフィックカフェ; %052-252-8429; www.pacifit.jp/lovecafe.html; 3-23-38 Sakae; items from ¥600; h11.30am-5pm Tue-Sun; v; bYaba-chō, exit 4)
Lovers of wholesome, delicious, healthy foods are in for a treat at this trendy, friendly vegan cafe preparing lunch sets and cafe items that are free of dairy, egg and white sugars. The changing menu usually features a choice of two soups, access to the organic salad bar and a main: the tofu teriyaki burgers are delicious.
ChomoranmenRamen¥
(map Google map; ちょもらん麺; %052-963-5121; 3-15-10 Nishiki; items ¥650-1100; h11.30am-12.30am; bSakae, exit 3)
Opposite the Nagoya TV Tower, these cheap, chunky handmade ramen bowls will fill you up. The walls are covered with photos of famous patrons. Someone will be happy to help you with the vending machine used to take orders if you get stuck.
Suzunami HontenSeafood¥¥
(map Google map; 鈴波本店; %052-261-1300; www.suzunami.co.jp/shop/shop_honten.html; 3-7-23 Sakae, Naka-ku; lunch sets ¥1300; h11am-2.30pm; a)
Delightfully traditional but not overly formal, this Nagoyan _kappo_ institution specialises in simple grilled fish lunches served with miso soup, rice and pickles, and finished off with _umeshu_ (plum wine). You'll likely have a short wait for a table.
Din Tai FungTaiwanese¥¥
(map Google map; 鼎泰豐; %052-533-6030; <http://d.rt-c.co.jp/nagoya>; 12F Takashimaya Department Store, 1-1-4 Meieki; items from ¥600; h11am-11pm; dJR Nagoya, Sakura-dōri exit)
The Nagoya branch of this globally acclaimed Taiwanese chain, located in the Takashimaya department store at Nagoya Station, is likely to please with its literally 'mouth-watering' _xiao long bao_ soup dumplings _(shōronpō)_ and an extensive menu of dim-sum delights. Best for duos and groups of friends: the more the merrier.
8INFORMATION
**Tourist Information Center – Nagoya Station** (名古屋駅観光案内所; %052-541-4301; 1-1-14 Meieki; h9am-7pm; dJR Nagoya)
8GETTING AROUND
Nagoya has an excellent subway system with six lines, clearly signposted in English and Japanese. Fares are ¥200 to ¥330 depending on distance. One-day passes, available at ticket machines, include subway transport and discounted admission to many attractions.
# KYOTO
#### Fushimi Inari-Taisha
#### Kyoto's Geisha Culture
#### Kinkaku-ji
#### Sights
#### Activities
#### Shopping
#### Eating
#### Drinking
#### Entertainment
#
Kyoto at a Glance
Kyoto is old Japan writ large: quiet temples, sublime gardens, colourful shrines and geisha scurrying to secret liaisons. With 17 Unesco World Heritage Sites, and more than 1000 Buddhist temples and 400 Shintō shrines, it is one of the world's most culturally rich cities. But Kyoto is not just about sightseeing. While the rest of Japan has adopted modernity with abandon, the old ways are still clinging on in Kyoto. Visit an old _shōtengai_ (market street) and admire the ancient speciality shops, including tofu sellers, _washi_ (Japanese handmade paper) stores and tea merchants.
Views across Higashiyama | SEAN PAVONE/SHUTTERSTOCK ©
With a Day in Port
Start your Kyoto experience with a visit to Fushimi Inari-Taisha, where you'll be entranced by the hypnotic arcades of _torii_ (gates) at this sprawling Shintō shrine. Nearby is Tōfuku-ji, a beautiful temple complex. Here you can meander through the expansive grounds and wander among the superb structures. In the afternoon take a taxi to downtown, hitting the excellent Nishiki Market, craft shops and department stores. End with a stroll through the historic geisha district of Gion.
Best Places for...
**Kaiseki** Kitcho Arashiyama
**Sushi** Chidoritei
**Soba noodles** Honke Owariya
**Coffee** Weekenders Coffee
**Matcha** Kaboku Tearoom
Getting from the Port
The Port of Kyoto, located at Maizuru, is approximately 90 minutes away by train or taxi from Kyoto. If getting the train into Kyoto, it's about a 10-minute taxi ride (¥775) from the port to Nishi-Maizuru Station. From here, take the Ltd Express train on the JR Hashidate line into Kyoto Station (around ¥2630), the main train station in the city. Train tickets are available at station ticket offices.
Fast Facts
Tourist information For bus and city maps and transport info, visit Kyoto Tourist Information Center.
**Transport** Kyoto is a compact city with an excellent public transport system. It has two efficient subway lines, operating from 5.30am to 11.30pm. Minimum adult fare is ¥210 (children ¥110).
**Wi-fi** You'll find a couple of computer terminals with internet at Kyoto Tourist Information Center. If you want constant access to wi-fi when you're out and about, your best bet is either renting a portable device or buying a data-only SIM for an unlocked smartphone.
TOP EXPERIENCE
# Fushimi Inari-Taisha
With seemingly endless arcades of vermilion _torii_ across a thickly wooded mountain, this vast complex is a world unto itself. One of the most impressive and memorable sights in all of Kyoto.
Great For...
Agc
yDon't Miss
The classic photo op from inside the tunnel of _torii_.
Explore Ashore
From the port in Maizuru, it's 90 minutes by train or taxi into Kyoto. If travelling by train, once at Kyoto Station, hop on the JR Nara Line to Inari Station (five minutes). From here it's about a five-minute walk to the shrine. Expect to spend a few hours or more here, especially if you want to explore the pathway up the mountain.
8Need to Know
伏見稲荷大社; 68 Yabunouchi-chō, Fukakusa, Fushimi-ku; admission free; hdawn-dusk; dJR Nara line to Inari or Keihan line to Fushimi-Inari
_Torii_ (gates) | TAKASHI IMAGES/SHUTTERSTOCK ©
### History
Fushimi Inari-Taisha was dedicated to the gods of rice and sake by the Hata family in the 8th century. As the role of agriculture diminished, deities were enrolled to ensure prosperity in business. Nowadays the shrine is one of Japan's most popular, and is the head shrine for some 40,000 Inari shrines scattered the length and breadth of the country.
### Messenger of Inari
As you explore the shrine, you will come across hundreds of stone foxes. The fox is considered the messenger of Inari, the god of cereals, and the stone foxes, too, are often referred to as 'Inari'. The key often seen in the fox's mouth is for the rice granary. On an incidental note, the Japanese traditionally see the fox as a sacred, somewhat mysterious figure capable of 'possessing' humans – the favoured point of entry is under the fingernails.
### Hiking the Grounds
A pathway wanders 4km up the mountain and is lined with dozens of atmospheric subshrines. The walk around the upper precincts is a pleasant day hike. It also makes for a very eerie stroll in the late afternoon and early evening, when the various graveyards and miniature shrines along the path take on a mysterious air. It's best to go with a friend at this time.
Tōfuku-ji | PICACCH/GETTY IMAGES ©
### What's Nearby?
Home to a spectacular garden, several superb structures and beautiful precincts, Tōfuku-ji (東福寺; %075-561-0087; www.tofukuji.jp; 15-778 Honmahi, Higashiyama-ku; Hōjō garden ¥400, Tsūten-kyō bridge ¥400; h9am-4pm; dKeihan line to Tōfukuji or JR Nara line to Tōfukuji) is one of the best temples in Kyoto. It is linked to Fushimi Inari-Taisha by the Keihan and JR train lines. The present temple complex includes 24 subtemples. The huge **San-mon** is the oldest Zen main gate in Japan, the **Hōjō** (Abbot's Hall) was reconstructed in 1890, and the gardens were laid out in 1938.
The northern garden has stones and moss neatly arranged in a checkerboard pattern. From a viewing platform at the back of the gardens you can observe the **Tsūten-kyō** (Bridge to Heaven), which spans a valley filled with maples.
TOP EXPERIENCE
# Kyoto's Geisha Culture
Though dressed in the finest silks and often astonishingly beautiful, geisha are first and foremost accomplished musicians and dancers. These now-rare creatures – seemingly lifted from another world – still entertain in Kyoto today.
Great For...
hdu
yDon't Miss
A stroll through atmospheric Gion.
Explore Ashore
From the port in Maizuru, the quickest way to reach the Gion district is by taxi, which will take you about 90 minutes. Allow a few hours to wander around and be sure to veer off the main drag, where you'll escape the crowds and see some of the area's impossibly atmospheric backstreets.
8Need to Know
Gion, on the Kamo-gawa's east bank, is Kyoto's most-famous geisha district.
oTop Tip
Check with the Kyoto Tourist Information Center for events with local geisha.
_Maiko_ in Gion | JURI POZZI/SHUTTERSTOCK ©
### Geiko & Maiko
The word geisha literally means 'arts person'; in Kyoto the term used is _geiko_ – 'child of the arts'. It is the _maiko_ (apprentice _geiko_ ) who are spotted on city streets in ornate dress, long trailing obi and towering wooden clogs, their faces painted with thick white make-up, leaving only a suggestive forked tongue of bare flesh on the nape of the neck. As geisha grow older their make-up becomes increasingly natural; by then their artistic accomplishments need no fine casing. At their peak in the 1920s, there were around 80,000 geisha in Japan. Today there are approximately 1000 (including apprentices), with nearly half working in Kyoto.
### Life of a Geisha Then & Now
Prior to the mid-20th century, a young girl might arrive at an _okiya_ (geisha living quarters) to work as a maid. Should she show promise, the owner of the _okiya_ would send her to begin training at the _kaburenjo_ (school for geisha arts) at around age six. She would continue maid duty, waiting on the senior geisha of the house, while honing her skills and eventually specialising in one of the arts, such as playing the _shamisen_ (three-stringed instrument resembling a lute or a banjo) or dance.
Geisha were often indebted to the _okiya_ who covered their board and training. Given the lack of bargaining chips that have been afforded women in history, there is no doubt that many geisha of the past, at some point in their careers, engaged in compensated relationships; this would be with a _danna_ (a patron) with whom the geisha would enter a contractual relationship not unlike a marriage (and one that could be terminated). A wealthy _danna_ could help a woman fulfil her debt to the _okiya_ or help her start her own. Other geisha married, which required them to leave the profession; some were adopted by the _okiya_ and inherited the role of house mother; still others worked into old age.
Today's geisha begin their training no earlier than their teens – perhaps after being inspired by a school trip to Kyoto – while completing their compulsory education (in Japan, until age 15). Then they'll leave home for an _okiya_ (they do still exist) and start work as an apprentice. While in the past a _maiko_ would never be seen out and about in anything but finery, today's apprentices act much like ordinary teens in their downtime. For some, the magic is in the _maiko_ stage and they never proceed to become geisha; those who do live largely normal lives, free to live where they choose, date as they like and change professions when they please.
_Geiko_ entering a teahouse | KEKYALYAYNEN/SHUTTERSTOCK ©
### Hanamachi
Traditionally, the districts where geisha were licensed to entertain in _ochaya_ (teahouses) were called _hanamachi_ , which means 'flower town'. Of the five that remain in Kyoto, Gion (map Google map; 祇園周辺; Higashiyama-ku; bTōzai line to Sanjō, dKeihan line to Gion-Shijō) is the grandest. Many of Kyoto's most upmarket restaurants and exclusive hostess bars are here.
On the other side of the river, Ponto-chō (map Google map; 先斗町; Ponto-chō, Nakagyō-ku; bTōzai line to Sanjo-Keihan or Kyoto-Shiyakusho-mae, dKeihan line to Sanjo, Hankyū line to Kawaramachi) has a different feel, with very narrow lanes. Not much to look at by day, the street comes alive at night, with wonderful lanterns, traditional wooden exteriors, and elegant Kyotoites disappearing into the doorways of elite old restaurants and bars.
### Experiencing Geisha Culture
Modern _maiko_ and geisha entertain their clients in exclusive restaurants, banquet halls and traditional _ochaya_ much like they did a century ago. This world is largely off limits to travellers, as a personal connection is required to get a foot in the door, though some tour operators can act as mediator. Of course, these experiences can cost hundreds of dollars (if not more).
Ryokan Gion Hatanaka offers a rare chance to witness geisha perform and then interact with them. If your cruise schedule allows, the inn's Kyoto Cuisine & Maiko Evening (map Google map; ぎおん畑中; %075-541-5315; www.kyoto-maiko.jp; 505 Gion-machi, Minami-gawa, Higashiyama-ku; per person ¥19,000; h6-8pm Mon, Wed, Fri & Sat; gKyoto City bus 206 to Gion or Chionin-mae, dKeihan line to Gion-Shijō) is an evening of elegant Kyoto _kaiseki_ (haute cuisine) food and personal entertainment by both Kyoto _geiko_ and _maiko_.
#### Geisha Dances
An excellent way to experience geisha culture is to see one of Kyoto's _odori_ (annual public dance performances), a city tradition for over a century. Get tickets as early as you can.
Miyako Odori map Google map is held throughout April, usually at Gion Kōbu Kaburen-jō Theatre. See for more.
Gion Odori (map Google map; 祇園をどり; %075-561-0224; Gion, Higashiyama-ku; with/without tea ¥4500/4000; hshows 1.30pm & 4pm; gKyoto City bus 206 to Gion) is held from 1 to 10 November, at the Gion Kaikan Theatre (祇園会館).
Kyō Odori (map Google map; 京おどり; %075-561-1151; Miyagawachō Kaburenjo, 4-306 Miyagawasuji, Higashiyama-ku; with/without tea from ¥2800/2200; hshows 1pm, 2.45pm & 4.30pm; dKeihan line to Gion-Shijō) takes place from the first to the third Sunday in April at the Miyagawa-chō Kaburen-jō Theatre (宮川町歌舞練場).
Kamogawa Odori (map Google map; 鴨川をどり; %075-221-2025; Ponto-chō, Sanjō-sagaru, Nakagyō-ku; seat ¥2300, special seat with/without tea ¥4800/4200; hshows 12.30pm, 2.20pm & 4.10pm; bTōzai line to Kyoto-Shiyakusho-mae) is held from 1 to 24 May at Ponto-chō Kaburen-jō Theatre.
Photographing Geisha
A photo of a _maiko_ is a much-coveted Kyoto souvenir; however, bear in mind that these are young women – many of whom are minors – on their way to work. Be respectful and let them pass.
Performance at Kamogawa Odori | DANITA DELIMONT/ALAMY STOCK PHOTO ©
#### Maiko Makeover
Ever wondered how you might look as a _maiko_? Give it a try at Maika (map Google map; 舞香; %075-551-1661; www.maica.tv; 297 Miyagawa suji 4-chōme, Higashiyama-ku; maiko/geisha from ¥6500/8000; dKeihan line to Gion-Shijo or Kiyomizu-Gojo) in Gion. The basic treatment includes full make-up and formal kimono. If you don't mind spending some extra yen, it's possible to head out in costume for a stroll through Gion (and be stared at like never before!). The process takes about an hour. Call to reserve at least one day in advance.
TOP EXPERIENCE
# Kinkaku-ji
Kyoto's famed 'Golden Pavilion', Kinkaku-ji is one of Japan's best-known sights. The main hall, covered in brilliant gold leaf, shining above its reflecting pond, is truly spectacular.
Great For...
hAg
yDon't Miss
The mirror-like reflection of the temple in the Kyō-ko pond is extremely photogenic.
Explore Ashore
From the port, it's quickest to get here by taxi, or take the train from Nishi-Maizuru Station to Kyoto Station. From here, catch the Kyoto City bus 205 to Kinkakuji-michi. It's about a 10-minute walk to Kinkaku-ji. You'll need at least a few hours to explore the famed 'Golden Pavilion' and the expansive grounds.
8Need to Know
金閣寺; 1 Kinkakuji-chō, Kita-ku; adult/child ¥400/300; h9am-5pm; gKyoto City bus 205 from Kyoto Station to Kinkakuji-michi, gKyoto City bus 12 from Sanjō-Keihan to Kinkakuji-michi
MARCOCIANNAREL/SHUTTERSTOCK ©
### History
Originally built in 1397 as a retirement villa for shogun Ashikaga Yoshimitsu, whose son converted Kinkaku-ji to a Buddhist temple in compliance with his wishes. In 1950 a young monk consummated his obsession with the temple by burning it to the ground. The monk's story is fictionalised in Mishima Yukio's 1956 novel _The Temple of the Golden Pavilion_. In 1955 a full reconstruction was completed, following the original design but extending the gold-foil covering to the lower floors.
### The Pavilion & Grounds
The three-storey pavilion, covered in bright gold leaf with a bronze phoenix on top of the roof, is naturally the highlight. But there's more to this temple than its shiny main hall. Don't miss the Ryūmon-taki waterfall and Rigyo-seki stone, which looks like a carp attempting to swim up the falls. Nearby, there is a small gathering of stone Jizō figures onto which people throw coins and make wishes. The quaint teahouse Sekka-tei embodies the spirit of _wabi-sabi_ (rustic simplicity) of the Japanese tea-ceremony ethic.
Ryōan-ji | WAYNE EASTEP/GETTY IMAGES ©
### What's Nearby?
You've probably seen a picture of the rock garden here – it's one of the symbols of Kyoto and one of Japan's better-known sights. Ryōan-ji (龍安寺; www.ryoanji.jp; 13 Goryōnoshitamachi, Ryōan-ji, Ukyō-ku; adult/child ¥500/300; h8am-5pm Mar-Nov, 8.30am-4.30pm Dec-Feb; gKyoto City bus 59 from Sanjō-Keihan to Ryoanji-mae) belongs to the Rinzai school and was founded in 1450. The garden, with an austere collection of 15 carefully placed rocks apparently adrift in a sea of sand, is enclosed by an earthen wall. The designer, who remains unknown to this day, provided no explanation.
An early-morning visit on a weekday is probably your best hope of seeing the garden free from the ever-present crowds.
Myōshin-ji (妙心寺; www.myoshinji.or.jp; 1 Myoshin-ji-chō, Hanazono, Ukyō-ku; main temple free, other areas of complex adult/child ¥500/100; h9.10-11.40am & 1-4.40pm, to 3.40pm Nov-Feb; gKyoto City bus 10 from Sanjo-Keihan to Myōshin-ji Kita-mon-mae) is a separate world within Kyoto, a walled-off complex of temples and subtemples that invites lazy strolling. The subtemple of **Taizō-in** contains one of the city's more interesting gardens. Myōshin-ji dates to 1342 and belongs to the Rinzai school.
Downtown Kyoto & Kyoto Station Area
1Sights
1Kyoto Imperial PalaceC1
2Kyoto StationC6
3Nijō-jōA2
4Nishiki MarketC3
5Ponto-chōD3
7Shopping
6AritsuguD3
Ippōdō Tea(see 14)
7TakashimayaD4
8Wagami no MiseC4
5Eating
9BioteiC3
10Café Bibliotec Hello!C2
11Honke OwariyaC2
12Roan KikunoiD4
13YoshikawaC3
6Drinking & Nightlife
14Kaboku TearoomD2
15Roots of all EvilC6
16TaiguD3
17Weekenders CoffeeC3
3Entertainment
18Kamogawa OdoriD3
1Sights
With over 1000 Buddhist temples and 400 Shintō shrines scattered over the city and into the hills, it's not hard to guess what most of your sightseeing time will be spent doing. The Southern and Northern Higashiyama areas are where the majority of the big-hitting temples lie. Downtown Kyoto is the hotspot for shopping and dining, but it does have a few worthy sights, including the impressive Nijō-jō and the famous food market, Nishiki. Around Kyoto Station and South Kyoto, there are a few good temples and the famous Fushimi Inari-Taisha shrine.
### 1 Downtown Kyoto
Nijō-jōCastle
(map Google map; 二条城; 541 Nijōjō-chō, Nijō-dōri, Horikawa nishi-iru, Nakagyō-ku; adult/child ¥600/200; h8.45am-5pm, last entry 4pm, closed Tue Dec, Jan, Jul & Aug; bTōzai line to Nijō-jō-mae, dJR line to Nijō)
The military might of Japan's great warlord generals, the Tokugawa shoguns, is amply demonstrated by the imposing stone walls and ramparts of their great castle, Nijō-jō, which dominates a large part of northwest Kyoto. Hidden behind these you will find a superb palace surrounded by beautiful gardens. Avoid crowds by visiting just after opening or shortly before closing.
Nijō-jō | GIANCARLO LIGUORI/SHUTTERSTOCK ©
Nishiki MarketMarket
(map Google map; 錦市場; Nishikikōji-dōri, btwn Teramachi & Takakura, Nakagyō-ku; h9am-5pm; bKarasuma line to Shijō, dHankyū line to Karasuma or Kawaramachi)
Head to the covered Nishiki Market to check out the weird and wonderful foods that go into Kyoto cuisine. It's in the centre of town, one block north of (and parallel to) Shijō-dōri, running west off Teramachi covered arcade. Wander past stalls selling everything from barrels of _tsukemono_ (pickled vegetables) and cute Japanese sweets to wasabi salt and fresh sashimi skewers. Drop into Aritsugu here for some of the best Japanese chef's knives money can buy.
Daitoku-jiBuddhist Temple
(大徳寺; 53 Daitokuji-chō, Murasakino, Kita-ku; gKyoto City bus 205 or 206 to Daitokuji-mae, bKarasuma line to Kitaōji)
For anyone with the slightest fondness for Japanese gardens, don't miss this network of lanes dotted with atmospheric Zen temples. Daitoku-ji, the main temple here, serves as headquarters for the Rinzai Daitoku-ji school of Zen Buddhism. It's not usually open to the public but there are several subtemples with superb, carefully raked _karen-sensui_ (dry landscape) gardens well worth making the trip for. Highlights include Daisen-in, Kōtō-in, Ryōgen-in and Zuihō-in.
Kōtō-inBuddhist Temple
(高桐院; 73-1 Daitokuji-chō, Murasakino, Kita-ku; ¥400; h9am-4.30pm; gKyoto City bus 205 or 206 to Daitokuji-mae, bKarasuma line to Kitaōji)
On the far western edge of the Daitoku-ji complex, the sublime garden of this subtemple is one of the best in Kyoto and worth a special trip. It's located within a fine bamboo grove that you traverse via a moss-lined path. Once inside there is a small stroll garden that leads to the centrepiece: a rectangle of moss and maple trees, backed by bamboo. Take some time on the verandah here to soak it all up.
Kyoto Imperial PalaceHistoric Building
(map Google map; 京都御所, Kyoto Gosho; MAP; %075-211-1215; www.kunaicho.go.jp; Kyoto Gyōen, Kamigyō-ku; h9am-4.30pm Tue-Sun Mar-Sep, to 4pm Oct-Feb, last entry 40min before closing; bKarasuma line to Marutamachi or Imadegawa) F
The Kyoto Imperial Palace, known as the Gosho in Japanese, is a walled complex that sits in the middle of the **Kyoto Imperial Palace Park**. While no longer the official residence of the Japanese emperor, it's still a grand edifice, though it doesn't rate highly in comparison with other attractions in Kyoto. Visitors can wander around the marked route in the grounds where English signs explain the history of the buildings. Entrance is via the main Seishomon Gate, where you'll be given a map.
Higashiyama
1Sights
1Chion-inB4
2Eikan-dōD3
3Ginkaku-jiD1
4GionB5
5Hōnen-inD1
6Kiyomizu-deraB5
7Kyoto National MuseumA6
8Nanzen-jiD3
9Path of Philosophy \\(Tetsugaku-no-Michi\\)D1
10Shōren-inB4
11Yasaka-jinjaB4
2Activities, Courses & Tours
12Camellia Tea ExperienceB5
13MaikaA5
5Eating
14ChidoriteiA4
15Kagizen YoshifusaA4
16KikunoiB5
17Omen Kodai-jiB5
6Drinking & Nightlife
18% ArabicaB5
3Entertainment
19Gion OdoriA4
20Kyō OdoriA5
21Kyoto Cuisine & Maiko EveningB4
22MinamizaA4
23Miyako OdoriA4
### 1 Southern Higashiyama
Kiyomizu-deraBuddhist Temple
(map Google map; 清水寺; %075-551-1234; www.kiyomizudera.or.jp; 1-294 Kiyomizu, Higashiyama-ku; adult/child ¥400/200; h6am-6pm, closing times vary seasonally; gKyoto City bus 206 to Kiyōmizu-michi or Gojō-zaka, dKeihan line to Kiyomizu-Gojō)
A buzzing hive of activity perched on a hill overlooking the basin of Kyoto, Kiyomizu-dera is one of Kyoto's most popular and most enjoyable temples. It may not be a tranquil refuge, but it represents the favoured expression of faith in Japan. The excellent website is a great first port of call for information on the temple, plus a how-to guide to praying here. Note that the Main Hall is undergoing renovations and may be covered, but is still accessible.
Shōren-inBuddhist Temple
(map Google map; 青蓮院; 69-1 Sanjōbō-chō, Awataguchi, Higashiyama-ku; adult/child ¥500/free; h9am-5pm; bTōzai line to Higashiyama)
This temple is hard to miss, with its giant camphor trees growing just outside the walls. Fortunately, most tourists march right on past, heading to the area's more famous temples. That's their loss, because this intimate little sanctuary contains a superb landscape garden, which you can enjoy while drinking a cup of green tea (¥500; ask at the reception office, not available in summer).
Chion-inBuddhist Temple
(map Google map; 知恩院; www.chion-in.or.jp; 400 Rinka-chō, Higashiyama-ku; adult/child ¥500/250, grounds free; h9am-4.30pm, last entry 3.50pm; bTōzai line to Higashiyama)
A collection of soaring buildings, spacious courtyards and gardens, Chion-in serves as the headquarters of the Jōdo sect, the largest school of Buddhism in Japan. It's the most popular pilgrimage temple in Kyoto and it's always a hive of activity. For visitors with a taste for the grand, this temple is sure to satisfy.
Yasaka-jinjaShintō Shrine
(map Google map; 八坂神社; %075-561-6155; www.yasaka-jinja.or.jp; 625 Gion-machi, Kita-gawa, Higashiyama-ku; h24hr; bTōzai line to Higashiyama) F
This colourful and spacious shrine is considered the guardian shrine of the Gion entertainment district. It's a bustling place that is well worth a visit while exploring Southern Higashiyama; it can easily be paired with Maruyama-kōen, the park just up the hill.
Kyoto National MuseumMuseum
(map Google map; 京都国立博物館; www.kyohaku.go.jp; 527 Chaya-machi, Higashiyama-ku; admission varies; h9.30am-5pm, to 8pm Fri & Sat, closed Mon; gKyoto City bus 206 or 208 to Sanjūsangen-dō-mae, dKeihan line to Shichijō)
The Kyoto National Museum is the city's premier art museum and plays host to the highest-level exhibitions in the city. It was founded in 1895 as an imperial repository for art and treasures from local temples and shrines. The **Heisei Chishinkan** , designed by Taniguchi Yoshio and opened in 2014, is a brilliant modern counterpoint to the original red-brick **main hall** building, which was closed and undergoing structural work at the time of research. Check the _Kyoto Visitor's Guide_ to see what's on while you're in town.
### 1 Northern Higashiyama
Ginkaku-jiBuddhist Temple
(map Google map; 銀閣寺; 2 Ginkaku-ji-chō, Sakyō-ku; adult/child ¥500/300; h8.30am-5pm Mar-Nov, 9am-4.30pm Dec-Feb; gKyoto City bus 5 to Ginkakuji-michi stop)
Home to a sumptuous garden and elegant structures, Ginkaku-ji is one of Kyoto's premier sites. The temple started its life in 1482 as a retirement villa for shogun Ashikaga Yoshimasa, who desired a place to retreat from the turmoil of a civil war. While the name Ginkaku-ji literally translates as 'Silver Pavilion', the shogun's ambition to cover the building with silver was never realised. After Ashikaga's death, the villa was converted into a temple.
Nanzen-jiBuddhist Temple
(map Google map; 南禅寺; www.nanzenji.com; 86 Fukuchi-chō, Nanzen-ji, Sakyō-ku; adult/child from ¥300/150, grounds free; h8.40am-5pm Mar-Nov, to 4.30pm Dec-Feb; gKyoto City bus 5 to Eikandō-michi, bTōzai line to Keage)
This is one of the most rewarding temples in Kyoto, with its expansive grounds and numerous subtemples. At its entrance stands the massive **San-mon**. Steps lead up to the 2nd storey, which has a great view over the city. Beyond the gate is the main hall of the temple, above which you will find the **Hōjō** , where the Leaping Tiger Garden is a classic Zen garden well worth a look.
Eikan-dōBuddhist Temple
(map Google map; 永観堂; %075-761-0007; www.eikando.or.jp; 48 Eikandō-chō, Sakyō-ku; adult/child ¥600/400; h9am-5pm; gKyoto City bus 5 to Eikandō-michi, bTōzai line to Keage)
Perhaps Kyoto's most famous (and most crowded) autumn-foliage destination, Eikan-dō is a superb temple just a short walk south of the famous Path of Philosophy. Eikan-dō is made interesting by its varied architecture, its gardens and its works of art. It was founded as Zenrin-ji in 855 by the priest Shinshō, but the name was changed to Eikan-dō in the 11th century to honour the philanthropic priest Eikan.
Path of Philosophy (Tetsugaku-no-Michi)Area
(map Google map; 哲学の道; Sakyō-ku; gKyoto City bus 5 to Eikandō-michi or Ginkakuji-michi, bTōzai line to Keage)
The Tetsugaku-no-Michi is one of the most pleasant walks in Kyoto. Lined with a great variety of flowering plants, bushes and trees, it is a corridor of colour throughout most of the year. Follow the traffic-free route along a canal lined with cherry trees that come into spectacular bloom in early April. It only takes 30 minutes to do the walk, which starts at Nyakuōji-bashi, above Eikan-dō, and leads to Ginkaku-ji.
Shūgaku-in Rikyū Imperial VillaNotable Building
(修学院離宮; %075-211-1215; www.kunaicho.go.jp; Shūgaku-in, Yabusoe, Sakyō-ku; htours 9am, 10am, 11am, 1.30pm & 3pm Tue-Sun; gKyoto City bus 5 from Kyoto Station to Shūgakuinrikyū-michi) F
One of the highlights of northeast Kyoto, this superb imperial villa was designed as a lavish summer retreat for the imperial family. Its gardens, with their views down over the city, are worth the trouble it takes to visit. The one-hour tours are held in Japanese, with English audio guides free of charge. You must be over 18 years to enter and bring your passport.
### 1 Arashiyama
Arashiyama Bamboo GrovePark
(嵐山竹林; Ogurayama, Saga, Ukyō-ku; hdawn-dusk; gKyoto City bus 28 from Kyoto Station to Arashiyama-Tenryuji-mae, dJR Sagano/San-in line to Saga-Arashiyama or Hankyū line to Arashiyama, change at Katsura) F
The thick green bamboo stalks seem to continue endlessly in every direction and there's a strange quality to the light at this famous bamboo grove. It's most atmospheric on the approach to Ōkōchi Sansō villa and you'll be unable to resist trying to take a few photos, but you might be disappointed with the results: photos just can't capture the magic of the place. The grove runs from outside the north gate of Tenryū-ji to just below Ōkōchi Sansō.
Ōkōchi SansōHistoric Building
(大河内山荘; 8 Tabuchiyama-chō, Sagaogurayama, Ukyō-ku; adult/child ¥1000/500; h9am-5pm; gKyoto City bus 28 from Kyoto Station to Arashiyama-Tenryuji-mae, dJR Sagano (San-in) line to Saga-Arashiyama or Hankyū line to Arashiyama, change at Katsura)
This is the lavish estate of Ōkōchi Denjirō, an actor famous for his samurai films. The sprawling gardens may well be the most lovely in all of Kyoto, particularly when you consider the brilliant views eastwards across the city. The house and teahouse are also sublime. Be sure to follow all the trails around the gardens. Hold onto the tea ticket you were given upon entry to claim the _matcha_ and sweet that's included with admission.
Tenryū-jiBuddhist Temple
(天龍寺; %075-881-1235; www.tenryuji.com; 68 Susukinobaba-chō, Saga-Tenryū-ji, Ukyō-ku; adult/child ¥800/600, garden only ¥500/300; h8.30am-5pm; gKyoto City bus 28 from Kyoto Station to Arashiyama-Tenryuji-mae, dJR Sagano (San-in) line to Saga-Arashiyama or Hankyū line to Arashiyama, change at Katsura)
A major temple of the Rinzai school, Tenryū-ji has one of the most attractive gardens in all of Kyoto, particularly during the spring cherry-blossom and autumn-foliage seasons. The main 14th-century Zen garden, with its backdrop of the Arashiyama mountains, is a good example of _shakkei_ (borrowed scenery). Unfortunately, it's no secret that the garden here is world class, so it pays to visit early in the morning or on a weekday.
### 1 Kyoto Station Area
Kyoto StationNotable Building
(map Google map; 京都駅; www.kyoto-station-building.co.jp; Karasuma-dōri, Higashishiokōji-chō, Shiokōji-sagaru, Shimogyō-ku; dKyoto Station)
The Kyoto Station building is a striking steel-and-glass structure – a kind of futuristic cathedral for the transport age – with a tremendous space that arches above you as you enter the main concourse. Be sure to take the escalator from the 7th floor on the east side of the building up to the 11th-floor glass corridor, Skyway (open 10am to 10pm), that runs high above the main concourse of the station, and catch some views from the 15th-floor Sky Garden terrace.
Kyoto Station | MANUEL ASCANIO/SHUTTERSTOCK ©
2Activities
Camellia Tea ExperienceTea Ceremony
(map Google map; 茶道体験カメリア; %075-525-3238; www.tea-kyoto.com; 349 Masuya-chō, Higashiyama-ku; per person ¥2000; gKyoto City bus 206 to Yasui)
Camellia is a superb place to try a simple Japanese tea ceremony. It's located in a beautiful old Japanese house just off Ninen-zaka. The host speaks fluent English and explains the ceremony simply and clearly to the group, while managing to perform an elegant ceremony. The price includes a bowl of _matcha_ and a sweet.
The Tea Ceremony
_Chanoyu_ (literally 'water for tea') is usually translated as 'tea ceremony', but it's more like performance art, with each element – from the gestures of the host to the feel of the tea bowl in your hand – carefully designed to articulate an aesthetic experience. It's had a profound and lasting influence on the arts in Japan; whether you take part in a ceremony or simply pause to admire a teahouse, _sadō_ (the way of tea) will colour your Kyoto experience.
GREG ELMS/LONELY PLANET ©
Funaoka OnsenOnsen
(船岡温泉; 82-1 Minami-Funaoka-chō-Murasakino, Kita-ku; ¥430; h3pm-1am Mon-Sat, from 8am Sun; gKyoto City bus 206 to Senbon Kuramaguchi)
This old _sentō_ (public bath) on Kuramaguchi-dōri is Kyoto's best. It boasts an outdoor bath, a sauna, a cypress-wood tub, an electric bath, a herbal bath and a few more for good measure. To get here _,_ head west about 400m on Kuramaguchi-dōri from the Kuramaguchi and Horiikawa intersection. It's on the left, not far past Lawson convenience store. Look for the large rocks.
7Shopping
Kyoto has a fantastic variety of both traditional and modern shops. Most are located in the Downtown Kyoto area, making the city a very convenient place to shop. Whether you're looking for fans, kimono and tea, or the latest electronics, hip fashion and ingenuous gadgets, Kyoto has plenty to offer.
AritsuguHomewares
(map Google map; 有次; %075-221-1091; 219 Kajiya-chō, Nishikikōji-dōri, Gokomachi nishi-iru, Nakagyō-ku; h9am-5.30pm; dHankyū line to Kawaramachi)
While you're in Nishiki Market, have a look at this store – it has some of the best kitchen knives in the world. Choose your knife – all-rounder, sushi, vegetable – and the staff will show you how to care for it before sharpening and boxing it up. You can also have your name engraved in English or Japanese. Knives start at around ¥10,000.
Ippōdō TeaTea
(map Google map; 一保堂茶舗; %075-211-3421; www.ippodo-tea.co.jp; Teramachi-dōri, Nijō-agaru, Nakagyō-ku; h9am-6pm; bTōzai line to Kyoto-Shiyakusho-mae)
This old-style tea shop sells some of the best Japanese tea in Kyoto, and you'll be given an English leaflet with prices and descriptions of each one. Its _matcha_ makes an excellent souvenir. Ippōdō is north of the city hall, on Teramachi-dōri. It has an adjoining teahouse, Kaboku Tearoom; last orders at 5.30pm.
Wagami no MiseArts & Crafts
(map Google map; 倭紙の店; %075-341-1419; 1st fl, Kajinoha Bldg, 298 Ōgisakaya-chō, Higashinotōin-dōri, Bukkōji-agaru, Shimogyō-ku; h9.30am-5.30pm Mon-Fri, to 4.30pm Sat; bKarasuma line to Shijō)
This place sells a fabulous variety of _washi_ for reasonable prices and is a great spot to pick up a gift or souvenir. Look for the Morita Japanese Paper Company sign on the wall out the front.
TakashimayaDepartment Store
(map Google map; 高島屋; %075-221-8811; Shijō-Kawaramachi Kado, Shimogyō-ku; h10am-8pm; dHankyū line to Kawaramachi)
The _grande dame_ of Kyoto department stores, Takashimaya is almost a tourist attraction in its own right, from the mind-boggling riches of the basement food floor to the wonderful selection of lacquerware and ceramics on the 6th. Check out the kimono display on the 5th floor.
Takashimaya | TK KURIKAWA/SHUTTERSTOCK ©
5Eating
Kyoto is one of the world's great food cities. In fact, when you consider atmosphere, service and quality, it's hard to think of a city where you get more bang for your dining buck. You can pretty much find a great dining option in any neighbourhood, but the majority of the best spots are clustered downtown.
### 5Downtown Kyoto
Café Bibliotec Hello!Cafe¥
(map Google map; カフェビブリオティックハロー!; %075-231-8625; 650 Seimei-chō, Nijō-dōri, Yanaginobanba higashi-iru, Nakagyō-ku; meals from ¥850; h11.30am-midnight; W; bTōzai line to Kyoto-Shiyakusho-mae)
As the name suggests, books line the walls of this cool cafe located in a converted _machiya_ attracting a mix of locals and tourists. It's a great place to relax with a book or to tap away at your laptop over a coffee (¥450) or light lunch. Look for the huge banana plants out the front.
Honke OwariyaNoodles¥
(map Google map; 本家尾張屋; %075-231-3446; www.honke-owariya.co.jp; 322 Kurumaya-chō, Nijō, Nakagyō-ku; dishes from ¥810; h11am-7pm; bKarasuma or Tōzai lines to Karasuma-Oike)
Set in an old sweets shop in a traditional Japanese building on a quiet downtown street, this is where locals come for excellent soba (buckwheat-noodle) dishes. The highly recommended house speciality, _hourai soba_ (¥2160), comes with a stack of five small plates of soba with a selection of toppings, including shiitake mushrooms, shrimp tempura, thin slices of omelette and sesame seeds.
BioteiVegetarian¥
(map Google map; びお亭; %075-255-0086; 2nd fl, M&I Bldg, 28 Umetada-chō, Sanjō-dōri, Higashinotōin nishi-iru, Nakagyō-ku; lunch/dinner sets from ¥890/1385; h 11.30am-2pm Tue-Fri, 5-8.30pm Tue, Wed, Fri & Sat; v; bTōzai or Karasuma lines to Karasuma-Oike)
Located diagonally across from Nakagyō post office, this is a favourite of Kyoto vegetarians, serving à la carte and daily sets with dishes such as deep-fried crumbed tofu and black seaweed salad with rice, miso and pickles. The seating is rather cramped but the food is excellent, beautifully presented and carefully made from quality ingredients.
Roan KikunoiKaiseki¥¥¥
(map Google map; 露庵菊乃井; %075-361-5580; www.kikunoi.jp; 118 Saito-chō, Kiyamachi-dōri, Shijō-sagaru, Shimogyō-ku; lunch/dinner from ¥7000/13,000; h11.30am-1.30pm & 5-8.30pm Thu-Tue; dHankyū line to Kawaramachi or Keihan line to Gion-Shijō)
Roan Kikunoi is a fantastic place to experience the wonders of _kaiseki_. It's a lovely intimate space located right downtown. The chef takes an experimental and creative approach and the results are a wonder for the eyes and palate. Highly recommended. Reserve at least a few days in advance.
YoshikawaTempura¥¥¥
(map Google map; 吉川; %075-221-5544; www.kyoto-yoshikawa.co.jp; 135 Matsushita-chō, Tominokōji, Oike-sagaru, Nakagyō-ku; lunch ¥3000-25,000, dinner ¥8000-25,000; h11am-1.45pm & 5-8pm; bTōzai line to Karasuma-Oike or Kyoto-Shiyakusho-mae)
This is the place to go for delectable tempura with a daily changing menu. Attached to the Yoshikawa ryokan, it offers table seating, but it's much more interesting to sit and eat around the small intimate counter and observe the chefs at work. Reservation is required for the private tatami room, and counter bar for dinner. Note: counter bar is closed Sunday.
Kaiseki Cuisine
In a city blessed with excellent dining options, one not to be missed is the refined and elegant experience of _kaiseki_ cuisine. _Kaiseki_ consists of a number of small courses, largely vegetarian, served on exquisite dinnerware where the preparation and service is as outstanding as the food itself. Diners are usually served in private rooms at speciality restaurants, such as the highly regarded Kikunoi and Kitcho Arashiyama. Prices are elevated for this fine-dining experience, but you don't need to spend a week's travel budget on dinner to get a taste of _kaiseki_.
_Kaiseki_ dishes | KPG_PAYLESS/SHUTTERSTOCK ©
### 5Southern Higashiyama
Kagizen YoshifusaTeahouse¥
(map Google map; 鍵善良房; %075-561-1818; www.kagizen.co.jp; 264 Gion machi, Kita-gawa, Higashiyama-ku; kuzukiri ¥1080, tea & sweet ¥880; h9.30am-6pm, closed Mon; dHankyū line to Kawaramachi, Keihan line to Gion-Shijō)
This Gion institution is one of Kyoto's oldest and best-known _okashi-ya_ (sweet shops). It sells a variety of traditional sweets and has a lovely tearoom out the back where you can sample cold _kuzukiri_ (transparent arrowroot noodles) served with a _kuro-mitsu_ (sweet black sugar) dipping sauce, or just a nice cup of _matcha_ and a sweet.
Escape the Crowds
**Gion** Be sure to veer off the main drag in the Gion district, where you'll escape the crowds and see some of the area's impossibly atmospheric backstreets.
Path of Philosophy The crowds are usually gone by 5pm here, leaving this scenic pathway to locals and savvy travellers. A great option if your cruise schedule permits.
**Hōnen-in** Escape the crowds and find yourself at this lovely Buddhist sanctuary (法然院; MAP; 30 Goshonodan-chō, Shishigatani, Sakyō-ku; h6am-4pm; gKyoto City bus 5 to Ginkakuji-michi) F.
**Northwest Kyoto** This area has some superb temples and shrines that are worth making the trek for. Aside from Kinkaku-ji, the main attraction, you've got quiet temple complexes, Myōshin-ji and Ninna-ji, that are the perfect places to spend some time strolling around, minus the crowds.
Path of Philosophy | MYPIXELDIARIES/SHUTTERSTOCK ©
Omen Kodai-jiNoodles¥
(map Google map; おめん 高台寺店; %075-541-5007; 362 Masuya-chō, Kōdaiji-dōri, Shimokawara higashi-iru, Higashiyama-ku; noodles from ¥1150; h11am-9pm; gKyoto City bus 206 to Higashiyama-Yasui)
Housed in a remodelled Japanese building with a light, airy feeling, this branch of Kyoto's famed Omen noodle chain is the best place to stop while exploring the Southern Higashiyama district. Upstairs has fine views over the area. The signature udon (thick, white wheat noodles) served in broth with a selection of fresh vegetables is delicious.
ChidoriteiSushi¥
(map Google map; 千登利亭; %075-561-1907; 203 Rokken-cho, Donguri-dori, Yamato-oji Nishi-iru, Higashiyama-ku; sushi sets ¥600-2200; h11am-8pm, closed Thu; dKeihan line to Gion-Shijō)
Family owned Chidoritei is a snug little sushi restaurant tucked away in the backstreets of Gion away from the bustle. It's a great place to try delicious traditional Kyoto _saba-zushi –_ mackerel hand pressed into lightly vinegared rice and wrapped in _konbu_ (a type of seaweed). In summer, the speciality here is conger-eel sushi.
KikunoiKaiseki¥¥¥
(map Google map; 菊乃井; %075-561-0015; www.kikunoi.jp; 459 Shimokawara-chō, Yasakatoriimae-sagaru, Shimokawara-dōri, Higashiyama-ku; lunch/dinner from ¥10,000/16,000; hnoon-1pm & 5-8pm; dKeihan line to Gion-Shijō)
Michelin-starred chef Mutara serves some of the finest _kaiseki_ in the city. Located in a hidden nook near Maruyama-kōen, this restaurant has everything necessary for the full over-the-top _kaiseki_ experience, from setting to service to exquisitely executed cuisine, often with a creative twist. Reserve at least a month in advance.
### 5Arashiyama
Arashiyama YoshimuraNoodles¥
(嵐山よしむら; %075-863-5700; Togetsu-kyō kita, Saga-Tenryū-ji, Ukyō-ku; soba from ¥1000, sets from ¥1278; h11am-5pm; gKyoto City bus 28 from Kyoto Station to Arashiyama-Tenryuji-mae, dJR Sagano/San-in line to Saga-Arashiyama or Hankyū line to Arashiyama, change at Katsura)
For a tasty bowl of soba noodles and a million-dollar view over the Arashiyama mountains and the Togetsu-kyō bridge, head to this extremely popular eatery (prepare to queue at peak times) just north of the famous bridge, overlooking the Katsura-gawa. There's an English menu but no English sign; look for the big glass windows and the stone wall.
Meal at Arashiyama Yoshimura | BRENDA LAM/STOCKIMO/ALAMY STOCK PHOTO ©
ShigetsuVegetarian, Japanese¥¥
(篩月; %075-882-9725; 68 Susukinobaba-chō, Saga-Tenryū-ji, Ukyō-ku; lunch sets ¥3500, ¥5500 & ¥7500; h11am-2pm; v; gKyoto City bus 28 from Kyoto Station to Arashiyama-Tenryuji-mae, dJR Sagano/San-in line to Saga-Arashiyama or Hankyū line to Arashiyama, change at Katsura)
To sample _shōjin-ryōri_ , try Shigetsu in the precincts of Tenryū-ji. This healthy fare has been sustaining monks for more than a thousand years in Japan, so it will probably get you through an afternoon of sightseeing, although carnivores may be left craving something more. Shigetsu has beautiful garden views. Prices include temple admission.
Kitcho ArashiyamaKaiseki¥¥¥
(吉兆嵐山本店; %075-881-1101; www.kyoto-kitcho.com; 58 Susukinobaba-chō, Saga-Tenryūji, Ukyō-ku; lunch/dinner from ¥51,840/64,800; h11.30am-3pm & 5-9pm Thu-Tue; c; gKyoto City bus 28 from Kyoto Station to Arashiyama-Tenryuji-mae, dJR Sagano/San-in line to Saga-Arashiyama or Hankyū line to Arashiyama, change at Katsura)
Considered one of the best _kaiseki_ restaurants in Kyoto (and Japan, for that matter), Kitcho Arashiyama is the place to sample the full _kaiseki_ experience. Meals are served in private rooms overlooking gardens. The food, service, explanations and atmosphere are all first rate. Make bookings online via its website well in advance.
6Drinking
Kyoto is a city with endless options for drinking, whether it's an expertly crafted single-origin coffee in a hipster cafe, a rich _matcha_ at a traditional tearoom, carefully crafted cocktails and single malts in a sophisticated six-seater bar, or Japanese craft beer in a brewery. Check ahead in _Kansai Scene_ to see what's going on.
### 6Downtown Kyoto
Weekenders CoffeeCoffee
(map Google map; ウィークエンダーズ コーヒー; %075-746-2206; www.weekenderscoffee.com; 560 Honeyana-chō, Nakagyō-ku; coffee from ¥430; h7.30am-6pm Thu-Tue; dHankyū line to Kawaramachi)
Weekenders is a tiny coffee bar tucked away in a traditional-style building at the back of a parking lot in Downtown Kyoto. Sure, it's a strange location, but it's where you'll find some of the city's best coffee being brewed by roaster-owner Masahiro Kaneko. It's mostly takeaway with a small bench out front.
TaiguPub
(map Google map; ダイグ ガストロ パブ; %075-213-0214; 1st fl, 498 Kamikoriki-chō, Nakagyō-ku; h11.30am-11pm; W; bTōzai line to Kyoto-Shiyakusho-mae)
Looking out on scenic Kiyamachi-dōri, Taigu (formerly Tadg's Gastro Pub) is a good spot for an evening drink. Choose from an extensive selection of craft beers (including several rotating Japanese beers on tap), a variety of wines, sake and spirits. It also does pub-style meals.
Kaboku TearoomTeahouse
(map Google map; 喫茶室嘉木; Teramachi-dōri, Nijō-agaru, Nakagyō-ku; h10am-6pm; bTōzai line to Kyoto-Shiyakusho-mae)
A casual tearoom attached to the Ippōdō Tea store, Kaboku serves a range of teas and provides a great break while exploring the shops in the area. Try the _matcha_ and grab a counter seat to watch it being prepared.
### 6Southern Higashiyama
% ArabicaCoffee
(MAP; %075-746-3669; 87 Hoshino-chō, Higashiyama-ku; coffee from ¥300; h8am-6pm; gKyoto City bus 206 to Higashiyama-Yasui)
This branch of % Arabica sits in the shadow of nearby Yasaka Pagoda on an atmospheric stone paved street. Grab a takeaway single-origin brew and continue strolling and sightseeing in the area. There's usually a queue out the front of Kyoto's pretty young things taking Instagrammable selfies as they wait.
### 6Kyoto Station Area
Roots of all EvilBar
(map Google map; www.nokishita.net; Kyoto Tower, B1 Karasuma-dōri, Shichijō-sagaru, Shimogyō-ku; h11am-11pm; dKyoto Station) S
Stop by this standing bar in the Kyoto Tower Sando food basement for creative gin cocktails. It offers interesting herbal, spicy and floral gin infusions. Cocktails from ¥800.
Vermillion Espresso BarCafe
(map Google map; バーミリオン; www.vermillioncafe.com; 85 Onmae-chō, Fukakusa-inari, Fushimi-ku; h9am-5pm; W; dJR Nara line to Inari or Keihan line to Fushimi-Inari)
A Melbourne-inspired cafe, tiny Vermillion takes its name from the colour of the _torii_ of the nearby Fushimi Inari-Taisha shrine. It does standout coffee, as well as a small selection of cakes, which can be taken away or enjoyed at the communal table. It's on the main street, just a short hop from Inari Station.
3Entertainment
MinamizaTheatre
(map Google map; 南座; www.kabukiweb.net; Shijō-Ōhashi, Higashiyama-ku; dKeihan line to Gion-Shijō)
This theatre in Gion is the oldest kabuki theatre in Japan. The major event of the year is the **Kaomise festival** in December, which features Japan's finest kabuki actors.
Miyako OdoriDance
(都をどり; MAP; %075-541-3391; www.miyako-odori.jp; Gion Kōbu Kaburen-jō Theatre, 570-2 Gion-machi, Minamigawa, Higashiyama-ku; tickets from ¥4000; hshows 12.30pm, 2.20pm & 4.10pm; gKyoto City bus 206 to Gion, dKeihan line to Gion-Shijō)
This 45-minute dance is a wonderful geisha performance. It's a real stunner and the colourful images are mesmerising. It's held throughout April, usually at Gion Kōbu Kaburen-jō Theatre. The building is under ongoing renovations until around 2021 and performances will be held at Minamiza in the meantime.
8INFORMATION
TOURIST INFORMATION
**Kyoto Tourist Information Center** (京都総合観光案内所, TIC; MAP; %075-343-0548; 2F Kyoto Station Bldg, Shimogyō-ku; h8.30am-7pm; dKyoto Station) Stocks bus and city maps, has plenty of transport info and English speakers are available to answer your questions. Note that it's called 'Kyo Navi' in Japanese (in case you have to ask someone). It also has a couple of computer terminals with internet (10 minutes ¥100).
8GETTING AROUND
BUS
Kyoto has an intricate network of bus routes providing an efficient way of getting around at moderate cost. Most of the routes used by visitors have announcements and bus-stop information displays in English. Most buses run between 7am and 10pm, though a few run earlier or later.
Bus entry is usually through the back door and exit is via the front door. Inner-city buses charge a flat fare (¥230 for adults, ¥120 for children ages six to 12, free for those younger), which you drop into the clear plastic receptacle on top of the machine next to the driver on your way out. A separate machine gives change for ¥100 and ¥500 coins or ¥1000 notes.
TAXI
Taxis are a convenient, but expensive, way of getting from place to place about town. A taxi can usually be flagged down in most parts of the city at any time. There are also a large number of _takushī noriba_ (taxi stands) in town, outside most train/subway stations, department stores etc.
There is no need to touch the back doors of the cars at all – the opening/closing mechanism is controlled by the driver.
TRAIN & SUBWAY
The main train station in Kyoto is Kyoto Station, which is in the south of the city, just below Shichijō-dōri and is actually two stations under one roof: JR Kyoto Station and Kintetsu Kyoto Station.
In addition to the private Kintetsu line that operates from Kyoto Station, there are two other private train lines in Kyoto: the Hankyū line that operates from Downtown Kyoto along Shijō-dōri and the Keihan line that operates from stops along the Kamo-gawa.
TOP EXPERIENCE
# Nara
Japan's first permanent capital, Nara (奈良) is one of the country's most rewarding destinations. With eight Unesco World Heritage Sites, it's second only to Kyoto as a repository of Japan's cultural legacy.
Great For...
h # A
yDon't Miss
The awe-inspiring Daibutsu (Great Buddha), a towering effigy first cast in the 8th century.
Explore Ashore
The nearest ports to Nara are those in Kyoto and Osaka. The Kintetsu Nara line is the fastest and most convenient connection between Kyoto (Kintetsu Kyoto Station, in Kyoto Station) and central Nara (Kintetsu Nara Station), via direct, all-reserved trains (¥1130, 35 minutes) or express trains (¥620, 50 minutes), which usually require a change at Yamato-Saidaiji. The Kintetsu Nara line connects Osaka (Namba Station) with Nara (Kintetsu Nara Station; ¥560, 45 minutes).
8Need to Know
Nara is popular as a day trip from Kyoto or Osaka – there's just enough time to see the highlights.
Kōfuku-ji | SEANPAVONEPHOTO/GETTY IMAGES ©
Nara's highlights all occupy a compact area in and around Nara-kōen, a large, grassy park home to many (somewhat) tame deer.
Tōdai-ji (東大寺; www.todaiji.or.jp; 406-1 Zōshi-chō; Daibutsu-den adult/child ¥600/300; hDaibutsu-den 7.30am-5.30pm Apr-Oct, 8am-5pm Nov-Mar) is home to **Daibutsu (Great Buddha)** , Nara's star attraction and one of the largest bronze statues in the world. It was unveiled in 752, upon the completion of the **Daibutsu-den** (大仏殿, Great Buddha Hall), built to house it. Both have been damaged over the years; the present statue was recast in the Edo period. The Daibutsu-den is the largest wooden building in the world; incredibly, the present structure, rebuilt in 1709, is a mere two-thirds of the size of the original.
Southeast of Tōdai-ji is Kasuga Taisha (春日大社; www.kasugataisha.or.jp; 160 Kasugano-chō; h6am-6pm Apr-Sep, 6.30am-5pm Oct-Mar) F. Founded in the 8th century, this sprawling shrine at the foot of Mikasa-yama was created to protect Nara. It was ritually rebuilt every 20 years, according to Shintō tradition, until the late 19th century and is still kept in pristine condition. Many of its buildings are painted vermilion, in bold contrast to the cedar roofs and surrounding greenery. The corridors are lined with hundreds of lanterns, which are illuminated during the twice-yearly Mantōrō lantern festival ( h3 Feb, 14 & 15 Aug).
On the west side of Nara-kōen is the Nara National Museum (奈良国立博物館, Nara Kokuritsu Hakubutsukan; %050-5542-8600; www.narahaku.go.jp; 50 Noboriōji-chō; ¥520, special exhibitions ¥1100-1420; h9.30am-5pm Tue-Sun), a world-class museum of Buddhist art. Built in 1894 and strikingly renovated in 2016, the Nara Buddhist Sculpture Hall & Ritual Bronzes Gallery displays a rotating selection of about 100 _butsu-zō_ (statues of Buddhas and bodhisattvas) at any one time, about half of which are National Treasures or Important Cultural Properties. Chinese bronzes in the Ritual Bronzes Gallery date as far back as the 15th century BC. Each image has detailed English explanations.
Further west is Kōfuku-ji (興福寺; www.kohfukuji.com; grounds free, Tōkondō ¥300, National Treasure Museum ¥600, combined ticket ¥800; hgrounds 24hr, Tōkondō 9am-5pm), which was founded in Kyoto in 669 and relocated here in 710. The original Nara temple complex had 175 buildings, though many have been lost over the years to fires and periods of medieval warfare. Of those that remain, the most impressive are the Tōkondō (東金堂; Eastern Golden Hall) and the temple's two pagodas: the three-storey pagoda (三重塔) dates to 1181 and is a rare example of Heian-era architecture, while the 50.1m five-storey pagoda (五重塔), last reconstructed in 1426, is Japan's second-tallest pagoda.
Daibutsu (Great Buddha) | BENNY MARTY/SHUTTERSTOCK ©
# OSAKA
#### Eating Out in Osaka
#### Osaka-jō
#### Sights
#### Activities
#### Shopping
#### Eating
#### Drinking
#
Osaka at a Glance
If Kyoto was the city of the courtly nobility and Tokyo the city of the samurai, then Osaka (大阪) was the city of the merchant class. Japan's third-largest city is a place where things have always moved a bit faster, where people are a bit brasher and interactions are peppered with playful jabs – and locals take pride in this. Osaka is not a pretty city in the conventional sense – though it does have a lovely river cutting through the centre – but it packs more colour than most. The acres of concrete are cloaked in dazzling neon; shopfronts are vivid, unabashed cries for attention.
Osaka cityscape | SEAN PAVONE/SHUTTERSTOCK ©
With a Day in Port
Start with a visit to Osaka-jō, then take the subway to Tennōji for a view over the city at Abeno Harukas and a dip at Spa World, and enjoy a _kushikatsu_ lunch at Ganso Kushikatsu Daruma Honten. Hop back on the subway to Nipponbashi and wander through Kuromon Ichiba market before heading over to Dōtombori. There are plenty of places to eat here – try Japanese haute cuisine at Shoubentango-tei or _okonomiyaki_ (savoury pancakes) at Chibō. If you have time, stick around to see the area's neon lights at dusk.
Best Places for...
**City views** Abeno Harukas
**Coffee** Brooklyn Roasting Company
**History** Osaka-jō
**Markets** Kuromon Ichiba
**Tempura** Yotaro Honten
**Youth culture** Amerika-Mura
Getting from the Port
Ships dock at Tempozan Passenger Terminal. From the terminal it's an easy 500m walk to Osakako Station, from where you can get to either JR Osaka Station or Namba Station (near Dōtombori) by train in about 20 minutes. For Osaka-jō, head straight down the Chūō (green) line for 30 minutes to Morinomiya Station.
Fast Facts
**Money** ATMs in post offices and 7-Eleven convenience stores take international cards. Major banks and post offices have currency exchange services.
**Wi-fi** Increasingly available at cafes and public areas around town.
TOP EXPERIENCE
# Eating Out in Osaka
Osaka has a rich food culture that ranks as the number one reason to visit: its unofficial slogan is _kuidaore_ ('eat until you drop'). You'll find great food at street counters, in train station basements and along shopping arcades, behind both graceful traditional facades and loud, over-the-top shopfronts. It's most famous for its comfort food – dishes that are deep-fried or grilled and stuffed with delicacies such as octopus and squid.
Great For...
kru
8Need to Know
The Minami district is the centre of Osaka's eating and drinking scene. Many street-food counters have tables and chairs out the back.
Explore Ashore
To reach the Minami district from the ferry terminal, catch the train from Osakako Station on the Chūō (green) line to Hommachi Station, then change to the Midō-suji (red) line and head south to Namba Station. The journey should take about 30 minutes. Leave yourself at least a couple of hours to graze at a few different stops.
_Tako-yaki_ (octopus dumpling) shops | SURACHET JO/SHUTTERSTOCK ©
### Okonomiyaki
Thick, savoury pancakes filled with shredded cabbage and your choice of meat, seafood, vegetables and more (the name means 'cook as you like'). Often prepared on a _teppan_ (steel plate) set into your table, the cooked pancake is brushed with a Worcestershire-style sauce, decoratively striped with mayonnaise and topped with dried bonito flakes, which seem to dance in the rising steam. Slice off a wedge using a tiny _kote_ (trowel), and – warning – allow it to cool a bit before taking that first bite.
Chibō (map Google map; 千房; %06-6212-2211; www.chibo.com; 1-5-5 Dōtombori, Chūō-ku; mains ¥885-1675; h11am-1am Mon-Sat, to midnight Sun; bMidō-suji line to Namba, exit 14) is one of Osaka's most famous _okonomiyaki_ restaurants. It almost always has a line, but it moves fast because there is seating on multiple floors (though you might want to hold out for the coveted tables overlooking Dōtombori canal).
### Tako-yaki
These doughy dumplings stuffed with octopus ( _tako_ in Japanese) are grilled in specially made moulds. They're often sold as street food, served with pickled ginger, topped with savoury sauce, powdered _aonori_ (seaweed), mayonnaise and bonito flakes, and are eaten with toothpicks. Nibble carefully first as the centre can be molten hot!
Try them at Wanaka Honten (map Google map; わなか本店; %06-6631-0127; <http://takoyaki-wanaka.com>; 11-19 Sennichi-mae, Chūō-ku; tako-yaki per 8 from ¥450; h10am-11pm Mon-Fri, from 8.30am Sat & Sun; bMidō-suji line to Namba, exit 4), which uses custom copper hotplates (instead of cast iron) to make dumplings that are crisper on the outside than usual (but still runny inside).
yDon't Miss
Dōtombori is Osaka's biggest street-food destination; it gets awfully crowded in the evening.
_Kushikatsu_ | PAIKONG/SHUTTERSTOCKS ©
### Kushikatsu
_Yakitori_ refers to skewers of grilled meat, seafood and/or vegetables; _kushikatsu_ is the same ingredients crumbed, deep fried and served with a savoury dipping sauce (double-dipping is a serious no-no). For many Japanese, a pilgrimage to Ganso Kushikatsu Daruma Honten (map Google map; 元祖串かつ だるま本店; %06-6645-7056; www.kushikatu-daruma.com; 2-3-9 Ebisu-Higashi, Naniwa-ku; skewers ¥120-240; h11am-10.30pm; bMidōsuji line to Dōbutsuen-mae, exit 5) is a necessary part of any visit to Osaka. Opened in 1929, it's said to be the birthplace of _kushikatsu_.
### Kaiten-sushi
This Osaka invention (from the 1950s) goes by many names in English: conveyor-belt sushi, sushi-go-round or sushi train. It's all the same – plates of sushi that run past you along a belt built into the counter (you can also order off the menu). Kaiten Sushi Ganko (map Google map; 回転寿司がんこ; %06-4799-6811; Eki Maré, Osaka Station City, Kita-ku; plates ¥130-735; h11am-11pm; dJR Osaka, Sakurabashi exit), inside JR Osaka's Eki Marché food court, is a popular choice – meaning the two whirring tracks of plates are continuously restocked with fresh options.
### Kappō-ryōri
Osaka's take on Japanese haute cuisine is casual: the dishes are similar to what you might find at a Kyoto _ryōtei_ (a formal restaurant with tatami seating) – incorporating seasonal ingredients and elaborate presentation – but at _kappō_ restaurants, diners sit at the counter, chatting with the chef, who hands over the dishes as they're finished. Despite the laid-back vibe these restaurants can be frightfully expensive. Shoubentango-tei (map Google map; 正弁丹吾亭; %06-6211-3208; 1-7-12 Dōtombori, Chūō-ku; dinner course ¥3780-10,800; h5-10pm; bMidō-suji line to Namba, exit 14) isn't, despite its pedigree: established over 100 years ago, it was a literati hangout in the early 20th century. It's a wonderful option if your cruise schedule allows. Even the cheapest course, which includes five dishes decided that day by the chef, tastes – and looks – like a luxurious treat. Reservations are necessary for all but the cheapest course.
TOP EXPERIENCE
# Osaka-jō
After unifying Japan in the late 16th century, General Toyotomi Hideyoshi built this castle (1583) as a display of power using, it's said, the labour of 100,000 workers. Although the present structure is a 1931 concrete reconstruction (refurbished in 1997), it's nonetheless quite a sight, looming dramatically over the surrounding park and moat. Inside, a museum displays historical artefacts.
Great For...
vAh
yDon't Miss
Swing by bakery Gout to pick up gourmet picnic supplies.
Explore Ashore
Nearby Morinomiya Station is on the Chūō (green) line, as is Osakako Station (near the ferry terminal). Simply hop on an eastbound train and you'll be there in 30 minutes. You'll need about three hours if you want to properly explore the grounds, castle and museum.
8Need to Know
大阪城; Osaka Castle; MAP; www.osakacastle.net; 1-1 Osaka-jō, Chūō-ku; grounds/castle keep free/¥600, combined with Osaka Museum of History ¥900; h9am-5pm, hours vary in spring & summer; bChūō line to Tanimachi 4-chōme, exit 9, dJR Loop line to Osaka-jō-kōen
YOSHIO TOMII/GETTY IMAGES ©
### The Castle Walls
Hideyoshi's original granite structure was said to be impregnable, yet it was destroyed in 1614 by the armies of Tokugawa Ieyasu (the founder of the Tokugawa shogunate). Ieyasu had the castle rebuilt – using the latest advancements to create terrifically imposing walls of enormous stones. The largest are estimated to weigh over 100 tonnes; others are engraved with the crests of feudal lords.
### The Turrets & Gates
There are 13 structures on the castle grounds that date back to the 17th-century reconstruction of the castle. **Sengan-yagura** (千貫櫓, Sengan Turret), next to **Ote-mon** (大手門) – the main gate, on the western side of the castle – and **Inui-yagura** (乾櫓, Inui Turret), in the northwestern corner of the grounds, are the oldest: they date to 1620.
HOLGS/GETTY IMAGES ©
### The Main Keep & Museum
By the 20th century, most of the castle was in ruins. Osaka citizens raised money themselves to rebuild the main keep; in 1931 the new tower was revealed, with bright white walls and glittering gold-leaf tigers stalking the eaves. Inside, a museum displays historical artefacts, paintings, scrolls and suits of armour from the feudal era.
### The Grounds
From the 8th-floor observatory inside the main keep, there are excellent views of the castle's sprawling, grassy grounds. For local residents, these grounds are the ultimate draw of the historical structure. Where soldiers once trained, families and couples now enjoy picnics and strolls.
### Top Tips
oIt's free to walk the castle grounds; admission is for the main keep only.
oYou can take an elevator up to the 5th floor of the keep, but you have to hike the rest of the way to the 8th floor (visitors with disabilities can take the elevator to the 8th floor).
oThe main keep, with its stairs and cramped, crowded passageways, can be challenging with small children.
oVisit the grounds on a warm weekend and you might catch local musicians staging casual shows on the lawns.
Minami
1Sights
1Abeno HarukasD6
Abeno Harukas Art Museum(see 1)
2Amerika-MuraA1
3DōtomboriB2
4Kuromon IchibaC2
5Triangle ParkA1
2Activities, Courses & Tours
6Spa WorldC5
7Shopping
7Dōguya-suji ArcadeB3
8Standard BooksB1
9Time Bomb RecordsA1
5Eating
10ChibōB2
11Ganso Kushikatsu Daruma HontenC5
12Imai HontenB2
13Shoubentango-teiB2
14Wanaka HontenB3
3Entertainment
15National Bunraku TheatreC2
1Sights
DōtomboriArea
(map Google map; 道頓堀; www.dotonbori.or.jp; bMidō-suji line to Namba, exit 14)
Highly photogenic Dōtombori is the city's liveliest night spot and the centre of the southern part of town. Its name comes from the 400-year-old canal, Dōtombori-gawa, now lined with pedestrian walkways and with a riot of illuminated billboards glittering off its waters. Don't miss the famous **Glico running man** sign. South of the canal is a pedestrianised street that has dozens of restaurants vying for attention with the flashiest of signage.
Abeno HarukasNotable Building
(map Google map; あべのハルカス; www.abenoharukas-300.jp; 1-1-43 Abeno-suji, Abeno-ku; observation deck adult ¥1500, child from ¥500-700, under 4yr free; hobservation deck 9am-10pm; bMidō-suji to Tennōji, dJR Loop line to Tennōji)
This César Pelli–designed tower, which opened in March 2014, is Japan's tallest building (300m, 60 storeys). The observatory on the 16th floor is free, but admission is required for the highly recommended top-level **Harukas 300 observation deck** , which has incredible 360-degree views of the whole Kansai region through windows that run several storeys high. There's also an open-air atrium. It houses Japan's largest department store (Kintetsu, floors B2–14), the Abeno Harukas Art Museum (map Google map; あべのハルカス美術館; %06-4399-9050; www.aham.jp; 16th fl, Abeno Harukas; admission varies by exhibition; h10am-8pm Tue-Fri, to 6pm Sat & Sun; bMidō-suji line to Tennōji, dJR Loop line to Tennōji), a hotel, offices and restaurants.
Amerika-MuraArea
(map Google map; アメリカ村, America Village, Ame-Mura; www.americamura.jp; Nishi-Shinsaibashi, Chūō-ku; bMidō-suji line to Shinsaibashi, exit 7)
West of Midō-suji, Amerika-Mura is a compact enclave of hip, youth-focused and offbeat shops, plus cafes, bars, tattoo and piercing parlours, nightclubs, hair salons and a few discreet love hotels. In the middle is Triangle Park (map Google map; 三角公園, Sankaku-kōen;, an all-concrete 'park' with benches for sitting and watching the fashion parade. Come nighttime, it's a popular gathering spot.
Osaka Aquarium KaiyūkanAquarium
(海遊館; %06-6576-5501; www.kaiyukan.com; 1-1-10 Kaigan-dōri, Minato-ku; adult ¥2300, child ¥600-1200; h10am-8pm, last entry 7pm; bChuō line to Osaka-kō, exit 1)
Kaiyūkan is among Japan's best aquariums. An 800m-plus walkway winds past displays of sea life from around the Pacific 'ring of fire': Antarctic penguins, coral-reef butterflyfish, unreasonably cute Arctic otters, Monterey Bay seals and unearthly jellyfish. Most impressive is the ginormous central tank, housing a whale shark, manta rays and thousands of other fish. Note there are also captive dolphins here, which some visitors may not appreciate; there is growing evidence that keeping cetaceans in captivity is harmful for the animals.
Kuromon IchibaMarket
(map Google map; 黒門市場, Kuromon Market; www.kuromon.com; Nipponbashi, Chūō-ku; hmost shops 9am-6pm; bSakai-suji line to Nipponbashi, exit 10)
An Osaka landmark for over a century, this 600m-long market is in equal parts a functioning market and a tourist attraction. Vendors selling fresh fish, meat, produce and pickles attract chefs and local home cooks; shops offering takeaway sushi or with grills set up (to cook the steaks, oysters, giant prawns etc that they sell) cater to visitors – making the market excellent for grazing and photo ops.
2Activities
Cycle OsakaCycling Tours
(MAP; %080-5325-8975; www.cycleosaka.com; 2-12-1 Sagisu, Fukushima-ku; half-/full-day tours ¥5000/10,000; dJR Loop line to Fukushima)
The English-speaking guides here lead well-organised tours to sights both well known and less well known, along the riverbanks and through the markets. The food route (¥8000) is particularly recommended. Fees include bicycle and helmet rental, water and food. It also rents out bikes (¥1500 per day).
Spa WorldOnsen
(map Google map; スパワールド; %06-6631-0001; www.spaworld.co.jp; 3-4-24 Ebisu-higashi, Naniwa-ku; day pass ¥1300; h10am-8.45am the next day; bMidō-suji line to Dōbutsu-en-mae, exit 5, dJR Loop line to Shin-Imamiya)
This huge, seven-storey onsen (hot-spring) complex contains dozens of options from saunas to salt baths, styled after a mini-UN's worth of nations. Gender-separated 'Asian' and 'European' bathing zones (bathe in the buff, towels provided) switch monthly. Swimsuits (rental ¥600, or BYO) are worn in swimming pools and _ganbanyoku_ (stone baths; additional ¥800 Monday to Friday, ¥1000 Saturday and Sunday).
Universal Studios JapanAmusement Park
(ユニバーサルスタジオジャパン, Universal City; %0570-200-606; www.usj.co.jp; 2-1-33 Sakura-jima, Konohana-ku; 1-day pass adult/child ¥7400/5100; hvaries seasonally; dJR Yumesaki line to Universal City)
Modelled after sister parks in the US, 'USJ' bursts with Hollywood movie–related rides, shows, shops and restaurants. Top billing goes to the ¥45 billion (!) Wizarding World of Harry Potter, a painstakingly recreated Hogsmeade Village (shop for magic wands, Gryffindor capes and butterbeer) plus the 'Harry Potter and the Forbidden Journey' thrill ride through Hogwarts School.
Bunraku
Bunraku is traditional Japanese puppet theatre. Almost-life-sized puppets are manipulated by black-clad, on-stage puppeteers, to evoke dramatic tales of love, duty and politics. The art form may not have originated in Osaka but it became popular here. Bunraku's most famous playwright, Chikamatsu Monzaemon (1653–1724), wrote plays about Osaka's merchants and the denizens of the pleasure quarters, social classes otherwise generally ignored in the Japanese arts at the time.
Bunraku has been recognised on the Unesco World Intangible Cultural Heritage list, and the National Bunraku Theatre (map Google map; 国立文楽劇場; %06-6212-2531, ticket centre 0570-07-9900; www.ntj.jac.go.jp; 1-12-10 Nipponbashi, Chūō-ku; full performance ¥2400-6000, single act ¥500-1500; hopening months vary, check the website; bSakai-suji line to Nipponbashi, exit 7) works to keep the tradition alive, with performances and an exhibition in the lobby about the history of bunraku and its puppeteers and main characters. Learn more at www2.ntj.jac.go.jp/unesco/bunraku/en.
Bunraku puppet | COWARDLION/SHUTTERSTOCK ©
7Shopping
Osaka is the biggest shopping destination in western Japan, with an overwhelming number of malls, department stores, shopping arcades, electronics dealers, boutiques and second-hand shops. More and more places are offering to waive the sales tax on purchases over ¥10,000 (look for signs in the window; passport is required).
Dōguya-suji ArcadeMarket
(map Google map; 道具屋筋; www.doguyasuji.or.jp/map_eng.html; Sennichi-mae, Chūō-ku; h10am-6pm; bMidō-suji line to Namba, exit 4)
This long arcade sells just about anything related to the preparation, consumption and selling of Osaka's principal passion: food. There's everything from bamboo steamers and lacquer miso soup bowls to shopfront lanterns, plastic food models and, of course, moulded hotplates for making _tako-yaki_ (octopus dumplings). Hours vary by store.
Standard BooksBooks
(map Google map; スタンダードブックストア; %06-6484-2239; www.standardbookstore.com; 2-2-12 Nishi-Shinsaibashi, Chūō-ku; h11am-10.30pm; bMidō-suji line to Shinsaibashi, exit 7)
This cult-fave Osaka bookstore prides itself on not stocking any bestsellers. Instead, it's stocked with small-press finds, art books, indie comics and the like, plus CDs, quirky fashion items and accessories.
Time Bomb RecordsMusic
(MAP; %06-6213-5079; www.timebomb.co.jp; B1, 9-28 Nishi-Shinsaibashi, Chūō-ku; hnoon-9pm; bMidō-suji line to Shinsaibashi, exit 7)
One of the best record stores in the city, Time Bomb stocks an excellent collection of vinyl and CDs from '60s pop and '70s punk to alternative, soul and psychedelic. Find out about gigs around town here, too.
5Eating
For more on eating in Osaka
GoutBakery¥
(map Google map; グウ; %06-6585-0833; 1-1-10 Honmachi, Chūō-ku; bread from ¥200; h7.30am-8pm, closed Thu; bTanimachi line to Tanimachi 4-chōme, exit 4)
One of Osaka's best bakeries, Gout (pronounced 'goo', as in French) sells baguettes, pastries, croissants, sandwiches and coffee to take away or eat in. It's perfect for picking up picnic supplies before heading to nearby Osaka-jō.
Yoshino SushiSushi¥¥
(map Google map; 吉野鯗; %06-6231-7181; www.yoshino-sushi.co.jp; 3-4-14 Awaji-machi, Chūō-ku; lunch from ¥2700; h11am-1.30pm Mon-Fri; bMidō-suji line to Honmachi, exit 1)
In business since 1841, Yoshino specialises in Osaka-style sushi, which is _hako-sushi_ (pressed sushi). This older version of the dish (compared to the newer, hand-pressed Tokyo-style _nigiri-sushi)_ is formed by a wooden mould, resulting in Mondrian-esque cubes of spongy omelette, soy-braised shiitake mushrooms, smokey eel and vinegar-marinated fish on rice. Reservations recommended.
Yotaro HontenTempura¥¥
(map Google map; 与太呂本店; %06-6231-5561; 2-3-14 Kōraibashi, Chūō-ku; tempura set ¥2500, sea bream rice ¥4300; h11am-1pm & 5-7pm, closed Thu; bSakaisuji line to Kitahama)
This two-Michelin-starred restaurant specialises in exceptionally light and delectable tempura served at the counter, where you can watch the chefs, or in private rooms. The tasty sea bream dish serves two to three people and the filling tempura sets are fantastic value. Look for the black-and-white sign and black slatted bars across the windows. Reserve in advance through your hotel.
Imai HontenUdon¥¥
(map Google map; 今井本店; %06-6211-0319; www.d-imai.com; 1-7-22 Dōtombori, Chūō-ku; dishes from ¥800; h11am-10pm, closed Wed; bMidō-suji line to Namba, exit 14)
Step into an oasis of calm amid Dōtombori's chaos to be welcomed by staff at one of the area's oldest and most-revered udon specialists. Try _kitsune udon_ – noodles topped with soup-soaked slices of fried tofu. Look for the traditional exterior and the willow tree outside.
Kita (Umeda)
1Sights
1Osaka-jōD3
2Activities, Courses & Tours
2Cycle OsakaA2
5Eating
3GoutC3
4Kaiten Sushi GankoB1
5Yoshino SushiB3
6Yotaro HontenC3
6Drinking & Nightlife
740 Sky Bar & LoungeB2
8Brooklyn Roasting CompanyC2
6Drinking
Brooklyn Roasting CompanyCoffee
(map Google map; %06-6125-5740; www.brooklynroasting.jp; 1-16 Kitahama, Chūō-ku; coffee from ¥350; h8am-8pm Mon-Fri, 10am-7pm Sat & Sun; W; bSakaisuji line to Kitahama, exit 2)
With its worn leather couches, big communal table and industrial fittings, this is a little slice of Brooklyn in Osaka and the perfect pit stop while exploring Naka-no-shima. Sip well-crafted coffee (almond and soy milk available, too) on the wide riverside terrace and watch the boats go by. If hunger strikes, there's a small selection of donuts and pastries.
40 Sky Bar & LoungeCocktail Bar
(map Google map; %06-6222-0111; www.conradhotels3.hilton.com; 3-2-4 Nakanoshima, Kita-ku, Conrad Osaka; cover after 8.30pm ¥1400; h10am-midnight; bYotsubashi line to Higobashi, exit 2)
If heights aren't your thing, you'll need a stiff drink once you've peered down over the city from the 40th floor at this ultrasuave hotel bar. Service is impeccable and there's a good range of food and bar snacks to go with well-made cocktails.
8INFORMATION
DANGERS & ANNOYANCES
Osaka has a rough image in Japan, with the highest number of reported crimes per capita of any city in the country – though it remains significantly safer than most cities of comparable size. Still, it's wise to employ the same common sense here that you would back home. Purse snatchings are not uncommon, so be mindful.
INTERNET ACCESS
An increasing number of cafes have wi-fi or internet access, and Osaka has been expanding free wi-fi in public areas around town (details at www.ofw-oer.com/en).
POST
**Osaka Central Post Office** (大阪中央郵便局; MAP; Basement fl, Eki-mae Dai-1 Bldg, 1-3-1 Umeda, Kita-ku; postal services 9am-9pm, ATM 7am-11.30pm Mon-Fri, 8am-11.30pm Sat, 8am-9pm Sun; bYotsubashi line to Nishi-Umeda, dJR Osaka, Sakurabashi exit)
TOURIST INFORMATION
**Osaka Visitors Information Center Umeda** (大阪市ビジターズインフォメーションセンター・梅田; MAP; %06-6345-2189; www.osaka-info.jp; h7am-11pm; dJR Osaka, north central exit) is the main tourist office, with English information, pamphlets and maps. It's on the 1st floor of the central north concourse of JR Osaka Station. There is also a branch on the 1st floor of **Nankai Namba Station** (大阪市ビジターズインフォメーションセンター・なんば; MAP; %06-6631-9100; h9am-8pm; bMidō-suji line to Namba, exit 4, dNankai Namba). The tourist information website (www.osaka-info.jp) is a good resource, too.
Discount Passes
**Enjoy Eco Card** (エンジョイエコカード; weekday/weekend ¥800/600, child ¥300) One-day unlimited travel on subways, city buses and Nankō Port Town line, plus admission discounts. At subway ticket machines, push 'English', insert cash, select 'one-day pass' or 'one-day pass weekend'.
**ICOCA Card** Rechargeable, prepaid transport pass with an IC-chip, which you wave over the reader at ticket gates. Works on most trains, subways and buses in the Kansai area. Purchase it (¥2000, including ¥500 deposit) at any ticket machine. Return the card to any station window to get the deposit and any credit back.
**Osaka Amazing Pass** (大阪周遊パス; www.osp.osaka-info.jp/en/) Foreign visitors to Japan can purchase one-day passes (¥2500) for unlimited travel on city subways, buses and trains, and admission to around 35 sights (including Osaka-jō). Passes are sold at tourist information centres and city subway stations.
**Yokoso Osaka Ticket** (www.howto-osaka.com/en/ticket/ticket/yokoso.html; ¥1500) Includes one-day travel on city subway and Nankō Port Town lines, plus admission discounts. Buy online in advance.
8GETTING AROUND
Trains and subways should get you everywhere you need to go. There are eight subway lines, but the one that short-term visitors will find most useful is the Midō-suji (red) line, running north–south and stopping at Shin-Osaka, Umeda (next to Osaka Station), Shinsaibashi, Namba and Tennōji stations. Single rides cost ¥180 to ¥370 (half-price for children). Fair warning: Osaka's larger stations can be disorienting, particularly Osaka Station. Exits are often confusingly labelled, even for Japanese. The Metro Osaka Subway app (available from the iTunes store) is very handy to have.
# KŌBE
#### Kitano-chō
#### Sights
#### Shopping
#### Eating
#### Drinking
#
Kōbe at a Glance
Perched on a hillside sloping down to the sea, Kōbe (神戸) is one of Japan's most attractive and cosmopolitan cities. It was a maritime gateway from the earliest days of trade with China and home to one of the first foreign settlements after Japan reopened to the world in the mid-19th century. Kōbe is compact and walkable, allowing you to immerse yourself in the city's distinct atmosphere and dining options.
Kōbe port and city views | F11PHOTO/SHUTTERSTOCK © KOBE PORT TOWER ARCHITECT: NIKKEN SEKKEI COMPANY
With a Day in Port
Wander the streets of Kitano-chō, admiring the historic streetscapes. Stop for lunch and sample Kōbe's famous beef. Learn about the sake-making process at Hakutsuru Sake Brewery Museum, and sample the the end result at Sake Yashiro.
Best Places for...
**Kōbe beef** Kōbe Plaisir
**A quick snack** Isuzu Bakery
**A breath of fresh air** Nunobiki Falls
**Strolling the city streets** Kitano-chō
Getting from the Port
There are two main arrival points in Kōbe. Cruise ships generally dock at **Kōbe Port Terminal** , linked to centrally located Sannomiya Station by a frequent and fast monorail service, the **Port Liner** (ポートライナー; www.knt-liner.co.jp). **Naka Pier Cruise Terminal** is for smaller ships; there's usually a free shuttle running to central Kōbe, just five minutes away.
Fast Facts
**Money** There are money changers near Sannomiya Station and at both ports, and ATMs that accept foreign-issued cards at Sannomiya Station, Shin-Kōbe and Harbor Land.
**Tourist information** At Kōbe Port Terminal and Naka Pier.
**Wi-fi** Free wi-fi is available for tourists throughout Kōbe, including at both port terminals; stop by a tourist information centre for access.
TOP EXPERIENCE
# Kitano-chō
Nestled between Mt Rokko and Kōbe city is lovely Kitano-chō. Kōbe's port was opened to foreign trade in the 1860s, and the incoming traders and immigrants settled in what is today Nankin-machi and here in Kitano-chō. The _ijinkan_ (literally 'foreigners' houses') here are among the best-preserved in Japan.
Great For...
hcs
yDon't Miss
Exploring the area's house museums, cafes, shops and streets.
Explore Ashore
From Kōbe Port Terminal, take the Port Liner to Sannomiya Station; Kitano-chō is a short walk northwest of the station.
From Naka Pier, take the shuttle to Motomachi Station, then take a train to Sannomiya Station and head northwest, or Shin-Kōbe Station and head southwest to Kitano-chō.
8Need to Know
北野町; bShin-Kōbe, dJR Shin-Kōbe
Weathercock House | COWARDLION/SHUTTERSTOCK ©
### Historic Homes
For generations of Japanese tourists, the pleasant, hilly neighbourhood of Kitano-chō is Kōbe, thanks to the dozen or so well-preserved homes of (mostly) Western trading families and diplomats who settled here during the Meiji period. These _ijinkan_ – strangely, though naturally, incongruent, as each is built in the architectural style of the owner's home country – are now mostly cafes, restaurants and souvenir shops.
Two of the best-preserved homes, the red-brick **Weathercock House** , built in 1909 for a German trader, and the wooden, jade-green **Moegi House** , built in 1903 for the former US consul, are open as museums ( h9am to 6pm; combined ticket ¥650). Many of the original furnishings are intact – you'll see the lengths that expats a century ago went to in order to maintain their native lifestyles.
### Coffee Break
A big chain wouldn't normally be worth listing, but Starbucks Ijinkan (map Google map; スターバックス異人館; %078-230-6302; 3-1-31 Kitano-chō, Chūō-ku; h8am-10pm; dJR Sannomiya) is different: it's housed in a beautifully preserved former _ijinkan_ , c 1907. Buy a cuppa and ensconce yourself in period antiques and furniture (albeit amid some of the standard Starbucks decor). It can be crowded.
Nunobiki Herb Gardens & Ropeway | GAID KORNSILAPA/SHUTTERSTOCK ©
### View from Above
At the northeastern edge of Kitano-chō, just before Shin-Kōbe Station, is Nunobiki Herb Gardens & Ropeway (布引ハーブ園&ロープウェイ; ropeway 1 way/return ¥950/1500, return after 5pm ¥900; h10am-5pm Mon-Fri, to 8.30pm Sat & Sun 20 Mar-19 Jul & Sep-Nov, 10am-8.30pm daily 20 Jul-31 Aug, to 5pm Dec-19 Mar; bShin-Kōbe, dJR Shin-Kōbe), offering an escape from the city on a 400m-high mountain ridge and sweeping views across town to the bay. During the day (to 5pm), after taking the ropeway up, you can descend on foot to the midway station through the landscaped herb gardens, which include some nicely placed benches and hammocks. From here you can return by ropeway or continue on for about 20 minutes to the Nunobiki Falls (布引の滝, Nunobikinotaki; bShin-Kōbe, dJR Shin-Kōbe) F; follow the road (it's signposted) and keep a lookout for the staircase on your right (not well signposted) that leads to the waterfall path.
You'd never guess that such a beautiful natural sanctuary could sit so close to the city. This revered waterfall in four sections (the longest is 43m tall) has been the subject of art, poetry and worship for centuries – some of the poems are reproduced on stone tablets at the site. It's accessible by a steep 400m path from Shin-Kōbe Station. Take the ground-floor exit, turn left and walk under the station building to the path.
Kōbe
1Sights
1Ikuta-jinjaB2
2Kitano-chōB1
3Nankin-machiB2
4Port of Kōbe Earthquake Memorial ParkB3
7Shopping
5Daimaru Department StoreB2
6Kōbe Harbor LandB3
5Eating
7DaichiB2
8Isuzu BakeryC1
9Kōbe PlaisirB2
10MikamiC1
11ModernarkB2
12Wanto BurgerB2
6Drinking & Nightlife
13Sake YashiroB2
14Starbucks IjinkanB1
1Sights
Hakutsuru Sake Brewery MuseumBrewery
(白鶴造酒資料館; %078-822-8907; www.hakutsuru-sake.com; 4-5-5 Sumiyoshi Minami-machi, Higashi-Nada-ku; h9.30am-4pm; dHanshin main line to Sumiyoshi) F
Hakutsuru is a major sake brewer in Kōbe's Nada-gogō district, a major sake-brewing centre. The self-guided tour through the old wooden brewery (the current, modern brewery is behind it) is a fascinating look at traditional sake-making methods: videos (with English) show real footage from inside the original brewery alongside old equipment. You can sample some sake at the end.
Take a local Hanshin-line train eight stops east from Sannomiya to Sumiyoshi Station (¥190, 15 minutes). Exit the station, walk south towards the elevated highway and cross under it, then take your first left and then a right; the entrance is on the right. Use the blue-and-white crane logo atop the factory as your guide.
Port of Kōbe Earthquake Memorial ParkMonument
(map Google map; 神戸港震災メモリアルパーク; Meriken Park; bKaigan line to Minato Motomachi, dMotomachi) F
At 5.46am on 17 January 1995 the Great Hanshin Earthquake struck this region. It was Japan's strongest since the Great Kantō Quake of 1923 devastated Tokyo. Kōbe bore the brunt of the damage – 6000 killed, over 30,000 injured, toppled expressways and nearly 300,000 lost buildings. This simple, open-air, harbourside museum tells the story through artefacts and a video presentation in English. Most striking is a section of the dock that was left as it was after that devastating day.
Ikuta-jinjaShinto Shrine
(map Google map; 生田神社; %078-321-3851; 1-2-1 Shimo-Yamate-dōri, Chūō-ku; h7am-sunset; dJR Sannomiya) F
Kōbe's signature shrine is said to date from 201, though it's been rebuilt many a time – a symbol of resilience for the city. It's right in the middle of Sannomiya, providing a peaceful retreat from the urban bustle.
Ikuta-jinja | MTAIRA/SHUTTERSTOCK ©
Nankin-machiArea
(map Google map; 南京町; Chinatown; Sakaemachi-dōri, Chūō-ku; bKaigan line to Kyūkyoryūchi-Daimaru-mae, dJR or Hanshin lines to Motomachi)
Kōbe's Chinatown – Nankin comes from Nanjing; _machi_ just means town – dates to the early days of the city opening its port to foreign traders. It was rebuilt after the 1995 earthquake and has all the visual signifiers of Chinatowns the world over: tiered gates at the cardinal entrances (except for the north side, guarded by lions) and lots of restaurants.
It's definitely touristy, but it's fun: most restaurants have stalls out the front selling street food, like _nikuman_ (steamed buns, usually filled with pork; _baozi_ ) and _chimaki_ (sticky rice wrapped in bamboo leaves, also often filled with pork; they're also called _zongzi_ ) for a few hundred yen each.
7Shopping
Kōbe Harbor LandMall
(map Google map; 神戸ハーバーランド; www.harborland.co.jp; Higashi Kawasaki-chō, Chūō-ku; h10am-9pm; c; bKaigan line to Harbor Land, dJR Kōbe line to Kōbe)
This bayside complex has several malls (Umie and Mosaic), with branches of many mainstream shops. Some restaurants here have views over the water and are family friendly. Harbor Land is a short walk from Naka Pier.
Daimaru Department StoreDepartment Store
(map Google map; 大丸; www.daimaru.co.jp/kobe; 40 Akashi-machi, Chūō-ku; h10am-8pm; bKaigan line Kyūkyorūchi-Daimaru-mae)
Large department store at the western edge of Kyū-Kyoryuchi (the former foreigners' settlement).
5Eating
Isuzu BakeryBakery¥
(map Google map; イスズベーカリー; %078-222-4180; www.isuzu-bakery.jp; 2-1-4 Nunobiki-chō, Chūō-ku; bread & pastries ¥120-560; h8am-8pm; dJR Sannomiya)
The most famous of Kōbe's bakeries, Isuzu is particularly famous for its crisp, fluffy 'curry pan' (カレーパン; ¥160), a deep-fried doughnut stuffed with beef curry. There's a huge variety of sweet and savoury options (and, with no English signs, you never quite know which you're going to get). Grab a tray and tongs and take your selections to the cashier.
MikamiShokudo, International¥
(map Google map; 味加味; %078-242-5200; 2-5-9 Kanō-chō, Chūō-ku; mains ¥480-1800, set meals from around ¥850; h11.30am-3pm & 5-11pm Wed-Mon; dJR Sannomiya, dJR Shin-Kōbe)
Mikami is a beacon of good food in the otherwise forlorn zone between Shin-Kōbe Station and Sannomiya. It does excellent _teishoku_ (set meals); the _katsu_ (crumbed and fried) dishes are especially good.
It's located on the street one block west of the main road connecting Shin-Kōbe Station and Sannomiya, about halfway between the two; look for an ivy-covered building.
ModernarkCafe¥
(map Google map; モダナーク; %078-391-3060; <http://modernark-cafe.chronicle.co.jp>; 3-11-15 Kitanagasa-dōri, Chūō-ku; mains ¥950-1150; h11.30am-10pm; dMotomachi)
This adorably funky cafe with a glassed-in verandah is Kōbe's go-to spot for organic vegetarian and vegan meals and cakes, served with herbal tea or homemade sangria. Look for the thicket of potted trees out the front.
Famous Kōbe Beef
Kōbe is known worldwide for its top-class beef, considered by many to be the best in the world. Highly marbled, it's naturally tender and rich in flavour. It's also held to very strict regulations. Splurge on the cut rather than the size; the fat content makes Kōbe beef very filling.
Kōbe Plaisir (map Google map; 神戸プレジール; %078-571-0141; <https://kobe-plaisir.jp>; 2-11-5 Shimo-Yamate-dōri, Chūō-ku; lunch/dinner Kōbe-beef set menus from ¥7500/11,000; h11.30am-3pm & 5-10.30pm; bSannomiya, dJR Sannomiya) A great place to try Kōbe beef prepared in a variety of styles.
Wanto Burger (map Google map; ワントバーガー; %078-392-5177; www.wantoburger.com; 3-10-6 Shimo-Yamate-dōri, Chūō-ku; burgers ¥1080-3800; hnoon-3pm & 5-10pm Tue-Fri, noon-10pm Sat, to 5pm Sun; dJR Sannomiya) Serves towering, teetering burgers made with Kōbe beef.
Daichi (map Google map; 大地; %078-333-6688; www.koubegyuu.com/shop/daichi; 1-1-3 Motomachi-dōri, Chūō-ku; steak meals from ¥2500; h11am-9pm; bKaigan line to Kyūkyorūchi-Daimaru-mae, dMotomachi) Kōbe beef teppanyaki at entry-level prices.
HUNGRYWORKS/SHUTTERSTOCK ©
6Drinking
Sake YashiroBar
(map Google map; さけやしろ; %078-334-7339; 4-6-15 Ikuta-chō, Chūō-ku; h4-11.30pm; dJR Sannomiya)
This standing bar has a daunting selection of 90 kinds of sake, including about 50 from local brewers, on its (Japanese-only) menu. Anticipating your needs, staff have made a cheat sheet in English of their top five local picks, all priced ¥880 by the glass. Look for the denim door curtains. A great option if your cruise schedule allows it.
8INFORMATION
**Kōbe Information Centre** (神戸市総合インフォメーションセンター; %078-322-0220; www.feel-kobe.jp; JR Sannomiya; h9am-7pm; dSannomiya) On the ground floor outside of JR Sannomiya Station's east gate. There's a smaller information counter on the 2nd floor of Shin-Kōbe Station, outside the main _shinkansen_ gate. Both have good English city maps.
8GETTING AROUND
Kōbe is small enough to get around on foot.
BUS
**City-loop buses** (per ride/day pass ¥260/660, children half-price) stop at most of the city's sightseeing spots and its main stations several times an hour (10am to 6pm); look for the retro-style green buses. Purchase tickets on board or at the information centre.
TRAIN
The Seishin-Yamate subway line connects Shin-Kōbe and Sannomiya Stations (¥210, two minutes).
The Kaigan subway line runs from just south of Sannomiya Station to Minato Motomachi and Harbor Land Stations.
Connections to Surrounding Cities
Kōbe is well connected to surrounding cities. The JR Kōbe line runs fast _shinkaisoku_ (special rapid trains) from Sannomiya Station to **Himeji** (¥970, 40 minutes), **Kyoto** (¥1080, 50 minutes) and **Osaka** (¥410, 20 minutes). Shin-Kōbe Station, north of Sannomiya, is on the Tōkaidō/San-yō and Kyūshū _shinkansen_ lines. Destinations include **Himeji** (¥2700, 25 minutes), **Hiroshima** (¥9490, 70 minutes), **Kyoto** (¥2810, 30 minutes) and **Shin-Osaka** (¥1500, 15 minutes).
# KŌCHI
#### Kōchi-jō
#### Godaisan
#### Sights
#### Eating
#### Drinking
#
Kōchi at a Glance
Kōchi (高知) is a smart, compact city with a deserved reputation for enjoying a good time. The castle here is largely undamaged and remains a fine example of Japanese architecture. Also claimed by Kōchi is a samurai of great national significance – during the Meiji Restoration, Sakamoto Ryōma was instrumental in bringing down the feudal government. The central part of the city is 12km north and inland from the sea and the liveliest part of town is where the tramlines cross near Harimaya-bashi, a tiny red replica of a bridge made famous by song and film in Japan. The main Obiyamachi shopping arcade runs perpendicular to Harimayabashi-dōri.
Views from Godaisan | MITUMAL/GETTY IMAGES ©
With a Day in Port
Eat your way along Obiyamachi Arcade to Kōchi-jō. Visit Chikurin-ji, one of the famed 88 Sacred Temples of Shikoku, then learn about the art of making _washi_ (Japanese paper) at Ino Japanese Paper Museum.
Best Places for...
**History** Kōchi-jo
**Cheap eats** Hirome Ichiba
**A quiet drink** Kinako Cafe
**Spectacular scenery** Iya Valley
Getting from the Port
Cruise operators generally put on a free shuttle bus from Kōchi port into town, stopping at Kōchi bus terminal. Otherwise a taxi is a good option. There's no public transport between the port and downtown.
Fast Facts
**Money** International ATMs are available at the post office next to JR Kōchi Station. Currency exchange available at port.
Tourist information Temporary quayside information booths greet most arrivals. See for other tourist information offices.
**Wi-fi** Log on to Kōchi Free Wi-fi (www.visitkochijapan.com/travelers_kit/wifi).
TOP EXPERIENCE
# Kōchi-jō
A visit to Kōchi-jo offers plenty of variety: gardens, views, a museum, a walk through Kōchi's eating and entertainment district and, of course, a well-preserved historic castle.
Great For...
Acv
yDon't Miss
The views: the main castle keep offers sweeping views across the city, and this is the only castle in Japan where both the main keep and gate can be viewed at once, making for a great photo op.
Explore Ashore
Take a shuttle or taxi from the port to the Kōchi bus terminal, adjacent to JR Kōchi train station. From here, it's a half-hour walk to the castle. Alternatively, take a tram (about 10 minutes), changing lines at Harimaya-bashi (はりまや橋) junction.
8Need to Know
高知城; 1-2-1 Marunouchi; ¥420; h9am-5pm
MARLON TROTTMANN/SHUTTERSTOCK ©
### History
Kōchi-jō is one of just a dozen castles in Japan to have survived with its original _tenshu-kaku_ (keep) intact. The castle was originally built during the first decade of the 17th century by Yamanouchi Katsutoyo, who was appointed _daimyō_ (domain lord) by Tokugawa Ieyasu after he fought on the victorious Tokugawa side in the Battle of Sekigahara in 1600. A major fire destroyed much of the original structure in 1727; the castle was largely rebuilt between 1748 and 1753.
Kōchi-jō was the product of an age of peace – it never came under attack and for the remainder of the Tokugawa period it was more like a stately home than a military fortress. The fee is for entry to the castle itself; it's free to walk in the surrounding grounds. The approach to the castle is a steep climb, with plenty of stairs, and can be hot in summer.
### Kōchi Castle Museum of History
This museum (高知城歴史博物館; %088-871-1600; www.kochi-johaku.jp; 2-7-5 Ōtesuji; ¥500; h9am-6pm Mon-Sat, from 8am Sun) celebrating the history of Kōchi castle is an architectural achievement in its own right. Entry is free to the museum shop (1st floor) and to the 2nd floor cafe and terrace – both with marvellous views of the castle and its grounds. The entry fee gives you access to the 3rd floor, where you'll find interesting exhibitions on the history of the castle and the city of Kōchi.
### Obiyamachi Arcade
Kōchi's main eating and entertainment district is in the area around the Obiyamachi Arcade and the Harimaya-bashi junction where the tramlines meet. Walking through the arcade up to the castle (about 2km) gives you a good taste of what Kōchi has to offer, and there's plenty to see along the way. Hirome Ichiba (map Google map; ひろめ市場; %088-822-5287; www.hirome.co.jp; 2-3-1 Obiyamachi; dishes from ¥300; h8am-11pm, from 7am Sun), a full block of mayhem at the end of the main arcade, just before the castle, is the hub of Kōchi's cheap-eats scene. On weekends, it positively heaves with young people. Dozens of mini-restaurants and bars specialising in everything from _gomoku rāmen_ (seafood noodles) to _tako-yaki_ (octopus balls) surround communal tables.
Obiyamachi Arcade | WINHORSE/GETTY IMAGES ©
TOP EXPERIENCE
# Godaisan
Several kilometres east of the town centre, and north of the port, is the mountain of Godaisan (五台山), where you can enjoy excellent views of the city from a lookout point (展望台). Near the top of the hill is Chikurin-ji, one of the famous 88 temples of Shikoku. By the entrance gates is the Kōchi Prefectural Makino Botanical Garden, a network of gardens and parkland.
Great For...
fha
yDon't Miss
Tropical plants are on display year-round in the botanic gardens' greenhouse.
Explore Ashore
Take a shuttle into town to Kōchi bus station. From here, take a My-Yū tourist bus to Godaisan. The gardens lie between the port and the city centre, so a taxi is a more direct option.
8Need to Know
There's a restaurant and cafe in the gardens; otherwise grab a bento box on the way in and enjoy a picnic in the beautiful gardens.
Chikurin-ji | JOHN STEELE/ALAMY STOCK PHOTO ©
### Chikurin-ji
The extensive grounds of Chikurin-ji (竹林寺; %088-882-3085; www.chikurinji.com; 3577 Godaisan) F feature a five-storey pagoda and thousands of statues of the Bodhisattva Jizō, guardian deity of children and travellers. The temple's Treasure House (¥400; h8am to 5pm) hosts an impressive collection of Buddhist sculpture from the Heian and Kamakura periods; the same ticket gets you in to see the temple's lovely Kamakura-period garden opposite.
Five-storey pagoda, Chikurin-ji | THANYARAT07/GETTY IMAGES ©
### The 88 Sacred Temples of Shikoku
Shikoku (四国), the island upon which Kōchi sits, is home to the 88 Sacred Temples of Shikoku, Japan's most famous pilgrimage.
The _henro_ (pilgrim on the 88 Temple Circuit) is one of the most distinctive sights of any trip to Shikoku – solitary figures in white, trudging purposefully through heat haze and downpour alike on their way from temple to temple.
Although the backgrounds and motives of the _henro_ may differ widely, they all follow in the legendary footsteps of Kōbō Daishi, the monk who attained enlightenment on Shikoku, established Shingon Buddhism in Japan and made significant contributions to Japanese culture. The idea behind making the 1400km, 88 Temple Circuit is to do so accompanied by the spirit of Kōbō Daishi himself – hence the inscription on pilgrims' backpacks and other paraphernalia: 同行二人 _(dōgyō ninin)_ , meaning 'two people on the same journey'.
A pilgrim's routine at each temple is mostly the same: a bang on the bell and a chant of the Heart Sutra at the Daishi-dō (one of the two main buildings in each temple compound), before filing off to the _nōkyō-jo_ (desk), where the pilgrims' book is inscribed with beautiful characters detailing the name of the temple and the date of the pilgrimage.
### Kōchi Prefectural Makino Botanical Garden
Next to the Chikurin-ji entrance gates on the south side of Godaisan is the impressive Kōchi Prefectural Makino Botanical Garden (高知県立牧野植物園; %088-882-2601; www.makino.or.jp; 4200-6 Godaisan; ¥720; h9am-5pm), which features more than 3000 different plant species.
Kōchi
1Sights
1Harimaya-bashiD3
2Kōchi Castle Museum of HistoryB3
3Kōchi-jōA3
4Sunday MarketB2
5Eating
5HabotanC3
6HakobeD3
7Hirome IchibaB3
8Kinako CafeC3
9Tosa IchibaD3
6Drinking & Nightlife
10AmontilladoC3
11Tosa-shu BaruC3
1Sights
Ino Japanese Paper MuseumMuseum
(いの町紙の博物館; %088-893-0886; www.kamihaku.com/en; 110-1 Saiwai-chō, Ino-chō; ¥500; h9am-5pm Tue-Sun)
Discover the history and development of _washi_ (Japanese paper) at Ino, about 10km west of downtown Kōchi. There are demonstrations of _nagashizuki_ papermaking techniques and on the first Sunday of every month, there's a papermaking class (¥400; in Japanese only). Check out the excellent English website for details. The museum is a 10-minute walk from both the Ino JR and tram stations.
Harimaya-bashiLandmark
(map Google map; 播磨屋橋)
This tiny reconstructed bridge from the Edo period is renowned throughout Japan thanks to a romantic song in which it features. For older Japanese people, this is _the_ major Kōchi landmark and obligatory photos are taken, though many are surprised by how small it is. The tram station and the city's busiest intersection are named after it.
Katsura-hamaBeach
(桂浜)
Katsura-hama is a popular beach 12km south of central Kōchi at the point where Kōchi's harbour empties out into the bay. Strong currents prohibit swimming, but it's a lovely spot to stroll, with a small **shrine** perched on an oceanside promontory. Just before the beach itself is Sakamoto Ryōma Memorial Museum (坂本龍馬記念館; %088-841-0001; www.ryoma-kinenkan.jp; 830 Urado-shiroyama; ¥700; h9am-5pm), with exhibits dedicated to the life of a local hero who was instrumental in bringing about the Meiji Restoration in the 1860s.
Public buses run to Katsura-hama from Kōchi Station (¥690, 35 minutes, six daily) and Harimaya-bashi (¥620, 25 minutes, frequent). The My-Yū bus runs as far as Katsura-hama before heading back to Kōchi.
5Eating
With its long Pacific coastline, Kōchi Prefecture is known for its seafood, particularly _katsuo-tataki,_ seared bonito fish that is thinly sliced and eaten with grated ginger. _Sawachi-ryōri_ is a huge plate (a _sawachi_ ) of seafood, with various varieties of both sashimi and sushi.
Central Obiyamachi Arcade offers a plethora of tasty dining options.
Kinako CafeCafe¥
(map Google map; きなこCafe; %088-875-2255; www.hitosara.com/0006109127; 1-1-7 Obiyamachi; meals from ¥800; h11am-3pm & 5-11pm Tue-Sat, lunch only Sun)
This tiny, lovingly run place serves tasty set meals at lunchtime, then morphs into a jazz and wine bar serving top-quality _otsumami_ (snacks) in the evenings. A great little place to relax after time on your feet in the Obiyamachi shopping arcade.
HakobeOkonomiyaki¥
(map Google map; はこべ; %088-823-0084; 1-2-5 Obiyamachi; dishes ¥650-1200; h11am-midnight)
This is one of the few remaining cook-it-yourself _okonomiyaki_ (pancake) joints in Kōchi serving cheap and cheerful Japanese pancakes. The 'mix' of _ika_ (squid), _ebi_ (shrimp) and _tori_ (chicken) is heavenly. Other alternatives include _buta_ (pork) and _yasai_ (vegetables). They bring it out and you cook it on the hotplate. It's slap bang in the heart of the arcade.
Sunday Street Market
Our favourite street market (日曜市; Ōte-suji; h5am-6pm Sun Apr-Sep, 5.30am-5pm Sun Oct-Mar) in Shikoku is 300 years old and takes place every Sunday along 1.3km of Ōte-suji, the main road leading to the castle. Around 430 colourful stalls sell fresh produce, tonics and tinctures, knives, flowers, garden stones, wooden antiques and everything else imaginable.
Antiques for sale | AKIYOKO/SHUTTERSTOCK ©
HabotanIzakaya¥
(map Google map; 葉牡丹; %088-872-1330; www.habotan.jp; 2-21 Sakai-machi; dishes ¥150-1100; h11am-11pm)
Red lanterns mark out this locals' _izakaya_ opposite Chūō-kōen that opens at the shockingly early hour of 11am. The food is under glass on the counter, so you can point at what you'd like to order. _Sashimi moriawase_ (a selection of sashimi) is ¥1050. Local booze includes Tosa-tsuru sake and Dabada Hiburi, a _shōchū_ (distilled grain liquor) made from chestnuts.
Tosa IchibaJapanese¥¥
(map Google map; 土佐市場; %088-872-0039; 1-3-11 Harimayachō; set meals from ¥1100; h11am-10.30pm)
Near the start of Obiyamachi Arcade, this is a good place to try local set meals, especially if you're struggling with Japanese menus. Most of the menu is displayed either outside or in the windows in plastic-model form. Pick what looks good and point it out to the friendly staff. There are lots of seafood options.
Iya Valley
The spectacular Iya Valley (祖谷渓) is a special place: winding your way around narrow cliff-hanging roads as the icy water of the Iya-gawa shoots along the ancient valley floor is a blissful travel experience. Beyond the remarkable scenery, highlights of the valley include the vine-covered bridges of Oku Iya Ni-jū Kazura-bashi (奥祖谷二重かずら橋; ¥550; h7am-5pm), and the surreal Nagoro (名頃かかしの里; Nagoro Scarecrow Village), populated by life-size scarecrow-type dolls.
You will need to be organised in order to set off and return to Kōchi port in a single day. To get here, take a train from Kōchi to JR Ōboke Station (¥3180, 50 minutes). From here infrequent buses head off around the valley, and it is also possible to hire a car (be aware that in this mountainous area, roads can be narrow).
With limited time, however, you'll make the most of a day trip with a tour. The extremely efficient Ōboke Station Tourist Information Office (大歩危駅観光内所; %0883-76-0877; www.miyoshi-tourism.jp/en; h8.30am-3.30pm Mon, Tue, Thu & Fri, to 5.30pm Sat & Sun) can help with organising your trip over the hill and into the Iya Valley. The English-speaking staff have tons of brochures and maps on hand.
Oku Iya Ni-jū Kazura-bashi | WORLDROADTRIP/SHUTTERSTOCK ©
6Drinking
Kōchi is a lively town. Head into the streets just north of Obiyamachi Arcade to find more than a few options for a drink. If your cruise schedule allows, check out the following places.
Tosa-shu BaruBar
(map Google map; 土佐酒バル; %088-823-2216; 1-9-5 Ōte-suji; h6pm-midnight Tue-Sun)
Without doubt, this nonsmoking bar with an extremely convivial atmosphere is the place to go to try Kōchi-made sake. Owner Kōji is passionate about sake and has offerings from all 18 breweries in Kōchi, three daily-changing _nomi-kurabe_ (tasting sets) and serves superb small dishes featuring local produce. He is a fountain of sake knowledge and plays great jazz.
AmontilladoPub
(map Google map; アモンティラード; %088-875-0599; www.irishpub-amontillado.owst.jp; 1-5-2 Obiyamachi; h5pm-1am)
If you feel like a pint of Guinness (¥880), pop into this Irish pub right on Obiyamachi Arcade. There's always plenty going on as it's popular with locals.
8INFORMATION
**Kōchi International Association** (高知県国際交流協会; %088-875-0022; www.kochi-kia.or.jp; 2nd fl, 4-1-37 Honmachi; h8.30am-5.15pm Mon-Sat) Friendly English-speaking staff, free internet access, a library and English newspapers and magazines.
**Tourist Information Office** (高知観光案内所; %088-826-3337; www.visitkochijapan.com; h8.30am-5pm, accommodation info to 7.30pm) The helpful tourist-information pavilion out the front of JR Kōchi Station provides English-language maps, Kōchi mini-guidebooks and more. There's always an enthusiastic English speaker on hand.
8GETTING AROUND
BICYCLE
Free rental bicycles can be picked up from the Tourist Information Office at the front of JR Kōchi Station. They're available from 8.30am to 5pm (bring ID).
BUS
The **My-Yū bus** (MY遊バス; www.visitkochijapan.com/about/Kochi_MYyou_EN.pdf; 1-/2-day pass ¥1000/1600) runs from **Kōchi bus terminal** (高知駅バスターミナル) to Godaisan to Katsura-hama and back. Purchase the pass at the Tourist Information Office in front of Kōchi Station; show your foreign passport and you'll get the pass for half price.
Public buses to Katsura-hama (¥270, 35 minutes, hourly) leave from the bus terminal.
TRAM
Kōchi's colourful tram service (¥200 per trip) has been running since 1904. There are two lines: the north–south line from the station intersects with the east–west tram route at the Harimaya-bashi junction. Pay when you get off and ask for a _norikae-ken_ (transfer ticket) if you have to change lines.
Tram at Harimayabashi Station | PETER ELVIN/ALAMY STOCK PHOTO ©
# HIROSHIMA
#### Peace Memorial Park
#### Sights & Activities
#### Shopping
#### Eating
#
Hiroshima at a Glance
To most people, Hiroshima (広島) means one thing: the city's name will forever evoke 6 August 1945, when Hiroshima was targeted in the world's first atomic-bomb attack. Peace Memorial Park is a constant reminder of that day, attracting visitors from all over the world with its powerful message of peace. Present-day Hiroshima, meanwhile, is far from depressing. With its wide, tree-lined boulevards, laid-back friendliness and vibrant eating and drinking scene, the city is an attractive destination in its own right. It's also the jumping-off point for visits to Miyajima, an island in Hiroshima Bay with a captivating seaside shrine.
Hiroshima views | SEAN PAVONE/SHUTTERSTOCK ©
With a Day in Port
Contemplate the legacy of WWII at the Peace Memorial Park and Hiroshima Peace Memorial Museum. Stop for a snack at Okonomi-mura, then browse for souvenirs at Tokyu Hands and Mitsukoshi department stores or head out to photo-friendly Miyajima.
Best Places for...
**Comic book fans** Hiroshima City Manga Library
**Sampling okonomiyaki** Okonomi-mura
**Picking up a new paperback** Global Lounge
Getting from the Port
**Ujina Wharf** Trams (30 minutes, ¥180) run from nearby Hiroshima Port Station to downtown (tram line 1 or 3) and the Peace Memorial Park (tram 3). Some cruise companies offer free shuttles to the park.
**Itsukaichi Wharf** It's a couple of kilometres to the Hiroden-Itsukaichi tram stop. Cruise companies often run a shuttle to the stop; otherwise, taxis are a reliable and inexpensive alternative. From here, tram line 2 runs to the Peace Memorial Park and downtown (about 40 minutes, ¥180).
Fast Facts
**Money** ATMs accepting foreign-issued cards can be found at the main Hiroshima train station, and at Naka post office (6-36 Motomachi), northeast of the Atomic Bomb Dome. Currency exchange is available at both ports.
**Tourist information** Enthusiastic, English-speaking staff offer tourist information at the ports.
**Wi-fi** Free wi-fi is available at the Peace Memorial Park, the main train station and both cruise ship terminals.
TOP EXPERIENCE
# Peace Memorial Park
Hugged by rivers on both sides, Peace Memorial Park is a large, leafy space criss-crossed by walkways and dotted with memorials to the victims of the 1945 atomic bomb.
Great For...
vgh
8Need to Know
平和記念公園; Heiwa-kinen-kōen; jGenbaku-dōmu-mae
Explore Ashore
Some cruise companies offer a shuttle to the park, and taxis are readily available. Tram 3 (30 minutes, ¥180) runs here from the Ujina Wharf area. From Itsukaichi Wharf, take a taxi, shuttle bus or walk the couple of kilometres to Hiroden-Itsukaichi tram stop. From here, tram line 2 runs to the park (about 40 minutes, ¥180).
5Take a Break
Choose a park bench along the riverside opposite the Atomic Bomb Dome.
Cenotaph | WORLDSTOCK/SHUTTERSTOCK © ARCHITECT: KENZŌ TANGE
### The Bombing of Hiroshima
At 8.15am on 6 August 1945, the US B-29 bomber _Enola Gay_ released the 'Little Boy' atomic bomb over Hiroshima. The 2000°C (3630°F) blast obliterated 90% of the city and instantly killed 80,000 people. The bomb exploded over the town centre, filled with wooden homes and shops. This created intense firestorms that raced through the city for three days and destroyed 92% of buildings, fuelled by broken gas pipes and electrical lines. Toxic black rain fell 30 minutes after the blast, carrying 200 different types of radioactive isotopes, contaminating the thirsty wounded who drank it.
Around 350,000 people were present that day. In the following months, 130,000 died of radiation exposure and other secondary effects, including intensive burns. Most casualties were civilians, including firefighters and 90% of the city's doctors who came to help; 20,000 forced Korean labourers; and 6000 junior-high-school students who had been clearing fire breaks in anticipation of a regular attack.
The Japanese government says around 187,000 atomic-bomb survivors were still alive in 2015, many living through the mental trauma, cancers and other effects of radiation. No residual radiation remains today.
### Atomic Bomb Dome
The starkest reminder of the destruction visited upon Hiroshima in WWII is the Atomic Bomb Dome (map Google map; 原爆ドーム, Genbaku Dome; 1-10 Otemachi; h24hr; jGenbaku-dōmu-mae) F. Built by a Czech architect in 1915, it was the Industrial Promotion Hall until the bomb exploded almost directly above it. Everyone inside was killed, but the building was one of very few left standing near the epicentre. A decision was taken after the war to preserve the shell as a memorial.
### Hiroshima Peace Memorial Museum
The main building, Hiroshima Peace Memorial Museum (map Google map; 広島平和記念資料館; www.pcf.city.hiroshima.jp; 1-2 Nakajima-chō, Naka-ku; adult/child ¥200/free; h8.30am-7pm Aug, to 6pm Mar-Jul & Sep-Nov, to 5pm Dec-Feb; jGenbaku-dōmu-mae or Chūden-mae), houses a collection of items salvaged from the bomb's aftermath. The displays are confronting and personal – ragged clothes, a child's melted lunch box, a watch stopped at 8.15am – and there are some grim photographs. The east building presents a history of Hiroshima and of the development and destructive power of nuclear weapons.
yDon't Miss
The pond's Flame of Peace map Google map (平和の灯) will only be extinguished when every nuclear weapon has been destroyed.
### Memorial Hall for the Atomic Bomb Victims
A softly lit internal walkway leads down into this deeply moving, memorial space (国立広島原爆死没者追悼平和祈念館; www.hiro-tsuitokinenkan.go.jp; 1-6 Nakajima-chō, Naka-ku; h8.30am-7pm Aug, to 6pm Mar-Jul & Sep-Nov, to 5pm Dec-Feb; jGenbaku-dōmu-mae or Hon-dōri) F
whose walls show a panorama of Hiroshima at the time of the bomb. A fountain at the centre represents the moment the bomb was dropped, while the water offers relief to the victims. An adjoining room shows the names and photographs of those who perished.
### Children's Peace Monument
The Children's Peace Monument (map Google map; 原爆の子の像) was inspired by Sasaki Sadako, just two years old at the time the bomb was dropped in 1945. At age 11 she developed leukaemia, and decided to fold 1000 paper cranes. In Japan, the crane is a symbol of longevity and happiness, and Sadako believed if she folded 1000 she would recover. Sadly she died before reaching her goal, but her classmates folded the rest. Surrounding the monument are strings of thousands of colourful paper cranes sent by school children from around the country and the world.
Children's Peace Monument | DFLC PRINTS/SHUTTERSTOCK © DESIGNERS: KAZUO KIKUCHI & KIYOSHI IKEBE
### Cenotaph
The curved concrete cenotaph (map Google map; 原爆死没者慰霊碑) houses a list of the names of all the known victims of the atomic bomb. It stands at one end of the pond at the centre of the park, framing the Flame of Peace.
Hiroshima
1Sights
1Atomic Bomb DomeA2
2CenotaphA2
3Children's Peace MonumentA2
4Flame of PeaceA2
5Hiroshima City Manga LibraryD3
6Hiroshima Peace Memorial MuseumA2
7Hiroshima-jōB1
8Memorial Hall for the Atomic Bomb VictimsA2
9Peace Memorial ParkA2
2Activities, Courses & Tours
10Hiroshima Sightseeing Loop BusD1
7Shopping
11Global LoungeB2
12MitsukoshiB2
13Tokyu HandsB2
5Eating
14Okonomi-muraB3
15TōshōD3
1Sights & Activities
Hiroshima City Manga LibraryLibrary
(map Google map; 広島市まんが図書館; %082-261-0330; www.library.city.hiroshima.jp/manga; 1-4 Hijiyama-kōen; h10am-5pm Tue-Sun; jHijiyama-shita)
An obvious pit stop for manga (Japanese comics) enthusiasts, this library has a small section of foreign-language manga and a collection of vintage and rare manga. Grab the English-language pamphlet and head up to the 2nd floor.
Hiroshima-jōCastle
(map Google map; 広島城, Hiroshima Castle; www.rijo-castle.jp; 21-1 Moto-machi; tower ¥370; h9am-6pm Mar-Nov, to 5pm Dec-Feb; jKamiya-chō)
Also known as Carp Castle (鯉城; Rijō), Hiroshima-jō was originally constructed in 1589, but much of it was dismantled following the Meiji Restoration. What remained was totally destroyed by the bomb and rebuilt in 1958. In the north end there's a small five-level museum with historical items, but most visitors go for the tower with views over the impressive moat. The surrounding park is a pleasant (and free) place for a stroll. Enter from the east or south.
Mazda MuseumMuseum
(マツダミュージアム; %082-252-5050; www.mazda.com/about/museum; hby reservation Mon-Fri; dMukainada) F
Mazda is popular for the chance to see the impressive 7km assembly line. English-language tours (90 minutes) are available at 10am weekdays, but it's best to check the website or with the tourist office for the current times. Reservations are required and can be made online or by phone.
The museum is a short walk from JR Mukainada (向洋) Station, two stops from Hiroshima on the San-yō line.
Hiroshima Sightseeing Loop BusBus
(map Google map; www.chugoku-jrbus.co.jp; single/day pass ¥200/400)
The _meipurū-pu_ (loop bus) has two overlapping routes – orange and green – taking in the main sights and museums of the city, including the Peace Memorial Park and Atomic Bomb Dome. Both routes begin and end on the _shinkansen_ entrance (north) side of Hiroshima Station, running from about 9am to 6pm (the green route runs later during summer).
7Shopping
Browse the busy shop-filled Hon-dōri covered arcade for clothes and beauty products. Namiki-dōri is another shopping street, with a range of fashionable boutiques. Hiroshima also has branches of the big-name department stores, such as Tokyu Hands (map Google map; 東急ハンズ広島店; <http://hiroshima.tokyu-hands.co.jp>; 16-10 Hatchō-bori; h10am-8pm; jTate-machi), packed with homewares, must-have gadgets, and gifts; and classy Mitsukoshi (map Google map; 広島三越; <http://mitsukoshi.mistore.jp/store/hiroshima>; 5-1 Ebisu-chō; h10.30am-7.30pm; jEbisu-chō), with its designer labels and small basement-floor gourmet food hall and supermarket.
Hiroshima Reading
'Hiroshima' (1946) by John Hersey – the article by the Pulitzer Prize–winning writer (available at www.newyorker.com).
_Hiroshima: Three Witnesses_ (1990); ed Richard H Minear – translation of first-hand accounts of three authors.
_Black Rain_ (1965) by Ibuse Masuji – a novel depicting the lives of those who survived.
_Sadako and the Thousand Paper Cranes_ (1977) by Eleanor Coerr – aimed at younger readers, based on the true story of Sasaki Sadako.
Global LoungeBooks
(map Google map; グローバル・ラウンジ; %082-244-8145; www.hiroshima-no1.com/lounge.html; 2nd fl, Kensei Bldg, 1-5-17 Kamiya-chō; h11.30am-9pm Mon-Thu, to 11pm Fri & Sat; jKamiya-chō-higashi)
Global Lounge (aka Outsider) has a big selection of secondhand English-language books (mostly paperbacks). You can grab a coffee and use the internet (¥200 per 15 minutes) while you're here.
5Eating
Hiroshima has an excellent range of Japanese and international eating options for all budgets, especially west of Peace Memorial Park and south of the Hon-dōri covered arcade. Many restaurants offer good-value set-lunch menus, and mall basements are budget-friendly. Hiroshima is famous for oysters (often available right on the dock) and _Hiroshima-yaki_ (noodle- and meat-layered _okonomiyaki_ ; savoury pancakes).
Day Trip to Miyajima
The small island of Miyajima (宮島) is home to some good hikes, temples and a much-photographed _torii_ (shrine gate) that seems to float on the water at high tide. Unfortunately, the _torii_ is closed for repairs for two to three years from June 2019, but Itsukushima-jinja (厳島神社; 1-1 Miyajima-chō; ¥300; h6.30am-5.30pm Jan-Nov, to 5pm Dec), which traces its origins back as far as the late 6th century, is open throughout. The shrine's unique pier-like construction is a result of the island's sacred status: commoners were not allowed to set foot on the island and had to approach by boat through the _torii_.
Beyond the shrine, sacred Misen is Miyajima's highest mountain (530m), and the island's finest walk. You can avoid most of the uphill climb by taking the two-stage ropeway (弥山; www.miyajima-ropeway.info; ropeway one way/return adult ¥1000/1800, child ¥500/900; h9am-5pm) with its giddying sea views, which leaves you with a 30-minute walk to the top, where there is an excellent observatory. The cheeky deer will eat your map right out of your pocket if you're not careful.
There are a few ferry options to Miyajima. The mainland ferry terminal is a short walk from Hiroden-miyajima-guchi tram stop, about 20 minutes from Itsukaichi station on tram line 2. Setonaikai Kisen operates high-speed ferries direct to Miyajima from Ujina Wharf. The walk from your cruise berth to the ferry pier can be up to a couple of kilometres – you may prefer a taxi. A handy Aqua Net ferry runs directly from the Peace Memorial Park.
Itsukushima-jinja | ITZAVU/SHUTTERSTOCK ©
Okonomi-muraOkonomiyaki¥
(map Google map; お好み村; www.okonomimura.jp; 2nd-4th fl, 5-13 Shintenchi; dishes ¥800-1300; h11am-2am; jEbisu-chō)
This Hiroshima institution is a touristy but fun place to get acquainted with _okonomiyaki_ and chat with the cooks over a hot griddle. There are 25 stalls spread over three floors, each serving up hearty variations of the local speciality. Pick a floor and find an empty stool at whichever counter takes your fancy. Look for the entrance stairs off Chūō-dōri, on the opposite side of the square to the white Parco shopping centre.
Chefs at Okonomi-mura | LUCAS VALLECILLOS/ALAMY STOCK PHOTO ©
TōshōTofu¥¥
(map Google map; 豆匠; %082-506-1028; www.toufu-tosho.jp; 6-24 Hijiyama-chō; set meals ¥2000-5000; h11am-3pm & 5-10pm Mon-Sat, to 9pm Sun; v; jDanbara-1-chōme)
In a traditional wooden building overlooking a large garden with a pond and waterfall, Tōshō specialises in homemade tofu, served in a variety of tasty and beautifully presented forms by kimono-clad staff. Even the sweets are tofu based. There is a range of set courses, with some pictures and basic English on the menu.
8INFORMATION
In addition to the tourist offices, check out Hiroshima Navigator (www.hiroshimacvb.jp) for tourism and practical information, as well as downloadable audio guides to the sights.
**Hiroshima Rest House** (広島市平和記念公園レストハウス; %082-247-6738; www.mk-kousan.co.jp/rest-house; 1-1 Nakajima-machi; h8.30am-7pm Aug, to 6pm Mar-Jul & Sep-Nov, to 5pm Dec-Feb; jGenbaku-dōmu-mae) In Peace Memorial Park next to Motoyasu-bashi bridge; has comprehensive information, English-speaking staff and a small shop selling souvenirs.
**Tourist Information Office** (観光案内所; %082-261-1877; h9am-5.30pm; W) Inside Hiroshima Station near the south exit, with English-speaking staff. There is another branch at the **north (shinkansen) exit** ( %082-263-6822; h9am-5.30pm).
8GETTING AROUND
Most sights in Hiroshima are accessible either on foot or with a short tram (streetcar) ride.
Hiroshima's trams (www.hiroden.co.jp) will get you almost anywhere you want to go for a flat fare of ¥180. You pay by dropping the fare into the machine by the driver as you get off the tram. If you have to change trams to get to your destination, you should ask for a _norikae-ken_ (transfer ticket).
# NAGASAKI
#### Nagasaki Atomic Bomb Museum
#### Sights
#### Tours
#### Shopping
#### Eating
#
Nagasaki at a Glance
It's both unfortunate and important that the name Nagasaki (長崎) is synonymous with the dropping of the second atomic bomb. Spend some time here and you'll find that this welcoming, peaceful city also boasts a colourful history of trade with Europe and China, interesting churches, shrines and temples, and an East-meets-West culinary scene, all set prettily around a gracious harbour.
Not that the WWII history can be overlooked: it's as much a part of the city's fabric as the hilly landscape and cobblestones, and a visit to the scenes of atomic devastation is a must.
Scenic views across Nagasaki | ROMIX CHANG/EYEEM/GETTY IMAGES ©
With a Day in Port
Visit the Nagasaki Atomic Bomb Museum and surrounding sites, then explore the beautiful gardens and historic homes of Glover Garden. You can also take a cable car up Inasa-yama and soak in the hot baths of Onsen Fukunoyu.
Best Places for...
**Historic sites** Dejima
**Shopping** Hamanmachi
**Nagasaki-style kaiseki** Shippoku Hamakatsu
Getting from the Port
Cruise ships dock at Matsugae Pier. It's a short walk from here to Ourakaigan-dori tram stop. A tram to downtown takes about five minutes.
Fast Facts
**Money** Currency exchange is available at the wharf.
Tourist information Information services greet arrivals. Also see for tourist information offices.
**Wi-fi** There is free wi-fi at the port, JR Nagasaki Station, Dejima Wharf and many other locations.
TOP EXPERIENCE
# Nagasaki Atomic Bomb Museum
Urakami, the hypocentre of the atomic explosion, is today a prosperous, peaceful suburb. While nuclear ruin seems comfortably far away seven decades later, many sights here keep the memory alive.
Great For...
vca
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Recording a message for peace, and hearing those left by others, at the Memorial Hall.
Explore Ashore
It's a short walk from Matsugae Pier to Ourakaigan-dori tram stop. The tram ride from here to the Atomic Bomb Museum takes about half an hour.
8Need to Know
長崎原爆資料館; %095-844-1231; www.nagasakipeace.jp; 7-8 Hirano-machi; ¥200, audioguide ¥154; h8.30am-6.30pm May-Aug, to 5.30pm Sep-Apr; jGenshi Shiryokan/Atomic Bomb Museum
Nagasaki National Peace Memorial Hall for the Atomic Bomb Victims | F11PHOTO/SHUTTERSTOCK ©
### The Museum
On 9 August 1945, the world's second nuclear weapon detonated over Nagasaki. This sombre place recounts the city's destruction and loss of life through photos and artefacts, including mangled rocks, trees, furniture, pottery and clothing, a clock stopped at 11.02 (the time of the bombing), first-hand accounts from survivors, and stories of heroic relief efforts. Exhibits also include the post-bombing struggle for nuclear disarmament, and conclude with a chilling illustration of which nations bear nuclear arms.
### Nagasaki National Peace Memorial Hall for the Atomic Bomb Victims
Adjacent to the museum and completed in 2003, this minimalist memorial (国立長崎原爆死没者追悼平和祈念館; www.peace-nagasaki.go.jp; 7-8 Hirano-machi; admission free; h8.30am-6.30pm May-Aug, to 5.30pm Sep-Apr; jHeiwa Kōen/Peace Park) by Kuryū Akira is a profoundly moving place. It's best approached by quietly walking around the sculpted water basin, commemorating those who cried for water in their dying days. In the hall below, 12 'pillars of light', containing shelves of books of the names of the deceased, reach skyward. Listen to survivors' messages and leave your own digital message for peace at 'peace information counters'.
### Atomic Bomb Hypocentre Park
A must-see for anyone coming to Nagasaki for its historic significance, this park (長崎爆心地公園; jHeiwa Kōen/Peace Park) houses a smooth, black-stone column that marks the point above which the atomic bomb exploded. Nearby are bomb-blasted relics, including a section of the wall of the Urakami Cathedral (map Google map; 浦上天主堂; 1-79 Motō-machi; h9am-5pm; jAtomic Bomb Museum).
### Peace Park
North of the hypocentre, Peace Park (map Google map; 平和公園, Heiwa-kōen; jŌhashi) is presided over by the 10-tonne bronze Nagasaki Peace Statue (平和祈念像), designed in 1955 by Kitamura Seibō. It also includes the dove-shaped Fountain of Peace (1969) and the Peace Symbol Zone, a sculpture garden with contributions on the theme of peace from around the world. On 9 August a rowdy antinuclear protest is held within earshot of the more formal official memorial ceremony for those lost to the bomb.
Peace Park | RYUSHI/SHUTTERSTOCK ©
### Take a Break
Stop by Hibakusha no Mise (map Google map; 被爆者の店; %095-844-8809; 8-20 Okamachi; h8.45am-5pm) for snacks, candy, _castella_ , toys or trinkets – profits go to _hibakusha_ (atomic-bomb survivor) organisations.
Nagasaki
1Sights
1Atomic Bomb Hypocentre ParkC2
2DejimaB3
3Inasa-yamaA1
4Nagasaki Atomic Bomb MuseumD2
5Nagasaki National Peace Memorial Hall for the Atomic Bomb VictimsD2
6Nagasaki RopewayA1
7Peace ParkC1
8Peace StatueD1
9Urakami CathedralD1
2Activities, Courses & Tours
10Nagasaki Harbour CruisesB3
7Shopping
11Amu PlazaB2
12FukusayaC3
13Hamanmachi Shopping ArcadeC3
14Hibakusha no MiseC1
15Mirai Nagasaki CocowalkA1
5Eating
16Dejima WharfB3
17No no BudoB2
18Shippoku HamakatsuC3
19ShōkandōC2
1Sights
DejimaHistoric Site
(map Google map; 出島; %095-829-1194; www.nagasakidejima.jp; 6-1 Dejima-machi; ¥510; h8am-7pm mid-Jul–mid-Oct, to 6pm mid-Oct–mid-Jul; jDejima)
In 1641 the Tokugawa shogunate banished all foreigners from Japan, with the exception of one place: Dejima, an artificial island in Nagasaki harbour. From then until the 1850s, this tiny Dutch trading post was the sole sanctioned foreign presence in Japan. Today, 17 buildings, walls and structures (plus a miniature Dejima) have been painstakingly reconstructed here. The buildings are as instructive inside as they are appealing outside, filled with exhibits covering the spread of trade, Western learning and culture, archaeological digs, and rooms combining Japanese tatami (tightly woven floor matting) with Western wallpaper. There's excellent English signage. Allow at least two hours.
Free walking-tour maps of the entire site are available, and there's even a kimono-rental shop (¥2000/6000 per hour/day) for those who want to feel even more historically connected.
Glover GardenGardens
(グラバー園; %095-822-8223; www.glover-garden.jp; 8-1 Minamiyamate-machi; adult/student ¥610/300; h8am-9.30pm May–mid-Jul, to 6pm mid-Jul–Apr; jŌura Tenshudō)
Some two-dozen former homes of the city's Meiji-period European residents and other important buildings have been reassembled in this beautifully landscaped hillside garden, with breathtaking views across the harbour. Glover Garden is named after Scottish merchant and industrialist Thomas Glover (1838–1911), who built Japan's first railway and helped establish the shipbuilding industry, and whose arms-importing operations influenced the course of the Meiji Restoration.
Start by taking the moving walkways to the top of the hill, then work your way back down. The 'audio pen' guide, available near the ticket office, gives lots of detailed commentary and costs ¥700, although the map that comes with it can be confusing. The garden is about a 10-minute walk from the port.
Inasa-yamaMountain
(map Google map; 稲佐山, Mt Inasa) West of the harbour, the Nagasaki Ropeway cable car (長崎ロープウェイ; %095-861-3640; www.nagasaki-ropeway.jp; 8-1 Fuchi-machi; return ¥1230; h9am-10pm; jMori-machi)
ascends every 15 to 20 minutes to the top of 333m-high Inasa-yama, offering superb views over Nagasaki. A tower at the top offers even more panoramic views. Elsewhere on the mountain is Onsen Fukunoyu (温泉ふくの湯; %095-833-1126; 451-23 Iwami-machi; ¥800; h9.30am-1am Sun-Thu, to 2am Fri & Sat), which has wet baths, as well as _ganbanyoku_ stone baths (an additional ¥700), with temperatures from a balmy 38°C to an are-you-nuts 70°C. Family-style (private) baths are also available.
TTours
One-hour Nagasaki Harbour Cruises (map Google map; 長崎港めぐりクルーズ; %095-822-5002; Nagasaki Harbour Terminal Bldg; adult/child ¥2000/1000; hnoon & 4pm Thu-Mon) are a great way to see the picturesque city. Check at the ferry terminal for up-to-date schedules.
7Shopping
Local crafts and products are sold around and opposite JR Nagasaki Station, as well as in shops along busy Hamano-machi shopping arcade near Shianbashi tram stop. Ignore **tortoiseshell crafts** (べっ甲) sold around town: these may land you in jail if the shell is from an endangered species.
For mall shopping, Amu Plaza (map Google map; アミュプラザ長崎; 1-1 Onouemachi; dJR Nagasaki) at the station is nice and easy, and you can't miss Mirai Nagasaki Cocowalk (map Google map; みらい長崎ココウォーク; %095-848-5509; www.cocowalk.jp; 1-55 Morimachi; h10am-9pm; jMori-machi, dJR Urakami), a massive shopping, dining and cinema complex with a Ferris wheel (¥500) on the roof.
Youme Town, with ubiquitous mall shops, is by the harbour, and in the city centre Hamanmachi (www.hamanmachi.com/hamabura_map/en.htm) is a covered arcade housing an astonishing 700 shops.
Dejima Wharf | SANGA PARK/ALAMY STOCK PHOTO ©
5Eating
The Mirai Nagasaki Cocowalk shopping mall features some 20 restaurants on its 4th and 5th floors. Other good places for restaurant browsing and great views include the restaurant floors of the shopping mall Amu Plaza, especially the restaurants with a view on its 5th floor, and the harbourside Dejima Wharf (map Google map; 出島ワーフ; %095-828-3939; www.dejimawharf.com; 1-1-109 Dejimamachi; jDejima).
Shippoku HamakatsuKaiseki¥¥
(map Google map; 卓袱浜勝; %095-826-8321; www.sippoku.jp; 6-50 Kajiya-machi; lunch/dinner from ¥1500/3500, shippoku courses ¥3900-7900; h11am-10pm; jShianbashi)
Come here if you'd like to experience _shippoku-ryōri_ (Nagasaki-style _kaiseki_ ) and still have something left to spend at the shops. Menus are filling and varied, and there's a choice of Japanese- or Western-style seating.
No no BudoBuffet¥¥
(map Google map; 野の葡萄; %095-895-8515; 5th fl, Amu Plaza, 1-1 Onouemachi; buffet lunch/dinner ¥1600/2100; h11am-11pm; jNagasaki-eki-mae, dJR Nagasaki)
Come for the buffet, stay for the view at the new Nagasaki branch of this much-loved casual buffet chain. Dozens of savoury and dessert offerings concentrate on organic and local produce, including an entire counter of Nagasaki specialities. The views from the far windows overlooking the harbour offer a great perspective on the city.
Castella Cake
No visit to Nagasaki is complete without a taste of _castella_ , a Portuguese-inspired dense sponge cake. This yellow, brick-shaped treat has become a must-have Nagasaki treat and souvenir. There seems to be a _castella_ shop by every tourist attraction.
Two of the finer shops are Fukusaya (map Google map; 福砂屋; %095-821-2938; www.fukusaya.co.jp; 3-1 Funadaiku-machi; h8.30am-8pm; jShianbashi), making the cakes since 1624, and Shōkandō (map Google map; 匠寛堂; %095-826-1123; www.shokando.jp; 7-24 Uo-no-machi; h9am-7pm; jMegane-bashi), across from Megane-bashi, supplier to the Japanese imperial family.
MELON SODA/SHUTTERSTOCK ©
8INFORMATION
A new multilingual **call centre** ( %095-825-5175) caters to English-speaking visitors.
**Nagasaki CityTourist Information Center** (長崎市総合観光案内所; %095-823-3631; www.at-nagasaki.jp/foreign/english; 1st fl, JR Nagasaki Station; h8am-8pm) Has brochures and maps in English. The English spoken is minimal, though.
**Nagasaki Prefectural Tourism Association & Visitors Bureau** ( %095-828-9407; www.visit-nagasaki.com; 8th fl, 14-10 Motofuna-machi; h9am-5.30pm; jŌhato)
8GETTING AROUND
Nagasaki is easy to navigate, with most sights easily accessible on foot or by tram.
There are four colour-coded tram routes numbered 1, 3, 4 and 5 (route 2 is for special events), and stops are signposted in English. It costs ¥120 to travel anywhere in town, but you can transfer for free at the Shinchi Chinatown (新地中華街) stop only: ask for a _noritsugi_ (transfer pass). Alternatively, all day, unlimited tram passes are available for ¥500 from tourist information centres.
# KANAZAWA
#### Kenroku-en
#### Kanazawa Castle Park
#### Sights
#### Tours
#### Shopping
#### Eating & Drinking
#
Kanazawa at a Glance
The array of cultural attractions in Kanazawa (金沢) makes the city the drawcard of the Hokuriku region and a rival to Kyoto as the historical jewel of mainland Japan. Best known for Kenroku-en, a castle garden dating from the 17th century, it also boasts beautifully preserved samurai and geisha districts, attractive temples, a wealth of museums and a wonderful market (and far fewer tourists than Kyoto – for now).
Kenroku-en | TKKURIKAWA/GETTY IMAGES ©
With a Day in Port
Stroll the serene pathways of Kenroku-en, one of Japan's best gardens, and pause for reflection at nearby DT Suzuki Museum. You can explore Kanazawa Castle Park's original and masterfully recreated buildings, surrounded by paths and gardens, and then step back in time at former geisha house Kaikarō.
Best Places for...
**Thatched cottages** Shirakawa-gō
**Tea ceremonies** Gyokusen-an Rest House
**Market shopping** Ōmi-chō Market
**Golden souvenirs** Sakuda Gold Leaf Company
Getting from the Port
Some cruise operators offer a shuttle service for the short trip to downtown – it usually takes about 20 minutes. Otherwise, a taxi (around ¥2500) is your best bet.
Fast Facts
**Money** Head into town for ATMs and currency exchange.
Tourist information Temporary information booths greet arrivals. See also for tourist information centres.
**Wi-fi** Free wi-fi is available at the port, JR Kanazawa Station, Ishikawa Foundation for International Exchange, and key sights around town.
TOP EXPERIENCE
# Kenroku-en
Those in the know rate Kenroku-en as among the finest gardens in Japan, and a visit doesn't disappoint. Strolling the gentle paths reveals delightful details and vistas at every turn, and each season brings its own charm and palette.
Great For...
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Look for poles, ropes and wires supporting and guiding trees and expert gardeners at work.
Explore Ashore
Buses regularly make the 20-minute trip (¥200) from JR Kanazawa Station to the gardens. A taxi from the station costs around ¥1200 and takes about 10 minutes.
8Need to Know
兼六園; %076-234-3800; www.pref.ishikawa.jp/siro-niwa/kenrokuen/e; 1-1 Marunouchi; adult/child/senior ¥310/100/free; h7am-6pm Mar–mid-Oct, 8am-4.30pm mid-Oct–Feb
CATALIN DANIEL CIOLCA/GETTY IMAGES ©
### The Gardens
This Edo-period garden draws its name ( _kenroku_ means 'combined six') from a renowned Sung-dynasty garden in China that dictated six attributes for perfection: seclusion, spaciousness, artificiality, antiquity, abundant water and broad views. Kenroku-en has them all. Arrive before the crowds.
It's believed that the garden, originally belonging to an outer villa of Kanazawa-jō, was developed from the 1620s to the 1840s and was so named in 1822. It was first opened to the public in 1871.
### Sigure-tei Teahouse
Kenroku-en's Sigure-tei teahouse offers green (¥310) and _matcha_ tea (¥720), accompanied by seasonal, traditional Japanese sweets and gorgeous views, in a beautiful traditional building.
### What's Nearby?
The spiritual DT Suzuki Museum (鈴木大拙館; %076-221-8011; www.kanazawa-museum.jp/daisetz; 3-4-20 Honda-machi; adult/child/senior ¥300/free/200; h9.30am-4.30pm Tue-Sun) is a tribute to Daisetsu Teitaro Suzuki, one of the foremost Buddhist philosophers of the modern age. Published in Japanese and English, Suzuki is largely credited with introducing Zen to the West. This stunning concrete complex embodies the heart of Zen.
A low-slung glass cylinder, 113m in diameter, forms the perimeter of the 21st Century Museum of Contemporary Art (map Google map; 金沢21世紀美術館; %076-220-2800; www.kanazawa21.jp; 1-2-1 Hirosaka; h10am-6pm Tue-Thu & Sun, to 8pm Fri & Sat). Museum entry is free, but admission fees are charged for special exhibitions. Inside, galleries are arranged like boxes on a tray. Check the website for event info and fees.
The small Ishikawa Prefectural Museum of Traditional Products & Crafts (map Google map; 石川県立伝統産業工芸館; %076-262-2020; www.ishikawa-densankan.jp; 2-1 Kenroku-machi; adult/child/senior ¥260/100/200; h9am-5pm, closed 3rd Thu of month Apr-Nov, closed Thu Dec-Mar) offers fine displays of over 20 regional crafts; many pieces are for sale if you fall in love with something. Pick up the free English-language audioguide.
DT Suzuki Museum | LEE YIU TUNG/SHUTTERSTOCK © ARCHITECT: TANIGUCHI YOSHIO
TOP EXPERIENCE
# Kanazawa Castle Park
The original castle on this site burned down long ago, with only one original gate still standing, supplemented by a couple of skilful reconstructions. Nevertheless, it's an imposing sight; spend an hour or two wandering through the gardens, admiring the buildings and conjuring the castle's dramatic past.
Great For...
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A tea ceremony at Gyokusen-an Rest House in the adjacent Gyokusen Inmaru Garden.
Explore Ashore
The castle is directly across from Kenroku-en, so it's easy to move from one to the other. From JR Kanazawa Station, take a bus (20 minutes, ¥200) or taxi (¥1200, 10 minutes).
8Need to Know
金沢城公園, Kanazawa-jō Kōen; %076-234-3800; www.kanazawa-tourism.com/eng/guide/guide1_1.php?no=2; 1-1 Marunouchi; buildings/grounds ¥310/free; hgrounds 7am-6pm Mar-15 Oct, 8am-5pm 16 Oct-Feb, castle 9am-4.30pm
ANDREAS H/SHUTTERSTOCK ©
### History
Originally built in 1580, this massive structure was called the 'castle of 1000 tatami' and housed the Maeda clan for 14 generations until it was destroyed by fire in 1881. The elegant surviving gate, **Ishikawa-mon** (built in 1788), provides a dramatic entry from Kenroku-en; holes in its turret were designed for hurling rocks at invaders. Two additional buildings, the **Hishi-yagura** (diamond-shaped turret) and **Gojikken-nagaya** (armoury), were reconstructed using traditional means in 2001.
### What's Nearby?
Adjacent to the Kanazawa Castle Park, Gyokusen Inmaru Garden (map Google map; 玉泉院丸庭園, Gyokusen Inmaru Teien; %076-234-3800; www.pref.ishikawa.jp/siro-niwa/kanazawajou/e/gyokusen-in; 1-1 Marunouchi; admission free; h7am-6pm) was first constructed in 1634 but abandoned in the Meiji era. Its five-year reconstruction was completed in 2015. Features include a small waterfall, bridges and many traditional elements. While the garden's focal point is the Gyokusen-an Rest House, it's the overall picture of beauty and refinement that impresses most. The garden and teahouse are illuminated spectacularly on Friday and Saturday evenings between sunset and 9pm.
The handsome Gyokusen-an Rest House (map Google map; 玉泉庵; %076-234-3800; 1-1 Marunouchi; tea ceremony ¥720; h7am-6pm Mar-15 Oct, 8am-5pm 16 Oct-Feb) is the perfect setting in which to experience _cha-dō_ (a tea ceremony), one of Japan's oldest, most intricate and unique customs. Enjoy serene views accompanied by _matcha_ green tea with _wagashi_ (Japanese sweets; ¥720).
Gyokusen Inmaru Garden | MANUEL ASCANIO/SHUTTERSTOCK ©
Audio buffs will dig the Kanazawa Phonograph Museum (map Google map; 金沢蓄音器館; %076-232-3066; www.kanazawastation.com/kanazawa-phonograph-museum; 2-11-21 Owari-chō; adult/student/senior ¥300/free/200; h10am-5pm) of old-time phonographs and SP records, with daily demonstrations at 11am, 2pm and 4pm.
Ishikawa Local Products Center (map Google map; 石川県観光物産館, Ishikawa-ken Kankō-bussankan; %076-222-7788; www.kanazawa-kankou.jp; 2-20 Kenroku-machi; h10am-6pm) offers an overview of Kanazawa crafts, on the kitschy side, under one roof.
Kanazawa
1Sights
121st Century Museum of Contemporary ArtC3
2Gyokusen Inmaru GardenC2
3Gyokusen-an Rest HouseC2
4Ishikawa Prefectural Museum of Traditional Products & CraftsC3
5KaikarōD2
6Kanazawa Castle ParkC3
7Kanazawa Phonograph MuseumC2
8Kenroku-enC3
9Nagamachi Yūzen-kanA2
10Ōmi-chō MarketB2
11ShimaD1
7Shopping
12Ishikawa Local Products CenterC3
13MurakamiB3
14Sakuda Gold Leaf CompanyD1
5Eating
15Chōhachi Kanazawa Ekimae-tenB1
16Curio Espresso & Vintage DesignB2
17Daiba Kanazawa EkimaeB1
18Full of BeansB3
19Janome-sushi HontenB3
20Kaiseki TsurukoB2
21Kanazawa Todoroki-teiC2
22Restaurant JiyūkenD2
Sentō(see 10)
6Drinking & Nightlife
23Oriental BrewingC1
1Sights
Just north of the Asano-gawa, Higashi-chaya-gai (Higashi Geisha District) is an enclave of narrow streets established early in the 19th century for geisha to entertain wealthy patrons. The slatted wooden facades of the geisha houses are romantically preserved. It's very picturesque around sunset.
Ōmi-chō MarketMarket
(map Google map; 近江町市場; 35 Ōmi-chō; h9am-5pm)
Between Kanazawa Station and Katamachi you'll find this market, reminiscent of Tokyo's old Tsukiji market. A bustling warren of fishmongers, buyers and restaurants, it's a great place to watch everyday people in action or indulge in the freshest sashimi and local produce. The nearest bus stop is Musashi-ga-tsuji.
Ōmi-chō Market | TKKURIKAWA/GETTY IMAGES ©
KaikarōMuseum
(map Google map; 懐華樓; %076-253-0591; www.kaikaro.jp/eng/index.html; 1-14-8 Higashiyama; adult/child ¥750/500; h9am-5pm)
In Higashi-chaya-gai, Kaikarō is an early-19th-century geisha house refinished with contemporary fittings and art, including a red-lacquered staircase. If your cruise schedule allows, evening geisha performances include a short lecture in English by the proprietor, followed by a demonstration of traditional party games by geisha themselves. Performances last 1½ hours; tickets start at ¥6500.
Myōryū-jiBuddhist Temple
(妙立寺; Ninja-dera; %076-241-0888; www.myouryuji.or.jp/en.html; 1-2-12 Nomachi; adult/child ¥1000/700; hby reservation only 9am-4pm Mon-Fri, to 4.30pm Sat & Sun)
Completed in 1643 in Teramachi, the temple was designed to protect its lord from attack. It contains hidden stairways, escape routes, secret chambers, concealed tunnels and trick doors. Contrary to popular belief, it has nothing to do with ninja. Admission is by tour only (in Japanese with an English guidebook). Phone for reservations with English-speaking staff.
Nagamachi Yūzen-kanMuseum
(map Google map; 長町友禅館; %076-264-2811; www.kagayuzen-club.co.jp; 2-6-16 Nagamachi; ¥350; h9.30am-5pm Thu-Mon Mar-Nov)
In a non-traditional building at the edge of the Nagamachi district, the Nagamachi Yūzen-kan displays some splendid examples of _Kaga Yūzen_ kimono dyeing and demonstrates the process. Enquire ahead about trying the silk-dyeing process yourself (¥4000).
ShimaMuseum
(map Google map; 志摩; %076-252-5675; www.ochaya-shima.com; 1-13-21 Higashiyama; adult/child ¥500/300; h9am-6pm)
This traditional-style former geisha house dates from 1820 and has an impressive collection of elaborate combs, and picks for _shamisen_ (three-stringed instruments resembling a lute or banjo).
Kanazawa Yuwaku Edo VillageHistoric Building
(金沢湯涌江戸村, Kanazawa Yuwaku Edo-mura; %076-235-1267; www.kanazawa-museum.jp/edomura/english/index.html; 35-1 Yurakuwara-machi; adult/student/senior ¥300/free/200; h9am-5pm Wed-Mon; g12)
In Yuwaku Onsen, about 14km southeast of Kanazawa along Rte 10, you'll find this attractive collection of reconstructed Edo-period buildings arranged as an open-air museum showcasing artefacts from the era (1603–1868). Take the bus from JR Kanazawa Station (¥600, 45 minutes) – get off at Yuwaku Onsen stop and walk for about 300m, following the signs.
TTours
Kanazawa Walking ToursWalking
( %803 044 3191; www.kanazawa-tours.com; half-day tours from ¥3700)
KWT's English-speaking guides get rave reviews from happy customers. Public tours go ahead when a minimum of six people have booked; private tours start at ¥22,000 per half-day and are fully customisable.
Exploring Shirakawa-gō
The remote, mountainous districts of Shirakawa-gō (白川郷) and Gokayama are best known for farmhouses in the thatched _gasshō-zukuri_ style. They're rustic and lovely whether set against the vibrant colours of spring, draped with the gentle mists of autumn, or peeking through a carpet of snow, and they hold a special place in the Japanese heart.
Most of Shirakawa-gō's sights (and crowds) are in **Ogimachi** (often referred to simply as Shirakawa-gō). The less crowded, more isolated villages of **Suganuma** and **Ainokura** , in the Gokayama district of Toyama Prefecture, have the most ambience; other sights are spread over many kilometres along Rte 156. All three villages are Unesco World Heritage Sites.
Passionate debate continues around the impact that tour buses have upon these unique communities, and how best to mitigate disruption to local life. To avoid the crowds, steer clear of weekends, holidays and cherry-blossom and autumn-foliage seasons.
A plethora of day tours are available from Kanazawa; ask at the Kanazawa Tourist Information Center. Nōhi Bus (濃飛バス; %0577-32-1688; www.nouhibus.co.jp/english) services Shirakawa-gō (1½ hours, ¥3600 round-trip) approximately once an hour, and Suganuma slightly less frequently (one hour, ¥3600 round-trip); reserve your ticket in advance.
Suganuma | BEIBAOKE/SHUTTERSTOCK ©
7Shopping
The Hirosaka shopping street, between Kōrinbō 109 department store and Kenroku-en, has some upmarket craft shops on its south side. Other major department stores are found towards JR Kanazawa Station (Forus, Meitetsu M'za) and on Hyakumangoku-dōri between Kōrinbō and Katamachi (Daiwa, Atrio Shopping Plaza). The funky Tatemachi Shopping Promenade is also here.
Sakuda Gold Leaf CompanyArts & Crafts
(map Google map; 金銀箔工芸さくだ; %076-251-6777; www.goldleaf-sakuda.jp; 1-3-27 Higashiyama; h9am-6pm)
Here you can observe the _kinpaku_ (gold-leaf) process and pick up all sorts of gilded souvenirs, including pottery, lacquerware and, er...golf balls. It also serves tea containing flecks of gold leaf, which is reputedly good for rheumatism. Even the toilet walls are lined with gold and platinum.
MurakamiFood
(map Google map; 村上; %076-264-4223; 2-3-32 Nagamachi; h8.30am-5pm)
If a flowering tree made of candy excites you, head to Murakami. At this handsome _wagashi_ (Japanese sweets) shop you'll also find _fukusamochi_ (red-bean paste and pounded rice in a crêpe) and _kakiho_ (soybean flour rolled in black sesame seeds).
5Eating & Drinking
The shiny, architecturally stunning JR Kanazawa Station building is brimming with eateries. Its neighbour, Forus department store, has excellent dining floors, as does the basement of Meitetsu M'Za department store, opposite Ōmi-chō Market with its fresh-from-the-boat restaurants.
Daiba Kanazawa EkimaeIzakaya¥
(map Google map; 台場金沢駅前店; %076-263-9191; Kanazawa Miyako Hotel 1F, 6-10 Konohana-machi; items from ¥460; h11am-3pm & 5pm-midnight)
This trendy spot in the Kanazawa Miyako Hotel building has a comprehensive Japanese menu and a limited English one with all the Western favourites and some local specialities. It's a great place for your first _izakaya_ (pub-restaurant) experience.
Full of BeansCafe¥
(map Google map; フルオブビーンズ; %076-222-3315; www.fullofbeans.jp; 41-1 Satomi-chō; meals from ¥850; h11.30am-3.30pm & 5-10pm Thu-Tue)
A variety of Japanese dishes and _yōshoku_ (Western-style meals) are served at this stylish cafe in the quieter backstreets of Katamachi – the website will give you a sense of the vibe. It's a good place to try inimitable Kanazawa speciality _hanton raisu:_ a bowl of rice topped with an omelette, fried seafood, ketchup and tartare sauce (available at lunch).
Curio Espresso & Vintage DesignCafe¥
(map Google map; %076-231-5543; 1-13 Yasue-cho; sandwiches from ¥600; h9am-6pm Sat-Mon, from 8am Wed-Fri)
Brewing Seattle-style coffee that would satisfy even the most hardened coffee snob, this sweet little cafe is a quaint spot to grab a break near the station. The menu features Western favourites (including barbecue pulled pork) you'll be hard-pressed to find elsewhere in this part of Japan.
Traditional Crafts
During the Edo period Kanazawa's ruling Maeda family fuelled the growth of important crafts. Many are still practised today.
**Kanazawa and Wajima lacquerware** Decoration is applied to luminous black lacquerware through _maki-e_ (decorating with gold or silver power) or gilding. Artists must take great care that dust does not settle on the final product.
**Ōhi pottery** The deliberately simple, almost primitive designs, rough surfaces, irregular shapes and monochromatic glazes of Ōhi pottery have been favoured by tea practitioners since the early Edo period.
**Kutani porcelain** Known for its elegant shapes, graceful designs and bright, bold colours. Typical motifs include birds, flowers, trees and landscapes.
**Kaga Yūzen silk dyeing** This laborious, specialised method is characterised by strong colours and realistic depictions of nature, such as flower petals that have begun to brown around the edges. White lines between elements where ink has washed away are typical.
**Gold leaf** A lump of pure gold the size of a ¥10 coin is rolled to the size of a tatami mat, becoming as thin as 0.0001mm. The gold leaf is then cut into squares of 10.9cm – the size used for mounting on walls, murals or paintings – or cut again for gilding on lacquerware or pottery. Over 98% of Japan's gold leaf is produced in Kanazawa.
Ōhi pottery | QUANG MINH/SHUTTERSTOCK ©
ForusFood Hall¥
( %076-265-8111; www.forus.co.jp/kanazawa; 3-1 Horikawa Shin-machi; h11am-10pm)
Forus department store has a wide variety of great Japanese restaurants and bakeries on its 6th floor.
Forus | TK KURIKAWA/SHUTTERSTOCK ©
SentōChinese¥¥
(map Google map; 仙桃; %076-234-0669; 2F Ōmichō Ichiba, 88 Aokusa-machi; dishes from ¥650, set menus from ¥980; h11am-3pm & 5-10.30pm Wed-Mon)
Upstairs in Ōmi-chō Market, chefs from Hong Kong prepare authentic Szechuan- and Hong Kong–style dishes (including dim sum) from scratch. Delicious set menus are excellent value.
Janome-sushi HontenSushi¥¥
(map Google map; 蛇之目寿司本店; %076-231-0093; 1-1-12 Kōrinbō; set menu ¥3000, Kaga ryōri sets from ¥4400; hnoon-2pm & 5.30-10.30pm Thu-Tue)
Kanazawa institution Janome-sushi Honten has been known for sashimi and Kaga cuisine since 1931.
Kanazawa Todoroki-teiBistro¥¥
(map Google map; 金沢とどろき亭; %076-252-5755; 1-2-1 Higashiyama; plates from ¥1500; h11.30am-3.30pm & 6-11.30pm)
The art-deco, woody, candelit atmosphere of this Western-style bistro near Higashi-chaya-gai is a big selling point. The Taisho-era (1912–26) building with vaulted ceilings is a little rough around the edges, but that's part of its charm.
Restaurant JiyūkenShokudo¥¥
(map Google map; レストラン自由軒; %076-252-1996; www.jiyuken.com; 1-6-6 Higashiyama; meals ¥700-1890; h11.30am-3pm & 5-9pm)
This _shokudō_ (all-round, inexpensive restaurant) in the heart of Higashi-chaya-gai has been serving _yōshoku_ (Western food) – or at least Japanese takes on Western food – such as omelettes, hamburgers and curry rice, since 1909. Daily set lunches (¥995) are good value.
Chōhachi Kanazawa Ekimae-tenJapanese¥¥
(map Google map; 長八 金沢駅前店; %076-256-1843; www.cho-hachi.jp; 5-5 Konohana-machi; items from ¥420; h11am-11pm)
This upmarket regional _izakaya_ has an emphasis on seafood – as you'd expect – with plenty of sushi and sashimi to sample in a classy though booze-friendly setting.
Kaiseki TsurukoJapanese¥¥¥
(map Google map; 懐石 つる幸; %076-264-2375; www.turukou.com; 6-5 Takaoka-machi; lunch/dinner from ¥10,000/15,000; hnoon-3pm & 6-10pm)
_Kaiseki_ (Japanese haute cuisine) dining is a holistic experience of hospitality, art and originality. This outstanding restaurant is a true gourmand's delight, offering an experience beyond what you might enjoy in a ryokan. Dress to impress.
Oriental BrewingBrewery
(map Google map; %076-255-6378; www.orientalbrewing.com; 3-2-22 Higashiyama; h11am-10pm)
You can't miss this trendy brewhouse at the entrance to Higashi-chaya-gai: it's always humming with Japanese and international guests, who love the mellow, friendly vibe and the original yeasty ales brewed on-site.
Kanazawa Specialities
Seafood is the staple of Kanazawa's _Kaga ryōri_ (Kaga cuisine); even the most humble train-station _bentō_ (boxed meal) usually features some type of fish. _Oshi-zushi,_ a thin layer of fish pressed atop vinegar rice, is said to be the precursor to modern sushi. Another favourite is _jibuni,_ flour-coated duck or chicken stewed with shiitake and green vegetables.
_Jibuni_ | BONCHAN/SHUTTERSTOCK ©
8INFORMATION
Check out <https://visitkanazawa.jp> for general city information.
**KanazawaTourist Information Center** (石川県金沢観光情報センター; %076-232-6200, KGGN 076-232-3933; <http://kggn.sakura.ne.jp>; 1 Hirooka-machi; h9am-7pm) This brilliant office inside JR Kanazawa Station, one of Japan's best, has helpful staff, maps and pamphlets in a variety of languages, and the excellent, free English-language magazine _Eye on Kanazawa_. The Goodwill Guide Network (KGGN) is also here to assist with free guiding in English – two weeks' notice is requested.
**Ishikawa Foundation for International Exchange** ( %076-262-5931; www.ifie.or.jp; 1-5-3 Honmachi; h9am-8pm Mon-Fri, to 5pm Sat & Sun) Offers information, a library, satellite-TV news and free internet access. It's on the 3rd floor of the Rifare building, a few minutes' walk southeast of JR Kanazawa Station.
8GETTING AROUND
BICYCLE
Bikes can be rented from **JR Kanazawa Station Rent-a-Cycle** (駅レンタサイクル; %076-261-1721; per hour/day ¥200/1200; h8am-8.30pm) and **Hokutetsu Rent-a-Cycle** (北鉄レンタサイクル; %076-263-0919; per 4hr/day ¥630/1050; h8am-5.30pm), both by the station's west exit.
There's also a pay-as-you-go bicycle-rental system called 'Machi-nori'. For the low-down in English, a downloadable map is available at www.machi-nori.jp.
BUS
Buses depart from the circular terminus in front of JR Kanazawa Station's east exit. Any bus from station stop 7, 8 or 9 will take you to the city centre (¥200). The round-trip journey is free if you have a JR pass. The Kanazawa Loop Bus (single ride/day pass ¥200/500, every 15 minutes from 8.30am to 6pm) circles the major tourist attractions in 45 minutes. On Saturday, Sunday and holidays, the Machi-bus goes to Kōrinbō for ¥100. Purchase day passes from the Hokutetsu Kankō service centre inside JR Kanazawa Station; there's another centre opposite the Ōmi-chō Market bus stop.
For more information, see www.hokutetsu.co.jp/en/en_round.
# HOKKAIDŌ
#### Hokkaidō Food & Beer Culture
#### Kushiro-shitsugen National Park
#### Otaru
#### Sapporo
#### Hakodate
#### Kushiro
#
Hokkaidō at a Glance
Hokkaidō (北海道) is a land of wide-open spaces, with large swathes of wilderness, primeval forests, tropical-blue caldera lakes and bubbling hot springs. In the summer, all this (plus the cooler, drier weather) draws hikers, cyclists and strollers, while winter is a different beast entirely, with cold fronts from Siberia bringing huge dumps of light, powdery snow. The island's stunning natural scenery tends to overshadow everything else that Japan's northernmost island has to offer, which is a lot: there is excellent food, a vibrant capital city and a compelling history.
Otaru Canal TREVOR DOBSON/GETTY IMAGES ©
With a Day in Port
In Otaru, explore the museums and restaurants along historic Otaru Canal. In Sapporo, visit Japan's oldest brewery or the Hōheikyō hot spring. Take in the views from Hakodate-yama in Hakodate, and in Kushiro make tracks for Kushiro-shitsugen National Park.
Best Places for...
**Seafood** Kikuyo Shokudo
**Souvenir shopping** Kitaichi Sangōkan
**Ramen** Menya Saimi
**Snow sports** Sapporo Teine
Getting from the Port
Hokkaidō has three port areas: Otaru (near Sapporo), Hakodate and Kushiro.
**Otaru** Otaru Port is a 1.5km walk from Otaru Canal and 2km from Otaru Station. From here regular trains make the 30-minute journey to Sapporo.
**Hakodate** A regular shuttle (¥320, 30 minutes) runs between the Cruise Port Terminal and the main train station; a taxi costs about ¥2000. Buses 1 and 19 also head to the city centre.
**Kushiro** The port is a five-minute walk to Kushiro Fisherman's Wharf MOO, 15 minutes to downtown. From Nishikoku Pier 4 it's a 15-minute drive to downtown.
Fast Facts
**Otaru** ATMs accepting foreign cards are at Canal Plaza. There is tourist information at Canal Plaza and Otaru Station. Wi-fi is free at Otaru Station.
**Hakodate** There are plenty of ATMs in the city centre. Tourist information can be found at the cruise port and at JR Hakodate Station. Wi-fi is available at the pier, main train station and on trams.
Kushiro Look for Japan Post Bank and 7-Eleven ATMs at Kushiro Station. Tourist-information booths greet arrivals and there's also a tourist office. There is wi-fi is free at the port and Kushiro Fisherman's Wharf MOO.
TOP EXPERIENCE
# Hokkaidō Food & Beer Culture
Hokkaidō is a fantastic place to eat, serving up specialities different from what you might find elsewhere in Japan – thanks to its bountiful land, ample coast and a climate that favours belly-warming dishes. Sapporo has the liveliest dining scene, while in coastal areas, fresh, seasonal seafood is tops.
Great For...
kru
yDon't Miss
The Tsugaru Strait is famous for its squid, which can be sampled in Hakodate's morning seafood market.
Eating Out
If you're generally an adventurous (or curious) eater, don't let the absence of an English menu put you off. Instead, tell the staff (or ideally the chef), 'omakase de onegaishimasu' (I'll leave it up to you).
Almost every city in Hokkaidō, large or small, has its own _ji-biru_ (地ビール; microbrew). Microbrewed beer makes a great companion for local dishes.
Ramen | MACKNIMAL/SHUTTERSTOCK ©
### Food
Want to make the most of your meals in Hokkaidō? Keep an eye out for the following regional delicacies.
#### Seafood
For many Japanese travellers, Hokkaidō is synonymous with crab. Winter is the season for _tarabagani_ (タラバガニ; king crab), _zuwaigani_ (ズワイガニ; snow crab) and _kegani_ (毛蟹; horse hair crab) from the frigid waters of the Sea of Okhotsk. Restaurants in Sapporo do lavish crab feasts but you don't have to spend heaps: _kani-jiru_ (かに汁) – miso soup made with crab – is a decadent treat that many _shokudō_ (inexpensive restaurants) will serve.
Summer, meanwhile, is _uni_ (うに; sea urchin) season. Fish markets, sushi restaurants and _shokudō_ serve _uni-don_ (うに丼), a bowl of rice topped with a mountain of fresh roe; you can also get it with other toppings, for example _kaisen-don_ (海鮮丼; mixed seafood on rice).
Spring is the start of squid season, which moves slowly north through autumn. Hakodate is particularly known for squid (it even has a squid festival!). Try _ika-sōmen_ (イカそうめん), which is raw squid sliced thin like noodles.
King crab | HELOVI/GETTY IMAGES ©
#### Ramen
In Sapporo the signature style is hearty miso-ramen (味噌ラーメン) and in Hakodate, it's _shio_ - _ramen_ (塩ラーメン), a light, salt-seasoned broth. In a nod to two of the prefecture's staple products, butter and corn, you'll often have the option to top off your ramen with either (or both).
#### Jingisukan
This dish of charcoal-grilled mutton is the unofficial symbol of Hokkaidō, a legacy of the island's short-lived, 19th-century sheep-rearing program. Its name – a Japanese rendering of Genghis Khan – comes from the unique shape of the cast-iron hotplate used to grill the meat, thought to resemble the warlord's helmet. The meat is grilled on the peak of the hotplate, allowing the juices to run down the sides to the onions and leeks sizzling on the brim. Jingisukan (ジンギスカン) is served all over the island and is best accompanied by copious amounts of beer.
### Beer
Sapporo Brewery, founded in 1876, was Japan's first brewery. Its first brewmaster, Nakagawa Seibei, trained in Germany, bringing home knowledge of the beverage, considered exotic in Japan. Today, Sapporo is the most popular Japanese beer outside of Japan – though much of what is sold overseas is also produced overseas. For die-hard beer fans, a trip to Hokkaidō means not only getting to sample Sapporo from the source, but also tasting Sapporo Classic, a beer in the Sapporo lineup sold only in Hokkaidō. You can try both at the original factory, now the Sapporo Beer Museum, or the newer factory, Hokkaidō Brewery.
Sapporo may be synonymous with beer, but beer in Hokkaidō is not synonymous with Sapporo. Almost every city has its own microbrew.
Note that breweries have become very strict about drinking and driving. If you'll be driving, you won't be allowed to taste at the end of a tour.
The legendary Sapporo Beer Museum (サッポロビール博物館; %011-748-1876; www.sapporoholdings.jp/english/guide/sapporo; N7E9 Higashi-ku; admission free; h10.30am-6.30pm; p; g88 to Sapporo Biiru-en, bTōhō line to Higashi-Kuyakusho-mae, exit 4) is in the original Sapporo Beer brewery – a pretty, ivy-covered brick building. There's no need to sign up for the tour; there are plenty of English explanations throughout about Japan's oldest beer. At the end there's a tasting salon (beers ¥200 to ¥300).
Afterwards, head next door to the Sapporo Biergarten for more beer and _jingisukan_.
From the subway it's a 10-minute walk; the bus stops right out front.
oLocal Knowledge
As Hokkaidō's capital city and transport hub, Sapporo gets all the seafood (such as crab), produce (eg potatoes and corn) and dairy products (such as butter and cream) for which Hokkaidō is famous.
Sapporo Beer Museum | TWOKIM IMAGES/SHUTTERSTOCK ©
#### Pubs & Breweries
The Sapporo Biergarten (サッポロビール園; %reservation hotline 0120-150-550; www.sapporo-bier-garten.jp; N7E9 Higashi-ku; h11.30am-10pm; g88 to Sapporo Biiru-en, bTōhō line to Higashi-Kuyakusho-mae, exit 4), next to the Sapporo Beer Museum, has no fewer than five beer halls, the best of which is Kessel Hall. Here you can tuck into _jingisukan_ washed down with all-you-can-drink draught beer direct from the factory (¥3900 per person). Reservations are highly recommended. From the subway it's a 10-minute walk; the bus stops right out front.
**Hokkaidō Brewery** (サッポロビール北海道工場; %011-748-1876; www.sapporoholdings.jp/english/guide/hokkaido; 542-1 Toiso, Eniwa; admission free; htours 10am-4pm Tue-Sun) is one of the current brewing and bottling facilities for Sapporo beer. Guided tours are led (in Japanese only) by very enthusiastic brand ambassadors past windows that allow visitors to peer into the high-tech factory. You need to make reservations by 5pm the day before (best get a Japanese-speaker to do this). Note that the facility is not in operation every day; when you reserve be sure to ask. Non-drivers get two free beers at the end!
Hokkaidō Brewery is a 40-minute train ride from Sapporo; take the JR Chitose line towards the airport and get off at JR Sapporo Beer Teien Station.
Hakodate Beer (はこだてビール; %0138-23-8000; www.hakodate-factory.com/beer; 5-22 Ōtemachi; pints ¥875, dishes ¥400-1700; h11am-3pm & 5-10pm Thu-Tue; jUōichiba-dōri) makes its beer right here on the bay with groundwater from Hakodate-yama. You can buy bottles or sample the brews on tap, served here along with typical Japanese-inflected pub food (like chips and fried squid). The Hakodate Weizen is its most popular brew.
Visit Otaru Sōko No 1 (map Google map; 小樽倉庫 No 1; %0134-21-2323; www.otarubeer.com/jp; 5-4 Minato-machi; beer ¥500-1300; h11am-11pm), a converted warehouse on the canal, to taste the local microbrew, Otaru Beer, on tap. Its pilsner and dunkel beers are the best, though even Germans give the thumbs up to the _Hefeweizen_.
TOP EXPERIENCE
# Kushiro-shitsugen National Park
Kushiro-shitsugen National Park (釧路湿原国立公園), at 269 sq km, is Japan's largest undeveloped wetland. It was designated a national park in 1987 to combat urban sprawl and protect the habitat of numerous species, chiefly the _tanchō-zuru_ (red-crowned white crane), the traditional symbol of both longevity and Japan.
Great For...
fgc
yDon't Miss
From JR Kushiro-shitsugen Station, walk uphill for 15 minutes to the Hosooka Marsh Viewpoint (細岡展望台) for great views.
Explore Ashore
A rental car or organised tour is the easiest way to get around the park. The JR Senmō main line train runs from Kushiro to Kushiro-shitsugen (¥360, 20 minutes), on the east side of the park. The bus from Kushiro Station to Akanko Onsen stops at the Japanese Crane Reserve (¥910, one hour) and Akan International Crane Centre (¥1450, 1¼ hours).
8Need to Know
Cranes can be seen year-round, but the best time to spot them is during winter when they gather at feeding spots.
Akan International Crane Centre 'GRUS' | T.IMAI/SHUTTERSTOCK ©
### Cranes
In the early 20th century, cranes were thought to be extinct due to overhunting and habitat destruction. In 1926, however, some 20 birds were discovered in the marshes here; with concentrated conservation efforts, they now number over 1000.
You can see a few cranes in breeding pens at the Akan International Crane Centre 'GRUS' (阿寒国際ツルセンター【グルス】; %0154-66-4011; www.aiccgrus.wixsite.com/aiccgrus; 23-40 Kami-Akan, Akan-chō; adult/child ¥470/240; h9am-5pm Apr-Oct, to 4.30pm Nov-Mar) but the real attraction is the Crane Observation Centre (8.30am to 4.30pm November to March), a winter feeding ground that is your best chance to see cranes outside of a bird park. Inside there are lots of interesting photos and some fun exhibits.
The bus from Kushiro Station to Akanko Onsen stops here (¥1450, 1¼ hours), or follow Rte 240 between Kushiro and Akanko.
Run by Kushiro Zoo, the Kushiro Japanese Crane Reserve (釧路市丹頂鶴自然公園, Tanchō-zuru Shizen-kōen; %0154-56-2219; www.kushiro-tancho.jp; 112 Tsuruoka; adult/child ¥470/110; h9am-6pm Apr-early Oct, 9am-4pm early Oct-Mar) has been instrumental in increasing the crane population. There are currently 14 _tanchō-zuru_ living here, though they are free to leave anytime they like (the fences are for people, not the birds).
The bus from Kushiro Station to Akanko Onsen stops here (¥910, one hour), or follow Rte 240 between Kushiro and Akanko.
### Kushiro-shitsugen Norokko Train
The Kushiro-shitsugen Norokko Train (釧路湿原ノロッコ号; hJun-Oct) is the best way to see the wetlands without a car: once or twice daily, a vintage train with large picture windows makes a slow journey from Kushiro via Kushiro-shitsugen (¥360) as far as Tōro Station (¥540). It's very popular so be sure to reserve a seat (plus ¥520). The tourist info booth at Kushiro Station can help.
In February, an old steam locomotive, the **Fuyu-shitsugen Norokko Train** , plies the same route; it doesn't run every day though and you'll need to book ahead.
Otaru
1Sights
1Otaru CanalB2
2Otaru Music Box MuseumC3
2Activities, Courses & Tours
3Otaru Canal CruiseB1
7Shopping
4Kitaichi SangōkanC3
5ShichifukuB2
5Eating
6Kita-no Aisukurīmu-ya-sanB2
7Otaru Sushi-kōB2
6Drinking & Nightlife
8Otaru Sōko No 1B2
## Otaru
1Sights & Activities
Otaru's sights are clustered around its canal. The area is easily walkable. A few of the museums and historical buildings require a bus trip or a short taxi ride.
**Mt Tengu** looms above the town. Take a bus (<http://tenguyama.ckk.chuo-bus.co.jp>; 20 minutes, two to three an hour) to the foot of the mountain; from here a scenic ropeway continues up the mountain. Views spread out across the city and the Sea of Japan. There's plenty to explore up here, including ski fields, a restaurant, chipmunk park and a scenic bobsleigh.
Otaru CanalCanal
(map Google map; 小樽運河)
Historic Otaru canal is lined with warehouses from the late 19th and early 20th centuries. This was a time when traditional Japanese architecture was infused with Western-style building techniques, so some of the buildings are quite interesting. Most have been restored and now house museums and cafes. Unfortunately the canal itself is half-buried by a major thoroughfare, despite the best lobbying efforts of local preservationists.
Otaru Music Box MuseumMuseum
(map Google map; 小樽オルゴール堂; %0134-22-1108; www.otaru-orgel.co.jp; 4-1 Sumiyoshi-chō; h9am-6pm, to 7pm mid-Jul–mid-Sep) F
This museum has clearly, uh, struck a chord: there are now five of them in town, with over 25,000 music boxes on display. Actually everything is for sale. While it's mostly new stuff for the tourist market, on the 2nd floor of this main museum (a charming red-brick structure from 1912) there are some truly impressive antiques.
Otaru Canal CruiseCruise
(map Google map; %0134-31-1733; www.otaru.cc; 5-4 Minato-machi; adult/child day cruise ¥1500/500, night cruise ¥1800/500; h9am-9pm)
The view of the canal is prettiest from this vantage point on the water. Cruises depart from Chūō-bashi and last 40 minutes; though recommended, no advance booking is necessary.
7Shopping
ShichifukuAntiques
(map Google map; 七福; %0134-22-2257; 1-16 Sakaimachi; h11am-5pm Wed-Mon)
This tiny cluttered shop has all sorts of fascinating stuff, from expensive ornamental hairpins to kitschy lamps to 100-year-old sake cups.
Kitaichi SangōkanGlass
(map Google map; 北一硝子三号館; %0134-33-1993; www.kitaichiglass.co.jp; 7-26 Sakaimachi; h8.45am-6pm)
Local glassmaker Kitaichi is a hit with tourists, with numerous shops clustered east of the canal, including this, the biggest one. Pretty souvenirs include etched crystal tumblers and delicate pendant lamps.
5Eating
Kita-no Aisukurīmu-ya-sanIce Cream¥
(map Google map; 北のアイスクリーム屋さん; %0134-23-8983; 1-2-18 Ironai; ice cream from ¥300; h9.30am-6pm)
Housed in a converted warehouse that was built in 1892, just back from the canal, this legendary Otaru ice-cream parlour scoops up some seriously 'special' ice cream flavours, such as wasabi, beer, and _natto_. The _ika-sumi_ (squid ink) is actually just mildly sweet. Melon, a more ice-cream friendly flavour, is divine.
Otaru Sushi-kōSushi¥¥
(map Google map; 小樽 すし耕; %0134-21-5678; www.denshiparts.co.jp/sushikou; 2-2-6 Ironai; sushi sets ¥2000-3800; hnoon-9pm Thu-Tue)
Come here for excellent sushi sets and _kaisen-don_ (bowls of rice topped with sashimi) featuring Hokkaidō specialities such as _sake_ (salmon), _ikura_ (salmon roe), _uni_ (sea urchin) and _kani_ (crab). Note that it often closes for a few hours in the afternoon and fills up fast at dinner, so reservations are recommended.
8INFORMATION
**Canal Plaza Tourist Information Centre** (運河プラザ観光案内所; %0134-33-1661; 2-1-20 Ironai; h9am-6pm) Housed in Otaru's oldest warehouse, with lots of pamphlets and brochures in English for Otaru and surrounding areas.
**Otaru Station Tourist Information Centre** (小樽駅観光案内所; %0134-29-1333; h9am-6pm) Pick up an English map at this kiosk in the station.
8GETTING AROUND
Kitarin (きたりん; %070-5605-2926; www.kitarin.info; 2-22 Inaho; 2hr ¥900; h9am-6.30pm Mon, Tue & Thu-Sat, from 6.30am Sun Apr-Nov, 9am-6.30pm Mon-Sat, from 6.30am Sun Jul-Sep) is a friendly bike rental spot near JR Otaru Station that has everything you'll need for a fun day touring around town.
## Sapporo
Japan's fifth-largest city, and the prefectural capital of Hokkaidō, Sapporo (札幌) is a dynamic urban centre that offers everything you'd want from a Japanese city: a thriving food scene, stylish cafes, neon-lit nightlife, shopping galore – and then some. Summer is the season for beer and food festivals. In February, despite the bitter cold, Sapporo's population literally doubles during the famous Snow Festival.
1Sights & Activities
**Hokkaidō Chūō Bus Tours** (<http://teikan.chuo-bus.co.jp/en>) runs half-day city tours (adult/child ¥2600/1300) that take in sights that are awkward to reach by public transport.
Moiwa-yama RopewayCable Car
(もいわ山ロープウェイ; %011-561-8177; <http://moiwa.sapporo-dc.co.jp>; 5-3-7 Fushimi; adult/child return ¥1700/850; h10.30am-10pm; jRōpuwei-iriguchi)
At 531m, Moiwa-yama has fantastic, panoramic views over the city. Part of the fun is getting there. First you take a gondola for five minutes, then switch to a cute little cable car for two more minutes. Free shuttle buses run to the ropeway from the Rōpuwei-iriguchi tram stop; otherwise it's a 10-minute walk.
Sapporo TeineSnow Sports
(サッポロテイネ; %011-223-5830, bus pack reservations 011-223-5901; www.sapporo-teine.com; day pass adult/child ¥5200/2600; h9am-5pm Nov-May, to 9pm Dec-Mar; c)
You can't beat Teine for convenience, as the slopes, which hosted skiing events for the 1972 Winter Olympics, lie quite literally on the edge of Sapporo. Teine has two zones: the lower, more beginner- and family-oriented **Olympia Zone** ; and the higher, more challenging **Highland Zone**. There are 15 runs and nine lifts. A variety of packages bring the price down.
Frequent trains on the JR Hakodate line run between Sapporo and Teine (¥260, 10 minutes). From JR Teine Station, shuttle buses run to both zones.
From Sapporo: Jōzankei
Jōzankei (定山渓) sits along the Toyohira-gawa, deep in a gorge. It's the closest major onsen town to Sapporo and an easy escape for those after some R&R. The resort is especially pretty (and popular) in autumn, when the leaves change colour – a sight that can be viewed from many an outdoor bath. Five buses run between Sapporo Eki-mae Bus Terminal and Jōzankei daily (¥770, one hour).
Most hotels and ryokan allow nonguests to use their onsen baths for a fee (¥500 to ¥1500). There's also **Hōheikyō** (豊平峡; %011-598-2410; www.hoheikyo.co.jp; 608 Jōzankei; adult/child ¥1000/500; h10am-10.30pm) further up the road, often voted as one of Hokkaidō's best onsen. It's home to Hokkaidō's largest outdoor bath, and is a stunner, set above town on the gorge's forested slope. The whole rambling structure is shack-like, which adds to the appeal of having stumbled upon something great. The door curtains indicating which baths are for men and which are for women are swapped daily. These waters are purportedly ideal for improving women's skin.
Oddly enough, there's an Indian restaurant on the ground floor.
SEAN PAVONE/SHUTTERSTOCK ©
5Eating
Menya SaimiRamen¥
(麺屋彩未; %011-820-6511; Misono 10-jō Toyohira-ku; ramen from ¥750; h11am-3.15pm & 5-7.30pm Tue-Sun; p; bTōhō line to Misono, exit 1)
Sapporo takes its ramen very seriously and Saimi is oft-voted the best ramen shop in the city (and sometimes the country) – and it's not overrated. You will have to queue, which is annoying, but you will be rewarded with a mind-blowing meal for the same price as a convenience store _bentō_. Get the _miso ramen_.
Ganso Ramen YokochōRamen¥
(元祖さっぽろラーメン横丁; www.ganso-yokocho.com; S5W3 Chūō-ku; ramen from ¥800; h11am-3am; bNamboku line to Susukino, exit 3)
This famous alleyway in the Susukino entertainment district is crammed with ramen shops, including branches of several venerable Hokkaidō shops. It's been around since 1952, and is keen to distinguish itself from all the 'imposter' ramen alleys.
It can be a little tricky to find (old as it is, it doesn't glow as bright as everything else in Susukino), but all locals know where it is. Look for 'Ganso' as there are other ramen alleys nearby. Hours for individual shops vary.
Milk MuraIce Cream¥
(ミルク村; %011-219-6455; S4W3-7-1; per serving ¥1300; hnoon-11pm Tue-Sun; bNamboku line to Susukino, exit 1)
A grown-up twist on the classic ice-cream parlour, Milk Mura serves mugs of soft-serve ice cream accompanied by three tiny chalices of your choice of liquors – and there are dozens to choose from. Bottles, some ancient-looking, cover the counters, fairy lights twinkle and chansons play in the background. Bonus: one free refill of ice cream.
8GETTING THERE & AWAY
Twice-hourly _kaisoku_ (rapid) trains on the JR Hakodate line connect Otaru and Sapporo (¥1160, 30 minutes).
## Hakodate
Built on a narrow strip of land between Hakodate Harbour to the west and the Tsugaru Strait to the east, Hakodate (函館) is the southern gateway to the island of Hokkaidō. Under the Kanagawa Treaty of 1854, the city was one of the first ports to open up to international trade, and as such hosted a small foreign community. That influence can still be seen in the Motomachi district, a steep hillside that's sprinkled with European buildings and churches; the waterfront lined with red-brick warehouses; and in the nostalgic streetcar that still makes the rounds of the city.
1Sights
Hakodate-yamaMountain
(函館山)
Mention you've been to Hakodate and every Japanese person you know will ask if you took in the night view from atop Hakodate-yama (334m) – it's that famous! If your cruise schedule allows it, you want to get up here for sunset or after dark: what's striking is seeing the lit-up peninsula (which locals say is shaped like Hokkaidō itself) against the pitch-black waters. In addition to the viewing platform and parking area, those who hunt will find the remains of an old fort behind the buildings, with interesting foundations intact.
There are a few ways to get here: by ropeway (函館山ロープウェイ; %0138-23-3105; www.334.co.jp; 19-7 Motomachi; adult/child return ¥1280/780; h10am-10pm 25 Apr-15 Oct, 10am-9pm 16 Oct-24 Apr), bus, car or foot. Buses for the ropeway (¥240, 10 minutes) and the summit (¥400, 30 minutes, mid-April to mid-November) depart from bus stop 4 at JR Hakodate Station. You can also walk to the ropeway in 10 minutes from the Jūjigai tram stop; alternatively you can hike up one of several trails (all take about an hour) between May and late October. Note that the road to the summit is often closed to private vehicles after sunset because it gets too crowded.
Hakodate | SEAN PAVONE/SHUTTERSTOCK ©
Hakodate Morning MarketMarket
(函館朝市, Hakodate Asa-ichi; www.hakodate-asaichi.com; 9-19 Wakamatsu-chō; h5am-noon; dJR Hakodate) F
With crabs grilling over hot coals, freshly caught squid packed tightly in ice-stuffed styrofoam and the sing-song call of vendors, Hakodate Morning Market does a fantastic impression of an old-time seafood market – though the visitors today are tourists not wholesale buyers. (The commercial market that was here originally has since moved to a bigger space.)
5Eating & Drinking
For many visitors, eating is the whole reason to come to Hakodate. Squid, caught in the Tsugaru Strait, is the city's speciality. Hakodate is also known for its _shio-ramen_ (塩ラーメン; ramen in a light, salt-flavoured broth).
Kikuyo ShokudoSeafood¥
(きくよ食堂; www.hakodate-kikuyo.com/asaichi; Hakodate Morning Market; mains from ¥1080; h5am-2pm; dJR Hakodate)
Inside Hakodate Morning Market, Kikuyo Shokudo got its start in the 1950s as a counter joint to feed market workers and is now one of the top reasons to come to Hakodate. The speciality here is the _Hakodate tomoe-don_ (函館巴丼; ¥1780), rice topped with raw _uni_ (sea urchin), _ikura_ (salmon roe) and _hotate_ (scallops). There's a picture menu.
You can also custom-make _kaisen-don_ (raw seafood over rice) from the list of toppings or sample another Hakodate speciality: _ika-sōmen_ (raw squid sliced very thinly like noodles; ¥1150).
Tea Shop YūhiTeahouse
(ティーショップ夕日; %0138-85-8824; 25-18 Funami-chō; tea sets from ¥600; h10am-dusk Fri-Tue mid-Mar–Nov; gFunami-chō Kōryū-ji mae, jHakodate Dokku-mae)
Filling the halls of a wooden building from 1885 (actually the old Hakodate Quarantine Office) is this magical teahouse overlooking the water. It's lit only by natural light so closes after the sun sets. In the meantime, you can while away the afternoon refilling your tiny pot of single-origin green tea, and nibbling on the _wagashi_ (Japanese sweets) and pickles that accompany it.
Ōnuma Kōen
Sitting inside Ōnuma Quasi-National Park (大沼国定公園), Ōnuma Kōen (大沼公園), 25km north of Hakodate, is a popular getaway, especially for families. Sitting beneath the impressive volcano, Komaga-take (駒ケ岳; 1131m), is the lake Ōnuma (大沼), punctuated by tiny islands. It's a pretty diversion if you're craving some fresh air.
A series of linked walking paths around Ōnuma's small islands starts not far from the train station; pick up a map at the tourist information centre (大沼観光案内所; %0138-67-2170; www.onuma-guide.com; h8.30am-5.30pm; W). Rental bicycles (¥500/1000 per hour/day), which you can use to ride the 14km perimeter road around the lake, are available outside JR Ōnuma Kōen Station.
CHONGBUM THOMAS PARK/SHUTTERSTOCK ©
8INFORMATION
**Hakodate Tourist Information Centre** (函館市観光案内所; %0138-23-5440; h9am-7pm Apr-Oct, 9am-5pm Nov-Mar) is inside JR Hakodate Station, and offers English brochures and maps.
8GETTING AROUND
Single-trip fares on trams and buses generally cost around ¥250. One-day transport passes can be purchased at the tourist information centre or on-board.
You can rent bikes from **Hakorin** (はこりん; %0138-22-9700; 4-19 Suehiro-chō; per day ¥1600; h9am-6.30pm), which can be found at the community center outside JR Hakodate Station.
## Kushiro
1Sights
Just 600m south of the main train station, **Kushiro Children's Museum Kodomo Yugakukan** (<http://kodomoyugakukan.jp/>; hclosed Mon) has science displays, a planetarium, a big indoor sandpit and plenty more besides.
Washō MarketMarket
(和商市場, Washō Ichiba; %0154-22-3226; www.washoichiba.com; 13-25 Kurogane-chō; mains ¥1000-2000; h8am-5pm Mon-Sat, to 4pm Sun Apr-Dec, closed Sun Jan-Mar)
This fish market is as much a sightseeing spot as a place to eat. The speciality here is called _katte-don_ (勝手丼) – literally 'rice bowl as you like it'. First buy a bowl of rice from one of the vendors on the perimeter then head to a fish monger and have them top it off with your choice of raw fish. If you want to get even more in the mood, rent a kimono (¥1000) and walk around in style.
It's a couple of minutes' walk south of JR Kushiro Station.
5Eating & Drinking
As you'd expect from a port city, seafood is Kushiro's speciality. Look for _robatayaki (_ seafood and vegetables grilled over a charcoal fire) and _katte-don_.
There are cafes and bakeries in the train station, but few options in the streets nearby.
Kushiro Fisherman's Wharf MOOMall
(<http://www.moo946.com>)
A short walk or shuttle ride from the town's ports is this large mall packed with shops, restaurants and bars. In the warmer months, _robata_ seafood grills are set up along the riverside here. During the colder months, the gardens in EGG, next door, offer indoor greenery.
Kushiro | DAVORLOVINCIC/GETTY IMAGES ©
8INFORMATION
The Kushiro City Tourist Information Center ( h9am-5.30pm) at JR Kushiro Station provides info on Kushiro and the surrounding area, and can help with sightseeing tours.
# OKINAWA-HONTŌ
#### Tsuboya Pottery Street
#### WWII Memorial Sites
#### Naha
#
Okinawa-hontō at a Glance
Okinawa-hontō is the largest island in the Nansei-shotō (Southwest Islands) and its capital, Naha (那覇), is the busiest city. If Tokyo were a pie, and you cut a tiny slice, dropped it on an island in the Pacific, and served it with a dollop of Florida, Naha might be what you'd get. The city plays host to an interesting mix of young Japanese holidaymakers, American GIs looking for off-base fun and a growing number of foreign tourists. The action centres on Kokusai-dōri (International Blvd), and overlooking it all from a safe distance to the east is Shuri-jō, a wonderfully restored castle that was once the home of royalty.
Kokusai-dōri, Naha | SUCHART BOONYAVECH/SHUTTERSTOCK ©
With a Day in Port
Wander along Tsuboya Pottery Street, admiring the handcrafted pottery and local houses, then gain insight into Okinawa's wartime past at Okinawa Prefectural Peace Memorial Museum. Don't miss sampling distinctive Okinawan specialities at Daichi Makishi Kōsetsu Ichiba.
Best Places for...
**DIY crafting** Naha City Traditional Arts & Crafts Center
**People-watching** Kokusai-dōri and surrounding arcades
**Shopping** American Village
**Castle reconstructions** Shuri-jō
Getting from the Port
Most cruise arrivals have a shuttle service to town. Otherwise it's a 1.5km walk or taxi ride to Naha town.
Fast Facts
**Money** There's currency exchange at the dock and ATMs in town.
Tourist information English-language information services are set up to greet cruise ships, and there's a tourist office in Naha.
**Wi-fi** There is free wi-fi at the port and at a number of hotspots in town.
TOP EXPERIENCE
# Tsuboya Pottery Street
One of the best parts of Naha is this neighbourhood, a centre of ceramic production from 1682, when Ryūkyū kilns were consolidated here by royal decree. Even if you're not looking for pottery souvenirs, the area is well worth a wander.
Great For...
chg
yDon't Miss
The lanes off the main street contain some classic crumbling, old Okinawan houses.
Explore Ashore
Take the shuttle from the port to town, then take the monorail to Makishi Station. From here it's a 600m walk southwest to Tsuboya Pottery Street. To get here from Kokusai-dōri, walk south through the entirety of Heiwa-dōri arcade (about 350m).
8Need to Know
When the wandering and shopping get too much, there's no shortage of cafes in the area, many of them serving up your order on locally made pottery.
ASIA/ALAMY STOCK PHOTO ©
Slender, cobblestone Tsuboya Pottery Street is lined with pottery workshops, and with shops that sell the resulting products. You can watch the craftspeople at work, see the kilns used, and take a short class in pottery making.
Most shops along this old-timey street sell all the popular Okinawan ceramics, including _shiisā_ (lion-dog roof guardians) and containers for serving _awamori_ (Okinawan liquor distilled from rice), the local firewater.
As you wander around town, here and elsewhere, keep an eye out for _shiisā_ on the rooftops, as well as traditional red earthenware roof tiles. There's plenty of variety available here, from antique wares to freshly made pottery in traditional styles, to some modern new designs. A handcrafted teapot, pendant necklace or hanging _shiisā_ makes for a wonderful souvenir, unique to Okinawa.
### Tsuboya Pottery Museum
This excellent museum (壺屋焼物博物館; %098-862-3761; www.edu.city.naha.okinawa.jp/tsuboya; 1-9-32 Tsuboya; adult/concession ¥350/280; h10am-6pm Tue-Sun) houses some fine examples of traditional Okinawan pottery. Here you can also inspect potters' wheels and _arayachi_ (unglazed) and _jōyachi_ (glazed) pieces. There's even a cross-section of a _nobori-gama_ (kiln built on a slope) set in its original location, where crushed pieces of pottery that date back to the 17th century lie embedded in earth.
### Ryūkyū Ryōri Nuchigafū
For a memorable, elegant meal in Naha, don't pass up a meal at the hilltop Nuchigafū (琉球料理ぬちがふう; %098-861-2952; www.facebook.com/RyukyuCuisine.Nuchigafu; 1-28-3 Tsuboya; set meals from ¥3000; h11.30am-5pm & 5.30-10pm Wed-Mon), off the southern end of Tsuboya Pottery Street. The building was formerly a lovely Okinawan teahouse, and before that a historic Ryūkyūan residence. Children aged 11 and older are welcome.
### What's Nearby?
Right on Kokusai-dōri, Naha City Traditional Arts & Crafts Center (map Google map; 那覇市伝統工芸館; %098-868-7866; www.kogeikan.jp; 2nd fl, 3-2-10 Makishi; ¥350; h9am-6pm) houses a notable collection of traditional Okinawan crafts by masters of the media. You can also try your hand at Ryūkyūan glassblowing, weaving, _BINGATA_ (painting on fabric) and pottery-making in workshops (¥1500 to ¥3000), and make your own souvenir from Okinawa.
_Shiisā_ (lion-dog guardian) | VASSAMON ANANSUKKASEM/SHUTTERSTOCK ©
TOP EXPERIENCE
# WWII Memorial Sites
Okinawa's most important war memorials are clustered in the Peace Memorial Park, located in the city of Itoman on the southern coast of the island. A visit to the area is highly recommended for those with an interest in wartime history or seeking a deeper understanding of the modern Okinawan identity.
Great For...
vcg
yDon't Miss
Take a break from the museums to admire the coastal scenery and ocean views.
Explore Ashore
Southern Okinawa-hontō is conveniently served by regular buses from Naha. Renting a car or hiring a taxi, while expensive, will give you more freedom to explore the area's diverse attractions. A one-way taxi to the Peace Memorial Park is approximately ¥3000 to ¥3500.
8Need to Know
Most points of interest in this area either have restaurants on site, or have eateries nearby that are geared towards tourist traffic.
Peace Memorial Park | HELLORF ZCOOL/SHUTTERSTOCK ©
During the closing days of the Battle of Okinawa, the southern part of Okinawa-hontō served as one of the last holdouts of the Japanese military and an evacuation point for wounded Japanese soldiers. A number of sites memorialise this history.
### Peace Memorial Park
Housing Okinawa's most important war memorials, the Peace Memorial Park (平和祈念公園; 550 Mabuni; hdawn-dusk) occupies an appropriately peaceful coastal location in the southern city of Itoman.
To reach the park, take bus 89 from Naha Bus Terminal to the Itoman Bus Terminal (¥580, one hour, every 20 minutes), then transfer to bus 82, and get off at Heiwa Kinen-dō Iriguchi (¥470, 30 minutes, hourly).
Cornerstone of Peace | HARISMOYO/SHUTTERSTOCK ©
### Okinawa Prefectural Peace Memorial Museum
This museum (沖縄県平和祈念資料館; %098-997-3844; www.peace-museum.pref.okinawa.jp; 614-1 Aza Mabuni, Itoman; ¥300; h9am-5pm), the centrepiece of the Peace Memorial Park, focuses on the suffering of the Okinawan people during the island's invasion and under the subsequent American Occupation. While some material may stir debate, the museum's mission is to serve as a reminder of the horrors of war, so that such suffering is not repeated. There is a free English-language audio guide available, providing great detail on the 2nd-floor exhibit.
Outside is the Cornerstone of Peace (平和の礎; hdawn-dusk) F, inscribed with the names of everyone who died in the Battle of Okinawa.
### What's Nearby?
Located above a cave that served as an emergency field hospital during the closing days of the Battle of Okinawa, the Himeyuri Peace Museum (ひめゆり平和祈念資料館; %098-997-2100; www.himeyuri.or.jp; 671-1 Ihara; ¥310; h9am-5.30pm) is a haunting monument whose mission is to promote peace, driven by survivors and alumnae of the school. Here 240 female high-school students were pressed into service as nurses for Japanese military wounded.
As American forces closed in, the students were summarily dismissed and, thus abandoned, most perished. Excellent, comprehensive interpretive signage is provided in English. Bus 82 stops outside.
Naha
1Sights
1Daichi Makishi Kōsetsu IchibaC3
2Naha City Traditional Arts & Crafts CenterC3
3Okinawa Prefectural Museum & Art MuseumD1
4Tsuboya Pottery MuseumC3
5Tsuboya Pottery StreetC3
7Shopping
6San-A Naha Main PlaceD1
5Eating
7Ryūkyū Ryōri NuchigafūC3
8YūnangiB3
6Drinking & Nightlife
9Helios PubB3
8Information
Naha City Tourist Information Office(see 2)
## Naha
1Sights
Okinawa Prefectural Museum & Art MuseumMuseum
(map Google map; 沖縄県立博物館・美術館; %098-941-8200; www.museums.pref.okinawa.jp; Omoromachi 3-1-1; prefectural/art museum ¥410/310; h9am-6pm Tue-Thu & Sun, to 8pm Fri & Sat)
Opened in 2007, this museum of Okinawa's history, culture and natural history is easily one of the best museums in Japan. Displays are well laid out, attractively presented and easy to understand, with excellent bilingual interpretive signage. The art-museum section holds interesting special exhibits (admission prices vary) with an emphasis on local artists. It's about 15 minutes' walk northwest of the Omoromachi monorail station.
Shuri-jōCastle
(首里城; %098-886-2020; www.oki-park.jp; 1-2 Kinjō-chō, Shuri; ¥820, with 1- or 2-day monorail pass discounted to ¥660; h8.30am-7pm Apr-Jun & Oct-Nov, to 8pm Jul-Sep, to 6pm Dec-Mar, closed 1st Wed & Thu Jul)
This reconstructed castle was originally built in the 14th century and served as the administrative centre and royal residence of the Ryūkyū kingdom until the 19th century. Enter through the **Kankai-mon** (歓会門) and go up to the **Hōshin-mon** (奉神門), which forms the entryway to the inner sanctum of the castle. Visitors can enter the impressive **Seiden** (正殿), which has exhibits on the castle and the Okinawan royals.
Shuri-jō | FOTOSEARCH/GETTY IMAGES ©
Daichi Makishi Kōsetsu IchibaMarket
(map Google map; 第一牧志公設市場; 2-10-1 Matsuo; h8am-8pm, restaurants 10am-7pm)
A great place to sample everyday Okinawan eats is at one of the 2nd-floor eateries in this covered food market just off Ichibahon-dōri, about 200m south of Kokusai-dōri. The colourful variety of fish and produce on offer here is amazing.
Shikina-enGardens
(識名園; %098-855-5936; 421-7 Aza Māji; ¥400; h9am-6pm Thu-Tue Apr-Sep, to 5.30pm Oct-Mar)
Around 4km east of the city centre is a Chinese-style garden containing stone bridges, a viewing pavilion and a villa that belonged to the Ryūkyū royal family. Despite its flawless appearance, everything here was painstakingly rebuilt after WWII. To reach the garden, take bus 2, 3 or 5 to the Shikinaen-mae stop (¥230, 20 minutes).
Former Japanese Navy Underground HeadquartersMuseum
(旧海軍司令部壕; Kyūkaigun Shireibu-gō; %098-850-4055; <http://kaigungou.ocvb.or.jp>; 236 Tomishiro, Tomigusuku; ¥440; h8.30am-5pm Oct-Jun, to 5.30pm Jul-Sep)
Directly south of Naha in Kaigungo-kōen is the Former Japanese Navy Underground Headquarters, where 4000 men committed suicide or were killed as the Battle of Okinawa drew to its bloody conclusion. Only 250m of the tunnels are open, but you can wander through the maze of corridors, see the commander's final words on the wall of his room, and inspect the holes and scars in other walls from the grenade blasts that killed many of the men.
To reach the site, take bus 55 or 98 from Naha Bus Terminal to the Uebaru Danchi-mae stop (¥220, 10 minutes, several hourly). From there it's a five-minute walk – follow the English signs (the entrance is near the top of the hill).
7Shopping
American VillageConcept Store
( %098-926-5678; www.okinawa-americanvillage.com; 15-69 Mihama, Chatan-cho)
This amusement-park-esque, American-themed shopping mall is as kitsch as they come, but closer exploration will provide a fascinating glimpse into modern Okinawan life, where off-duty GIs shop for memories of home alongside Chinese tourists on the hunt for Americana. There are some excellent vintage-clothing stores, a bunch of fun dining options and a big-ass Ferris wheel to boot.
Take the 20, 28 or 29 bus from Naha to the Kuwae stop (40 minutes, ¥720).
American Village | RICHIE CHAN/SHUTTERSTOCK ©
San-A Naha Main PlaceShopping Centre
(map Google map; サンエー那覇メインプレイス; %098-951-3300; www.san-a.co.jp/nahamainplace; 4-4-9 Omoromachi; h9am-11pm)
Naha's busiest downtown mall is always a hive of activity for its many duty-free stores (including Tokyū Hands – great for, well, anything you can think of), cinema complex and array of enticing eateries where you should expect to queue, any time of day.
5Eating & Drinking
AshibiunāOkinawan¥
(あしびうなぁ; %098-884-0035; www.ryoji-family.co.jp/ryukyusabo.html; 2-13 Shuri Tonokura-chō; lunch sets ¥800-1280; h11.30am-3pm & 5.30pm-midnight)
Perfect for lunch after touring Shuri-jō, Ashibiunā has a traditional ambience and picturesque garden. Set meals feature local specialities such as _gōyā champurū_ , _okinawa-soba_ and _ikasumi yaki-soba_. On the road leading away from Shuri-jō, Ashibiunā is located on the right, just before the intersection to the main road.
YūnangiOkinawan¥¥
(map Google map; ゆうなんぎい; %098-867-3765; 3-3-3 Kumoji; dishes ¥750-1400; hnoon-3pm & 5.30-10.30pm Mon-Sat)
You'll be lucky to get a seat here, but if you do, you'll be treated to some of the best Okinawan food around, served in traditional but bustling surroundings. Try the _okinawa-soba_ set (¥1400), or choose from the picture menu. It's on a side street off Kokusai-dōri – look for the wooden sign with white lettering above the doorway.
Helios PubPub
(map Google map; ヘリオスパブ; %098-863-7227; www.helios-food-service.co.jp; 1-2-25 Makishi; h11.30am-11pm Sun-Thu, to midnight Fri & Sat)
Craft-beer lovers who tire of Orion can perk up bored palates with a sample flight of four house brews (¥900) and pints for ¥525. Edibles cover the pub-menu gamut, all very reasonably priced.
Kokusai-dōri
The city's main artery is **Kokusai-dōri** (国際通り), a riot of neon, noise, souvenir shops, bustling restaurants and Japanese young things out strutting their stuff. It's a festival of tat and tackiness, but it's good fun if you're in the mood for it.
Many people prefer the atmosphere of the three covered shopping arcades that run south off Kokusai-dōri: **Ichibahon-dōri** (市場本道り), **Mutsumibashi-dōri** (むつみ橋通り) and **Heiwa-dōri** (平和通り).
PAWINP/GETTY IMAGES ©
8INFORMATION
**Naha CityTourist Information Office** (那覇市観光案内所; %098-868-4887; www.visitokinawa.jp; 3-2-10 Makishi; h9am-8pm) Located in the Tenbus Building, it provides free maps and information.
8GETTING AROUND
The Yui Rail monorail runs from Naha International Airport in the south to Shuri in the north. Prices range from ¥200 to ¥290; a one-day pass costs ¥700. Kenchō-mae Station sits at the western end of Kokusai-dōri, while Makishi Station is at its eastern end.
Driving here can be quite the nightmare: despite its size, Naha's traffic jams make for slow going.
# KEELUNG & TAIPEI
#### Chiang Kai-shek Memorial Hall
#### Taipei
#### Jiufen & Jinguashi
#
Keelung & Taipei at a Glance
Keelung, home to the famous Miaokou Night Market, is perfectly placed for forays to Taipei, and to the impressive natural and historic sights of Taiwan's northeast coast. Taipei is a tough little city whose beauty lies in its blend of Chinese culture with a curious fusion of Japanese, Southeast Asian and American influences. Taoist temples buzz with the prayers of the hopeful, the wooden boards of Japanese-era mansions creak under the feet of visitors and, best of all, nature is knitted into the city's very fabric.
Clinging to hillsides overlooking the sea, the former mining towns of Jiufen and Jinguashi serve up a captivating mix of yesteryear charm, industrial heritage, whimsical teahouses and enough snacks to feed half the country.
Taipei skyline | RICHIE CHAN/SHUTTERSTOCK ©
With a Day in Port
In Taipei, follow Taiwan's path to democracy at Chiang Kai-shek Memorial Hall, then glimpse some of the treasures of the National Palace Museum, if it's open – fingers crossed! Or, tap into the richness of Jiufen and Jinguashi's mining heritage, followed by food, drink, entertainment and local life at Keelung's Miaokou Night Market, right by the cruise port.
Best Places for...
**Signature dishes** Yongkang Beef Noodles
**A city stroll** Dihua Street
**Small wonders** Miniatures Museum of Taiwan
**Souvenirs** Lin Hua Tai Tea Company and Lao Mian Cheng Lantern Shop
**Tea and coffee** Jiufen Teahouse and Lugou Cafe
Getting from the Port
A 700m (10-minute) walk from Keelung port brings you to Keelung Station, from where regular trains depart for Taipei Main Station (NT$65, 50 minutes).
Bus 788, departing just before Keelung Station, runs to Jiufen and Jinguashi (NT$30, 45 minutes).
Fast Facts
**Currency** New Taiwanese dollar (NT$)
**Language** Mandarin, Taiwanese
**Money** There are ATMs and currency exchange at Keelung port. ATMs almost always have the option of choosing an English-language service.
Tourist information The Keelung Visitor Centre is a short walk from the port, on the right-hand side of Keelung Station. Jiufen also has an office.
**Wi-fi** Free at Keelung port, and in Taipei at many cafes, restaurants and malls. The government's free service, iTaiwan (itaiwan.gov.tw/en), has hotspots at MRT stations and major tourist sites.
TOP EXPERIENCE
# Chiang Kai-shek Memorial Hall
This vast public square is an imposing sight, flanked on three sides by neoclassical structures – Chiang Kai-shek's memorial in front and the National Theatre and Concert Hall on either side. It's a must-see for all visitors to Taiwan, not only for the spectacle itself but because it opens a window to the political history of Taiwan.
Great For...
vaA
yDon't Miss
The changing of the guards – every hour, on the hour.
Explore Ashore
Take the train from Keelung port to Taipei Main Station, then the MRT to Chiang Kai-shek Memorial Hall station.
8Need to Know
中正紀念堂; Zhōngzhèng Jìniàn Táng; %02-2343 1100; www.cksmh.gov.tw; 21 Zhongshan S Rd; 中山南路21號; h9am-6pm; p; mChiang Kai-shek Memorial Hall
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ASIASTOCK/SHUTTERSTOCK ©
This grandiose monument to authoritarian leader Chiang Kai-shek is a popular attraction, and rightly so. It is a sobering feeling standing in the massive courtyard. Chiang's blue-roofed hall is a prime example of the neoclassical style, favoured by Chiang Kai-shek as a counterpoint to the Cultural Revolution's destruction of real classical culture in China.
Entrance to the main hall is made via a series of 89 steps (the age of Chiang when he died). Inside the cavernous hall is an artefact museum with Chiang's two Cadillacs, various documents and articles from daily life. The hourly changing of the honour guard is probably the most popular sight with most visitors. Note the colour of the guards' uniforms, which change every three months: blue is the air force, green is the land army and white is the navy.
At night the locals take over and the whole area really comes to life. Joggers lap the square, teenagers practise dance steps and the two halls buzz with activity as people arrive to watch a concert. In 2007 the surrounding park was renamed 'Liberty Square' in honour of Taiwan's long road to democracy. Many democracy protests in the 1980s took place here, and it is fitting that the public has changed the nature of this space.
For a time it was conceivable that the memorial itself would be renamed and the Chiang sculpture removed. That didn't happen, and the reasons (which will vary depending on who you ask) pretty much summarise where modern Taiwan is at, both politically and socially.
### What's Nearby?
The long-running and often hectic Jinfeng Braised Meat Rice (map Google map; 金峰滷肉飯; Jīnfēng Lǔròu Fàn; 10 Roosevelt Rd; 羅斯福路10號; dishes NT$30-60; h8am-1am; mChiang Kai-shek Memorial Hall) serves Taiwanese comfort food quickly and cheaply, without fuss or atmosphere. Try the _lǔròu fàn_ (滷肉飯; rice and meat strips), _kōng ròu fàn_ (焢肉飯; slow-braised pork belly and rice) or _fènglí kǔguā jī_ (鳳梨苦瓜雞; bitter melon pineapple chicken).
The pearl milk tea (NT$85) at **Chun Shui Tang** (春水堂; Chūnshuǐ Táng; www.chunshuitang.com.tw; ground fl, National Concert Hall; h11.30am-8.50pm; mChiang Kai-shek Memorial Hall) is supposed to be the best in the city – pink, frothy and creamy with smaller, firmer pearls and only lightly sweetened. There are branches across the city, but this one on the ground floor of the National Concert Hall is one of the nicest. Traditional light noodle dishes and Chinese desserts are also available.
Taipei
1Sights
1Bao'an TempleB1
2Chiang Kai-shek Memorial HallB3
3Dihua StreetA2
4Miniatures Museum of TaiwanC2
5Taipei 101D3
7Shopping
6Lao Mian Cheng Lantern ShopA2
7Lin Hua Tai Tea CompanyB2
8National Cultural and Creative Gift CentreB3
5Eating
9Addiction Aquatic DevelopmentC1
10Jinfeng Braised Meat RiceB3
11Yongkang Beef NoodlesB3
6Drinking & Nightlife
12Chun Shui TangB3
13Lugou CafeA2
## Taipei
1Sights
National Palace MuseumMuseum
(故宮博物院; Gùgōng Bówùyuàn; %02-6610 3600; www.npm.gov.tw/en; 221 Zhishan Rd, Sec 2; 至善路二段221號; NT$350; h8.30am-6.30pm Sun-Thu, to 9pm Fri & Sat; p; gR30)
Home to the world's largest and arguably finest collection of Chinese art, this vast museum covers treasures in painting, calligraphy, statuary, bronzes, lacquerware, ceramics, jade and religious objects. The historical range is truly outstanding.
There are controversial plans to partially or even wholly close the museum in 2020 for three years while the building is renovated, with exhibits to move to the Southern Branch in Chiayi in the meantime. Check for the latest before visiting.
Taipei 101Tower
(map Google map; 台北101; Táiběi Yīlíngyī; %02-8101 8800; www.taipei-101.com.tw; adult/child NT$600/540; h9am-10pm, last ticket sale 9.15pm; p; mTaipei 101)
Towering above the city like the gigantic bamboo stalk it was designed to resemble, 508m-tall Taipei 101 is impossible to miss. The observation deck on the 89th floor (head to the 5th floor to buy tickets and ascend) offers 360-degree views of the city. The tower itself has several floors of luxury brands and a very busy and decent food court in the basement.
The 4th-floor atrium is full of light and space and offers a nice break from the sightseeing hordes. Budget around an hour (or two if you plan to eat).
A money changer (the only non-Asian currencies exchanged are US dollars and euros) and a helpful information desk are in the basement.
Dihua StreetHistoric Site
(map Google map; 迪化街; Díhuà Jiē; mBeimen, mDaqiaotou)
This former 'Centre Street' has long been known for its Chinese medicine shops, fabric market and lively Lunar New Year sundry market. In recent years it has attracted numerous restoration and cultural projects and it's now a magnet for young entrepreneurs eager to breathe new life into the neighbourhood with cafes, restaurants, art studios and antique shops.
Thankfully, this gentrification hasn't squashed the original atmosphere – fancy ceramic shops sit side-by-side with long-term tenants selling sacks of dried mushrooms and agricultural produce.
Bao'an TempleTaoist Temple
(map Google map; 保安宮; Bǎoān Gōng; www.baoan.org.tw/english; 61 Hami St; 哈密街61號; h7am-10pm; mYuanshan) F
Recipient of a Unesco Asia-Pacific Heritage Award for both its restoration and its revival of temple rites and festivities, the Bao'an Temple is a must-visit when in Taipei. This exquisite structure is loaded with prime examples of the traditional decorative arts, and the yearly folk arts festival is a showcase of traditional performance arts.
Miniatures Museum of TaiwanMuseum
(map Google map; 袖珍博物館; Xiùzhēn Bówùguǎn; %02-2515 0583; www.mmot.com.tw; 96 Jianguo N Rd, Sec 1; 建國北路一段96號; adult/child NT$200/160; h10am-6pm Tue-Sun; c; mSongjiang Nanjing)
Whimsical, wondrous and fantastically detailed are the creative works at this private museum located in the basement of a nondescript tower block. On display are dozens of doll-house-sized replications of Western houses, castles, chalets, palaces and villages, as well as scenes from classic children's stories such as _Pinocchio_ and _Alice in Wonderland._ If you're coming by MRT, take exit 5.
7Shopping
With its endless markets, back-alley emporiums and glittering shopping malls, Taipei offers the complete gamut of shopping experiences. Taiwan has a rich tradition of wood, ceramic, metal and glass production and young designers are now pushing the envelope with everything from clothing to furniture. Good gift ideas are packaged organic teas, ceramic decorative tiles and the iconic pineapple cake.
Lin Hua Tai Tea CompanyTea
(map Google map; 林華泰茶行; Línhuátài Cháháng; %02-2557 3506; 193 Chongqing N Rd, Sec 2; 重慶北路二段193號; h7.30am-9pm; mDaqiaotou)
This is the oldest tea-selling shop in Taipei, and dates back to 1883. The current fourth-generation merchants are more than happy to talk tea and let you sample the wares, which sit in large metal drums. Prices per _jin_ (600g) are clearly written on the top of each drum. Ask for a tour of the tea factory in the back.
Lao Mian Cheng Lantern ShopArts & Crafts
(map Google map; 老綿成, Lǎomiànchéng; 298 Dihua St, Sec 1; 迪化街一段298號; h9am-7.30pm; mDaqiaotou)
Handmade lamps with painted dragons, bold flowers, bamboo and calligraphy – as big as a gym ball or as small as a fist. There are also concertinaed paper lanterns, purses and cushion covers. This tumbledown marvel of a shop was opened back in 1915 by the current owner's grandfather. It's sometimes closed on Sunday.
National Cultural and Creative Gift CentreGifts & Souvenirs
(map Google map; 國家文創禮品舘; Guójiā Wénchuàng Lǐpǐn Guǎn; www.handicraft.org.tw; 1 Xuzhou Rd; 徐州路1號; h9am-6pm; W; mNTU Hospital)
Four floors of jade, ceramics, tea sets, jewellery, scrolls, Kinmen knives, Kavalan whisky and handmade soap are just highlights of the variety on offer here. Colourful Franz porcelain is featured in a special section. There's a money-changing facility and a selection of National Palace Museum Shop products.
5Eating & Drinking
Yongkang Beef NoodlesNoodles$$
(map Google map; 永康牛肉麵; Yǒngkāng Niúròumiàn; %02-2351 1051; 17, Lane 31, Jinshan S Rd, Sec 2; 金山南路二段31巷17號; small/large bowl NT$220/240; h11am-3.30pm & 4.30-9pm; a; mDongmen)
Open since 1963, this is one of Taipei's top spots for beef noodles, especially of the _hóngshāo_ (紅燒; red spicy broth) variety. Beef portions are generous, and melt in your mouth. Other worthwhile dishes include steamed ribs. Expect queues.
Addiction Aquatic DevelopmentSeafood$$$
(map Google map; 上引水產; Shàng Yǐn Shuǐchǎn; www.addiction.com.tw; 18, Alley 2, Lane 410, Minzu E Rd; 民族東路410巷2弄18號; h10am-midnight, fish market opens at 6am; a; mXingtian Temple)
Housed in the former Taipei Fish Market – you can't miss it, it's a huge blue-and-slate-grey building – is this collection of chic eateries serving the freshest seafood imaginable. There's a stand-up sushi bar, a seafood bar (with wine available), hotpot, an outdoor grill, a wholesale area for take-home seafood and a lifestyle boutique. This place is popular and doesn't take reservations.
Addiction Aquatic Development | THEBIGLAND/SHUTTERSTOCK ©
Lugou CafeCafe
(map Google map; 爐鍋咖啡; Lúguō Kāfēi; %02-2555 8225; www.facebook.com/luguocafeartyard; 1, 2nd fl, Lane 32, Dihua St, Sec 1; 迪化街一段32巷1號2樓; h11am-7pm; W; mBeimen)
Speciality coffees (including some local choices such as Alishan) on the 2nd floor of a heritage building (originally the chemist AS Watson & Co) on Dihua St. Mismatched furniture, eclectic decor, Frank Sinatra jazz – grab a window seat and slip back in time. The coffee is a pleasure, the sandwiches not so much.
8INFORMATION
**Taiwan Tourism Bureau** Runs information booths all over the city, provides maps and pamphlets, and is staffed by friendly English-speaking workers.
**Tourist Hotline** ( %0800-011 765) Useful 24-hour, toll-free service in English, Japanese and Chinese.
8GETTING AROUND
**Bus** Great network but routes on timetables are written in Chinese only; can be slow when they get stuck in traffic. Fares are NT$15 on most short routes within the city centre.
**MRT** Quickest way to get around; super reliable. Runs from 6am to midnight. Fares vary from NT$20 to NT$65.
**Taxi** Yellow cabs are fairly inexpensive and ubiquitous, but traffic can be frustrating.
**Walk** If you stick to one or two neighbouring districts, Taipei is a very walkable city.
EASYCARD
oEasyCard is the stored-value card of the Taipei Rapid Transit Association (TRTA) and can be bought in most MRT stations for a returnable deposit of NT$100.
oEasyCards can be used for the MRT, buses, some local trains, nonreserved HSR rides, some taxis, the YouBike shared-bicycle program (<http://taipei.youbike.com.tw/en>) and purchases at all convenience stores, Starbucks and dozens of other shops.
Yehliu Geopark
Stretching far out into the East China Sea, the limestone cape of **Yehliu Geopark** (野柳地質公園; Yěliǔ Dìzhí Gōngyuán; %02-2492 2016; www.ylgeopark.org.tw; 167-1 Gangdong Rd, Wanli District, 野柳里港東路167-1號; adult/child NT$80/40; h7.30am-6pm May-Sep, to 5pm Oct-Apr, visitor centre 8am-5pm) has long attracted people to its delightfully odd rock formations. It's a geologist's dreamland but also a fascinating place for the day tripper. Aeons of wind and sea erosion can be observed first-hand in hundreds of pitted and moulded rocks with quaint (but accurate) names such as **Fairy's Shoe** (仙女鞋; Xiānnǚ Xié) and **Queen's Head** (女王頭; Nǚwáng Tóu), which truly looks just like a silhouette of the famous Nefertiti bust.
The visitor information centre has an informative English brochure explaining the general conditions that created the cape and also the specific forces that formed different kinds of rock shapes, such as the mushroom rocks, marine potholes and honeycomb rocks. Tourism shuttle buses stop directly outside the park entrance.
The park gets very crowded on weekends and during holidays, with many tourists swarming around Queen's Head waiting to take pictures. Try to visit early morning, if possible on a weekday.
Frequent bus 790 runs between Keelung and Yehliu (NT$30, 40 minutes).
JIYOUNG JEONG/SHUTTERSTOCK ©
## Jiufen & Jinguashi
Nestled against the mountains and hemmed in by the sea are Jiufen (九份; Jiǔfèn) and its neighbour Jinguashi (金瓜石; Jīnguāshí), 10 minutes by bus away from Jiufen's main road. Both were mining centres during the Japanese era; by the 1930s Jiufen was so prosperous it was known as 'Little Shanghai'.
Miaokou Night Market
Mere steps from the port at Keelung, **Miaokou Night Market** (基隆廟口夜市; Jīlóng Miàokǒu Yèshì; www.miaokow.org; Rensan Rd; 仁三路) is probably the most famous night market in Taiwan. Miaokou became known for its great food during the Japanese era, when a group of merchants started selling snacks at the mouth of the **Dianji Temple** (奠濟宮). Nowadays, Miaokou is considered the best place in Taiwan for street snacks, especially seafood.
The market covers several streets; stalls on the main street are all numbered and have signs in English, Japanese and Chinese explaining what's on the menu.
Despite the name, there's plenty to eat and do here all day long.
LIU YU SHAN/SHUTTERSTOCK ©
1Sights
Jishan StreetArea
(基山街; Jīshān Jiē; Jiufen Old Street)
Countless snack stalls and souvenir shops line the narrow 'old street' threading through Jiufen. Hugely popular, the street can become intolerably crowded by the afternoon, so plan accordingly. Shuqi St, with its famously steep steps, Japanese-era theatre and teahouses, intersects a few hundred meters along Jishan St.
Grazing on local snacks is the de rigueur pastime here. Look for _yùyuán_ (芋圓; taro balls), _yúwán_ (魚丸; fish balls), _cǎozǐ gāo_ (草仔糕; herbal cakes) and _hēitáng gāo_ (黑糖糕; molasses cake). If the crowds get too much, you can take refuge in a teahouse.
Jishan St begins beside the 7-Eleven on the main road.
6Drinking
Jiufen TeahouseTeahouse
(九份茶坊; Jiǔfèn Cháfǎng; %02-2496 9056; www.jioufen-teahouse.com.tw; 142 Jishan St, 基山街142號; h10.30am-9pm; W)
Step back in time at this century-old wooden teahouse full of antique furnishings and cosy nooks to hunker down in. The tea selection includes aged pu'ers, roasted Oriental Beauty and Tieguanyin. A pot (with unlimited water refills) starts at NT$600, plus NT$100 per guest, so it's an expensive place to drink solo. Find it just west of the Shuqi St steps on Jishan St.
Sweet snacks include pineapple cake and oolong tea cheesecake. In the basement is a ceramic studio and exhibition area, with high-quality pieces for sale.
Jiufen Teahouse | HEMIS/ALAMY STOCK PHOTO ©
Shu-ku Tea StoreTeahouse
(樹窟奇木樓; Shùkū Qímùlóu; %02-2497 9043; 38 Fotang Ln, 佛堂巷38號; teas/snacks from NT$300/50; h10am-10pm Sun-Wed & Fri, to midnight Sat; W)
This creaking two-storey teahouse from the Japanese era has the look and feel of a frontier gambling den. Inside you can almost picture the miners squatting on makeshift benches, shuffling cards and warming their hands on a metal teapot. There's no minimum order, making it a good spot for an evening beer. Grab a terrace table for views over the twinkling illuminations of Jiufen.
To get here follow Jishan Rd past the main tourist area until it starts to descend steeply. Just past a couple of homestays look for the English sign to the teahouse on the left.
8INFORMATION
The Jiufen Visitor Information Centre (九份旅遊服務中心; %02-2406 3270; 89 Qiche Rd, 車路89號; h9am-6pm) is worth a visit for the informative history sections (in English). It's just down the street on the opposite side from the Jiufen Kite Museum.
8GETTING THERE & AROUND
Bus 788, departing just before Keelung Station, runs to Jiufen and Jinguashi (NT$30, 45 minutes). Buses pass the Jiufen bus stop near the 7-Eleven first and then proceed to Jinguashi (the final stop). The two towns are 3km apart and are served by buses every 20 minutes or so.
# SHÀNGHĂI
#### Exploring the Bund
#### Yùyuán Gardens & Bazaar
#### The French Concession
#### Sights
#### Shopping
#### Eating
#### Drinking
#
Shànghǎi at a Glance
Rapidly becoming a world metropolis, Shànghǎi typifies modern China while being unlike anywhere else in the nation. Awash with cash, ambition and economic vitality, Shànghǎi is, for the movers and shakers of business, the place to be. For all its modernity and cosmopolitanism, however, Shànghǎi is part and parcel of the People's Republic of China, and its challenges are multiplying as fast as cocktails are mixed and served on the Bund.
Shànghǎi cityscape | SVEN HANSCHE/SHUTTERSTOCK ©
With a Day in Port
People-watch while strolling along the Bund, a gorgeous curve of larger-than-life heritage architecture. Following this, take some time to contemplate and reflect among the harmonious compositions of Yùyuán Gardens – then join the hectic throng in the attached bazaar. If you're in the mood for shopping, browse the boutiques of the French Concession.
Best Places for...
**Street art and galleries** M50 and Beaugeste
**Views** Shanghai Tower
**Street food** Huanghe Road Food Street and Yùyuán Bazaar
**Families** Shànghǎi Disneyland
Getting from the Port
**Shànghǎi Port International Cruise Terminal** (上海港国际客运中心; Shànghǎi Gǎng Guójì Kèyùn Zhōngxīn; Gaoyang Rd), 1km north of the Bund, is a short walk from the International Cruise Terminal metro station. For small and medium-sized ships.
**Shànghǎi Waigaoqiao International Cruise Terminal** (aka Haitong Pier) No public transport; take a taxi to the city (¥95, 50 minutes). Little used.
**Shànghǎi Wusongkou International Cruise Terminal** (aka Baoshan Cruise Terminal) For larger ships. Nearest metro station is Baoyang Road, 3km west (¥25, 12 minutes); take a taxi to the city centre (¥100, 50 minutes).
Fast Facts
**Curreny** Yuán (元; ¥)
**Language** Mandarin, Cantonese
**Money** ATM at Shànghǎi Port International Cruise Terminal; moneychanger at Wusongkou.
Tourist information Shànghǎi Port International Cruise Terminal has a tourist information service.
**Wi-fi** Available at many cafes and throughout the subway system. Note that some popular sites, such as Facebook and Gmail, are blocked in China.
TOP EXPERIENCE
# Exploring the Bund
Symbolic of colonial Shànghǎi, the Bund was once the city's Wall St, a place of feverish trading and fortunes made and lost. Today, it's the bars, restaurants and hypnotising views that pull the crowds.
Great For...
vAc
yDon't Miss
The astonishing views across the Huángpǔ River to Pǔdōng.
Explore Ashore
Shànghǎi Port International Cruise Terminal is an interesting, 1km walk from the Bund. In a taxi it's just a few minutes away. From Wusongkou port, a taxi is easiest (¥100, 50 minutes); otherwise, take the metro to East Nanjing Road.
8Need to Know
外滩, Wàitān; MAP; 3 East Zhongshan No 1 Rd; 3 中山东一路; mLine 2, 10 to East Nanjing Rd
Fairmont Peace Hotel | DENIS LININE/GETTY IMAGES ©
### Peace Hotel
Lording it over the corner of East Nanjing and East Zhongshan Rds is the most famous building on the Bund, the landmark Fairmont Peace Hotel (map Google map; 费尔蒙和平饭店, Fèi'ěrméng Hépíng Fàndiàn; %021 6321 6888; www.fairmont.com; 20 East Nanjing Rd; 南京东路20号; d ¥2500-4000; n a W s; mLine 2, 10 to East Nanjing Rd), constructed between 1926 and 1929. It was originally built as Sassoon House, with Victor Sassoon's famous Cathay Hotel on the 4th to 7th floors. It wasn't for the hoi polloi, with a guest list running to Charlie Chaplin, George Bernard Shaw, and Noel Coward, who penned _Private Lives_ here in four days in 1930 when he had the flu.
Sassoon himself spent weekdays in his personal suite on the top floor, just beneath the green pyramid. The building was renamed the Peace Hotel in 1956.
### Custom House
The neoclassical Custom House (map Google map; 自订的房子, Zì Dìng De Fángzi; 13 East Zhongshan No 1 Rd; 中山东一路13号; mLine 2, 10 to East Nanjing Rd, exit 1), established at this site in 1857 and rebuilt in 1927, is one of the most important buildings on the Bund. Capping it is Big Ching, a bell modelled on London's Big Ben. Clocks were by no means new to China, but Shànghǎi was the first city in which they gained widespread acceptance and the lives of many became dictated by a standardised, common schedule.
Custom House | GRAFISSIMO/GETTY IMAGES ©
### Hongkong & Shanghai Bank Building
Adjacent to the Custom House, the Hongkong & Shanghai Bank Building (map Google map; HSBC Building, 汇丰大厦; 12 East Zhongshan No 1 Rd; 中山东一路12号; mLine 2, 10 to East Nanjing Rd) was constructed in 1923. The bank was first established in Hong Kong in 1864 and in Shànghǎi in 1865 to finance trade, and soon became one of the richest in Shànghǎi, arranging the indemnity paid after the Boxer Rebellion. The magnificent mosaic ceiling inside the entrance was plastered over until its restoration in 1997 and is therefore well preserved.
### Promenade
The Bund offers a host of things to do, but most visitors head straight for the riverside promenade to pose for photos in front of Pǔdōng's ever-changing skyline.
TOP EXPERIENCE
# Yùyuán Gardens & Bazaar
With its shaded corridors, glittering pools and whispering bamboo, the Yùyuán Gardens are a delightful escape from Shànghǎi's glass-and-steel modernity. Aim to arrive at 8.30am; from 10am onwards the crowds get increasingly dense.
Great For...
vAr
yDon't Miss
Hunting out the delightfully ornate inner garden stage.
Explore Ashore
From Shànghǎi Port International Cruise Terminal, it's a short metro ride to Yuyuan Garden metro station, or a 3km walk. From Wusongkou port, a taxi is easiest (¥110, 50 minutes); otherwise, take a taxi to Baoyang Road station and ride the subway.
8Need to Know
豫园、豫园商城, Yùyuán & Yùyuán Shāngchéng; MAP; Anren St; 安仁街; high/low season ¥40/30; h8.30am-5.15pm, last entry at 4.45pm; mLine 10 to Yuyuan Garden
DOVE LEE/GETTY IMAGES ©
### The Gardens
The Yùyuán Gardens were founded by the Pan family, who were rich Ming-dynasty officials. The gardens took 18 years (from 1559 to 1577) to be nurtured into existence, only to be ransacked during the Opium War in 1842, when British officers were barracked here, and again during the Taiping Rebellion, this time by the French.
#### Three Ears of Corn Hall & the Rockeries
As you enter, **Three Ears of Corn Hall** (三穗堂; Sānsuìtáng) is the largest of the halls in the gardens. The **rockeries** (假山; _jiǎshān_ ) attempt to recreate a mountain setting within the flatland of the garden, so when combined with **ponds** (池塘; _chítáng_ ) they suggest the 'hills and rivers' _(shānshuǐ)_ of China's landscapes.
#### Hall of Heralding Spring & Inner Garden
In the east of the gardens, keep an eye out for the **Hall of Heralding Spring** (点春堂; Diǎnchūn Táng), which in 1853 was the headquarters of the Small Swords Society, a rebel group affiliated with the Taiping rebels. To the south, the **Exquisite Jade Rock** (玉玲珑; Yù Línglóng) was destined for the imperial court in Běijīng until the boat carrying it sank outside Shànghǎi.
South of the Exquisite Jade Rock is the **inner garden** (内园; _nèiyuán_ ), where you can also find the beautiful **stage** (古戏台; _gǔxìtái_ ) dating from 1888, with a gilded, carved ceiling and fine acoustics, as well as the charming **Hall for Watching Waves** (观涛楼; Guāntāo Lóu).
### Take a Break
Grab a tray of dumplings from the famed Nánxiáng Steamed Bun Restaurant (map Google map; 南翔馒头店; 85 Yuyuan Rd, Yùyuán Bazaar; 豫园商城豫园路85号; 12 dumplings on 1st fl ¥22; h1st fl 10am-9pm, 2nd fl 7am-8pm, 3rd fl 9.30am-7pm; mLine 10 to Yuyuan Garden).
### The Bazaar
Next to the Yùyuán Gardens entrance rises the Mid-Lake Pavilion Teahouse (map Google map; 湖心亭, Húxīntíng; Yùyuán Bazaar; 豫园商城; tea ¥50; h9am-9pm; mLine 10 to Yuyuan Garden), one of the most famous teahouses in China.
Surrounding all this is the restored bazaar area, where scores of speciality shops and restaurants jostle over narrow laneways and small squares in a mock 'ye olde Cathay' setting.
At the heart of the melee, south of the Yùyuán Gardens exit, is the venerable Temple of the Town God (map Google map; 城隍庙, Chénghuáng Miào; Yùyuán Bazaar, off Middle Fangbang Rd; 豫园商城方浜中路; ¥10; h8.30am-4.30pm; mLine 10 to Yuyuan Garden), dedicated to the protector of the city of Shànghǎi.
TOP EXPERIENCE
# The French Concession
For local boutiques, head along leafy backstreets such as Nanchang, Changle, Fumin or Xinle Rds. Xīntiāndì has high-end brands, while Tiánzǐfáng is home to a number of cool gift stores.
Great For...
zhr
yDon't Miss
Getting thoroughly lost down the disorientating alleyways of Tiánzǐfáng.
Explore Ashore
From Wusongkou port, a taxi is easiest (¥125, 55 minutes); otherwise, take a taxi to Baoyang Road station and ride the subway. From the Shànghǎi Port International Cruise Terminal, make the short walk to the International Cruise Terminal metro station. For Xīntiāndì, head to South Huangpi Rd or Xintiandi station. For Tiánzǐfáng, take the metro to Dapuqiao.
yTop Tip
Eccentric, unconventional Bell Bar map Google map (<http://bellbar.cn>; Tianzifang, back door No 11, Lane 248, Taikang Rd; 泰康路248弄11号后门田子坊; h10am-2am; W; mDapuqiao) is a delightful Tiánzǐfáng hideaway. It's in the second alley on the right.
Tiánzǐfáng | MAOYUNPING/SHUTTERSTOCK ©
### Tiánzǐfáng
A shopping complex housed within a grid of tiny alleyways, Tiánzǐfáng is probably the most accessible, authentic, charming and vibrant example of Shànghǎi's trademark traditional back-lane architecture. A community of design studios, cafes and boutiques, it's a much-needed counterpoint to Shànghǎi's mega-malls and skyscrapers.
There are three main north–south lanes (Nos 210, 248 and 274) criss-crossed by irregular east–west alleyways, which makes exploration disorienting and fun. Most shops and boutiques are slim and bijoux. One gallery to seek out is Beaugeste (map Google map; 比极影像, Bǐjí Yǐngxiàng; %021 6466 9012; www.beaugeste-gallery.com; 5th fl, No 5, Lane 210, Taikang Rd; 泰康路210弄5号520室田子坊; h10am-6pm Sat & Sun; mDapuqiao) F, which has thought-provoking contemporary photography exhibits.
Just outside the complex on Taikang Rd, an enormous peony bloom covers the exterior of the Líulí China Museum (琉璃艺术博物馆, Líulí Yìshù Bówùguǎn; MAP; www.liulichinamuseum.com; 25 Taikang Rd; 泰康路25号; adult/child under 18yr ¥20/free; h10am-5pm Tue-Sun; mDapuqiao), dedicated to glass sculpture.
### Xīntiāndì
With its own namesake metro station, Xīntiāndì has been a Shànghǎi icon for a decade or more. An upscale entertainment and shopping complex modelled on traditional _lòngtáng_ (alleyway) homes, this was the first development in the city to prove that historic architecture makes big commercial sense.
The heart of the complex, cleaved into a pedestrianised north and south block, consists of largely rebuilt traditional _shíkùmén_ (stone-gate houses), brought bang up to date with a modern spin. But while the layout suggests a flavour of yesteryear, don't expect too much historic magic or cultural allure. Serious shoppers – and diners – will eventually gravitate towards the malls at the southern tip of the south block. Beyond the first mall, which holds some top-notch restaurants on the 2nd floor – including Din Tai Fung (map Google map; 鼎泰丰; www.dintaifung.com.cn; Xīntiāndì South Block, 2nd fl, Bldg 6; 兴业路123弄新天地南里6号楼2楼; 10 dumplings ¥60-96; h10am-midnight; mSouth Huangpi Rd, Xintiandi) and Shanghai Min (map Google map; 小南国, Xiǎo Nán Guó; Xīntiāndì South Block, 2nd fl, Bldg 6; 兴业路123弄新天地南里6号楼2楼; dishes ¥35-198; h11am-10pm; mSouth Huangpi Rd, Xintiandi) – is the Xīntiāndì Style (map Google map mall; 新天地时尚, Xīntiāndì Shíshàng; MAP; 245 Madang Rd; 马当路245号; h10am-10pm; mXintiandi) showcasing local brands and chic pieces.
Xīntiāndì | LMSPENCER/SHUTTERSTOCK ©
The Bund, Old Town & Pŭdōng
1Sights
1Aurora MuseumE4
2Custom HouseC4
3Fairmont Peace HotelC3
4Hongkong & Shanghai Bank BuildingC4
5Jīnmào TowerF4
6Shanghai TowerF5
7Temple of the Town GodC6
8The BundC3
9Yuanmingyuan RoadB3
10Yùyuán Gardens & BazaarC6
7Shopping
Blue Shanghai White(see 11)
11Sūzhōu CobblersC4
5Eating
12M on the BundC4
13Nánxiáng Steamed Bun RestaurantC6
14Shanghai GrandmotherC4
15Yi CafeE4
6Drinking & Nightlife
16Mid-Lake Pavilion TeahouseC6
Patio Lounge(see 5)
1Sights
### 1 The Bund & People's Square
West of the Bund, People's Square is ground central for Shànghǎi sightseeing, with world-class museums, art galleries and a beautiful park.
Yuanmingyuan RoadArea
(map Google map; 圆明园路, Yuánmíngyuán Lù; MAP; mLine 2, 10 to East Nanjing Rd)
Like a smaller, more condensed version of the Bund, the pedestrianised, cobblestone Yuanmingyuan Rd is lined with a mishmash of colonial architecture. Running parallel with the Bund, just one block back, some fine examples of renovated red-brick and stone buildings dating from the 1900s include the art-deco YWCA Building (No 133) and Chinese Baptist Publication building (No 209), the ornate 1907 red-brick Panama Legation building (No 97) and the 1927 neoclassical Lyceum Building.
Shanghai MuseumMuseum
(map Google map; 上海博物馆, Shànghǎi Bówùguǎn; MAP; www.shanghaimuseum.net; 201 People's Ave; h9am-5pm Tue-Sun, last entry 4pm; c; mLine 1, 2, 8 to People's Square) F
This must-see museum escorts you through the craft of millennia and the pages of Chinese history. It's home to one of the most impressive collections in the land: take your pick from the archaic green patinas of the Ancient Chinese Bronzes Gallery through to the silent solemnity of the Ancient Chinese Sculpture Gallery; from the exquisite beauty of the ceramics in the Zande Lou Gallery to the measured and timeless flourishes captured in the Chinese Calligraphy Gallery.
### 1 Jìng'ān
Jade Buddha TempleBuddhist Temple
(玉佛寺, Yùfó Sì; cnr Anyuan & Jiangning Rds; 安远路和江宁路街口; ¥20; h8am-4.30pm; mLine 7, 13 to Changshou Rd, exit 5)
One of Shànghǎi's few active Buddhist monasteries, this temple was built between 1918 and 1928. The highlight is a transcendent Buddha crafted from pure jade, one of five shipped back to China by the monk Hui Gen at the turn of the 20th century.
M50Arts Centre
(M50创意产业集聚区, M50 Chuàngyì Chǎnyè Jíjùqū; www.m50.com.cn/en; 50 Moganshan Rd; 莫干山路50号; mLine 13 to Jiangning Rd) F
Shànghǎi may be known for its glitz and glamour, but it's got an edgy subculture too. The industrial M50 art complex is one prime example, where galleries have been set up in disused factories and cotton mills, utilising the vast space to showcase contemporary Chinese emerging and established artists. There's a lot to see, so plan to spend half a day poking around the site.
Shanghai Natural History MuseumMuseum
(map Google map; 上海自然博物馆, Shànghǎi Zìrán Bówùguǎn; MAP; %021 6862 2000; www.snhm.org.cn; 510 West Beijing Rd; 北京西路510号; adult/senior/teen/under 13yr ¥30/25/12/free; h9am-5.15pm Tue-Sun; mLine 1 to Shanghai Natural History Museum)
Perhaps not quite on the same scale as the Smithsonian, this new sleek space would nevertheless be a fitting choice for a _Night at the Museum_ movie. As comprehensive as it is entertaining and informative, the museum is packed with displays of taxidermied animals, dinosaurs and cool interactive features. Its architecture is also a highlight, with a striking design that is beautifully integrated in its art-filled Jìng'ān Sculpture Park (静安雕塑公园, Jìng'ān Diāosù Gōngyuán; MAP; 128 Shimen 2nd Rd; 石门二路128号; h6am-8.30pm; mLines 2, 12, 13 to West Nanjing Rd, Line 13 to Shanghai Natural History Museum) F setting.
### 1 Pǔdōng
Shanghai TowerNotable Building
(map Google map; 上海中心大厦, Shànghǎi Zhōngxīn Dàshà; MAP; www.shanghaitower.com.cn; cnr Middle Yincheng & Huayuanshiqiao Rds; ¥180; h8.30am-9.30pm, last admission 8.30pm; mLujiazui)
China's tallest building dramatically twists skywards from its footing in Lùjiāzuǐ. The 121-storey, 632m-tall, Gensler-designed tower topped out in August 2013 and opened in mid-2016. The observation deck on the 118th-floor is the world's highest.
Views from Shanghai Tower | MICHAEL GORDON/SHUTTERSTOCK ©
Jīnmào TowerNotable Building
(map Google map; 金茂大厦, Jīnmào Dàshà; MAP; %021 5047 5101; 88 Century Ave; 世纪大道88号; adult/student/child ¥120/90/60; h8.30am-10pm; mLujiazui)
Resembling an art-deco take on a pagoda, this crystalline edifice is a beauty. It's essentially an office block with the high-altitude Grand Hyatt renting space from the 53rd to 87th floors. You can zip up in the elevators to the 88th-floor **observation deck** , accessed from the separate podium building to the side of the main tower (aim for clear days at dusk for both day and night views).
Shànghǎi Disneyland
After a decade of planning and diplomatic wrangling, the Magic Kingdom finally arrived in the Middle Kingdom in 2016, offering up a spectacular serving of Disney (上海迪士尼乐园, Shànghǎi Díshìní Lèyuán; %021 3158 0000; www.shanghaidisneyresort.com; Shanghai Disney Resort, Pudong; adult/child 1.0-1.4m & senior from ¥499/375; h8.30am-10pm; mDisney Resort) seasoned with a dash of Chinese culture. 'Main Street USA' has become the locally inspired yet rather sterile 'Gardens of the Imagination', and you can gnaw the ears off a steamed Mickey Mouse pork bun at snack vendors throughout the park.
Much has been said about the queues; if you're serious about packing in all the big rides in a day, aim to arrive at least 30 minutes before the park opens, and play a tactical Fast Pass game (the longest lines are at Roaring Rapids, Soaring Over the Horizon and TRON). Alternatively, for groups of three, a cool ¥6300 (¥9000 at peak times) gets you a 'Premier Tour' with fast access to all the rides.
With younger kids in tow you can takes things at a more leisurely pace, and there are plenty of roving musical performances, costumed characters to meet and the excellent parades (12pm and 3.30pm) and fireworks display (8.30pm), which don't require any waiting.
YAORUSHENG/GETTY IMAGES ©
Aurora MuseumMuseum
(map Google map; 震旦博物馆, Zhèn Dàn Bówùguǎn; MAP; %021 5840 8899; www.auroramuseum.cn; Aurora Bldg, 99 Fucheng Rd; 富城路99号震旦大厦; ¥60; h10am-5pm Tue-Thu, Sat & Sun, to 9pm Fri, last entry 1hr before closing; mLujiazui)
Designed by renowned Japanese architect, Andō Tadao, the Aurora Museum is set over six floors of the Aurora building and houses a stunning collection of Chinese treasures. Artefacts and antiquities on display include pottery from the Han dynasty; jade dating back from the Neolithic to the Qing dynasty; blue and white porcelain spanning the Yuan, Ming and Qing dynasties; as well as Buddhist sculptures from the Gandharan and Northern Wei period. Don't miss the jade burial suit of 2903 tiles sewn with gold wire.
7Shopping
Sūzhōu CobblersFashion & Accessories
(map Google map; 摩登绣鞋; www.suzhou-cobblers.com; Unit 101, 17 Fuzhou Rd; 福州路17号101室; h10am-6.30pm; mLine 2, 10 to East Nanjing Rd)
Right off the Bund, this cute boutique sells exquisite hand-embroidered silk slippers, bags, hats and clothing. Patterns and colours are based on the fashions of the 1930s, and as far as the owner, Huang 'Denise' Mengqi, is concerned, the products are one of a kind. Slippers start at ¥650 and the shop can make to order.
Blue Shanghai WhiteCeramics
(map Google map; 海晨, Hǎi Chén; MAP; %021 6323 0856; www.blueshanghaiwhite.com; Unit 103, 17 Fuzhou Rd; 福州路17号103室; h10.30am-6.30pm; mLine 2, 10 to East Nanjing Rd)
Just off the Bund, this little boutique is a great place to browse for a contemporary take on a traditional art form. It sells a tasteful selection of hand-painted Jǐngdézhèn porcelain teacups, teapots and vases, displayed together with the shop's ingeniously designed wooden furniture.
PilingpalangCeramics
(map Google map; 噼呤啪啷; %021 6219 5020; www.pilingpalang.com; Shanghai Centre, Shop 116, 1376 West Nanjing Rd; 上海商城南京西路1376号东峰116; h10am-9.30pm; mLines 2, 12 & 13 to West Nanjing Rd)
You'll find gorgeous vibrant coloured ceramics, cloisonné and lacquer, in pieces that celebrate traditional Chinese forms while adding a modern and deco-inspired slant. Tea caddies and decorative trays make for great gifts or souvenirs.
French Concession, People's Square & Jìng'ān
1Sights
1BeaugesteF6
2Jìng'an Sculpture ParkE1
3Liúli China MuseumG6
4Shanghai MuseumG2
5Shanghai Natural History MuseumE1
7Shopping
6PilingpalangC2
7Xīntiāndì StyleG4
5Eating
8Brut EateryA3
9Commune SocialC1
10Din Tai FungG4
11Huanghe Road Food StreetG1
12Jiājiā Soup DumplingsG1
13Jian Guo 328D6
14Shanghai MinG4
15Sìchuān CitizenA6
16Yang's Fry DumplingsG1
6Drinking & Nightlife
17BarbarossaG2
18Bell BarF6
19Café del VolcánD5
20Goose Island BrewhouseE2
21SumerianD2
5Eating
As much an introduction to regional Chinese cuisine as a magnet for talented chefs from around the globe, Shànghǎi has staked a formidable claim as the Middle Kingdom's hottest dining destination.
Huanghe Road Food StreetChinese$
(map Google map; 黄河路美食街, Huánghé Lù Měishí Jiē; MAP; mLine 1, 2, 8 to People's Square)
With a prime central location near People's Park, Huanghe Rd covers all the bases from cheap lunches to late-night post-theatre snacks. You'll find large restaurants, but it's best for dumplings – get 'em fried at Yang's (小杨生煎馆, Xiǎoyáng Shēngjiān Guǎn; MAP; 97 Huanghe Rd; 黄河路97号; dumplings from ¥9; h6.30am-8pm; mLine 1, 2, 8 to People's Square) or served up in bamboo steamers across the road at Jiājiā Soup Dumplings (map Google map; 佳家汤包, Jiājiā Tāngbāo; MAP; 90 Huanghe Rd; 黄河路90号; 12 dumplings ¥25; h7am-8pm; mLines 1, 2, 8).
_Xiǎolóngbāo_ at Jiājiā Soup Dumplings | MARK ANDREWS/ALAMY STOCK PHOTO ©
Shanghai GrandmotherShanghai$
(map Google map; 上海姥姥, Shànghǎi Lǎolao; %021 6321 6613; 70 Fuzhou Rd; 福州路70号; dishes ¥25-150; h10.30am-9.30pm; mLine 2, 10 to East Nanjing Rd)
This packed eatery is within easy striking distance of the Bund and cooks up all manner of home-style dishes. You can't go wrong with the classics here: braised aubergine in soy sauce, Grandmother's braised pork, crispy duck, three-cup chicken and _mápó dòufu_ (麻婆豆腐; tofu and pork crumbs in a spicy sauce) rarely disappoint.
Jian Guo 328Shanghai$
(map Google map; 建国, Jiànguó; %021 6471 3819; 328 West Jianguo Rd; 建国西路328号; mains ¥22-58; h11am-2pm & 5-9.30pm; mJiashan Rd)
Frequently crammed, this boisterous, narrow, two-floor spot tucked away on Jiànguó Rd does a roaring trade on the back of excellent well-priced Shanghainese cuisine. You can't go wrong with the MSG-free menu, but highlights include the deep-fried duck legs, eggplant casserole, scallion oil noodles and yellow croaker fish spring rolls. Reserve.
Sìchuān CitizenSichuan$
(map Google map; 龙门阵茶屋, Lóngménzhèn Cháwū; %021 54041235; 378 Wukang Rd; 武康路378号; dishes ¥26-98, set lunch ¥38-68; h11am-10.30pm; W v; mShanghai Library)
The subdued evening lighting and welcoming service concocts a warm and homely atmosphere at this popular outpost of Sìchuān cuisine in Shànghǎi. The extensive photo menu is foreigner friendly and includes a sizeable vegetarian selection. The _dàndàn_ noodles (担担面) are textbook spicy, while the pork wontons in hot oil (¥10) are spot on.
Brut EateryCafe$
(map Google map; 悦璞食堂; 698 Yuyuan Rd, 愚园路698号; mains from ¥46; h8am-10pm; mLine 2 & 11 to Jiangsu Rd)
An extremely popular cubby hole casual eatery with half a dozen tables, plus steps with cushions and mini-side tables out front. Diners queue and then sit shoulder to shoulder with other patrons for Californian Chinese chef Jun Wu's creations. The waffles and chicken is a winner – with six-spice fried chicken, a large bouncy waffle, pickled watermelon radish, jujube honey and candied walnuts.
Commune SocialTapas$$
(map Google map; 食社; Shíshè; %021 6047 7638; www.communesocial.com; 511 Jiangning Rd; 江宁路511号; tapas ¥38-238, 9-course tasting menu per person ¥629; hnoon-2.30pm Tue-Sun, 6-10.30pm Tue-Thu, 5.30-10.30pm Fri & Sat, 11.30am-10pm Sun; m Line 7 to Changping Rd)
A venture by UK celebrity chef Jason Atherton, this natty Neri & Hu–designed restaurant blends a stylish, yet relaxed, vibe with sensational tasting dishes, exquisitely presented by chef Scott Melvin. It's divided neatly into upstairs cocktail bar with terrace, downstairs open-kitchen tapas bar and dessert bar. It's the talk of the town, but has a no-reservations policy, so prepare to queue.
M on the BundEuropean$$$
(map Google map; 米氏西餐厅, Mǐshì Xīcāntīng; %021 6350 9988; www.m-restaurantgroup.com/mbund; 7th fl, 20 Guangdong Rd; 广东路20号7楼; mains ¥200-400, 2-course set lunch ¥198, weekend brunch 2-/3-courses ¥298/328; h11.30am-2.30pm & 6-10.30pm; mLine 2, 10 to East Nanjing Rd)
M exudes a timelessness and level of sophistication that eclipses the razzle-dazzle of many other upscale Shànghǎi restaurants. The menu ain't radical, but that's the question it seems to ask you – is breaking new culinary ground really so crucial? Crispy suckling pig and tajine with saffron are, after all, simply delicious just the way they are.
Yi CafeCafe$$$
(map Google map; 怡咖啡; Yí Kāfēi; %021 6882 8888; www.shangri-la.com; 2nd fl, Pudong Shangri-La, 33 Fucheng Rd; 富城路33号2楼; buffet meals from ¥218; hbreakfast 6-10.30am, lunch 11.30am-2.30pm, dinner 5.30-10pm; W; mLujiazui)
If you're squabbling over what to eat for lunch, brunch or dinner, settle your differences at smart-casual Yi Cafe. With 12 open kitchens and a walk-through layout, it's a veritable Asian–Southeast Asian–international food fest with endless menus. Be sure to cultivate a real hunger before you stop by. The buffet breakfasts easily match Pǔdōng's sightseeing calorific demands.
Dumplings
Shànghǎi's favourite dumpling is the _xiǎolóngbāo_ (小笼包; 'little steamer buns'), copied everywhere else in China but only true to form here. _Xiǎolóngbāo_ are normally bought by the _lóng_ (笼; steamer basket) and dipped in vinegar.
There's an art to eating them, as they're full of a delicious but scalding gelatinous broth: the trick is to avoid both burning your tongue and staining your shirt (not easy), while road-testing your chopstick skills.
Tradition attributes the invention of the dumpling – filled with pork, or in more upmarket establishments with pork and crab – to Nánxiāng, a village north of Shànghǎi city.
Another Shanghainese speciality is _shēngjiān_ (生煎) _,_ scallion-and-sesame-seed-coated dumplings that are fried in an enormous flat-bottomed wok, which is covered with a wooden lid. These are also pork-based; again, watch out for the palate-scorching, scalding oil, which can travel.
Top dumpling joints:
Yang's Fry Dumplings Simply scrumptious.
Din Tai Fung Outstanding _xiǎolóngbāo_.
Nánxiáng Steamed Bun Restaurant Round-the-block lines.
Jiājiā Soup Dumplings Humble spot serving some of the city's best _xiǎolóngbāo_.
Chef at Nánxiáng Steamed Bun Restaurant | BOGOSHIPDA/SHUTTERSTOCK ©
6Drinking
SumerianCafe
(map Google map; 苏美尔人, Sū Měi Ěr Rén; www.sumeriancoffee.com; 415 North Shaanxi Rd; 陕西北路415号; coffee from ¥28; h7.30am-6pm Mon, to 7.30pm Tue-Sun; W; mLine 2, 12, 13 to West Nanjing Rd, exit 1)
Run by a bright and sunny team of staff, good-looking Sumerian packs a lot into a small space. The real drawcard here is the coffee – the cafe roasts its own single-origin beans sourced seasonally from Ethiopia, El Salvador and China. It does good pour-overs and lattes, as well as a nitro and eight-hour cold drip. The homemade bagels are also a standout, with a delicious selection of toppings and spreads.
Café del VolcánCafe
(map Google map; www.cafevolcan.com; 80 Yongkang Rd; 永康路80号; coffee ¥26-46; h8am-8pm Mon-Fri, 10am-8pm Sat & Sun; W; mSouth Shaanxi Rd)
Tiny Café del Volcán offers a pit stop from the bustle of bar-heavy Yongkang Rd. The minimalist cafe has just a few wooden box tables sharing the space with the roasting machine. The coffee here is excellent and its signature beans come from the owner's coffee plantation in Guatemala – in the family for 120 years – while other single-origin beans are from Ethiopia, Kenya, Panama and Yúnnán.
BarbarossaBar
(map Google map; 芭芭露莎会所, Bābālùshā Huìsuǒ; www.barbarossa.com.cn; People's Park, 231 West Nanjing Rd; 南京西路231号人民公园内; h11am-2am; W; mLine 1, 2, 8 to People's Square, exit 11)
Set back in People's Park alongside a pond, Barbarossa is all about escapism. Forget Shànghǎi, this is Morocco channelled by Hollywood set designers. The action gets steadily more intense as you ascend to the roof terrace, via the cushion-strewn 2nd floor, where the hordes puff on fruit-flavoured hookahs. At night, use the park entrance just east of the former Shànghǎi Race Club building (上海跑马总会; Shànghǎi Pǎomǎ Zǒnghuì).
Happy hour (from 2pm to 8pm) is a good time to visit for two-for-one cocktails.
Barbarossa | OSTILL IS FRANCK CAMHI/SHUTTERSTOCK ©
Patio LoungeLounge
(map Google map; <http://shanghai.grand.hyatt.com>; Grand Hyatt, Jīnmào Tower, 88 Century Ave; 世纪大道88号君悦大酒店; afternoon tea for 4 ¥368; h11.30am-11pm Sun-Thu, to midnight Fri & Sat; mLujiazui)
Have a drink or indulge in afternoon tea with the spectacular 33-floor atrium of the Grand Hyatt soaring above you in the Jīnmào Tower.
Goose Island BrewhouseBrewery
(map Google map; %021 6219 0268; www.gooseisland.com; 209 Maoming Bei Lu, 茂名北路209号; h11.30am-midnight Sun-Thu, 11.30am-2am Fri & Sat; mLine 2, 12, 13 to West Nanjing Rd)
You'll likely spot this beer brand all over town – this warehouse-style space over two floors is where it's brewed in enormous vats. Choose from dozens of white, blonde, amber and brown ales, poured from taps shaped like goose heads. A full food menu includes hearty oxtail soup, hickory smoked pork ribs, IPA fried chicken and roasted kimchi nachos. A few patio tables are available in the alley outside.
Tea Tasting
It may be a rather clichéd choice, but there's no doubt that a Yíxīng teapot and a package of oolong tea makes for a convenient gift. But how do you go about a purchase? Two things to remember: first of all, be sure to taste (品尝; _pǐncháng_ ) and compare several different teas – flavours vary widely, and there's no point in buying a premium grade if you don't like it.
Tasting is free (免费; _miǎnfèi_ ) and fun, but it's good form to make some sort of purchase afterwards. Second, tea is generally priced by the _jīn_ (斤; 500g), which may be more tea than you can finish in a year. Purchase several _liǎng_ (两; 50g) instead – divide the list price by 10 for an idea of the final cost. Some of the different types of tea for sale include oolong (乌龙; _wūlóng_ ), green (绿; _lǜ_ ), flower (花茶; _huāchá_ ) and _pu-erh_ (普洱; _pǔ'ěr_ ) – true connoisseurs have a different teapot for each type of tea.
Tea for sale | ZVONIMIR ATLETIC/SHUTTERSTOCK ©
8INFORMATION
Shànghǎi has about a dozen or so rather useless **Tourist Information & Service Centres** (旅游咨询服务中心; Lǚyóu Zīxún Fúwù Zhōngxīn) where you can at least get free maps and (sometimes) information. Locations include the following:
**Jìng'ān** (MAP; %021 6248 3259; Shop 19, Lane 1678, 18 West Nanjing Rd; 南京西路1678弄18号; h10am-6pm; mLine 2, 7 to Jing'an Temple)
**Pǔdōng** (MAP; 168 West Lujiazui Rd; 陆家嘴西路168号; h9am-5pm)
**The Bund** (MAP; h9.30am-9.30pm; mEast Nanjing Rd)
8GETTING AROUND
**Bicycle** Good for small neighbourhoods, but distances are too colossal for effective transport about town.
**Bus** With a wide-ranging web of routes, buses may sound tempting, but that's before you try to decipher routes and stops or attempt to squeeze aboard during the crush hour. Buses also have to contend with Shànghǎi's traffic, which can slow to an agonising crawl.
**Metro** The rapidly expanding metro and light railway system works like a dream; it's fast, efficient and inexpensive. Rush hour on the metro operates at overcapacity, however, and you get to savour the full meaning of the big squeeze.
**Taxi** Ubiquitous and cheap, but flagging one down during rush hour or during a rainstorm requires staying power of a high order.
**Walking** This is only really possible within neighbourhoods, and even then the distances can be epic and tiring.
# JEJU ISLAND
#### Sanbanggul-sa
#### Sights
#### Tours
#### Eating & Drinking
#
Jeju Island at Glance
Jeju-do (제주도), South Korea's largest island, has long been the country's favourite domestic holiday destination thanks to its beautiful beaches, lush countryside and seaside hotels designed for rest and relaxation.
Explore tangerine-trimmed country roads, jagged coasts and narrow lanes dotted with cottage-style homes made from black lava rock. The ocean is never far away, so plunge into blue seas to view coral as colourful as the sunsets and dig into Jeju-do's unique cuisine, including seafood caught by _haeneyo_ (female free divers).
Seongsan Ilchul-bong | ZKRUGER/GETTY IMAGES ©
With a Day in Port
Find Buddha in Sanbanggul-sa, a cave at the top of a mountain, or go underground in Manjang-gul, part of the world's largest lava-tube cave system. You can also sample gardens, lava tubes and a folk village at Hallim Park.
Best Places for...
**Climbing a volcano** Seongsan Ilchul-bong
**Coastal walks** Yongmeori Coast
**Local culture** Jeju Folk Village
**Waterfalls** Cheonjiyeon Pokpo
Getting from the Port
Most cruise ships dock at Jeju-do's capital, **Jeju-si** (제주시), on the island's north side; from here it's about 2km into the city. There is usually a shuttle service and taxis waiting. Others dock at the new **Jeju Naval Base** near Gangjeong in the south, not far from atmospheric Seogwipo.
Both make convenient bases for exploring the small island. Inexpensive buses run from the ports into Jeju-si and Seogwipo, and head out all over the island. If you plan on visiting more than one sight, then all-day taxi hire is a good investment.
Fast Facts
**Currency** Korean won (₩)
**Language** Korean
**Money** Jeju-si terminal has an ATM that accepts foreign-issued cards. At the time of research there was only currency exchange, not an ATM, at the southern port. Bring currency, or look for an ATM in Seogwipo. Most ATMs on Jeju-do do not accept foreign-issued cards: bring currency with you to be sure.
Tourist information There is a tourist office at Jeju-si terminal.
**Wi-fi** There is free service at the Jeju-si terminal, on public buses and at many public buildings and tourist sites on the island.
TOP EXPERIENCE
# Sanbang-san
Hugging the southwest corner of the island, the sleepy village of Sagye-ri boasts a number of terrific sights, including dramatic coastlines and incredible rock formations, but most attractive is the imposing Sanbanggul-sa (395m). Its temples peer out to sea, and at the top of a short hike, a cave holds the dramatic spectacle of a stone Buddha in a cave dripping with water.
Great For...
gcf
yDon't Miss
Gorgeous views out across the sea.
Explore Ashore
Buses (₩1200, every 20 minutes) travel between Sanbanggul-sa and Jeju-si Intercity Bus Terminal (bus 250 or 251, 75 minutes) and Jungang Rotary (bus 202, one hour) in Seogwipo.
8Need to Know
산방굴사; 218-10 Sanbang-ro, Andeok-myeon; adult/youth/child ₩1000/700/500, parking ₩1000; hsunrise-sunset; p
Sanbanggul-sa | LOES KIEBOOM/SHUTTERSTOCK ©
### Sanbanggul-sa
A steep, 20-minute walk up the south face of the craggy Sanbang-san is a small stone Buddha in a 5m-high cave called Sanbanggul-sa. From Sagye-ri, the walk up looks more daunting than it really is, but after reaching the cave you'll be delighted because of the powerful 'wow' factor. Lower down, by the defunct ticket office and cafe, are more-modern shrines and statues with free admission. There is a separate ticket office just before the cave.
### Hamel Memorial
The Hamel Memorial (하멜상선전시관; combo ticket with Sanbanggul-sa adult/youth/child ₩2500/2000/1500) is housed in a replica of a Dutch ship. Hendrick Hamel (1630–92), one of the survivors of a shipwreck near Jeju in 1653, was forced to stay in Korea for 13 years before escaping in a boat to Japan. Later he was the first Westerner to write a book on the 'hermit kingdom'.
### Yongmeori Coast
A short walk from Sanbanggul-sa towards the ocean brings you to theYongmeori coast (용머리해안; combo ticket with Sanbanggul-sa adult/youth/child ₩2500/2000/1500; h8am-5.30pm), a spectacular seaside trail with soaring cliffs pockmarked by erosion into catacombs, narrow clefts and natural archways. Some say the rock formation looks like a dragon's head, hence the name (dragon, 용, _yong,_ and head, 머리, _meori_ ).
From the temple entrance, cross the street and walk towards the shipwreck. Note: the walk along the cliffs closes during very high seas.
Yongmeori coast | LOESKIEBOOM/GETTY IMAGES ©
### Sanbangsan Land
This 'viking' pirate ship ride (산방산 랜드; %064-794 1425; 24-32 Sagyenam-ro 216beon-gil; ride ₩2000; h9am-6pm; c) sits between Sanbang-san and the coast. You'll hear the screams of visitors as they are launched higher than any other similar ship in Korea. The ride was made mildly famous when it inspired the song 'Viking' by K-Indie group Peppertones.
### Take a Break
If you like seafood, check out the restaurants along the road from Sanbang-san to the port.
1Sights
Jeju Folk VillageVillage
(제주민속촌; %064-787 4501; <http://jejufolk.com>; 631-34 Minsokhaean-ro, Pyoseon-myeon; adult/youth/child ₩11,000/8000/7000; h8.30am-6pm, to 5pm Oct-Feb; g201, Pyeosolli Office stop)
The educational Jeju Folk Village gathers together traditional buildings from across the island (some reconstructions, others hundreds of years old) in an attractively designed park. Various sections cover Jeju's culture from shamans to _yangban_ (aristocrats), and the differences between mountain, hill-country and fishing villages.
Seongsan Ilchul-bongVolcano
(성산일출봉; %064-783 0959; <http://jejuwnh.jeju.go.kr>; 284-12 Ilchul-ro, Seongsan-eup; adult/youth ₩2000/1000; h1hr before sunrise-8pm; g201, 210, Seongsan Ilchulbong Tuff Cone Entrance stop)
This majestic 182m-high, extinct tuff volcano, shaped like a giant punchbowl, is one of Jeju-do's most impressive sights and a Unesco World Heritage Site. The forested crater is ringed by jagged rocks, though there's no lake because the rock is porous. From the entrance, climbing the steep stairs to the crater rim only takes 20 minutes.
Buses run to adjacent Seongsan-ri village from Jeju-si Intercity Bus Terminal (201 and 210, 70 to 90 minutes, every 20 minutes).
Cheonjiyeon PokpoWaterfall
(천지연폭포; adult/child ₩2000/1000; h7am-10pm)
This popular 22m-high waterfall is reached after a 10-minute walk through a beautifully forested, steep gorge. The waterfall can be impressive following heavy rain; at other times it's more noisy than wide. Well worth visiting in the evening, too, when the illuminated gorge takes on a romantic atmosphere. The falls are on Olle Trail 6; you can easily walk here from town or take the Seogwipo City Tour Bus.
Manjang-gulCave
(만장굴; %064-710 7905; <http://jejuwnh.jeju.go.kr>; 182 Manjanggul-gil, Gujwa-eup; adult ₩2000, youth & child ₩1000; h9am-6pm; g711, Manjang-gul stop)
Manjang-gul is the main access point to the lava-tube caves. In total the caves are 7.4km long, with heights between 2m and 23m. In this section you can walk around 1km underground to a 7m-high lava pillar, the cave's outstanding feature. The immense black tunnel with swirling walls looks like the lair of a giant serpent and it's hard to imagine the geological forces that created it aeons ago, moulding rock as if it were play dough.
Take a jacket and good shoes, as the cave ceiling drips, the ground is wet and uneven and the temperature inside is a chilly 10°C, regardless of the weather outside.
Hallim ParkGardens
(한림공원; %064-796 0001; www.hallimpark.co.kr; 300 Hallim-ro, Hallim-eup; adult/youth/child ₩11,000/8000/7000; h8.30am-7pm Mar-Sep, to 6pm Oct-Feb; p c; g202, Hallim Park stop)
Hallim Park offers a botanical and bonsai garden, a mini folk village and walks through a lava-tube cave. The caves are part of a 17km-long lava-tube system and are said to be the only lava caves in the world to contain stalagmites and stalactites.
Hallim Park | TUPIKOV/GETTY IMAGES ©
TTours
Jeju City Tour BusBus
( %064-748 3211; www.jejugoldenbus.com; day pass adult/child ₩12,000/8000; h9 departures 9am-7pm, closed 3rd Mon of month)
A day pass on the blue, white and orange Jeju City Tour Bus is a convenient way to explore multiple sights on a 22-stop hop-on, hop-off circuit in and around Jeju-si, including the ferry terminal.
Seogwipo City Tour BusBus
(www.seogwipo.go.kr/group/culture/tourism/electricity.htm; rides with/without T-money card ₩1150/1200; h9am-9.35pm, every 35-40min; W)
The 880 bus makes it easy to see all of Seogwipo's main sights in and around downtown in one day. Using a T-money card, you get two free transfers within 40 minutes of tapping off one ride and making another.
Tourism Controversy
Home to barely 600,000, Jeju Island receives some 15 million visitors each year. To help cope with the increasing arrivals, a second (controversial) port was built in the island's south. Some welcome the additional income tourism brings to the island, but there are also concerns about the sustainability of the industry, which brings increasing litter, traffic and demand on the island's freshwater supplies. As a visitor you're unlikely to see much evidence of Jeju's struggles to adapt to increasing visitor numbers (beyond the traffic). Where you can, spend money in local and traditional businesses. Be respectful. Don't litter, and try to minimise waste by bringing your own reusable water bottle and tote bag.
Seogwipo | LOESKIEBOOM/GETTY IMAGES ©
Yeha Bus ToursBus
( %064-713 5505; www.yehatour.com; adult/youth ₩109,000/89,000; h8.30am-5.30pm)
You get bus travel, sight entrance fees, lunch and a guide to explain everything on this one-day excursion. The company operates three routes that run to some of the most popular destinations on the island.
5Eating & DRINKING
In Jeju-si, Black Pork Street ( _heukdwaeji geori_ on Gwandeong-ro 15-gil) is a string of barbecue restaurants serving the island's speciality, black-skinned pig. Plenty of regular Korean and seafood restaurants run behind the Tapdong promenade on Jungang-ro 2-gil and 1-gil.
In Seogwipo, the art street Lee Jung Seop-ro and surrounds is the best area for interesting, ever-changing restaurants. The southern and eastern side of the harbour is promoted as 'Chilsimni Food Street' with traditional Korean seafood and black-pork restaurants.
DasoniVegan$
(다소니; %064-753 5533; 24 Onam-ro 6-gil, Jeju-si; mains from ₩6000, set lunch from ₩11,000; h11am-10pm; g312, Ora 1 Dong stop)
Sit cross-legged at rustic wooden tables, peering out into the wild garden of this meat-free restaurant. Local Jeju produce is used for dishes such as sticky rice wrapped in lotus leaves, or acorn jelly, delighting even non-vegetarians. The lunch photo menu has ample interesting _banchan_ , such as green chive _pajeon_. Mention if you don't eat fish as it's used in a couple of dishes.
Haejin Seafood RestaurantSeafood$$
(해진횟집; %064-757 4584; 1435-2 Geonip-dong, Jeju-si; mains ₩12,000-50,000; h10.30am-midnight)
Of the many restaurants overlooking the harbour, Haejin is the largest and one of the most popular places to try Jeju-do's seafood specialities such as cuttlefish, eel, squid, octopus, sea cucumber and abalone. The set meal (₩30,000) feeds two people.
Dongmun MarketMarket$$
(동문재래시장; 20 Gwandeong-ro 14-gil, Jeju-si; mains ₩10,000-25,000, snacks from ₩500; h8am-9pm)
This traditional Korean food market is fun for a wander and a peek at local seafood for sale, which you can have cooked up on the spot at small restaurants. It's also a good place to stock up on _gamgyul_ , Jeju's traditional citrus fruit, or to snack on _mandu_ (dumplings), _hotteok_ (fried, syrup-filled pancakes) and black-pork cabbage rolls.
Dongmun Market | DANIELVFUNG/GETTY IMAGES ©
Saesom GalbiBarbecue$$
(새섬 갈비; %064-732 4001; 32 Soldongsan-ro 10beon-gil, Seogwi-dong, Seogwipo; mains ₩12,000-30,000; h11.30am-10.30pm)
Perched on a cliff overlooking the harbour, this is the place for barbecued beef or pork. The atmosphere is informal and boisterous thanks to the weathered floors, open dining concept and giddy staff. Side dishes are modest, but the meat is top-notch. Look for a black and white building.
Nilmori Dong DongBar
(닐모리동동; %064-745 5008; www.nilmori.com; 2396 Yongdamsam-dong, Jeju-si; h10am-11pm, to 10pm Nov-Mar)
On the coastal road behind the airport is this eclectic cafe-bar-restaurant that often stages craft exhibitions and other arty events. A ₩6000 taxi ride from Shin Jeju, it's a worthwhile stop if you're looking for a place to eat (pizza and pasta from ₩15,000), drink and sample the local arts scene before or after strolling the oceanfront promenade.
8INFORMATION
**Tourist Information Centre Ferry Terminal** ( %064-758 7181; Jeju-si Ferry Terminal; h6.30am-8pm) At Jeju-si's ferry terminal.
www.visitjeju.net/en Packed with useful info, and offers a live chat service.
8GETTING AROUND
BUS
It is possible to travel by bus across the whole island from Jeju-si, with the furthest destinations between one and two hours away.
Streams of city and round-island buses originate from the **Intercity Bus Terminal** (제주시외버스터미널; %064-753 1153; 174 Seogwang-ro, Orail-dong); tourist information offices can provide a timetable. All regular fares are ₩1200. Most stops have convenient screens with live departure information and maps in English.
TAXI
The charge is ₩2800 for the first 2km; a 15km journey costs about ₩10,000. You can hire a taxi for around ₩150,000 a day.
# BUSAN
#### Beomeo-sa
#### Sights & Activities
#### Shopping
#### Eating & Drinking
#
Busan at a Glance
Home to majestic mountains, glistening beaches, steaming hot springs and fantastic seafood, South Korea's second-largest city is a rollicking port town with tonnes to offer. From casual tent bars and chic designer cafes to fish markets teeming with every species imaginable, Busan (부산) has something for all tastes. Rugged mountain ranges slice through the urban landscape, and events such as the Busan International Film Festival underscore the city's desire to be a global meeting place.
Gamcheon Culture Village | PINGLABEL/SHUTTERSTOCK ©
With a Day in Port
Explore serene Beomeo-sa, Busan's most magnificent temple, then select fresh seafood for lunch at Jagalchi Fish Market. Top it off by bathing with the locals at Spa Land.
Best Places for...
**City views** Geumgang Park Cable Car
**Tea break** Maru
**Photo ops** Gamcheon Culture Village
**Shopping** Shinsegae Centum City
Getting from the Port
The **International Passenger Terminal** (부산항 국제여객터미널; %051 400 1200; www.busanpa.com; 45-39 Choryang-dong; h8am-11.30pm; mLine 1 to Choryang, Exit 6) is about a 15-minute walk from Choryang subway station; cruise operators often offer a shuttle service to the station. From here it's a short ride to central Nampo-dong metro station.
Larger ships often dock at the **International Cruise Terminal** at Yeongdo; a free shuttle takes about 30 minutes to reach Nampo-dong station.
Fast Facts
**Currency** Korean won (₩)
**Language** Korean
**Money** ATMs that accept foreign cards are common: look for one that has a 'Global' sign or the logo of your credit-card company. Portable ATMs are often brought in to greet cruise ships.
Tourist information The international passenger terminal has a tourist information service. There is also an office at Busan station.
**Wi-fi** Busan is a wired city – many public areas and tourist attractions have open wi-fi networks and most cafes and restaurants have password-protected access.
TOP EXPERIENCE
# Beomeo-sa
Busan's most magnificent temple and one of Korea's five great temples, Beomeo-sa temple complex sits high above Busan. It's not close to the port, but the interesting temple buildings, hiking trails and serene atmosphere make it worth the journey.
Great For...
hcg
yDon't Miss
Before heading back to the city, visit the _pajeon_ (파전; green onion pancake) restaurants near the bus stop.
Explore Ashore
Take a shuttle to Nampo-dong or Choryang station, then take Line 1 straight up to Beomeo-sa station. At street level from the station, spin 180 degrees, turn left at the corner and walk 200m to the terminus. Catch bus 90 (₩1200, 20 minutes, every 15 minutes) or take a taxi (₩5000) to the temple entrance.
8Need to Know
범어사; %051 508 3122; www.beomeo.kr; 250 Beomeosa-ro; h8.30am-5.30pm; mLine 1 to Beomeosa, Exit 5
ISARINT SANGMANEE/SHUTTERSTOCK ©
### The Temple
This magnificent, 1300-year-old temple is Busan's best sight. Despite its city location, Beomeo-sa is a world away from the urban jungle, with impressive architecture set against an extraordinary mountain backdrop. The temple complex features several beautiful buildings, gates and steles sprinkled around paths and courtyards. In spring the masses of wisteria bloom lavender; autumn brings spectacular foliage.
Beomeo-sa can be a busy place on weekends and holidays, as the path leading to the temple is the northern starting point for trails across Geumjeong-san.
### Buddhism in Korea
When first introduced during the Koguryo dynasty in AD 370, Buddhism in Korea coexisted with shamanism. Buddhism was persecuted during the Joseon period, when temples were tolerated only in remote mountains. The religion suffered another sharp decline after WWII as Koreans pursued worldly goals. But South Korea's success in achieving developed-nation status, coupled with a growing interest in spiritual values, is encouraging a Buddhist revival. Temple visits have increased and large sums of money are flowing into temple reconstruction. According to 2015 data from Statistics Korea, 15% of the population claims to be Buddhist.
ZKRUGER/SHUTTERSTOCK ©
### Geumjeong Fortress
Trails from the temple complex lead uphill to **Geumjeong-san** (금정산; Geumjeong Mountain), home to Geumjeong Fortress (금정산성) F. Travellers expecting to see a fortress here will be disappointed; the 'fortress' consists of four gates and 17km of stone walls encircling 8 sq km of mountaintop. Not all is lost, though, because this is where you'll find some of the city's best hiking, and the opportunity to see Korean hikers sporting the very latest in alpine fashion.
For those with leftover time and energy, there's a steep walk up to the main ridge, heading from the left side of Beomeo-sa, which takes about an hour. Follow the trail left and head to Bukmun (북문; North Gate). The 8.8km hike from Beomeo-sa to Nammun (남문; South Gate) is a comfortable walk with a couple of steep stretches. From here you can continue on to the Geumgang Park Cable Car (금강공원 케이블카; <http://geumgangpark.bisco.or.kr>; one way/return adult ₩5000/8000, child ₩4000/6000; h9am-5pm; mLine 1 to Oncheonjang, Exit 1) – the panoramic view is breathtaking. All up the walk from the temple to the top of the cable car takes around four hours. The cable car is a 15-minute walk from Oncheonjang station.
Busan
1Sights
1Jagalchi Fish MarketA3
2Activities, Courses & Tours
2City Tour BusanB1
7Shopping
3Gukje MarketA3
5Eating
4Jacky's SeafoodA3
6Drinking & Nightlife
5Fermentation KitchenA3
1Sights & Activities
Jagalchi Fish MarketMarket
(map Google map; 자갈치 시장; %051 245 2594; <http://jagalchimarket.bisco.or.kr>; 52 Jagalchihaean-ro; h8am-10pm, closed 1st & 3rd Tue of month; mLine 1 to Jagalchi, Exit 10)
Anyone with a love of seafood and a tolerance for powerful odours could easily spend an hour exploring the country's largest fish market. Narrow lanes outside the main building teem with decades-old stalls and rickety food carts run by grannies who sell an incredible variety of seafood, including red snapper, flounder and creepy-crawly creatures with undulating tentacles.
Inside the main building, dozens of 1st-floor vendors sell just about every edible sea animal, including crabs and eels, two Busan favourites. After buying a fish, the fishmonger will point you to a 2nd-floor seating area where your meal will be served (service charge per person ₩4000).
Gamcheon Culture VillageArchitecture
(감천문화마을; h24hr; mLine 1 to Toseong-dong, Exit 8) F
This historically rich, mountainside slum became a tourist destination after an arty makeover in 2009, when students decided to brighten up the neighbourhood with clever touches up the stairs, down the lanes and around the corners. Today it's a colourful, quirky community of Lego-shaped homes, cafes and galleries, ideal for an hour or two of strolling and selfies. Buy a map (₩2000) and join the scavenger hunt. Comfortable walking shoes recommended.
From the metro station, cross the street and walk to the bus stop in front of the hospital. Catch minibus 2 or 2-2 (₩900, 10 minutes) up the steep hill to the village. A taxi from the hospital (₩3000) is faster.
Haedong YonggungsaTemple
(해동 용궁사; %051 722 7744; www.yongkungsa.or.kr/en; 86 Yonggung-gil, Gijang-eup; g181 to Yonggungsa Temple stop, mLine 2 to Haeundae, Exit 7) F
One of the country's few temples situated on the coast, there are spectacular views of the temple grounds and surrounding ocean. Located quite north of the city, it gets congested on the weekends – but the vistas, elaborate altars, and statues of towering zodiac animals and a giant gold Buddha make the venture well worth it.
Haedong Yonggungsa | SIRICHAISTUDIO/SHUTTERSTOCK ©
City Tour BusanBus
(map Google map; 부산 시티 투어버스; %051 464 9898; www.citytourbusan.com; 206 Jungang-daero, Busan Station; adult/child ₩15,000/8000; htour times vary; mLine 1 to Busan station, Exit 1)
City Tour runs six daytime routes with different themes. Buy a Loop Tour ticket and you can jump on and off the bus all day. All buses start at Busan station.
7Shopping
Gukje MarketMarket
(map Google map; 국제시장; %051 245 7389; Sinchang-dong 4(sa)-ga; h8.30am-8.30pm; mLine 1 to Jagalchi, Exit 7)
West of Nampo-dong, this traditional market has hundreds of small booths with a staggering selection of items, from leather goods to Korean drums.
Bujeon MarketMarket
(부전시장; %051 818 1091; 23 Jungang-daero 783beon-gil; h4am-8pm; mLine 1 to Bujeon, Exit 5)
You could easily spend an hour getting lost in this enormous traditional market specialising in produce, seafood and knick-knacks.
Soup at Bujeon Market | PHOTONN/SHUTTERSTOCK ©
The World's Largest Shopping Complex
Shinsegae Centum City (신세계 센텀시티; %1588 1234; www.shinsegae.com; 35 Centumnam-daero; h10.30am-8pm; mLine 2 to Centum City, Shinsegae Exit) is the world's largest shopping complex – bigger than Macy's in New York – with everything you'd expect in a temple of commerce.
There's a skating rink, indoor golf driving range, shops with seemingly every brand name in the universe and a place to recuperate – Spa Land ( %051 745 2900; www.shinsegae.com; 1st fl, Shinsegae Centum City; adult/youth weekdays ₩13,000/10,000, weekends ₩15,000/12,000; h6am-midnight, last entry 10.30pm; mLine 2 to Centum City, Exit 3), Asia's largest bathhouse. The bathing area isn't particularly impressive, but the _jjimjil-bang_ (the area where people wear loose-fitting clothes) is immense – there's a panoply of relaxation rooms of various temperatures and scents. Kids under 13 are not permitted.
Shinsegae Centum City | CHANAWAT PHADWICHIT/SHUTTERSTOCK ©
5Eating & Drinking
Yetnal JjajangKorean$
(옛날짜장; %051 809 8823; 15 Gaya-daero 784beon-gil; meals from ₩4000; h11am-10pm; mLine 1 or 2 to Seomyeon, Exit 7)
A sterling example of a successful restaurant owner who won't update the interior. According to superstition, the good fortune a successful shop enjoys can be lost if the interior were changed. Consequently, some shoddy-looking restaurants, like this one, serve great food. See noodles get hand-pulled as you enjoy the excellent _jjajangmyeon_ (짜장면; black bean-paste noodles) and _jjambbong_ (짬뽕; spicy seafood soup).
Jacky's SeafoodSeafood$$
(map Google map; 돼지초밥 횟집; %051 246 2594; 52 Jagalchihaean-ro, 2F; h9am-10pm, closed 1st & 3rd Tue of month; mLine 1 to Jagalchi, Exit 10)
Buying a raw-fish dinner couldn't be easier thanks to Jacky, the affable owner of this seafood restaurant. He speaks fluent English and uses signboards to help customers make smart seasonal food choices. It's on the 2nd floor of the main Jagalchi building.
Fermentation KitchenCocktail Bar
(map Google map; 발효주방, Barhyo Kitchen; %010 3041 1320; www.facebook.com/barhyokitchen; 2F, 83 Gwangbok-ro jung-gu; makgeolli from ₩16,000; hnoon-12.30am Sun-Thu, to 1.30am Fri & Sat; W; mLine 1 to Nampo, Exit 3)
Fermentation Kitchen is a great place to sample _makgeolli_ (traditional Korean rice wine). The restaurant-bar serves special carbonated _makgeolli_ in wine glasses alongside modern takes on Korean dishes. While _makgeolli_ purists might not prefer the venue's high-end feel, the prices here are reasonable.
MaruTeahouse
(마루; %051 803 6797; Saesak-ro 17-1, Jin-gu; h10am-10pm; mLine 1 or 2 to Seomyeon, Exit 9)
Splendid herbal teas and a warm interior make this an excellent alternative to the sterile sameness of chain coffee shops. The dark and earthy twin flower tea (쌍화차) is a speciality.
8INFORMATION
Busan Station Tourism Office (부산역 관광 안내소; %051 441 6565; 206 Jungang-daero; h9am-8pm; m Line 1 to Busan station, Exit 8 or 10) Maps and helpful staff, located on the 2nd floor.
8GETTING AROUND
**Bus** Busan's bus system is extensive; adult cash fares are ₩1300/1800 for regular/express buses.
**Subway** Busan's four-line subway uses a two-zone fare system that costs ₩1400 per ride for one zone and ₩1600 for longer trips if using single-journey paper tickets; a one-day pass costs ₩4500.
**Taxi** Plentiful and easy to hail on the street. Basic fares start at ₩3300 (with a 20% night premium). Avoid black-and-red deluxe taxis if possible, because the fares can run high.
# In Focus
## Northeast Asia Today
Tourist numbers, the tech industry, average ages and geopolitical tensions are all on the rise.
Higashiyama, Kyoto | GUITAR PHOTOGRAPHER/SHUTTERSTOCK ©
## History
Follow the region's path from its cultural birth to the cataclysms of the 20th century.
## Arts & Architecture
From traditional gardens to contemporary architecture and K-Pop, Northeast Asian arts excel and intrigue.
## Food & Drink
A sampling platter of the diverse dishes, tastes and tipples that await.
## The People of Northeast Asia
A window into the life of the region's people.
# Northeast Asia Today
Ageing populations, booming tourist numbers, riding the tech boom, regional geopolitical tensions (old and new) and money, money, money. Northeast Asia is diverse and complex, but the same themes emerge across the region.
Shànghǎi | DOVE LEE/GETTY IMAGES ©
## Japan
Japan's stubbornly stagnant economy and dramatically declining population may well be harbingers of the kinds of problems other developed nations will face as their populations taper off. And while many developed countries have recently focused inwards, Japan is taking tentative steps towards looking out. Will the country grow to embrace a new, yet-to-be-defined kind of cosmopolitanism, setting a model for others to follow?
Japan has long hoped to boost its underdeveloped inbound-tourism industry. Then it got real by relaxing visa regulations for visitors from its Asian neighbours. Along with the periodically weak yen, this has resulted in a dramatic uptick of foreign visitors. Inbound numbers have more than doubled since 2010; in 2017 the country logged 28.7 million visitors, already overshooting the target of 20 million set for 2020 – the year Tokyo holds the Summer Olympics.
There is hand wringing, of course. How do we please these tourists? Where are we going to park all the tour buses? And will we ever be able to visit Kyoto in peace again?
But there is also intense fascination. What, exactly, do foreigners find interesting about Japan? There has been an explosion of TV shows trying to figure that out, interviewing tourists and even sending TV personalities to check out places listed in the Lonely Planet guide.
## Shànghǎi
The Shanghainese may natter about traffic gridlock and chat about the latest celebrity faux pas or political scandal, but what they really talk about is cash. Labelled _xiǎozī_ – 'little capitalists' – by the rest of the land, the Shànghǎi Chinese know how to make _qián_ (money) and, equally importantly, how to flaunt it. Ever since Shànghǎi first prospered under foreign control, wealth creation has been indivisible from the Shànghǎi psyche. Whether it's the stock market, apartment price tags or the latest Dior evening bag, money's the talk of the town.
## South Korea
Plagued with high youth unemployment, growing social welfare liabilities, old-age poverty and a rapidly declining birth rate, South Korea today faces multiple challenges. Relations with China and Japan have been uncertain.
Yet South Korea is today, by any measure, one of the world's star performers. Its top companies, such as Samsung, LG and Hyundai, make products the world wants. South Korea is now possibly the most wired nation on earth. The talented younger generation has created such a dynamic pop culture that _hallyu_ (the Korean Wave) has swept the globe. And a dramatic rapprochement between North and South Korea promises – but does not guarantee – to replace decades of hostility.
## Taipei
With the January 2016 victory of the Democratic Progressive Party (DPP) and the 2018 reelection of Taipei mayor Ko Wen-je, a self-styled man of the people, the mood in Taipei is a mixture of youthful hope and trepidation. You can see that hope in the blossoming of art districts – Songshan and Huashan Cultural Parks, Dihua St – led by young designers and entrepreneurs. However, many residents feel that old-school corruption continues to blight the city, citing a number of construction projects that are behind schedule, including Taipei Dome and the airport MRT connection.
# History
The modern cities of Northeast Asia glitter with the promise of tomorrow, but even amid the high-rises and neon, you'll find compelling stories of the region's past at every turn. Age-old power struggles have long defined the region's fortunes, bringing conflict, invasion and rebellion, as well as cultural cross-pollination and economic interdependency.
Wall painting, Bao'an Temple, Taipei | ANNAPURNA MELLOR/GETTY IMAGES ©
Guardian sculptures, Beomeo-sa, Busan | ISARINT SANGMANEE/SHUTTERSTOCK ©
## Japan
### Early Japan
The earliest traces of human life in Japan date to around 30,000 years ago, but it is possible that people were here much earlier. The first recognisable culture to emerge was the neolithic Jōmon, from about 13,000 BC.
Agriculture-based settlement led to territories and boundaries being established, and the rise of kingdoms, the most powerful of which was ruled by the Yamato clan in the Kansai region. The Yamato clan would go on to found the court in Nara and then later Heian-kyō (Kyoto), from where the imperial dynasty would rule for over a millennia.
### The Rise & Fall of the Heian Court
In Kyoto over the next few centuries courtly life reached a pinnacle of refined artistic pursuits and etiquette, captured famously in the novel _The Tale of Genji,_ written by the court-lady Murasaki Shikibu in about 1004. But it was also a world increasingly estranged from the real one. Manipulated over centuries by the politically powerful Fujiwara family, the imperial throne was losing its authority.
Out in the provinces powerful military forces were developing. Some were led by distant imperial family members, barred from succession claims and hostile to the court. Their retainers included skilled warriors known as samurai (literally 'retainer'). An all-out feud developed between the two main clans of disenfranchised nobles, the Minamoto and the Taira.
The Taira initially prevailed, but by 1185 Kyoto had fallen and the Taira had been pursued to the western tip of Honshū. A naval battle ensued, won by the Minamoto.
### The Kamakura Shogunate
Minamoto Yoritomo did not seek to become emperor, but wanted the new emperor to give him legitimacy by conferring the title of shogun (generalissimo), which was granted in 1192, and in practice he was in charge. He left many existing offices and institutions in place and set up a base in his home territory of Kamakura (not far from present-day Tokyo) rather than Kyoto. Yoritomo established a feudal system – which would last almost 700 years as an institution – centred on a loyalty-based lord–vassal system.
After Yoritomo died in 1199, Yoritomo's widow, of the Hōjō clan, acted first as regent before claiming the shogunate outright. It was during the Hōjō shogunate that the Mongols, under Kublai Khan (r 1260–94), twice tried to invade, in 1274 and 1281. On both occasions they were ultimately defeated by storms that destroyed much of their fleet. The typhoon of 1281 prompted the idea of divine intervention, with the coining of the term kamikaze (literally 'divine wind'). Later this term was used to describe Pacific War suicide pilots who, said to be infused with divine spirit, gave their lives to protect Japan from invasion.
Despite victory, the Hōjō suffered: their already depleted finances could not cover the payment promised to the warriors enlisted to fight the Mongols. Dissatisfaction towards the shogunate came to a head under the unusually assertive emperor Go-Daigo (1288–1339), who banded together with the promising young general Ashikaga Takauji (1305–58) to overthrow the Hōjō. Ashikaga claimed the mantle of shogun, setting up a base in Kyoto.
### The Warring States
With a few exceptions, the Ashikaga shoguns were relatively ineffective. Without strong, centralised government and control, the country slipped into civil war; the period from 1467 to 1603 is known as the Sengoku (Warring States) era. In 1543 the first Europeans arrived – another game changer – bringing with them Christianity and firearms. The warlord Nobunaga Oda (1534–82) was quick to apprehend the advantage of the latter. Starting from a relatively minor power base, his skilled and ruthless generalship produced a series of victories. In 1568 he seized Kyoto and held de facto power until, betrayed by one of his generals, he was killed in 1582. Another of his generals, Hideyoshi Toyotomi (1536–98), took up the torch, disposing of potential rivals among Nobunaga's sons and taking the title of regent.
Hideyoshi's power had been briefly contested by Tokugawa Ieyasu (1543–1616), son of a minor lord allied to Nobunaga. After a brief struggle for power, Ieyasu agreed to a truce with Hideyoshi; in return, Hideyoshi granted him eight provinces in eastern Japan. While Hideyoshi intended this to weaken Ieyasu by separating him from his ancestral homeland Chūbu (now Aichi Prefecture), the upstart looked upon the gift as an opportunity to strengthen his power. He set up his base in a small castle town called Edo (which would one day become Tokyo). On his deathbed, Hideyoshi entrusted Ieyasu, who had proven to be one of his ablest generals, with safeguarding the country and the succession of his young son Hideyori (1593–1615). Ieyasu, however, had bigger ambitions and soon went to war against those loyal to Hideyori, finally defeating them at the legendary Battle of Sekigahara in 1600. He chose Edo as his permanent base and ushered in two and a half centuries of Tokugawa rule.
The Way of the Warrior
Samurai followed a code of conduct that came to be known as _bushidō_ (the way of the warrior), drawn from Confucianism, Shintō and Buddhism. Confucianism required a samurai to show absolute loyalty to his lord, possess total self-control, speak only the truth and display no emotion. Since his honour was his life, disgrace and shame were to be avoided above all else, and all insults were to be avenged. Seppuku (ritual suicide by disembowelment), also known as hara-kiri, was an accepted means of avoiding the dishonour of defeat. From Buddhism, the samurai learnt the lesson that life is impermanent – a handy reason to face death with serenity. Shintō provided the samurai with patriotic beliefs in the divine status both of the emperor and of Japan.
### Tokugawa Rule
Ieyasu and his successors kept tight control over the provincial _daimyō_ (warlords), who ruled as vassals for the regime.
Early on, the Tokugawa shogunate adopted a policy of _sakoku_ (seclusion from the outside world). Following the Christian-led Shimabara Rebellion, Christianity was banned and several hundred thousand Japanese Christians were forced into hiding. All Westerners, except the Protestant Dutch, were expelled by 1638. Overseas travel for Japanese was banned (as well as the return of those already overseas). And yet, the country did not remain completely cut off: trade with Asia and the West continued through the Dutch and the Ryūkyū empire (now Okinawa) – it was just tightly controlled and, along with the exchange of ideas, funnelled exclusively to the shogunate. Japan's cities grew enormously during this period: Edo's population topped one million in the early 1700s, dwarfing much older London and Paris.
### The Meiji Restoration
In 1853 and again the following year, US commodore Matthew Perry steamed into Edo-wan (now Tokyo Bay) with a show of gunships – which the Japanese called _kurofune_ (black ships), because they were cloaked in pitch – and demanded Japan open up to trade and provisioning. The shogunate was no match for Perry's firepower and agreed to his demands. Soon other Western powers followed suit. Japan was obliged to sign what came to be called the 'unequal treaties', opening ports and giving Western nations control over tariffs. Anti-shogun sentiment was high and following a series of military clashes between the shogun's armies and the rebels, the last shogun – Yoshinobu (1837–1913) – agreed to retire in 1867.
In 1868, the new teenage emperor Mutsuhito (1852–1912; later known as Meiji) was named the supreme leader of the land, commencing the Meiji period (1868–1912; Enlightened Rule). The institution of the shogun was abolished and the shogun's base at Edo was refashioned into the imperial capital and given the new name, Tokyo (Eastern Capital). In truth, the emperor still wielded little actual power.
Above all, the new leaders of Japan – keen observers of what was happening throughout Asia – feared colonisation by the West. They moved quickly to modernise, as defined by the Western powers, to prove they could stand on an equal footing with the colonisers.
### Rise of a Global Power
A key element of Japan's aim to become a world power was military might. Using the same 'gunboat diplomacy' on Korea that Perry had used on the Japanese, in 1876 Japan was able to force on Korea an unequal treaty of its own. Using Chinese 'interference' in Korea as a justification, in 1894 Japan manufactured a war with China; victorious, Japan gained Taiwan and the Liaotung Peninsula. When Japan officially annexed Korea in 1910, there was little international protest. Japan entered WWI on the side of the Allies, and was rewarded with a council seat in the newly formed League of Nations. It also acquired German possessions in East Asia and the Pacific.
Yet as the 1920s rolled around, a sense of unfair treatment by Western powers once again took hold in Japan. The Washington Conference of 1921–2 set naval ratios of three capital ships for Japan to five American and five British; around the same time, a racial-equality clause Japan proposed to the League of Nations was rejected. In the fall of 1931, members of the Japanese army stationed in Manchuria, there to guard rail lines leased by China to Japan, detonated explosives along the track and blamed the act on Chinese dissidents. This ruse, which gave the Japanese army an excuse for armed retaliation, became known as the Manchurian Incident. Within months the Japanese had taken control of Manchuria and installed a puppet government. The League of Nations refused to acknowledge the new Manchurian government; in 1933 Japan left the league.
Skirmishes continued between the Chinese and Japanese armies, leading to full-blown war in 1937. Following a hard-fought victory in Shànghǎi, Japanese troops advanced south to capture Nanjing. Over several months somewhere between 40,000 and 300,000 Chinese were killed in what has become known as the Nanjing Massacre or Rape of Nanjing. To this day, the number of deaths and the prevalence of rape, torture and looting by Japanese soldiers is hotly debated among historians (and government nationalists) on both sides.
### WWII & Occupation
Encouraged by Germany's early WWII victories, Japan signed a pact with Germany and Italy in 1940. With France and the Netherlands distracted and weakened by the war in Europe, Japan quickly moved on their colonial territories – French Indo-China and the Dutch West Indies – in Southeast Asia. Tensions between Japan and the United States intensified, as the Americans, alarmed by Japan's aggression, demanded Japan back down in China. When diplomacy failed, the USA barred oil exports to Japan – a crucial blow. Japanese forces struck at Pearl Harbor on 7 December 1941, damaging much of America's Pacific fleet.
Japan advanced swiftly across the Pacific; however, the tide started to turn in the Battle of Midway in June 1942, when much of its carrier fleet was destroyed. Japan had overextended itself, and over the next three years was subjected to an island-hopping counter-attack. By mid-1945, Japan, ignoring the Potsdam Declaration calling for unconditional surrender, was preparing for a final Allied assault on its homeland. On 6 August the world's first atomic bomb was dropped on Hiroshima, killing 90,000 civilians. And on 9 August another atomic bomb was dropped, this time on Nagasaki, with another 50,000 deaths. Emperor Hirohito formally surrendered on 15 August.
The terms of Japan's surrender to the Allies allowed the country to hold on to the emperor as the ceremonial head of state, but Hirohito no longer had authority – nor was he thought of as divine – and Japan was forced to give up its territorial claims in Korea and China. In addition, America occupied the country under General Douglas MacArthur, a situation that would last until 1952 (Okinawa would remain occupied until 1972).
### The Boom Years
In the 1950s Japan took off on a trajectory of phenomenal growth that is often described as miraculous (jump-started by US procurement for the Korean War). Throughout the 1960s, Japan's GDP grew, on average, 10% a year. The new consumer class, inspired by the images of affluence introduced during the American occupation, yearned for the so-called 'three sacred treasures' of the modern era (a play on the three sacred treasures of the imperial family: the sword, the mirror and the jewel) – a refrigerator, a washing machine and a television. By 1964, 90% of the population had them.
Growth continued through the '70s and reached a peak in the late '80s. Based on the price paid for the most expensive real estate in the late 1980s, the land value of Tokyo exceeded that of the entire US. The wildly inflated real-estate prices and stock speculation fuelled what is now known as the 'Bubble economy'. It seemed like things could only go up – until they didn't.
### Heisei Doldrums
In 1991, just two years after the Heisei Emperor ascended the throne, the bubble burst and Japan's economy went into a tailspin. The 1990s were christened the 'Lost Decade', but that has since turned into two, and probably three, as the economy continues to slump along, despite government intervention. Long-time prime minister Abe Shinzō's so-called Abenomics plan, which included a devaluing of the yen, has had some positive effects on corporate gains – and also on inbound tourism (making Japan a cheaper place to visit!) – and generated some 'Japan is back!' headlines, but ordinary people have seen little change. By now a whole generation has come of age in a Japan where lifelong employment – the backbone of the middle class – is no longer a guarantee.
With the abdication of the Heisei Emperor in 2019, the era came to a close and so, many hope, will the malaise it came to symbolise.
## Shànghǎi
In just a few centuries, Shànghǎi went from being an insignificant walled town south of the mouth of the Yangzi River to becoming China's leading and wealthiest metropolis. A dizzying swirl of opium, trade, foreign control, vice, glamour, glitz, rebellion, restoration and money, Shànghǎi's story is a rags-to-riches saga of decadence, exploitation and, ultimately, achievement.
Up until around the 7th century AD, Shànghǎi was little more than marshland, but by the late 17th century, Shànghǎi supported a population of 50,000 on cotton production, fishing and trade in silk and tea.
By the 18th century, the British passion for Chinese tea was increasingly matched by China's craving for opium (yāpiàn), the drug that would virtually single-handedly create latter-day Shànghǎi and earn the city its bipolar reputation as the splendid 'Paris of the East' and the infamous 'Whore of the Orient'. Trading tensions culminated in war; the Treaty of Nanking, which concluded the First Opium War in 1842, was Shànghǎi's moment of reckoning. Its signing spelled the death of old Shànghǎi and the birth of the new Shànghǎi: an open, lawless and spectacularly prosperous trading city. Years of rebellion, exploitation, and, finally, war and occupation ended with the declaration of the People's Republic of China in 1949.
In 1990 the central government began pouring money into Shànghǎi, beginning the city's stunning turnaround. Obsessively comparing itself to Hong Kong, the Huángpǔ River city closed the gap on the ex-British territory with breathtaking rapidity during the noughties. The process was unparalleled in scale and audacity.
## South Korea
Koreans can trace a continuous history on the same territory reaching back thousands of years. The present politically divided peninsula is mirrored by distant eras such as the Three Kingdoms period (57 BC–AD 668), when the kingdoms of Goguryeo, Silla and Baekje jockeyed for control of territory that stretched deep into Manchuria. Korea's relationship with powerful neighbours China and Japan has also long defined the country's fortunes, while ties to the West have added further complexity to national self-understanding.
## Taiwan
Taipei is an architectural hotpot of temples, run-down walk-ups, colonial finery, and modern skyscrapers and shopping malls. Three hundred years ago it was just a scattering of indigenous settlements; since then it's been a Chinese tea-trading post, a Japanese colony and a Kuomintang (KMT) base.
In 1709, settlers from China's Fujian province received permission from the Qing government to settle and develop the island, and in 1886 Taipei became the capital of the newly founded Taiwan province. China ceded Taiwan to Japan under the Treaty of Shimonoseki in 1895 and Japanese troops entered Taipei that same year. After Japan's defeat in WWII, Taiwan was returned to China.
In 1949, Nationalist forces fled the Communist takeover of mainland China for Taiwan. With the remarkable growth of Taiwan's economy starting in the 1960s, the capital attracted people from all over and architectural anarchy played out in the drive to provide housing for the masses. Since the late '90s and the country's democratisation, the capital has made a remarkable transformation into one of the most liveable and vibrant cities in Asia. Today, Taipei dreams of success and international recognition – a perplexing product of decades of turmoil.
South Korea's Jeju-do
According to legend, Jeju-do was founded by three brothers who came out of holes in the ground and established the independent Tamna kingdom. Early in the 12th century the Goryeo dynasty took over, but in 1273 Mongol invaders conquered the island, contributing a tradition of horsemanship, a special horse _(jorangmal)_ and quirks in the local dialect.
The Japanese colonial period of the early 20th century can be traced through abandoned military bases and fortifications on the island. From 1947 to 1954, as many as 30,000 locals were massacred by right-wing government forces in events collectively labelled the 'April 3 Incident'.
Recent decades have seen Jeju-do's economy shift from mainly agriculture to tourism. In 2006 the island was made into a special autonomous province, giving it a level of self-government that is encouraging further economic development. Ambitious carbon-free electricity generation ventures are being tested.
## Timeline
**c 10,000 BC**
Ancestors of Taiwan's present-day indigenous people first come to the island by sea and begin settling around the island.
**AD mid-5th century**
Writing is introduced to Japan by scholars from the Korean kingdom of Baekje and is based on the Chinese system of characters.
**1274**
With help from Korea, a Mongol army attempts to conquer Japan but is thwarted by a heavy sea storm (kamikaze).
**1543**
Portuguese, the first Westerners, arrive by chance in Japan, bringing firearms and Christianity.
**1553**
The wall around Shànghǎi Old City is constructed to fend off Japanese pirates. The wall stands until the fall of the Qing dynasty.
**1638**
The _sakoku_ policy of Japanese national isolation is in place.
**1853–54**
US commodore Matthew Perry's 'black ships' arrive off the coast of Shimoda, forcing Japan to open up for trade.
**1859**
Five international ports are established in Japan: Yokohama, Hakodate, Kōbe, Niigata and Nagasaki.
**1861–64**
The Treaty of Tianjin forces open Taiwan ports Anping, Tamsui, Keelung and Kaohsiung to Western trade.
**1876**
The Japanese prevail in getting Korea to sign the Treaty of Ganghwa, formally opening up three of the nation's ports to international trade.
**1895**
The Treaty of Shimonoseki concludes the First Sino-Japanese War, forcing China to cede territories (including Taiwan) to Japan.
**1910**
Korean Emperor Sunjong refuses to sign the Japan–Korea Annexation Treaty, but Japan effectively annexes Korea in August.
**1931–7**
Japan takes control of Manchuria and eventually Shànghǎi, too.
**1941**
Japan enters WWII by striking Pearl Harbor without warning on 7 December.
**1945**
Hiroshima and Nagasaki become victims of atomic bombings on 6 and 9 August.
**1947**
The Taiwanese government suppresses a public uprising, killing thousands of people in what is later known as the 2-28 Incident.
**1949**
Communist forces take Shànghǎi and the People's Republic of China (PRC) is proclaimed.
**1953**
The armistice ending the Korean War is signed by the US and North Korea, but not South Korea.
**1987**
After 38 years, martial law is lifted in Taiwan, setting the stage for the island's eventual shift from authoritarian rule to democracy.
**2010**
China surpasses Japan as the world's second-largest economy after the USA.
**2011**
The Great East Japan Earthquake strikes off the coast of Tōhoku, generating a tsunami that kills many thousands.
**2012**
Anti-Japanese demonstrations are held in Shànghǎi and other cities across China in response to Japanese claims to the Diàoyú Islands.
**April 2019**
Emperor Akihito, the first Japanese emperor of the modern age to abdicate, steps down on 30 April, ushering in the new Reiwa era.
**May 2019**
Taiwan becomes the first Asian nation to legalise same-sex marriage.
# Arts & Architecture
Centuries of cross-pollination, isolation, migration and trade have gifted this region with a strong and complex artistic tradition. It's fascinating to pick out common trends and unique cultural facets, aesthetics from the West that have been incorporated into the traditions of the region, and vice versa.
Shànghǎi | AAAAIMAGES/GETTY IMAGES © ORIENTAL PEARL TOWER, ARCHITECT: JIANG HUAN CHENG
## Cinema
### Golden Age of Japanese Cinema
The Japanese cinema of the 1950s – the era of acclaimed auteurs Ozu Yasujirō, Mizoguchi Kenji and Kurosawa Akira – is responsible for a whole generation of Japanophiles. Ozu (1903–63) was the first great Japanese director, known for his piercing, at times heartbreaking, family dramas. Mizoguchi (1898–1956) began by shooting social realist works in the 1930s but found critical acclaim with his reimagining of stories from Japanese history and folklore.
Kurosawa (1910–98) is an oft-cited influence for film-makers around the world. His films are intense and psychological; the director favoured strong leading men and worked often with the actor Mifune Toshirō. Kurosawa won the Golden Lion at the Venice International Film Festival and an honorary Oscar for the haunting _Rashōmon_ (1950), based on the short story of the same name by Akutagawa Ryūnosuke and starring Mifune as a bandit. Japanese cinema continues to produce directors of merit but has not emerged as the influential cultural force that its heyday seemed to foreshadow.
### Anime
Miyazaki Hayao (b 1941), who together with Takahata Isao (1935–2018) founded Studio Ghibli, is largely responsible for anime gaining widespread, mainstream appeal abroad. Thematically, his works are noteworthy for their strong female characters and environmentalism; _Nausicaä of the Valley of the Wind_ (1984) is an excellent example. He was given an Academy Honorary Award in 2014.
Among the best-known anime is _Akira_ (1988), Ōtomo Katsuhiro's psychedelic fantasy set in a future Tokyo inhabited by speed-popping biker gangs and psychic children. _Ghost in the Shell_ (1995) is an Ōshii Mamoru film with a sci-fi plot worthy of Philip K Dick involving cyborgs, hackers and the mother of all computer networks. The works of Kon Satoshi (1963–2010), including the Hitchcockian _Perfect Blue_ (1997), the charming _Tokyo Godfathers_ (2003) and the sci-fi thriller _Paprika_ (2006), are also classics.
One new director to watch is Shinkai Makoto: his 2016 _Your Name_ was both a critical and box-office smash – the second-highest-grossing domestic film ever, after _Spirited Away_.
Ang Lee
One of the world's most famous directors, Ang Lee (1954–) is known best for his megahits _The Life of Pi_ (2012) and _Crouching Tiger, Hidden Dragon_ (2000). Ang's first film was _Pushing Hands_ (1992), filmed in New York. His next movie, _The Wedding Banquet_ (1993), took a bold step in exploring homosexuality in Chinese culture. Ang then joined Hollywood and filmed _Sense and Sensibility_ (1995), _The Ice Storm_ (1997), _Brokeback Mountain_ (2005), and _Lust Caution_ (2007). Lee's accolades have included the Golden Bear (Berlin), the Golden Lion (Venice), and Best Director (Academy Awards).
## Shànghǎi Architecture
Jaw-dropping panoramas of glittering skyscrapers are its trump card, but Shànghǎi is no one-trick pony: the city boasts a diversity of architectural styles that will astound most first-time visitors. Whether you're an art deco hound, a neoclassical buff, a fan of English 1930s suburban-style villas, 1920s apartment blocks or Buddhist temple architecture, Shànghǎi has it covered.
### Lòngtáng & Shíkùmén
Even though Shànghǎi is typified by its high-rise and uniform residential blocks, near ground level the city comes into its own with its low-rise _lòngtáng_ and _shíkùmén_ (stone gate) architecture. Here, both Western and Asian architectural motifs were synthesised into harmonious, utilitarian styles that still house a large proportion of Shànghǎi's residents.
### Concession Architecture
For many foreign visitors, Shànghǎi's modern architectural vision is a mere side salad to the feast of historic architecture lining the Bund and beyond. Remnants of old Shànghǎi, these buildings are part of the city's genetic code, inseparable from its sense of identity as the former 'Paris of the East'.
### Building the Bund
The Bund – Shànghǎi's most famous esplanade of concession buildings – was built on unstable foundations due to the leaching mud of the Huángpǔ River. Bund buildings were first built on concrete rafts that were fixed onto wood pilings, which were allowed to sink into the mud. Because of the lack of qualified architects, some of the earliest Western-style buildings in Shànghǎi were partially built in Hong Kong, shipped to Shànghǎi, then assembled on-site.
### Modern Architecture
Charm and panache may ooze from every crevice of its concession-era villas, _shíkùmén_ buildings and art deco marvels, but for sheer wow factor, look to the city's modern skyline. Shànghǎi's tall towers get all the media attention, but many of the city's most iconic and noteworthy contemporary buildings are low-rise.
Contemporary Korean Cinema
Korean cinema is today embraced by both local audiences (thanks partly to government quotas that mandate a certain amount of screen time for domestic films) and the international festival circuit. Yeon Sang-ho's zombie apocalypse thriller _Train to Busan_ (2016) set a record as the first Korean film of the year to reach more than 10 million theatregoers.
Some films worth watching include the jaw-dropping action-revenge flick _Oldboy_ (Park Chan-wook; 2003); the critically acclaimed monster epic _The Host_ (Bong Joon-ho; 2006); the controversial, and hypersexual, _Pieta_ (Kim Ki-duk; 2012), a Golden Lion winner at Venice; and anything by low-budget, shoe-gazer Hong Sang-soo – his 2017 _On the Beach at Night Alone_ won a handful of awards.
## K-Pop
K-Pop, with its catchy blend of pop R&B, hip hop and EDM – complete with synchronised dance moves – shows no sign of fading away. As soon as critics declare it over, new groups emerge to capture hearts (and endorsements) around Asia and, more recently, the United States. In 2018 one of the top groups of the moment, BTS – which stands for _'bangtan sonyeondan'_ or 'bulletproof boy scouts' – became the first-ever K-Pop act to take the number-one spot on the _Billboard_ 200 with the album _Love Yourself: Tear._ The group of seven young men are acclaimed for speaking out on subjects that are especially taboo in Korean culture, such as LGBTQ rights, mental health and the pressure to succeed.
But it's not just about covetable hairstyles and infectious tunes. According to the Korea Creative Content Agency, K-Pop was responsible for a record ₩5.3 trillion in revenue based on album, concert ticket, merchandise and music-streaming sales generated overseas in 2016.
K-Indie is the artist-driven alternative to K-Pop. Hunt for new underground bands at Korean Indie (www.koreanindie.com).
## Traditional Japanese Arts
### Gardens
Flowering plants are only one component of the Japanese garden, which may be composed of any combination of vegetation (including trees, shrubs and moss), stones of varying sizes, and water. Some gardens are not limited to that which falls within their walls, but take into account the scenery beyond (a technique called _shakkei_ or 'borrowed scenery'). Often they are meant to evoke a landscape in miniature, with rocks standing in for famous mountains of myth or Chinese literature; raked gravel may represent flowing water. Garden elements are arranged asymmetrically and shapes, such as the outline of a pond, are often irregular. The idea is that the garden should appear natural, or more like nature in its ideal state; in reality most gardens are meticulously maintained – and entirely by hand.
Gardens may be designed as spaces of beauty, for leisure and entertainment purposes, or they might be a designation of sacred space (most fall somewhere in between). The white gravel that appears in some temple gardens is rooted in Shintō tradition: there are gravel courtyards at Ise-jingū, which dates to the 3rd century and is considered Japan's most sacred spot.
You'll encounter four major types of gardens during your horticultural explorations.
**Funa asobi** Meaning 'pleasure boat' and popular in the Heian period, such gardens feature a large pond for boating and were often built around nobles' mansions.
**Shūyū** These 'stroll' gardens are intended to be viewed from a winding path, allowing the design to unfold and reveal itself in stages and from different vantages. Popular during the Heian, Kamakura and Muromachi periods, a celebrated example is the garden at Ginkaku-ji in Kyoto.
**Kanshō** Zen rock gardens (also known as _kare-sansui_ gardens) are an example of the type of 'contemplative' garden intended to be viewed from one vantage point and designed to aid meditation. Kyoto's Ryōan-ji is perhaps the most famous example.
**Kaiyū** The 'varied pleasures' garden features many small gardens with one or more teahouses surrounding a central pond. Like the stroll garden, it is meant to be explored on foot and provides the visitor with a variety of changing scenes, many with literary allusions. The imperial villa of Katsura Rikyū in Kyoto is the classic example.
### The Tea Ceremony
_Chanoyu_ (literally 'water for tea') is usually translated as 'tea ceremony', but it's more like performance art, with each element carefully designed to articulate an aesthetic experience. It's had a profound and lasting influence on the arts in Japan, one that has percolated through all the divergent arts wrapped up in it: architecture, landscape design, ikebana (flower arranging), ceramics and calligraphy.
The culture of drinking _matcha_ (powdered green tea) entered Japan along with Zen Buddhism in the 12th century. Like everything else in monastic life – the sweeping of the temple grounds and the tending of the garden, for example – the preparation of tea was approached as a kind of working meditation. The practice was later taken up by the ruling class, and in the 16th century the famous tea master Sen no Rikkyū (1522–1591) is credited with laying down the foundations of _wabi-sabi_ – and with raising tea to an art form.
More than just a place to drink tea, a Japanese teahouse is a distillation of an artistic vision; even today, no architect would turn down a commission to work on one. Visitors to a teahouse approach via the _roji_ ('dewy' path), formed by irregular stepping stones. The path represents a space of transition – a place to clear one's mind and calm one's spirit before entering the teahouse. The doorway is purposely low, causing those who enter to stoop, and thus humble themselves. All are considered equal inside the teahouse (swords were to remain outside). Gardens all over Japan have _chashitsu_ (teahouses).
### Wabi-sabi
_Wabi-sabi_ is a Japanese aesthetic that embraces the notion of ephemerality and imperfection and is Japan's most distinct – though hard to pin down – and profound contribution to the arts. _Wabi_ roughly means 'rustic' and connotes the loneliness of the wilderness, while _sabi_ can be interpreted as 'weathered', 'waning' or 'altered with age'. Together the two words signify an object's natural imperfections, arising in its inception, and the acquired beauty that comes with the patina of time. It is most often evoked in descriptions of the tea ceremony. Ceramics made for the tea ceremony – and this is where Japanese ceramics finally came into their own – often appeared dented or misshapen or had a rough texture, with drips of glaze running down the side. The teahouses too, small, exceedingly humble and somewhat forlorn (compared to the manors they were attached to) also reflected _wabi-sabi_ motifs, as did the ikebana (flower arrangements) and calligraphy scrolls that would be placed in the teahouse's _tokanoma_ (alcove).
### Painting
Traditionally, paintings were done in black ink or mineral pigments on _washi_ (Japanese handmade paper; itself an art form), scrolls (that either unfurled horizontally or were designed to hang vertically), folding screens or sliding doors.
Paintings of the Heian era (794–1185) depicted episodes of court life, like those narrated in the novel _Genji Monogatari_ _(The Tale of Genji),_ or seasonal motifs, often on scrolls. Works such as these were later called _yamato-e_ (Yamato referring to the imperial clan), as they distinguished themselves thematically from those that were mere copies of Chinese paintings. Gradually a series of style conventions evolved to further distinguish _yamato-e;_ one of the most striking is the use of a not-quite-bird's-eye perspective peering into palace rooms without their roofs (the better to see the intrigue!).
With the rise of Zen Buddhism in the 14th century, minimalist monochrome ink paintings came into vogue; the painters themselves were priests and the quick, spontaneous brush strokes of this painting style were in harmony with their guiding philosophies.
It was during the Muromachi period (1333–1573) that the ruling class became great patrons of Japanese painters, giving them the space and the means to develop their own styles. Two styles emerged at this time: the Tosa school and the Kano school.
The Tosa clan of artists worked for the imperial house, and were torch-bearers for the now classic _yamato-e_ style, using fine brushwork to create highly stylised figures and elegant scenes from history and of the four seasons; sometimes the scenes were half-cloaked in washes of wispy gold clouds.
The Kano painters were under the patronage of the Ashikaga shogunate and employed to decorate their castles and villas. It was they who created the kind of works most associated with Japanese painting: decorative polychromatic depictions of mythical Chinese creatures and scenes from nature, boldly outlined on large folding screens and sliding doors.
# Food & Drink
Eating is a highlight of any trip to Northeast Asia. Each region and town has its own signature dishes and preparations, and while there's no shortage of fine-dining options, your most memorable bites are likely to be found at a streetside noodle bar, aromatic market or tiny teahouse.
Preparation of dumplings, Shànghǎi | DFLC PRINTS/SHUTTERSTOCK ©
## Japan
At its best, Japanese food is highly seasonal, drawing on fresh local ingredients coaxed into goodness with a light touch. Rice is central: the word for 'rice' and for 'meal' are the same – _gohan_. Miso soup and pickled vegetables often round out the meal. But from there Japanese food can vary tremendously; it can be light and delicate (as it is often thought to be), but it can also be hearty and robust.
### Dining Out
When you enter a restaurant in Japan, you'll be greeted with a hearty _irasshaimase_ (Welcome!). In all but the most casual places, the waiter will next ask you _nan-mei sama_ (How many people?). Indicate the answer with your fingers, which is what the Japanese do. More and more restaurants these days (especially in touristy areas) have English menus.
Often the bill will be placed discreetly on your table. If not, you can ask for it by catching the server's eye and making an 'x' in the air with your index finger. You can also say _o-kanjō kudasai_. At some restaurants, you can summon the server by pushing a call bell on the table. On your way out, if you were pleased with your meal, give your regards to the staff or chef with the phrase, _gochisō-sama deshita_ , which means 'it was a real feast'.
There's no tipping, though higher-end restaurants usually tack on a 10% service fee. During dinner service, some restaurants may instead levy a kind of cover charge (usually a few hundred yen); this will be the case if you are served a small appetiser (called _o-tsumami_ , or 'charm') when you sit down. Payment is usually settled at the register near the entrance.
Signature Drinks
**Japan** Microbrews, _nihonshū_ (sake), _o-cha_ (green tea), _ryokucha_ (leaf tea) and _matcha_ (powdered tea).
**Shànghǎi** Coffee and craft cocktails.
**South Korea** _Nokcha_ (green tea) and _soju_ (local vodka).
**Taiwan** Bubble tea _(boba cha),_ oolong tea and third-wave coffee.
### Eat Like a Local
All but the most extreme type-A chefs will say they'd rather have foreign visitors enjoy their meal than agonise over getting the etiquette right. Still, a few points to note if you want to make a good impression: there's nothing that makes a Japanese chef grimace more than out-of-towners who over-season their food – a little soy sauce and wasabi goes a long way (and heaven forbid, don't pour soy sauce all over your rice; it makes it much harder to eat with chopsticks). It's perfectly OK, even expected, to slurp your noodles. They should be eaten at whip speed, before they go soggy (letting them do so would be an affront to the chef); that's why you'll hear diners slurping, sucking in air to cool their mouths.
Don't stick your chopsticks upright in a bowl of rice or pass food from one pair of chopsticks to another – both are reminiscent of Japanese funeral rites. When serving yourself from a shared dish, it's polite to use the back end of your chopsticks (ie not the end that goes into your mouth) to place the food on your own small dish.
Lunch is one of Japan's great bargains; however, restaurants can only offer cheap lunch deals because they anticipate high turnover. Spending too long sipping coffee after finishing your meal might earn you dagger eyes from the kitchen.
## Shànghǎi
Brash, stylish and forward-thinking, Shànghǎi's culinary scene typifies the city's craving for foreign trends and tastes. As much an introduction to regional Chinese cuisine as a magnet for talented chefs from around the globe, Shànghǎi has staked a formidable claim as the Middle Kingdom's hottest dining destination.
Local Shànghǎi cuisine has been heavily influenced by the culinary styles of neighbouring provinces, and many of the techniques, ingredients and flavours originated in the much older cities of Yángzhōu, Sūzhōu and Hángzhōu. Broadly speaking, dishes tend to be sweeter and oilier than in other parts of China. Spiciness is anathema to Shànghǎi cooking.
Many places have English and/or picture menus, although they aren't always as comprehensive (or comprehensible) as the Chinese version. In any case, if you see a dish on someone else's table that looks absolutely delicious, just point at it when the waiter comes – no one will think you're being rude.
## South Korea
Options range from casual bites at a market stall to elaborate multicourse meals at lavish restaurants. While the basic building blocks of the cuisine are recognisably Asian (garlic, ginger, green onion, black pepper, vinegar and sesame oil), Korean food combines them with three essential sauces: _ganjang_ (soy sauce), _doenjang_ (fermented soybean paste) and _gochujang_ (hot red-pepper paste). The main course is nearly always served with _bap_ (boiled rice), soup, kimchi and a procession of _banchan_ (side dishes).
Seafood and black pork are Jeju-do specialities, but you'll also find horse meat and more regular Korean dishes. You'll see the island's citrus fruit _gamgyul_ everywhere, from juices in stalls at remote sights to crates of the mandarin fruit in markets.
## Taiwan
The Taiwanese love to eat out so much that many apartments, especially studios, don't even come with a kitchen. You've got local food at all budget levels – from big bowls of noodle soup for little more than NT$50 to fine dining that requires reservations days in advance. Gourmands know that some of Asia's best street eats are found in markets in and around Taiwan's cities.
Taiwanese cuisine can be divided into several styles of cooking, though the boundaries are often blurred: there's Taiwanese, Hakka, Fujianese and the gamey fare of the indigenous peoples. Most regional Chinese cuisines can also be found as well, the most popular being Cantonese. A healthy influx of Southeast Asian immigrants has 'tanged' up taste buds too, and the Japanese legacy has given the capital some of the best Japanese food outside of Tokyo.
## Top Dining Experiences
**Markets** Visit any market in Taipei for a filling meal that's light on your wallet.
**Ramen** Your basic Japanese ramen is a big bowl of crinkly egg noodles in broth, served with toppings such as _chāshū_ (sliced roast pork), _moyashi_ (bean sprouts) and _menma_ (fermented bamboo shoots). The broth can be made from pork or chicken bones or dried seafood; usually it's a top-secret combination of some or all of the above. Well-executed ramen is a complex, layered dish – though it rarely costs more than ¥1000 a bowl.
**Hoe** A Busan speciality, a typical _hoe_ (sounds like 'when' without the 'n') dinner starts with appetisers such as raw baby octopus still wiggling on the plate. For the main course, sliced raw fish is dipped into a saucer of _chogochujang_ , a watery red-pepper sauce, or soy sauce mixed with wasabi. Finish with rice and a boiling pot of _maeuntang_ (spicy fish soup).
**Shànghǎi street food** Excellent and usually quite safe to eat. It generally consists of tiny dumpling and noodle shops along with vendors selling snacks such as _cōngyóu bǐng_ (green onion pancakes), _bāozi_ (steamed buns), _chòu dòufu_ (stinky tofu) and _dìguā_ (baked sweet potatoes).
**Okonomiyaki** This Japanese savoury pancake is stuffed with cabbage plus meat or seafood (or cheese or kimchi...), which you grill at the table and top with _katsuo bashi_ (bonito flakes), nori (seaweed), mayonnaise and Worcestershire sauce.
**Sushi** At an average _sushi-ya_ (sushi restaurant) in Japan a meal should run between ¥2000 and ¥5000 per person. You can order à la carte – often by just pointing to the fish in the refrigerated glass case on the counter. But the most economical way to eat sushi is to order a set, usually of around 10 to 12 pieces, which may be served all at once or piece by piece.
# The People of Northeast Asia
Each new port brings with it a chance to meet new people and experience a new culture. Knowing a little about the lifestyles and beliefs of locals gives background and context to these experiences.
Performance at Hyakumangoku Matsuri, Kanazawa | M REZA FAISAL/SHUTTERSTOCK ©
## Japan
The people of Japan are depicted as inscrutable. Or reticent. Or shy. They can be, but often they're not. Japan is typically considered a homogeneous nation, and ethnically this is largely true (though there are minority cultures). But there are also deep divides between urban and rural, stubbornly persistent gendered spheres and growing social stratification. Increasingly, the Japanese are grappling with the problems faced by developed nations the world over.
### Population
The population of Japan is approximately 126.5 million. That alone makes Japan a densely populated nation. But the population is unevenly distributed: about nine out of 10 people live in an area classified as urban. Roughly 36 million live within the Greater Tokyo Metropolitan Area, which encompasses the cities of Tokyo, Kawasaki and Yokohama, plus the commuter towns stretching deep into the suburbs; it's the most heavily populated metropolitan area in the world. Nearly 20 million live in the Kyoto–Osaka–Kōbe conurbation (often called Keihanshin). Japan has 13 cities in which the population exceeds one million.
But the population, in general, is shrinking and getting older: for the last two decades the country's birth rate has hovered consistently around 1.4 – among the lowest in the world. The population peaked at 128 million in 2007 and has been in decline since; the latest estimates see a decline of 20 million (roughly one sixth of the total population) in the next 25 years. Currently over one in four Japanese is over the age of 65; in 25 years, if current trends hold, the number will be one in three and less than one in 10 will be a child under the age of 15.
### Work Life
Over 70% of Japanese work in the service industry, a broad category that covers white-collar jobs, retail, care-giving and so on. A quarter of the population works in manufacturing, though these jobs are on the decline. Just 3.4% of Japanese today still work full-time in agriculture, forestry and fishing. It's a huge shift: until the beginning of last century, the majority of Japanese lived in close-knit rural farming communities.
For much of the 20th century, the backbone of the middle class was the Japanese corporation, which provided lifetime employment to the legions of blue-suited, white-collar workers, almost all of them men (nicknamed 'salarymen'), who lived, worked, drank, ate and slept in the service of the companies for which they toiled. Families typically consisted of a salaryman father, a housewife mother, kids who studied dutifully to earn a place at one of Japan's elite universities, and an elderly in-law who had moved in.
Since the recession of the 1990s (which plagues the economy to this day), this system has faltered. Today, roughly 37% of employees are considered 'nonregular', meaning they are on temporary contracts, often through dispatch agencies. In many cases they are doing work that once would have been done by full-time, contracted staff – only now with lower pay, less stability and fewer benefits.
Shinjuku, Tokyo | F11PHOTO/SHUTTERSTOCK ©
### Minority Cultures
Hidden within the population stats are Japan's invisible minorities – those who are native-born Japanese, who appear no different from other native-born Japanese but who can trace their ancestry to historically disenfranchised peoples. Chief among these are the descendants of the Ainu, the native people of Hokkaidō, and Okinawans. Prior to being annexed by Japan in the 19th century, Hokkaidō and Okinawa (formerly the Ryūkyū Empire) were independent territories. Following annexation, the Japanese government imposed assimilation policies that forbade many traditional customs and even the teaching of native languages.
The number of Japanese who identify as Ainu is estimated to be around 20,000, though it is likely that there are many more descendants of Hokkaidō's indigenous people out there – some who may not know it, perhaps because their ancestors buried their identity so deep (for fear of discrimination) that it became hidden forever. There are maybe 10 native speakers of Ainu left; however, in recent decades movements have emerged among the younger generation to learn the language and other aspects of the culture.
Today's Okinawans have a strong regional identity, though it is less about their ties to the former Ryūkyū Empire and more about their shared recent history since WWII. The Okinawans shouldered an unequal burden, both of casualties and of occupation.
We Japanese
It's common to hear Japanese begin explanations of their culture by saying, _ware ware nihonjin_ , which means, 'we Japanese'. There's a strong sense of national cohesion, reinforced by the media, which plays up images of Japan as a unique cultural Galapagos; TV programs featuring foreign visitors being awed and wowed by the curious Japanese way of doing things are popular with viewers. The Japanese, in turn, are often fascinated (and intimidated) by what they perceive as the otherness of outside cultures.
### Religion
Shintō and Buddhism are the main religions in Japan. They are not mutually exclusive: for much of history they were intertwined. Only about one-third of Japanese today identify as Buddhist and the figure for Shintō is just 3%; however, many Japanese participate in rituals rooted in both, which they see as integral parts of their culture and community ties. Generally it is said in Japan that Shintō is concerned with this life: births and marriages, for example, are celebrated at shrines. Meanwhile, Buddhism deals with the afterlife: funerals and memorials take place at temples.
### Shintō
Shintō, or 'the way of the gods', is the native religion of Japan. Its innumerable _kami_ (gods) are located mostly in nature (in trees, rocks, waterfalls and mountains, for example), but also in the mundane objects of daily life, like hearths and wells. _Kami_ can be summoned through rituals of dance and music in the shrines the Japanese have built for them, where they may be beseeched with prayers for a good harvest or a healthy pregnancy, for example, and in modern times for success in business or school exams.
Shintō's origins are unclear. For ages it was a vague, amorphous set of practices and beliefs. It has no doctrine and no beginning or endgame; it simply is. One important concept is _musubi,_ a kind of vital energy that animates everything ( _kami_ and mortals alike). Impurities _(tsumi)_ interfere with _musubi,_ so purification rituals are part of all Shintō rites and practices. For this reason, visitors to shrines first wash their hands and mouth at the _temizu_ (font). Some traditional rites include fire, which is also seen as a purifying force. In the late 19th and early 20th centuries, Shintō was reconfigured by the imperialist state into a national religion centred on emperor worship. This ended with Japan's defeat in WWII, when Emperor Hirohito himself publicly renounced his divinity. It's unclear what those who today identify as Shintō actually believe.
Regardless of belief, there are customs so ingrained in Japanese culture that many continue to perform them anyway, as a way of carrying on family and community traditions. Shrines are still the place to greet the New Year, a rite called Hatsu-mōde; to celebrate the milestones, such as Coming-of-Age Day and Shichi-go-san; and where the lovelorn come to pray for a match. At the very least, many would say, doing such things can't hurt.
### Buddhism
Buddhism in Japan is part of the Mahāyāna (Great Vehicle) tradition, which teaches that anyone (as opposed to just monks) can attain salvation in this lifetime. A key figure in Mahāyāna Buddhism is the bodhisattva, a compassionate being who, on the cusp of achieving Buddha-hood, delays transcendence in order to help others. By the time Buddhism arrived in Japan in the 6th century, having travelled from India via Tibet, China and Korea, it had acquired a whole pantheon of deities. More importantly, it didn't so much supplant Shintō as elaborate on it. Over time, Shintō _kami_ became integrated into the Buddhist cosmology while many new deities were adopted as _kami;_ those with similar aspects were seen as two faces of the same being.
Over the centuries, several distinct sects developed in Japan. Zen is the most well-known internationally, for its meditative practice _zazen_ (seated meditation), but there are others, too, like the older esoteric Shingon sect (which shares similarities with Tibetan Buddhism) and the populist Pure Land sect (which has the greatest number of adherents). Regardless of sect, the most popular deity in Japan is Kannon, a bodhisattva who embodies mercy and compassion and is believed to have the power to alleviate suffering in this world.
Given its association with the afterlife, many turn to Buddhism later in life. (And because of its role in funeral rites, many young Japanese have a dour view of the religion). But, like Shintō, there are certain practices carried out by believers and non-believers alike. The Buddhist festival of O-Bon, in midsummer, is when the souls of departed ancestors are believed to pay a short visit. Families return to their hometowns to sweep gravestones, an act called _ohaka-mairi,_ and welcome them. Only the most staunch non-believer could avoid the creeping sense that skipping such rituals would be tempting fate.
### Women in Japan
Women have historically been viewed as keepers of the home, responsible for overseeing the household budget, monitoring the children's education and taking care of the day-to-day tasks of cooking and cleaning. Of course this ideal was rarely matched by reality: labour shortfalls often resulted in women taking on factory work and, even before that, women often worked side by side with men in the fields.
As might be expected, the contemporary situation is complex. There are women who prefer the traditionally neat division of labour. They tend to opt for shorter college courses, often at women's colleges. They may work for several years, enjoying a period of independence before settling down, leaving the role of breadwinner to the husband and becoming full-time mums.
While gender discrimination in the workforce is illegal, it remains pernicious. And while there is less societal resistance to women working, they still face enormous pressure to be doting mothers. Most women see the long hours that Japanese companies demand as incompatible with child-rearing, especially in the early years; few fathers are willing or, given their own work commitments, able to pick up the slack. Attempts at work-life balance, such as working from home, can result in guilt trips from colleagues or bosses. Working women have coined the phrase 'maternity harassment' to describe the remarks they hear in the office after announcing a pregnancy, the subtle suggestions that she quit so as not to cause trouble. Six out of 10 women quit work after having their first child.
And yet many return: women do in fact make up over 40% of the workforce – not far off the global average; however, over half of them are working part-time and often menial, low-paying jobs. They hold only 9.3% of managerial positions. Women in full-time positions make on average 73% of what their male counterparts make; up from 60% in the 1990s. Women also continue to spend far more time on unpaid labour (including childcare and housework duties): 3¾ hours per day, compared to men's 40 minutes. These are among the most dramatic imbalances in the developed world.
Identity & the Shànghǎi Dialect
Older Shanghainese are highly conscious of the disappearance of the Shànghǎi dialect (Shanghaihuà), under assault from the increased promotion of the Mandarin (Pǔtōnghuà) dialect and the flood of immigrant tongues. It's a deeply tribal element of Shànghǎi culture and heritage, so the vanishing of the dialect equals a loss of identity. Fewer and fewer young Shanghainese and children are now able to speak the pure form of the dialect, or can understand it, and prefer to speak Mandarin. Youngsters might not care, but older Shanghainese agonise over the tongue's slow extinction. The most perfectly preserved forms of Shanghaihuà survive in rural areas around Shànghǎi, where Mandarin has less of a toehold. The Shanghainese may remind themselves of the Chinese idiom – _jiùde bù qù, xīnde bù lái_ ('If the old doesn't go, the new doesn't arrive') – but it may offer scant consolation.
## South Korea
Once divided strictly along nearly inescapable social-class lines, South Koreans today are comparatively better off in terms of economic opportunities and are more individualistic in their world view. Nuclear rather than extended families have become the norm, and birth rates are among the lowest in the developed world. Still, strong traces linger of Korea's particular identity; remnants of its Confucian past coexist alongside 'imported' spiritual beliefs and a striking devotion to displays of material success.
### Contemporary & Traditional Culture
Driven by the latest technology and fast-evolving trends, Korea can sometimes seem like one of the most cutting-edge countries on the planet. People tune into their favourite TV shows via their smart phones. In PC- _bang_ (computer-game rooms) millions of diehard fans battle at online computer games.
General fashions too tend to be international and up to the moment. However, it's not uncommon to see some people wearing _hanbok,_ the striking traditional clothing that follows the Confucian principle of unadorned modesty. Women wear a loose-fitting short blouse with long sleeves and a voluminous long skirt, while men wear a jacket and baggy trousers.
Today _hanbok_ is worn mostly at weddings or special events, and even then it may be a more comfortable 'updated' version. Everyday _hanbok_ is reasonably priced, but formal styles, made of colourful silk and intricately embroidered, are objects of wonder and cost a fortune.
Mono-Culturalist South Korea
South Korea is a monocultural society. As of 2016, _foreigners_ (the local name given to foreign nationals) numbered 2 million or 3.9% of the population. Much like a foreigner among any homogenous group of people, you can expect to get stared at in public. This can be more intense depending on how melanin-rich your skin is, and often lingers most unabashedly from people of older generations.
## Taiwan
First-time visitors to Taiwan often expect to find a completely homogenised society, with little difference in thinking, customs and attitudes from one generation to the next, from city to countryside, or even from person to person. In fact, the country is a multiethnic melting pot. Customs and traditions go back and forth between groups and evolve over time; these days, family background and life experience are far more indicative of a person's attitudes and beliefs than simple ethnicity.
### Lifestyle
Despite the low birth and marriage rate, family still remains central to Taiwanese life. Both young and old are generally deeply committed to each other.
Most people in Taiwan live in crowded urban conditions. However, with low taxes, cheap utilities, fresh local foods, to say nothing of excellent low-cost universal medical care, people enjoy a good balance between the cost of living and quality of life. (On the other hand, stagnating wages are a major problem for young people.) Life expectancy is 83 years for women and 77 years for men.
### The Taiwanese Character
Taiwanese have often been characterised as some of the friendliest people in the world. Reports from Western travellers and officials in Taiwan in the 1930s read like modern accounts, which suggests friendliness is a deep long-standing quality. Some claim this is likely due to Taiwan's immigrant background, in which trust among strangers was paramount.
### Taiwan's Modernity
Just as traditional rites are used to celebrate the opening of businesses and honour the passing of lives, in Taiwan, pop culture is part and parcel of many religious processions. It is not uncommon to spot scantily clad pole dancers busting moves on large vehicles at these events, or dance music pumping out of converted cars with gull-wing doors and badass lights, not to mention bros sporting tats and trainers strutting along to the temple dressed as deities. Whatever one's opinion of such modern manifestations of faith, they're not meant to be disrespectful of tradition. If anything, they show how deeply ingrained faith is in the lives of Taiwanese of all ages. And for outsiders, the ease with which the Taiwanese sashay in and out of tradition and modernity is what makes this country so fascinating.
Survival Guide
#### DIRECTORY A–Z
#### Accessible Travel
#### Climate
#### Discount Cards
#### Health
#### Insurance
#### Internet Access
#### Language
#### LGBT+ Travellers
#### Money
#### Opening Hours
#### Safe Travel
#### Telephone
#### Time
#### Toilets
#### Tourist Information
#### Visas
#### TRANSPORT
#### Getting There & Away
#### Getting Around
# Directory A–Z
## MAccessible Travel
Accessibility throughout the region is improving, but has some way to go.
On the plus side, many buildings have access ramps, major train stations have lifts, traffic lights have speakers playing melodies when it is safe to cross, and train platforms have raised dots and lines to provide guidance for the visually impaired. You'll find most service staff will go out of their way to be helpful, even if they don't speak much English. Major sights take great pains to be wheelchair friendly and many have wheelchairs you can borrow for free.
On the negative side, many city streets are still rather difficult to negotiate – streets can be narrow and busy, and pavements cluttered, uneven or nonexistent. In Shànghǎi, the city's traffic, overpasses and underpasses are the greatest challenges to travellers with disabilities. Try to take a lightweight chair for navigating around obstacles and for collapsing into the back of taxis.
oDownload Lonely Planet's free Accessible Travel guide from <http://lptravel.to/AccessibleTravel>.
oJapan Accessible Tourism Center (www.japan-accessible.com) is a good resource.
oTaiwan Access for All Association (twaccess4all.wordpress.com) provides advice and assistance.
Tōdai-ji, Nara | LUCIANO MORTULA - LGM/SHUTTERSTOCK ©
## a
Discount Cards
Seniors over the age of 65 are frequently eligible for discounts, and in Taipei and China, 70-and-overs often get free admission, so make sure you take your passport when visiting sights as proof of age.
## Climate
## F
Health
oHealth is generally of high standard throughout the region.
oTreatment can be expensive; make sure you are fully insured for your trip. Note, though, the only insurance accepted at Japanese hospitals is Japanese insurance. You'll have to pay up front and apply for a reimbursement when you get home.
oIn Japan, most hospitals do not have doctors and nurses who speak English.
oExpect to pay from around ¥20,000 and upwards for emergency care.
oHealth concerns for travellers to Shànghǎi include worsening atmospheric pollution, traveller's diarrhoea and winter influenza. The air quality in Shànghǎi can be appalling. If you suffer from asthma or other allergies you should anticipate a worsening of your symptoms and may need to increase your medication.
oIn South Korea, the language barrier will be the biggest obstacle. International clinics in hospitals in large cities will likely have English-speaking doctors, but expect to pay between ₩40,000 to ₩80,000 for the consultation alone.
oMany Taiwanese doctors have trained in Western countries and speak at least some English.
Japan Helpline
English-speaking operators at Japan Helpline ( %0570-000-911) are available 24 hours a day to help you negotiate tricky situations. If you don't have access to mobile service, use the contact form on the website (<http://jhelp.com/english/index.html>).
## a
Insurance
A travel-insurance policy to cover theft, loss and medical problems is essential. Worldwide travel insurance is available at www.lonelyplanet.com/travel-insurance. You can buy, extend and claim online anytime – even if you're already on the road.
For health insurance information.
## I
Internet Access
**Japan** Many cities in Japan (including Tokyo, Osaka and Kyoto) have free wi-fi networks for travellers, though the system is still clunky in areas.
**Shànghǎi** Getting internet access will be one constant source of frustration if you rely heavily on being connected, and are used to a lightning-fast service. The Chinese authorities remain mistrustful of the internet, and censorship is heavy-handed. Many popular social networking sites and email providers are blocked – the list changes regularly, so check before you arrive.
**South Korea** With the world's fastest connections and one of the highest rates of internet usage, you'll find abundant free internet access, either via a computer or wi-fi in cafes, public streets and tourist information centres.
**Taiwan** Free wi-fi is widely accessible in cafes, restaurants, and in some shopping malls.
## r
Language
**Japan** English use is not widespread, though cities and popular destinations are well-signposted in English and will have Tourist Information Centres (TICs) with English-speaking staff; restaurants in these areas will also often have English menus. Most Japanese are more comfortable with written than spoken English, so whenever possible, email is often the best means of communicating.
**Shànghǎi** Outside hotels, English is not widely spoken. You'll be able to get by in tourist areas, but it's useful to learn a few basic phrases. Some restaurants may not have an English menu. You'll find yourself surrounded by written Chinese wherever you travel, so a Pleco app (www.pleco.com) or phrasebook is useful.
**South Korea** It's relatively easy to find English speakers in the big cities, but not so easy in smaller towns and the countryside. Learning a few key phrases will help you enormously in being able to decode street signs, menus and timetables.
**Taiwan** Although on the street you will hear Mandarin and Taiwanese, plenty of young and middle-aged Taiwanese speak reasonable English, especially anyone working in the tourist trade. You might have some trouble, though, with taxi drivers. MRT announcements are also in English, and many signs are in English too. Any restaurant that is midrange or above is very likely to have an English menu. Saying all that, a few polite phrases in Mandarin will go a long way.
## t
LGBT+ Travellers
**Japan** Gay and lesbian travellers are unlikely to encounter problems in Japan. There are no legal restraints on same-sex sexual activities in Japan apart from the usual age restrictions.
**Shànghǎi** Local law is ambiguous in its attitude to LGBT people; generally the authorities take a dim view of same-sex couples but there's an increasingly confident scene, as indicated by gay bars and the annual event-stuffed Shanghai Pride (www.shpride.com). Shànghǎi heterosexuals are not, by and large, particularly homophobic, especially the under-40s. Young Chinese men sometimes hold hands; this carries no sexual overtones.
**South Korea** Korea has never passed any laws that mention homosexuality, but this shouldn't be taken as a sign of tolerance or acceptance. Attitudes are changing, especially among young people, but virtually all local gays and lesbians choose to stay firmly in the closet. Gay and lesbian travellers who publicise their sexual orientation tend to receive less than positive reactions.
**Taiwan** In 2019, Taiwan became the first Asian nation to legalise same-sex marriage. Foreign-born gay and lesbian travellers will find Taipei friendly, open-minded and exciting. It's common to see LGBT couples holding hands on the streets, though not common to see them kissing.
Tap Water
**Japan** Tap water is fine to drink.
**Shànghǎi** Don't drink tap water or eat ice. Bottled water is readily available. Boiled water is OK.
**South Korea** Some of the cleanest tap water in the world. Filtered or bottled water is served free in most restaurants and machines with free purified hot and cold water are at most shopping plaza entrances.
**Taiwan** Tap water here is supposed to be drinkable, but nobody does. There are drinking water dispensers in major tourist sites, temples, some MRT stations and hospitals.
## a
Money
### ATMs
oATMs are widespread throughout the region, though they may not be open 24 hours.
oMany ATMs in Japan and South Korea do not accept foreign-issued cards. In Japan, most Seven Bank ATMs at 7-Eleven convenience stores (open 24 hours) and Japan Post Bank ATMs at post offices accept most overseas cards and have instructions in English. In South Korea, look for one that has a 'Global' sign or the logo of your credit-card company.
oIn Shànghǎi and Taipei, ATMs generally accept Visa, MasterCard, Cirrus and Maestro cards, as well as JCB and Plus in Taipei. Most operate 24 hours. Bank of China and the Industrial & Commercial Bank of China are the best bets in Shànghǎi.
### Cash
Many places in Japan – particularly outside the cities – don't accept credit cards. Smaller restaurants and shops are common cash-only places, so it's wise to keep cash on hand.
### Credit Cards
Credit cards are increasingly accepted, but plenty of places, including budget or smaller restaurants, stalls and shops still require cash. Always check before deciding to order in a restaurant. It's also always wise to carry some cash to be sure.
### Exchanging Money
The best rates are given by banks. Note that not all banks will change money and many will only change US dollars. In Japan and China, you will need your passport in order to change money.
Exchange rates in China are uniform wherever you change money, so there's little need to shop around. Whenever you change foreign currency into Chinese currency you will be given a money-exchange voucher recording the transaction. You need to show this to change your yuán back into any foreign currency. Changing Chinese currency outside China is a problem, though it's quite easily done in Hong Kong.
Note that you receive a better exchange rate when withdrawing cash from ATMs than when exchanging cash or travellers cheques in Japan.
### Tipping
oTipping is not customary throughout the region.
oThere's no need to tip in bars or taxis.
oJapanese high-end restaurants usually add a 10% service fee to the bill, as do some in Shànghǎi.
oGuides don't require a tip, but a small gift is appreciated. In Taipei, a 10% addition to the fee if you are happy with the service is common.
## J
Opening Hours
### Japan
Some outdoor attractions (such as gardens) may close earlier in the winter. Standard opening hours:
**Banks** 9am to 3pm (some to 5pm) Monday to Friday.
**Bars** From around 6pm to late.
**Department stores** 10am to 8pm.
**Museums** 9am to 5pm, last entry by 4.30pm; often closed Monday (if Monday is a national holiday then the museum will close on Tuesday instead).
**Post offices** 9am to 5pm Monday to Friday; larger ones have longer hours and open Saturday.
**Restaurants** Lunch 11.30am to 2pm; dinner 6pm to 10pm; last orders taken about half an hour before closing.
### Shànghǎi
Businesses in China close for the week-long Chinese New Year (usually in February) and National Day (beginning 1 October).
**Bank of China** Branches 9.30am to 11.30am and 1.30pm to 4.30pm Monday to Friday. Some also open Saturday and Sunday. Most have 24-hour ATMs.
**Bars** Around 5pm to 2am (some open in the morning).
**China Post** Most major offices 8.30am to 6pm daily; sometimes open until 10pm. Local branches closed weekends.
**Museums** Most open weekends; a few close Monday. Ticket sales usually stop 30 or 60 minutes before closing.
**Offices and government departments** Generally 9am to noon and 2pm to 4.30pm Monday to Friday.
**Restaurants** Most 11am to 10pm or later; some 10am to 2.30pm and 5pm to 11pm or later.
**Shops** Malls and department stores generally 10am to 10pm.
### South Korea
**Banks** 9am to 4pm Monday to Friday; ATMs 7am to 11pm (or 24 hours).
**Bars** 6pm to 1am, longer hours Friday and Saturday.
**Cafes** 7am to 10pm.
**Restaurants** 11am to 10pm.
**Shops** 10am to 8pm.
### Taiwan
Some restaurants and cafes and many museums are closed on Mondays. Bars and some restaurants often close an hour or so later on Fridays and Saturdays.
**Banks** 9am to 3.30pm Monday to Friday.
**Cafes** Noon to 8pm (often closed Monday).
**Convenience stores** Most are 24 hours.
**Department stores** 11am to 9.30pm.
**Government offices** 8.30am to 5.30pm Monday to Friday.
**Museums** 9am to 5pm Tuesday to Sunday.
**Night markets** 5pm to midnight.
**Offices** 9am to 5pm Monday to Friday.
**Post offices** 8am to 5pm Monday to Friday; larger offices may open till 9pm and have limited hours on weekends.
**Restaurants** 11.30am to 2pm and 5pm to 9pm.
**Shops** 10am to 9pm.
**Supermarkets** Until at least 8pm; sometimes 24 hours.
## L
Safe Travel
Northeast Asia is generally a very safe region for travel – urban streets are safe and muggings or violent assaults uncommon. Still, it's wise to keep up the same level of caution and common sense that you would back home.
In Shànghǎi, crossing the road is probably the greatest danger: develop avian vision and a sixth sense to combat the shocking traffic. Don't end up in an ambulance: Chinese drivers never give way.
Likewise traffic is your biggest risk in South Korea and Taipei. In South Korea, drivers almost never stop for pedestrian crossings that are not protected by traffic lights, and they routinely jump red lights late at night, so take care on pedestrian crossings even if they are protected by lights. In Taipei and South Korea, watch out for 'wayward' scooters on the roads (or pedestrian crossings, or pavements...).
Smoking
**Japan** In many cities (including Tokyo, Osaka and Kyoto) smoking is banned in public spaces but allowed inside bars and restaurants. Designated smoking areas are set up around train stations.
**Shànghǎi** From 2010, antismoking legislation in Shànghǎi required a number of public venues (including bars and restaurants) to have designated nonsmoking areas and to install signs prohibiting smoking. However, you'll often find this rule flouted in bars and some restaurants.
**South Korea** Nationwide ban on smoking in public enclosed spaces such as bars and restaurants, on train platforms and 10m from station exits. Smoking is not allowed on many tourist streets.
**Taiwan** Not allowed in public facilities, public transport, shopping malls and restaurants and this is strictly enforced. Even some parks are marked smoke-free.
## K
Telephone
oJapan operates on the 3G network, so overseas phones with 3G technology should work. Prepaid SIM cards that allow you to make voice calls are not available in Japan. Data-only SIM cards for unlocked smartphones are available at large electronics stores (such as Bic Camera, Yodobashi Camera etc) in major cities. You'll need to download and install an APN profile; ask staff to help you if you are unsure how to do this (they usually speak some English).
oIn Shànghǎi, a mobile phone should be the first choice for calls, but ensure your mobile is unlocked for use in China if taking your own.
oMost networks in South Korea use the WCDMA 2100 MHz network, as well as one of five different 4G LTE bands. Most unlocked recent smartphones will work with a Korean SIM. Mobile phones and portable wi-fi eggs can be hired.
oLocal SIM cards in Taipei should fit most overseas-bought mobiles. They come with prepaid plans.
## W
Time
**Japan & South Korea** Nine hours ahead of Greenwich Mean Time (GMT); do not have daylight saving time.
**Shànghǎi & Taiwan** Eight hours ahead of GMT/UTC. There is no daylight-saving time.
## GToilets
oPublic toilets in the region are generally plentiful, free and clean.
oThe exception is in Shànghǎi. Often charging a small fee, toilets here run from the sordid to coin-operated portaloos and modern conveniences. The best bet is to head for a top-end hotel, where someone will hand you a towel, pour you some aftershave or exotic hand lotion and wish you a nice day.
oYou will come across both Western-style toilets and traditional squat toilets. When you are compelled to squat, the correct position is facing the hood, away from the door.
oIn Japan, the katakana for 'toilet' is トイレ, and the kanji is お手洗い. Also good to know: the kanji for female (女) and male (男).
oIn Shànghǎi and Taiwan, look for the Chinese characters for men (男) and women (女).
oIn Korean, public toilets are _hwajangsil_ (화장실).
oToilet paper is usually provided (except in Shànghǎi), but it is still a good idea to carry tissues with you. In South Korea, toilet paper is usually outside the cubicles.
oMany places in Taiwan ask you not to flush toilet paper but to put it in the waste-paper basket beside the toilet.
## CTourist Information
### Japan
Tourist information offices ( _kankō annai-sho;_ 観光案内所) can be found inside or in front of major train stations. Staff may not speak much English; however, there are usually English-language materials and staff are accustomed to the usual concerns of travellers. Many have free wi-fi.
**Japan National Tourism Organization** (JNTO; www.jnto.go.jp) is Japan's government tourist bureau. It produces a great deal of useful literature in English, which is available from its overseas offices as well as its **TIC** (MAP; %03-3201-3331; 1st fl, Shin-Tokyo Bldg, 3-3-1 Marunouchi, Chiyoda-ku; h9am-5pm; W; bChiyoda line to Nijūbashimae, exit 1) in Tokyo.
### Shànghǎi
Shànghǎi has about a dozen or so rather useless Tourist Information & Service Centres. For competent English-language help, call the **Shànghǎi Call Centre** ( %021 962 288), a free 24-hour English-language hotline that can respond to cultural or transport enquiries (and even provide directions for your cab driver).
### South Korea
If you need interpretation help or information on practically any topic, any time of the day or night, you can call BBB ( %1588 5644; www.bbbkorea.org).
### Taiwan
Visitor information centres are present in most city train stations and popular scenic areas. They stock English-language brochures, maps, and train and bus schedules, and usually staff can speak some English. Welcome to Taiwan (<http://eng.taiwan.net.tw/>) is the official site of the Taiwan Tourism Bureau; the **Tourist Hotline** ( %0800-011 765) is a useful 24-hour service in English, Japanese and Chinese.
## E
Visas
### Japan
Citizens of 67 territories, including Australia, Canada, Hong Kong, Korea, New Zealand, Singapore, the UK, the USA, and almost all European nations will be automatically issued a _tanki-taizai_ (temporary-visitor visa) on arrival. Typically this visa is good for 90 days. For a complete list of visa-exempt territories, consult www.mofa.go.jp/j_info/visit/visa/short/novisa.html#list.
For additional information on visas and regulations, contact your nearest Japanese embassy or consulate, or visit the website of the Ministry of Foreign Affairs of Japan (www.mofa.go.jp).
### Shànghǎi
Citizens from a number of countries including the USA, Australia, Canada, New Zealand, Germany, Sweden and France, can transit through Shànghǎi for up to 144 hours without a visa as long as they have visas for their onward countries and proof of passage out of China. Your departure point and destination should not be in the same country. Note also that you are not allowed to visit other cities in China during your transit.
### South Korea
With a confirmed onward ticket, visitors from the USA, nearly all Western European countries, New Zealand, Australia and around 30 other countries receive 90-day permits on arrival. About 30 countries do not qualify for visa exemptions. Citizens from these countries must apply for a tourist visa, which allows a stay of 90 days.
As rules are always changing, see www.hikorea.go.kr for more visa information.
### Taiwan
Tourists from most European countries, Canada, the US, Australia (until December 2019; see Taiwan's Ministry of Foreign Affairs website for updates), New Zealand, South Korea and Japan are given visa-free entry for stays of up to 90 days.
# Transport
Flights, cars and tours can be booked online at lonelyplanet.com/bookings.
## (Getting There & Away
### Air
#### Japan
Japan's major international airports include the following:
**Narita International Airport** (www.narita-airport.jp) About 75 minutes east of Tokyo by express train, Narita gets the bulk of international flights to Japan; most budget carriers flying to Tokyo arrive here.
**Haneda Airport** (www.tokyo-airport-bldg.co.jp) Tokyo's more convenient airport – about 30 minutes by train or monorail to the city centre – Haneda, also known as Tokyo International Airport, is getting an increasing number of international arrivals; domestic flights to/from Tokyo usually arrive/depart here.
**Kansai International Airport** (www.kansai-airport.or.jp) Serves the key Kansai cities of Kyoto, Osaka, Nara and Kōbe.
#### Shànghǎi
**Pǔdōng International Airport** (PVG; 浦东国际机场; Pǔdōng Guójì Jīchǎng; %021 6834 7575, flight information 96990; www.shairport.com) Located 30km southeast of Shànghǎi, near the East China Sea. Most international flights operate from here.
**Hóngqiáo International Airport** (SHA; 虹桥国际机场; Hóngqiáo Guójì Jīchǎng; %021 5260 4620, flight information 021 6268 8899; www.shairport.com; mHongqiao Airport Terminal 1, mHongqiao Airport Terminal 2) Located 18km west of the Bund.
#### South Korea
International travellers can fly directly to **Gimhae International Airport** (김해 국제 공항; MAP; %051 974 3114; www.airport.co.kr/gimhaeeng/index.do; mBusan-Gimhae LRT, Exit Airport), 27km west of Busan's city centre.
#### Taiwan
**Taiwan Taoyuan International Airport** ( %03-273 3728; www.taoyuan-airport.com) is about 40km west of Taipei, while **Taipei Songshan Airport** (松山機場; Sōngshān Jīchǎng; MAP; www.tsa.gov.tw/tsa; 340-9 Dunhua N Rd; 敦化北路340-9; mSongshan Airport) is just north of the city centre and services direct international flights to China, Japan and South Korea, plus domestic routes.
## yGetting Around
### Car & Motorcycle
#### Japan
oDriving in Japan is quite feasible, even for the mildly adventurous. Most roads are signposted in English; roads are in excellent condition; road rules are generally adhered to; and petrol, while expensive, is not prohibitively so.
oTypical rates for a small car are ¥5000 to ¥7000 per day, with reductions for rentals of more than one day. On top of the rental charge, there's about a ¥1000-per-day insurance cost. Prices among major agencies are comparable.
oToyota Rent-a-Car (<https://rent.toyota.co.jp>) and Nippon Rent-a-Car (www.nrgroup-global.com) have large rental networks and booking in English is possible online.
#### Shànghǎi
It is possible to hire a car in Shànghǎi, but the bureaucratic hurdles are designed to deter would-be foreign drivers. You will need a temporary or long-term Chinese driving licence. For most visitors, it is more advisable to hire a car and a driver.
#### South Korea
Driving in South Korea is not recommended for first-time visitors. Korea has an appalling road-accident record, and foreign drivers in large cities are likely to spend most of their time lost, stuck in traffic jams, looking for a parking space or taking evasive action.
#### Taiwan
By the standards of many countries, driving in Taiwan can be chaotic and dangerous. Not recommended.
### Local Transport
#### Japan
Japan's larger cities are serviced by subways or trams, buses and taxis; indeed, many locals rely entirely on public transport. Note that all public transport except for taxis shuts down between midnight and 5am.
##### Bus
The city where you'll find yourself relying on public buses is Kyoto. Though the city has a subway system, it is not convenient for all major tourist sites.
##### Subway & Tram
Kyoto, Osaka, Tokyo and Sapporo have subway systems, which are usually the fastest and most-convenient way to get around the city. Stops and line names are posted in English. Hiroshima has trams.
Fares are typically ¥150 to ¥250, depending on how far your ride (half-price for children). If you plan to zip around a city in a day, an unlimited-travel day ticket (called _ichi-nichi-jōsha-ken_ ) is a good deal; most cities offer them and they can be purchased at station windows.
IC Cards in Japan
IC cards are prepaid travel cards with chips that work on subways, trams and buses in the Tokyo, Kansai, Sapporo and Hiroshima metro areas. They save you the trouble of having to purchase paper tickets and work out the correct fare for your journey. Each region has its own card, but they can be used interchangeably in any region where IC cards are used; however, they cannot be used for intercity travel.
The two most frequently used IC cards are **Suica** (www.jreast.co.jp/e/pass/suica.html) from JR East and **Icoca** (www.westjr.co.jp/global/en/ticket/icoca-haruka) from JR West; purchase them at JR travel counters at Narita and Haneda or Kansai airports, respectively. Cards can also be purchased and topped up from ticket-vending machines in any of the cities that support them. Both require a ¥500 deposit, which you get back when you return your card to any JR ticket window.
To use the card, simply swipe it over the reader at the ticket gates or near the doors on trams and buses.
##### Taxi
oTaxis are ubiquitous in big cities. They can be found in smaller cities and even on tiny islands, too, though usually just at transport hubs (train and bus stations and ferry ports) – otherwise you'll need to get someone to call one for you.
oTransit stations have taxi stands where you are expected to queue. In the absence of a stand, hail a cab from the street by standing on the curb and sticking your arm out.
oFares are fairly uniform throughout Japan and all cabs run by the meter.Flagfall (posted on the taxi windows) is around ¥600 to ¥710 for the first 2km, after which it's around ¥100 for each 350m (approximately). There's also a time charge if the speed drops below 10km/h and a 20% surcharge between 10pm and 5am.
oA red light means the taxi is free and a green light means it's taken.
oDrivers rarely speak English, though fortunately most taxis now have navigation systems. It's a good idea to have your destination written down in script, or better yet, a business card with an address.
#### Shànghǎi
The rapidly expanding metro and light railway system works like a dream; it's fast, efficient and inexpensive. Rush hour on the metro operates above capacity, however, and you get to savour the full meaning of the big squeeze.
With a wide-ranging web of routes, buses may sound tempting, but that's before you try to decipher routes and stops or attempt to squeeze aboard during the crush hour. Buses also have to contend with Shanghai's traffic, which can slow to an agonising crawl.
Taxis are ubiquitous and cheap, but flagging one down during rush hour or during a rainstorm requires staying power of a high order.
#### South Korea
Busan has a subway (metro) system. It's a cheap and convenient way of getting around and station names are in English as well as Korean.
Local city buses provide a frequent and inexpensive service. The main problem with local buses is finding and getting on the right bus. Timetables, stop names and destination signs on buses are rarely in English, and drivers usually don't speak English. The app Naver Map is available in English and has accurate journey planner information for the whole country.
Taxis are numerous almost everywhere and fares are inexpensive. Every taxi has a meter that works on a distance basis but switches to a time basis when the vehicle is stuck in a traffic jam. Tipping is not a local custom and is not expected or necessary.
Since few taxi drivers speak English, plan how to communicate with the driver; if you have a mobile phone you can also use the 1330 tourist advice line to help with interpretation. Ask to be dropped off at a nearby landmark. It can be useful to write down your destination or a nearby landmark in _hangeul_ on a piece of paper.
#### Taiwan
Buses throughout the country are generally reliable, cheap and comfortable. In Taipei, routes on timetables are written in Chinese only, and buses can be slow when they get stuck in traffic.
Taipei has a Mass Rapid Transit (MRT; <http://english.metro.taipei/>) metro system. It is clean, safe, convenient and reliable. All signs and ticket machines are in English. English signs around stations indicate which exit to take to nearby sights. Posters indicate bus transfer routes.
Taxis are ubiquitous in Taiwan's cities, though traffic can be frustrating and drivers are unlikely to speak much English. Outside urban areas, taxi drivers will either use meters or ask for a flat rate (the smaller the town the more likely the latter).
# Behind the Scenes
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## Acknowledgements
Cover photograph: Yokohama, Japan; Prisma by Dukas Presseagentur GmbH/Alamy Stock Photo ©
Climate map data adapted from Peel MC, Finlayson BL & McMahon TA (2007) 'Updated World Map of the Köppen-Geiger Climate Classification', Hydrology and Earth System Sciences, 11, 1633–44.
Illustrations here and here by Michael Weldon.
## This Book
This 1st edition of Lonely Planet's _Cruise Ports Northeast Asia_ guidebook was researched and written by Ray Bartlett, Andrew Bender, Jade Bremner, Stephanie d'Arc Taylor, Dinah Gardner, Trent Holden, Craig McLachlan, Rebecca Milner, Kate Morgan, MaSovaida Morgan, Thomas O'Malley, Simon Richmond, Phillip Tang and Benedict Walker. It was curated by Imogen Bannister, William Allen, Jenna Myers and Kathryn Rowan.
This guidebook was produced by the following:
**Destination Editor** James Smart
**Senior Product Editors** Kate Chapman, Anne Mason
**Product Editor** Carolyn Boicos
**Senior Cartographer** Diana Von Holdt
**Book Designer** Fergal Condon
**Assisting Editors** Paul Harding, Lauren O'Connell
**Assisting Cartographer** Anthony Phelan
**Cover Researcher** Naomi Parker
**Thanks to** Ronan Abayawickrema, Andi Jones, Alison Lyall, Akamatsu Naoko, Alison Ridgway, Claire Rourke, Jacqui Saunders, Jaeyoon Adela Shin, Angela Tinson, Guan Yuanyuan
**eBook Thanks to** Julie J. Dodkins, Craig Kilburn, Wayne Murphy, John Taufa and Juan Winata.
### Our Story
A beat-up old car, a few dollars in the pocket and a sense of adventure. In 1972 that's all Tony and Maureen Wheeler needed for the trip of a lifetime – across Europe and Asia overland to Australia. It took several months, and at the end – broke but inspired – they sat at their kitchen table writing and stapling together their first travel guide, _Across Asia on the Cheap_. Within a week they'd sold 1500 copies. Lonely Planet was born.
Today, Lonely Planet has offices in Franklin, London, Melbourne, Oakland, Dublin, Beijing and Delhi, with more than 600 staff and writers. We share Tony's belief that 'a great guidebook should do three things: inform, educate and amuse'.
# Our Writers
###### Ray Bartlett
Ray Bartlett has been travel writing for nearly two decades, bringing Japan, Korea, Mexico, Tanzania, Guatemala, Indonesia and many parts of the United States to life in rich detail for top-industry publishers, newspapers and magazines. Ray currently divides his time between homes in the USA, Japan and Mexico.
###### Andrew Bender
Award-winning travel and food writer Andrew Bender has written three dozen Lonely Planet guidebooks (from Amsterdam to Los Angeles, Germany to Taiwan and more than a dozen titles about Japan), plus numerous articles for lonelyplanet.com. Andy also is a tour leader and tour planner for visits to Japan. Follow him on Twitter @wheresandynow.
###### Jade Bremner
Jade has been a journalist for more than a decade. She has lived in and reported on four different regions. Wherever she goes she finds action sports to try, the weirder the better, and it's no coincidence many of her favourite places have some of the best waves in the world. Jade has edited travel magazines and sections for _Time Out_ and _Radio Times_ and has contributed to the _Times_ , CNN and the _Independent_. She feels privileged to share tales from this wonderful planet we call home and is always looking for the next adventure.
###### Stephanie d'Arc Taylor
A native Angeleno, Stephanie grew up with the west LA weekend ritual of going for Iranian sweets after _tenzaru soba_ in Little Osaka. Later, she quit her PhD to move to Beirut and become a writer. Since then, she has published work with the _New York Times, Guardian, Roads & Kingdoms_ and _Kinfolk Magazine,_ and co-founded Jaleesa, a venture-capital-funded social impact business in Beirut. Follow her on Instagram @zerodarctaylor.
###### Dinah Gardner
Dinah is a freelance writer focusing on travel and politics. Since 2015 she has been happily based in Taiwan, one of Asia's most charming and courteous countries. She's lived in and written about Vietnam, Tibet, China, Hong Kong, Nepal and Bhutan.
###### Trent Holden
A Geelong-based writer, located just outside Melbourne, Trent has worked for Lonely Planet since 2005. He's covered 30 plus guidebooks across Asia, Africa and Australia. With a penchant for megacities, Trent's in his element when assigned to cover a nation's capital – the more chaotic the better – to unearth cool bars, art, street food and underground subculture. On the flipside he also writes books to idyllic tropical islands across Asia, in between going on safari to national parks in Africa and the subcontinent. When not travelling, Trent works as a freelance editor, reviewer and spending all his money catching live gigs.
###### Craig McLachlan
Craig has covered destinations all over the globe for Lonely Planet for two decades. Based in Queenstown, New Zealand for half the year, he runs an outdoor activities company and a sake brewery, then moonlights overseas for the other half, leading tours and writing for Lonely Planet. Craig has completed a number of adventures in Japan and his books are available on Amazon. Check out www.craigmclachlan.com.
###### Rebecca Milner
California-born and living in Tokyo since 2002, Rebecca has co-authored Lonely Planet guides to Tokyo and Japan. She's also a freelance writer covering travel, food and culture. Rebecca has been published in the _Guardian,_ the _Independent,_ the _Sunday Times Travel Magazine,_ the _Japan Times_ and more.
###### Kate Morgan
Having worked for Lonely Planet for over a decade now, Kate has been fortunate enough to cover plenty of ground working as a travel writer on destinations such as Shanghai, Japan, India, Russia, Zimbabwe, the Philippines and Phuket. She has done stints living in London, Paris and Osaka but these days is based in one of her favourite regions in the world – Victoria, Australia. In between travelling the world and writing about it, Kate enjoys spending time at home working as a freelance editor.
###### MaSovaida Morgan
MaSovaida is a Lonely Planet writer and multimedia storyteller whose wanderlust has taken her to more than 35 countries across six continents. Prior to freelancing, she was Lonely Planet's Destination Editor for South America for four years and worked as an editor for newspapers and NGOs in the Middle East and United Kingdom. Follow her on Instagram @MaSovaida.
###### Thomas O'Malley
A British writer based in Beijing, Tom is a world-leading connoisseur of cheap eats, dive bars, dark alleyways and hangovers. He has contributed travel stories to everyone from the BBC to _Playboy,_ and reviews hotels for the _Telegraph_. Under another guise, he is a comedy scriptwriter. Follow him by walking behind at a distance.
###### Simon Richmond
Journalist and photographer Simon Richmond has specialised as a travel writer since the early 1990s and first worked for Lonely Planet in 1999 on its _Central Asia_ guide. He's long since stopped counting the number of guidebooks he's researched and written for the company, but countries covered include Australia, China, India, Iran, Japan, Korea, Malaysia, Mongolia, Myanmar (Burma), Russia, Singapore, South Africa and Turkey.
###### Phillip Tang
Phillip Tang grew up on a typically Australian diet of _pho_ and fish'n'chips before moving to Mexico City. A degree in Chinese and Latin American cultures launched him into travel and then writing about it for Lonely Planet's _Canada, China, Japan, Korea, Mexico, Peru_ and _Vietnam_ guides. Follow his writing at hellophillip.com, photos @mrtangtangtang and tweets @philliptang.
###### Benedict Walker
A beach baby from Newcastle, Australia, Benedict turned 40 in 2017 and decided to start a new life in Leipzig, Germany. Writing for Lonely Planet was a childhood dream and he has covered big chunks of Australia, Canada, Germany, Japan, USA, Switzerland, Sweden and Japan. Follow him on Instagram @wordsandjourneys.
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**Published by Lonely Planet Publications Pty Ltd**
ABN 36 005 607 983
October 2019
ISBN 9781788686877
© Lonely Planet 2019 Photographs © as indicated 2019
All rights reserved. No part of this publication may be copied, stored in a retrieval system, or transmitted in any form by any means, electronic, mechanical, recording or otherwise, except brief extracts for the purpose of review, and no part of this publication may be sold or hired, without the written permission of the publisher. Lonely Planet and the Lonely Planet logo are trademarks of Lonely Planet and are registered in the US Patent and Trademark Office and in other countries. Lonely Planet does not allow its name or logo to be appropriated by commercial establishments, such as retailers, restaurants or hotels. Please let us know of any misuses: lonelyplanet.com/ip.
Although the authors and Lonely Planet have taken all reasonable care in preparing this book, we make no warranty about the accuracy or completeness of its content and, to the maximum extent permitted, disclaim all liability arising from its use.
| {
"redpajama_set_name": "RedPajamaBook"
} | 1,261 |
Q: Nest js authorization where should i give user calss property of Roles in nest js Documentation i've read about Basic RBAC implementation but the last thing of this section says
"To make sure this example works, your User class must look as follows"
class User {
roles: Role[];
}
where should this line is going to be in
A: Check out authentication part of documentation. In implementing passport strategies paragraph you have UsersService defined like this:
import { Injectable } from '@nestjs/common';
// This should be a real class/interface representing a user entity
export type User = any;
@Injectable()
export class UsersService {
private readonly users = [
{
userId: 1,
username: 'john',
password: 'changeme',
},
{
userId: 2,
username: 'maria',
password: 'guess',
},
];
async findOne(username: string): Promise<User | undefined> {
return this.users.find(user => user.username === username);
}
}
You can create user.ts file near this service and import it here instead of defining type. How this class should look depends on source from which you get it. In this example users are hard-coded but usually that would be some kind of database entity.
Hard-coded example
For this hard-coded example I would do User class like this:
user.ts
import { Role } from "./role.enum";
export class User {
userId: number;
username: string;
password: string;
roles: Role[];
}
Where roles are in enum defined in authorization part of documentation
role.enum.ts
export enum Role {
User = 'user',
Admin = 'admin',
}
All this is joined inside service like this:
users.service.ts
import { Injectable } from '@nestjs/common';
import { User } from './user.entity';
import { Role } from "./role.enum";
@Injectable()
export class UsersService {
private readonly users: User[] = [
{
userId: 1,
username: 'john',
password: 'changeme',
roles: [Role.Admin]
},
{
userId: 2,
username: 'maria',
password: 'guess',
roles: [Role.User]
},
];
async findOne(username: string): Promise<User | undefined> {
return this.users.find(user => user.username === username);
}
}
Database example
Usually you would use some kind of database (more on database integration here), when using TypeOrm those classes would look like this:
user.entity.ts
import { Role } from "../role.enum";
import { Injectable } from '@nestjs/common';
import { UserEntity } from '../hard-coded/user';
import { InjectRepository } from "@nestjs/typeorm";
import { Repository } from "typeorm";
@Entity()
export class UserEntity {
@PrimaryGeneratedColumn() userId: number;
@Column() username: string;
@Column() password: string;
// should have some kind of join table
@ManyToMany() roles: Role[];
}
users.service.ts
@Injectable()
export class UsersService {
constructor(@InjectRepository(UserEntity) private usersRepository: Repository<UserEntity>){}
async findOne(username: string): Promise<UserEntity | undefined> {
return this.usersRepository.findOne({ username });
}
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,976 |
Ilbesheim (Donnersbergkreis) este o comună din landul Renania-Palatinat, Germania.
Comune din Renania-Palatinat | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,963 |
Scientists discover mechanism involved in breast cancer's spread to bone
by Gale Scott
Feb. 3, 2011, noon
Research by Yibin Kang, an associate professor of molecular biology at Princeton, has uncovered the exact mechanism in individuals with advanced breast cancer that lets traveling tumor cells disrupt normal bone growth in cases when the cancer spreads to the bone.
Photo by Brian Wilson
Image for news media
In a discovery that may lead to a new treatment for breast cancer that has spread to the bone, a Princeton University research team has unraveled a mystery about how these tumors take root.
Cancer cells often travel throughout the body and cause new tumors in individuals with advanced breast cancer -- a process called metastasis -- commonly resulting in malignant bone tumors. What the Princeton research has uncovered is the exact mechanism that lets the traveling tumor cells disrupt normal bone growth. By zeroing in on the molecules involved, and particularly a protein called "Jagged1" that sends destructive signals to cells, the research team has opened the door to drug therapies that could block this disruptive process. Doctors at other medical centers who have reviewed the research have found it promising.
"Right now we don't have many treatments to offer these patients," said Yibin Kang, an associate professor of molecular biology at Princeton who led the research team. "Doctors can manage the symptoms of this bone cancer, but they can't do much more. Our findings suggest there could be a new way of treatment," one that could slow or halt these bone tumors.
Breast cancer spreads to the bone in 70 to 80 percent of patients with advanced breast cancer, and it can also spread to the brain, lung and liver. Metastatic bone cancer is also a frequent occurrence among patients with advanced prostate, lung and skin cancers. In findings that will be published online in the journal Cancer Cell on Feb. 3, the team's research shows that breast tumor cells are able to give bone cells the wrong instructions through a process known as cell signaling -- with disastrous effects for the patient.
Breast cancer's spread to the bone relies on interactions among tumor cells (blue); specialized bone cells that break down the bone, called osteoclasts (pink); specialized cells that rebuild bone tissue, called osteoblasts (brown); and the bone matrix. A "signaling protein" called Jagged1 sends destructive instructions that activate a group of molecules that work together, one molecule activating the next, in what's called called the "Notch signaling pathway" (green flash) in the bone cells. Notch signaling stimulates the bone degrading activity of osteoclasts, releasing tumor growth factors such as the TGF-beta protein (red bubbles) from the bone matrix. Meanwhile, Notch signaling in bone-building osteoblasts increases the expression of another secreted protein, IL-6 (orange bubbles), which feeds back to tumor cells to promote their growth, forming a vicious cycle in bone metastasis. (Illustration by Stephen Cheng)
The billions of cells in a living human body must communicate to develop, repair tissue and effectively maintain normal physiological functions. Cell signaling is part of a complex system that enables them to do that but, in patients with cancer, the relationship between signaling molecules and the molecules that communicate with them has gone awry.
Signaling molecules are those that can be received and read by a cell through a receptor molecule on its surface. Once the signaling molecules connect with a receptor, their union sets off a process that leads to the receiving cell changing its behavior. The sequence of events that follows involves a signaling pathway, which is a group of molecules that work together, one molecule activating the next until a specific function is carried out, such as renewing an organ's cells. There are many such signaling pathways.
But in the case of metastatic breast cancer, a disruptive pathway is formed. The signaling molecule, also known as a ligand, connects with a receptor molecule on certain bone cells and activates a cellular pathway that ultimately disrupts healthy bone renewal. Kang's team identified the signaling molecule as Jagged1, and the receptor molecule as one that activates a cellular pathway known as the "Notch pathway."
This finding gives cancer researchers a specific target, Kang said -- that of developing ways "to neutralize Jagged1's destructive power" and keeping it from interfering with normal bone growth.
At the Memorial Sloan-Kettering Cancer Center in New York City, Jacqueline Bromberg, a physician who also studies breast cancer, said the findings of Kang's team are promising.
"The bone is the most common site for metastasis in patients with breast cancer," said Bromberg, who met Kang several years ago while he was a postdoctoral fellow at Sloan-Kettering. She noted that although there are treatments that can slow these tumors, such as estrogen-blockers, radiation and chemotherapy, "we have few therapies which effectively eradicate bone metastasis."
At the Indiana University School of Medicine in Indianapolis, oncology professor Theresa Guise said the Princeton discoveries "show critical interactions between the tumor cells and bone cells." She added that the team has made a valuable contribution to research in that it "has dissected the contribution of the tumor and the micro-environment in this process."
Finding has link to earlier breast cancer work
The research builds on earlier work begun six years ago by Kang's laboratory that looked at how several different signaling pathways promote the spread of cancer to the bone. In a study published in the journal Nature Medicine in 2009, Kang showed that a pathway known as TGF beta plays a role in the growth of bone tumors. But until the recent study, it was not clear that Jagged1 plays a crucial role in that process. Before the current work focused on identifying the series of interconnected events that create the network of destructive pathways, Kang and Nilay Sethi, a dual degree student who recently finished his Ph.D. in molecular biology at Princeton, worked to find first which of the signaling molecules were at work in patients with breast cancer that had metastasized to the bone.
"It turned out that tumor samples from patients with breast cancer that had spread to the bone had higher levels of Jagged1," said Sethi, who is now completing his medical degree at the University of Medicine and Dentistry of New Jersey-Robert Wood Johnson Medical School.
Kang collaborated on the research with Nilay Sethi (left), a dual degree student who recently finished his Ph.D. in molecular biology at Princeton and is now completing his medical degree at the University of Medicine and Dentistry of New Jersey-Robert Wood Johnson Medical School. Sethi also previously worked with Kang to identify -- as a precursor to the current findings -- the signaling molecules at work in patients with breast cancer that has spread to the bone. (Photo by Brian Wilson)
The current research shows that, when the Jagged1 signaling molecule binds to its receptor molecule on the bone-producing cells, the interaction turns on the signaling pathway called Notch, and that leads to dramatic changes in bone growth. "It's like a key finding its matching lock, and opens a floodgate of information," Kang said. "Unfortunately, in this case, the Jagged1-Notch signaling is misused by cancer cells to serve a destructive purpose."
In healthy bone, specialized bone cells called osteoclasts scour the bone surface and use a combination of enzymes and acids to break down the old bone. Then another group of bone cells called osteoblasts deposit a new layer of bone matrix to rebuild the bone tissue. Working just like cellular excavators and paving machines, the bone-scrubbing osteoclasts and bone-building osteoblasts work in sync every day to renew the bone and maintain its strength. When these cells' activity gets out of balance, bone diseases can result.
While tumor cells lack the specialized tools that osteoclasts have to break down the bone, they are able to use the destructive Jagged1 molecule to disrupt the balanced activity of bone renewal, forcing the osteoclasts and osteoblasts to behave in a way that allows the tumor cells to invade the bone, Kang explained.
For example, by activating Notch signaling in osteoclasts, Jagged1 makes osteoclasts mature more quickly from their precursor cells, known as monocytes. A massive accumulation of these bone-scouring osteoclasts becomes the front line of the invasive force of tumor cells. That speeds up the breakdown of bone tissue and clears the way for tumor cells to expand into a malignant mass in the bone.
"Meanwhile, Jagged1 instructs the osteoblasts to secrete elevated levels of Interleukin-6, a tumor growth factor, so the cancer grows even faster," Kang said. "It's a one-two punch."
Creating further damage, the breakdown of the bone matrix releases a large quantity of another protein called TGF-beta, another signaling molecule that is embedded in the bone matrix during the bone-building process. In their earlier work published in 2009, Kang and colleagues showed that the TGF-beta protein derived from bones fuels the malignant growth of bone metastasis.
In the current study, some experiments conducted by Sethi established a surprising new link between TGF-beta and the Jagged1 molecule in bone metastasis.
"When tumor cells use the hijacked osteoclasts to break down the bone and release TGF-beta, it signals back to tumor cells to further stimulate the expression in Jagged1 in tumor cells," Sethi said. "The link between the Jagged1/Notch and TGF-beta pathways establishes a vicious cycle, essentially driving the unstoppable expansion of tumors and the destruction of skeletal tissues."
As a medical student, Sethi said he is acutely aware of the consequence of bone metastasis. "These patients suffer a lot. They have fractures, severe bone pain and debilitating nerve compression," he said. In addition, as the bone breaks down, calcium builds up in the blood, causing other life-threatening complications.
Blocking destructive pathway a potential treatment path
The key to stopping the process appears to be finding a way to neutralize the Jagged1 signaling molecule or its receptor Notch.
Kang has several ideas on how scientists may learn how to do just that. One way to interrupt the destructive process is to put a roadblock in the Notch pathway. There is a way to do that by halting the activity of gamma secretase -- an enzyme that plays a key role when the Notch pathway is activated -- because without it the delivery of instructions to bone cells cannot be completed. The pharmaceutical firm Merck & Co. has developed one such experimental drug that stops gamma secretase, known as a gamma secretase inhibitor or GSI, and the company has provided it to Kang's lab to support his team's work.
The drug has already shown promise treating metastatic bone cancer, Kang said. In animal experiments, the inhibitors have been proven to block the disease-causing signaling between tumor cells and bone cells, communication mediated by Jagged1 and Notch. Kang said GSI can reduce bone metastasis significantly, along with a dramatic reduction of bone destruction.
He hopes his team's new data showing that GSIs appear to work to halt the spread of cancer to the bone will result in clinicians starting a clinical trial of GSI to fight breast cancer metastases in the near future.
According to Kang, there are few drugs currently available to relieve symptoms associated with bone metastases, and none is able to completely stop the cancer. If Kang's findings lead to a drug that can halt or slow this process, it could affect the 200,000 patients that the NCI estimates are diagnosed every year with breast cancer. It might work for some other cancer patients as well, Kang said.
Sloan-Kettering's Bromberg said Kang's recent discovery "underlies the importance of targeting the environmental milieu" in which disease develops, in this case the activity of the Notch signaling pathway and specific interactions between cancer cells and the specialized cells that break down and rebuild bone.
Kang's work was funded by the New Jersey Commission on Cancer Research, the San Francisco-based Brewster Foundation founded by 1969 Princeton alumnus Leonard Schaeffer, U.S. Department of Defense, American Cancer Society, Merck & Co., the National Institutes of Health and the Champalimaud Foundation in Lisbon, Portugal.
A new weapon against bone metastasis? Princeton lab develops antibody to fight cancer
Team finds breast cancer gene linked to disease spread
Princeton scientists discover an interaction that helps cancers spread to bone
New cancer therapy from Yibin Kang's lab holds potential to switch off major cancer types without side effects
Princeton team discovers new organelle involved in cancer metastasis
Research team targets self-cannibalizing cancer cells
Kang finds keys to control the 'driver of cancer's aggressiveness' | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 311 |
Homepage / Policy Templates / Auditing Policy Template
Auditing Policy Template
By cacoPosted on October 9, 2020 October 9, 2020
Auditing policy template, A policy is a predetermined course of action based as a direct toward accepted business plans and objectives. The intent of this policy may be to set a mandate, offer a strategic direction, or reveal just how management treats a subject. Generally, a policy should include advice on what, why, and people, but not how. Policies vary infrequently and often set the path for the near future. Policies create expectations and guidelines for action.
The term, coverage, can also be utilized to describe regulator and legislative improvements or public policy. And then to confuse this even further, schools and universities have a tendency to consider with respect to Institutional Policies. In summary, the expression, Coverage, might be considered the strategies, plans, goals, objectives, strategies, rules, strategies, or protocol to companies or institutions. For the context of policies and procedures, refer to a Policy Statement as the basic objectives, aims, vision, approaches, and company culture. Think of the policy as the guiding statement for processes.
Component of the policy statement must clearly express why the policy has been written and what is hoped to be achieved by its own implementation. Section of this consultative process ahead of the execution of policy has to be a testing of this process and ideas regarding the policy has to be applied. One of the typical problems within organizations is that folks among level of their organization believed policy following year it meant to solve the particular issue may not necessarily exist across the whole organization. The assumptions that were made about why policy has to be implemented have to be analyzed within the organizational context. Is a perceived problem in one department a rule issue that has to be dealt with from an organizational perspective or is a specific issue relating to that division and had particular staff within the Department.
Though the link between policy formation and execution is a significant element of the process difficulties are frequently encountered when attempting to translate objectives into actions. Implementation might be the most demanding aspect of policy making because of the failure to anticipate opposition to policy, or because the financial, intellectual and other resources needed for successful execution have been jeopardized.
Policies also have the capacity to bring a measure of security in to manufacturing or service delivery procedures and supply advice in to dealing with difficult events. Organizational policies might be empowering, allowing management and employees the chance to use wisdom and experience to create greater opportunity for the business. The capacity for any organization to catch and use best practices can put them leaders in any business.
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"redpajama_set_name": "RedPajamaCommonCrawl"
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Цзи — 12-я буква китайского алфавита чжуинь. В разных системах романизации имеет разное написание. В составе слога может быть только инициалью.
Как инициаль Цзи образует 14 слогов. В словарях на основе пиньиня инициали расположены в следующем порядке:
чжуинь | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,886 |
\section{INTRODUCTION}
There are three reasons to focus attention on indirect detection signatures in the photon spectrum arising from
the annihilation or decay of very low-mass dark matter ($m_X \sim {\cal O}(100\, {\rm MeV})$)~\cite{Boddy:2015efa}:
\begin{itemize}
\item{If dark matter couples dominantly to quarks and is sufficiently light, then the annihilation/decay
products are dominated by $\gamma$s and $\pi^0$s, producing striking signatures in the photon spectrum; }
\item{A variety of new astronomical instruments which can vastly improve sensitivity to ${\cal O}(1-100)\, {\rm MeV}$
photons are under consideration;}
\item{Direct detection experiments tend to lose sensitivity at such low masses, while indirect
detection strategies may well be the most effective.}
\end{itemize}
For a dark matter initial state with center-of-mass energy $\sqrt{s} < 2m_{\pi^\pm}$, the only kinematically
accessible non-leptonic two-body final states are $\gamma \gamma$, $\gamma \pi^0$ and $\pi^0 \pi^0$. Since the $\pi^0$ will
decay almost exclusively to $\gamma \gamma$, low-mass dark matter is essentially ``guaranteed" to produce interesting
indirect detection signatures in the photon spectrum, provided it couples to quarks.
Moreover, since sensitivity to photons in this energy range is relatively poor, there are a variety of proposals for
new instruments which would dramatically improve sensitivity in this ``MeV gap,"~\cite{Greiner:2011ih} including
the Advanced Compton Telescope (ACT)~\cite{Boggs:2006mh}, the Advanced Pair Telescope (APT)~\cite{Buckley:2008fk}, the
Gamma-Ray Imaging, Polarimetry and Spectroscopy (GRIPS) detector~\cite{Greiner:2011ih}, the Advanced Energetic Pair Telescope
(AdEPT)~\cite{Hunter:2013wla}, the Pair-Production Gamma-Ray Unit (PANGU)~\cite{Wu:2014tya}, the Compton Spectrometer and
Imager (COSI)~\cite{Kierans:2014lr}, and ASTROGAM~\cite{astrogam}.
In this proceedings contribution, we describe the bounds on dark matter annihilation or decay to these final states
arising from current data (from COMPTEL, EGRET and Fermi), and the future sensitivity of other instruments under consideration.
We begin by describing a class of low-mass dark matter models which produce distinctive photon spectra.
We then describe the general features of indirect detection strategies for probing these models,
utilizing either the diffuse gamma ray flux or a
search of dwarf galaxies. We describe the current bounds arising from existing gamma ray data sets in this energy range (as well as
from the Cosmic Microwave Background (CMB)), and the sensitivity of future contemplated instruments. We end with a discussion of our
results.
\section{MODELS AND SPECTRA}
We consider the case of low-mass dark matter whose dominant Standard Model coupling is to quarks. Indirect detection is possible
through either dark matter annihilation or decay; in either case, we refer to the center-of-mass energy of the relevant process
as $\sqrt{s}$, and assume $\sqrt{s} < 2m_{\pi^\pm}$. The only non-leptonic two-body final states that are
kinematically allowed are $\gamma \gamma$, $\gamma \pi^0$, and $\pi^0 \pi^0$. Additional leptonic or three-body final states are also
available, but the relevant annihilation/decay rates are suppressed by factors of $\alpha$ or $sG_F$, and we assume they are negligible.
For each two-body final state, the energies of the prompt photons and neutral pions are determined by $\sqrt{s}$. The
neutral pion decays through the process $\pi^0 \rightarrow \gamma \gamma$ with $\sim 99\% $ efficiency,
resulting in a ``box-like" spectrum, characteristic
of monoenergetic photons from an isotropically boosted source. As a result, all
of the final state products produce distinctive photon signatures.
If we assume that weak interactions are negligible and that the fundamental dark matter-quark interaction is $C$-invariant, then we may
classify final states by their $C$ eigenvalues. The photon injection spectrum associated with each final state is determined by kinematics, and are
as follows:
\begin{itemize}
\item $\pi^0 \pi^0$ ($C$-even):
\begin{eqnarray}
\frac{dN_\gamma}{dE} &=& \frac{4}{\Delta E} \left[\Theta(E-E_-)-\Theta(E - E_+)\right] ,
\nonumber\\
E_\pm &=& \frac{\sqrt{s}}{4} \pm {\Delta E \over 2} \ , \qquad
\Delta E = {\sqrt{s} \over 2}\sqrt{1- {4m_{\pi^0}^2 \over s} } \ .
\end{eqnarray}
\item $\gamma \pi^0$ ($C$-odd):
\begin{eqnarray}
\frac{dN_\gamma}{dE} &=& \delta (E-E_0) + \frac{2}{\Delta E} \left[\Theta(E-E_-)-\Theta(E - E_+)\right] ,
\nonumber\\
E_0 &=& \frac{\sqrt{s}}{2} \left(1-\frac{m_{\pi^0}^2}{s}\right)
\nonumber\\
E_\pm &=& \frac{\sqrt{s}}{4} \left(1+\frac{m_{\pi^0}^2}{s}\right) \pm {\Delta E \over 2} \ , \qquad
\Delta E = \frac{\sqrt{s}}{2} \left(1-\frac{m_{\pi^0}^2}{s} \right) \ .
\end{eqnarray}
\item $\gamma\gamma$ ($C$-even):
\begin{eqnarray}
\frac{dN_\gamma}{dE} &=& 2\delta (E-E_0)
\nonumber\\
E_0 &=& \frac{\sqrt{s}}{2} \ .
\end{eqnarray}
\end{itemize}
Depending on the details of the model, as well as the $C$ eigenvalue and energy of the initial state, it is possible for any final
state to dominate. We will therefore analyze the detection prospects for each final state channel assuming the branching fraction
to that channel is 1.
The above photon injection spectra must be convolved with an energy resolution function to determine the spectrum observed at
any particular detector. For simplicity, we will assume in our analysis that the energy resolution function for each detector
can be well-approximated by a Gaussian with an energy-independent fractional width.
For channels in which a $\pi^0$ is produced just above threshold, the $\pi^0$ will decay nearly at rest, producing a very narrow
box-like feature ($\Delta E$ small) which may mimic a line. This feature will provide an excellent signature for a detector
whose energy range is large enough to contain the peak. In the $\gamma \pi^0$ channel, this box-like feature will dominate the sensitivity
of an experiment only if it is sufficiently narrow; for large enough $\sqrt{s}$, the monoenergetic photon will be a larger driver of sensitivity.
\section{SEARCHES OF THE DIFFUSE FLUX AND OF DWARF GALAXIES}
We will focus on signals of dark matter annihilation/decay in the diffuse gamma ray flux, and in
gamma ray emission from dwarf spheroidal galaxies. This analysis is described in detail in~\cite{Boddy:2015efa}.
The diffuse flux of gamma rays has been measured in the energy range of
interest by COMPTEL and EGRET~\cite{Strong:2004de}. The data are relatively smooth and can be fit to a power law~\cite{Boddy:2015efa}:
\begin{equation}
d^2 \Phi / dE\, d\Omega = (2.74 \times 10^{-3} ~\rm cm^{-2}\rm s^{-1}\rm sr^{-1}\, {\rm MeV}^{-1}) ( E /\, {\rm MeV} )^{-2.0} \ .
\label{eq:bkg-fit}
\end{equation}
A indirect detection search in the diffuse gamma ray flux is essentially a search for a sharp feature
in the observed photon spectrum. On the other hand, the observed diffuse photon spectrum constitutes the
foreground to a search for dark matter in dwarf galaxies.
To determine the sensitivity of current and future instruments to searches for diffuse gamma ray emission,
we consider both a ``conservative" and ``optimistic" analysis. In the conservative analysis, we exclude
models for which the expected number of photons from dark matter annihilation/decay exceeds the observed
number of counts by $2\sigma$ in any one energy bin.\footnote{In determining bounds from current data,
we utilize the actual flux measurements and energy binning of the relevant instrument. In estimating the sensitivity
of future experiments, we assume that the observed flux is consistent with Equation~\ref{eq:bkg-fit}, and adopt an
optimal energy binning for the relevant experiment, given an estimate for its energy resolution.}
This analysis would be appropriate if there is little
confidence in one's understanding of the underlying astrophysical backgrounds. But in a more optimistic case,
one might be confident that the underlying astrophysical background exhibited no sharp features. In that case,
one could instead estimate the systematic uncertainty in a smooth fit to the diffuse gamma ray flux (following
Reference~\cite{Strong:2004de},
we estimate the systematic uncertainty to be 15\%), and exclude models for which the expected number of photons from the dark matter
signal exceeded twice this uncertainty in any one energy bin.
It is important to note that, for either a conservative or optimistic analysis of the diffuse
gamma ray flux, statistical uncertainties are subleading. As a result, sensitivity is not significantly
affected by the exposure or angular resolution of the instrument. Instead, the sensitivity to a line signal is
proportional to $\epsilon^{-1}$, which determines the instrument's ability to distinguish a sharp feature in the data.
For an analysis of dwarf galaxies, however, we assume that it is possible to estimate the foreground photon spectrum
arising from astrophysical sources (and from diffuse gamma ray emission due dark matter annihilation/decay along the line
of sight) by looking slightly
off-axis. One then excludes models for which the number of photons expected from dark matter annihilation/decay
within the dwarf galaxy could not be accommodated by a $2\sigma$ downward statistical fluctuation in the number of foreground
photons within the set of energy bins which encompass the entire dwarf galaxy dark matter signal. Since the sensitivity is controlled
by statistical uncertainties, it is proportional to $\sqrt{A_\textrm{eff} T_\textrm{obs} / \epsilon}$ for a line search,
where $A_\textrm{eff}$ is the effective area and $T_\textrm{obs}$ is the run time.
We thus see that a larger $A_\textrm{eff}$ and larger $T_\textrm{obs}$ would improve the
sensitivity of a dwarf galaxy search, while an improved energy resolution would improve the sensitivity of both
dwarf galaxy and diffuse emission searches. The energy range, energy and angular resolutions ($1\sigma$), and effective area
of the relevant instruments are listed in Table~\ref{tab:experiments}.
Note that the listed values for the resolutions and effective areas are given at a particular energy, and our analysis is performed with these benchmark numbers.
If possible, we use values corresponding to photon energies at or near $100\, {\rm MeV}$ with photon detection at normal incidence.
For the experiments that cover a lower energy range, we use the performance goal values.
In the case that only an estimated range is provided, we use the more pessimistic (worse resolution, smaller effective area) end of that range.
We list two benchmark points for ASTROGAM: one for photon detection via Compton scattering (below $10\, {\rm MeV}$) and one for detection via pair production (above $10\, {\rm MeV}$).
\begin{table}[h]
\centering
\begin{tabular}{cccccc}
\hline
Detector & Source & Energy Range [MeV] & $\epsilon$
& PSF & $A_\textrm{eff}$ [$\rm cm^2$] \\
\hline
ACT & \cite{Boggs:2006mh}
& 0.2 -- 10 & 1\% & $1^\circ$ & 1000 \\
GRIPS & \cite{Greiner:2011ih}
& 0.2 -- 80 & 3\% & $1.5^\circ$ & 200 \\
AdEPT & \cite{Hunter:2013wla}
& 5 -- 200 & 15\% & $0.5^\circ$ & 600 \\
COMPTEL & \cite{Weidenspointner:1999thesis,Kappadath:1998thesis}
& 0.8 -- 30 & 2\% & $2^\circ$ & 50 \\
EGRET & \cite{Thompson:1993lr}
& 30 -- $10^4$ & 12.5\% & $2.8^\circ$ & 1000 \\
Fermi-LAT & \cite{Atwood:2009ez}
& 20 -- $3\cdot 10^5$ & 7.5\% & $2^\circ$ & 4000 \\
GAMMA-400 & \cite{Galper:2014pua}
& 100 -- $3\cdot 10^6$ & 12\% & $2^\circ$ & 3000 \\
ASTROGAM (below $10\, {\rm MeV}$) & \cite{astrogam}
& 0.3 -- 10 & 1\% & $0.5^\circ$ & 119 \\
ASTROGAM (above $10\, {\rm MeV}$) & \cite{astrogam}
& 10 -- 3000 & 30\% & $0.5^\circ$ & 514
\end{tabular}
\caption{Experimental parameters used to determine indirect detection bounds for dark matter annihilation and decay.
The values between experiments are not directly comparable, since they may have been taken at different photon energies.
The width of the point spread function (PSF) and $A_\textrm{eff}$
values are not needed in the analysis for COMPTEL, EGRET, and Fermi, but they are included for completeness.}
\label{tab:experiments}
\end{table}
\section{CURRENT BOUNDS AND FUTURE SENSITIVITY}
In Figure~\ref{fig:constraints}, we plot current constraints on diffuse emission of photons from dark matter annihilation (left panel)
and decay (right panel) using data from COMPTEL, EGRET and Fermi-LAT, applying a conservative analysis (the details are described in~\cite{Boddy:2015efa}).
The $\gamma \gamma$, $\gamma \pi^0$ and $\pi^0 \pi^0$ channels are depicted with solid, dashed and dotted contours,
respectively. Note that, although Fermi's energy range goes down as far as $20\, {\rm MeV}$, their diffuse flux analysis only
extends down to $100\, {\rm MeV}$, in order to reduce backgrounds from cosmic ray interactions with the atmosphere.
The $J$-factors used in estimating
the dark matter signal flux are obtained from~\cite{Cirelli:2010xx}.
We also plot bounds on the annihilation cross section (assuming $s$-wave annihilation) and decay rate~\cite{Slatyer} which arise
from measurements by Planck~\cite{Ade:2015xua} of the Cosmic Microwave Background (CMB) spectrum. Note that,
although CMB constraints exceed those of indirect detection for the case of dark matter annihilation, the CMB
constraints are subleading for the case of dark matter decay. This is not surprising, given that the
dark matter annihilation scales quadratically with dark matter density; the rate of dark matter annihilation
in the early Universe is thus greatly enhanced relative to the current epoch.
\begin{figure}[ht]
\centerline{\includegraphics[width=0.95\textwidth]{constraints}}
\caption{Diffuse gamma ray flux constraints on dark matter annihilation (left panel) and decay (right panel) to the $\gamma \gamma$ (solid),
$\gamma \pi^0$ (dashed), and $\pi^0 \pi^0$ (dotted) channels obtained from data from COMPTEL (blue), EGRET (red) and
Fermi-LAT (green). Also shown are constraints which can be obtained from Planck data (black). The vertical
black dashed lines are the kinematic thresholds for the $\gamma \pi^0$ and $\pi^0 \pi^0$ channels.}
\label{fig:constraints}
\end{figure}
In Figure~\ref{fig:constraints-future}, we plot the sensitivity of a variety of future instruments, in the case
of either a diffuse emission search, or a 5-year search of photons from Draco (the $J$-factor from Draco is obtained
from~\cite{Geringer-Sameth:2014yza}).
A detailed description of the analysis is found in~\cite{Boddy:2015efa}.
The results of conservative and optimistic analyses of diffuse emission are
depicted as the boundaries of the solid bands, while the sensitivity of the analysis of Draco is depicted by
the hatched regions whose thicknesses represent the $1\sigma$ systematic uncertainties in $J$.
\begin{figure}[ht]
\begin{tabular}{c}
\includegraphics[width=0.95\textwidth]{constraint3cetup} \\
\includegraphics[width=0.95\textwidth]{constraint2cetup} \\
\includegraphics[width=0.95\textwidth]{constraint1cetup} \\
\end{tabular}
\caption{The projected sensitivity of ASTROGAM, AdEPT, and GRIPS to dark matter annihilation (left panels) or
decay (right panels) in the $\gamma \gamma$ (top row), $\gamma \pi^0$ (middle row) and $\pi^0 \pi^0$ (bottom row)
channels. The shaded regions are bounded by contours which describe sensitivity of a conservative or
optimistic analysis of diffuse gamma ray emission, as described in the text. The hatched region describes the
sensitivity contour for a search of Draco, when the $J$-factor is varied through $1\sigma$ systematic uncertainties.
The black line describes the exclusion contour from Planck data. The dashed vertical lines are the kinematic thresholds
for the $\gamma \pi^0$ and $\pi^0 \pi^0$ channels.
}
\label{fig:constraints-future}
\end{figure}
One can see several features in the sensitivities shown in Figure~\ref{fig:constraints-future}.
In the $\gamma\gamma$ and $\gamma\pi^0$ channels, ASTROGAM's Compton detector can detect the lower energy photons with a high energy resolution; consequently, it has the greatest sensitivity in the $\gamma\gamma$ channel in a diffuse gamma ray search.
Similarly, the enhanced sensitivity of GRIPS over AdEPT (and ASTROGAM in the pair-production regime) to the $\gamma \gamma$ channel in a diffuse gamma ray search is due to its better energy resolution.
ASTROGAM is the least sensitive for a diffuse search in its pair production regime, given the pessimistic projected 30\% energy resolution;
using a more optimistic 20\% would bring its sensitivities more in line with those of AdEPT.
However, AdEPT, GRIPS, and ASTROGAM all have similar sensitivity to the same channel in a search of dwarf galaxies because the greater effective area of AdEPT and ASTROGAM compensates for poorer energy resolution.
For the $\gamma \gamma$ and $\gamma \pi^0$
channels, the sensitivity of GRIPS is suppressed at higher energies due to the the relatively low upper limit of its energy range ($80\, {\rm MeV}$),
compared to AdEPT and ASTROGAM.
Additionally, GRIPS will miss a fraction of the box-like feature arising from $\pi^0$ decay, unless the pion is nearly at rest.
Comparing the cases of dark matter annihilation and dark matter decay, one sees that a search of dwarf spheroidal galaxies shows a
greater improvement in sensitivity, relative to diffuse flux searches, for the case of dark matter annihilation. This is not surprising, since
the enhanced dark matter density within a dwarf galaxy will lead to a quadratic enhancement in the annihilation rate, but only a linear
enhancement in the decay rate.
\section{CONCLUSIONS}
We have considered a class of models in which low-mass ($\sqrt{s} < 2m_{\pi^\pm}$) dark matter couples dominantly to quarks. For these
models, kinematic considerations favor the $\gamma \gamma$, $\gamma \pi^0$ and $\pi^0 \pi^0$ final states for dark matter
annihilation or decay, regardless of the details of the interaction of dark matter with quarks. These models thus generically
predict sharp and striking signals in the photons spectrum in the energy range ${\cal O}(1-100)\, {\rm MeV}$.
This is especially interesting because, although there is currently a dearth of instruments focused on this
energy range, the astrophysics community is considering several plans to fill this ``MeV gap." These new instruments
could improve sensitivity to these indirect detection channels by up to a few orders of magnitude. Indeed, although
constraints from CMB observations are by far the most stringent current limits on dark matter annihilation, searches of
dwarf galaxies by future instruments could exceed those limits by more than an order of magnitude.
New instruments searching for photons in the ${\cal O}(1-100)\, {\rm MeV}$ range may exceed previous instruments
in effective area, energy resolution and angular resolution, providing a variety of paths for improving sensitivity to low-mass
dark matter.
\section{ACKNOWLEDGMENTS}
This research is funded in part by NSF CAREER grant PHY-1250573. JK thanks CETUP*
(Center for Theoretical Underground Physics and Related Areas), for its hospitality and partial support during the 2015 Summer Program.
\bibliographystyle{aipnum-cp}%
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,455 |
\section{Introduction}
Glitches, and post-glitch relaxations, are widely believed to be
effects caused by (the superfluid component in) the crust of
neutron stars (see, eg., \markcite{LGS8} Lyne \& Graham-Smith
1998; \markcite{KLGJ03} Krawczyk~et. al. 2003). There exist,
however, observational data on glitches that could not be possibly
due to the role of the stellar crust. The data have been
previously explained \markcite{APC} (Alpar, Pines \& Cheng 1990;
hereafter APC) in terms of a suggested spin-up of (a part of) the
crustal superfluid by the spinning down crust (``the container'')
over a time much larger than the associated relaxation timescale.
However, a closer look at the relative rotation of the superfluid
and its vortices reveals that the suggested mechanism fails
quantitatively by, at least, more than one order of magnitude. In
addition, the suggested spin-up process is also argued to be in
contradiction with the well-known requirements for a superfluid
spin-up. Hence, the (pinned) superfluid in the crust is not the
primary cause of the post-glitch relaxation. On the other hand,
the pinning of the superfluid vortices in the crust, and also in
the core, of a neutron star has recently been objected by some
authors on the account of the possible observations of long period
precession in isolated pulsars (Jones \& Anderson 2001; Link 2003;
Buckley, Metlitski \& Zhitnitsky 2004). Thus the post-glitch
relaxation must be driven by mechanism(s) other than that due only
to the crust superfluidity, whether the pinning is realized or
not. In section 2, the general role of an assumed superfluid
component in (the crust or in the core of) a neutron star on the
observable post-glitch behavior of the star is briefly described.
In section 3, the relevant observational data and the problem
raised by these observations against any model of post-glitch
relaxation based on the effects of the crust alone are
highlighted. The earlier suggested resolution \markcite{APC} (APC)
of the problem is then stated. In section 4, a quantitative
evaluation of the suggested mechanism is given, indicating a large
disagreement with the data. The subsection 4.1 presents a more
detailed discussion of the rotation of the different components in
the crust, paying particular attention to the vortex lines, and
arrives at the same conclusion as already deduced, in the section
4. In section 5, the feasibility of the suggested process, of
spinning up of a pinned superfluid component in the crust during
the spinning down of the crust itself, is questioned, altogether.
The possibility of such a process is argued to be ruled out, on a
general dynamical ground, and also according to the vortex creep
formulation. We conclude in section 6, with a speculative
suggestion for the possible cause of the observed effect.
\section{Crustal Superfluid: An Overview}
The spin-down rate $\dot\Omega_{\rm c}$ of the crust of a neutron
star, with a moment of inertia $I_{\rm c}$, obeys \markcite{BPP}
(Baym et~al. 1969b)
\begin{eqnarray}
I_{\rm c} \dot\Omega_{\rm c} = N_{\rm em} -
\Sigma I_{\rm i}\dot\Omega_{\rm i}
\end{eqnarray}
where $N_{\rm em}$ is the negative electromagnetic torque on the
star, and $\dot\Omega_{\rm i}$ and $I_{\rm i}$ denote the rate of
change of rotation frequency and the moment of inertia of each of
the separate components, respectively, which are summed over.
Steady state implies \(\dot\Omega_{\rm i} =\dot\Omega_{\rm c} =
\dot \Omega \equiv {N_{\rm em} \over I}\), for all $i$, where \(
I= I_{\rm c}+\Sigma I_{\rm i}\) is the total moment of inertia of
the star. Different models for the post-glitch recovery, and in
particular the model of vortex-creep, invoke a
decoupling-recoupling of a superfluid component in the {\em crust}
of neutron stars \markcite{AAP,J91a,EL}(Alpar et al. 1984; Jones
1991a; Epstein, Link \& Baym 1992). The rest of the star including
the core (superfluid) is assumed in these models to be
rotationally coupled to the non-superfluid constituents of the
crust, on timescales much shorter than that resolved in a glitch.
The role of any superfluid component of a neutron star in its
post-glitch behavior is understood as follows. Spinning down (up)
of a superfluid at a given rate is associated with a corresponding
rate of outward (inward) radial motion of its vortices. If
vortices are subject to pinning, as is assumed for the superfluid
in the crust of a neutron star, a spin-down (up) would require
unpinning of the vortices. This may be achieved under the
influence of a Magnus force $\vec{F}_{\rm M}$ acting on the
vortices, which is given, per unit length, as \markcite{S89}
\begin{eqnarray}
\vec{F}_{\rm M} & = & - \rho_{\rm s} \vec{\kappa} \times
(\vec{v}_{\rm s} - \vec{v}_{\rm L})
\end{eqnarray}
where $\rho_{\rm s}$ is the superfluid density, $\vec{\kappa}$ is
the vorticity of the vortex line directed along the rotation axis
(its magnitude $\kappa = { h \over 2 m_{\rm n}}$ for the neutron
superfluid, where $m_{\rm n}$ is the mass of a neutron), and
$\vec{v_{\rm s}}$ and $\vec{v_{\rm L}}$ are the local superfluid
and vortex-line velocities. Thus, if a lag \( \omega \equiv
\Omega_{\rm s} - \Omega_{\rm c}\) exist between the rotation
frequency $\Omega_{\rm s}$ of the superfluid and that of the
vortices (pinned and co-rotating with the crust) a radially
directed Magnus force \((F_{\rm M})_r= \rho_{\rm s} \kappa r
\omega \) would act on the vortices, where $r$ is the distance
from the rotation axis, and \(\omega >0 \) corresponds to an
outward directed $(F_{\rm M})_r$, vice-versa. The crust-superfluid
may therefore follow the steady-state spin-down of the star by
maintaining a critical lag $\omega_{\rm crit}$ which will enables
the vortices to overcome the pinning barriers. The critical lag is
accordingly defined through the balancing $(F_{\rm M})_r$ with the
pinning forces.
At a glitch a sudden increase in $\Omega_{\rm c}$ would result in
\( \omega<\omega_{\rm crit}\), hence the superfluid becomes
decoupled and could no longer follow the spinning down of the star
(ie. its container). If, as is suggested \markcite{AI}, the glitch
is due to a sudden outward release of some of the pinned vortices
the associated decrease in $\Omega_{\rm s}$ would also add to the
decrease in $\omega$, in the same regions. Therefore a fractional
increase ${\Delta \dot \Omega_{\rm c} \over \dot \Omega_{\rm c}}$
same as the fractional moment of inertia of the decoupled
superfluid would be expected. This situation will however persist
only till \( \omega=\omega_{\rm crit}\) is restored again (due to
the spinning down of the crust) and the superfluid re-couples, as
illustrated by $\Omega_{\rm s}$ and $\Omega_{\rm c}$ curves in
Fig.~1. The vortex creep model suggests \markcite{AAP} (Alpar
et~al 1984) further that a superfluid spin-down may be achieved
even while \( \omega < \omega_{\rm crit}\), due to the creeping of
the vortices via their thermally activated and/or quantum
tunnelling movements. A superfluid spin-down with a steady-state
value of $\omega < \omega_{\rm crit}$, and also a post-glitch
smooth gradual turn over to the complete re-coupling for each
superfluid layer is thus predicted in this model. It may be
however noticed that the predicted gradual (exponential) recovery
of the crustal spin frequency is not an effect peculiar to the
creep process. It is mainly caused due to the assumed varying
amplitude of the glitch-induced jump in $\Omega_{\rm s}$ in the
different layers of the superfluid (corresponding to their assumed
varying critical lag values), which are thus re-coupled at various
times. A similar behavior should be also expected even in the
absence of any creeping, given the same series of the superfluid
layers. The induced $\Delta\dot\Omega_{\rm c} \over
\dot\Omega_{\rm c}$ during a superfluid decoupling phase according
to the creep model would be indeed the same as (or slightly
smaller than) otherwise.
\section{Observational Constraint}
The more recent glitches observed in Vela, and one in PSR~0355+54,
have shown values of
\begin{eqnarray}
{\Delta \dot \Omega_{\rm c} \over \dot \Omega_{\rm c}} > 10\%
\end{eqnarray}
with recovery timescales $\sim 0.4$~d, and $\sim 44$~d,
respectively \markcite{L87,APC,F95} (Lyne 1987; APC; Flanagan
1995). The data hence imply (Eq.~1) that a part of the star with a
fractional moment of inertia $> 10\%$ (up to $60\%$) is decoupled
from the crust during the observed post-glitch response. This is,
however, in sharp contradiction with the above glitch models,
since for the moment of inertia $I_{\rm crust}$ of the crustal
superfluid
\begin{eqnarray}
{I_{\rm crust} \over I} \lesssim 2.5\%
\end{eqnarray}
\markcite{APC}(APC). The disagreement with the data
is indeed a fundamental shortcoming for the crustal models, and
not just a quantitative mismatch. Because, the predicted increase
for ${\Delta \dot \Omega_{\rm c} \over \dot \Omega_{\rm c}}$ in
these models is naturally bound to be smaller than the fractional
moment of inertia of the decoupled superfluid (also see the best
fit results of \markcite{AC3}Alpar et~al. 1993); the other
possibility raised in APC, to account for the larger spin-down
rates, is the point of issue in the following.
It has been suggested \markcite{APC}(APC) that the observed large
values of ${{\Delta \dot \Omega_{\rm c} \over \dot \Omega_{\rm
c}}} \sim 20 \%$ over a time scale $\tau_{\rm sp} \sim 0.4$~d, in
Vela, could be accounted for by assuming that part of the crustal
superfluid {\it spins up}, over the {\it same} time period
$\tau_{\rm sp}$ (see Fig.~1a). The superfluid would thus be
expected to act as a source of an additional spin-down torque on
the rest of the star and could, in principle, result in ${\Delta
\dot \Omega_{\rm c} \over \dot \Omega_{\rm c}}$ values much larger
than the fractional moment of inertia of the decoupled component.
For this to be realized, a region of the crust-superfluid with a
moment of inertia $I_{\rm sp}$ and a spin frequency $\Omega_{\rm
sp}$ has been assumed to support a tiny (positive) steady-state
lag $\omega_{\rm sp} \equiv \Omega_{\rm sp} -\Omega_{\rm c} \sim
3.5 \times 10^{-6} \ {\rm rad \ s}^{-1}$, in contrast to the much
larger steady-state value of the lag \( \omega \geq 10^{-2} \ {\rm
rad \ s}^{-1} \) in the rest of the crust-superfluid. Hence, a
glitch of a size \(\Delta\Omega_{\rm c} \sim 10^{-4} \ {\rm rad \
s}^{-1}\) would result in a ``reversed'' situation with \(
\Omega_{\rm c} >> \Omega_{\rm sp}\), which is further suggested
\markcite{APC} (APC) to be followed by a spinning up of the
superfluid over the time period $\tau_{\rm sp}$, as indicated in
Fig.~1a.
\section{A Quantitative Check}
The above spin-up scenario is however unable to account for the
observed effect, quantitatively. It assumes \markcite{APC} (APC)
that the total frequency difference ($\Omega_{\rm c}-\Omega_{\rm
sp}$), initially induced by the glitch, is slowly relaxed during
the period $\tau_{\rm sp}$. In contrast, we argue that only a
small fraction of the initial jump in the superfluid rotation rate
might be at all preserved for any such ``long-term'' spin-up
process. This is because the superfluid would be otherwise
rotating much slower than its vortices which are, by virtue of
their assumed pinning, co-rotating with the crust (see Fig.~1a).
That is, the rotational lag between the superfluid and its
vortices would be {\em much larger} than the associated critical
lag. If so, the pinning could not impede the vortex motions (see
above) and a fast superfluid spin-up should take place. It may be
recalled that the critical lag is, by definition, the minimum lag
required for the Magnus force on vortices to overcome the pinning
forces. When the instantaneous lag exceeds its critical value, the
pinning forces (in the azimuthal direction) would act as a major
source for the torque on the superfluid, resulting in a relaxation
even faster than in the absence of any pinning
\markcite{TT,ACG}(Tsakadze \& Tsakadze 1980; Adams, Cieplak \&
Glaberson 1985). In order to allow for the suggested {\it large}
frequency difference between the superfluid and the crust, while
maintaining a rotational lag (between the superfluid and its
vortices) {\em smaller} than the associated critical value, one is
forced to assume that the pinning is ``switched off'', which would
be in contradiction with the assumed pinning conditions.
Nevertheless, the superfluid relaxation for such free (unpinned)
vortices should still take place very quickly, as is further
discussed below.
Thus, the upper limit on the frequency difference $\Delta\Omega$
between the crust and the superfluid ($\Omega_{\rm sp}$), at the
beginning of the time period of interest $\tau_{\rm sp}$ and {\em
after} the ``fast'' early relaxation of the superfluid (discussed
above), would be $\Delta\Omega = \omega_{\rm sp} \sim
3.5\times10^{-6}\ {\rm rad~s}^{-1}$; see the discussion in \S4.1
below for a more detailed reasoning. This is the maximum
permissible frequency difference that one might, in principle,
consider to be further equilibrated between the crust and the
superfluid. In contrast, a value of $\Delta\Omega =
\Delta\Omega_{\rm c}\sim 1.3\times10^{-4}\ {\rm rad~s}^{-1}$ has
been adopted in APC. The corresponding time scale $\tau_{\rm sp}$,
for an assumed spin-up of the superfluid, may be estimated from
\markcite{BPP}(Basym et~al. 1969) (see also Eq.~2b in APC)
\begin{eqnarray}
\left(\Delta\dot\Omega_{\rm c}\right)_{\rm sp}=
{I_{\rm sp}\over I} { \Delta\Omega \over \tau_{\rm sp}}
\end{eqnarray}
where $(\Delta\dot\Omega_{\rm c})_{\rm sp}$ is the magnitude of
the change in $\dot\Omega_{\rm c}$ due to the spinning up of the
superfluid. Adopting the same parameter values as in APC, ie.
\({{(\Delta\dot\Omega_{\rm c})_{\rm sp}}/{\dot\Omega_{\rm c}}}=
0.2\), \(\frac{I_{\rm sp}}{I}=5.3\times10^{-3}\), \(\Delta\Omega=
\omega_{\rm sp}= 3.5\times10^{-6}\ {\rm rad~s}^{-1}\), and
$\dot\Omega_{\rm c}= 9.5\times10^{-11}\ {\rm rad~s}^{-2}$ for
Vela, Eq.~5 then sets an upper limit of
\begin{eqnarray}
\tau_{\rm sp}< 0.3 \ {\rm hr},
\end{eqnarray}
which is {\it too short} in comparison with the observed
timescales $\sim 0.4$~d. Hence, the crust-superfluid cannot be the
cause for the observed large spin-down rates even in the case of
1988 glitch of the Vela pulsar, addressed in APC. The disagreement
between the predicted and observed timescales would be even worse
for the case of 1991 glitch of the same pulsar, having observed
values of \({\Delta\dot\Omega_{\rm c}/{\dot\Omega_{\rm c}}} \sim
60\% \) over a similar relaxation time \markcite{F95}(Flanagan
1995). Also, an attempt to apply the same crust-superfluid spin-up
scenario to the case of PSR~0355+54 would result in more than {\it
three} orders of magnitudes difference between the predicted
$\tau_{\rm sp}$ and the observed relaxation time $\sim 40$~days.
\subsection{Further reasoning for \(\omega_{\rm sp}\), against
\(\Delta\Omega_{\rm c}\)}
The above, rather obvious, conclusion (about the proper value of
the frequency difference between the crust and the superfluid at
the beginning of the long term relaxation) may be further
explained by focussing attention on the behavior of the rotation
frequency $\Omega_{\rm L}$ of the {\it vortices}, in the region of
interest identified by $\Omega_{\rm sp}$. Since this has not been
explicitly specified in APC we, therefore, discuss the two
exclusive possibilities that might, in principle, arise and which
could be physically justified. Both cases lead, however, to the
same conclusion; intermediate cases for which no justification
exist should naturally fall in between (and there is no indication
in APC for any special effect due to such cases). It may be noted
that the cases to be considered should not be, however, paralleled
to the classification of (strong, weak, super-weak) pinning
regions, invoked in the literature on the vortex creep model. The
latter is based on the relative magnitude of the critical lag and
reflects the long term behavior of the superfluid relaxation
toward its steady state lag value. In contrast, the following two
cases concern the instantaneous response of the originally pinned
vortices upon a sudden jump in the rotation rate of the container
(see Fig.~1). The vortices might be spun up along with the crust
(container), and remain pinned {\em during} the sudden spin-up of
the container (case {\bf a}). Else, they could relax to a state of
co-rotation with the local superfluid, assuming the pinning to be
temporarily broken ({\bf b}). Hence, the rotational frequency of
the vortices in the region of interest would be such that either
\begin{eqnarray}
\Omega_{\rm L} &=& \Omega_{\rm c} \ \ \ \ \ {\rm (pinning \ conditions), or \ else} \\
\Omega_{\rm L} &=& \Omega_{\rm sp} \ \ \ \ \ {\rm (Helmholtz \
theorem)},
\end{eqnarray}
just {\it at} the beginning of the interval $\tau_{\rm sp}$,
namely after the jump in $\Omega_{\rm c}$ (the observable glitch)
has been accomplished (see Fig.~1a),
In the case {\bf (a)}, the superfluid ($\Omega_{\rm sp}$) must
have also been spun up, along with the crust and the vortices, to
(at least) a state such that \( \Omega_{\rm sp}-\Omega_{\rm c}=
-\omega_{\rm sp}\) (contrast with the scenario adopted by APC as
depicted in Fig.~1a). Otherwise the pinning would be broken
(contrary to the assumption) by the associated radial Magnus force
on the vortices. That is, if the superfluid rotation rate is
assumed to retain its pre-glitch value, while the pinned vortices
have been spun up along with the crust, the instantaneous
(negative) lag between the superfluid and its vortices far exceeds
its critical value. Under such conditions, the superfluid
(spin-up) relaxation could not be impeded by the pinning forces.
The relaxation would occur on short timescales similar to the case
of free vortices, also according to the vortex creep model (see,
eg., the discussion related to Eq.~11 in Alpar et~al. 1984). Such
a fast relaxation of the superfluid in the crust of a neutron
star, when the lag exceeds its critical value, is in fact invoked
in the vortex creep model as the cause of the glitches
\markcite{AI,AAP}(Anderson \& Itoh 1975; Alpar et~al. 1984). Given
the existing (two minute) upper limit on the rise time of the
glitch \markcite{F95}(Flanagan 1995), the superfluid spin-up (for
$\Omega_{\rm sp}$, in the present case, until its rotational lag
with its vortices drops to values smaller than the critical value)
has to be likewise accomplished on a time scale of a minute
(contrast with $\tau_{\rm sp}$). Formally, this may be verified
from the following relation which is prescribed, in the creep
model, for such cases when the value of the lag $\omega
>> \omega_{\rm crit}$ \markcite{CAP}
\begin{eqnarray}
v_r = v_0 \exp{[- \frac{E_{\rm p}}{{\rm k}T} \left(
\frac{\omega_{\rm crit}-\omega}{\omega_{\rm crit}}\right)] /
\left\{ \exp[- \frac{E_{\rm p}}{{\rm k}T} \left(\frac{\omega_{\rm
crit}-\omega}{\omega_{\rm crit}}\right)]+1\right\}},
\end{eqnarray}
which amounts to
\begin{eqnarray}
v_r \sim v_0,
\end{eqnarray}
where $v_r$ is the vortex radial velocity, and $v_0\sim10^7 \ {\rm
cm}/{\rm s}$ corresponds to a spin-up (down) time scale $\sim
0.1$~s. Indeed, laboratory experiments on superfluid Helium have
also showed \markcite{T75,A87,TT} (Tsakadze \& Tsakadze 1975;
Alpar 1987; Tsakadze \& Tsakadze 1980) that a pinned superfluid
either spins up {\em along} with its vessel, or it never does so
during the subsequent spinning down of the vessel (for conditions
corresponding to $|\Omega_{\rm sp} -\Omega_{\rm L}| < \omega_{\rm
sp}$).
The case {\bf (b)}, on the other hand, is not in accord with the
general pinning conditions assumed in the vortex creep model, and
is not likely to be invoked in that context. Nevertheless, the
superfluid spin-up in the crust of a neutron star, for such a case
of free unpinned vortices, is again expected to occur over very
short timescales. The longest timescale for the spin-up of the
crust by freely moving vortices, due to nuclear scattering alone,
has been estimated \markcite{EL}(Epstein et~al. 1992) to be only
$\lesssim 5$~s, for the Vela pulsar. It is only natural that the
conclusions of the above two cases are the same, as the pinned
vortices should behave like the free ones, once the critical lag
is exceeded.
Therefore, and in either cases ({\bf a} or {\bf b}), the
superfluid would be spun up within a period of {\em only few
seconds} to (at least) a frequency such that \(\Omega_{\rm
sp}-\Omega_{\rm c}=-\omega_{\rm sp}\), while the observable jump
in $\Omega_{\rm c}$ takes place at the glitch (see Fig.~1b). It is
noted that the steady-state lag $\omega_{\rm sp}$ according to the
vortex creep model, in the so-called non-linear regime, would be
slightly smaller than the critical lag (though slightly larger in
the absence of any creeping). The difference is however a tiny
fraction of the critical lag \markcite{AAP}(Alpar et~al. 1984),
and may therefore be neglected in the present discussion if a
non-linear regime is assumed. In contrast, a ``linear'' regime is
also invoked in the vortex creep model for which $\omega_{\rm sp}
<< \omega_{\rm cr}$. However, the above conclusion remains the
same, even for this case, and a "rapid" superfluid spin-up is
again expected until $|\omega| \lesssim \omega_{\rm sp}$ is
achieved! This is because, according to the creep model the
spin-down (up) rate depends "exponentially" on the difference
$(\omega-\omega_{\rm sp})$; see Eq. 28 in Alpar et~al. (1984).
Hence, a relaxation of the superfluid under the assumed conditions
with $\omega_{\rm cr}> |\omega| > \omega_{\rm sp}$ should again
take place on a time scale much shorter than the observed effect
over $\tau_{\rm sp}$, even for the case of a linear regime.
\section{Superfluid Spin-up}
Moreover, the suggested spin-up scenario of APC should be
dismissed at once since the required torque on the superfluid,
during $\tau_{\rm sp}$, may not be realized at all, under the
assumed conditions of (creeping of the) pinned vortices (see
Fig.~1a). That is the pinned superfluid could not be spun {\em up}
by the crust (ie. its container) while the latter is spinning {\em
down}. This is simply because a spinning down vessel (or even one
with a stationary constant rotation rate) albeit rotating faster
than its contained superfluid could not result in any further {\em
spin up} of the vortex lattice which is, by virtue of the assumed
pinning, already {\em co-rotating} with it! As is well-known, an
inward radial motion of the vortices, associated with a spin-up of
the superfluid, requires the presence of a corresponding forward
azimuthal external force acting on the vortices. This is indeed a
trivial fact, considering that any torque on the bulk superfluid
has to be applied primarily on the vortices. However, no {\em
forward} azimuthal force (via scattering processes between the
constituents particles of the vortex-cores and the crust) may be
exerted by the spinning {\em down} crust on the vortex lattice
which is already co-rotating with it. The azimuthal external force
$F_{\rm ext}$, being the viscous drag of the permeating electron
(and phonon) gas co-rotating with the crust, depends on the
relative azimuthal velocity $v_{\rm rel}$ between the {\it crust}
and the {\it vortices}, as well as the associated
velocity-relaxation timescale $\tau_v$ of the vortices. The
external drag force, per unit length, is given as
\markcite{AS8,JM8}
\begin{eqnarray} n_{\rm v} F_{\rm ext} & = & \rho_{\rm c} {v_{\rm
rel} \over \tau_v },
\end{eqnarray}
where $n_{\rm v}$ is the number density of the vortices per unit
area, and $\rho_{\rm c}$ is the effective density of the
``crust''. Hence, for a spin-up of the superfluid to be achieved,
the crust may impart the corresponding torque on the vortices only
if it (tends to) rotates faster than the vortices, so that $v_{\rm
rel}$ points to the proper forward direction. Accordingly, a
superfluid spin-up requires the crust to be itself spinning up, or
else if the crust is spinning down, the vortices must be already
rotating slower than the crust; a requirement which is against the
pinning condition. It should be trivially clear that the Magnus
force could not be responsible for the required external torque,
as it is an internal force exerted by the superfluid itself.
Therefore, {\em no further superfluid spin-up} might be expected
to occur during the interval $\tau_{\rm sp}$, namely after the
initial fast spinning up of the crust, as well as the superfluid
and its {\em vortices}, has been accomplished during the glitch
rise time (compare Fig.~1a with Fig.~1b).
The suggested long-term (over time $\tau_{\rm sp}$) superfluid
spin-up in APC is a generalization of the vortex creep model to
the case of a {\em negative} lag, in contrast to the usual
applications of the model to spin-downs driven by a positive lag.
However, according to the existing formulation of the vortex creep
model, a spinning up of the superfluid would require a {\it
positive} accelerating torque $N_{\rm em}$ acting on the whole
star (see, eg., Eqs.~28, and 38 in Alpar et~al. 1984). Application
of the same formalism (as is attempted in Eq.~5 of APC) to the
suggested case of an spin-up in presence of the given {\it
negative} $N_{\rm em}$ is not, a priori, justified; it is indeed
contradictory.
The vortex creep model suggests that a radial Magnus force, due to
a superfluid rotational lag, results in a radial bias in the
otherwise randomly directed creeping of the vortices
\markcite{AAP} (Alpar et~al. 1984; see Jahan-Miri 2005 for a
critical discussion of the vortex creep model on this, and other,
grounds). This might be, mistakenly, interpreted to imply that
given a negative lag the inward creeping motion of the vortices,
hence a superfluid spin-up, should necessarily follow,
irrespective of the presence or absence of the needed torque on
the superfluid. As already noted, the role of driving the vortices
inward, ie. spinning up of the superfluid, may not be assigned to
the Magnus force. The Magnus force associated with the rotational
lag is a {\em radial} force and is also an internal force exerted
by the superfluid {\em itself}; both properties disqualifying it
from being the source of a torque on the superfluid. Accordingly,
the point to be emphasized is that the obvious requirement for a
spin-up process, namely the realization of the needed torque, is
indeed missing in the suggested mechanism of APC. Moreover, the
inability of the superfluid to be spun up, in this case, is {\it
not} a direct consequence of the fact that pinned vortices may not
respond freely to an applied external torque. Rather, the vortices
under the assumed conditions do not have any ``tendency'' for an
inward radial motion, in spite of the presence of an inward radial
Magnus force which is balanced by the pinning forces. Thus
creeping motion of the vortices may not be invoked as a
resolution; radial creep should be prohibited accordingly. A
change in the spin frequency of a superfluid involves not only a
radial motion of the vortices but also a corresponding azimuthal
one, as may be also verified from the solution of equation of
motion of vortices during a superfluid rotational relaxation (see
Eq.~9 in Alpar \& Sauls 1988, and Eq.~4 in Jahan-Miri 1998). The
torque may be transmitted only during such an azimuthal motion and
would nevertheless require and initiate a radial motion as well.
Therefore, purely {\it radial} creeping of the vortices, which is
implied by the existing formulation of the vortex creep model, may
not be invoked as a spinning-up mechanism during the transition
from \(\Omega_{\rm sp} - \Omega_{\rm L}= -\omega_{\rm sp}\) to
\(\Omega_{\rm sp} \gtrsim \Omega_{\rm L}\). That is to say, no
radial (creeping) motion of the vortices is permitted, for the
assumed case, because the spinning down crust could not impart any
{\em forward} azimuthal force on the pinned vortices. The
superfluid would rather remain decoupled at a constant value of
$\Omega_{\rm sp}$ (if not spinning down) during this transition
which is achieved due only to the spinning down of the crust, as
depicted in Fig.~1b.
\section{Concluding}
Decoupling of (a part of) the moment of inertia of the crust of a
neutron star at a glitch, from the rest of the co-rotating star,
could readily account for the excess post-glitch spin-down rates
comparable to the fractional moment of inertia of the decoupled
part. The same preliminary fact applies to a (partial) decoupling
of a (pinned) superfluid component in the crust, or elsewhere in
the star, as well. A decoupled component (say, in the crust)
could, in principle, result in an even larger excess spin-down
rate of the star if it is further assumed to be spinning up while
the rest of the star is spinning down; ie. a {\em negative}
coupling instead of a mere decoupling. Nevertheless, here we have
shown that the only suggested mechanism for such a {\em negative}
coupling of a pinned superfluid part in the crust not only fails
quantitatively to account for the observed effect in pulsars, it
is also ruled out conceptually since the required torque on the
superfluid could not be realized at all.
Given the standard picture of the interior of a neutron
star\markcite{S89,P92}(Sauls 1989; Pines \& Alpar 1992), one is
thus left to speculate on the possible role of the stellar core to
induce the observed effect. That is, the observed large spin-down
rates, over timescales of a day and more, should be caused by a
decoupling of (a part of) the stellar core. The large moment of
inertia $I_{\rm core}$ of the core, with \( {I_{\rm core} \over I}
\sim 90~\% \), may easily account for the observations.
Nevertheless, a non-superfluid component in the core would couple
to the crust on very short timescales ($< 10^{-11}$~s)
\markcite{BP9}(Baym et~al. 1969a), and could not have any
footprint left in the observed post-glitch relaxation. Also, a
core-superfluid with free (unpinned) vortices would be again
expected to have very short coupling timescales of the order of
less than one or two minutes \markcite{AS8,P92,JM8}(Alpar \& Sauls
1988; Pines \& Alpar 1992; Jahan-Miri 1998). However, the pinning
of the superfluid vortices to the superconductor fluxoids in the
core of neutron stars, might offer a way out of the dilemma. The
effect has been originally suggested on theoretical grounds
\markcite{MT,S89,JO91b}(Muslimov \& Tsygan 1985; Sauls 1989;
Jones 1991b), while its observable consequences for the rotational
dynamics of a neutron star as well as its magnetic evolution have
been investigated by various authors
\markcite{SB90,JO91b,CCD,JM6,RZC,JM00,JM02}(Srinivasan 1990; Jones
1991b; Chau, Cheng \& Ding 1992; Jahan-Miri 1996; Ruderman, Zhu \&
Chen 1998; Jahan-Miri 2000; 2002).
Very briefly, the peculiar feature of the assumed pinning in the
core, that is the {\em moving} nature of the {\em pinning sites},
has to be highlighted, in this regard. The fluxoids are indeed
predicted to undergo a steady outward radial motion throughout the
active lifetime of a pulsar \markcite{CCD,JM0} (Chau, Cheng \&
Ding 1992; Jahan-Miri 2000). At a glitch, a departure in the lag
from its earlier critical value, causes a (dynamically partial)
decoupling of the core, which may explain the observed initial
large spin-down rates soon after a glitch (that could not be
possibly caused by the crust, as discussed above). Nevertheless
the core superfluid does spin down even before the critical lag
value is restored, simply because the pinning barriers (the
fluxoids), hence the superfluid vortices pinned to them, are
moving radially, at all times. Otherwise, for the core superfluid
to remain completely decoupled (the vortices being stationary) the
superfluid rotation lag should amount to its critical value! since
a crossing-through of the vortices and fluxoids, ie. unpinning
events, would be inevitable. For the core superfluid, a {\em
decoupling} accompanies and implies {\em unpinning!}, contrary to
the usual case of stationary pinning sites, as for the crust.
Hence, during a post-glitch recovery phase (while the lag is still
far from its critical value) the vortices move out along with the
fluxoids, keeping the superfluid in a spinning down state, albeit
at a slower rate than before the glitch. A quantitative modelling
of the effects of a pinned superfluid component in the core on the
post-glitch response, as well as its role in a (free) precession
of the star, remains to be further studied in details.
This work was supported by a grant from the Research Committee of
Shiraz University.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,417 |
{"url":"https:\/\/verso.mat.uam.es\/web\/index.php\/es\/agenda\/icalrepeat.detail\/2020\/03\/03\/3755\/-\/seminario-t-grupos-uam-ucm-uc3m-icmat","text":"Anual Mensual Semanal Hoy Buscar Ir al mes espec\u00edfico Enero Febrero Marzo Abril Mayo Junio Julio Agosto Septiembre Octubre Noviembre Diciembre 2019 2020 2021 2022 2023 2024 2025 2026\nSeminario T. Grupos UAM-UCM-UC3M-ICMAT\n\nSeminario T. Grupos UAM-UCM-UC3M-ICMAT\n\n3\/3\/20, 11:15, Aula Gris 2, ICMAT\n\nDiego Martinez (UC3M and ICMAT)\n\nTitle:\u00a0\u00a0\u00a0 Quasidiagonality vs amenability of discrete groups\n\nAbstract:\u00a0\u00a0\u00a0 An operator in a Hilbert space is (informally) said to be quasidiagonal if its' behaviour can be approximated by some of its' corners' behaviour. This notion was introduced by Halmos in the seventies, and has since been used extensively in various areas of mathematics. In this talk we will introduce it and study its' relation to amenability of discrete groups. In particular, we shall prove that if the left regular representation of a group is quasidiagonal then the group itself is amenable. We also show the converse in the case of the integers (using Berg's technique) and, more generally, in the case of residually finite amenable groups. The construction for the general case remains open.\n\nLocalizaci\u00f3n\u00a0 3\/3\/20, 11:15, Aula Gris 2, ICMAT","date":"2021-06-13 20:45:55","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8373443484306335, \"perplexity\": 3371.380417906826}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-25\/segments\/1623487610841.7\/warc\/CC-MAIN-20210613192529-20210613222529-00078.warc.gz\"}"} | null | null |
{"url":"https:\/\/mtex-toolbox.github.io\/EBSDReferenceFrame.html","text":"Reference Frame Alignment edit page\n\nThe most important difference between MTEX and many other EBSD software is that in MTEX the Euler angle reference is always the map reference frame. This mean the $$x$$ and $$z$$ axes of the map are exactly the rotation axes of the Euler angles.\n\nIn case the map coordinates and the Euler angles in your data are with respect to different reference frames it is highly recommended to correct for this while importing the data into MTEX. This section explains in detail how to do this.\n\nOn Sreen Orientation of the EBSD Map\n\nMany people are concerned when the images produced by MTEX are not aligned exactly as they are in their commercial software. It is indeed very important to understand exactly the alignment of your data. However, the important point is not whether a map is upside down on your screen or not. The important point is how your map aligns with the specimen, as we want to use the map to describe properties of the specimen.\n\nThere are basically two components in an EBSD data set that refer to the specimen reference frame: the spatial coordinates $$x$$, $$y$$ and the Euler angles $$\\phi_1$$, $$\\Phi$$, $$\\phi_2$$. To explain the difference have a look at the EDAX export dialog\n\nHere we have the axes $$x$$ and $$y$$ which describe how the map coordinates needs to be interpreted and the axes $$A_1$$, $$A_2$$, $$A_3$$ which describe how the Euler angles, and in consequence, the pole figures needs to be interpreted. We see that in none of these settings the map reference system coincides with the Euler angle reference frame.\n\nThis situation is not specific to EDAX but occurs as well with EBSD data from Oxford or Bruker, all of them using different reference system alignments. For that reason MTEX strongly recommends to transform the data such that both map coordinates and Euler angles refer to the same coordinate system.\n\nDoing this we have two choices:\n\n1. transform everything to the reference system $$x$$, $$y$$ using the option 'convertEuler2SpatialReferenceFrame'. This will keep the map coordinates while changing the Euler angles\n2. transform everything to the reference system $$A_1$$, $$A_2$$, $$A_3$$ using the option 'convertSpatial2EulerReferenceFrame'. This will keep the Euler angles while changing the map coordinates.\n\nIn the case of EDAX data imported from an *.ang file we still need to specify the export option used by the EDAX software. This is done by the options 'setting 1', 'setting 2', 'setting 3' or 'setting 4'.\n\nSince setting 2 is default for most EDAX exports a typical command for importing data from an ang file would look like this\n\nThe plot does not yet fit the alignment of the map in the EDAX software as it plots the x-axis be default to east and the z-axis into the plane. This is only a plotting convention and can be set in MTEX by\n\nOther plotting conventions are plotx2north, plotx2west, plotx2south and plotzOutOfPlane. Note that these options only alter the orientation of the EBSD map and the pole figures on the screen but does not change any data.\n\nVerify the reference system\n\nOne way of verifying the reference systems is to visualize crystal shapes on top of the orientation map. To do this we proceed as follows\n\nIt may also be helpful to inspect pole figures\n\nAs pole figures display data relative to the specimen reference frame MTEX automatically aligns them on the screen exactly as the spatial map above, i.e., according to our last definition with x pointing towards east and y to the south.\n\nChange the map reference system\n\nIn order to manually change the map reference frame one may apply a rotation to the map coordinates only. E.g. to flip the map left to right while preserving the Euler angles one can do\n\nChange the Euler angle reference system\n\nAnalogously we may change the Euler angle reference frame while keeping the map coordinates\n\nChanging both reference system simultaneously\n\nSometimes it is necessary to relate the EBSD data to a different external reference frame, or to change the external reference frame from one to the other, e.g. if one wants to concatenate several ebsd data sets where the mounting was not done in perfect coincidence. In these cases the data has to be rotated or shifted by the commands rotate and shift. The following commands rotate both reference frames of the entire data set by 5 degree about the z-axis.","date":"2023-02-01 13:29:36","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7980356812477112, \"perplexity\": 766.7887495579512}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764499934.48\/warc\/CC-MAIN-20230201112816-20230201142816-00333.warc.gz\"}"} | null | null |
Chitona connexa é uma espécie de insetos coleópteros polífagos pertencente à família Oedemeridae.
A autoridade científica da espécie é Fabricius, tendo sido descrita no ano de 1798.
Trata-se de uma espécie presente no território português.
Referências
Ligações externas
Chitona connexa - Biodiversity Heritage Library - Bibliografia
Chitona connexa - NCBI Taxonomy Database
Chitona connexa - Global Biodiversity Information Facility
Chitona connexa - Encyclopedia of Life
Coleópteros polífagos de Portugal
connexa
Coleópteros descritos em 1798 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,304 |
\section{Introduction}
Due to the advent of large area surveys in the past few years, extensive progress has been made in the search for low-mass active galactic nuclei (AGNs) with estimated black hole masses $\ensuremath{M_\mathrm{BH}} \lesssim10^{6}~\ensuremath{M_{\odot}}$. Through searches for galaxies with low stellar velocity dispersions or weak broad-line emission in the Sloan Digital Sky Survey (SDSS), the number of candidate broad-line type 1 \citep{GH04, GH07c} and narrow-line type 2 \citep{BGH08} low-mass AGNs has increased to number in the hundreds. Multi-wavelength studies (e.g. Gallo \etal\ 2008, Satyapal \etal\ 2008) have begun to provide new avenues for finding these low-mass and low-luminosity AGNs that would not typically be identified in the optical, allowing us to observe a larger portion of the total energy output. X-ray observations are of key importance for detecting the primary ionizing continuum of the AGN and determining the total luminosity as well as constraining the obscuration toward the central engine.
Current unification schemes explain the observational differences between type 1 and type 2 AGNs by the viewing angle from which we observe the central engine. For a type 2 object, an obscuring torus blocks the light coming from the innermost region, which contains the broad emission-line and X-ray-emitting regions. Therefore in the classical AGN unification picture \citep{AM85}, a type 2 object will show the underlying properties of a type 1 object if the effects of the obscuration are removed. Hence, type 1 and 2 objects with comparable black hole masses and luminosities should also show similar optical narrow emission-line spectra, since the narrow-line emitting region remains largely unobscured. By systematically searching for galaxies of both types 1 and 2 with similar stellar velocity dispersions and narrow emission-line luminosities, one can develop comparable samples of type 1 and type 2 objects with similar black hole masses to test if the unified model is applicable across the full range of black hole masses found in AGNs, or if the lack of broad emission lines in low-mass type 2 objects results from changes in the structure of AGNs at low bolometric luminosities \citep{Nicastro00, Laor, ES06} rather than due to absorption.
The two best studied AGNs with $\ensuremath{M_\mathrm{BH}}~<~10^{6}~\ensuremath{M_{\odot}}$ are located in the late-type spiral NGC~4395 \citep{FS89} and in the dwarf elliptical POX~52 \citep{Kunth87, Barth04}, respectively. NGC~4395 has been shown to vary rapidly in the X-ray \citep{Iwasawa00, Shih03, Moran05}, including dramatic changes in spectral slope ($\Gamma~\approx~0.6-1.7$, Moran \etal\ 2005) over a few years. POX~52 shows similar rapid variability, along with substantial changes in the absorbing column density in $< 1$~year \citep{Thornton}. Additionally, \emph{XMM-Newton}\ and \emph{Chandra}\ have been used to investigate the X-ray properties of low-mass type 1 AGN samples \citep{GH07a, Desroches, Mini} showing that they seem to be scaled down versions of their more massive counterparts with similar hardness ratios and photon indices. The X-ray properties of the type 2 counterparts of these AGNs have not previously been studied systematically.
We present \emph{XMM-Newton}\ observations of four galaxies selected from the low-mass Seyfert 2 sample of \citet{BGH08} to have the lowest stellar velocity dispersions in the sample in order to quantify the absorption and emission properties of this population. Our goal is to investigate whether obscuration can explain the lack of broad-line emission in low-mass Seyfert 2 galaxies. From measurements of X-ray luminosities and spectral fitting, we estimate intrinsic absorbing column densities, bolometric luminosities, and corresponding Eddington ratios in order to investigate the differences between type 1 and type 2 objects in this mass range. Throughout this paper we assume $H_{0}~=~70$~\kms~Mpc\ensuremath{^{-1}}, $\Omega_m$ = 0.3, and $\Omega_\Lambda = 0.7$. All estimates of Galactic foreground column densities are calculated based on Galactic \ion{H}{1} maps \citep{DL90, Kalberla05}, using the HEASARC online $N_H$ calculator\footnotemark.
\footnotetext{http://heasarc.gsfc.nasa.gov/cgi-bin/Tools/w3nh/w3nh.pl}
\begin{deluxetable}{lllcc}
\tablecaption{Observation Details}
\tablehead{
\colhead{Galaxy} & \colhead{Obs. ID} & \colhead{Obs. Date} & \colhead{Exp. Time}
& \colhead{Cor. Exp.} \\
\colhead{} & \colhead{} & \colhead{(UT)} & \colhead{(s)} & \colhead{Time (s)}}
\startdata
SDSS J011905.14+003745.0 & 0400570301 & 2006 Jul 26 & 26,739 & 18,040 \\
SDSS J103234.85+650227.9 & 0400570401 & 2006 May 6 & 24,013 & 19,354 \\
SDSS J110912.40+612346.7 & 0400570201 & 2006 Nov 25 & 23,613 & 23,613 \\
SDSS J144012.70+024743.5 & 0400570101 & 2006 Aug 8 & 22,915 & 17,120 \\
\enddata
\tablecomments{Cor. Exp. Time is the exposure time of each observation, corrected for the time lost due to background flares.}
\label{obsDate}
\end{deluxetable}
\section{Sample Selection}
Barth \etal\ (2008, hereafter BGH08) searched SDSS for nearby low-mass active galaxies with absolute magnitudes fainter than $M_g = -20$ mag and emission-line ratios consistent with a Seyfert 2 classification \citep{Ho, Kauffmann, Kewley}. They obtained stellar velocity dispersions from high-resolution Keck spectra and found $39 < \ensuremath{\sigma_{*}} < 95$ \kms\ for the sample of 29 galaxies. These type 2 galaxies have a similar range of [\ion{O}{3}] line luminosities and stellar velocity dispersions as the sample of type 1 objects found by \citet{GH04, GH07c}. We selected the four objects from the BGH08 sample with the lowest stellar velocity dispersions and therefore the lowest estimated black hole masses for X-ray observations.
{\it SDSS J011905.14+003745.0} ($z~=~0.0327$): This galaxy has the smallest measured stellar velocity dispersion, $\ensuremath{\sigma_{*}}~=~39~\pm~8$, in the BGH08 sample. Optical spectropolarimetry data obtained by BGH08 found no polarized emission lines or a polarized continuum.
{\it SDSS J103234.85+650227.9} ($z~=~0.0056$): Also known as NGC~3259, which is designated as a Hubble type SBbc. This is the nearest galaxy in the BGH08 sample. High-resolution Keck spectra confirm the presence of weak broad H\ensuremath{\alpha}\ emission. Soft X-ray emission from this object has been previously detected by \emph{ROSAT}\ \citep{Boller92, Moran96}. \citet{Seth} also note it as an example of a galaxy with both an AGN and a nuclear star cluster. BGH08 did not list a stellar mass for this galaxy, so using the prescription of \citet{Bell03} and the SDSS catalogue Petrosian magnitudes ($u = 14.94, r = 12.88$ and $z=12.49$), we estimate a stellar mass of $\mathrm{log}\ (M_\star/\ensuremath{M_{\odot}}) \approx 9.87$.
{\it SDSS J110912.40+612346.7} ($z~=~0.0067$): Also known as UCG~06192 or MCG +10-16-069. BGH08 identified this object as a nearly identical type 2 version of the nearby narrow-line Seyfert 1 (NLS1) NGC~4395. Both objects have late-type spiral host galaxies and high-excitation optical spectra with narrow-line ratios consistent with low metallicities, with the exception that SDSS~J110912\ shows no evidence for broad-line emission. It also has the lowest stellar mass of any Seyfert 2 galaxy in the \citet{Kauffmann} SDSS AGN catalog, with log\ $(M_{*}/\ensuremath{M_{\odot}})=8.07$ and a host galaxy luminosity of $M_g = -16.8$ mag. However, if we estimate the stellar mass using the prescription of \citet{Bell03} as above, and the SDSS catalogue Petrosian magnitudes ($u = 16.66, r = 15.21$ and $z=15.59$), we find $\mathrm{log}\ (M_\star/\ensuremath{M_{\odot}}) \approx 8.69$. BGH08 were unable to measure \ensuremath{\sigma_{*}}\ for this galaxy, but they demonstrate that the well-established correlation between \ensuremath{\sigma_{*}}\ and [\ion{O}{3}] linewidth for Seyfert 2 galaxies \citep{NW96} holds for galaxies with stellar velocity dispersions as low as $\ensuremath{\sigma_{*}} \sim 40-80$ \kms. From the measured $\mathrm{FWHM}$([\ion{O}{3}])\ $= 66 \pm 1$ \kms, this correlation suggests a stellar velocity dispersion of $\ensuremath{\sigma_{*}} \sim \mathrm{FWHM}$([\ion{O}{3}])$/2.35 = 28$ \kms. BGH08 also obtained spectropolarimetry data for this object, finding a significant polarized continuum component, but no polarized emission-lines from a hidden broad-line region. In the same observation, the blue spectrum shows [\ion{Ne}{5}] $\lambda3426$ emission, giving additional evidence for AGN activity.
{\it SDSS J144012.70+024743.5} ($z~=~0.0297$): Also known as Tol 1437+030. This galaxy was also previously detected by the \emph{ROSAT}\ All-Sky Survey and a high-resolution Keck spectrum shows evidence for possible, but very weak broad H\ensuremath{\alpha}\ emission (BGH08). Its spectrum is also very similar to those of NGC~4395 and POX~52, with similar narrow-line ratios and detected high-ionization lines, but much weaker broad H\ensuremath{\alpha}\ emission. We again use the prescription of \citet{Bell03} and the SDSS catalogue Petrosian magnitudes ($u = 18.02, r = 16.40$ and $z=15.91$) to estimate a stellar mass of $\mathrm{log}\ (M_\star/\ensuremath{M_{\odot}}) \approx 9.85$ for this object. We note that the AGN light is relatively bright in this object and therefore our stellar mass estimate should reflect an upper limit to the actual stellar mass of the galaxy.
\section{Observations and Data Reduction}
Each object was observed using the EPIC instrument on \emph{XMM-Newton}\ for $\sim 25$ ks. Due to the low signal-to-noise (S/N) of our observations, we focus our attention on the data taken with the EPIC-pn instrument, which has a higher quantum efficiency than the EPIC-MOS instruments. Observation dates and actual exposure times (with soft proton flares excluded) for each object can be found in Table \ref{obsDate}. At most, $32.5\%$ of the exposure time was lost due to soft proton flaring in SDSS~J011905, $25.3\%$ was lost in SDSS~J144012, $19.4\%$ was lost in SDSS~J103234, and no time was lost in SDSS~J110912. All data were reduced using the Science Analysis System (SAS, version 7.1.0) and XSPEC (version 12.4.0aa) following the guidelines of the SAS Cookbook and SAS ABC-Guide. Each object was extracted in a circular region with a radius of $30\arcsec$. Due to the proximity of all four objects to the edge of their respective chips, background regions free of sources were used with radii of $45\arcsec$, located on the same chip an average of $107\arcsec$ away from the source. Only events corresponding to patterns $0-4$ (single or double pixel events) were used for the pn event files of objects SDSS~J103234\ and SDSS~J144012. The event files for the other two objects, SDSS~J011905\ and SDSS~J110912, were limited to events corresponding to patterns $0-12$ (single, double, triple and quadruple pixel events) in order to maximize the S/N. In addition to pattern filtering, events were excluded that occurred next to the edges of the CCD or next to bad pixels, and all event files were restricted to an energy range of $0.3-10.0$ keV. The source count rates for all objects were low enough to neglect the effects due to pile-up.
\section{Results}
No counts above background are detected within the extraction region of SDSS~J011905. Assuming Possion statistics we estimate a 3$\sigma$ upper limit of $<~6.6$ counts from the background in the source extraction region, using the method of \citet{Gehrels}. The other three objects are each detected with a $>~3\sigma$ significance in the $0.5-10$ keV energy range, with the net counts in the range of $27-163$ for each detected object.
\begin{figure}
\epsscale{1.0}
\plotone{f1.eps}
\caption{Fraction of encircled energy as a function of radius. The solid line shows the encircled energy curve for the \emph{XMM-Newton}\ PSF. The data points are normalized such that 87\% of the total energy is encircled at a radius of $R = 30\arcsec$.}
\label{encirc}
\end{figure}
\subsection{Radial Profiles}
We use the SAS task {\it calview} to determine the EPIC-pn point spread function (PSF) at the time and CCD chip location of each of the three detected objects. For each object, we plot the encircled energy curve for the \emph{XMM-Newton}\ PSF along with the fraction of encircled energy as a function of radius (Figure \ref{encirc}). The radius that encircles $50\%$ of the flux from a point source is $\sim 10\arcsec$, which translates to a physical diameter of $\sim 3$ kpc for SDSS~J103234\ and SDSS~J110912, and $\sim 12$ kpc for SDSS~J144012. This covers a considerable portion of the disk of SDSS~J103234, more than half of the disk of SDSS~J110912, and the entirety of SDSS~J144012. We see no evidence for extended emission outside of the physical extent of the PSF, except in object SDSS~J110912\ where we see a strong mismatch between the fractional encircled energy of the object and what is expected from a point source. The slope of the data is much steeper than that expected from the PSF, suggesting that we see only extended emission and not a PSF-dominated source. This may be due to high obscuration of the central engine and a few X-ray binaries within the source region contaminating our detection of the central engine.
\begin{deluxetable}{lccccccccc}
\rotate
\tabletypesize{\footnotesize}
\tablewidth{9.5in}
\tablecaption{X-ray Parameters}
\tablehead{
\colhead{Galaxy} & \colhead{X-ray} & \colhead{Net} & \colhead{Count Rate ($s^{-1}$)}
& \colhead{$C_S~(s^{-1}$)} & \colhead{$C_H~(s^{-1}$)} & \colhead{HR}
& \colhead{$\Gamma_\mathrm{HR}$} &\colhead{Flux ($\mathrm{erg~cm^{-2}~s^{-1}}$)}
& \colhead{$L_\mathrm{X}~(\mathrm{erg~s^{-1}})$} \\
\colhead{} & \colhead{offset (\arcsec)} & \colhead{Counts} & \colhead{} & \colhead{} & \colhead{} & \colhead{} & \colhead{} & \colhead{} & \colhead{}
}
\startdata
SDSS J011905 & \nodata & $<$ 6.6 & $<$ 0.0004 & \nodata & \nodata & \nodata & \nodata & $< 5.9 \times 10 ^{-15}$ & $< 1.3 \times 10 ^{40}$ \\
SDSS J103234 & 2.28 & 140.8 & $0.0065 \pm 0.0008$ & $0.0032 \pm 0.0005$ & $0.0033 \pm 0.0005$ & $\phn0.01 \pm 0.06$ & $1.1 \pm 0.1$ & $(3.4 \pm 0.7) \times 10^{-14}$ & $(2.5 \pm 0.5) \times 10^{39}$ \\
SDSS J110912 & 1.83 & \phn26.7 & $0.0012 \pm 0.0006$ & $0.0007 \pm 0.0004$ & $0.0005 \pm 0.0005$ & $-0.13 \pm 0.16$ & $1.4 \pm 0.2$ & $(4.7 \pm 2.6) \times 10^{-15}$ & $(4.6 \pm 2.5) \times 10^{38}$ \\
SDSS J144012 & 0.64 & 163.2 & $0.0082 \pm 0.0009$ & $0.0059 \pm 0.0007$ & $0.0023 \pm 0.0006$ & $-0.43 \pm 0.05$ & $1.8 \pm 0.1$ & $(1.7 \pm 0.4) \times 10^{-14}$ & $(3.4 \pm 0.9) \times 10^{40}$ \\
\enddata
\tablecomments{X-ray offset is the positional difference between the optical and X-ray positions. Total counts is the number of counts in the $0.5-10.0$ keV energy range, $C_S$ is the count rate from $0.5-2.0$ keV and $C_H$ is the count rate from $2.0-10.0$ keV. Flux and $L_{X}$ are based on the $2-10$ keV energy range and are inferred from a power law with photon index $\Gamma_{\rm HR}$ and Galactic absorption.}
\label{counts}
\end{deluxetable}
\subsection{Hardness Ratios}
Separating the events by energy, we investigate the hard ($C_H,~2.0-10.0$ keV) and soft ($C_S,~0.5-2.0$ keV) count rates using the
hardness ratio (HR $= [C_H - C_S]/[C_H + C_S]$). SDSS~J144012\ showed the softest spectrum in the
sample, with HR $= -0.43 \pm 0.05$. The other two objects, SDSS~J103234\ and SDSS~J110912, each had similar hard and soft count rates, resulting in HR $= 0.01 \pm 0.06$ and HR $= -0.13 \pm 0.16$, respectively.
We use the \emph{XMM-Newton}\ response matrices, auxiliary response file (ARF) and redistribution matrix file
(RMF), to create model spectra in order to calculate a photon index ($\Gamma_{\rm HR}$) from the
HR following the method of \citet{Gall05}. These models assume the neutral absorber is set to
the Galactic value in the direction of the object and the AGN is described by a simple power law. We caution that the intrinsic slope of the power-law continuum may not be well described by this simplistic model if the spectrum contains more complex components, such as a high level of absorption or a soft excess due to a thermal component. We include this analysis as a simple indicator of spectral slope, particularly for those objects where detailed spectral modeling is not feasible due to low S/N. SDSS~J144012\ has a photon index ($\Gamma_{\rm HR} = 1.8 \pm 0.1$) that is similar to many
Seyfert 1 galaxies, including POX 52, which had $\Gamma_{\rm HR} = 1.7$ when observed in an unobscured state with \emph{Chandra}\ \citep{Thornton}. X-ray surveys of unobscured AGNs have found average power-law slopes of $\Gamma =1.9$ \citep{Nandra97, Nandra05}. SDSS~J103234\ shows a much harder
photon index ($\Gamma_{\rm HR} = 1.1 \pm 0.1$), similar to that seen in NGC~4395
\citep{Moran05}, and SDSS~J110912\ has a photon index of $\Gamma_{\rm HR} = 1.4 \pm 0.2$.
All count rates, HR, and $\Gamma_{\rm HR}$ can be found in Table \ref{counts}.
\subsection{Flux Estimates}
We estimate the $2-10$ keV flux from the same model spectra used to derive the photon indices from the HR. Again, these model spectra assume a neutral absorber set to the Galactic value and a power law with a slope derived as above and do not account for any additional components present in the spectra. The X-ray luminosities (\ensuremath{L_{\mathrm{X}}}) are derived from these fluxes accounting for the distance of the object and Galactic absorption corrections are negligible. These flux estimates are consistent with those derived using the energy conversion factors calibrated by \citet{Hasinger} and found in the {\it XMM-Newton User's Handbook}. Individual flux and \ensuremath{L_{\mathrm{X}}}\ estimates can be seen in Table \ref{counts}.
\begin{figure}
\epsscale{1.0}
\plotone{f2.eps}
\caption{Light curves of SDSS~J103234\ ({\it top panel}) and SDSS~J144012\ ({\it bottom panel}) binned by
500 s each.}
\label{LightCurve}
\end{figure}
\subsection{Light Curves}
The two brightest objects in the sample, SDSS~J103234\ and SDSS~J144012, have high enough count rates to search
for temporal variations. Using 500 s time bins, we create light curves
(Figure \ref{LightCurve}) for these two objects, excluding any background flares present during
the observations. We attempt to quantify any variability in these sources using the normalized
excess variance ($\sigma^{2}$) of \citet{Nandra}:
\begin{equation}
\sigma^2_\mathrm{nxs} = \frac{1}{N \mu^2} \sum_{i=1}^{N} [(X_i - \mu)^2 - \sigma_i^2],
\label{excessvariance}
\end{equation}
where $X_i$ denotes the count rate of the $i$-th point in the light curve, $\sigma_i$ is its
uncertainty, $\mu$ is the mean of the $X_i$ values over the entire light curve, and $N$ is the
number of points in the light curve. The excess variance using 500 s time bins for SDSS~J103234\ and SDSS~J144012\ is $\sigma_{nxs}^{2}~=~-0.09~\pm~0.76$ and $\sigma_{nxs}^{2}~=~-0.56~\pm~1.2$, respectively. In order to increase the S/N in each data point, we enlarge the time bins to 1000 s and calculate an excess variance of
$\sigma_{nxs}^{2}~=~1.3~\pm~13$ and $\sigma_{nxs}^{2}~=~0.08~\pm~1.5$ for SDSS~J103234\ and SDSS~J144012,
respectively. In each case, $\sigma_{nxs}^{2}$ is consistent with zero, meaning that there is no evidence for intrinsic source variability.
Previous \emph{ROSAT}\ detections of SDSS~J103234\ and SDSS~J144012\ as part of the \emph{ROSAT}\ All Sky Survey suggest a decrease in flux over a $\sim 10$ year time period. Assuming a photon index in the range of $\Gamma = 1-2$ and no absorption or thermal components, the estimated luminosity in the $0.1-2.4$ keV band from \emph{ROSAT}\ is $L_{X} = (0.6 - 2.8) \times 10^{40}$ erg~s\ensuremath{^{-1}}\ and $L_{X} = (1.8 - 8.7) \times 10^{41}$ erg~s\ensuremath{^{-1}}\ for SDSS~J103234\ and SDSS~J144012, respectively. \emph{XMM-Newton}\ images of SDSS~J103234\ and SDSS~J144012\ show no other objects with similar or larger fluxes within the large (96\arcsec) PSF of the \emph{ROSAT}\ All Sky Survey, so contamination of the \emph{ROSAT}\ luminosities is unlikely. This is up to an order of magnitude larger than the luminosities derived in this work and could be larger if a substantial amount of absorbing material were present at the time the \emph{ROSAT}\ observations were taken. Variations of this magnitude have been observed before and are typically explained by variations in the absorbing material, especially at such soft energies. The Seyfert 2 galaxy NGC 4388 was observed to have a factor of $\sim 10$ increase in flux due to an order of magnitude decrease in the absorbing column density, typically at $N_{\rm H} \approx\ 3~\times~10^{23}~\mathrm{cm^{-2}}$ \citep{Elvis04}, over the course of a year. Similarly, NGC 4358 has shown order of magnitude variations in the $0.5 - 2$ keV luminosity due to $\sim 25\%$ variations in the absorbing column density over a one month time period \citep{Fruscione05}. This object has also seen factors of $2-3$ variations in absorbed flux due to continuum variability and not changes in the obscuring material. Therefore, it is reasonable to expect that the change in flux for both SDSS~J103234\ and SDSS~J144012\ are due to either continuum or absorbing column density variability or a combination of both.
\subsection{Spectral Fitting}
SDSS~J103234\ and SDSS~J144012\ are the only objects in the sample with high enough S/N for spectral
fitting, albeit over a limited range of energy. In both objects, the source spectrum becomes indistinguishable from that of the background at the high-energy end, due to low source counts. We choose to minimize the Cash $C$ statistic \citep{Cash79} in order to optimize the spectral fits instead of the often used $\chi^{2}$ statistic because it does not require a minimum number of counts per bin and the results are independent of the bin size used (for further discussion, see Cash 1979). Therefore, the $C$ statistic is more reliable than the $\chi^{2}$ statistic when fitting low S/N spectra.
\begin{figure}
\begin{center}
\epsscale{1.1}
\plotone{f4.eps}
\end{center}
\caption{The spectrum of SDSS~J103234\ from $0.3-5.0$ keV modeled ({\it black line}) with ({\it a})
an absorbed power law with absorption set at the Galactic value, ({\it b}) an absorbed (Galactic
value) power law (photon index set to $\Gamma = 1.1$) with a thermal disk blackbody, and
({\it c}) an absorbed (Galactic value) power law ($\Gamma = 1.1$) with a thermal disk blackbody
and a partial covering absorption component. Residuals are calculated as
Residual = (Data - Model)/Model.}
\label{1032spec}
\end{figure}
\subsubsection{SDSS~J103234}
Due to low S/N, SDSS~J103234\ could only be fit over the $0.3-5.0$ keV energy range and therefore the data were rebinned to 15 channels per bin at energies $< 1.0$ keV and 80 channels per bin for energies $> 1.0$ keV in order to increase the S/N in each bin. At energies above $\sim 5$ keV, the number of source counts in a given bin were comparable to the background level and therefore, no useful spectral information could be extracted. Because of the degeneracies involved in fitting such a small spectral region with multiple components, we first fit a simple absorbed power law. We first allowed the absorbing column density to vary freely, but this produced an absorbing column density of zero. Therefore, we fixed the absorbing column density to the minimum value possible, the Galactic value of $N_{\rm H} = 1.18 \times 10^{20}~\mathrm{cm ^{-2}}$ for all following model fits. The best fit ($C = 54.32$ using 18 PHA bins and 16 dof) was a $\Gamma = 1.6 \pm 0.5$ power law that shows strong, systematic residuals at the soft and hard-energy ends of the spectrum (see Figure \ref{1032spec}). X-ray studies of low-mass type 1 Seyfert galaxies often show a soft excess, presumably due to a thermal component, with similar temperatures and strengths to those seen in narrow-line Seyfert 1 galaxies \citep{GH07a, Thornton, Mini, Desroches}. Modifying the model to include a thermal disk blackbody and allowing all parameters to vary freely (except for the column density for reasons discussed above) resulted in an unrealistic photon index of $\Gamma = -0.7^{+0.7}_{-1.0}$. Using the same absorbed power law with a thermal blackbody model, we tested setting the power-law slope to $\Gamma = 1.0$, increasing this slope by $0.5$ increments in subsequent model fits until $\Gamma = 3.0$, while allowing the blackbody temperature to vary freely. This allowed us to test more complex models over our limited energy range, while still keeping the number of free parameters to a minimum. Using this technique, we found the model fit with the photon index set at $\Gamma = 1.0$ produced the best result and therefore, we fix the photon index to $\Gamma = 1.1$, the value derived from the HR, for all further model fits. Fixing the photon index to this value in the absorbed power law and thermal blackbody model improves slightly ($C = 37.63$ using 18 PHA bins and 15 dof) with a blackbody temperature of $kT = 0.14 \pm 0.05$ keV, but still slightly underpredicts the spectrum at energies of $>~2.0$ keV.
Finally, we note that this spectrum flattens out at energies $> 1.0$ keV, similar to the flattening seen at energies between $1-5$ keV in the \emph{XMM-Newton}\ spectrum of POX~52 when it was observed to be in a partially-covered state \citep{Thornton}. With this in mind, we add a partial-covering component to our model and keeping the Galactic absorber fixed, we again test the incremental photon index values, finding similar results as before. We therefore fixed the photon index to value derived from the HR, $\Gamma = 1.1$ and find the best fit ($C~=~17.93$ using 18 PHA bins and 13 dof) from this model includes a $kT~=~0.20$ keV blackbody and an additional absorbing column density of $N_{\rm H}~=~4.3~\times~10^{22}~\mathrm{cm ^{-2}}$ covering $95\%$ of the X-ray-emitting region. This model is more complex than the previous models tested, but better fits the flattened region between energies $1-5$ keV. If this model accurately describes the observed emission, we would expect to see the spectrum of SDSS~J103234\ decrease at energies $> 5$ keV and follow the shape of the power-law component. Additional observations with a higher S/N are needed to confirm this prediction, but based on the data currently available, we select the partially-covered absorbed power law as our best-fit model. We also note that we modeled the spectrum using multiple background regions surrounding the source and saw no significant changes that might affect our conclusions as to the best-fit model.
\begin{figure}
\begin{center}
\epsscale{1.1}
\plotone{f3.eps}
\end{center}
\caption{The spectrum of SDSS~J144012\ from $0.3-1.0$ keV modeled ({\it black line}) with
({\it a}) an absorbed (set at the Galactic value) power law, and ({\it b}) an absorbed (Galactic
value) power law with a Raymond-Smith plasma. Residuals are calculated as
Residual = (Data - Model)/Model.}
\label{1440spec}
\end{figure}
\subsubsection{SDSS~J144012}
The spectrum of SDSS~J144012\ extends from $0.3-1.0$ keV, above which the S/N is too low for spectral fitting, and was rebinned to 10 channels per bin. We start with a simple absorbed power-law model with the absorption fixed to the Galactic value ($N_{\rm H}~=~2.90~\times~10^{20}~\mathrm{cm^{-2}}$), with the understanding that the best-fit power law may not accurately describe the intrinsic underlying continuum over the full $0.5-10.0$ keV range. The left panel of Figure \ref{1440spec} shows the spectrum of SDSS~J144012\ over-plotted with the best-fit $\Gamma~=~2.7~\pm~0.5$ power law ($C~=~26.60$ using 13 PHA bins and 11 degrees of freedom, dof). This power law is steeper than what is commonly seen in Seyfert 1 galaxies \citep{Nandra97} and does not fit energies below $0.6$ keV well. We also tested allowing the column density to vary freely, but this did not improve the fit quality and so we choose the Galactic value for simplicity. Therefore, the simple absorbed power law is a poor model for describing the X-ray spectrum of this source.
In order to better fit the soft-energy end of the spectrum, we added a thermal component to the absorbed power law. We first added a blackbody component to the absorbed power law, allowing the thermal temperature of the blackbody and the photon index of the power law to vary freely, while holding the column density fixed to the Galactic value, for the reasons discussed above. This model was unable to fit the peak in the spectrum, seen at $E \sim 0.5$ keV, despite the range of parameter values tested, resulting in typical Cash statistics of $C > 23$.
Next, we tested replacing the blackbody component with a hot, diffuse plasma model, using either the Raymond-Smith plasma \citep{Raymond} or the MEKAL plasma \citep{Mewe85, Mewe86, Kaastra92, Liedahl92} models. We tested both of these models individually, fixing the redshift parameter to $z=0.0297$ and the abundance parameter to the solar value. We again tested allowing the column density to vary freely, but found the best results were achieved when the absorbing column density was fixed to the Galactic value. All other parameters were allowed to vary freely in each component. Using the Raymond-Smith plasma component produced a best fit ($C~=~18.73$ using 13 PHA bins and 9 dof; Figure \ref{1440spec}) with a power-law photon index of $\Gamma = 1.5^{+0.7}_{-3.0}$ and a plasma temperature of $kT = 0.13^{+0.05}_{-0.02}$ keV. This temperature is within the range of typical values of $kT \sim 0.1 - 0.2$ keV seen in narrow-line Seyfert 1 galaxies and PG quasars \citep{Leighly, Piconcelli}. The model using the MEKAL plasma component resulted in a very similar best fit ($C~=~17.94$ using 13 PHA bins and 8 dof), with a MEKAL plasma temperature of $kT = 0.14$ keV and a corresponding photon index of $\Gamma = 1.0^{+1.4}_{-1.0}$. We note that the photon indices of both of these models are not well constrained with lower bounds of $\Gamma \leq 0$. This is most likely due to the very small energy range over which we are attempting to fit these models. Both model fits are nearly indistinguishable from each other, except that the MEKAL model uses one additional free parameter. Therefore, we select the model containing the Raymond-Smith plasma as our best-fit model for simplicity.
\begin{figure}
\epsscale{1.0}
\plotone{f5.eps}
\caption{Plot of \ensuremath{L_{\oiii}}\ vs ${\rm L_{2-10~keV}}$ with our sample ({\it red asterisks}) along with the objects ({\it black, filled squares}) from \citet{Panessa}, which includes quasars and Seyfert 1 and 2 galaxies, all corrected for X-ray absorption. The open symbols represent NGC~4395 ({\it green circle}; Panessa \etal\ 2006, corrected to the updated distance of 4.3 Mpc; Thim \etal\ 2004), POX~52 ({\it green triangle}; Barth \etal\ 2004, Thornton \etal\ 2008) and low-mass Seyfert 1 objects ({\it blue squares}; Greene \& Ho 2004, Desroches \etal\ 2009).
The solid line represents the least-squares fit derived by \citet{Panessa} and the two dotted lines represent the 1$\sigma$ scatter of the Panessa \etal\ sample about the fit. Unless otherwise displayed, error bars for our sample are smaller than the plot symbol.}
\label{LoiiiLx}
\end{figure}
\begin{deluxetable}{lccccccc}
\rotate
\tabletypesize{\footnotesize}
\tablewidth{8.4in}
\tablecaption{Derived Parameters}
\tablehead{
\colhead{Galaxy} & \colhead{\ensuremath{\sigma_{*}}~(\kms)} & \colhead{\ensuremath{M_\mathrm{BH}}~(\ensuremath{M_{\odot}})} & \colhead{\ensuremath{L_{\mathrm{Edd}}}~$(\mathrm{erg~s^{-1}})$} & \colhead{\ensuremath{L_{\mathrm{bol}}}([OIII])~$(\mathrm{erg~s^{-1}})$} & \colhead{\ensuremath{L_{\mathrm{bol}}}([OIII])/\ensuremath{L_{\mathrm{Edd}}}} & \colhead{\ensuremath{L_{\mathrm{bol}}}(X-ray)~$(\mathrm{erg~s^{-1}})$} & \colhead{\ensuremath{L_{\mathrm{bol}}}(X-ray)/\ensuremath{L_{\mathrm{Edd}}}} }
\startdata
SDSS J011905 & $39 \pm 8$ & $1.1 \times 10^{5}$ & $1.4 \times 10^{43}$ & $5.8 \times 10^{43}$ & \phn4.2 & $< 2.7 \times 10^{41}$ & $< 0.02$ \\
SDSS J103234 & $43 \pm 4$ & $1.6 \times 10^{5}$ & $2.0 \times 10^{43}$ & $9.3 \times 10^{41}$ & \phn\phn0.05 & \phn\phn$5.0 \times 10^{40}$ & \phn\phn\phn0.003 \\
SDSS J110912 & \phn$28 \pm 1$\footnotemark & $5.0 \times 10^{4}$ & $6.3 \times 10^{42}$ & $1.1 \times 10^{42}$ & \phn0.2 & \phn\phn$9.2 \times 10^{39}$ & \phn\phn\phn0.001 \\
SDSS J144012 & $45 \pm 4$ & $2.0 \times 10^{5}$ & $2.5 \times 10^{43}$ & $3.5 \times 10^{44}$ & 14.1 & \phn\phn$6.8 \times 10^{41}$ & \phn\phn0.03 \\
\enddata
\tablecomments{Stellar velocity dispersion measurements are from BGH08, except for SDSS~J110912,
which is calculated from $\ensuremath{\sigma_{*}}~=~\mathrm{FWHM([OIII])}/2.35$. \ensuremath{L_{\mathrm{bol}}}([OIII]) was estimated from
the [\ion{O}{3}] luminosity using the bolometric correction of $\ensuremath{L_{\mathrm{bol}}}/L_\mathrm{[OIII]}~=~3500$.
\ensuremath{L_{\mathrm{bol}}}(X-ray) was estimated using the bolometric correction $\ensuremath{L_{\mathrm{bol}}}/L_\mathrm{X}~=~\kappa$, where
$\kappa~=~20$ \citep{VF07}.}
\footnotetext{This velocity dispersion was estimated based on the FWHM of the [\ion{O}{3}] line.}
\label{Lboltable}
\end{deluxetable}
\section{Discussion}
\subsection{\ensuremath{L_{\oiii}}-\ensuremath{L_{\mathrm{X}}}\ Correlation}
The relationship between the luminosity of the [\ion{O}{3}] emission line at $5007$ \AA\ (\ensuremath{L_{\oiii}}) and the
$2-10$ keV luminosity has been studied for a range of objects, including type 1 and 2 Seyfert galaxies and quasars, to determine if \ensuremath{L_{\oiii}}/\ensuremath{L_{\mathrm{X}}}\ is similar among all Seyfert galaxies or whether the relationship has any additional dependence on properties such as accretion rate, luminosity, and black hole mass. \citet{Kraemer} investigated the range of X-ray and [\ion{O}{3}] luminosities in both broad-line and narrow-line Seyfert 1 galaxies, finding little difference between the two populations. \citet{Heckman05} followed this study with another, in which they included both Seyfert 1 and 2 galaxies, specifically investigating if this relationship extended to Seyfert 2 galaxies and whether or not \ensuremath{L_{\mathrm{X}}}\ needed to be corrected for absorption. They found that if the \ensuremath{L_{\mathrm{X}}}\ of a Seyfert 2 galaxy was corrected for absorption, the correlation remained intact with minimal scatter added due to the uncertainties involved in the absorption correction. \citet{Panessa} included a wider variety of objects to their sample in order to include a larger luminosity range than previous used, including objects with \ensuremath{L_{\mathrm{X}}} $\sim 10^{37-38}$ erg~s\ensuremath{^{-1}}, and found that the correlation remained approximately the same. An important outcome of this is that the optical [\ion{O}{3}] luminosity can be used as a tracer of the intrinsic X-ray luminosity, and therefore used to estimate the amount of absorption seen in the X-ray. We note that both the \citet{Heckman05} and \citet{Panessa} samples include a selection of radio-loud and radio-quiet AGN, while our four objects are defined as radio-quiet using the standard \citet{Kellermann} definition and the [\ion{O}{3}] luminosity to infer an optical luminosity.
We plot the \ensuremath{L_{\oiii}}\ measurements for our four objects against our estimates of \ensuremath{L_{\mathrm{X}}}\ along with the \ensuremath{L_{\oiii}}-\ensuremath{L_{\mathrm{X}}}\ relation derived by \citet{Panessa} in Figure \ref{LoiiiLx}. All four objects are X-ray weak with respect to the relation, although SDSS~J103234\ is within the $1\sigma$ scatter of the relationship, which is 0.6 dex in \ensuremath{L_{\mathrm{X}}}\ at fixed \ensuremath{L_{\oiii}}. SDSS~J110912\ is $\sim 0.9$ dex below the relation and SDSS~J144012\ and the upper limit of SDSS~J011905\ are both $>2\sigma$ outliers, falling $\sim 2.2$ dex and $1.5$ dex below the relation, respectively.
We use the \ensuremath{L_{\oiii}}-\ensuremath{L_{\mathrm{X}}}\ correlation from \citet{Panessa} and calculate the expected $2 - 10$~keV luminosity from the observed \ensuremath{L_{\oiii}}\ values. The [\ion{O}{3}] luminosities are determined from the SDSS spectra and corrected for Galactic extinction \citep[BGH08]{Kauffmann}. Comparing these values to the \ensuremath{L_{\mathrm{X}}}\ values measured from the \emph{XMM-Newton}\ data, we can attempt to quantify the level of intrinsic absorption within each galaxy. The observed \ensuremath{L_{\mathrm{X}}}\ of SDSS~J103234\ is consistent with the \ensuremath{L_{\mathrm{X}}}\ derived from \ensuremath{L_{\oiii}}, so no additional absorption is needed to reconcile the two \ensuremath{L_{\mathrm{X}}}\ values. SDSS~J110912\ needs an absorbing column density of $N_{\rm H} = 8.8 \times 10^{21}~\mathrm{cm^{-2}}$ in order to bring the observed \ensuremath{L_{\mathrm{X}}}\ to the value suggested by its [\ion{O}{3}] luminosity. Due to the low \ensuremath{L_{\mathrm{X}}}\ of the upper limit of SDSS~J011905, a considerable amount of absorption, $N_{\rm H} > 1.5 \times 10^{22}~\mathrm{cm^{-2}}$, is needed to bring the observed and predicted \ensuremath{L_{\mathrm{X}}}\ values into agreement. However, without a proper detection of SDSS~J011905, the magnitude of the intrinsic absorbing column density will remain unknown. SDSS~J144012\ also falls below the \ensuremath{L_{\oiii}}-\ensuremath{L_{\mathrm{X}}}\ relation, suggesting that there is a considerable amount of absorption in this object. Using our measured \ensuremath{L_{\mathrm{X}}}, we estimate the absorbing column density needed to account for its displacement from the \ensuremath{L_{\oiii}}-\ensuremath{L_{\mathrm{X}}}\ correlation to be $N_{\rm H} = 2.3 \times 10^{22}~\mathrm{cm^{-2}}$.
It is unclear whether an absorbing column density of $N_{\rm H} \sim 10^{22}~\mathrm{cm^{-2}}$ is large enough to completely obscure all of the broad-line emission from a source, or even how the X-ray absorbing column and optical extinction are related. X-ray and optical surveys of AGN find $10-20\%$ of objects show the properties of one AGN type in the optical and another in X-ray, {\it e.g.} a narrow-line AGN with no absorption in the X-ray \citep{Perola, Silverman, Tozzi}. Among well-studied bright Seyfert galaxies, there are examples of objects with substantial broad-line emission in the optical, but with moderate levels of absorption observed in the X-ray. NGC 3227 is one of these objects with obvious broad-line emission and an X-ray absorbing column density of $N_{\rm H} \approx 6.5 \times 10^{22}~\mathrm{cm^{-2}}$ (Gondoin \etal\ 2003, see Piconcelli \etal\ 2006 and Jim{\'e}nez-Bail{\'o}n \etal\ 2008 for further examples). NGC 3227 and galaxies with similar optical line ratios are typically classified as intermediate Seyferts, due to the relative flux of the broad and narrow components of the permitted lines. The difference in appearance between intermediate Seyferts and more typical Seyfert 1 galaxies is often attributed to some amount of obscuration. Whether the level of X-ray absorption seen in galaxies like NGC 3227 is related to the amount of optical extinction in other objects, such as those in our sample, remains uncertain.
If we compare our measurements with other \ensuremath{L_{\oiii}}-\ensuremath{L_{\mathrm{X}}}\ correlations, we find that the results can change substantially. For example, using the relationships derived by \citet{Heckman05} or \citet{Netzer}, we find that the expected X-ray luminosity calculated from the observed \ensuremath{L_{\oiii}}\ values are an order of magnitude lower than if the \citet{Panessa} relationship is used, which would suggest little to no absorption is present in any of our objects. However, both the \citet{Heckman05} and \citet{Netzer} samples contain objects more luminous than \ensuremath{L_{\mathrm{X}}} $\sim 10^{41}$ erg~s\ensuremath{^{-1}}, up to 1-3 orders of magnitude larger than observed in our objects. \citet{Netzer} also found a luminosity dependance in the \ensuremath{L_{\oiii}}/\ensuremath{L_{\mathrm{X}}}\ ratio, which would explain different results for samples with substantially different ranges in luminosity. The \cite{Panessa} sample includes objects with the same range of X-ray and [\ion{O}{3}] luminosities as our sample, making it the more appropriate sample for comparisons.
\subsection{X-ray Binary Contamination}
X-ray observations of low-mass AGNs, including NGC~4395 \citep{Moran05}, POX 52 \citep{Thornton} and SDSS-selected objects \citep{GH07a, Desroches, Mini}, show that the type 1 population is predominantly low-luminosity, with typical luminosities of $\ensuremath{L_{\mathrm{X}}}\ \approx 8 \times\ 10^{39} - 10^{43}$ erg~s\ensuremath{^{-1}}. The X-ray luminosity is much lower for the population of type 2 AGNs in this sample ($\ensuremath{L_{\mathrm{X}}}\ \approx 5 \times\ 10^{38} - 4 \times\ 10^{40}$ erg~s\ensuremath{^{-1}}) and is close to the collective luminosity one would expect from a population of X-ray binaries in a host galaxy. This possible contamination is amplified by the fact that the \emph{XMM-Newton}\ PSF covers a large fraction of each galaxy in our sample. We now consider how much of the observed X-ray flux might arise from non-nuclear sources in each of our host galaxies.
\citet{Gilfanov04} examined the relationship between the X-ray luminosity and stellar mass of old populations, and found a typical ratio of $\ensuremath{L_{\mathrm{X}}}/M_\star\ = 8.3 \times\ 10^{28}$ erg~s\ensuremath{^{-1}}\ensuremath{M_{\odot}}\ensuremath{^{-1}}. Given the stellar mass range of our sample, $\mathrm{log}\ (M_\star/\ensuremath{M_{\odot}}) = 8 - 10$, it is unlikely that the observed X-ray fluxes are significantly contaminated by low-mass X-ray binaries associated with the old stellar population. However, high-mass X-ray binaries associated with recent star formation can result in a higher X-ray luminosity. \citet{Lehmer} examined the relationship between the $0.5-8$ keV X-ray luminosity of late-type, star-forming galaxies and their stellar mass. They found $\ensuremath{L_{\mathrm{X}}}/M_\star\ = 1.6 \times\ 10^{30}$ erg~s\ensuremath{^{-1}}\ensuremath{M_{\odot}}\ensuremath{^{-1}}\ for star-forming galaxies with stellar masses of $\mathrm{log}\ (M_\star/\ensuremath{M_{\odot}}) = 9 - 10$.
Of the objects in our sample, the contamination by X-ray binaries is potentially most significant for SDSS~J110912. It has a late-type morphology and the bluest host galaxy colors in the BGH08 sample (with $g-r \approx 0.3$). Based on the Lehmer \etal\ results and the estimated host galaxy mass described in \S2, the predicated luminosity due to high-mass X-ray binaries is close to (and might even exceed) the observed X-ray luminosity, indicating that a large fraction of the observed X-ray flux might be non-nuclear. Additionally, the observed X-ray flux is more spatially extended than the PSF, as seen in the steep slope of the encircled energy curve for the object (Figure \ref{encirc}). However, without deeper and higher-resolution X-ray data, we cannot clearly determine the relative amounts of nuclear and non-nuclear emission. In the other late-type disk galaxy in our sample, SDSS~J103234, the radial profile of the X-ray emission is more consistent with a point-like source. If the $\ensuremath{L_{\mathrm{X}}}/M_\star$ ratio found by Lehmer \etal\ applies to this galaxy, then X-ray binaries could in principle account for the observed X-ray luminosity. However, the SDSS image shows that most of the recent star formation in this galaxy is located in the spiral arms at distances of $\gtrsim 10\arcsec$ from the nucleus. If the X-ray luminosity of this galaxy was dominated by high-mass X-ray binaries then it would be noticeably extended in the \emph{XMM-Newton}\ image rather than compact, so it appears unlikely that high-mass X-ray binaries make a significant contribution to the observed X-ray flux. For SDSS~J144012, the predicted luminosity due to high-mass X-ray binaries is a factor of 3 smaller than the observed X-ray luminosity. Although we can not rule out the possibility that some observed properties, such as $\Gamma$ and HR, might be affected by the presence of high-mass X-ray binaries, we conclude that the observed X-ray flux is most likely dominated by emission from the AGN.
\subsection{Bolometric Luminosity and Eddington Ratio}
We investigate the accretion power of these objects by deriving estimates of their Eddington ratios,
\ensuremath{L_{\mathrm{bol}}}/\ensuremath{L_{\mathrm{Edd}}}. The \ensuremath{\mbh-\sigma_{*}}\ relation allows us to estimate a black hole mass from the stellar
velocity dispersion (\ensuremath{\sigma_{*}}) of the host galaxy \citep{Gebhardt, FM}. BGH08 used their measurements of \ensuremath{\sigma_{*}}\ along with the \ensuremath{\mbh-\sigma_{*}}\ relation of \citet{Tre02} to estimate a black hole mass for each object, which includes an additional offset in black hole mass seen in other low-mass Seyfert 1 galaxies \citep{Barth05}. This offset probably reflects a flattening of the \ensuremath{\mbh-\sigma_{*}}\ relation at low masses \citep{Wyithe06, GH06}, but without a more detailed study of the \ensuremath{\mbh-\sigma_{*}}\ relation in this mass range, we follow the example of \citet{Barth05} and assume a uniform offset.
A common estimator of bolometric luminosity in the optical is based on the [\ion{O}{3}] $\lambda5007$ line luminosity because it is assumed to be dominated by unobscured AGN emission regardless of AGN type, rather than by emission from star-forming regions. We first estimate the bolometric luminosity from \ensuremath{L_{\oiii}}\ for each object using the bolometric correction of \ensuremath{L_{\mathrm{bol}}}/\ensuremath{L_{\oiii}}~$=~3500$ derived by \citet{Heckman} from a low-redshift sample of Seyfert 1 galaxies and quasars.
We also use a broad-band $2-10$ keV X-ray bolometric correction from \citet{VF07, VF09}. Because a larger wavelength range is used to estimate \ensuremath{L_{\mathrm{bol}}}, X-ray bolometric corrections tend to produce better estimates of the intrinsic \ensuremath{L_{\mathrm{bol}}}\ than corrections based on narrow-band luminosities, assuming the unabsorbed X-ray luminosity is used. The $2-10$ keV energy range also probes the primary continuum emission from the central engine producing a better estimate of the bolometric luminosity of the object. \citet{VF09} find that highly accreting objects tend to require a larger X-ray bolometric correction than those accreting at a lower rate. For \ensuremath{L_{\mathrm{bol}}}/\ensuremath{L_{\mathrm{X}}}~$=~\kappa$, objects with an intrinsic \ensuremath{L_{\mathrm{bol}}}/\ensuremath{L_{\mathrm{Edd}}}~$>~0.2$ should have a bolometric correction of $\kappa~\sim~110$, objects with $0.1 <$\ensuremath{L_{\mathrm{bol}}}/\ensuremath{L_{\mathrm{Edd}}}$< 0.2$ should have $\kappa~\sim~45$, and for those objects with intrinsic \ensuremath{L_{\mathrm{bol}}}/\ensuremath{L_{\mathrm{Edd}}}~$<~0.1$, $\kappa~\sim~20$. We find that with this two-tier bolometric correction, no objects in our sample are accreting at a high enough rate to warrant the higher bolometric correction. Therefore, we apply the X-ray bolometric correction of \ensuremath{L_{\mathrm{bol}}}/\ensuremath{L_{\mathrm{X}}}~$=~20$ to the unabsorbed X-ray luminosities of each of our objects to obtain an estimate of the bolometric luminosity. For each object, estimates of stellar velocity dispersion, black hole mass, Eddington luminosity and bolometric luminosity can be seen in Table \ref{Lboltable}.
The Eddington ratios from \ensuremath{L_{\mathrm{bol}}}(X-ray) and the absorption-corrected X-ray luminosities are systematically lower than those determined from the [\ion{O}{3}] luminosity by a factor of $\sim 30-400$. Underestimating the intrinsic absorption in these objects could explain a small portion of this discrepancy, but it is mostly due to a difference in the bolometric corrections themselves. \citet{Lamastra09} recently evaluated the \ensuremath{L_{\oiii}}\ bolometric correction of \citet{Heckman}, finding that even low levels of extinction in the narrow-line region cause bolometric luminosities to be systematically over-estimated. By correcting \ensuremath{L_{\oiii}}\ for this extinction and including a dependance on luminosity, they find the \ensuremath{L_{\oiii}}\ bolometric corrections to be over an order of magnitude lower than in \citet{Heckman}. The resulting bolometric luminosities more closely resemble the bolometric luminosities derived using X-ray bolometric corrections. This luminosity-dependent [\ion{O}{3}] bolometric correction may resolve the discrepency observed between our bolometric luminosities derived from \ensuremath{L_{\oiii}}\ and \ensuremath{L_{\mathrm{X}}}. Regardless of the bolometric correction used, SDSS~J144012\ has the highest Eddington ratio in the sample with \ensuremath{L_{\mathrm{bol}}}(X-ray)/\ensuremath{L_{\mathrm{Edd}}}$~\approx~0.03$. A careful look of the spectral energy distributions of these objects using recently observed \emph{Spitzer}\ IRS spectra along with existing multi-wavelength data should better determine the bolometric luminosities of these sources.
\subsection{SDSS~J110912}
SDSS~J110912\ is an object of particular interest, not only for the strong similarity between it and NGC 4395, but also because it has the lowest detected X-ray luminosity in the sample. The radial profile of SDSS~J110912\ shows possible evidence for extended emission and the X-ray luminosity of $\ensuremath{L_{\mathrm{X}}}\ \sim 5 \times 10^{38}$ erg~s\ensuremath{^{-1}}\ is so low that it could be contaminated by a collection of X-ray binaries in the host galaxy. On average, low-mass X-ray binaries have photon indices in the range of $\Gamma \approx 1.5-1.8$ (e.g. Matsumoto 1997; Irwin \etal\ 2003) and high-mass X-ray binaries have $\Gamma \approx 1-2$ (e.g. Sasaki \etal\ 2003), both of which are comparable to the measured spectral slope of SDSS~J110912\ ($\Gamma = 1.4 \pm 0.2$). X-ray variability is usually a better distinguishing parameter between X-ray binaries and AGNs since variability scales with black hole mass \citep{McHardy} and a collection of X-ray binaries would not vary coherently. Unfortunately, our observations contain too few counts to properly investigate the temporal variability of SDSS~J110912\ to attempt to determine the degree of contamination due to the stellar population.
If the X-ray emission detected is related to AGN activity, it is still unclear whether the central engine is obscured or if we are observing a weakly accreting AGN with no broad-line region. The estimated black hole mass for SDSS~J110912\ is very tentative, since BGH08 were unable to measure a stellar velocity dispersion for this galaxy, and the \ensuremath{\mbh-\sigma_{*}}\ relation used to estimate the black hole mass is poorly constrained at these low masses. Given the strong morphological and spectral similarities between NGC 4395 and SDSS~J110912, it is conceivable that they also share comparable black hole masses. Then, the defining difference between these two objects would be the lack of broad-line emission in SDSS~J110912\ (BGH08). If SDSS~J110912\ falls within the normal scatter of the \ensuremath{L_{\oiii}}-\ensuremath{L_{\mathrm{X}}}\ relation and therefore there is little internal absorption, one could speculate that SDSS~J110912\ represents a nearly identical ``true'' type 2 version of NGC~4395 with no broad-line region. There have been a few suggested cases of type 2 objects without a broad-line region (see Ghosh \etal\ 2007, Gliozzi \etal\ 2007, Bianchi \etal\ 2008), but \citet{BN} recently show that many of the candidate ``true'' type 2 objects can also be fit with more complex spectral models, including high amounts of absorption.
Various models attempt to explain how an accreting black hole might fail to form a broad-line region, typically due to a combination of low AGN luminosity and black hole mass (for a review, see Ho 2008). \citet{Laor} suggested that since the radius of the BLR decreases as the luminosity of an AGN decreases, there might exist a luminosity threshold below which the BLR would cease to exist. For a black hole with $\ensuremath{M_\mathrm{BH}} \sim 10^{5}$~\ensuremath{M_{\odot}}, this luminosity would be $L_\mathrm{min} = 6 \times 10^{35}$~erg~s\ensuremath{^{-1}}\ and $L_\mathrm{min} = 6 \times 10^{37}$~erg~s\ensuremath{^{-1}}\ for a $10^{6}$~\ensuremath{M_{\odot}}\ black hole, both of which are $2-6$ orders of magnitude below the bolometric luminosities of NGC 4395 and SDSS~J110912. If SDSS~J110912\ is indeed a "true" type 2 Seyfert, this scenario can not explain the lack of the broad-line region.
Alternatively, if the BLR is formed due to a radiation-driven wind flowing off of the accretion disk, as has been suggested by \citet{MC97}, then at very low luminosities the outflow may decrease to levels unable to sustain the BLR. Nicastro (2000, see also Nicastro \etal\ 2003) has explored a model in which there exists a threshold \ensuremath{L_{\mathrm{bol}}}\ below which the radiation-driven wind is unable to produce the broad-line emission. This suggests that at lower \ensuremath{L_{\mathrm{bol}}}, unobscured AGNs would be "true" type 2 objects. The calculations of \citet{Nicastro00} show that this threshold lies at $\ensuremath{L_{\mathrm{bol}}}/\ensuremath{L_{\mathrm{Edd}}}\ \lesssim 10^{-3}$, below which the objects would be unable to produce the broad-line region.
Using the X-ray results, we can examine where these low-mass AGNs lie relative to the predicted thresholds for BLR formation. We find that SDSS~J103234\ and NGC~4395 both have Eddington ratios close to the hypothetical threshold for BLR formation in the Nicastro model (NGC 4395: $\ensuremath{L_{\mathrm{bol}}}/\ensuremath{L_{\mathrm{Edd}}}\ \approx 10^{-3}$; Peterson \etal\ 2005). However, optical spectra show definite broad-line emission in NGC~4395 and weak broad-line emission in SDSS~J103234\ (BGH08). SDSS~J110912\ has a very uncertain Eddington ratio of $\ensuremath{L_{\mathrm{bol}}}/\ensuremath{L_{\mathrm{Edd}}}\ \approx 0.001$ which lies at the threshold for BLR formation in the Nicastro model. Therefore, there exists the possibility that SDSS~J110912\ accretes at a low enough rate to explain the lack of broad-line emission. However, this seems unlikely given that SDSS~J110912\ and NGC 4395 have such similar narrow emission-line luminosities, and presumably similar ionizing luminosities.
Given that the observed \ensuremath{L_{\mathrm{X}}}\ of SDSS~J110912\ is an order of magnitude lower than that of NGC~4395, but they have nearly identical [\ion{O}{3}] luminosities, we conclude that the most likely explanation is that the central engine of SDSS~J110912\ is obscured, although we are unable to accurately determine the amount of X-ray absorption in SDSS~J110912. If a substantial fraction of the observed \ensuremath{L_{\mathrm{X}}}\ is due to X-ray binaries, then that increases the discrepancy between \ensuremath{L_{\oiii}}\ versus \ensuremath{L_{\mathrm{X}}}\ and strengthens the case for an obscured nucleus. \citet{ES06} present a model in which the radiation-driven wind produces the obscuring material, such that objects with \ensuremath{L_{\mathrm{bol}}}\ $\lesssim 10^{42}$ erg~s\ensuremath{^{-1}}\ would be unable to produce the obscuring torus. If the observed properties of SDSS~J110912\ are indeed the result of obscuration, then this would indicate that the obscuring torus could still persist even at AGN luminosities more than an order of magnitude below the threshold suggested by Elitzur \& Shlosman.
\section{Summary and Conclusions}
We find all four objects in the sample to be X-ray faint with X-ray luminosities approximately an order of magnitude lower than those seen in the \citet{GH04} sample \citep{GH07a}, but only two objects, SDSS~J011905\ and SDSS~J144012\ show evidence of moderate to substantial absorption with estimated column densities of $N_{\rm H} \sim 10^{22}~\mathrm{cm^{-2}}$. SDSS~J103234\ shows little evidence of absorption which is consistent in the context of the unified model with the previous detection of broad emission lines from high-resolution optical spectra. It is unclear without further observations whether SDSS~J110912\ is truly lacking a broad-line region or if it is absorbed and the emission detected is due to a combination of X-ray binaries in the host galaxy and weak emission from the AGN, but given the low observed X-ray luminosity, we believe SDSS~J110912\ contains at least a moderate amount of absorption.
Two objects had high enough S/N ratios for spectral fitting. SDSS~J103234\ has a spectrum similar to the partially absorbed spectrum of POX~52 discussed by \citet{Thornton}, and is well fit with a high partial-covering fraction of 95\%, in the $0.3~-~5.0$ keV range probed. The spectrum of SDSS~J144012\ was well fit over an energy range of $0.3-1.0$ keV with a power law combined with a thermal plasma component and Galactic absorption and there was no clear evidence from the spectral fit for the high absorption predicted from the \ensuremath{L_{\oiii}}-\ensuremath{L_{\mathrm{X}}}\ correlation.
By comparing type 1 and 2 objects with similar masses, we have the opportunity to further investigate the absorbing properties of low-mass AGNs and whether or not line-of-sight absorption can explain the presence or lack of broad emission lines, or if other processes, such as accretion rate, play a role. If high S/N observations are obtained, X-ray spectra are an excellent tool that can be used to quantify the amount of absorption in an object. IR spectroscopy is another important tool used to investigate absorption and reprocessing of the AGN continuum. We plan to investigate both low-mass Seyfert 1 and 2 objects using {\it Spitzer} spectra in order to better constrain the bolometric luminosities of these objects and further investigate the presence of an obscuring torus.
\acknowledgments The analysis of \emph{XMM-Newton}\ data presented herein was supported by grant
NNX06AF08G from NASA. This work was also supported by the National Science Foundation under grant AST-0548198. This research has made use of the NASA/ IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
\newpage
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\section{Introduction}\label{sec:intro}
In the past twenty years, the usage of the Internet has transitioned
from being primarily academic/research-oriented to one that is
primarily commercial in nature. In the current Internet environment,
each commercial entity is inherently interested only in its own
profit. Developing network mechanisms that are designed to handle
selfish behavior has therefore gained increasing attention in recent
years. The game theoretic approach, which was originally designed to
model and guide decisions in economic markets, provides a valuable
set of tools for dealing with selfish behavior
\cite{Srivastava:2005, Ozdaglar:2007, Altman:2006, Saad:2009,
Osborne:2004, MacKenzie:2006}.
In this work, we consider the network congestion problem at a single
intermediate store-and-forwarding spot in the network. Several users
send their packets to a single server with Poisson arrival rate. The
server processes the packets on a first come first serve (FCFS)
basis with an exponentially distributed service time. This is an
M/M/1 queueing model~\cite{Ross:1997}. There exists a trade-off in
this M/M/1 queueing model between throughput (representing the
benefit from service), and delay (representing the waiting cost in
the queue). In the gateway congestion control context
\cite{RFC:1994}, a measure that is widely used to describe this
trade-off is called ``Power", which is defined as the weighted ratio
of the throughput to the delay. When the users are selfish, we can
formulate a basic M/M/1 queueing game. In this game, we assume that
the users are selfish, and each control their own input arrival rate
to the server. Each user's utility is modeled to be the power ratio
for that user's packets.
This classic M/M/1 queueing game has been formulated and studied in
\cite{Kumar:1981,Douligeris:1992,Zhang:1992,Dutta:2003,Yi:2009}. The
results from these prior works and our own results in this work are
in agreement that the basic M/M/1 queuing game has an inefficient
Nash Equilibrium. We are therefore motivated to design an incentive
mechanism to force the users to operate at an equilibrium that is
globally efficient. In particular, we focus on the design of a
packet dropping scheme implemented at the server for this purpose.
Our objective is that the dropping scheme should be as simple as
possible, and it should minimize the Price of Anarchy (PoA, the
ratio of the social optimum welfare to the welfare of the worst Nash
equilibrium) to be as close to 1 as possible.
A key contribution of this work is the formulation of a modified
M/M/1 queuing game with a randomized packet dropping policy at the
server. We consider a simple and low overhead policy in our
formulation, wherein the server need only monitor the sum of the
rates of all users in the system. We show that this modified game
with a packet dropping scheme is an \emph{ordinal potential
game}~\cite{Monderer:1996}, which implies the existence of at least
one pure Nash Equilibrium.
We show first that utilizing a step-function for packet dropping
whereby the server drops all the packets when the sum-rate is
greater than a threshold (and none when the sum-rate is below the
threshold), results in infinite number of undesired Nash Equilibria
which harms the PoA.
This raises the question whether a more sophisticated approach can
do better. We show that indeed this is possible. In particular, we
develop an incentive mechanism with a linear packet dropping that
can improve the system efficiency to be arbitrarily close to the
global optimal point (i.e., a PoA arbitrarily close to 1). This
mechanism is similar to the Random Early Detection (RED) used for
congestion avoidance on the Internet~\cite{FloydJacobson:1993}. We
prove the uniqueness of NE of the game with this mechanism. We also
show that best response dynamics will converge to the unique NE.
Our paper is organized as follows. Section \ref{sec:related}
summarizes the related work. We present the model of an M/M/1 queue
game in Section \ref{sec:prob}. The social welfare and Price of
Anarchy are described in section \ref{sec:anarchy} to investigate
the efficiency of the NE. Then, in section \ref{sec:scheme}, we
propose to design an incentive packet dropping scheme implemented at
the server to improve the efficiency. Section \ref{sec:potential}
proves that the game defined with packet dropping policy is an
ordinal potential game by giving the potential function. Section
\ref{sec:best} shows the best response function. In section
\ref{sec:step}, we show the behavior when utilizing a simple
step-function for packet dropping. In section \ref{sec:linear} we
propose the RED-like linear packet dropping incentive scheme. We
show that with this scheme, it is possible to make the Price of
Anarchy arbitrarily close to the optimal point. The uniqueness of NE
of such a game is proved in section \ref{sec:uniqueness}. In section
\ref{sec:convergence}, we show that the best response dynamics will
converge to the unique Nash Equilibrium. In section
\ref{sec:estimation}, we undertake simulations to see how the
process of statistically estimating the input arrival rates in a
real system would impact the PoA. We conclude the work in section
\ref{sec:conclusion}.
\section{Related Work}\label{sec:related}
Throughput-delay tradeoffs in M/M/1 queues with selfish users have
been previously studied in
\cite{Kumar:1981,Douligeris:1992,Zhang:1992,Dutta:2003,Yi:2009}. A
utility function for each user is defined as the corresponding
application's power and each user is treated as a player in such a
game and adjusts its arrival rate to handle the trade-off between
throughput and delay. Every user is assumed to be selfish and only
wants to maximize its own utility function in a distributed manner.
Bharath-Kumar and Jaffe \cite{Kumar:1981} wrote one of the earliest
papers on the formulation of throughput-delay tradeoffs in M/M/1
queues with selfish users. The paper discusses the properties of
power as a network performance objective function. A class of greedy
algorithms where each user updates its sending rate synchronously to
the best response of all other users' rates to maximize the power is
proposed. Convergence of the best response to an equilibrium point
is shown in this paper.
Douligeris and Mazumdar \cite{Douligeris:1992} extended
Bharath-Kumar and Jaffe's work to the case with different weighting
factors defined in the power function for different users and
provided analytical results describing the Nash Equilibrium. They
showed that the equilibrium point that the greedy best response
dynamic algorithm converged to was a unique Nash Equilibrium.
The work by Zhang and Douligeris \cite{Zhang:1992} proved the
convergence of the best response dynamics for this basic M/M/1
queueing game under the multiple users case. Thus all these prior
works (\cite{Kumar:1981, Douligeris:1992, Zhang:1992}) studied only
variants of the basic game. Their work, along with ours, shows that
this basic game results in an inefficient outcome. Our work is the
first to develop a mechanism design for this problem that addresses
this shortcoming by showing how to achieve near-optimal performance
using a packet-dropping policy.
Dutta \textit{et al.} \cite{Dutta:2003} studied a related problem
involving a server that employs an oblivious active queue management
scheme, i.e. drops packets depending on the total queue occupancy
with the same probability regardless of which flow they come from.
They also consider an M/M/1 setting with users offering Poisson
traffic to a server with exponential service time. The users'
actions are the input rates and the utilities the goodput/output
rates. The existence and the quality of symmetric Nash equilibria
are studied for different packet dropping policies. Although our
work also explores oblivious packet dropping schemes, it is
different from and somewhat more challenging to analyze than
\cite{Dutta:2003}, because our utility function reflects the
tradeoff between goodput and delay.
In another, more recent work, \cite{Yi:2009}, Su and van der Schaar
have discussed linearly coupled communication games in which users'
utilities are linearly impacted by their competitors' actions. An
M/M/1 FCFS queuing game with the power as the utility function is
one illustrative example of linearly coupled communication games.
They also quantify the Price of Anarchy in this case, and
investigate an alternative solution concept called Conjectural
Equilibrium, which requires users to maintain and operate upon
additional beliefs about competitors.
There have been also several other papers related to queueing games,
albeit with different formulations. Haviv and
Roughgarden~\cite{Haviv:2007} considered a system with multiple
servers with heterogeneous service rates. Arrivals from customers
are routed to one of the servers, and the routing decisions are
analyzed based on NE or social optimization schemes. PoA is shown to
be upper bounded by the number of servers for the social optimum. Wu
and Starobinski \cite{Wu:2006} analyzed the PoA of $N$ parallel
links where the delays of links are characterized using unbounded
delay functions such as M/M/1 or M/G/1 queueing functions.
Economides and Silvester \cite{Economides:1991} studied a
multiserver two-class queueing game and developed the routing
policy.
For more general surveys on game theoretic formulations of
networking problems, we refer the reader to \cite{Altman:2006,
LiuKrishnamachariKapadia:2008}.
\section{Problem Formulation}\label{sec:prob}
We consider a M/M/1 FCFS queue game as shown in Fig. \ref{fig:1}.
There are $m$ users with independent Poisson arrivals and the
arrival rates are $\lambda_1, \lambda_2, \dots, \lambda_m$. There is
a single server and the service time is exponentially distributed
with mean $\frac{1}{\mu}$.
We consider each user as a player for this game and the users are
selfish. Each player wants to maximize its own utility function by
adjusting its rate sending to the queue.
\begin{figure}[h!]
\centering
\includegraphics[width=0.45\textwidth]{fig1.eps}
\caption{An M/M/1 queue} \label{fig:1}
\end{figure}
Note that there is a tradeoff between the throughput and delay for
each user, i.e., given the rates of all other users, if the input
rate increases, the delay increases too. In this paper, we consider
the measurement of this tradeoff between the throughput and delay of
the each user, and it is known as the ``power'', which is widely
used in the gateway congestion control context \cite{RFC:1994}. We
consider the power as the utility function of each user to measure
its throughput-delay tradeoff. For a given user $i$, the power is
defined as:
\begin{equation}
\text{Power} = \frac{\text{Throughput}^{\alpha_i}}{\text{Delay}},
\end{equation}
where ${\alpha_i}$ is a parameter chosen based on the relative
emphasis placed on throughput versus delay. ${\alpha_i} > 1$ when
throughput is more important, while $0< {\alpha_i} < 1$ when we want
to emphasis delay more, and ${\alpha_i} = 1$ when the throughput and
delay are emphasized equally.
For M/M/1 queue, the throughput for user $i$ is $T_i = \xlie$ where
$\xlie$ is the effective rate served by the server. The delay for
user $i$ is calculated as: $D_i = \frac{1}{\mu - \sum\limits_{i =
1}^m \xlie}$.
So the power for user $i$ can be expressed as:
\begin{equation}
P_i = \frac{T_i^{\alpha_i}}{D_i} = (\xlie)^{\alpha_i}(\mu - \sum\limits_{i = 1}^m \xlie).
\end{equation}
In this M/M/1 game, each player is selfish and wants to adjust its
arrival rate $\lambda_i$ to maximize its own utility function.
Throughout the paper, we assume that the queue is stable and thus $0
\leq \sum\limits_{i = 1}^m \xlie < \mu$.
When there is no dropping policy implemented at the server, $\xlie =
\xli$, and the optimization problem for each player $i$ is:
\begin{eqnarray}
\max & & U_i(\lambda_i, \lambda_{-i}) =\lambda_i^{\alpha_i}(\mu - \sum\limits_{i = 1}^m \xli) \label{equ:4}\\
s.t. & & \sum \lambda_i < \mu \nonumber\\
& & \lambda_i \geq 0 \quad \forall i = 1, 2, \ldots, m \nonumber
\end{eqnarray}
\section{Social Welfare and Price of Anarchy}\label{sec:anarchy}
In \cite{Douligeris:1992} the above M/M/1 queue game is studied and
a unique pure NE is proved to be:
\begin{equation}
\label{equ:7}
\lambda_i^{NE} = \frac{\mu \alpha_i}{\sum\limits_{k = 1}^{m}\alpha_k + 1}, \forall \; i.
\end{equation}
When $\alpha_i = \alpha, \forall i$, this unique NE is expressed as
$\lambda_i^{NE} = \frac{\mu \alpha}{\alpha m + 1}, \forall \; i$.
Now suppose all users cooperate to achieve the maximal system
utility. We consider two ways to define the social optimal function:
the sum of the utilities of all the users and the sum of the
logarithm of the utilities of all the users. Defining the social
optimal function as the sum of the utilities of all the users is a
common way for evaluating the system efficiency and we present the
analysis results under this definition first. However, the fairness
among the users should also be considered and it is not revealed
under this definition; so we also consider a log-sum-utility social
welfare function which provides for utility fairness.
We can measure the efficiency of the system using two well known
measures called the Price of Anarchy (PoA) and Price of Stability
(PoS), that respectively compare the performance of selfish users in
the worst and best case Nash Equilibrium with the global optimum
achievable with non-selfish users. The definition of PoA and PoS of
a game $G$ is:
\begin{equation}
PoA(G) \triangleq \max\limits_{a \in \mathcal{E}(G)}
\frac{U(a^{OPT})}{U(a)}.
\end{equation}
\begin{equation}
PoS(G) \triangleq \min\limits_{a \in \mathcal{E}(G)}
\frac{U(a^{OPT})}{U(a)}.
\end{equation}
where $\mathcal{E}$ is the set of all the Nash Equilibriums in game
$G$.
\subsection{Sum-utility}
The optimization problem is defined as:
\begin{eqnarray}
\max &\quad \sum \lambda_i^{\alpha} (\mu - \sum \lambda_i) \\
s.t. &\quad 0 \leq \sum \lambda_i < \mu \nonumber\\
&\quad \lambda_i \geq 0 \quad \forall i = 1, 2, \ldots, m \nonumber
\end{eqnarray}
Here we consider two cases:
1) $\alpha >1 $
First calculate $U^{OPT}$.
\begin{equation}
\begin{split}
U^{OPT} & = \max_{\lambda_i} \sum \lambda_i^\alpha (\mu - \sum
\lambda_i) \\
& \leq \max_{\lambda_i} (\sum \lambda_i)^\alpha (\mu - \sum
\lambda_i)\\
& = \max_{\lambda} \lambda^\alpha (\mu - \lambda) \label{eqn:Uopt1}
\end{split}
\end{equation}
We can get $\lambda^* = \frac{\mu \alpha}{\alpha + 1}$.
Equality holds in equation \ref{eqn:Uopt1} when $\lambda_i =
\lambda^*$ for some $i$, and $\lambda_i = 0, \forall j \neq i$.
Hence this is also the solution for $P_{sys}^{OPT}$.
\begin{equation}
U^{OPT} = \frac{\alpha^\alpha \mu^{\alpha +
1}}{(\alpha+1)^{\alpha+1}}. \nonumber
\end{equation}
Then we calculate $U^{NE}$ when players are selfish:
\begin{equation}
U^{NE} = \frac{m \alpha^\alpha \mu^{\alpha + 1}}{(\alpha m
+1)^{\alpha+1}}. \nonumber
\end{equation}
Note that there is only one NE in the game, so PoA and PoS are the
same and they are derived as below:
\begin{equation}
PoA(G) = PoS(G) = \frac{U^{OPT}}{U^{NE}} =\frac{(\alpha m +1)^{\alpha+1}}{m (\alpha+1)^{\alpha+1}}.
\end{equation}
In this case we find that the PoA and PoS are proportional to
$m^\alpha$.
2) $\alpha <1 $
The calculation is similar as above, and details are omitted.
\begin{equation}
\begin{split}
U^{OPT} & = \max_{\lambda_i} \sum \lambda_i^\alpha (\mu - \sum
\lambda_i)\\ \nonumber
& \leq m \max_{\lambda_i} (\frac{\sum \lambda_i}{m})^\alpha (\mu - \sum
\lambda_i)\\
& =\max_{\lambda} m^{1-\alpha}\lambda^\alpha (\mu -
\lambda) .
\end{split}
\end{equation}
We also get $\lambda^* = \frac{\mu \alpha}{\alpha + 1}$,
\begin{equation}
U^{OPT} = \frac{m^{1-\alpha} \alpha^\alpha \mu^{\alpha +
1}}{(\alpha+1)^{\alpha+1}} . \nonumber
\end{equation}
PoA and PoS are:
\begin{equation}
PoA(G) = PoS(G) = \frac{U^{OPT}}{U^{NE}} =\frac{(\alpha m +1)^{\alpha+1}}{m^\alpha (\alpha+1)^{\alpha+1}}.
\end{equation}
In this case we find that the PoA and PoS are proportional to $m$.
Thus in both cases, we find that the PoA and PoS degrade linearly or
worse with the number of users.
\subsection{Sum-log-utility}
Now let's consider the sum of the logarithm of the utilities of all
the users. The reason we consider the logarithm function in the
social welfare is because when all users cooperate to achieve the
optimum, fairness among the users should also be considered, and a
logarithmic function would ensure this. The social welfare
optimization problem is:
\begin{eqnarray}
\max & & \sum\limits_{i = 1}^m \log \left[ \lambda_i^{\alpha} (\mu - \sum\limits_{i = 1}^m \lambda_i) \right] \label{equ:2}\\
s.t. & & 0 \leq \sum\limits_{i = 1}^m \lambda_i < \mu \nonumber\\
& & \lambda_i \geq 0 \quad \forall i = 1, 2, \ldots, m \nonumber
\end{eqnarray}
Note that for each player, maximizing the logarithm of its utility
function is equivalent to maximizing the utility function itself.
Therefore the NE remains the same as before.
Denote $\lambda = \sum\limits_{i = 1}^m \lambda_i$. We have the
following theorem for finding out the social optimum:
\theorem\label{claim:1} The solution for the social welfare
optimization problem is: $\xopt_i = \frac{\mu \xa}{m(\xa + 1)}$.
\begin{IEEEproof} see Appendix \ref{appendix:proof01}. \end{IEEEproof}
Note that $\lambda_i^{NE}$ is shown in (\ref{equ:7}) and by
substituting it into (\ref{equ:4}), we get the power for user $i$
as:
\begin{equation}
U_{i}^{NE} = \frac{\alpha^\alpha \mu^{\alpha + 1}}{(\alpha m
+1)^{\alpha+1}} \nonumber
\end{equation}
In general, the log-utility terms can be negative. To ensure that
both the numerator and denominator terms in the PoA and PoS are
non-negative in this case, we use a monotonic exponential mapping.
Note that there is only one NE in the game, so PoA and PoS are the
same, and they are derived as below:
\begin{equation}
\label{equ:8}
\begin{split}
PoA(G) = PoS (G) & = \frac{e^{U_{}^{OPT}}}{e^{U_{}^{NE}}} =
\frac{ \left( \frac{ \xa^\xa \mu^{\xa+1} }{ m^\xa (\xa + 1)^{\xa +1} }\right)^m }
{ \left( \frac{ \xa^\xa \mu^{\xa+1} }{ (\xa m + 1)^{\xa+1} } \right)^m }\\
& =
\left(\frac{ (\xa m + 1)^{\xa+1} }{ m^\xa (\xa + 1)^{\xa +1} }\right)^m > 1.
\end{split}
\end{equation}
From (\ref{equ:8}) we can see that PoA increases monotonically as
$m$ increases and goes to infinity as $m$ goes to infinity. So we
want to implement an incentive mechanism to improve the PoA.
\section{An Incentive Packet Dropping Scheme}\label{sec:scheme}
Note that $\lambda_i^{NE} = \frac{\mu \alpha}{\alpha m + 1} >
\frac{\mu \xa}{m(\xa + 1)} = \xopt_i$. This inspires us to find an
incentive packet dropping mechanism implemented at the server and we
wish this packet dropping mechanism to be as simple as possible. So
we consider the case where the server need only monitor the sum of
the rates of all users in the system and implement the packet
dropping policy based only on this information. Then the packet
dropping function could be expressed as $P_d(\sum \lambda_i)$. So
the optimization problem for each user $i$ with a dropping policy in
the system is:
\begin{equation}
\begin{split}
\max &\qquad U_i(\lambda_i, \lambda_{-i}) =(\lambda_i (1 - P_d(\sum \lambda_i)))^{\alpha_i} \\
& \qquad\qquad(\mu - \sum(\lambda_i(1 - P_d(\sum
\lambda_i)))) \\
s.t. &\qquad \sum \lambda_i (1 - P_d(\sum \lambda_i)) < \mu \\
&\qquad \lambda_i \geq 0 \quad \forall i = 1, 2, \ldots, m
\end{split}
\end{equation}
To facilitate the derivation, denote $P(\sum \lambda_i) = 1 -
P_d(\sum \lambda_i)$ and thus $P(\cdot)$ is the probability of
keeping packets in the system. Then the optimization problem for
each player $i$ is:
\begin{eqnarray}
\max && U_i(\lambda_i, \lambda_{-i}) =(\lambda_i P(\sum \lambda_i))^{\alpha_i}\nonumber\\
&&\qquad\qquad(\mu - \sum(\lambda_i P(\sum
\lambda_i)))) \label{equ:30}\\
s.t. && \sum \lambda_i P(\sum
\lambda_i) < \mu \label{equ:31}\\
&& \lambda_i \geq 0 \quad \forall i = 1, 2, \ldots, m
\end{eqnarray}
We denote the above game as $G_p = (N,
\{\mathcal{A}_i\}, \{U_i\} )$.
\section{Potential Game}\label{sec:potential}
In this section, we prove that when the dropping function is a
function which only depends on the sum of total incoming rates, the
game is a potential game and thus there exists at least one pure NE.
\definition a game $G = (N, \{\mathcal{A}_i\}, \{U_i\})$ is called
an \emph{ordinal potential game} if there exists a global function
$\phi : \mathcal{A} \longrightarrow \mathds{R}$ such that for every
player $i \in N$, for every $a_{-i} \in \mathcal{A}_{-i}$ and for
every $a'_i, a_i'' \in \mathcal{A}_i$,
\begin{equation}
sgn(U_i(a_i', a_{-i}) - U_i(a_i'', a_{-i}) ) = sgn(\phi(a_i', a_{-i}) - \phi(a_i'', a_{-i}) )
\end{equation}
where $sgn(x)$ is the sign function that takes on the value -1 when
$x<0$, 0 when $x=0$, and 1 when $x > 0$.
Also, the following Theorem \ref{theorem:1} holds for the existence
of NE in a potential game:
\theorem\label{theorem:1} [Monderer-Shapley,
1996~\cite{Monderer:1996}] Every potential game with finite-players,
continuous utilities, and compact strategy sets possesses at least
one pure-strategy equilibrium.
Now we will prove that the M/M/1 queueing game with a packet
dropping function $P_d(\sum \lambda_i)$ is a potential game.
\theorem\label{claim:potential} $G_p$ is a ordinal potential game
with
potential function \\
\scalebox{0.9}{ $
\phi(\lambda_1, \lambda_2, \dots, \lambda_m) = \left(\mu - P(\sum \lambda_i) \sum\limits_{i = 1}^m \lambda_i
\right) \left( \prod\limits_{i = 1}^m (\lambda_i P(\sum
\lambda_i))^{\xa_i} \right)
$ }
\begin{IEEEproof}
\begin{equation}
\begin{split}
& \phi(\xli', \xB) - \phi(\xli'', \xB)\nonumber \\
& = \left(\mu - P(\lambda_i' + \xB) ( \sum\limits_{j \neq i }^m
\lambda_j + \xli')
\right) \\
&\qquad\qquad\left( \prod\limits_{j \neq i}^m (\lambda_j P(\sum
\lambda_j))^{\xa_j} \right) \xli'^{\xa_i} P(\lambda_i' + \xB)^{\xa_i} \\
& \quad - \left(\mu - P(\lambda_i'' + \xB) ( \sum\limits_{j \neq i }^m
\lambda_j + \xli'')
\right) \\
&\qquad\qquad\left( \prod\limits_{j \neq i}^m (\lambda_j P(\sum
\lambda_j))^{\xa_j} \right) \xli''^{\xa_i} P(\lambda_i'' + \xB)^{\xa_i} \\
& = \left( \prod\limits_{j \neq i}^m (\lambda_i P(\sum
\lambda_i))^{\xa_i} \right) \left[
(\mu - P(\lambda_i' + \xB)\right.\\
&\qquad\qquad( \sum\limits_{j \neq i }^m
\lambda_j + \xli')
) (\xli' P(\lambda_i' + \xB))^{\xa_i}\\
& - (\mu - P(\lambda_i'' + \xB) ( \sum\limits_{j \neq i }^m
\lambda_j + \xli'')
) (\xli'' P(\lambda_i'' + \xB))^{\xa_i}
]\\
& = \left( \prod\limits_{j \neq i}^m (\lambda_i P(\sum
\lambda_i))^{\xa_i} \right) \left(U_i(\xli', \xB) - U_i(\xli'', \xB) \right)
\end{split}
\end{equation}
\end{IEEEproof}
Note that $G_p$ has a finite number of players and continuous
utilities. However its strategy sets are not compact in
(\ref{equ:31}) so we could not directly apply Theorem
\ref{theorem:1} to claim there exists at least one NE in $G_p$. But
we modify the $G_p$ to be the equivalent game as follows:
\begin{equation}
\begin{split}
\max &\qquad U_i(\lambda_i, \lambda_{-i}) =(\lambda_i P(\sum \lambda_i)))^{\alpha_i}\\
&\qquad\qquad (\mu - \sum(\lambda_i P(\sum
\lambda_i))))\\
s.t. &\qquad \sum \lambda_i P(\sum
\lambda_i) \leq \mu \\
&\qquad \lambda_i \geq 0 \quad \forall i = 1, 2, \ldots, m
\end{split}\label{eqn:compactStrategy}
\end{equation}
since any solution to the maximization problem in $G_p$ will not
satisfy $\sum \lambda_i P(\sum
\lambda_i) = \mu$. Now strategy sets of $G_p$ are compact and thus there exists at least one NE in $G_p$.
Note that in the following when we describe PoA and PoS for the
packet dropping game $G_p$, we respectively compare the worst and
best NE obtained for this game with respect to the social welfare
(global optimum) that can be obtained through cooperation without
packet dropping.
\section{Best Response Function}\label{sec:best}
From now, for tractability, we consider the case $\alpha_i = \alpha,
\forall i$ for our proposed incentive packet dropping scheme.
$\forall i$, let
\begin{equation}
\frac{\partial U_i(\lambda_i, \lambda_{-i}')}{\partial \lambda_i}=
0. \nonumber
\end{equation}
If $P(\sum \lambda_i)$ is differentiable with respect to
$\lambda_i$, we will have
\begin{equation}
\label{equ:9}
\begin{split}
& \xa P \mu - (\xa +1) P P' \xli \xB - (\xa + 1) P P'
\xli^2 \\
& - \xa P^2 \xB - (\xa+1) P^2 \xli + \xa P' \xli \mu = 0
\end{split}
\end{equation}
where $P'$ is the derivative of $P(\sum \lambda_i)$ with respect to
$\lambda_i$.
The above defines an implicit best response function
$\mathfrak{F}(\xli, \xB) = 0$ which shows the relationship between
$\xli$ and $\xB$.
\section{Step Dropping Function}\label{sec:step}
An intuitive dropping policy that first comes to mind is a step
function as shown in Fig. \ref{fig:2}.
\begin{figure}[h]
\centering
\includegraphics[width=0.2\textwidth]{fig2.eps}
\caption{Step dropping function $P_d(\sum \lambda_i)$} \label{fig:2}
\end{figure}
The expression of $P_d(\sum \lambda_i)$ is:
\begin{equation}
P_d(\sum \lambda_i) = \left\{
\begin{array}
{r@{\quad:\quad}l}
0 & \sum \lambda_i \leq \lambda^*\\
1 & \sum \lambda_i > \lambda^*
\end{array}
\right.
\end{equation}
We have the following result for the corresponding packet dropping
game.
\theorem \label{claim:c3} $\lambda'$ is a N.E. if and only if $\sum
\lambda_i' = \lambda^*$.
\begin{IEEEproof} see Appendix \ref{appendix:proof02}. \end{IEEEproof}
Based on Theorem \ref{claim:c3}, the NEs of the game with the step
dropping function are not unique. $\text{PoS} = 1$ since there
exists a NE with $\xli = \xopt_i, \forall i$. However, in the
sum-utility case, $\text{PoA} = m^{\xa-1}$ when $\xa > 1$, and
$\text{PoA} = m^{1-\xa}$ when $\xa < 1$. Moreover, PoA is infinite
in the sum-log-utility case since there exists a NE which has one
user $i$ with $\xli = 0$. Hence this is not a desirable result for
improving the efficiency. We therefore next consider a slightly more
sophisticated dropping function that has a linear profile.
\section{Linear Dropping Function}\label{sec:linear}
\begin{figure}[h]
\centering
\includegraphics[width=0.45\textwidth]{fig3.eps}
\caption{Illustration of $P_d(\sum \lambda_i)$ and $P(\sum \lambda_i)$} \label{fig:3}
\end{figure}
We consider the game with the following linear function of $P(\sum
\lambda_i)$ (and thus the packet dropping function $P_d(\sum
\lambda_i) = 1 - P(\sum \lambda_i)$ is also a linear function.) Fig.
\ref{fig:3} illustrates $P_d(\sum \lambda_i)$ and $P(\sum
\lambda_i)$.
\begin{equation}
\label{equ:15} P(\sum \lambda_i) = \left\{
\begin{array}
{l@{\quad:\quad}l}
1 & 0 \leq \sum \lambda_i \leq r_1\\
A (\sum \lambda_i) + D & r_1 \leq \sum \lambda_i \leq r_2\\
0 & \sum \lambda_i \geq r_2
\end{array}
\right.
\end{equation}
where
\begin{equation} \label{eq:1} \left\{ \begin{aligned}
A & = \frac{1}{r_1 - r_2} \\ \nonumber
D & = -A r_2
\end{aligned} \right.
\end{equation}
\begin{equation}
P' = \frac{\partial P}{\partial \xli } = A . \nonumber
\end{equation}
For linear dropping scheme, (\ref{equ:9}) becomes:
\begin{equation}
\label{equ:10}
\begin{split}
& \xa P \mu - (\xa +1) P A \xli \xB - (\xa + 1) P A
\xli^2 \\
& - \xa P^2 \xB - (\xa+1) P^2 \xli + \xa A \xli \mu = 0
\end{split}
\end{equation}
The above also defines an implicit function $\mathfrak{F}(\xli, \xB)
= 0$.
Denote $\xlie = P(\sum \lambda_i)\xli$ and $\xBe = P(\sum
\lambda_i)\xB$. First we want find out if we could design a dropping
policy in this linear form such that the system could have a NE that
is the same as the social optimum. If not, we will then explore how
much efficiency it could achieve.
\theorem\label{claim:c4} There does not exist a linear packet
dropping policy such that $PoA=1$.
\begin{IEEEproof}
Assume the above Theorem does not hold, when $P \neq 0$,
substituting $\xli$ and $\xB$ with $\xlie/P$ and $\xBe/P$ we have,
\begin{equation}
\begin{split}
& \xa P \mu - \frac{1}{P}(\xa +1) A \xlie \xBe - \frac{1}{P}(\xa +
1) A (\xlie)^2 \\
& \quad - \xa P \xBe - (\xa+1) P \xlie + \frac{1}{P}\xa A
\xlie
\mu = 0\\[1mm] \nonumber
\Longrightarrow \quad & P (\xa \mu - \xa \xBe - (\xa
+1)\xlie) \\
& = \frac{1}{P} [ (\xa +1)A \xlie \xBe + (\xa +1)A (\xlie)^2 - \xa A
\xlie \mu ] \nonumber
\end{split}
\end{equation}
Since $\xopt = \frac{\mu \xa}{\xa + 1}$ implies $\xa \mu = (\xa +
1) \xopt$, we have
\begin{equation}
\label{equ:11}
\begin{split}
\quad& P [(\xa + 1) \xopt - \xa \xBe - (\xa +1)\xlie] \\
\quad& =\frac{1}{P} A \xlie[ (\xa +1)(\xBe + \xlie) - (\xa +1) \xopt
] \nonumber
\end{split}
\end{equation}
\begin{equation}
\label{equ:11}
\begin{split}
\Longrightarrow &\quad P [(\xa + 1) (\xopt - \xBe - \xlie) + \xBe] \qquad\qquad\\
&= \frac{1}{P} A \xlie (\xa +1)(\xBe + \xlie - \xopt )
\end{split}
\end{equation}
Note that $P\xli + P\xB = \xopt$ implies that $\xlie + \xBe =
\xopt$. So the right-hand side of the equality is $0$. While the
left-hand side of the equality is $P \xBe$. Since $\xBe \neq 0$, so
$P \xBe \neq 0$. Thus the left-hand side of the equality is not $0$
and this leads to a contradiction. Therefore Theorem \ref{claim:c4}
holds.
\end{IEEEproof}
Theorem \ref{claim:c4} shows that we could not design a linear
packet dropping policy with $PoA = 1$. The following theorem shows
that we could design an incentive packet dropping policy such that
PoA could be arbitrarily close to 1.
\theorem\label{claim:c5} Given any $\epsilon$, there exists a linear
packet dropping policy such that $1< PoA \leq 1+ \epsilon$.
\begin{IEEEproof}
Note (\ref{equ:11}) in the proof of Theorem \ref{claim:c4} implies:
\begin{equation}
\label{equ:12}
P^2 [(\xa + 1) (\xopt - \xBe - \xlie) + \xBe] =
A \xlie (\xa +1)(\xBe + \xlie - \xopt )
\end{equation}
The right-hand side of (\ref{equ:12}) is greater than $0$ only when
$\xBe + \xlie < \xopt$ (note that $A < 0$). Then given $A$ and
$\xlie, \xBe$ such that $\xBe + \xlie < \xopt$, we will have a
solution for $P^2$ and thus we could get the value of $D$.
This means that we can design a packet dropping scheme such that it
has a NE that satisfies $p\xli + p\xB \longrightarrow \xopt$ from
the left side (left approximation). If we can further prove that the
NE is unique in this game (see Theorem \ref{claim:c6}), then give
any $\epsilon
> 0$, we could find a linear packet dropping policy at the server
such that $1< PoA \leq 1+ \epsilon$.
\end{IEEEproof}
We propose Algorithm \ref{alg1} to show how to design the parameters
$r_1$ and $r_2$ in our proposed incentive packet dropping policy to
achieve a desired PoA such that $1< PoA \leq 1+ \epsilon$ given any
$\epsilon$. We denote $\lambda_e = \sum \lambda_i^e$. Line
\ref{line:1} ensures that the sum of the rates will be less than
$\mu$ before the server starts to drop packets. $\tilde{p}$ is the
value of $P(\sum \lambda)$ at the desired NE which is derived from
the desired PoA. $\tilde{p} = 1 - Pr\{\text{the packet dropping
probability at desired NE}\}$. Line \ref{line:2} is the calculation
of desired NE. The choice of $\widetilde{\lambda}$ is based on the
desired value of PoA, i.e., given $\epsilon
> 0$, we could accordingly derive the
value of a desired sum rate such that $1< PoA \leq 1+ \epsilon$.
Since $(\widetilde{\lambda_e}, \widetilde{p})$ is a solution of
$P(\sum \lambda)$, line \ref{line:3} shows how to therefore get the
expression of $A$ and $D$. Then at line \ref{line:4}, we could solve
the equation (\ref{equ:10}) given all the values above and get the
value of $r_2$. Based on the result of $r_2$, the value of $r_1$ is
calculated.
\begin{algorithm}
\caption{Parameter Calculation for Incentive Packet Dropping Scheme}
\label{alg1}
\textbf{Input:} PoA bound parameter $\epsilon$
\textbf{Output:} $r_1$ and $r_2$ of our proposed incentive packet
dropping policy in (\ref{equ:15}) such that $1< PoA \leq 1+
\epsilon$.
\begin{algorithmic}[1]
\State \label{line:1} Pick any $\tilde{p}$ such that $\frac{a}{a+1}<
\tilde{p} < 1$.
\State \label{line:2} Calculate a desired sum rate
$\widetilde{\lambda}$, of which
\begin{equation}
\widetilde{\lambda} = \{ \frac{\widetilde{\lambda_e}}{m
\widetilde{p}}, \frac{(m-1)\widetilde{\lambda_e}}{m
\widetilde{p}}\}.
\end{equation}
is the desired NE such that $1< PoA \leq 1+ \epsilon$. Note that
$\lambda_e = \tilde{p} \lambda$.
\State \label{line:3} Suppose $P(\sum \lambda_i) = A \sum \lambda_i
+ D$ pass through the point $(\widetilde{\lambda}, \widetilde{p})$.
Then we have
\begin{equation} \label{equ:16}
A = \frac{\widetilde{p}}{\widetilde{\lambda} - r_2}, D = -\frac{\widetilde{p} r_2}{\widetilde{\lambda} -
r_2}.
\end{equation}
\State \label{line:4} Insert the above values of the variables into
(\ref{equ:10}) and get the value of $r_2$.
\State \label{line:5} Insert the value of $r_2$ into (\ref{equ:16})
and get the value of $A$. Then $r_1 = \frac{1}{A} + r_2$
\end{algorithmic}
\end{algorithm}
Note that (\ref{equ:10}) is a quadratic equation for the parameters
$A$ and $D$ given the values of all the other variables. But with
Algorithm \ref{alg1}, we could always find a unique solution as
stated in Theorem \ref{claim:c5}.
\theorem \label{claim:c5} Algorithm \ref{alg1} yields a unique
linear packet dropping scheme, i.e., unique values for $r_1$ and
$r_2$ for any PoA bound.
\begin{IEEEproof}
After inserting the value $\widetilde{p}$, and $\widetilde{\lambda}
= \{ \frac{\widetilde{\lambda_e}}{m \widetilde{p}},
\frac{(m-1)\widetilde{\lambda_e}}{m \widetilde{p}}\}$ into
(\ref{equ:10}) at line \ref{line:4}, we have the equality
\begin{equation}
\label{equ:17}
\begin{split}
& \widetilde{p}^2 [(\xa + 1) (\xopt
- \widetilde{\lambda_e}) + \frac{(m-1)\widetilde{\lambda_e}}{m
\widetilde{p}}] \\
& = \frac{\widetilde{p}}{\widetilde{\lambda_e}/\widetilde{p} - r_2}
\frac{\widetilde{\lambda_e}}{m \widetilde{p}} (\xa
+1)(\widetilde{\lambda_e} - \xopt )
\end{split}
\end{equation}
It is obvious that the above is a linear equation of the variable
$r_2$. And thus we could get a unique solution of $r_2$. Therefore,
there is a always a unique solution of $r_1$ and $r_2$ provided by
Algorithm \ref{alg1}.
\end{IEEEproof}
Our proposed packet dropping scheme is similar to the Random Early
Detection (RED) algorithm. It is simple and easy to be implemented
with low overhead at the server. Fig. \ref{fig:6} shows an example
of our linear packet dropping policy with $\mu = 6$, $m = 2$ and
$\xa = 2$. (\ref{equ:2}) and (\ref{equ:8}) are used to calculate the
utility and PoA. Point A represents $\xopt$, which is then
calculated to be 4 ($\lambda_1 = \lambda_2 = 2$). We assume
$\tilde{p} = 0.9$, PoA bound parameter $\epsilon = 0.05$.
Implementing Algorithm \ref{alg1} with Matlab, we pick
$\widetilde{\lambda_e} = 3.9$, we then get $r_1 = 4.3012$, $r_2 =
4.622$, $A = -3.1154$, $D = 14.4000$. Point B represents the Nash
Equilibrium with our proposed packets dropping policy. Point C
represents the Nash Equilibrium of the original game without packet
dropping policy. The shaded area shows the cases where packet
dropping happens. For the comparison, the utilities are shown in the
figure and we can see that $PoA$ is improved from $1.3396$ to
$1.0455$.
\begin{figure}[h]
\centering
\includegraphics[width=0.30\textwidth]{figNew.eps}
\caption{An example of our incentive packet dropping scheme.} \label{fig:6}
\end{figure}
\section{Uniqueness of NE}\label{sec:uniqueness}
If we use the packet dropping scheme in algorithm \ref{alg1} we are
guaranteed that the game $G_p$ always has a NE with the desired PoA
bound. Now our question is whether the scheme yields a unique NE.
This is important not only for finding out whether our proposed
scheme is efficient but also for the convergence issues. As surveyed
in \cite{Altman:2009}, there are not many general results on
equilibrium uniqueness. We were unable to find any existing theorem
that we could use directly to prove the uniqueness of NE in our
M/M/1 queueing game. This makes the analysis of this incentive
design problem more challenging.
\theorem \label{claim:c6} There is a unique NE for the M/M/1 Game
with the linear packet dropping scheme described in
Algorithm~\ref{alg1}.
To prove \ref{claim:c6}, we first prove the following three lemmas.
\lemma \label{lemma:1} $|A|$ increases monotonically as $(\xopt
-\widetilde{\lambda_e})$ decreases where $\widetilde{\lambda_e}$ is
the total rate of all users at desired NE (as in Algorithm
\ref{alg1}).
\begin{IEEEproof} Note that (\ref{equ:17}) is equivalent to:
\begin{equation}
\label{equ:21}
\widetilde{p}^2 [(\xa + 1) (\xopt - \widetilde{\lambda_e}) + \frac{(m-1)\widetilde{\lambda_e}}{m
\widetilde{p}}] =
A \frac{\widetilde{\lambda_e}}{m
\widetilde{p}} (\xa +1)(\widetilde{\lambda_e} - \xopt ) \nonumber
\end{equation}
This means
\begin{equation}
\label{equ:20} \frac{(m-1)\widetilde{\lambda_e}}{m \widetilde{p}
(\xopt - \widetilde{\lambda_e})} = (\xa
+1)\left(|A|\frac{\widetilde{\lambda_e}}{m \widetilde{p}} -
\widetilde{p}^2 \right).
\end{equation}
Note that as $(\xopt -\widetilde{\lambda_e})$ decreases,
$\widetilde{\lambda_e}$ increases and $\frac{1}{\xopt -
\widetilde{\lambda_e}}$ increases, so the left-hand side of
(\ref{equ:20}) increase. This implies $|A|$ increases, and thus
Lemma \ref{lemma:1}.
\end{IEEEproof}
\lemma \label{lemma:2} $\forall \xB < r_1, \frac{\partial
U_i(\lambda_i, \lambda_{-i})}{\partial \lambda_i} > 0$ at $\lambda_i
= (r_1 - \xB)^+$.
\begin{IEEEproof}
Note that $P = 1$ at $r_1$, then
\begin{equation}
\begin{split}
&\;\; \frac{\partial U_i(\lambda_i, \lambda_{-i})}{\partial \lambda_i} \nonumber\\
= &\;\; \xa \mu - (\xa +1) A \xli \xB - (\xa + 1) A \xli^2 - \xa \xB \\
&\;\; -
(\xa+1) \xli + \xa A \xli \mu \nonumber\\[0mm]
= &\;\; \xa \mu - \xa \xB - (\xa +
1) \xli \\
&\;\; - A \xli [ (\xa + 1) (\xB +
\xli) - \xa \mu ]\nonumber\\[0mm]
= &\;\; \xa \mu - (\xa + 1) (\xB + \xli) + \xB \\
&\;\; - A \xli [ (\xa + 1)
(\xB +
\xli) - \xa \mu ]\nonumber\\[0mm]
= &\;\; [\xa \mu - (\xa + 1) (\xB + \xli) ](1+ A \xli) + \xB \nonumber\\[0mm]
= &\;\; [\xa \mu - (\xa + 1) r_1 ](1+ A \xli) + \xB \nonumber\\[0mm]
= &\;\; [(\xa + 1)\xopt - (\xa + 1) r_1 ](1+ A \xli) + \xB \nonumber\\[0mm]
= &\;\; (\xa + 1)(\xopt - r_1 )(1+ A (r_1 - \xB)) + \xB \label{equ:22}
\end{split}
\end{equation}
Denote (\ref{equ:22}) as $g(\lambda_{-i})$. Then,
\begin{equation}
\label{equ:23}
\frac{\partial g}{\partial \lambda_{-i}} = -(\xa + 1)(\xopt - r_1 )A +
1.
\end{equation}
When $|A|$ is large enough such that $r_1 > \xopt$ and $|A| >
\frac{1}{(\xa + 1)(r_1 -\xopt)}$, $\frac{\partial g}{\partial
\lambda_{-i}} < 0$.
From Lemma \ref{lemma:1} we know that as $\widetilde{\lambda_e}$
gets closer to $\xopt$, $|A|$ increases. This means that when we
design a dropping policy with $PoA$ approaching to $1$, $|A|$ could
be large enough such that $r_1 > \xopt$ and $|A| > \frac{1}{(\xa +
1)(r_1 -\xopt)}$.
So $g(\lambda_i)$ achieves the minimum value when $\xB = r_1$. Then
\begin{equation}
\begin{split}
\frac{\partial U_i(\lambda_i, \lambda_{-i})}{\partial \lambda_i}
&\;\;>\;\;
(\xa + 1)(\xopt - r_1) + r_1\\
&\;\;=\;\; (\xa + 1)\xopt - \xa r_1\\
&\;\;=\;\; \xa \mu - \xa r_1 > 0.
\end{split}
\end{equation}
\end{IEEEproof}
Lemma \ref{lemma:2} implies that given $\xB$, $U_i(\lambda_i,
\lambda_{-i})$ which is a function of $\lambda_i$, has a maxima at
$r_1- \lambda_{-i} < \lambda_i < r_2 - \lambda_{-i}$ as shown in
Fig. \ref{fig:4}.
\begin{figure}[h]
\centering
\includegraphics[width=0.3\textwidth]{fig4.eps}
\caption{Illustration of local maximum point of $U_i(\lambda_i,
\lambda_{-i})$} \label{fig:4}
\end{figure}
\begin{figure}[h]
\centering
\includegraphics[width=0.3\textwidth]{fig5.eps}
\caption{Illustration of local maximum point of $U_{i, max}^1$ and $U_{i, max}^2$} \label{fig:5}
\end{figure}
Given $\xB$, if $\xB + \frac{(\mu - \xB)\xa}{\xa + 1} < r_1$, then
$U_i(\lambda_i, \lambda_{-i})$ will reach a local maximal point when
$\lambda_i = \frac{(\mu - \xB)\xa}{\xa + 1}$ as shown in Fig.
\ref{fig:5}. Note that $P(\sum \lambda_i) = 1$ at this point. We
denote this local maximal value as $U_{i, max}^1$. Then
$U_i(\lambda_i, \lambda_{-i})$ will reach another local maximal
point with $\lambda_i^e = \frac{(\mu - \xB)\xa}{\xa + 1}$. Note that
$P(\sum \lambda_i) < 1$. We denote this local maximal value as
$U_{i, max}^2$.
\lemma \label{lemma:3} Given $\xB$, if $\xB + \frac{(\mu -
\xB)\xa}{\xa + 1} < r_1$, $U_{i, max}^1 < U_{i, max}^2$.
\begin{IEEEproof}
Note that
\begin{equation}
U_{i, max}^1 =(\lambda_i^1)^{\alpha}(\mu - (\lambda_i^1) - \xB),
\nonumber
\end{equation}
where $\lambda_i^1 = \frac{(\mu - \xB)\xa}{\xa + 1}$.
\begin{equation}
U_{i, max}^2 = (P \lambda_i^2)^{\alpha}(\mu - (P \lambda_i^1) - P
\xB). \nonumber
\end{equation}
Denote $\xlie = P \lambda_i^2$. Note that $\xlie$ ranges from $r_1 $
to 0 and we have $r_1 > \lambda_i^1$. Also note that
\begin{equation}
\max\limits_{\xlie} (\xlie)^{\alpha}(\mu - \xlie - P \xB) > \max\limits_{\xlie} (\xlie)^{\alpha}(\mu - \xlie -
\xB) \nonumber
\end{equation}
since $P \xB < \xB$. Thus, $U_{i, max}^2 > U_{i, max}^1$.
\end{IEEEproof}
We show in Lemma \ref{lemma:3} that given $\xB$, $U_i(\lambda_i,
\lambda_{-i})$ achieves the maximal point when $P < 1$ under the
condition that $\xB + \frac{(\mu - \xB)\xa}{\xa + 1} \leq r_1$. When
$\xB + \frac{(\mu - \xB)\xa}{\xa + 1} > r_1$, there is only one
maximal point for $U_i(\lambda_i, \lambda_{-i})$. When $\xB +
\frac{(\mu - \xB)\xa}{\xa + 1} = r_1$, $U_{i, max}^1$ and $U_{i,
max}^2$ will overlap, and since $r_1 > \xopt$, this case could not
result in a NE and thus we do not consider this case.
Lemma \ref{lemma:1}, Lemma \ref{lemma:2} and Lemma \ref{lemma:3}
shows that given $\xB$, $U_i(\lambda_i, \lambda_{-i})$ achieves the
maximal point when $P < 1$. Then we will prove the uniqueness of NE
based on the expression $P(\sum \xli) = A (\xli + \xB) + D$.
\begin{IEEEproof}[Proof of Theorem \ref{claim:c6}]
Suppose the $G_p$ has more than one NE. Note that the game is
symmetric, so there must exist one NE $\lambda = \{\lambda_1,
\lambda_2, \dots, \lambda_m\}$, such that $\exists \; i,j, \lambda_i
\neq \lambda_j$. This means there exists a NE $\lambda = \{\xli,
\xB\}$ and a constant $c$ such that $\lambda = \{\xli+c, \xB-c\}$ is
also a NE.
We insert $\lambda = \{\xli, \xB\}$ into (\ref{equ:12}) and we get:
\begin{equation}
\begin{split}
&[A(\xli + \xB)+D]^2 [(\xa + 1) (\xopt - \xBe - \xlie) + \xBe] \nonumber\\
&= A \xlie (\xa +1)(\xBe + \xlie - \xopt ) \nonumber
\end{split}
\end{equation}
\begin{equation}
\label{equ:18}
\begin{split}
\Longrightarrow \;&\frac{(\xa + 1) (\xopt - \xBe - \xlie) + \xBe}{\xlie}\\
&=\frac{1}{[A(\xli + \xB)+D]^2} A (\xa +1)(\xBe + \xlie - \xopt )
\end{split}
\end{equation}
We also insert $\lambda = \{\xli+c, \xB-c\}$ into (\ref{equ:12}) and
denote $\tilde{c} = \frac{c}{A(\xli + \tilde{c} + \xB -
\tilde{c})+D} = \frac{c}{A(\xli + \xB)+D}$. We have:
\begin{equation}
\begin{split}
&[A(\xli + \tilde{c} + \xB - \tilde{c})+D]^2 \\
&\qquad\qquad [(\xa + 1) (\xopt - \xBe
-\tilde{c}- \xlie + \tilde{c}) + \xBe-\tilde{c}] \nonumber\\
&= A (\xlie + \tilde{c}) (\xa +1)(\xBe - \tilde{c} + \xlie +
\tilde{c} - \xopt
) \nonumber
\end{split}
\end{equation}
\begin{equation}
\label{equ:19}
\begin{split}
\Longrightarrow \;& \frac{(\xa + 1) (\xopt - \xBe -
\xlie) + \xBe - \tilde{c}}{\xlie + \tilde{c}} \\
& = \frac{1}{[A(\xli + \xB)+D]^2} A (\xa +1)(\xBe + \xlie - \xopt )
\end{split}
\end{equation}
Note that the right-hand side of (\ref{equ:18}) and (\ref{equ:19})
are the same and thus the left-hand side of (\ref{equ:18}) and
(\ref{equ:19}) are equal to each other. So,
\begin{equation}
\begin{split}
& \frac{(\xa + 1) (\xopt - \xBe - \xlie) + \xBe}{\xlie}\\
& =\; \frac{(\xa + 1) (\xopt - \xBe - \xlie) + \xBe -
\tilde{c}}{\xlie + \tilde{c}}\\\nonumber
\Longrightarrow \;& (\xlie + \tilde{c})(\xa + 1) (\xopt - \xBe - \xlie) + (\xlie + \tilde{c})
\xBe \\
& =\; \xlie (\xa + 1) (\xopt - \xBe - \xlie) + \xlie (\xBe -
\tilde{c})\\
\end{split}
\end{equation}
\begin{equation}
\begin{split}
\Longrightarrow \;& \tilde{c}(\xa + 1)(\xopt - \xBe - \xlie) + \tilde{c} (\xBe + \xlie) = 0\\
\Longrightarrow \;& \tilde{c}[(\xa + 1)\xopt - \xa(\xBe + \xlie)] = 0\\
\Longrightarrow \;& \tilde{c}[\xa \mu - \xa(\xBe + \xlie)] = 0\\
\Longrightarrow \;& \tilde{c}\xa [\mu - (\xBe + \xlie)] = 0\\
\Longrightarrow \;& \frac{c \xa [\mu - (\xBe + \xlie)]}{A(\xli +
\xB)+D} = 0 . \nonumber
\end{split}
\end{equation}
Note that $\mu - (\xBe + \xlie) > 0$. This implies that $c = 0$ and
therefore Theorem \ref{claim:c6} holds.
\end{IEEEproof}
\section{Best Response Dynamics and Convergence}\label{sec:convergence}
In this section, we show that the best response dynamic
\cite{MacKenzie:2006}, a simple learning mechanism, will lead the
queuing game to converge to the pure Nash equilibrium.
Best response dynamic is a straightforward updating rule which
proceeds as follows: whenever player $i$ has an opportunity to
revise her strategy, she will choose the best response to the
actions of all the other players in the previous round.
Mathematically, for a game $G = (N, \{\mathcal{A}_i\}, \{U_i\})$,
let $a_i^t$ denotes the action of player $i$ in iteration $t$,
\begin{equation}
a_i^t = \arg\max_{a_i' \in \mathcal{A}_i} U_i(a_i', a_{-i}^{t-1}).
\end{equation}
In general, the best response dynamic is not guaranteed to converge.
However, if the process does converge, it is guaranteed to converge
to a NE. Now, we want to investigate the convergence of our proposed
M/M/1 Game with the packet dropping scheme, denoted as $G_p$ in the
previous section.
\theorem\label{theorem:10} Best response dynamic will converge to
the unique NE for the M/M/1 Game with the proposed packet dropping
scheme.
\begin{IEEEproof}
There is an important result about the convergence for ordinal
potential game as shown in Theorem $21$ in \cite{MacKenzie:2006}: if
$G$ is an ordinal potential game with a compact action space and a
continuous potential function, then the best response dynamic will
(almost surely) either converge to a NE or every limit point of the
sequence will be a NE.
We have showed in Theorem \ref{claim:potential} that $G_p$ is an
ordinal potential game, and although the original definition of the
game does not have a compact action space, the equivalent
modification as shown in (\ref{eqn:compactStrategy}) has a compact
action space. We can also see that the potential function is
continuous. We have also proved in Theorem \ref{claim:c6} that there
is a unique NE. Thus Theorem \ref{theorem:10} holds.
\end{IEEEproof}
\begin{figure}[h]
\centering
\includegraphics[width=0.37\textwidth]{fig7.eps}
\caption{Quiver plot for a two user example with $\mu = 10$, $\xa =
2$, $r_1 = 7.0321$ and $r_2 = 7.8222$. The vector length are scaled
to $\frac{1}{14}$ of the original length.} \label{fig:7}
\end{figure}
Figure \ref{fig:7} is an illustration of Theorem \ref{theorem:10} by
the quiver plot. In Figure \ref{fig:7}, on the lower triangle of a
grid (i.e., the feasible operating domain), we plot vector summation
for a two-user rate control queuing game with $\mu = 10$, $\xa = 2$,
$r_1 = 7.0321$ and $r_2 = 7.8222$. At each point, the vectors'
projections on $\lambda_1$ and $\lambda_2$ represent the best
response for the corresponding users in next iteration. To make the
plot neat, the length of each vector is scaled to $\frac{1}{14}$ of
the original length. The figure shows that at each point, the
players in the best response dynamic move towards the equilibrium
point. The length of the best response vectors are proportional to
the distance from the equilibrium point. At the equilibrium point,
the step size of the movement in the next iteration tends to zero,
which implies the convergence of the best response dynamic.
\section{Impact of Arrival Rate Estimation \label{sec:estimation}}
For a real system implementation, the server needs to estimate the
total arrival rate from users in order to apply the incentive packet
dropping scheme. The packets arrive randomly over time, so there
will be a difference between the estimated total rate and the
average total rate. This inaccuracy will cause a loss in the PoA.
While applying the packets dropping scheme, we note that the closer
to 1 the desired PoA is, the steeper (on the linear part) the packet
dropping scheme is, and therefore, the greater the impact of
estimation inaccuracy will be. So as the desired PoA approaches 1,
on the one hand the PoA of the real system should increase due to
the implementation of the incentive scheme, but on the other hand,
the sensitivity to estimation error will reduce the gain in PoA.
Therefore, the achieved PoA in practice may not be arbitrarily close
to 1.
We show this fact in Figure~\ref{fig:8} to~\ref{fig:11} where we
show simulation results from a 3-user queue with $\alpha = 2$. In
these simulations, we discretize time into slots. The server
estimates the mean arrival rate from the previous time slot and
applies the packet dropping function corresponding to a desired PoA
to all packets in the current slot (the users contribute arrivals at
a constant rate that corresponds to the equilibrium input for this
desired PoA). The running time for all the simulations is $10^5$
time slots. Figure~\ref{fig:8} and \ref{fig:9} show the simulation
results of PoA under different service rates for both the
sum-utility definition and sum-log-utility definition with the
instantaneous arrival rate to the server as the estimated arrival
rate. We can see that as the service rate varies from 500 to 5000
packets per time slot, the optimal point of PoA (i.e. the lowest
achievable PoA) is getting closer to 1 because the estimation
inaccuracy decreases. Also, the empirically achieved PoA is getting
closer to the desired PoA.
Note that when the service rate is low, the achievable PoA we get
could be very bad as shown in figure~\ref{fig:a1} and \ref{fig:b1}.
In these cases, using more history data/longer estimation lengths
will help to increase the estimation accuracy and improve PoA. The
comparison results under different estimation lengths for $\mu =
600$ packets per time slot are shown in figure~\ref{fig:10} and
\ref{fig:11}. These simulation results illustrate a tradeoff between
the optimal PoA and the overhead in computing and storage: while
estimating with more history data will increase the estimation
accuracy and therefore increase PoA, it increases the overhead in
terms of computing and storage.
\begin{figure*}[h]
\centering
\subfigure[$\mu = 500$.]
{
\includegraphics[width=0.31\textwidth]{fig_noise_normal_500.eps}
\label{fig:a1}
}
\subfigure[$\mu = 5000$.]
{
\includegraphics[width=0.31\textwidth]{fig_noise_normal_5000.eps}
\label{fig:a2}
}
\subfigure[$\mu = 50000$.]
{
\includegraphics[width=0.31\textwidth]{fig_noise_normal_50000.eps}
\label{fig:a3}
}
\caption{Simulation results of PoA under different service rates of a 3-user system with $\alpha = 2$ (sum-utility definition).}
\label{fig:8}
\end{figure*}
\begin{figure*}[h]
\centering
\subfigure[$\mu = 500$.]
{
\includegraphics[width=0.31\textwidth]{fig_noise_log_500.eps}
\label{fig:b1}
}
\subfigure[$\mu = 5000$.]
{
\includegraphics[width=0.31\textwidth]{fig_noise_log_5000.eps}
\label{fig:b2}
}
\subfigure[$\mu = 50000$.]
{
\includegraphics[width=0.31\textwidth]{fig_noise_log_50000.eps}
\label{fig:b3}
}
\caption{Simulation results of PoA under different service rates of a 3-user system with $\alpha = 2$ (sum-log-utility definition).}
\label{fig:9}
\end{figure*}
\begin{figure*}[p]
\centering
\subfigure[The estimated total rate got based on the instantaneous arrival rate.]
{
\includegraphics[width=0.31\textwidth]{fig_noise_normal_600_r1.eps}
\label{fig:c1}
}
\subfigure[The estimated total rate got by averaging the continuous arrival rates in 10 slots.]
{
\includegraphics[width=0.31\textwidth]{fig_noise_normal_600_r10.eps}
\label{fig:c2}
}
\subfigure[The estimated total rate got by averaging the continuous arrival rates in 100 slots.]
{
\includegraphics[width=0.31\textwidth]{fig_noise_normal_600_r100.eps}
\label{fig:c3}
}
\caption{Impact of estimation length on PoA of a 3-user system with $\mu = 600$, $\alpha = 2$ (sum-utility definition).}
\label{fig:10}
\end{figure*}
\begin{figure*}[p]
\centering
\subfigure[The estimated total rate got based on the instantaneous arrival rate.]
{
\includegraphics[width=0.31\textwidth]{fig_noise_log_600_r1.eps}
\label{fig:d1}
}
\subfigure[The estimated total rate got by averaging the continuous arrival rates in 10 slots.]
{
\includegraphics[width=0.31\textwidth]{fig_noise_log_600_r10.eps}
\label{fig:d2}
}
\subfigure[The estimated total rate got by averaging the continuous arrival rates in 100 slots.]
{
\includegraphics[width=0.31\textwidth]{fig_noise_log_600_r100.eps}
\label{fig:d3}
}
\caption{Impact of estimation length on PoA of a 3-user system with $\mu = 600$, $\alpha = 2$ (sum-log-utility definition).}
\label{fig:11}
\end{figure*}
\section{Conclusion}\label{sec:conclusion}
In this paper, we have designed a novel incentive mechanism for
M/M/1 queueing games with throughput-delay tradeoffs. Because the
original game yields an inefficient Nash equilibrium, we propose to
implement a linear packet dropping mechanism at the router. We show
how the parameters of this mechanism can be optimized to ensure
system efficiency that is arbitrarily close to the social welfare
solution. Further, we prove that the proposed modification has a
unique NE, and that the simple best response dynamics converges to
this solution. Future work could consider extensions of this work to
consider non-homogeneous users, other queuing models beyond the
M/M/1 model, more complex arrangements of multiple routers in a
network, as well as other system issues that may arise in practical
implementations.
\section*{Acknowledgment}
We would like to thank Professor Rahul Jain at University of
Southern California for his valuable comments.
\appendices
\section{PROOF OF THEOREM \ref{claim:1}}\label{appendix:proof01}
\begin{IEEEproof}
\begin{eqnarray}
&& \sum\limits_{i = 1}^m \log \left[ \lambda_i^{\alpha} (\mu - \sum\limits_{i = 1}^m \lambda_i) \right] \nonumber \\
=\; &&\xa \log (\prod \xli) + m \log(\mu - \lambda)\nonumber\\
\leq && \xa \log (\frac{ \sum \xli }{ m })^m + m \log (\mu -
\lambda) \label{eqn:35}\\
=\; && m \log ( \frac{\lambda}{m})^\xa (\mu - \lambda) ) \nonumber
\end{eqnarray}
Denote $f(\lambda) = \lambda^\xa (\mu - \lambda)$. So maximize
(\ref{equ:2}) is equivalent to maximize $f(\lambda)$. Take the
derivative of $f(\lambda)$ and let it equals 0. We get:
\begin{equation}
\frac{\partial f}{\partial \lambda} = 0 \Rightarrow \xopt =
\frac{\mu \xa}{\xa + 1}. \nonumber
\end{equation}
Note that equality holds in (\ref{eqn:35}) only when $\lambda_1 =
\lambda_2 = \dots = \lambda_m$. This implies $\xopt_i =
\frac{\xopt}{m} =\frac{\mu \xa}{m(\xa + 1)}$
\end{IEEEproof}
\section{PROOF OF THEOREM \ref{claim:c3}} \label{appendix:proof02}
\begin{IEEEproof} $(\Longleftarrow)$
Suppose $\sum \lambda_i' = \lambda^*$. $\forall i$, let
$\frac{\partial U(\lambda_i, \lambda_{-i}')}{\partial \lambda_i}=
0$. We get the optimal point $\lambda_i^{**} = \frac{(\mu - \sum_{j
\neq i} \lambda_j')\alpha_i}{\alpha_i+1}$.
Note that
\begin{equation}
\begin{array}{r@{\; \;}l}
\lambda_i' & = \lambda^* - \sum_{j \neq i} \lambda_j' = \frac{\alpha \mu}{\alpha + 1} - \sum_{j \neq i} \lambda_j' \\
& = \frac{(\mu - \sum_{j \neq i} \lambda_j')\alpha_i - \sum_{j \neq i} \lambda_j'}{\alpha_i+1} < \frac{(\mu - \sum_{j \neq i}
\lambda_j')\alpha_i}{\alpha_i+1} = \lambda_i^{**} . \nonumber
\end{array}
\end{equation}
Also, $\forall \lambda_i < \lambda_i^{**}, \frac{\partial
U(\lambda_i, \lambda_{-i}')}{\partial \lambda_i}> 0$, which means
$U(\lambda_i, \lambda_{-i}')$ increases monotonically with respect
to $0 \leq \lambda_i < \lambda_i^{**}$, so $U(\lambda_i',
\lambda_{-i}') > U(\lambda_i, \lambda_{-i}'), \forall \lambda_i \in
[0,\lambda_i')$. Also note that $U(\lambda_i, \lambda_{-i}') = 0,
\forall \lambda_i \in (\lambda_i^*, \mu - \sum_{j \neq i}
\lambda_j'$). Hence $\lambda_i' \in B_i (\lambda_{-i}')$.
Therefore, $\lambda'$ is a N.E.
$(\Longrightarrow)$
Suppose $\lambda'$ is a N.E., $\forall i, \lambda_i' \in B_i
(\lambda_{-i}')$.
$\forall \lambda_{-i}'$, consider the following two cases:
\subsubsection{$\sum_{j \neq i} \lambda_j' \leq \lambda^*$}\
Denote $\lambda_i'' = \lambda^* - \sum_{j \neq i} \lambda_j' $. Then
$<\lambda_i'', \lambda_{-i}'>$ is a N.E., $\lambda_i'' \in B_i
(\lambda_{-i}')$. $U(\lambda_i'', \lambda_{-i}') = U(\lambda_i',
\lambda_{-i}') > 0$. So $\lambda_i' \leq \lambda^* - \sum_{j \neq i}
\lambda_j' = \lambda''$ (if not so, $U(\lambda_i', \lambda_{-i}') =
0$).
Note that $U(\lambda_i, \lambda_{-i}')$ increases monotonically with
respect to $0 \leq \lambda_i < \lambda_i''$. Therefore, $\lambda' =
\lambda''$. $\sum \lambda_i' = \lambda^*$.
\subsubsection{$\sum_{j \neq i} \lambda_j' > \lambda^*$}\
Under this case, since $\sum \lambda'>\lambda^*$, we have $B_i
(\lambda_{-i}') =0 , \forall i$. Then $\sum_{j \neq i} \lambda_j'
\geq \lambda^*$ holds for all $i$.
$\forall i, \lambda_i' < \mu - \sum_{j \neq i} \lambda_j' < \mu -
\lambda^* = \mu - \frac{\mu \alpha}{\alpha + 1} = \frac{\mu}{\alpha
+ 1}$. So
\begin{equation}\label{equ5}
\sum_{i = 1}^m \lambda_i' < \frac{\mu m}{\alpha + 1} < \mu \Rightarrow m < \alpha +
1.
\end{equation}
However, note that
\begin{equation}\label{equ6}
\lambda^* = \frac{\mu \alpha}{\alpha + 1} < \sum_{j \neq i} \lambda_j' < \frac{\mu (m-1)}{\alpha +
1} \Rightarrow m > \alpha + 1
\end{equation}
Since (\ref{equ5}) and (\ref{equ6}) contradict each other, there is
no N.E. $\lambda'$ such that $\sum_{j \neq i} \lambda_j' >
\lambda^*$.
\end{IEEEproof}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,189 |
{"url":"http:\/\/tailieu.vn\/doc\/cau-truc-song-chuc-nang-trong-dien-ly-thuyet-p9-302038.html","text":"# C\u1ea5u tr\u00fac s\u00f3ng ch\u1ee9c n\u0103ng trong \u0111i\u1ec7n l\u00fd thuy\u1ebft P9\n\nChia s\u1ebb: Tien Van Van | Ng\u00e0y: | Lo\u1ea1i File: PDF | S\u1ed1 trang:10\n\n0\n46\nl\u01b0\u1ee3t xem\n11\n\n## C\u1ea5u tr\u00fac s\u00f3ng ch\u1ee9c n\u0103ng trong \u0111i\u1ec7n l\u00fd thuy\u1ebft P9\n\nM\u00f4 t\u1ea3 t\u00e0i li\u1ec7u\nDownload Vui l\u00f2ng t\u1ea3i xu\u1ed1ng \u0111\u1ec3 xem t\u00e0i li\u1ec7u \u0111\u1ea7y \u0111\u1ee7\n\nEM Eigenfrequencies in a Spheroidal Cavity Computation of eigenfrequencies in EM cavities is useful in various applicat ions. However, analytical calculation of these eigenfrequencies is severely limited by the boundary shape of these cavities. In this chapter, the interior boundary value problem in a prolate spheroidal cavity with a perfectly conducting wall and axial symmetry is solved analytically.\n\nCh\u1ee7 \u0111\u1ec1:\n\nB\u00ecnh lu\u1eadn(0)\n\nL\u01b0u\n\n## N\u1ed9i dung Text: C\u1ea5u tr\u00fac s\u00f3ng ch\u1ee9c n\u0103ng trong \u0111i\u1ec7n l\u00fd thuy\u1ebft P9\n\n1. Spheroidal Wave Functions in Electromagnetic Theory Le-Wei Li, Xiao-Kang Kang, Mook-Seng Leong Copyright \uf6d9 2002 John Wiley & Sons, Inc. ISBNs: 0-471-03170-4 (Hardback); 0-471-22157-0 (Electronic) 9 EM Eigenfrequencies in a Spheroidal Cavity 9.1 INTRODUCTION Computation of eigenfrequencies in EM cavities is useful in various applica- t ions. However, analytical calculation of these eigenfrequencies is severely limited by the boundary shape of these cavities. In this chapter, the interior boundary value problem in a prolate spheroidal cavity with a perfectly con- ducting wall and axial symmetry is solved analytically. By applying Maxwell\u2019s equations to the boundary, it is possible to obtain an analytical expression of the eigenfrequency fnSo using spheroidal wave functions regardless of whether the parameter c is small or large. An inspection of the plot of a series of fnSa values (confirmed in [64]) indicates that variation of fnSo with the coordinate parameter < is of the form fn&) = fnS(0)[ 1 + g(l)@ + gt2)\/c4 + gc3)\/t6 + 9 l] when c is small. By l fitting the fnSo, 5 evaluated onto an equation of its derived form, the first four expansion coefficients - g(O), g(l), gc2) and g13) are determined numerically using the least squares method. The method used to obtain these coefficients is direct and simple, although the assumption of axial symmetry may restrict its applications to those eigenfrequencies f72Sml, where m\u2019 = 0. 245\n2. 246 EM EIGENFREQUENCIES IN A SPHEROIDAL CAVITY 9.2 THEORY AND FORMULATION 9.2.1 Background Theory The prolate spheroidal body under consideration is shown in Fig. 9.1. In view of the fact that Mathematics handles only vector differential operations in the prolate spheroidal coordinates in accordance with the notations used in the book by Moon and Spencer [9, pp. 28-291, a temporary change of coordinates is necessarv. The new notation used is shown in Fig. 2.1. a Fig. 9.1 Geometry of the spheroidal cavity. As noted by Moon and Spencer (91,the vector Helmholtz equation is more complicated than the scalar counterpart, and its solution using the variable- separation principle may sometimes cause new problems. This is especially true in rotational systems like that of the spherical coordinates or spheroidal coordinates. In spheroidal coordinates, the solving of vector boundary value problems is further complicated by the fact that the vector wave equation is not exactly separable in spheroidal coordinates. Although another more general analysis has been performed using the vector wave functions, formed by operating on the scalar spheroidal wave functions with vector operators, the validity of the results obtained is doubtful. In view of these limitations,\n3. THEORY AND FORMULATION 247 several assumptions are made in the formulation of the current boundary problem in order to provide a truer, more accurate picture. 9.2.2 Derivation With axial symmetry assumed, it is possible to separate the field components into Et, Eq, and I$for the TM mode and Ht, &, and E4 for the TE mode. First, the TM mode is considered. With axial symmetry, I74 can be as- sumed simply as Hc#l F(c, W(c, 7). = (9 .1) By applying the Maxwell equations dB VxE = ---, (9.2a) dD VxH = dt, (9.2b) and using the formulation of V x X in the spheroidal coordinates where vxx = (9.3) d2K2 - v2) (9.4a) Q77= 4(1 - 72) \u2019 d2(C2 v2) - (9.4b) iI< = 4K2-l) \u2019 94 = %(1 - v2>(C2 - l), (9.4c) the following equations can be obtained: a2;p (C2 _ 1) + ,py - (c2 + amn) - c2tf2 + A] F(c,C) = 0, (9.5a) 1 a2g9q1 _ r72) _ ,py - (c2 + amn) - c2q2 + i-t-;;?] G(c, Q-)= 0. (9.5b) 4. 248 EM NGENFREQUENCIES IN A SPHEROIDAL CAVITY In the case when the semimajor axis of the spheroidal surface is close to the semiminor axis (d = dm 5. NUMERICAL RESULTS FOR TE MODES 249 By principle of duality, the fields components for the TE mode can be obtained by substituting & for H4, -& for Et, and -JY? for E?,, respectively. Hence, the resonance condition for the TE modes can be obtained by setting E+ = 0 at 5 = 50. From Eq. (9.8), the boundary condition requires that &n(c, I(=&)= 0. (9.11) 9.3 NUMERICAL RESULTS FOR TE MODES 9.3.1 Numerical Calculation Using the package created in previous chapters, the zeros of the radial func- tion, as required by the resonance condition in Eq. (9.11) can be found in a straightforward way. This is because coding the radial function into a package offers convenience of treating &,&,(1) {) as if it is normal function like cosine and sine. Hence, the command FindRoot in Mathematics can be employed to solve directly for the zeros of &&, 6. 250 EM NGElVFREQUENClES IN A SPHEROlDAL CAWTY From Eq. (9.12), the following equation relating the eigenfrequency of the spheroidal cavity can be obtained: f ~~0=-&[l+~(~)+~(;?)2+~($)3+-]. (9.13) Thus, by determining the coefficients, gl ,g2,g3, . . ., a closed-form equation for the eigenfrequency of a spheroidal body is obtained. For a given spheroidal dimension expressed in terms of d and &, the eigenfrequency of a spheroidal body can be computed quickly and accurately using Eq. (9.13). Hitherto, the coefficients have been solved only by Kokkorakis [65]. How- ever, only the first two expansion coefficients (91 and 92) of the seriesin (9.12) are given in his work. Moreover, except for the first coefficient g1 which can be obtained directly, the second coefficients can only be obtained by using a relatively complicated equation. Furthermore, the equation is obtained after a very lengthy derivation that spanned over than 50 equations. For the purpose of numerical comparison, a more direct and simpler ap- proach to solving the coefficients is employed in the present work. First, the series of values of g that satisfy the condition R&,c) = 0 over the range of c mentioned earlier are collected and placed in a list. Then, by means of the least squares method, these values of < and { are fitted onto a function of the form given in Eq. (9.12). In this way, the parameters go, gi, g2, g3, . . l , can be determined readily. In Mathematics, this is accomplished simply by two short statement commands. 9.3.2 Results and Comparison The values for the coefficients go, 91, g2, and g3 for the TE modes are calcu- lated and tabulated in Tables 9.1 and 9.2. Kokkorakis solved for the sameset of coefficients in a lengthy and complicated manner. A complete but smaller table has been published in his work [65]. By comparing the present tables and Kokkorakis\u2019s tabulated results, it is observed, first, that the first two coefficients produced with this method agree with Kokkorakis\u2019s evaluations to a minimum of five significant digits. This shows the capability of the method to produce equally accurate results by means of a simpler way. Second, it is almost impossible to produce the coefficients g3, g4, and g5 using Kokkorkis\u2019s method. The amount of analytic computation required using the method makes it impractical. On the other hand, the method presented here can be used to produce these coefficients effortlessly and almost instantly, without sacrificing any accuracy. Finally, in Kokkorakis\u2019s paper [65], it is claimed that the coefficients are valid in the case when c >> 1. However, there is no definite definition of how small < must be for the coefficients to be valid. In this chapter, the valid range of < has been determined, numerically, to be l\/S < 0.01 for rz = 1,2 and l\/c < 0.005\n7. NUMERICAL RESULTS FOR TE MODES 251 Table 9. I Coefficients go, 91, 92, and g3 for TE,,o Modes (s = 1, 2, and 3) n m =1 s=2 s-3 go 1 0 45.493410 7.725252 10.904120 2 0 5.763460 9.095012 12.322940 3 0 6.987932 10.417120 13.698020 4 0 8.182562 11.704910 15.039660 91\/90 1 0 0.400000 0.400000 0.400000 2 0 0.285714 0.285714 0.285714 3 0 0.266667 0.266667 0.266667 4 0 0.259752 0.259752 0.259785 92\/90 1 0 0.318057 0.405000 0.540398 2 0 0.234662 0.330848 0.467022 3 0 0.109708 0.0069634 -0.015400 4 0 0.100111 0.057204 0.001593 9490 1 0 0.000039 0.000049 0.000052 2 0 0.000033 0.000041 0.000065 3 0 0.000005 0.000001 0.000007 4 0 0.000006 0.000008 0.000001 Table 9.2 Coefficients go, 91, 92, and g3 for TE,,o Modes (s = 4, 5, and 6) n m s-4 s-5 s-6 go 1 0 14.066190 17.220750 20.371300 2 0 15.5146000 18.689040 21.853870 3 0 16.923620 20.121810 23.304250 4 0 18.301260 21.525420 24.727570 91\/90 1 0 0.400000 0.400000 0.400000 2 0 0.285729 0.285716 0.285729 3 0 0.266667 0.268331 0.266667 4 0 0.259741 0.259751 0.259764 92\/90 1 0 0.720727 0.945740 1.216530 2 0 0.639935 0.848433 1.098372 3 0 -0.051312 -0.272904 -0.258691 4 0 -0.060967 -0.139916 -0.226860 93\/90 1 0 0.000079 0.000117 0.000117 2 0 0.000090 0.000119 0.000132 3 0 -0.000007 -0.000010 -0.000025 4 0 -0.000008 -0.000006 -0.000031\n8. 252 EM EIGENFREQUENCIES IN A SPHEROIDAL CAVITY for n = 3,4. For other higher-order n, the valid range of < will have to be reduced further. 9.4 NUMERICAL RESULTS FOR TM MODES 9.4.1 Numerical Calculation Closed-form solutions of the eigenfrequencies for TM modes are obtained in a similar fashion. The variation of cc with 5 bears an identical form to the Eq. (9.13); that is, the eigenfrequency for the TM modes can be expressed in a form identical to those shown in (9.13) except that now, go has to be changed to satisfy the equation = \u20183 (9.14) x=go where js(x) represents the spherical Bessel functions. By comparison with the TE modes, two differences need to be considered in the programming aspect. First, the resonance condition has to be altered. Previously, for the TE modes, the condition stated in Eq. (9.11) is satisfied. In the TM modes, the boundary condition requires that Eq. (9.10) be satisfied. At the surface < = 50, the boundary condition becomes (9.15) With the new boundary condition, the zeros of the left-hand term of (9.10) have to be found instead of that of the radial function. In the program, the zeros of the radial derivative expression in Eq. (9.10) are evaluated using the same Newton\u2019s method. However, the function is now different, and so is the initial guess. For the TE modes, the various orders of zeros of the functions in Eq. (9.14) are used instead. 9.4.2 Results and Comparison Employing the same technique to determine the expansion coefficients gi , 92, 93, \u2018..7 a seriesof < values that forces the function in Eq. (9.10) to approach zero is collected and fitted into an equation of the form in Eq. (9.13). In this way, the various expansion coefficients are determined. Tabulations of various values obtained using this method for the TM modes are made and shown in Tables 9.3 and 9.4. The same observation and the same conclusion as for the TE modes can be drawn upon comparing of the two tables for the TM modes with those for the TE modes. Hence, they are not repeated here.\n9. NUMERICAL RESULTS FOR TM MODES 253 Table 9.3 Coefficients go, 91, g2, and g3 for TM,,0 Modes (S = 1, 2, and 3) n m S =l S =2 s=3 go 1 0 2.743707 6.116764 9.316616 2 0 3.870239 7.443087 10.713010 3 0 4.973420 8.721750 12.063590 4 0 6.061949 9.967547 13.380120 91\/90 1 0 0.472361 0.411295 0.404717 2 0 0.317536 0.291498 0.288341 3 0 0.287607 0.270829 0.268664 4 0 0.275250 0.263014 0.261515 92\/90 1 0 0.341865 0.365769 0.473216 2 0 0.241764 0.287367 0.398629 3 0 0.146803 0.094815 0.045170 4 0 0.127803 0.078719 0.002503 93\/m 1 0 0.000047 0.000050 0.000064 2 0 0.000007 0.000039 0.000054 3 0 0.000005 0.000003 0.000001 4 0 0.000017 0.000011 0.000001 Table 9.4 Coefficients go, 91, g2, and g3 for TM,,0 Modes (s = 4, 5, and 6) n m S =4 s=5 S =6 go 1 0 12.485940 15.643870 18.796250 2 0 13.920520 17.102740 20.272000 3 0 15.313560 18.524210 21.713930 4 0 16.674150 19.915400 23.127780 91\/m 1 0 0.402599 0.401648 0.401139 2 0 0.287621 0.286712 0.286420 3 0 0.267865 0.267472 0.267247 4 0 0.260747 0.260430 0.260245 m\/m 1 0 0.629327 0.831403 1.078787 2 0 0.498710 0.741883 0.971928 3 0 -0.015979 -0.090035 -0.177032 4 0 -0.029849 -0.100678 -0.183054 93\/m 1 0 0.000086 0.000113 0.000147 2 0 0.000033 0.000008 0.000076 3 0 0.000002 -0.000012 -0.000024 4 0 -0.000003 -0.000014 -0.000025\n10. 254 EM EIGENFREQUENCIES IN A SPHEROIDAL CAVITY 9.5 DISCUSSION In this chapter, one of the many possible applications of the spheroidal wave function package is presented in detail, (i.e., solving of an interior boundary value problem). The convenience of coding in Mathematics package is man- ifested by the ability of this program to find the zeros of complex functions such as radial functions simply with one statement. This problem, by itself, is a highly interesting topic. Due to the preoccupa- tion with the more important issue of completing the Mathematics package, the axial symmetry is assumed so as to reduce the complexity of the prob- lems. The more general and practical problem in which the assumption of axial symmetry is removed is a topic worth looking into for future investiga- tions. As indicated in previous chapters, the study of oblate spheroidal cavities can be achieved in a similar way or by sypmbolic transfer between the oblate and prolate coordinates. However, it should be noted that the assumed axial symmetry is kept in the z-direction and the assumedfield components are not changed in the symbolic programming.","date":"2017-11-20 00:27:13","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.45542222261428833, \"perplexity\": 707.1775752335133}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-47\/segments\/1510934805881.65\/warc\/CC-MAIN-20171119234824-20171120014824-00043.warc.gz\"}"} | null | null |
\section{Model}
We consider a source producing pairs of monochromatic particles with identical wave number $k_0$. These pairs propagate through a medium containing heterogeneities randomly arranged in space and characterised by a scattering mean free path $\ell$, see fig. \ref{fig:setup}. The medium has length $L$ and cross-section $A$, and is assumed to be connected to perfect leads (not shown in fig. \ref{fig:setup}). In such a geometry the incoming and outgoing wave fronts can be decomposed on a discrete set of $N\simeq k_0^2A$ transverse modes, each of them corresponding to a value of the transverse component of the wave vector compatible with the boundary conditions. The
statistical properties of transport observables are independent of the transverse shape of the medium in the limit $N\gg1$ that we assume from here on. Particles' coincidences between two modes $k\ne k^\prime$ are detected in transmission. Such a single-mode detection setup requires a detector area smaller than the typical size $R^2/N$ of a speckle spot, with $R$ the distance between sample and detector.
To quantify the coincident count statistics, we quantise the field before and after the disordered region, using the basis of the transverse modes \cite{Patra00}, and define the normalised correlation function
\begin{eqnarray}
C = \frac{\ave{:\! \hat{n}_k \hat{n}_{k'}\!\!:}}{\ave{\hat{n}_k} \times \ave{\hat{n}_{k'}}} \label{eq:correlation},
\end{eqnarray}
where $\hat{n}_{k}$ denotes the particle-number operator in the outgoing mode $k$, $\qmave{\ldots}$ the quantum expectation value, $:\,\,:$ the normal ordering of operators, and the overbar the average over a statistical ensemble of disordered samples. Since we are here primarily interested in the quantum statistics of the particles (fermions, bosons or distinguishable particles), we remain general in the following and do not specify how the two-particle state is initially distributed over the incoming modes. In the spirit of \cite{Beenakker09}, we thus write the initial density matrix in the general form
\begin{eqnarray}
\hat{\varrho} = \frac{1}{2}\!\sum_{i,j,i^\prime,j^\prime} \! w_{i j i^\prime j^\prime}\, \hat{a}^{\dagger}_{i} \hat{a}^{\dagger}_{j} \vert 0 \rangle \langle 0 \vert \hat{a}_{i^\prime} \hat{a}_{j^\prime},
\label{eq:stateindist}
\end{eqnarray}
where the operator $\hat{a}^{\dagger}_{i}$ creates a particle in the transverse mode labeled by index $i$, and all sums run from $1$ to $N$. Creation and annihilation operators fulfill the commutation relations $\hat{a}^{\dagger}_{i}\hat{a}^{\dagger}_{j}=\pm\hat{a}_{j}^{\dagger}\hat{a}_i^{\dagger}$, $\hat{a}_{i}\hat{a}_{j}=\pm\hat{a}_{j}\hat{a}_i$ and $\hat{a}^{\dagger}_{i}\hat{a}_{j}=\delta_{ij}\pm\hat{a}_{j}^{\dagger}\hat{a}_i$, with $+$ for bosons and $-$ for fermions. Due to these relations, the tensor $w_{iji^\prime j^\prime}$ can be chosen (anti-) symmetric under the exchange of the first and last two indices for (fermions) bosons. The prefactor $1/2$ in eq. (\ref{eq:stateindist}) guarantees the state normalization, $\text{tr}\hat{\rho}=\sum_{i,j}w_{ijij}=1$.
\begin{figure}
{\includegraphics[scale=1.2]{Setup.eps}}
\caption{A source produces pairs of particles characterised by a two-particle density matrix $\hat{\rho}$. These pairs are scattered from a disordered medium with length $L$, mean free path $\ell$, and supporting $N$ transverse modes. The coincidence rate between two outgoing modes $k$ and $k^\prime$ is analysed in transmission.
\label{fig:setup}}
\end{figure}
From the initial density matrix $\hat{\rho}$, the mean particle number in some outgoing mode $k$ is defined as
\begin{equation}
\qmave{\hat{n}_k}=\text{tr}[\hat{\rho}\,\hat{c}_k^\dagger(\underline{a}^\dagger)\hat{c}_k(\underline{a})],
\label{eq:state}
\end{equation}
where $\hat{c}_k(\underline{a})=\sum_i t_{ki}\hat{a}_i$ and $\hat{c}^\dagger_k(\underline{a}^\dagger)=\sum_i t_{ki}^*\hat{a}_i^\dagger$ are the input-output relations connecting the annihilation (creation) operator $\hat{c}_k$ ($\hat{c}_k^\dagger$) of the outgoing mode $k$ to the set of operators $\hat{a}_i$ ($\hat{a}_i^\dagger$) of the incoming modes $i$ through the (random) transmission matrix $t$ of the disordered medium. Substituting these relations into eq. (\ref{eq:state}), we readily obtain
\begin{equation}
\qmave{\hat{n}_k}=2\sum_{i,j,i^\prime}w_{iji^\prime j}t_{ki}t^*_{ki^\prime}.
\label{eq:nk}
\end{equation}
Similarly, from the definition
\begin{equation}
\qmave{:\!\hat{n}_k\hat{n}_{k^\prime}\!\!:}=\text{tr}[\hat{\rho}\,\hat{c}_k^\dagger(\underline{a}^\dagger)\hat{c}_{k^\prime}^\dagger(\underline{a}^\dagger)\hat{c}_k(\underline{a})\hat{c}_{k^\prime}(\underline{a})]
\label{state}
\end{equation}
of the particle-number correlation, we obtain
\begin{equation}
\qmave{:\!\hat{n}_k\hat{n}_{k^\prime}\!\!:}=2\!\sum_{i,j,i^\prime,j^\prime}w_{iji^\prime j^\prime}t_{ki}t^*_{k^\prime j}t^*_{ki^\prime}t_{k^\prime j^\prime}.
\label{eq:nknkp}
\end{equation}
Note that at this stage eqs. (\ref{eq:nk}) and (\ref{eq:nknkp}) hold for fermions \emph{and} bosons, provided the tensor $w_{iji^\prime j^\prime}$ is properly (anti-) symmetrised.
The next step in the derivation of the correlation function (\ref{eq:correlation}) consists in performing the ensemble averages. In eqs. (\ref{eq:nk}) and (\ref{eq:nknkp}), statistical properties of the disordered medium are encoded in the transmission matrix elements $t_{ki}$. In the limit $N\ell/L\equiv g\gg1$, which corresponds to a regime where particles are multiply scattered according to a diffusion process, these elements are normally distributed over the unitary group \cite{Beenakker97}. This property was notably used in \cite{Beenakker09} to calculate the statistical distribution of $\qmave{:\!\hat{n}_k\hat{n}_{k^\prime}\!\!:}$ for photons.
Here however, we aim at studying the behaviour of $C$ for \emph{arbitrary} values of the parameter $g$. For this purpose we make use of the unitarity and symmetry of the transmission matrix, which allows us to employ the polar decomposition \cite{Beenakker97, Mello88}
\begin{eqnarray}
t_{k i} = \sum_{a } u_{k a} \sqrt{\tau_a} v_{a i},
\label{eq:polard}
\end{eqnarray}
where $u$ and $v$ are random unitary matrices and $\tau_1, \dots, \tau_N$ are the eigenvalues of $t$.
Eq. (\ref{eq:polard}) is at the basis of the macroscopic description of disordered media \cite{Beenakker97}. Physically, the matrix $v$ first distributes a field amplitude incident in mode $i$ among the \emph{scattering channels} of the medium, each having its transmission coefficient $\tau_a$ (between 0 and 1). The matrix $u$ finally recombines the transmitted field amplitudes in the outgoing mode $k$.
For a medium with length much larger than its width, i.e in the limit $L\gg\sqrt{A}$, ensemble averaging can be carried out in two steps: first over the matrices $u$ and $v$, which are uniformly distributed over the unitary group (isotropy assumption), and second over the eigenvalues $\tau_1, \dots, \tau_N$, whose joint distribution follows the so-called DMPK equation \cite{Mello88}. Substituting the decomposition (\ref{eq:polard}) into eqs. (\ref{eq:nk}) and (\ref{eq:nknkp}), and performing the average over unitary matrices, we obtain
\begin{eqnarray}
C = \frac{1}{2} \frac{\sum_{a,b}\overline{ \tau_a\tau_b}\pm\sum_a\overline{\tau_a^2}}{\left(\sum_a\overline{\tau_a}\right)^2},
\label{eq:correlationfb}
\end{eqnarray}
where the positive sign refers to bosons and the negative sign to fermions. Eq. (\ref{eq:correlationfb}) is the first important result of this Letter. It shows that, when $L\gg\sqrt{A}$, the correlation function $C$ is independent of how the incident state is distributed over the incident modes of the disordered medium, and only depends on the statistical correlations between scattering channels \cite{Beenakker09}. This property originates from the fact that when deriving eq. (\ref{eq:correlationfb}), we assumed each field amplitude
incoming in a given mode to be equally distributed among the scattering channels of the medium (isotropy assumption). Another important comment concerns the prefactor $1/2$ in eq. (\ref{eq:correlationfb}), also found in \cite{Ott10, Cherroret11}. For the particular case of a two-photon Fock state with Fano factor $F=0$, this prefactor was shown to express itself as $1+(F-1)/2$ \cite{Smolka09}. Its value $1/2<1$ therefore signals the sub-Poissonian statistics, here of an arbitrary incident two-particle state.
We now comment on the structure of the mean correlation [numerator of eq. (\ref{eq:correlationfb})]. The latter consists of two terms. The first one, $\sum_{a,b}\overline{ \tau_a\tau_b}$, corresponds to the sum of all possible correlations between scattering channels. The second one, $\pm\sum_{a}\overline{\tau_a^2}$, corresponds to the sum of all possible autocorrelations of scattering channels and is affected by the specific statistics of quantum particles: fermions cannot both propagate in the same channel, therefore this sum appears with a minus sign, and cancels the autocorrelation contributions in the first term (anti-bunching effect). On the other hand, bosons tend to bunch in the scattering channels, as manifested by the positive sign in front of the second term. These bunching and anti-bunching effects
have important consequences on the magnitude of the correlation function $C$, as we now show.
\section{Numerics for bosons and fermions}
Eq. (\ref{eq:correlationfb}) is valid for any value of the parameter $g=N\ell/L$, provided $L\gg\sqrt{A}$. In order to clarify how bunching and anti-bunching effects would show up concretely in an experiment accessing the correlation function (\ref{eq:correlation}), we evaluated $C$ numerically as a function of $L/\ell$, for a fixed number of modes, $N =10$. For this purpose we computed each of the averages $\sum_a\overline{\tau_a^2}$, $\sum_{a,b}\overline{ \tau_a\tau_b}$ and $\sum_a\overline{\tau_a}$ from the DMPK equation, by means of a Markov chain Monte Carlo approach \cite{Krauth06}. Such a numerical procedure was already used in the context of the conductance distribution of metallic conductors \cite{Froufe02} and of intensity correlations of classical light in disordered media \cite{Cwilich06}.
\begin{figure}[h]
{\includegraphics[scale=0.86]{Ind_part.eps}}
\caption{Correlation function (\ref{eq:correlationfb}) for bosons (dots, blue online) and fermions (squares, red online), plotted as functions of $L/\ell$, for $N=10$. Diamonds (orange online) are the contribution $\sum_a\overline{\tau_a^2}/\sum_a\overline{\tau_a}^2$ to $C^\text{bosons}$. Dashed horizontal lines are the analytical prediction (\ref{eq:ballistic}), and dashed curves are given by eqs. (\ref{eq:locb}) and (\ref{eq:locf}). Vertical dotted lines indicate the crossovers $L\sim\ell$ and $L\sim N\ell$ from ballistic to diffusion and from diffusion to localisation, respectively.
\label{fig:ind_part}}
\end{figure}
At fixed $N$, the study of $C$ as a function of $L/\ell$ allows us to probe all possible regimes of transport in the disorder, from quasi-ballistic ($L\lesssim\ell$) to diffusive propagation ($\ell\ll L\ll N\ell$) and eventually Anderson localisation ($L\gg N\ell$). The results can be seen in fig. \ref{fig:ind_part}, for bosons (dots, blue online) and fermions (squares, red online). In the quasi-ballistic and diffusive regimes, $C$ is very close to $1/2$ for bosons and fermions, i.e. the correlation is hardly sensitive to the quantum statistics of the particles (the small difference observed in fig. \ref{fig:ind_part} is discussed in the next section). This picture dramatically changes as $L$ increases, at the onset of localisation ($L\sim N\ell$): the bosonic correlation function starts growing, while the fermionic counterpart decreases. Far in the localisation regime ($L\gg N\ell$), $C\gg1$ for bosons and $C\ll1$ for fermions. These radically different behaviours can be interpreted in the framework of the theory of active transmission channels \cite{Imry86, Stone91} by rewriting eq. (\ref{eq:correlationfb}) as $C^\text{bosons}= (1/2)\times\left(\sum_{a\ne b}\overline{ \tau_a\tau_b}+2\sum_a\overline{\tau_a^2}\right)/\left(\sum_a\overline{\tau_a}\right)^2$ and $C^\text{fermions}= (1/2)\times\left(\sum_{a\ne b}\overline{ \tau_a\tau_b}\right)/\left(\sum_a\overline{\tau_a}\right)^2$. As the length $L$ increases, more and more scattering channels become closed, $i.e.$ their transmission coefficient becomes exponentially small. Eventually, in the localisation regime, only one channel $a_0$ retains a fairly large transmission coefficient. In this limit, we thus have $\left(\sum_a\overline{\tau_a}\right)^2\simeq \overline{\tau_{a_0}}^2$, $\sum_a\overline{\tau_a^2}\simeq \overline{\tau_{a_0}^2}$ and $\sum_{a\ne b}\overline{ \tau_a\tau_b}\simeq \overline{ \tau_{a_0}\tau_{b_0}}$, where $b_0$ denotes a closed channel. Since the correlation between a closed and the open channel is typically very small compared to $\overline{\tau_{a_0}}^2$, we have $C^\text{fermions}\ll 1$. On the other hand, we have also $\overline{\tau_{a_0}\tau_{b_0}}\ll \overline{\tau_{a_0}^2}$, such that $C^\text{bosons}\simeq(1/2)\times\overline{\tau_{a_0}^2}/\overline{\tau_{a_0}}^2$. This ratio is very large because transmission fluctuations well exceed the mean transmission in the localisation regime \cite{Beenakker97}. To get a better picture of the weight of each term appearing in $C^\text{bosons}$ and $C^\text{fermions}$, in the different regimes of transport, we also show in fig. \ref{fig:ind_part} the contribution of channel autocorrelations to $C^\text{bosons}$, $\sum_a\overline{\tau_a^2}/\sum_a\overline{\tau_a}^2$ (diamonds, orange online).
It is instructive to compare the results in fig. \ref{fig:ind_part} for bosons (dots) with those obtained by Ott \emph{et al.}, fig. 4 of Ref. \cite{Ott10}, for the particular case of a two-photon Fock state. Our correlation function is insensitive to the form of the incident state, unlike in \cite{Ott10}, where the correlation function is constant for two photons incident in the same mode whereas it increases and saturates for two photons incident in two different modes. This difference relies on the different quantity appearing in the denominator of the correlation function of \cite{Ott10}, $\overline{\qmave{n_k}\qmave{n_k^\prime}}$, instead of $\overline{\qmave{n_k}}\times\overline{\qmave{n_k^\prime}}$ in our case, eq. (\ref{eq:correlation}).
\section{Analytical results}
In order to support our numerical observations, we now calculate explicitly $C$ in the quasi-ballistic, diffusive and localisation regimes. First, when $L\lesssim\ell$, we have $\tau_a\simeq1\, \forall a$, such that
\begin{equation}
C\simeq\frac{1}{2} \frac{N^2\pm N}{N^2}=\frac{1}{2}\left(1\pm\frac{1}{N}\right).
\label{eq:ballistic}
\end{equation}
Eq. (\ref{eq:ballistic}) is shown in fig. \ref{fig:ind_part} for bosons ($+$) and fermions ($-$) as dashed horizontal lines. The $1/N$ difference between the two types of particles is visible in the figure since we considered a finite value of $N$ for the numerics. In practice however, $N\gg1$ and this difference is negligible.
In the diffusive regime $\ell\ll L\ll N\ell$, averages over transmission eigenvalues can be evaluated by making use of the method of moments introduced in \cite{Mello91}. The result is a perturbation expansion of $C$ in powers of the parameter $1/g=L/(N\ell)\ll1$:
\begin{eqnarray}
C= \frac{1}{2} \left[1\pm\frac{2}{3g}+\mathcal{O} \left(\frac{1}{g^2}\right)\right].
\label{eq:diffusive}
\end{eqnarray}
In the regime of diffusive transport, bosonic bunching ($+$) and fermionic anti-bunching ($-$) in the scattering channels are thus visible, but remain small as long as $g\gg1$.
Finally, far in the localisation regime $L\gg N\ell$, $C$ can be calculated from the probability distribution of the transmission eigenvalues \cite{Beenakker97}. A straightforward calculation then yields:
\begin{eqnarray}
C^\text{bosons} = \frac{1}{3} \sqrt{\frac{\pi L}{2\xi}} \exp \left( \frac{L}{2 \xi} \right), \label{eq:locb}\\
C^\text{fermions} = \frac{1}{2} \sqrt{\frac{\pi L}{2 \xi}} \exp \left( - \frac{3 L}{2\xi} \right), \label{eq:locf}
\end{eqnarray}
where we have explicitly introduced the localisation length $\xi=N\ell$. Eqs. (\ref{eq:locb}) and (\ref{eq:locf}) are consistent with the discussion above, namely $C^\text{fermions}\ll1\ll C^\text{bosons}$. Analytical predictions (\ref{eq:locb}) and (\ref{eq:locf}) are shown in fig. \ref{fig:ind_part} as dashed curves, and agree well with our Monte Carlo simulations.
\section{Distinguishable particles}
To complete our discussion, we finally consider the scattering problem of a pair of \emph{distinguishable} particles. For this purpose, we equip them with an additional spin degree of freedom, indicated by the symbols $\uparrow$ and $\downarrow$. With this strategy, we consider an incident state of the form
\begin{eqnarray}
\hat{\rho} =\sum_{i,j,i^\prime,j^\prime} \! w_{i j i^\prime j^\prime}\, \hat{a}^{\dagger}_{i\uparrow} \hat{a}^{\dagger}_{j\downarrow} \vert 0 \rangle \langle 0 \vert \hat{a}_{i^\prime\uparrow} \hat{a}_{j^\prime\downarrow}.
\label{eq:statedist}
\end{eqnarray}
In comparison with eq. (\ref{eq:stateindist}), note the missing prefactor $1/2$. This originates from the new commutation relation involving the two particles which have now different spins, $\hat{a}_{k\uparrow}\hat{a}_{k\downarrow}^\dagger=\hat{a}_{k\downarrow}^\dagger\hat{a}_{k\uparrow}$. Normalization of the state ($\ref{eq:statedist}$) again reads $\text{tr}\hat{\rho}=\sum_{i,j}w_{ijij}=1$.
The formalism developed above for indistinguishable particles remains essentially the same for distinguishable particles, but care has to be taken in defining the particle-number and correlation operators. Indeed, since one detects particles on output of the medium irrespective of their spin, these operators must now be symmetrised with respect to the two particles, i.e
\begin{equation}
\hat{n}_k=\hat{c}_{k\uparrow}^\dagger\hat{c}_{k\uparrow}+\hat{c}_{k\downarrow}^\dagger\hat{c}_{k\downarrow}
\end{equation}
for the correlation operator in the outgoing mode $k$, and
\begin{equation}
:\!\hat{n}_k\hat{n}_{k^\prime}\!\!:=\hat{c}_{k\uparrow}^\dagger\hat{c}_{k^\prime\downarrow}^\dagger\hat{c}_{k\uparrow}\hat{c}_{k^\prime\downarrow}+
\hat{c}_{k\downarrow}^\dagger\hat{c}_{k^\prime\uparrow}^\dagger\hat{c}_{k\downarrow}\hat{c}_{k^\prime\uparrow}.
\end{equation}
for the coincidence rate operator between the outgoing modes $k$ and $k^\prime$. The input-output relations now read $\hat{c}_{k\uparrow(\downarrow)}=\sum_i t_{ki}^{\uparrow(\downarrow)}\hat{a}_{i\uparrow(\downarrow)}$ and $\hat{c}^\dagger_{k\uparrow(\downarrow)}=\sum_i t_{ki}^{*\uparrow(\downarrow)}\hat{a}_{i\uparrow(\downarrow)}^\dagger$ (note the spin labeling also in the transmission matrix elements). Quantum expectation values for $\hat{n}_k$ and $:\!\hat{n}_k\hat{n}_{k^\prime}\!\!:$ are now given by
\begin{equation}
\qmave{\hat{n}_k}=\sum_{iji^\prime}w_{iji^\prime j} t_{ki}^{\uparrow}t_{ki^\prime}^{*\uparrow}+
\sum_{ijj^\prime}w_{ijij^\prime} t_{kj}^{\downarrow}t_{kj^\prime}^{*\downarrow},
\label{eq:nk_d}
\end{equation}
and
\begin{equation}
\qmave{:\!\hat{n}_k\hat{n}_{k^\prime}\!\!:}=\sum_{iji^\prime i^\prime}w_{iji^\prime j^\prime}
\left(t_{ki}^{\uparrow}t_{ki^\prime}^{*\uparrow}
t_{k^\prime j}^{\downarrow}t_{k^\prime j^\prime}^{*\downarrow}+
t_{k^\prime i}^{\uparrow}t_{k^\prime i^\prime}^{*\uparrow}
t_{k j}^{\downarrow}t_{k j^\prime}^{*\downarrow}
\right).
\label{eq:nknkp_d}
\end{equation}
Note that in eq. (\ref{eq:nk_d}), the first (second) term on the right-hand side is nothing but the contribution of the particle with spin up (down) to the detected mean particle number in mode $k$. Similarly, the two terms on the right-hand side of eq. (\ref{eq:nknkp_d}) correspond to the two possible coincidence events, i.e. particle with spin up detected in mode $k$ and particle with spin down detected in mode $k^\prime$ for the first term, and vice versa for the second one. Finally, we again decompose transmission coefficients according to $t_{k i}^{\uparrow(\downarrow)} = \sum_{a = 1}^N u_{k a}^{\uparrow(\downarrow)} \sqrt{\tau_a} v_{a i}^{\uparrow(\downarrow)}$ and carry out the averages over the matrices $u^{\uparrow,\downarrow}$ and $v^{\uparrow,\downarrow}$. This yields:
\begin{eqnarray}
C^\text{disting} = \frac{1}{2} \frac{\sum_{a,b}\overline{ \tau_a\tau_b}}{\left(\sum_a\overline{\tau_a}\right)^2}.
\label{eq:correlationd}
\end{eqnarray}
Comparing with eq. (\ref{eq:correlationfb}), we see that the bunching/anti-bunching term has disappeared for distinguishable particles, as expected. We computed $C^\text{disting}$ numerically, using the same Monte Carlo approach as above to carry out the remaining averages over transmission eigenvalues. The results are shown in fig. \ref{fig:Cdist} as a function of $L/\ell$ (triangles, green online). For comparison we also show $C^\text{bosons}$ (dots, blue online).
\begin{figure}
{\includegraphics[scale=0.85]{Disting_part.eps}}
\caption{Correlation function for bosons (dots, blue online) and distinguishable particles (triangles, green online), plotted as functions of $L/\ell$ for $N=10$. The upper and lower dashed curves are the analytical predictions (\ref{eq:locb}) and (\ref{eq:correlationd}) respectively, and the vertical dotted line indicates the crossover $L\sim N\ell$ from diffusion to localisation.
\label{fig:Cdist}}
\end{figure}
As for bosons, the correlation function of distinguishable particles increases with $L/\ell$. This is expected since at the onset of localisation, one scattering channel $a_0$ dominates transport and $\sum_{a,b}\overline{\tau_a\tau_b}\simeq\overline{\tau_{a_0}^2}\gg(\sum_{a}\overline{\tau_a})^2\simeq\overline{\tau_{a_0}}^2$. Again, simple analytical results can be obtained in the quasi-ballistic regime of transport, where $C^\text{disting}=1/2$, and in the diffusion regime, where $C^\text{disting}=(1/2)\times\left[1+2/(15g^2)+\mathcal{O}(1/g^3)\right]$. On the other hand, far in the localisation regime we find
\begin{equation}
C^\text{disting}=\dfrac{1}{6}\sqrt{\dfrac{\pi L}{2\xi}}\exp\left(\dfrac{L}{2\xi}\right).
\end{equation}
This result is shown in fig. \ref{fig:Cdist} (lower dashed curve), and agrees well with the numerical calculations. It also confirms that the bunching effect of bosons is only fully visible in the localisation regime where
\begin{equation}
\frac{C^\text{bosons}}{C^\text{disting}} \stackrel{L \gg N\ell}{\longrightarrow} \; 2,
\label{eq:bunching}
\end{equation}
as also demonstrated by the numerical points in fig. \ref{fig:Cdist}.
\section{Conclusion} We have shown that particle-number correlations measured on output of a disordered medium are extremely sensitive to the quantum statistics of localised particles. This phenomenon reflects the bosonic bunching and fermionic anti-bunching in the scattering channels of the medium. An interesting extension of this work would be to analyse the scattering problem of many-particle quantum states.
\acknowledgments
We thank M. C. Tichy for useful discussions and S. E. Skipetrov for his comments on the manuscript. N. C. acknowledges financial support from the Alexander von Humboldt Foundation.
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{"url":"https:\/\/linearalgebras.com\/tag\/matrix-ring","text":"If you find any mistakes, please make a comment! Thank you.\n\n## Characterize the ideals consisting of all matrices with a single nonzero column\n\nSolution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.1 Solution: In Exercise 7.2.6, we saw that $AE_{i,j}$ is the matrix whose j-th column is the\u2026\n\n## In a noncommutative ring, the set of nilpotent elements need not be an ideal\n\nSolution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.31 Solution: We begin with a lemma. Lemma: Let $R$ be a ring with $1 \\neq 0$.\u2026\n\n## Characterize the two-sided ideals of a matrix ring\n\nSolution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.21 Solution: First, let $I \\subseteq M_n(R)$ be a two-sided ideal. Let $J \\subseteq R$ consist of\u2026\n\n## Embed a ring of quadratic integers in a ring of matrices\n\nSolution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.12 Solution: We begin with a lemma. Lemma: If $D \\in \\mathbb{Z}$ is not a perfect square,\u2026","date":"2023-02-09 06:30:17","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.687234103679657, \"perplexity\": 189.79239929142412}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764501407.6\/warc\/CC-MAIN-20230209045525-20230209075525-00859.warc.gz\"}"} | null | null |
Q: libtool slowing down gdb I have a larger C++ programm with lot of templates which i want to debug. Unfortunately gdb takes several minutes to read the symbols.
http://gcc.gnu.org/onlinedocs/gcc/Debugging-Options.html contains lots of options for debugging.
Which options would you suggest to make gdb faster/more usable.
Update: It looks like the slow down is caused by libtool. If gdb is launched via libtool --mode execute it is slow. If gdb is launched gdb .libs/foo it is reasonable fast. Any ideas why is much slower?
Update: Another suggestion was -fvisibility=hidden see http://gcc.gnu.org/wiki/Visibility
A: Sometimes using -fdebug-types-section can make things a bit faster. It isn't guaranteed though.
Several minutes to load ... I wonder how big this executable is. If I were desperate I might try only compiling selected modules with debug info. Or perhaps look to see if it is a gdb bug. If it is split into an executable and some shared libraries, and some parts don't change very often, you could also look into using the "gdb index" feature (see the manual) to speed up the loading of debuginfo for those modules.
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{"url":"http:\/\/www.maplesoft.com\/support\/help\/Maple\/view.aspx?path=Task\/DefIntegralMultivariateFcn","text":"Definite Integral of a Multivariate Function - Maple Programming Help\n\n# Online Help\n\n###### All Products\u00a0\u00a0\u00a0 Maple\u00a0\u00a0\u00a0 MapleSim\n\nHome : Support : Online Help : Tasks : Calculus - Multivariate : Integration : Task\/DefIntegralMultivariateFcn\n\nDefinite Integral of a Multivariate Function\n\n Description Calculate the definite integral\u00a0of a multivariate function.\n\nEnter the function as an expression.\n\n > ${3}{}{+}{}{x}{}{y}{}{+}{}{2}{}{\\mathrm{sin}}\\left({y}\\right){}{\\mathrm{cos}}{\\left({y}\\right)}^{{2}}{}$\n ${3}{+}{x}{}{y}{+}{2}{}{\\mathrm{sin}}{}\\left({y}\\right){}{{\\mathrm{cos}}{}\\left({y}\\right)}^{{2}}$ (1)\n\nSpecify the ranges of integration, and then calculate the definite integral of the function.\n\n >\n ${24}{}{\\mathrm{\u03c0}}$ (2)\n Commands Used\n See Also\n\n## Was this information helpful?\n\n Please add your Comment (Optional) E-mail Address (Optional) What is ? This question helps us to combat spam","date":"2016-12-11 06:04:17","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 3, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9914237260818481, \"perplexity\": 3561.3195735116788}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-50\/segments\/1480698544140.93\/warc\/CC-MAIN-20161202170904-00378-ip-10-31-129-80.ec2.internal.warc.gz\"}"} | null | null |
{"url":"http:\/\/en.wikipedia.org\/wiki\/Canonical_correlation","text":"Canonical correlation\n\nIn statistics, canonical-correlation analysis (CCA) is a way of making sense of cross-covariance matrices. If we have two vectors X = (X1, ..., Xn) and Y = (Y1, ..., Ym) of random variables, and there are correlations among the variables, then canonical-correlation analysis will find linear combinations of the Xi and Yj which have maximum correlation with each other.[1] T. R. Knapp notes \"virtually all of the commonly encountered parametric tests of significance can be treated as special cases of canonical-correlation analysis, which is the general procedure for investigating the relationships between two sets of variables.\"[2] The method was first introduced by Harold Hotelling in 1936.[3]\n\nDefinition\n\nGiven two column vectors $X = (x_1, \\dots, x_n)'$ and $Y = (y_1, \\dots, y_m)'$ of random variables with finite second moments, one may define the cross-covariance $\\Sigma _{XY} = \\operatorname{cov}(X, Y)$ to be the $n \\times m$ matrix whose $(i, j)$ entry is the covariance $\\operatorname{cov}(x_i, y_j)$. In practice, we would estimate the covariance matrix based on sampled data from $X$ and $Y$ (i.e. from a pair of data matrices).\n\nCanonical-correlation analysis seeks vectors $a$ and $b$ such that the random variables $a' X$ and $b' Y$ maximize the correlation $\\rho = \\operatorname{corr}(a' X, b' Y)$. The random variables $U = a' X$ and $V = b' Y$ are the first pair of canonical variables. Then one seeks vectors maximizing the same correlation subject to the constraint that they are to be uncorrelated with the first pair of canonical variables; this gives the second pair of canonical variables. This procedure may be continued up to $\\min\\{m,n\\}$ times.\n\nComputation\n\nDerivation\n\nLet $\\Sigma _{XX} = \\operatorname{cov}(X, X)$ and $\\Sigma _{YY} = \\operatorname{cov}(Y, Y)$. The parameter to maximize is\n\n$\\rho = \\frac{a' \\Sigma _{XY} b}{\\sqrt{a' \\Sigma _{XX} a} \\sqrt{b' \\Sigma _{YY} b}}.$\n\nThe first step is to define a change of basis and define\n\n$c = \\Sigma _{XX} ^{1\/2} a,$\n$d = \\Sigma _{YY} ^{1\/2} b.$\n\nAnd thus we have\n\n$\\rho = \\frac{c' \\Sigma _{XX} ^{-1\/2} \\Sigma _{XY} \\Sigma _{YY} ^{-1\/2} d}{\\sqrt{c' c} \\sqrt{d' d}}.$\n\nBy the Cauchy-Schwarz inequality, we have\n\n$\\left(c' \\Sigma _{XX} ^{-1\/2} \\Sigma _{XY} \\Sigma _{YY} ^{-1\/2} \\right) d \\leq \\left(c' \\Sigma _{XX} ^{-1\/2} \\Sigma _{XY} \\Sigma _{YY} ^{-1\/2} \\Sigma _{YY} ^{-1\/2} \\Sigma _{YX} \\Sigma _{XX} ^{-1\/2} c \\right)^{1\/2} \\left(d' d \\right)^{1\/2},$\n$\\rho \\leq \\frac{\\left(c' \\Sigma _{XX} ^{-1\/2} \\Sigma _{XY} \\Sigma _{YY} ^{-1} \\Sigma _{YX} \\Sigma _{XX} ^{-1\/2} c \\right)^{1\/2}}{\\left(c' c \\right)^{1\/2}}.$\n\nThere is equality if the vectors $d$ and $\\Sigma _{YY} ^{-1\/2} \\Sigma _{YX} \\Sigma _{XX} ^{-1\/2} c$ are collinear. In addition, the maximum of correlation is attained if $c$ is the eigenvector with the maximum eigenvalue for the matrix $\\Sigma _{XX} ^{-1\/2} \\Sigma _{XY} \\Sigma _{YY} ^{-1} \\Sigma _{YX} \\Sigma _{XX} ^{-1\/2}$ (see Rayleigh quotient). The subsequent pairs are found by using eigenvalues of decreasing magnitudes. Orthogonality is guaranteed by the symmetry of the correlation matrices.\n\nSolution\n\nThe solution is therefore:\n\n\u2022 $c$ is an eigenvector of $\\Sigma _{XX} ^{-1\/2} \\Sigma _{XY} \\Sigma _{YY} ^{-1} \\Sigma _{YX} \\Sigma _{XX} ^{-1\/2}$\n\u2022 $d$ is proportional to $\\Sigma _{YY} ^{-1\/2} \\Sigma _{YX} \\Sigma _{XX} ^{-1\/2} c$\n\nReciprocally, there is also:\n\n\u2022 $d$ is an eigenvector of $\\Sigma _{YY} ^{-1\/2} \\Sigma _{YX} \\Sigma _{XX} ^{-1} \\Sigma _{XY} \\Sigma _{YY} ^{-1\/2}$\n\u2022 $c$ is proportional to $\\Sigma _{XX} ^{-1\/2} \\Sigma _{XY} \\Sigma _{YY} ^{-1\/2} d$\n\nReversing the change of coordinates, we have that\n\n\u2022 $a$ is an eigenvector of $\\Sigma _{XX} ^{-1} \\Sigma _{XY} \\Sigma _{YY} ^{-1} \\Sigma _{YX}$\n\u2022 $b$ is an eigenvector of $\\Sigma _{YY} ^{-1} \\Sigma _{YX} \\Sigma _{XX} ^{-1} \\Sigma _{XY}$\n\u2022 $a$ is proportional to $\\Sigma _{XX} ^{-1} \\Sigma _{XY} b$\n\u2022 $b$ is proportional to $\\Sigma _{YY} ^{-1} \\Sigma _{YX} a$\n\nThe canonical variables are defined by:\n\n$U = c' \\Sigma _{XX} ^{-1\/2} X = a' X$\n$V = d' \\Sigma _{YY} ^{-1\/2} Y = b' Y$\n\nImplementation\n\nCCA can be computed using singular value decomposition on a correlation matrix.[4] It is available as a function in[5]\n\nHypothesis testing\n\nEach row can be tested for significance with the following method. Since the correlations are sorted, saying that row $i$ is zero implies all further correlations are also zero. If we have $p$ independent observations in a sample and $\\widehat{\\rho}_i$ is the estimated correlation for $i = 1,\\dots, \\min\\{m,n\\}$. For the $i$th row, the test statistic is:\n\n$\\chi ^2 = - \\left( p - 1 - \\frac{1}{2}(m + n + 1)\\right) \\ln \\prod _ {j = i} ^{\\min\\{m,n\\}} (1 - \\widehat{\\rho}_j^2),$\n\nwhich is asymptotically distributed as a chi-squared with $(m - i + 1)(n - i + 1)$ degrees of freedom for large $p$.[6] Since all the correlations from $\\min\\{m,n\\}$ to $p$ are logically zero (and estimated that way also) the product for the terms after this point is irrelevant.\n\nPractical uses\n\nA typical use for canonical correlation in the experimental context is to take two sets of variables and see what is common amongst the two sets. For example in psychological testing, you could take two well established multidimensional personality tests such as the Minnesota Multiphasic Personality Inventory (MMPI-2) and the NEO. By seeing how the MMPI-2 factors relate to the NEO factors, you could gain insight into what dimensions were common between the tests and how much variance was shared. For example you might find that an extraversion or neuroticism dimension accounted for a substantial amount of shared variance between the two tests.\n\nOne can also use canonical-correlation analysis to produce a model equation which relates two sets of variables, for example a set of performance measures and a set of explanatory variables, or a set of outputs and set of inputs. Constraint restrictions can be imposed on such a model to ensure it reflects theoretical requirements or intuitively obvious conditions. This type of model is known as a maximum correlation model.[7]\n\nVisualization of the results of canonical correlation is usually through bar plots of the coefficients of the two sets of variables for the pairs of canonical variates showing significant correlation. Some authors suggest that they are best visualized by plotting them as heliographs, a circular format with ray like bars, with each half representing the two sets of variables.[8]\n\nExamples\n\nLet $X = x_1$ with zero expected value, i.e., $\\operatorname{E}(X)=0$. If $Y = X$, i.e., $X$ and $Y$ are perfectly correlated, then, e.g., $a=1$ and $b=1$, so that the first (and only in this example) pair of canonical variables is $U = X$ and $V = Y =X$. If $Y = -X$, i.e., $X$ and $Y$ are perfectly anticorrelated, then, e.g., $a=1$ and $b=-1$, so that the first (and only in this example) pair of canonical variables is $U = X$ and $V = -Y =X$. We notice that in both cases $U =V$, which illustrates that the canonical-correlation analysis treats correlated and anticorrelated variables similarly.\n\nConnection to principal angles\n\nAssuming that $X = (x_1, \\dots, x_n)'$ and $Y = (y_1, \\dots, y_m)'$ have zero expected values, i.e., $\\operatorname{E}(X)=\\operatorname{E}(Y)=0$, their covariance matrices $\\Sigma _{XX} =\\operatorname{Cov}(X,X) = \\operatorname{E}[X X']$ and $\\Sigma _{YY} =\\operatorname{Cov}(Y,Y) = \\operatorname{E}[Y Y']$ can be viewed as Gram matrices in an inner product for the entries of $X$ and $Y$, correspondingly. In this interpretation, the random variables, entries $x_i$ of $X$ and $y_j$ of $Y$ are treated as elements of a vector space with an inner product given by the covariance $\\operatorname{cov}(x_i, y_j)$, see Covariance#Relationship_to_inner_products.\n\nThe definition of the canonical variables $U$ and $V$ is then equivalent to the definition of principal vectors for the pair of subspaces spanned by the entries of $X$ and $Y$ with respect to this inner product. The canonical correlations $\\operatorname{corr}(U,V)$ is equal to the cosine of principal angles.\n\nReferences\n\n1. ^ H\u00e4rdle, Wolfgang; Simar, L\u00e9opold (2007). \"Canonical Correlation Analysis\". Applied Multivariate Statistical Analysis. pp.\u00a0321\u2013330. doi:10.1007\/978-3-540-72244-1_14. ISBN\u00a0978-3-540-72243-4. edit\n2. ^ Knapp, T. R. (1978). \"Canonical correlation analysis: A general parametric significance-testing system\". Psychological Bulletin 85 (2): 410\u2013416. doi:10.1037\/0033-2909.85.2.410. edit\n3. ^ Hotelling, H. (1936). \"Relations Between Two Sets of Variates\". Biometrika 28 (3\u20134): 321\u2013377. doi:10.1093\/biomet\/28.3-4.321. JSTOR\u00a02333955. edit\n4. ^ Hsu, D.; Kakade, S. M.; Zhang, T. (2012). \"A spectral algorithm for learning Hidden Markov Models\". Journal of Computer and System Sciences 78 (5): 1460. arXiv:0811.4413. doi:10.1016\/j.jcss.2011.12.025. edit\n5. ^ Huang, S. Y.; Lee, M. H.; Hsiao, C. K. (2009). \"Nonlinear measures of association with kernel canonical correlation analysis and applications\". Journal of Statistical Planning and Inference 139 (7): 2162. doi:10.1016\/j.jspi.2008.10.011. edit\n6. ^ Kanti V. Mardia, J. T. Kent and J. M. Bibby (1979). Multivariate Analysis. Academic Press.\n7. ^ Tofallis, C. (1999). \"Model Building with Multiple Dependent Variables and Constraints\". Journal of the Royal Statistical Society: Series D (The Statistician) 48 (3): 371\u2013378. arXiv:1109.0725. doi:10.1111\/1467-9884.00195. edit\n8. ^ Degani, A.; Shafto, M.; Olson, L. (2006). \"Canonical Correlation Analysis: Use of Composite Heliographs for Representing Multiple Patterns\". Diagrammatic Representation and Inference. Lecture Notes in Computer Science 4045. p.\u00a093. doi:10.1007\/11783183_11. ISBN\u00a0978-3-540-35623-3. edit","date":"2014-09-24 02:35:54","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 90, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9372274875640869, \"perplexity\": 577.7359632710973}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-41\/segments\/1410657141651.17\/warc\/CC-MAIN-20140914011221-00148-ip-10-234-18-248.ec2.internal.warc.gz\"}"} | null | null |
{"url":"http:\/\/openstudy.com\/updates\/510185a9e4b03186c3f854a8","text":"## anonymous 3 years ago how to simplify a radical expression. ex: Simplify the prob 3Sqrrt(-243x^3y^10) i already know nSqrrt(a) * nSqrrt(B) = nSqrrt(AB)\n\n1. anonymous\n\nok so $$\\sqrt[3]{x^3}=x$$ for a start\n\n2. anonymous\n\nand since $$243=3^5$$ we have $$\\sqrt[3]{3^5}=3\\sqrt[3]{3^2}$$\n\n3. anonymous\n\nfinally $$\\sqrt[3]{y^{10}}=3\\sqrt[3]{y}$$","date":"2016-10-22 00:07:45","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8594818115234375, \"perplexity\": 7923.585813953191}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-44\/segments\/1476988718311.12\/warc\/CC-MAIN-20161020183838-00336-ip-10-171-6-4.ec2.internal.warc.gz\"}"} | null | null |
50 Happy Marriage Quotes for Your Happily Ever After
Cristina Montemayor
Author's Pinterest
Cristina Montemayor is a freelance writer and makeup artist whose work has appeared on HelloGiggles, Slate, Elite Daily, and Bustle.
Every couple that's been married for a significant amount of time is always asked the same question: What's the secret to a happy marriage? There's the traditional advice like "never go to bed angry," and the classic reminder that marriage requires compromise. But in order to live happily ever after, your marriage must be a happy one, filled with the kind of deep passion and radical acceptance that cultivates a blissful bond between two people. Of course, no marriage is happy all the time, but by focusing on your partner's strengths and expressing your love and appreciation every day, you'll be celebrating 50 years of wedded bliss in no time.
To celebrate the joys of marriage, we've put together a list of the best happy marriage quotes of all time. Whether you're engaged, newly married, or going on multiple decades married to the same person, you'll appreciate these 50 happy marriage quotes from literature, film, comedians, and celebrities.
50 Funny Quotes About Marriage That Are Too Relatable
"A happy marriage is a long conversation which always seems too short." — André Maurois
"Happy is the man who finds a true friend, and far happier is he who finds that true friend in his wife." — Franz Schubert
"Sensual pleasures have the fleeting brilliance of a comet; a happy marriage has the tranquility of a lovely sunset." — Ann Landers
"To get the full value of joy you must have someone to divide it with." — Mark Twain
"I love being married. It's so great to find that one special person you want to annoy for the rest of your life." — Rita Rudner
"The secret of a happy marriage is finding the right person. You know they're right if you love to be with them all the time." — Julia Child
"Marriage is like watching the color of leaves in the fall; ever changing and more stunningly beautiful with each passing day." — Fawn Weaver
"The highest happiness on earth is marriage." — William Lyon Phelps
"Marriage is a risk; I think it's a great and glorious risk, as long as you embark on the adventure in the same spirit." — Cate Blanchett
"A good marriage is one where each partner secretly suspects they got the better deal." — Unknown
"To be fully seen by somebody, then, and be loved anyhow — this is a human offering that can border on miraculous." — Elizabeth Gilbert
"Marriage is like a graph – it has its ups and downs and as long as things bounce back up again, you've got a good marriage. If it heads straight down, then you've got some problems!" — Julie Andrews
"We have a couple of rules in our relationship. The first rule is that I make her feel like she's getting everything. The second rule is that I actually do let her have her way in everything. And, so far, it's working." — Justin Timberlake
"I got gaps; you got gaps; we fill each other's gaps...Love is absolute loyalty. People fade, looks fade, but loyalty never fades. You can depend so much on certain people; you can set your watch by them. And that's love, even if it doesn't seem very exciting." — Sylvester Stallone
"A simple 'I love you' means more than money." — Frank Sinatra
"When you end up happily married, even the failed relationships have worked beautifully to get you there." — Julia Roberts
"There's no bad consequence to loving fully, with all your heart. You always gain by giving love. It's like that beautiful Shakespeare quote from Romeo and Juliet: 'My bounty is as boundless as the sea. My love is deep. The more I give to thee, the more I have. For both are infinite.'" — Reese Witherspoon
"A happy marriage is the union of two good forgivers." — Ruth Bell Graham
"I love you without knowing how, or when, or from where. I love you simply, without problems or pride: I love you in this way because I do not know any other way of loving but this, in which there is no I or you, so intimate that your hand upon my chest is my hand, so intimate then when I fall asleep your eyes close." — Pablo Neruda, 100 Love Sonnets
"Some people ask the secret of our long marriage. We take time to go to a restaurant two times a week. A little candlelight, dinner, soft music, and dancing. She goes Tuesdays, I go Fridays." — Henny Youngman
"A successful marriage requires falling in love many times, always with the same person." — Mignon McLaughlin
"If I had a flower for every time thought of you… I could walk through my garden forever." — Alfred Tennyson
"Being deeply loved by someone gives you strength, while loving someone deeply gives you courage." — Lao Tzu
"Every heart sings a song, incomplete, until another heart whispers back. Those who wish to sing always find a song. At the touch of a lover, everyone becomes a poet." — Plato
"Look, you want to know what marriage is really like? Fine. You wake up, she's there. You come back from work, she's there. You fall asleep, she's there. You eat dinner, she's there. You know? I mean, I know that sounds like a bad thing, but it's not." — Ray Barone
"There is no more lovely, friendly, and charming relationship, communion or company than a good marriage." — Martin Luther
"A great marriage is not when the 'perfect couple' comes together. It is when an imperfect couple learns to enjoy their differences." — Dave Meurer
"When a marriage works, nothing on Earth can take its place." — Helen Gahagan Douglas
"This is what marriage really means: helping one another to reach the full status of being persons, responsible beings who do not run away from life." — Paul Tournier
"Almost no one is foolish enough to imagine that he automatically deserves great success in any field of activity, yet almost everyone believes that he automatically deserves success in marriage." — Sydney J. Harris
"Love is but the discovery of ourselves in others, and the delight in the recognition." — Alexander Smith
"When you realize you want to spend the rest of your life with somebody, you want the rest of your life to start as soon as possible." — Meg Ryan as Sally Albright in When Harry Met Sally
"Love at first sight is easy to understand; it's when two people have been looking at each other for a lifetime that it becomes a miracle." — Sam Levenson
"To find someone who will love you for no reason, and to shower that person with reasons, that is the ultimate happiness." — Robert Brault
"After a while, you just want to be with the one that makes you laugh." — Chris Noth as Mr. Big, Sex and the City
"Being someone's first love may be great, but to be their last is beyond perfect." — Anonymous
"The greatest marriages are built on teamwork. A mutual respect, a healthy dose of admiration, and a never-ending portion of love and grace." – Fawn Weaver
"Love doesn't make the world go round; love is what makes the ride worthwhile." — Elizabeth Browning
"Love is a temporary madness. It erupts like volcanoes and then subsides. And when it subsides, you have to make a decision. You have to work out whether your roots have so entwined together that it is inconceivable that you should ever part. Because this is what love is." — Louis de Bernieres
"Happy marriages begin when we marry the ones we love and they blossom when we love the ones we marry." — Tom Mullen
"I love you not only for what you are, but for what I am when I am with you." — Roy Croft
"Love is like a friendship caught on fire." — Bruce Lee
"Marriage is a mosaic you build with your spouse. Millions of tiny moments that create your love story." — Jennifer Smith
"Marriage, ultimately, is the practice of becoming passionate friends." — Harville Hendrix
"Marriage is not a noun; it's a verb. It isn't something you get. It's something you do. It's the way you love your partner every day." — Barbara De Angelis
"Being in a long marriage is a little bit like that nice cup of coffee every morning – I might have it every day, but I still enjoy it." — Stephen Gaines
"Happy marriages begin when we marry the ones we love, and they blossom when we love the ones we married." — Tim Mullen
"Marriage is the highest state of friendship. If happy, it lessens our cares by dividing them, at the same time that it doubles our pleasures by mutual participation." — Samuel Richardson
"The secret of a happy marriage remains a secret." — Henny Youngman
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20 of Our Favorite Celebrity Couples Share Their Best Advice on Marriage | {
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EBONY.com, Contributor
The premiere online magazine destination for African-American cultural insight, news and perspective.
In Final State of the Union, Obama Answers Critics, Forges Vision
By: Richard Fowler
In his final State of the Union Address, President Barack Obama handled things a lot differently. Instead of laying out a laundry list of unachievable policies and promises, President Obama used his final address to Congress to speak to America's challenges and opportunities for today, tomorrow, and for generations to come. In his speech he made it clear that if we work together now, we'll keep building a future even more remarkable than our past.
Last night, Obama had the impossible job of trying to bring together a nation that has been torn part by high flying rhetoric, misguided presidential hopefuls, and the emergence of a new era of bigotry and hate. But with a cool, calm, and collected tone, this president delivered once again.
With income inequality at an all-time high and racial harmony at an all time low, the President's speech was one crafted and delivered to bring the nation together. And let's be real, even though we have a divided and gridlocked government there are areas where Republicans and Democrats can work together. The President highlighted a couple of those areas in the first two minutes of the speech." I hope we can work together this year on bipartisan priorities like criminal justice reform, and helping people who are battling prescription drug abuse. We just might surprise the cynics again," he said.
Our economic situation has improved quite a bit over the past seven years: More folks are heading back to work. More students are graduating high school and college. More folks have access to healthcare. And we are all paying less at the pump. Yet still, President Obama addressed a nation where folks are uncertain of the future and fear that the American dream is out of reach.
Throughout the speech, we heard from an honest, calm, and collected Obama. Instead of bashing Republicans, he urged the entire Congress to see beyond its differences and chart a new course of economic opportunity, technological innovation, and cooperative rhetoric in Washington.
For almost seven years, the president has acted on the belief that the full spectrum of American power should be used to move our national security interests forward and that diplomacy makes us safer than going it alone. Here at home, he believes that our democracy and economy works best when all citizens are engaged in the effort. For seven years, Obama has reminded us that we are a country that overcomes, innovates, creates, and seizes the future - a people who believe in the power of hope and change to push us towards progress and prosperity.
And while he is not the cause for most of the division and gridlock in Washington, the president was even bold enough to take some of the blame, stating: "Our public life withers when only the most extreme voices get attention. Most of all, democracy breaks down when the average person feels their voice doesn't matter; that the system is rigged in favor of the rich or the powerful or some narrow interest. Too many Americans feel that way right now. It's one of the few regrets of my presidency - that the rancor and suspicion between the parties has gotten worse instead of better."
Over the past seven years, many have bashed this President for not being strong enough, for not exercising enough force, and for not bringing our economy back. Last night the President graciously answered all the critics. He ticked off many of his accomplishments both foreign and domestic, and urged the citizens of America to rise above cynicism and fear, and affirm hope for decades to come.
I have covered this speech from the capitol building for the past four years and I can honestly say last night I felt something different. I don't agree with the President on every policy position he puts out. But I do believe it is time for our nation to come together and put aside the self-imposed barriers that divide us.
Richard Fowler's YouTube and radio show can be heard in more than 9.1 million homes. He frequently appears on Fox News, MSNBC, and C-SPAN. He is also a Senior Media Fellow for the New Leaders Council. Follow him on Twitter @Richardafowler
Black Voices State of the Union President Politics News United States | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,546 |
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Directions: Take I-64 East To Exit 123 New Albany, Turn Right Onto In-111 SE. Home Is Approximately 10miles Past Horseshoe Casino On The Right. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,957 |
using System.Linq;
using osu.Framework.Allocation;
using osu.Framework.Bindables;
using osu.Framework.Extensions.Color4Extensions;
using osu.Framework.Graphics;
using osu.Framework.Graphics.Containers;
using osu.Game.Beatmaps.ControlPoints;
using osu.Game.Graphics;
using osu.Game.Screens.Edit.Components.Timelines.Summary.Visualisations;
namespace osu.Game.Screens.Edit.Components.Timelines.Summary.Parts
{
public class EffectPointVisualisation : CompositeDrawable, IControlPointVisualisation
{
private readonly EffectControlPoint effect;
private Bindable<bool> kiai;
[Resolved]
private EditorBeatmap beatmap { get; set; }
[Resolved]
private OsuColour colours { get; set; }
public EffectPointVisualisation(EffectControlPoint point)
{
RelativePositionAxes = Axes.Both;
RelativeSizeAxes = Axes.Y;
effect = point;
}
[BackgroundDependencyLoader]
private void load()
{
kiai = effect.KiaiModeBindable.GetBoundCopy();
kiai.BindValueChanged(_ =>
{
ClearInternal();
AddInternal(new ControlPointVisualisation(effect));
if (!kiai.Value)
return;
var endControlPoint = beatmap.ControlPointInfo.EffectPoints.FirstOrDefault(c => c.Time > effect.Time && !c.KiaiMode);
// handle kiai duration
// eventually this will be simpler when we have control points with durations.
if (endControlPoint != null)
{
RelativeSizeAxes = Axes.Both;
Origin = Anchor.TopLeft;
Width = (float)(endControlPoint.Time - effect.Time);
AddInternal(new PointVisualisation
{
RelativeSizeAxes = Axes.Both,
Origin = Anchor.TopLeft,
Width = 1,
Height = 0.25f,
Depth = float.MaxValue,
Colour = effect.GetRepresentingColour(colours).Darken(0.5f),
});
}
}, true);
}
// kiai sections display duration, so are required to be visualised.
public bool IsVisuallyRedundant(ControlPoint other) => other is EffectControlPoint otherEffect && effect.KiaiMode == otherEffect.KiaiMode;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,630 |
\section{Rules of Evolve Map}
\section{Values of Des Function}
\end{document}
\section{Conclusion}\label{sec:con}
In this paper, we \CN{present a method to generate proactive robot behavior.} We \CN{show and discuss a first version of an integration of} to two stand-alone approaches to proactivity: $\eqm $, equilibrium maintenance, that infers opportunities for acting based on reasoning about the robot's possible actions, prediction about the future development of the state and about what is preferable; and $\uir$, human intention reasoning, that infers what to do next by recognizing the human's current intention and taking over doing the next action in the human's plan of acting. We show the benefits of both system that the other system is unable to produce such as; $\uir$ focuses on helping humans towards their intentions, \CN{whereas} $\eqm$ focuses on preventing humans to end up in undesirable situations. \CN{$\eqm$ (as of now) is ignorant of human intentions and therefore cannot generate proactive behavior to support the human to achieve them.} On the other hand, $\uir$ does not reason about \CN{how the state will evolve in the future and what is the overall desirability of different states, hence, it cannot generate proactive behavior based on reasoning on prediction of the state and benefit of acting effects. On a use case we first show the proactive behavior of $\uir$; we then show on the same use case the proactive behavior of $\eqm$; finally we apply a combination of both systems, $\uir$ and $\eqm$, on this very use case and observe the resulting proactive behavior. The use case is implemented and tested in a computer program with terminal input (state evolution) and output (inferred robot action). We show that the novel combined solution of $\uir$ and $\eqm$ achieves the best proactive behavior as it can take into account the intentions of the human, the desirability of state and benefit of action effects as well as prediction of the future state evolution. }
\SB{In future, we plan to test our system in a real robot system. In the current paper, we demonstrated our results on a imagined domestic robot that is capable of manipulating the world physically, but the implementation has been confined to the computer with inputs and outputs to the screen. We plan to use the Pepper Humanoid robot (which is described in \citep{Pandey2018AKind}) to conduct experiments akin to the ones described in Section~\ref{sec:exp}.
}
Apart from Pepper, our system is general enough that should be able to implement it on a great variety of physical robots or simulated agents, in diverse domains.
\section{Discussion and Conclusion}\label{sec:disc}
In this paper, we have analyzed two approaches to proactivity: $\uir$,
human intention recognition and reasoning, that infers proactive actions
by recognizing the human's intended plans and taking over the next
action in these plans; and $\eqm$, equilibrium maintenance, that infers
opportunities for acting by reasoning about possible future states and
about what states are preferable.
We have then defined a third approach which
combines these two types of proactivity, and have illustrated the three
approaches on a sample use case.
Our analysis shows that each approach can generate some proactive
behaviors but not others. $\uir$ focuses on helping humans towards
achieving their intentions, whereas $\eqm$ focuses on preventing humans
to end up in undesirable situations.
$\eqm$ does not
consider humans' intentions and therefore cannot generate proactive
behavior to support the human to achieve them; $\uir$, on the other hand, does not
reason about how the state will evolve and about the overall
desirability of future states, and therefore cannot generate proactive
behavior based on the predicted benefit of actions.
The combined system can take into account both, humans' intentions and the
desirability of future states. In this work, we have explored a rather
simple way to combine these two aspects, where $\uir$ and $\eqm$
independently propose proactive actions and one of those is selected.
This can be called \emph{late integration}. Future work will
investigate \emph{early} forms of integration, where reasoning on human
intentions, on available robot's actions, on future states and on
preferences among those states is done in an integrated fashion. This
tighter integration of $\uir$ and $\eqm$ will require a shared
formulation for the two.
Our current framework is built on state descriptions that only consider
the physical world. In future work, it will be interesting to include
the inner world of the human. We plan to explore the use of techniques
from the area of epistemic logic and epistemic planning to model
intentions, knowledge and beliefs of human agents. The $\des$-function
and benefit of acting can then also take into account the preferences of
mental states and how to bring preferable epistemic states about.
While we considered a single human in this paper, both $\uir$ and $\eqm$
can in principle consider multiple humans: one would then have to track
separately the single actions of each person and infer their intentions.
If the humans are collaborating, $\uir$ could consider all of the
humans' actions together to infer the collective intention. $\eqm$ can
fuse the single humans' preferences in one overall $\des$-function.
The results of $\eqm$, as well as the results of the combined system
$\uir$ + $\eqm$, strongly depend on the models of the dynamics of the
system $\Sigma$, which determines the prediction of the state evolution
(free-run), and on the modeling of preferences ($\des$-function).
To see this, consider the example in Section~\ref{sec:exp}. In state
$s_{1.0}$ the opportunity of $\uir$, gather the water bottle, is chosen
over the opportunity of $\eqm$, clean the dishes. If the desirability
function modeled a stronger undesirability of dirty dishes, then the
degree of the opportunity by $\eqm$ would have been higher and hence
this opportunity would have been chosen to be enacted.
Further, consider a slightly modified state dynamics, that differs from
the one in Figure~\ref{fig:stateev}. In these modified state dynamics, the states at time $4$ have weather conditions 'sun' and 'clouds' (instead of 'rain' and 'hail'). In this use case, $\eqm$ would only
infer to clean the dishes in state $s_{1.0}$ but it would not support
the human preparing for their hike because it is not reasoning on the
human's intention. $\uir$, on the other hand, could provide a lot of
support to the human to achieve their intention and would achieve a very
desirable final outcome: the human out on a hike with all their
belongings gathered.
In this paper, we have simply assumed that both $\Sigma$ and $\des$ are
given. Future work, however, might explore the use of machine learning
to learn probabilistic models of state evolution. Also hybrid techniques
(model-based and data-driven) are conceivable which should take into
account inferring the human's intentions as this is an indicator of what
the human will do next and thereby how the state will change. When
eliciting and reasoning on preferences, ideally, the proactive agent
should take into account the dynamic change of preferences, weigh
personal against common, long-term against short-term preferences, and
reason on uncertainty of what is desirable.
Finally, the example in Section~\ref{sec:exp} has been run with console
inputs and outputs. Given the promising results, the next step will be
to connect our system to a real Pepper robot
(\citep{Pandey2018AKind}) and conduct a user study in a real domestic
environment.
Since our system is based on general models, we also plan to test it on
a variety of physical robot systems or interactive agents in diverse domains.
\section{Experiments}\label{sec:exp}
In this section, we empirically explore the behavior of the presented
approaches to proactive behavior by running the same simulated task with
three different configurations of the system. We compare and analyze
the outcomes of the system shown in Figure~\ref{fig:system} when:
\begin{enumerate}
\item we only use intention based proactivity ($\uir$);
\item we only use predictive proactivity ($\eqm$);
\item we integrate both intention based and predictive proactivity.
\end{enumerate}
Figures~\ref{fig:system_hir} and Figure~\ref{fig:system_eqm} show the
systems used for the first two experiments, while the integrated system
used for the third experiment is the one previously shown in
Figure~\ref{fig:system}.
\begin{figure}[tbh!]
\centering
\begin{minipage}[b]{0.49\textwidth}
\includegraphics[width = \textwidth]{figures/hirr12.pdf
\caption{System model overview for $\uir$}
\label{fig:system_hir}
\end{minipage}
\hfill
\begin{minipage}[b]{0.49\textwidth}
\includegraphics[width = \textwidth]{figures/eqm12.pdf
\caption{System model overview for $\eqm$}
\label{fig:system_eqm}
\end{minipage}
\end{figure}
The code is available in a ``research bundle'' on the European
AI-on-demand platform, \url{ai4europe.eu}%
\footnote{\url{https://www.ai4europe.eu/research/research-bundles/proactive-communication-social-robots}}.
This research bundle includes the open source code, libraries, and a
form of a notebook allowing users to interact with the framework by
defining their environment.
\subsection{Task Description}
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=\textwidth, keepaspectratio]
{figures/state-evolve-VF.pdf}
\caption{States and possible state transitions (free-run) in our
scenario. Desirability values for each state are color-coded, as well
as indicated numerically. Green represents desirable states, while
pink to red represents less desirable states. The more undesirable a
state is, the more intense its red tone. }
\label{fig:stateev}
\end{center}
\end{figure}
We define a hypothetical scenario where a human moves inside a house
and collects objects in order to reach a goal. Figure ~\ref{fig:stateev}
graphically represents the dynamic system $\Sigma = \langle S, U, f
\rangle$ that models our scenario, where arrows show the state
transitions $f$ that correspond to possible evolutions of the
environment (including actions by the human) if there is no interference
from the robot. The figure also indicates the degree of desirability
$\des(s)$ of each state $s$.
In addition to $\Sigma$ and $\des$, the scenario includes the set of
action schemes given in Table~\ref{tab:actions} below, and a set $G_H$
of four human goals:
\begin{itemize}
\item \textbf{Hiking;} backpack collected, compass collected, water
bottle collected, human is outside.
\item \textbf{Promenade;} hat collected, dog collected, walking
stick collected, human is outside.
\item \textbf{Watch TV;} water bottle collected, sugar collected,
tea collected, remote control collected.
\item \textbf{Read Book;} glasses collected, book collected, tea
collected, sugar collected.
\end{itemize}
Each goal describes what must be true for it to be considered
reached. For example, the goal ``Hiking'' is reached when it is true
that backpack, compass and water bottle are collected and the human is
outside. The actions to reach the individual goals can be done both by
the human or the robot (except for going outside).
In our implementation, both the dynamic system and the action schemes
are modelled in PDDL. Recall that PDDL includes a domain definition and
a problem definition. In the domain definition, we model object
definitions, predicate definitions for logical facts, and action
definitions with preconditions and effects. In the problem definition,
we model the initial state of the environment in logical format, as well
as the goal state. Actions are defined for \textit{gathering} and \textit{leaving objects},
for \textit{telling the human they are ready to leave the house}, and
for \textit{cleaning the dishes}. Details are given in Table~\ref{tab:actions}. Some actions can be
executed by the robot, some can be executed by the human, and some by
both the human and the robot. The actions that are done by the human are
observed by the robot, and based on them the $\uir$ system recognizes
the human's intention. The $\eqm$ system, on the other hand, reasons
about potential robot actions while taking into account the human's
actions which are part of the free-run (uncontrollable state
transitions). Note that in this use case all actions are deterministic
except for \emph{cleaning the dishes} which is non-deterministic: the
action can have the effect that all dishes are clean or that they are
still half dirty.
The defined robot actions are used in the $\eqm$ system to infer
opportunities. $\uir$ recognizes human intention by inferring the
human's action plan. When the intention is recognized, $\uir$ can make
the robot proactively carry out the rest of the human's action plan on
the human's behalf. However, the human's action plan towards their goal
might contain an action that cannot be carried out by the robot. In that
case the robot transforms the action to a communication action where the
robot tells the human what they should do. For example, after having
collected all the necessary items, the human is supposed to leave the
house to reach their goal ``hiking''. The robot can collect all
necessary items but cannot leave the house, hence, it tells the human
``Everything has been collected. You are ready to leave now for going
hiking''.
\begin{table}[h]
\centering
\begin{tabular}{|l l l r|}
\hline
\textbf{Action} & \textbf{Precondition} & \textbf{Effect} & \textbf{Agent} \\ \hline \hline
Gather object & \textbf{and (} & human gathered object & human / robot \\
& obj is not gathered, & & \\
& human at home \textbf{)} & & \\ \hline
Leave object & \textbf{and (} & human not gathered object & human / robot \\
& obj is gathered, & & \\
& human at home \textbf{)} & & \\ \hline
Leave home & human at home & human not at home & human \\
\hline
Suggest human to leave home & human at home & human not at home & robot \\
\hline
Warn human & human at home & \textbf{and (} & robot \\
& & human at home, & \\
& & human warned \textbf{)} & \\
\hline
Clean dishes & \textbf{or (} & \textbf{or (} & human / robot \\
& dishes dirty, & dishes not dirty & \\
& dishes half dirty \textbf{)} & dishes half dirty ) & \\
\hline
\end{tabular}
\caption{The table provides the actions that the human and the robot
are capable to do. It provides the name of the action (possibly
including a parameter), preconditions of the actions and the
effects that will show after the action is applied, as well as
who can do the action (human and/or robot).}
\label{tab:actions}
\end{table}
The desirability function, $\des$, that computes the desirability degree
of each state, is assumed given. In our example scenario, we consider one specific run where the state
evolves as follows: $s_{0}$ , $s_{1.0}$ , $s_{2.0}$ , $s_{3.0}$ (see
Figure~\ref{fig:stateev}). The system starts in $s_{0}$ where the
weather is nice, time is morning and the human is having breakfast. This
state is very desirable, $\des(s_{0}) = 1.0$. Later the state is
changed to $s_{1.0}$ where the weather is still nice and the time is
still morning, but the human finished their breakfast so there are dirty
dishes and the human collected the backpack. This state is less
desirable, $\des(s_{1.0}) = 0.6$. Later the state evolves to $s_{2.0}$,
where the weather is cloudy and dishes are cleaned. In addition to the
backpack, now the compass is collected. The last state chance is to
$s_{3.0}$, where the weather is cloudy, time is morning and the human
has collected the water bottle in addition to the previously collected
belongings backpack and compass. Note that the predicate
``dishes-dirty'' changes from true (in $s_{1.0}$ and $s_{1.1}$) to false
(in $s_{2.0}$ and $s_{2.1}$). This is because the free-run state
evolution models all uncontrollable state transitions which includes the
environment and the human. Hence, the dishes not being dirty anymore
means that the human has taken care of cleaning them.
\subsection{Human Intention Recognition and Reasoning Only}
\label{ssec:hironly}
We consider the scenario described in Figure~\ref{fig:stateev} using
only human intention recognition and reasoning for achieving proactive
agent activity. This means we evaluate an implementation of the method
$\uir$ as described in Section~\ref{ssec:hir}. The architecture of the
system is shown in Figure~\ref{fig:system_hir}. Table~\ref{tab:hir}
lists the recognized human intentions in the respective state and the
proactive agent activity inferred.
\begin{table}[h!]
\centering
\begin{tabular}{|l|l|l|}
\hline
\textbf{State} & \textbf{Intention recognized} & \textbf{Proactive agent activity chosen - $\uir$} \\
\hline \hline
$s_0$ & ? & --- \\
\hline
$s_{1.0}$ & hiking & gather water bottle \\
\hline
$s_{2.0}'$ & hiking & tell human that he/she is ready to leave the house \\
\hline
$s_{3.0}$ & ? & --- \\
\hline
\end{tabular}
\caption{The state evolution and the proactive agent activity inferred in each state when using human intention recognition and reasoning only.}
\label{tab:hir}
\end{table}
In $s_0$, the $\uir$ cannot recognize yet what the human's intention is,
it could be any of the four known human goals, going on a hike or going
on a promenade, watching TV or reading a book.
Then the state advances to $s_{1.0}$ where a backpack is collected. In
this state, the $\uir$ is able to detect that the human's intention is
to go on a hike. The $\uir$ can infer to \emph{proactively} bring the
water bottle to the human as this is the next action inferred in the
human's action plan.
The action is dispatched and the robot proactively brings the water
bottle to the human (in simulation). Now the human has the backpack
(gathered by the human him-/herself) and the water bottle (gathered by
the robot). The state evolution advances to the next state
$s_{2.0}'$. In this state also a compass is gathered, which was done by
the human.
(For any state $s$ in
the free-run in Figure~\ref{fig:stateev}, $s'$ marks its equivalent on
which robot action has been applied.)
Again, the intent recognition detects that the human's intention is
going on a hike. The intention reasoning system detects that all
necessary items for going on a hike have been collected. Therefore, it
infers the \emph{proactive} activity of notifying the human that he/she
is ready to leave.
Note that, in state $s_{2.0}'$ (which is the state $s_{2.0}$ plus
applied robot action) the same predicates are true as in $s_{3.0}$. This
is eligible and expected as the robot's proactive acting is doing part
of the human's action plan based on human intention recognition and
reasoning. Therefore, a state $s_{2.0}'$ would not evolve into $s_{3.0}$
(which is identical), but into states $s_{4.0}$ or $s_{4.1}$ where the
human is outdoors.
Note that, once the human has left the house, proactive interaction from
our system with him/her is not possible. That is why there is no
intention recognized in $s_{4.0}, s_{4.1}$.
Note also that these states are quite undesirable ($\des(s_{4.0}) = 0.0$
and $\des(s_{4.1}) = 0.4$), as the user is outdoors while weather
conditions are unpleasant (\texttt{rain}) or even dangerous
(\texttt{hail}).
The algorithm for human intention recognition and reasoning neither does
any prediction of future states nor reasons about
desirability/preference. Therefore, it is ignorant of the upcoming
undesirable situation and cannot act on it.
\subsection{Equilibrium Maintenance Only}
\input{eqm}
\subsection{Human Intention Recognition and Reasoning and Equilibrium Maintenance}
\input{eqmhir}
\section{Introduction}\label{sec:intro}
Robots sharing the same spaces as humans, are preferred to be proactive by humans~\citep{harman2020action, pandey2013towards}.
However, a major part of the work on AI systems and robots are reactive --- responding to explicit requests and external events.
Some more recent work on making artificial agents and robots proactive exist, but often the solutions are domain-specific and prescriptive~\citep{umbrico2020holistic,
sirithunge2019proactive, peng2019design, harman2020action, kc2019case,
bremner2019proactive}.
In this work, we aim to address the question of finding a general solution to make robots proactive taking into account the human and their intention.
By proactive we mean the robot is able to act anticipatory and on own initiative. This definition follows the one in organizational psychology~\citep{grant2008the}. Acting on own initiative means the robot generates its own goals and decides which of them to pursue and when. Such a reasoning in particular needs to include prediction how the environment will evolve and what the human intends to and will do.
In our work we generate and select among opportunities for acting based on prediction of the state and intention of the human, as well as reasoning about what is desirable in general.
In particular, we propose a framework that is domain-unspecific and declarative and is able to reason on the benefit of acting now or later. Taking into account the knowledge and intention of the human, the framework predicts how the state will evolve and finds opportunities for acting that bring the system into a more desirable state.
The contributions of this paper are as follows: (i)~we introduce a framework that is able to infer acting decisions proactively, that is, on own initiative, based on prediction of how the state will evolve, reasoning about the robot's capabilities and what is overall desirable, and on based on user intention recognition; (ii)~we show how the user intention recognition can reduce the load of the state prediction by being able neglect directions in which the state can evolve based on the user's intention; (iii)~in experimental evaluation we show the benefit of having a system with both user intention recognition and proactivity to achieve the most favorable outcomes.
Contributions:
(i)~Improving Interaction between human and robot;
Including improving robot's trustability, transparency and legibility
(ii)~Preventing potential undesired outcomes; which occurs lack of knowledge
(iii)~Knowledge Repair; correcting user belief about world by inferring user's actions and reality
The remainder of this paper is organized as follows. In Section~\ref{sec:sota} we give an overview of the state-of-the-art in proactive artificial agents and robots, as well as human intention recognition. Section~\ref{sec:sys} describes the theoretical framework used in our system. In Section~\ref{sec:exp} we show the experiments we conducted. We discuss the outcomes of the experiments and some future directions in Section~\ref{sec:disc}, before we conclude in Section~\ref{sec:con}.
Finally, in Section~\ref{sec:con} we conclude.
\section{Introduction}
Humans can act on their own initiative.
Imagine the following scenario: you see your flatmate preparing to leave
for a hiking trip in a rainy zone. It is quite likely that you will
give your flatmate some advice like checking the weather forecast or
taking some extra equipment. Such behavior even occurs between
strangers. When people see a person holding garbage and looking around,
they tend to show where the garbage bin is since they recognized the
person's intention to dispose of their garbage. This type of intuitive
interaction is common between humans, and it is already observed in
infants~\citep{WarnekenTomasello.science2006}.
The question is, what happens if one of the actors is a robot?
The robot should be able to recognize and reason about the human's
intentions; to reason about the current and forecasted states of the
environment; to understand what states may be preferrable to others; and
to forsee problems that the human could face. The robot should also be
able to reason about the potential effects of its own actions, and
select and perform actions that support the human given this
context. The behavior of initiating own action taking into account all
these aspects is called \emph{proactive behavior}.
Most of the existing work in human-robot interaction rely on the human
taking the initiative: the human sets a request, and the robot generates
and executes a plan to satisfy it. However, in the above examples of
human-to-human interaction there is no explicit request. The
interaction works because humans are able to assess other humans'
intentions, anticipate consequences, and reason about preferred states.
In this paper, we are interested in proactive human-robot interaction,
that is, interactions where the robot behaves by acting on its own
initiative, in an anticipatory way, and without being given an explicit
goal~\citep{grant2008the,peng2019design,grosinger2019robots}. We
consider two types of proactive robot behavior: one in which the robot
understands the human's intentions and helps the human to achieve them; and
one in which the robot foresees possible future situations that are
undesirable (or desirable) according to the human's preferences, and
acts to avoid (or foster) them.
Specifically, we propose a framework that identifies opportunities for
acting and selects some of them for execution. \emph{Opportunities}
here are formal concepts grounded in the relation between acting,
preferences and state predictions.
Our framework includes two main mechanisms that contribute to initiating
proactive behavior; \emph{human intention recognition and reasoning} and
\emph{equilibrium maintenance}. The former mechanism is based on
recognizing human intent from a known list of possible intents that the
human can have. The latter one is based on predicting how the state may
evolve in time and comparing preferences of states resulting from
different actions (or inaction) \citep{grosinger2019robots}. These two
mechanisms correspond to the two types of proactive behavior mentioned
above: intention-based, and prediction-based. The whole framework
includes provisions to combine these mechanisms into an integrated
proactive system.
The main contributions of this paper are: (i) we propose a novel method
based on human intention recognition to generate intention-based
proactive robot behavior, that we call \emph{human intention recognition
and reasoning ($\uir$)}; (ii) we adapt an existing method based on
temporal predictions and state preferences, called \emph{equilibrium
maintenance ($\eqm$)}, to generate prediction-based proactive robot
behavior; (iii) we define an architecture to combine both methods to
create a proactive robot that considers both human intentions and
temporal predictions; and (iv) we compare all these using a sample case
study.
The rest of this paper is organized as follows. The next section
presents the necessary background together with related work on
intention recognition, proactivity, and their combination. In
Section~\ref{sec:sys} we define our systems for intention-based
proactivity and for prediction-based proactivity, together with their
integration. Section~\ref{sec:exp} describes the implementation and
shows the results of a task involving a simulated domestic robot and a
human. Finally, in Section~\ref{sec:disc} we discuss our results and
conclude.
\section{Keywords:} Proactive agents, Human intentions,
Autonomous robots, Social robot, Human-centered AI, Human-Robot
interaction}
\end{abstract}
\input{introduction}
\input{sotaV3}
\input{systemV5}
\input{experimentsV3}
\input{discussionV2}
\section*{Author Contributions}
SB and JG contributed equally to the concept, formalization,
implementation and experimentation reported in this paper. MC and AS
supervised all aspects above. All four authors contributed equally the
planning, writing and revision of the paper.
\section*{Acknowledgments}
This project has received funding from European Union's Horizon 2020 ICT-48 research and innovation actions under grant agreement No 952026 (HumanE-AI-Net) and from the European Union's Horizon 2020 research and innovation programme under grant agreement No 765955 (ANIMATAS).
\bibliographystyle{frontiersinSCNS_ENG_HUMS}
\section{Background and Related Work}\label{sec:sota}
In our work, we combine intention recognition and temporal predictions
to generate proactive behavior. Here we provide the relevant background
and related work on these research areas.
\subsection{Intention Recognition}
In order to assist humans, a robot requires some knowledge of the
human's goals and intentions.
In Belief-Desire-Intention (BDI) models,
\citep{rao1995bdi}, the agent represents the environment in terms of
beliefs that are true.
A set of desires, representing the agent's goals, guides the agent's
behavior. We may or may not know the agent's goals. The intention
represents the path that the agent is currently taking to reach a goal. \citet{Bratman1989} points out that the concept of intention is used to
characterize both the human's actions and mind (mental states). Actions
are considered as done with a certain intention. Humans attribute mental
states of intending to other agents such as having an intention to act
in certain ways now or later. In this paper, we consider an intention to be a mental state that is expressed through goal-directed actions.
{\it Intention recognition} is the process of inferring an agent's intention by analyzing their actions and their actions' effects on the environment
\citep{Han2013StateMaking}. Approaches in action recognition, goal
recognition and plan recognition have been used to infer intention. According to \citet{vanhorenbeke2021recognition}, intention recognition
systems can be classified as logic-based, classical machine learning,
deep learning and brain-inspired approaches, or they can be classified
in terms of the behavior of the observed human towards the observer. We take here a simplified view, and consider two classes of intention
recognition approaches: logic-based and probabilistic.
Logic-based approaches are defined by a set of domain-independent rules
that capture the relevant knowledge to infer the human's intention
through deduction \citep{sukthankar2014plan}. The knowledge can be
represented in different ways, including using plan representation languages
like STRIPS and PDDL that describe the state of the environment and the
effects of the possible actions.
Logic-based approaches work well in highly structured environments.
Logic representation can define different kinds of relationships
depending on the problem. These relationships allow to recognize humans'
intentions based on observations. Another advantage of logic-based
approaches is that they are highly expressive. The reasoning result can
potentially be traceable and human-understandable. However, many
logic-based approaches assume that the human is rational and try to find
the optimal intention that best fits the observations, while humans
often act in non-rational ways \citep{Dreyfus2007}. This makes
logic-based approaches less reliable in real-world problems. The
uncertainty in humans' rationality might be addressed by a combination
of logic-based with probabilistic reasoning techniques.
Probabilistic approaches exploit Bayesian networks and Markov models.
Bayesian networks are generative probabilistic graphical models that
represent random variables as nodes and conditional dependencies as
arrows between them \citep{vanhorenbeke2021recognition}. They can
provide the probability distribution of any set of random variables
given another set of observed variables. Some planning systems use Bayesian inference to reason about
intention. Such approaches are referred to as Bayesian inverse
planning. \citet{ramirez2009Plan} propose an approximate planning method
that generates a set of possible goals by using Bayesian inverse
planning methods on classical planning. The method assumes that humans
are perfectly rational, which means they only optimally pursue their
goals. As a result of this, the indecisive behavior of humans is not
tolerated. This limitation is partly addressed in \citet{ramirez2010}, that
introduces a more general formulation.
\citet{persiani2020Computational} offers an example of using Bayesian
inference in a logic based approach. The authors use classical planning
to generate an action plan for each goal, then they use a Bayesian prior
function to infer human intention. Probabilistic approaches are able to handle uncertainty, and can
therefore handle real-world settings such as non-rational agents,
interrupted plans and partial observability
\citep{vanhorenbeke2021recognition}. On the other hand, they are less
expressive than logic-based systems, since it is hard to understand the
reasoning behind the result. Scalability is another, well-known
difficulty with probabilistic approaches.
In this work, we adopt a logic-based approach
as done in \citet{persiani2020Computational}: we represent the robot's
knowledge in a symbolic form, which the robot uses to plan its actions.
We assume rational humans. The approach gives us the advantage of
getting results that are easily traceable and human-readable.
\subsection{Proactivity}
\emph{Proactive} AI systems and robots are opposed to \emph{reactive} AI
systems, which respond to explicit requests or external events. In
organizational psychology proactive behavior is understood as
\emph{anticipatory, self-initiated action}~\citep{grant2008the}. When
it comes to artificial agents, though, we lack a clear definition of
proactivity. Drawing inspiration from the human proactive process, we
can identify the functionalities that are needed for artificial
proactivity: context-awareness, activity recognition, goal reasoning,
planning, and plan execution and execution monitoring. Each one of
these functionalities in itself has been the subject of active
research~\citep{doush2020survey, wang2019deep, aha2018goal,
ghallab2016automated, hertzbergEtAl2016aireasoning}. Proactivity needs
to contemplate these areas jointly and in a separate process to each.
Context-awareness is not the central topic in proactivity, but it is
used to understand what the current situation is, and with this
knowledge it is possible to decide how to act. Goal Reasoning (GR) deals
with questions about generating, selecting, maintaining and dispatching
goals for execution~\citep{aha2018goal}. Planning can be described as searching and selecting an optimal action
trajectory to a goal that is given externally by the human or by some
trigger. Proactivity resides on the abstraction level above. It is
finding the acting decisions or goals that should be planned for, hence,
it produces the input to a planner. Finally, plan execution and
monitoring are employed by Proactivity to enact the acting decision
inferred and to invoke new reasoning on proactivity when execution
fails.
Recently there has been a number of promising works in the field of
artificial proactivity. \citet{baraglia2017efficient} address the
question whether and when a robot should take initiative during joint
human-robot task execution. The domain used is table-top manipulation
tasks. \citet{baraglia2017efficient} employ dynamic Bayesian networks to
predict environmental states and the robot's actions to reach them.
Initiation of action is based on a hard trigger: that at least one
executable action exists that does not conflict with human actions. In
contrast, in the work presented in this paper we aim to find a general
solution where acting is based on reasoning on first principles, rather than on
hard-coded triggers or rules.
\citet{bremner2019proactive} present a control architecture based on the
BDI-model incorporating an extra ethical layer in order to achieve
agents that are proactive, transparent, ethical and verifiable. They do
anticipation through embedded simulation of the robot and other
agents. Thereby, the robot can test what-if-hypotheses, e.g., what if I
carry out action $x$? The robot controller is given a set of goals,
task, and actions and thereof generates behavior alternatives, i.e.,
plans. The simulation module simulates them and predicts their
outcome. The ethical layer evaluates the plans and if needed invokes the
planner module to find new plans proactively.
Note that proactive plans are only generated if previously generated
plans from given goals fail against some given ethical rules, which
admittedly limits generality. The approach that we propose below is more
general since it generates proactive actions from first principles. On
the other hand, our approach does not takes ethics into account. \citet{umbrico2020holistic, umbrico2020toward} present a general-purpose
cognitive architecture with the aim to realize a Socially Assistive
Robot (SAR), specifically, for supporting elderly people in their home.
Their highly integrated framework includes a robot, a heterogeneous
environment and physiological sensors, and can do state assessment using
these sensors and an extensive ontology. However, their approach to
making the SAR proactive is based on hard-wired rules like ``user need:
high blood pressure $\rightarrow$ robot action: blood pressure
monitoring in context \emph{sleeping}''. \citet{peng2019design} are mainly interested in finding the right level
of proactivity. They use hand-coded policies for guiding the behavior of
a robotic shopping assistant, and find that users prefer medium
proactivity over high or low proactivity.
\subsubsection{Equilibrium Maintenance}
In this work we use Equilibrium Maintenance, $\eqm$, a mechanism
proposed by \citet{grosinger2019robots} for achieving proactivity.
$\eqm$ autonomously infers acting decisions based on temporal prediction
of one or several steps. $\eqm$ is a general approach based on a formal
model, and thus affords domain independence. This model is modular and
can cope with different agent capabilities, different preferences or
different predictive models. The relation between situations and
triggered actions is not hard-coded: decisions are inferred at run-time
by coupling action with state, predicted states and preferences and
choosing among acting alternatives at run-time. In
Section~\ref{ssec:eqm} we give a deeper description of $\eqm$.
A work that has comparable ideas to the ones in equilibrium maintenance
is the one on $\alpha$POMDPs by \citet{martins2019pomdp}. With the aim
to develop a technique for user-adaptive decision making in social
robots, they extend the classical POMDP formulation so that it
simultaneously maintains the user in valuable states and encourages the
robot to explore new states for learning the impact of its actions on
the user. As in all flavors of (PO)MDPs, however, the overall objective
is to find an optimal, reward-maximizing policy for action selection; by
contrast, the aim of $\eqm$ is to maintain an overall desirable world
state, be it by acting or by inaction. Instead of rewarding actions, as
done in MDPs, $\eqm$ evaluates the achieved effects of the actions (or
of being in-active).
\subsection{From Intention Recognition to Proactivity}
Several authors have proposed reactive systems based on intention
recognition.
\citet{Zhang2015} provide a framework for general proactive support in
human-robot teaming based on task decomposition, where priorities of
sub-tasks depend on the current situation. The robot re-prioritizes its
own goals to support humans according to recognized intentions.
Intentions are recognized by Bayesian inference following
\citet{ramirez2010}. Each goal's probability depends on the agent's
past and/or current belief, and the goal with the highest probability
from a candidate goal set is recognized as the current intention. Our
framework is similar to \citet{Zhang2015} in linking intention
recognition with the proactive behavior of the robot. In our case,
however, the robot does not have its own independent tasks to achieve:
the robot's only objective is to help the human proactively by enacting
actions to reach their goal.
\citet{sirithunge2019proactive} provide a review of proactivity focused
on perception: robots perceive the situation and user intention by human
body language before approaching the human. The review aims to identify
cues and techniques to evaluate the suitability of proactive
interaction. Their idea of proactivity is that the robot identifies a
requirement by the human and acts immediately. This differs from our
understanding of reasoning on proactivity: we generate proactive agent
behavior by considering the overall environment, the human's intentions,
the overall preferences and prediction on how the state will
evolve. This can result in the agent acting now or later or not at all.
\citet{harman2020action} aim at predicting what action a human is likely
to perform next, based on previous actions observed through pervasive
sensors in a smart environment. Predictions can enable a robot to
proactively assist humans by autonomously executing an action on their
behalf. So-called \emph{Action Graphs} are introduced to model order
constraints between actions. The program flow is as follows: (i)~action by the human is observed;
(ii)~next actions are predicted; (iii)~predicted actions are mapped to a
goal state; (iv)~a plan for the robot and a plan for the human are
created to reach the goal state; (v)~the robot decides which action it
should perform by comparing the robot's and the human's plan. The work presented in this paper shares some traits with the one by
\citet{harman2020action}: in both cases we reason on the human's
intentions, and make predictions about future states using action
models. In our case, however, predictions are made on how the system evolves
\emph{with} and \emph{without} robot actions, and proactive actions are
taken by comparing those predictions. Importantly, in our case these
actions might \emph{not} be part of the human's plan. Finally, the
trigger to perform proactivity reasoning in \citet{harman2020action} is
human action, while in our work this trigger is any state change, be it
caused by human action or by the environment.
In \citet{liu2021unified}, the authors' aim is to recognize and learn
human intentions online and provide robot assistance proactively in a
collaborative assembly task. They introduce the evolving hidden Markov
model (EHMM) which is a probabilistic model to unify human intention
inference and incremental human intention learning in real time. \citet{liu2021unified} conduct experiments where a fixed robot arm
assists a human according to recognized intention in assembling cubes
marked by a fiducial mark on top. One such configuration corresponds to
one particular intention. The human starts to assemble the cubes and the robot proactively
finishes the shape as soon as the intention is recognized or when a
maximally probable intention is found by doing one step prediction. In \citet{liu2021unified} proactivity results from strict one-to-one
links where one recognized intention always leads to the same action
sequence, using a 1-step prediction. In our approach, proactive robot behavior too can be based on recognizing intentions and their corresponding action sequences but it can also be inferred from first principles at run time using multiple steps
prediction.
\section{System}
\label{sec:sys}
We claimed that to initiate proactive behavior, robots must be equipped
with the abilities to recognize human intentions, to predict possible
future states and reason about their desirability, and to generate and
enact opportunities for acting that can lead to more desirable states.
In order to combine these abilities, we propose the general system model
shown in Figure~\ref{fig:system}.
\begin{figure}[thb]
\begin{center}
\includegraphics[ width=\textwidth,
keepaspectratio]{figures/proact_sys_arch
\caption{System Model; an autonomous system that initiates proactive behavior according to the situation of the environment, including the human.
}\label{fig:system}
\end{center}
\end{figure}
The system includes different components to offer a fully autonomous
interaction, namely: a situation assessment, a knowledge component, a planner, an intention-based proactivity component, a predictive
proactivity component, an action selection component and lastly an
executor.
The \textbf{situation assessment} and the \textbf{executor} components
act as interfaces to the physical environment. They respectively collect
and induce changes from/to the environment.
The \textbf{knowledge} component represents a model of the
environment. This model encodes the state evolution of the world, the
set of goals of the human, action plans of how the human can reach their
goals, robot capabilities as a set of action schemes, the state transition relation and a desirability function to compute the
degree of desirability of a state.
More specifically, we model the environment and its dynamics using a
standard dynamic system $\Sigma = \langle S, U, f \rangle$ where $S$ is
a set of states, $U$ is a finite set of external inputs (robot actions
or human actions) and $f \subseteq S \times U \times S$ is a transition relation. The
system's dynamics is modeled by the relation $f(s,u,s')$, which holds
iff $\Sigma$ can go from $s$ to $s'$ when input $u$ is applied in $s$.
To give $S$ a structure, we rely on a symbolic representation of world
states. Given a finite set $\mathcal{L}$ of predicates, we let $S \subseteq
{\mathcal{P}}(\mathcal{L})$, and denote by $s_c$ the current state. Each state $s \in
S$ is thus completely determined by the predicates that are true in $s$.
We denote by $G_H \subseteq S$ the set of human goals. Each goal $g \in
G_H$ is determined by predicates that are true in $g$. Given a goal $g$,
we denote by $s_g$ any state in $S$ where all predicates in $g$ (and
potentially more) are true, hence $g \subseteq s_g$. Finally, we denote
by $S_g \subseteq S$ the set of all states $s_g$ where the predicates of
$g$ are true.
The \textbf{planner}
is an off-the-shelf planner able to create a sequence of actions that
leads from the current state to a goal state. In our implementation, we
use \emph{Fastdownward}%
\footnote{\url{https://www.fast-downward.org/}},
a domain independent planner based on PDDL, the Planning Domain
Definition Language \citep{mcdermott_pddl_1998}. Both the human's plans and the robot's plans are formulated in PDDL, a standard language to
define planning domains and problems. The planning \emph{domain}
includes the predicates of $\mathcal{L}$ used for describing states, and
operators that model the available actions of humans and robots. The
planning \emph{problem} includes information about the available
objects, the current state $s_c$, and the goal of the human $g \in G_H$.
Given a domain and a problem, the planner finds the shortest plan
$\theta_g(s)$ between the current state $s_c$ and the given goal
$g$. This plan represents the sequence of actions that the agent should
do to reach any state $s_g$ where all predicates of $g$ are true.
The \textbf{intention-based proactivity} component and the
\textbf{predictive proactivity} component are both able to generate
proactive behavior, but they use two different methods which we describe
below. Finally, the \textbf{action selection} component integrates the
decisions generated by those two methods into an overall proactive
behavior to be executed by the robot.
To describe the main contribution of this paper, i.e., the integration
of intention-based and predictive proactivity, we first need to
introduce the individual systems which it is based on. In
Section~\ref{ssec:hir} we present our novel approach for intention-based
proactivity, $\uir$; In Section~\ref{ssec:eqm} we recall our existing
approach on equilibrium maintenance, $\eqm$; and in
Section~\ref{ssec:integr} we describe an integration of $\uir$ and
$\eqm$.
\subsection{Intention Based Proactivity: Human Intention Recognition and Reasoning}
\label{ssec:hir}
Experimental psychology shows that humans can interpret others'
intention by observing their actions, which is part of the so-called
Theory of Mind, ToM \citep{premack1978}. Interpreting actions in terms
of their final goal may give hints on why a human performed those
actions, and hence make us able to infer that human's intentions
\citep{Han2013StateMaking}. Inspired from these concepts, we define a framework called \textit{Human Intention Recognition and Reasoning} ($\uir$) for
generating proactive behavior based on intention recognition.
Intention recognition applies \emph{inverse planning} rules to recognize
the intention of the human in the form of an action plan. The robot can
then \emph{proactively} enact the next action in that action plan on
behalf of the human, or it can inform the human on which action to take
next in order to reach their goal.
There are different methods to recognize human intentions. We select
inverse planning since this is a straight-through logic-based approach
for fully observable systems. The approach has been widely used in other
systems for intention recognition~\citep{Han2013StateMaking,
persiani2020Computational, Farrell2020narrativeplanning}. While planning synthesizes a sequence of actions to reach a goal,
in inverse planning we observe the execution of a sequence of actions to infer the human's goal
and the corresponding plan. Once the user has committed to reaching a
goal, we say the user \emph{intends} to reach that goal $g$. We define
an intention $\mathfrak{i}(s)$ in state $s$ to be an action plan $\theta_g(s)$
to reach goal $g$ from state $s$. We infer human intentions $\mathfrak{I}(s)$ as defined in Equation~\ref{eq:intrec}:
\begin{equation}\label{eq:intrec}
\mathfrak{I}(s) = \{\theta_{\hat{g}}(s) \mid \hat{g} \in \argmin_{g \in G_H}(\mathrm{len}(\theta_g(s))) \}
\end{equation}
In words, for each goal $g$ in the set $G_H$ of the human's potential
goals, we use our planner to compute the shortest plan $\theta_g(s)$
that the human can perform to reach $g$ from the current state $s$. We
then select the goal $\hat{g}$ in $G_H$ to which the shortest of
these plans leads: $\theta_{\hat{g}}(s)$. The rationale behind this is that $\theta_{\hat{g}}(s)$ has the shortest
number of actions left to be executed, that is, the human already has
executed a large part of this plan.
Since we assume that the human is rational, it is plausible to infer
that the human intends to do all the remaining actions in
$\theta_{\hat{g}}(s)$ to reach $\hat{g}$ from $s$. Therefore, we take
the action list in $\theta_{\hat{g}}(s)$ to be the intention $\mathfrak{i}(s)$
of the human in state $s$.
This strategy has been originally proposed in logic-based approaches in
\citet{persiani2020Computational}.
Equation~\ref{eq:intrec} is implemented by
Algorithm~\ref{alg:humtrick}, called $\uir$, that returns the intention
$\mathfrak{i}(s) \in \mathfrak{I}(s)$. The returned intention is the residual action plan $\theta_{\hat{g}}(s)$ of the
human's recognized intention to be enacted proactively by the robot. If
the cardinality of the set of goals with shortest residual action plans, i.e., the cardinality of the set of intentions, is not $1$, the intention is
not recognized or it is ambiguous and an empty set is returned.
\begin{algorithm}[H]
\dontprintsemicolon
\SetKwFunction{Return}{return}
\SetKwFunction{FirstAction}{first}
${\widehat{G}} = \argmin_{g \in G_H}(\mathrm{len}(\theta_g(s)))$\\
\If{$\mid{\widehat{G}}\mid$ == 1}{
$\hat{g} = \mbox{first}({\widehat{G}})$ \\
\Return $\mathfrak{i}(s) = \theta_{\hat g}(s)$
}\Else{
\Return $\emptyset$
}
\caption{$\uir(s, G_H)$\label{alg:humtrick}}
\end{algorithm}
\subsection{Predictive Proactivity: Equilibrium Maintenance}\label{ssec:eqm}
For doing reasoning on predictive proactivity we employ a computational
framework called \emph{Equilibrium Maintenance}, fully described in
\citet{grosinger2019robots}. We only give a brief overview of the
framework here, the interested reader is referred to the cited reference
for details.
In our framework, the evolution of system $\Sigma$ by itself, that is,
when no robot action is performed, is modelled by its \emph{free-run
behavior} $\free{k}$. $\free{k}$ determines the set of states that can
be reached from an initial state $s$ in $k$ steps when applying the null
input $\bot$.
\begin{align*}
\free{0}(s) &= \{s\}
\\
\free{k}(s) &= \{s' \in S \mid \exists s'' :
f(s, \bot, s'') \land s' \in \free{k-1}(s'') \}.
\end{align*}
Desirable and undesirable states are modeled by $\des$, a fuzzy set of
$S$. The membership function $\mu_{\des}: S \rightarrow [0, 1]$ measures the
degree by which a state $s$ is desirable. $\des$ is extended from
states to sets of states in the obvious way: $\mu_{\des}(X) = \tmin{s \in
X}(\mu_{\des}(s))$, where $X \subseteq S$. We abbreviate $\mu_{\des}(\cdot)$ as
$\des(\cdot)$.
The available robot actions are modeled by \emph{action schemes}: partial
functions
$ \alpha : {\mathcal{P}}(S) \rightarrow \mathcal{P}^{+}(S) $
that describe how states can be transformed into other states by robot
acting. An action scheme $\alpha$ abstracts all details of action:
$ \alpha(X) = Y $
only says that there is a way to go from any state in the set of states
$X$ to some state in set $Y$. Action schemes can be at any level of
abstraction, from simple actions that can be executed directly, to
sequential action plans, or policies, or high level goals for one or
multiple planners. Applying an action scheme $\alpha$ in a state $s$
may bring about effects that are (or are not) desirable, possibly in $k$
steps in the future. We call \emph{benefit} the degree to which
an applied action scheme achieves desirable effects:
\begin{align}\label{eq:bnf}
\bnf(\alpha,s,k) = \tmin{X \in \dom(\alpha,s)} \des(\free{k}(\alpha(X))),
\end{align}
where
$\free{k}(X) = \bigcup_{s \in X}\free{k}(s)$ and $\dom(\alpha,s)$ is the
domain of $\alpha$ relevant in $s$.
With this background, \citet{grosinger2019robots} define seven different
types of \emph{opportunity} for acting, which are the foundation of
proactivity by equilibrium maintenance. We write $\opp_i(\alpha,s,k)$
to mean that applying action scheme $\alpha$ in state $s$ is an
opportunity of type $i$, by looking $k$ steps into the future.
\begin{align*}
\opp_0(\alpha,s,0) &= \min(1 - \des(s), \bnf(\alpha,s))\\
\opp_1(\alpha,s,k) &= \min(1 - \des(s), \tmax{s' \in \free{k}(s)}(\bnf(\alpha,s')))\\
\opp_2(\alpha,s,k) &= \min(1 - \des(s), \tmin{s' \in \free{k}(s)}(\bnf(\alpha,s'))) \\
\opp_3(\alpha,s,k) &= \tmax{s' \in \free{k}(s)}(\min(1 - \des(s'), \bnf(\alpha,s'))) \\
\opp_4(\alpha,s,k) &= \tmin{s' \in \free{k}(s)}(\min(1 - \des(s'), \bnf(\alpha,s'))) \\
\opp_5(\alpha,s,k) &= \min(\tmax{s' \in \free{k}(s)}(1 - \des(s')), \bnf(\alpha,s,k)) \\
\opp_6(\alpha,s,k) &= \min(\tmin{s' \in \free{k}(s)}(1 - \des(s')), \bnf(\alpha,s,k))
\end{align*}
To understand these opportunity types, consider for example the first
type $\opp_0$: the degree by which $\alpha$ is an opportunity of type
$0$ is the minimum of (i) the degree by which the current state $s$ is
undesirable, and (ii) the benefit of acting now. Intuitively, $\alpha$
is an opportunity of type $0$ if (and to the extent) we are in an
undesirable state, but enacting $\alpha$ would bring us to a desirable
one. As another example, consider $\opp_5$: here, we compute the
minimum of (i) the maximum undesirability of future states, and (ii) the
future benefit of acting now: intuitively, $\alpha$ is an opportunity of
type $5$ if (and to the extent) some future states within a look-ahead
$k$ are undesirable, but if we enact $\alpha$ now then all the $k$-steps
future states will be desirable.
Finally, we can define what it means for a system to be in equilibrium
from a proactivity perspective.
\begin{align}\label{eq:eq}
\eq(s,K) = 1 - \tmax{k,i,\alpha}\opp_i(\alpha,s,k),
\end{align}
where $k \in [0, K]$, $i \in [0, 6]$, $\alpha \in A$, where $A$ is
the set of all action schemes.
Intuitively, equilibrium is a measure of lack of opportunities: if there
are big opportunities, then the system is very much out of equilibrium;
if there are small opportunities, then the system is close to being in
equilibrium; if there are no opportunities at all, then the system is
fully in equilibrium. The notion of equilibrium is used in the
equilibrium maintenance algorithm $\eqm$ to achieve agent proactivity,
as shown in Algorithm~\ref{alg:eqmaintm}.%
\footnote{This algorithm is a slightly modified version of the original
version given in~\citet{grosinger2019robots}; this is done to
accommodate for the integration with human intention recognition and
reasoning, $\uir$.}
\begin{algorithm}[H]
\dontprintsemicolon
\SetKw{KwTrue}{true}
\SetKwFunction{Return}{return}
\SetKwFunction{Choose}{choose}
\If{$\eq(s,K) < 1$}{
$\opps \leftarrow \arg\max_{k,i,\alpha}(\opp_i(\alpha,s,k))$ \;
$\langle \alpha, s',\opp_i, k, \oppdeg \rangle \leftarrow $\Choose($\opps$) \;
\Return $\langle \alpha, s',\opp_i, k, \oppdeg \rangle$
} \Else{
\Return $\emptyset$
}
\caption{$\eqm(s, K)$\label{alg:eqmaintm}}
\end{algorithm}
\subsection{Action Selection: Integrating Human Intention Recognition
and Reasoning and Equilibrium Maintenance}
\label{ssec:integr}
$\uir$ and $\eqm$ are complementary approaches that create proactive
acting in different ways. We now explore how to integrate the two
systems. The action selection component in Figure~\ref{fig:system}
integrates the approaches at the result phase, after each system has
proposed their proactive action. However, each approach has a different
reasoning mechanism and affects the future states in different ways.
$\uir$ supports the human towards reaching their intentions. It infers
the human's intention and suggests, or enacts, a sequence of actions to
reach the human's goal starting from the current state.
$\eqm$ prevents the human from being in undesirable states by predicting
possible state evolutions, and reasoning on what is desirable and how
available robot actions could create benefit.
Integrating the two systems is not trivial.
Consider the hiking example in the opening of this paper, and suppose
that in a given state $s$, $\eqm$ infers an opportunity to warn the human
for hail, $\opp_{5}(\alpha_{\mathrm{warn}}, s, 2)$. Suppose that at the
same time $\uir$ recognized that the human intention is to go hiking and
infers to bring the compass to the human.
We have two competing goals for robot acting, and action selection needs
to weigh them via a common scale. We propose a solution for integrating
$\eqm$ and $\uir$ by turning the goal from $\uir$ into an opportunity of
type $\opp_0$, hence, $\opp_{0}(\alpha_{\mathrm{collect(compass)}}, s,
0)$ and check its degree. In other words, we check the desirability of the states that would be
achieved by the action when applied. Note that we use $\opp_0$ here
since the decisions by $\uir$ are meant to be acted upon immediately and
do not use multiple step lookahead, just like $\opp_0$. Once we have
converted the individual outputs from $\uir$ and from $\eqm$ to a common
format, that is, sets of opportunities, we collect all these
opportunities into a pool, from which the Action Selection component
(Figure~\ref{fig:system}) chooses an acting alternative.
To transform an $\uir$ acting decision into an opportunity of type
$\opp_0$ we temporarily modify the outcome of the $\des$-function. In the $\eqm$ framework, the $\des$-function does not take human
intentions into account. It does not model states with unfulfilled human
intentions as undesirable and those with fulfilled ones as
desirable. Such a $\des$-function would therefore not generate an
opportunity corresponding to an unfulfilled intention. We therefore
temporarily modify $\des$ to decrease the desirability of the current
state (Algorithm~\ref{alg:uir}, line 3), modeling the undesirability of
unfulfilled intention, and increase the desirability of the effects of
an action that fullfills the intention (line 4): this allows the
generation of an opportunity based on human intention recognition. For example, a state that would be desirable to the degree $0.7$ by
itself might only be $0.1$-desirable when a certain human intention has
been recognized. Conversely, we increase the desirability of the
effects that would manifest when an action of the human's intention is applied, which
would not be the case otherwise when no human intention was recognized,
e.g., with recognized human intention $\des(\alpha(s)) = 0.9$, without
recognized human intention $\des(\alpha(s)) = 0.3$.
\begin{algorithm}[H]
\dontprintsemicolon
\SetKw{KwTrue}{true}
\SetKwFunction{Increase}{increase}
\SetKwFunction{Decrease}{decrease}
\SetKwFunction{Return}{return}
\SetKwFunction{First}{first}
$\alpha(s) \leftarrow$ \First($\uir (s, G_H)$) \;
\If{$(\alpha \neq \bot)$}{
$\desp(s) \leftarrow$ \Decrease ($\des(s)$)
$\desp(\alpha(s)) \leftarrow$ \Increase ($\des(\alpha(s))$)
$\oppdeg \leftarrow \min(1 - \desp(s), \bnfp(\alpha,s))$
\Return $\langle \alpha, s,\opp_0, 0, \oppdeg \rangle$
}\Else{
\Return $\langle \rangle$
}
\caption{$\uir\!\text{-Opp}(s, G_H)$}
\label{alg:uir}
\end{algorithm}
In our experiments, we have implemented the \texttt{decrease} and
\texttt{increase} functions by scaling by a fixed value; exploring
better ways to implement these steps is a matter for further
investigation. The modified desirability function $\des'(s)$ is used in line 8 to
compute the degree of the opportunity of type $\opp_0$ for applying
action scheme $\alpha$ in the current state $s$. $\alpha$ is the first
action in the recognized intention (action plan) returned by $\uir$
(line 1). Note that the computation in line 5 uses a modified
$\bnf'(\alpha, s)$, which is based on $\des'(\alpha(s))$. This opportunity, and its degree, are returned in line 6, and represent
the opportunity based on human intention recognition.
Now that we have opportunities for acting based on prediction, as
returned from Algorithm~\ref{alg:eqmaintm}, and the one based on
reasoning on human intention, as returned from Algorithm~\ref{alg:uir},
we can decide which of them to enact in using the \emph{action
selection} Algorithm~\ref{alg:oppcomb}.
This algorithm continuously checks if the state has changed (line 4), be it by changes in the
environment or by application of robot action. If so,
it collects the opportunities coming from both proactivity systems,
$\eqm(s,K)$ and $\uir(s,G_H)$ (lines 5 and 6) and then chooses one of
these to be dispatched to the executive layer and enacted (line 8). The function $\Choose()$, like the $\Choose()$ in
Algorithm~\ref{alg:eqmaintm}, can implement several strategies. In our experiments, $\Choose()$ selects the opportunity with the highest
degree to be enacted. If there are several opportunities with highest
degree a decision is made by the opportunity type, how much benefit can
be achieved and the size of the look-ahead. More discussion on these
strategies can be found in
\citep{grosinger2019robots}.
\begin{algorithm}[H]
\dontprintsemicolon
\SetKw{KwTrue}{true}
\SetKwFunction{Return}{return}
\SetKwFunction{Choose}{choose}
\SetKwFunction{Add}{add}
\SetKwFunction{Dispatch}{dispatch}
\While {\KwTrue} {
$s \leftarrow$ current state \;
$\opps \leftarrow \{\}$\;
\If{$s$ has changed }{
$\opps.$\Add($\uir\!\text{-Opp}(s, G_H)$) \;
$\opps.$\Add($\eqm(s, K)$)\;
$\langle \alpha, s',\opp_i, k, \oppdeg \rangle \leftarrow $\Choose($\opps$) \;
\Dispatch($\alpha, s'$)\;
}
}
\caption{Action Selection ($K, G_H$
\label{alg:oppcomb}}
\end{algorithm}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,060 |
{"url":"https:\/\/www.gurobi.com\/documentation\/7.0\/refman\/c_grbfeasrelax.html","text":"Filter Content By\nVersion\n\n### GRBfeasrelax\n\n int GRBfeasrelax ( GRBmodel *model, int relaxobjtype, int minrelax, double *lbpen, double *ubpen, double *rhspen, double *feasobjP )\n\nModifies the input model to create a feasibility relaxation. Note that you need to call GRBoptimize on the result to compute the actual relaxed solution.\n\nThe feasibility relaxation is a model that, when solved, minimizes the amount by which the solution violates the bounds and linear constraints of the original model. This routine provides a number of options for specifying the relaxation.\n\nIf you specify relaxobjtype=0, the objective of the feasibility relaxation is to minimize the sum of the weighted magnitudes of the bound and constraint violations. The lbpen, ubpen, and rhspen arguments specify the cost per unit violation in the lower bounds, upper bounds, and linear constraints, respectively.\n\nIf you specify relaxobjtype=1, the objective of the feasibility relaxation is to minimize the weighted sum of the squares of the bound and constraint violations. The lbpen, ubpen, and rhspen arguments specify the coefficients on the squares of the lower bound, upper bound, and linear constraint violations, respectively.\n\nIf you specify relaxobjtype=2, the objective of the feasibility relaxation is to minimize the weighted count of bound and constraint violations. The lbpen, ubpen, and rhspen arguments specify the cost of violating a lower bound, upper bound, and linear constraint, respectively.\n\nTo give an example, a violation of 2.0 on constraint i would contribute 2*rhspen[i] to the feasibility relaxation objective for relaxobjtype=0, it would contribute 2*2*rhspen[i] for relaxobjtype=1, and it would contribute rhspen[i] for relaxobjtype=2.\n\nThe minrelax argument is a boolean that controls the type of feasibility relaxation that is created. If minrelax=0, optimizing the returned model gives a solution that minimizes the cost of the violation. If minrelax=1, optimizing the returned model finds a solution that minimizes the original objective, but only from among those solutions that minimize the cost of the violation. Note that GRBfeasrelax must solve an optimization problem to find the minimum possible relaxation for minrelax=1, which can be quite expensive.\n\nIn all cases, you can specify a penalty of GRB_INFINITY to indicate that a specific bound or linear constraint may not be violated.\n\nNote that this is a destructive routine: it modifies the model passed to it. If you don't want to modify your original model, use GRBcopymodel to create a copy before calling this routine.\n\nReturn value:\n\nA non-zero return value indicates that a problem occurred while computing the feasibility relaxation. Refer to the Error Code table for a list of possible return values. Details on the error can be obtained by calling GRBgeterrormsg.\n\nArguments:\n\nmodel: The original (infeasible) model. The model is modified by this routine.\n\nrelaxobjtype: The cost function used when finding the minimum cost relaxation.\n\nminrelax: The type of feasibility relaxation to perform.\n\nlbpen: The penalty associated with violating a lower bound. Can be NULL, in which case no lower bound violations are allowed.\n\nubpen: The penalty associated with violating an upper bound. Can be NULL, in which case no upper bound violations are allowed.\n\nrhspen: The penalty associated with violating a linear constraint. Can be NULL, in which case no constraint violations are allowed.\n\nfeasobjP: When minrelax=1, this returns the objective value for the minimum cost relaxation.\n\nExample usage:\n\n double penalties[];\nerror = GRBfeasrelax(model, 0, 0, NULL, NULL, penalties, NULL);\nerror = GRBoptimize(model);","date":"2023-04-01 16:28:37","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8016791939735413, \"perplexity\": 1436.6468162030067}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296950110.72\/warc\/CC-MAIN-20230401160259-20230401190259-00091.warc.gz\"}"} | null | null |
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